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Sample records for nonlinear transverse beam

  1. Suppressing Transverse Beam Halo with Nonlinear Magnetic Fields

    CERN Document Server

    Webb, Stephen D; Abell, Dan T; Danilov, Viatcheslav; Nagaitsev, Sergei; Valishev, Alexander; Danilov, Kirill; Cary, John R

    2012-01-01

    High intensity proton storage rings are central for the development of advanced neutron sources, drivers for the production of pions in neutrino factories or muon colliders, and transmutation of radioactive waste. Fractional proton loss from the beam must be very small to prevent radioac- tivation of nearby structures, but many sources of beam loss are driven by collective effects that increase with intensity. Recent theoretical work on the use of nonlinear magnetic fields to design storage rings with integrable transverse dynamics is extended here to include collective effects, with numerical results showing validity in the presence of very high beam current. Among these effects is the formation of beam halo, where particles are driven to large amplitude oscillations by coherent space charge forces. The strong variation of particle oscillation frequency with amplitude results in nonlinear decoherence that is observed to suppress transverse halo development in the case studied. We also present a necessary gen...

  2. On two transverse nonlinear models of axially moving beams

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.

  3. On two transverse nonlinear models of axially moving beams

    Institute of Scientific and Technical Information of China (English)

    DING Hu; CHEN LiQun

    2009-01-01

    Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit-ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av-eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif-ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte-gro-partial-differential equation gives better results for large amplitude vibration.

  4. Nonlinearities and effects of transverse beam size in beam position monitors

    Science.gov (United States)

    Kurennoy, Sergey S.

    2001-09-01

    The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The nonlinearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.

  5. Nonlinearities and effects of transverse beam size in beam position monitors

    Directory of Open Access Journals (Sweden)

    Sergey S. Kurennoy

    2001-09-01

    Full Text Available The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM are calculated and compared to those produced by a pencil beam. The nonlinearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.

  6. Transverse instabilities and pattern formation in two-beam-excited nonlinear optical interactions in liquids.

    Science.gov (United States)

    Bentley, Sean J; Heebner, John E; Boyd, Robert W

    2006-04-01

    We describe observations of various transverse instabilities that occur when two laser beams intersect in nonlinear optical liquids. Patterns that we observe include two types of conical emission and the generation of a linear array of spots. These results can be understood in terms of the physical processes of self-diffraction, two-beam-excited conical emission, and seeded modulational instability.

  7. Effect of transverse shears on complex nonlinear vibrations of elastic beams

    Science.gov (United States)

    Krysko, V. A.; Zhigalov, M. V.; Saltykova, O. A.; Krysko, A. V.

    2011-09-01

    Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ⩽ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.

  8. A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions

    Science.gov (United States)

    Rahmouni, A.; Beidouri, Z.; Benamar, R.

    2013-09-01

    The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the

  9. Nonlinear Large Displacement and Moderate Rotational Characteristics of Composite Beams Incorporating Transverse Shear Strain

    Science.gov (United States)

    1992-12-01

    Dugundji (12) have developed a theory to predict large deflections of laminated beams. Minguet and Dugundji assume transverse shear strains are constant...nine elements as shown in figure 3.3. 3.2 Cantilevered Composite Beam The next problem considered is one considered by Minguet and Dugundji (12) in...in figure 3.4. Minguet and Dugundji (M&D) formulated an updated Lagrangian displacement scheme based on Euler angles which track the rigid body motion

  10. Axial-transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions

    Science.gov (United States)

    Lenci, Stefano; Rega, Giuseppe

    2016-06-01

    The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.

  11. Transverse beam dynamics in non-linear Fixed Field Alternating Gradient accelerators

    Energy Technology Data Exchange (ETDEWEB)

    Haj, Tahar M. [Brookhaven National Lab. (BNL), Upton, NY (United States); Meot, F. [Brookhaven National Lab. (BNL), Upton, NY (United States)

    2016-03-02

    In this paper, we present some aspects of the transverse beam dynamics in Fixed Field Ring Accelerators (FFRA): we start from the basic principles in order to derive the linearized transverse particle equations of motion for FFRA, essentially FFAGs and cyclotrons are considered here. This is a simple extension of a previous work valid for linear lattices that we generalized by including the bending terms to ensure its correctness for FFAG lattice. The space charge term (contribution of the internal coulombian forces of the beam) is contained as well, although it is not discussed here. The emphasis is on the scaling FFAG type: a collaboration work is undertaken in view of better understanding the properties of the 150 MeV scaling FFAG at KURRI in Japan, and progress towards high intensity operation. Some results of the benchmarking work between different codes are presented. Analysis of certain type of field imperfections revealed some interesting features about this machine that explain some of the experimental results and generalize the concept of a scaling FFAG to a non-scaling one for which the tune variations obey a well-defined law.

  12. Effects of Transverse Beam Size in Beam Position Monitors

    CERN Document Server

    Kurennoy, S S

    2001-01-01

    The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The non-linearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.

  13. Effects of transverse beam size in beam position monitors.

    Energy Technology Data Exchange (ETDEWEB)

    Kurennoy, S. (Sergey)

    2001-01-01

    The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by the displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those from a pencil beam. The non-linearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.

  14. Investigation and optimization of transverse non-linear beam dynamics in the high-energy storage ring HESR

    Energy Technology Data Exchange (ETDEWEB)

    Welsch, Dominic Markus

    2010-03-10

    The High-Energy Storage Ring (HESR) is part of the upcoming Facility for Antiproton and Ion Research (FAIR) which is planned as a major extension to the present facility of the Helmholtzzentrum fuer Schwerionenforschung (GSI) in Darmstadt. The HESR will provide antiprotons in the momentum range from 1.5 to 15 GeV/c for the internal target experiment PANDA. The demanding requirements of PANDA in terms of beam quality and luminosity together with a limited production rate of antiprotons call for a long beam life time and a minimum of beam loss. Therefore, an effective closed orbit correction and a sufficiently large dynamic aperture of the HESR are crucial. With this thesis I present my work on both of these topics. The expected misalignments of beam guiding magnets have been estimated and used to simulate the closed orbit in the HESR. A closed orbit correction scheme has been developed for different ion optical settings of the HESR and numerical simulations have been performed to validate the scheme. The proposed closed orbit correction method which uses the orbit response matrix has been benchmarked at the Cooler Synchrotron COSY of the Forschungszentrum Juelich. A chromaticity correction scheme for the HESR consisting of sextupole magnets has been developed to reduce tune spread and thus to minimize the emittance growth caused by betatron resonances. The chromaticity correction scheme has been optimized through dynamic aperture calculations. The estimated field errors of the HESR dipole and quadrupole magnets have been included in the non-linear beam dynamics studies. Investigations concerning their optimization have been carried out. The ion optical settings of the HESR have been improved using dynamic aperture calculations and the technique of frequency map analysis. The related diffusion coefficient was also used to predict long-term stability based on short-term particle tracking. With a reasonable reduction of the quadrupole magnets field errors and a

  15. Analysis of beam envelope by transverse space charge effect

    Energy Technology Data Exchange (ETDEWEB)

    Toyama, Shin`ichi [Power Reactor and Nuclear Fuel Development Corp., Oarai, Ibaraki (Japan). Oarai Engineering Center

    1997-09-01

    It is important for high current accelerators to estimate the contribution of the space charge effect to keep the beam off its beak up. The application of an envelope equation is examined in previous report in which the beam is just coasting beam (non accelerating). The analysis of space charge effect is necessary for the comparison in coming accelerator test in PNC. In order to evaluate the beam behavior in high current, the beam dynamics and beam parameters which are input to the equation for the evaluation are developed and make it ready to estimate the beam transverse dynamics by the space charge. The estimate needs to have enough accuracy for advanced code calculation. After the preparation of the analytic expression of transverse motion, the non-linear differential equation of beam dynamics is solved by a numerical method on a personal computer. The beam envelope from the equation is estimated by means of the beam emittance, current and energy. The result from the analysis shows that the transverse beam broadening is scarecely small around the beam current value of PNC design. The contribution to the beam broadening of PNC linac comes from its beam emittance. The beam broadening in 100 MeV case is almost negligible in the view of transverse space charge effect. Therefore, the electron beam is stable up to 10 A order in PNC linac design. Of course, the problem for RF supply is out of consideration here. It is important to estimate other longitudinal effect such as beam bunch effect which is lasting unevaluated. (author)

  16. Transverse Beam Size Effects in Beam Position Monitors

    Science.gov (United States)

    Kurennoy, Sergey

    2001-04-01

    The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by the displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those from a pencil beam. The corrections to BPM signals due to a finite beam size are found analytically for a few particular transverse distributions of the beam current. The results for fields can also be directly applied for calculating the beam coupling impedances of small discontinuities.

  17. Vibration Analysis of Timoshenko Beams on a Nonlinear Elastic Foundation

    Institute of Scientific and Technical Information of China (English)

    MO Yihua; OU Li; ZHONG Hongzhi

    2009-01-01

    The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method (QEM) is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear de-formation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.

  18. Transverse Schottky spectra and beam transfer functions of coasting ion beams with space charge

    Energy Technology Data Exchange (ETDEWEB)

    Paret, Stefan

    2010-02-22

    A study of the transverse dynamics of coasting ion beams with moderate space charge is presented in this work. From the dispersion relation with linear space charge, an analytic model describing the impact of space charge on transverse beam transfer functions (BTFs) and the stability limits of a beam is derived. The dielectric function obtained in this way is employed to describe the transverse Schottky spectra with linear space charge as well. The difference between the action of space charge and impedances is highlighted. The setup and the results of an experiment performed in the heavy ion synchrotron SIS-18 at GSI to detect space-charge effects at different beam intensities are explicated. The measured transverse Schottky spectra and BTFs are compared with the linear space-charge model. The stability diagrams constructed from the BTFs are presented. The space-charge parameters evaluated from the Schottky and BTF measurements are compared with estimations based on measured beam parameters. The impact of collective effects on the Schottky and BTF diagnostics is also investigated through numerical simulations. For this purpose the self-field of beams with linear and non-linear transverse density-distributions is computed on a twodimensional grid. The noise of the random particle distribution causes fluctuations of the dipole moment of the beam which produce the Schottky spectrum. BTFs are simulated by exciting the beam with transverse kicks. The simulation results are used to verify the space-charge model. (orig.)

  19. Transverse vibration of nematic elastomer Timoshenko beams

    Science.gov (United States)

    Zhao, Dong; Liu, Ying; Liu, Chuang

    2017-01-01

    Being a rubber-like liquid crystalline elastomer, a nematic elastomer (NE) is anisotropic viscoelastic, and displays dynamic soft elasticity. In this paper, the transverse vibration of a NE Timoshenko beam is studied based on the linear viscoelasticity theory of nematic elastomers. The governing equation of motion for the transverse vibration of a NE Timoshenko beam is derived. A complex modal analysis method is used to obtain the natural frequencies and decrement coefficients of NE beams. The influences of the nematic director rotation, the rubber relaxation time, and the director rotation time on the vibration characteristic of NE Timoshenko beams are discussed in detail. The sensitivity of the dynamic performance of NE beams to director initial angle and relaxation times provides a possibility of intelligent controlling of their dynamic performance.

  20. Strongly Nonlinear Transverse Perturbations in Phononic Crystals

    Directory of Open Access Journals (Sweden)

    S. Nikitenkova

    2014-01-01

    Full Text Available The dynamics of the surface heterogeneities formation in low-dimensional phononic crystals is studied. It is shown that phononic transverse perturbations in this medium are highly nonlinear. They can be described with the help of the Riemann wave and may form stable wave structures of the finite amplitude. The Riemann wave deformation is described analytically. The Riemann wave time existence up to the beginning of the gradient catastrophe is calculated.

  1. A Hardware Transverse Beam Frequency Response Simulator

    CERN Document Server

    Ning, Jia

    2005-01-01

    We build an electronical instrument to get the frequency response close to the pattern of transverse beam frequency response. The method is to apply 1)a time delay circuit with ADC, FIFO RAM and DAC; 2)a phase shift circuit which is an all pass filter with adjustable phase shift in the frequency range of 25kHz to 30kHz; in a feedback loop of 3)a commutating filter which is a high Q band pass filter. We can dynamically adjust the center frequency, the side band distance during the testing. With this instrument, some beam instruments can be tested without using the real beam.

  2. Generate Uniform Transverse Distributed Electron Beam along a Beam Line

    CERN Document Server

    Jiao, Y

    2015-01-01

    It has been reported that transverse distribution shaping can help to further enhance the energy extraction efficiency in a terawatt, tapered X-ray free-electron laser. Thus, methods of creating and keeping almost uniform transverse distributed (UTD) beam within undulators are required. This study shows that a UTD electron beam can be generated within evenly distributed drift sections where undulators can be placed, by means of octupoles and particular optics. A concrete design is presented, and numerical simulations are done to verify the proposed method.

  3. Transverse Beam Matching Application for SNS

    CERN Document Server

    Chu, Chungming; Jeon Dong Oh; Plum, Michael

    2005-01-01

    An automated transverse beam matching application has been developed for the Spallation Neutron Source (SNS) beam transport lines. The application is written within the XAL Java framework and the matching algorithm is based on the simplex optimization method. Other functionalities, such as emittance calculated from profile monitor measurements (adopted from a LANL Fortran code), profile monitor display, and XAL on-line model calculation, are also provided by the application. Test results obtained during the SNS warm linac commissioning will be reported. A comparison between the emittances obtained from this application and an independent Trace-3D routine will also be shown.

  4. Transverse electron beam diagnostics at REGAE

    Energy Technology Data Exchange (ETDEWEB)

    Bayesteh, Shima

    2014-12-15

    The use of high-intensity electron and X-ray pulsed sources allows for the direct observation of atomic motions as they occur. While the production of such high coherent, brilliant, short X-ray pulses requires large-scale and costly accelerator facilities, it is feasible to employ a high-intensity source of electrons by exploiting a more compact design. The Relativistic Electron Gun for Atomic Exploration (REGAE) facility is a small linear accelerator at DESY, Hamburg, equipped with a photocathode radio frequency (RF) gun that produces relativistic ultra-short (<100 fs), low charge (<1 pC) electron bunches of high coherence. By means of time-resolved diffraction experiments, such an electron source can probe ultrafast laser-induced atomic structural changes that occur with a temporal resolution of ∝100 fs. A comprehensive characterization of the electron beam, for every pulse, is of fundamental importance to study the atomic motions with the desired resolution and quality. This thesis reports on the transversal diagnostics of the electron beam with an emphasis on a scintillator-based beam profile monitor. The diagnostics is capable of evaluating the beam parameters such as charge, energy, energy spread and transverse profile, at very low charges and on a shot-to-shot basis. A full characterization of the scintillator's emission, the optical setup and the detector (camera) of the profile monitor is presented, from which an absolute charge calibration of the system is derived. The profile monitor is specially developed to accommodate more applications, such as dark current suppression, overlapping the electron probe and the laser pump within 1 ns accuracy, as well as charge and transverse emittance measurements. For the determination of the transverse emittance two techniques were applied. The first one introduces a new method that exploits a diffraction pattern to measure the emittance, while the second one is based on a version of the Pepper-pot technique. A

  5. The refined theory of transversely isotropic piezoelectric rectangular beams

    Institute of Scientific and Technical Information of China (English)

    GAO; Yang; WANG; Minzhong

    2006-01-01

    The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur'e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.

  6. Diffusion measurement from observed transverse beam echoes

    Science.gov (United States)

    Sen, Tanaji; Fischer, Wolfram

    2017-01-01

    We study the measurement of transverse diffusion through beam echoes. We revisit earlier observations of echoes in the Relativistic Heavy Ion Collider and apply an updated theoretical model to these measurements. We consider three possible models for the diffusion coefficient and show that only one is consistent with measured echo amplitudes and pulse widths. This model allows us to parameterize the diffusion coefficients as functions of the bunch charge. We demonstrate that echoes can be used to measure diffusion much quicker than present methods and could be useful to a variety of hadron synchrotrons.

  7. Measurement and interpretation of transverse beam instabilities in the CERN large hadron collider (LHC) and extrapolations to HL-LHC

    CERN Document Server

    AUTHOR|(CDS)2067185; Arduini, Gianluigi; Barranco Navarro, Laura; Buffat, Xavier; Carver, Lee Robert; Iadarola, Giovanni; Li, Kevin Shing Bruce; Pieloni, Tatiana; Romano, Annalisa; Rumolo, Giovanni; Salvant, Benoit; Schenk, Michael; Tambasco, Claudia; Biancacci, Nicolo

    2016-01-01

    Since the first transverse instability observed in 2010, many studies have been performed on both measurement and simulation sides and several lessons have been learned. In a machine like the LHC, not only all the mechanisms have to be understood separately, but the possible interplays between the different phenomena need to be analysed in detail, including the beam-coupling impedance (with in particular all the necessary collimators to protect the machine but also new equipment such as crab cavities for HL-LHC), linear and nonlinear chromaticity, Landau octupoles (and other intrinsic nonlinearities), transverse damper, space charge, beam-beam (long-range and head-on), electron cloud, linear coupling strength, tune separation between the transverse planes, tune split between the two beams, transverse beam separation between the two beams, etc. This paper reviews all the transverse beam instabilities observed and simulated so far, the mitigation measures which have been put in place, the remaining questions an...

  8. Experimental evidence of adiabatic splitting of charged particle beams using stable islands of transverse phase space

    CERN Document Server

    Gilardoni, S S; Martini, M; Métral, E; Steerenberg, R; Müller, A-S

    2006-01-01

    Recently, a novel technique to perform multi-turn extraction from a circular particle accelerator was proposed. It is based on beam splitting and trapping, induced by a slow crossing of a nonlinear resonance, inside stable islands of transverse phase space. Experiments at the CERN Proton Synchrotron started in 2002 and evidence of beam splitting was obtained by summer 2004. In this paper the measurement results achieved with both a low- and a high-intensity, single-bunch proton beam are presented.

  9. Transverse beam feedback system for PLS storage ring

    CERN Document Server

    Huang, J Y; Kim, D T; Kang, H S; Hwang, W H; Nam, S H

    2001-01-01

    As the stored beam current increases over 240 mA, transverse coupled-beam instability limits higher beam current in Pohang Light Source. A bunch by bunch transverse feedback system has been developed to cure these beam instabilities. It consists of beam oscillation detectors, betatron phase adjuster, power amplifiers and a stripline kicker. Design of each circuit and its functions are described with simple trigonometric equations. The result of the beam test has shown more than 30 dB damping of the beam oscillation in the full bandwidth of the system.

  10. Stability Analysis of Nonlinear Vibrations of a Deploying Flexible Beam

    Institute of Scientific and Technical Information of China (English)

    JunfengLI; ZhaolinWANG

    1996-01-01

    Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage,The appendage is modeled as a finite deflection beam having linear constitutive equations.By taking the energy integral as Lyapunov function,it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam,according to the partial stablity theorem.

  11. Transverse beam compression on the Paul trap simulator experiment

    Directory of Open Access Journals (Sweden)

    Erik P. Gilson

    2007-12-01

    Full Text Available The Paul trap simulator experiment is a compact laboratory Paul trap that simulates a long, thin charged-particle bunch coasting through a kilometers-long magnetic alternating-gradient (AG transport system by putting the physicist in the beam’s frame of reference. The transverse dynamics of particles in both systems are described by similar equations, including all nonlinear space-charge effects. The time-dependent quadrupolar electric fields created by the confinement electrodes of a linear Paul trap correspond to the axially dependent magnetic fields applied in the AG system. Results are presented for experiments in which the lattice period and strength are changed over the course of the experiment to transversely compress a beam with an initial depressed tune of 0.9. Instantaneous and smooth changes are considered. Emphasis is placed on determining the conditions that minimize the emittance growth and the number of halo particles produced by the beam compression process. Both the results of particle-in-cell simulations performed with the warp code and envelope equation solutions agree well with the experimental data.

  12. Transverse Beam Size Effects on Longitudinal Profile Reconstruction

    CERN Document Server

    Andonian, G; Murokh, A; Dunning, M; Marcus, G; Rosenzweig, J; Williams, O; Yakimenko, V

    2010-01-01

    The use of coherent transition radiation autocorrelation methods to determine bunch length and profile information is examined with the compressed electron beam at the BNL ATF. A bi-gaussian fit is applied to coherent transition radiation auto-correlation data to extract the longitudinal current distribution. The effects of large transverse beam sizes are studied in theory and compared to experimental results. A suitable form of the correction factor is derived for beams with large transverse-longitudinal aspect ratios.

  13. Effects of transverse profile of pump field on second harmonic generation in periodic nonlinear materials

    Institute of Scientific and Technical Information of China (English)

    GaoJin-Yue; ZhangHan-Zhuang; YangJian-Bing

    2003-01-01

    We report on a theoreticalanalysis of the effects of a converging pump field of Gaussian transverse profile on second harmonic generation in a periodic nonlinear material with quasi-phase-matching. The outputs of the centre intensity and the intensity flux for second harmonic generation are derived by simulation, based on the parameters of quasi-phase-mismatch, the waist and focus positions of the input pump beam. The results show that when the transverse profile of the pump field is taken into account, the quasi-phase-match value and focus position of input beam for maximal second harmonic generation flollow new criteria.

  14. Effects of transverse profile of pump field on second harmonic generation in periodic nonlinear materials

    Institute of Scientific and Technical Information of China (English)

    张汉壮; 杨建冰; 高锦岳

    2003-01-01

    We report on a theoretical analysis of the effects of a converging pump field of Gaussian transverse profile on second harmonic generation in a periodic nonlinear material with quasi-phase-matching. The outputs of the centre intensity and the intensity flux for second harmonic generation are derived by simulation, based on the parameters of quasi-phase-mismatch, the waist and focus positions of the input pump beam. The results show that when the transverse profile of the pump field is taken into account, the quasi-phase-match value and focus position of input beam for maximal second harmonic generation follow new criteria.

  15. Nonlinear Analysis of Cable Vibration of a Multispan Cable-Stayed Bridge under Transverse Excitation

    OpenAIRE

    Kun Lin; Dujian Zou; Minghai Wei

    2014-01-01

    The nonlinear vibrations of cable in a multispan cable-stayed bridge subjected to transverse excitation are investigated. The MECS (multielements cable system) model, where multielements per cable stay are used, is built up and used to analyze the model properties of the multispan cable-stayed bridges. Then, a simplified two-degrees-of-freedom (2-DOFs) model, where the tower or the deck is reduced to a beam, is proposed to analyze the nonlinear dynamic behaviors of the beam and cable. The res...

  16. Nonlinear Analysis of Cable Vibration of a Multispan Cable-Stayed Bridge under Transverse Excitation

    Directory of Open Access Journals (Sweden)

    Kun Lin

    2014-01-01

    Full Text Available The nonlinear vibrations of cable in a multispan cable-stayed bridge subjected to transverse excitation are investigated. The MECS (multielements cable system model, where multielements per cable stay are used, is built up and used to analyze the model properties of the multispan cable-stayed bridges. Then, a simplified two-degrees-of-freedom (2-DOFs model, where the tower or the deck is reduced to a beam, is proposed to analyze the nonlinear dynamic behaviors of the beam and cable. The results of MECS model analysis show that the main tower in the multispan cable-stayed bridge is prone to the transverse vibration, and the local vibration of cables only has a little impact on the frequency values of the global modes. The results of simplified model analysis show that the energy can be transformed between the modes of the beam and cable when the nature frequencies of them are very close. On the other hand, with the transverse excitation changing, the cable can exhibit richer quasi-periodic or chaotic motions due to the nonlinear terms caused by the coupled mode between the beam and cable.

  17. Some Features of Transverse Instability of Partly Compensated Proton Beams

    Energy Technology Data Exchange (ETDEWEB)

    Vadim Dudnikov

    2001-10-23

    suppression of generation and accumulation of secondary particles is a traditional method for suppression the transverse electron-proton instability: improve the vacuum, use a gap in beam for electron removing, use cleaning electrodes, suppressing secondary emission. But opposite solution is also possible. Transverse e-p instability in proton rings can be damped by increasing beam density and the rate of secondary particles generation above a threshold level, with decrease of the unstable wavelength below a transverse beam size. In high current Proton Storage Rings (PSR) such as, the LANSCE PSR it is possible to reach this island of stability by multiturn, concentrated charge exchange injection without painting and by enhanced generation of secondary plasma. This possibility was demonstrated in smaller scale PSR at the INP, Novosibirisk [1]. Damping of the e-p instability allowed to accumulate a coasting, space charge compensated, circulating proton beam with intensity, corresponding to the Laslett tune shift of {Delta}{nu} = 5 in the ring with original tune of {nu} = 0.85. In the other PSR transverse instability of bunched beam was damped by a simple feed back [2,3]. In this article they discuss experimental observations of transverse instability of proton beams in different accelerators and storage rings and consider methods to damp the instability. The presented experimental dates could be useful for verification of computer simulation tools developed for investigation of space charge effects and beam instabilities in realistic conditions [4,5].

  18. THERMAL POST-BUCKLING OF AN ELASTIC BEAMS SUBJECTED TO A TRANSVERSELY NON-UNIFORM TEMPERATURE RISING

    Institute of Scientific and Technical Information of China (English)

    李世荣; 程昌钧; 周又和

    2003-01-01

    Based on the nonlinear geometric theory of axially extensible beams and by usingthe shooting method, the thermal post-buckling responses of an elastic beams, withimmovably simply supported ends and subjected to a transversely non-uniformly distributedtemperature rising, were investigated. Especially, the influences of the transversetemperature change on the thermal post-buckling deformations were examined and thecorresponding characteristic curves were plotted. The numerical results show that theequilibrium paths of the beam are similar to what of an initially deformed beam because ofthe thermal bending moment produced in the beam by the transverse temperature change.

  19. Stabilization of vortex beams in Kerr media by nonlinear absorption

    Science.gov (United States)

    Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.

    2016-11-01

    We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.

  20. Stabilization of vortex beams in Kerr media by nonlinear absorption

    CERN Document Server

    Porras, Miguel A; Leblond, Hervé; Malomed, Boris A

    2016-01-01

    We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.

  1. Experimental evidence of adiabatic splitting of charged particle beams using stable islands of transverse phase space

    Directory of Open Access Journals (Sweden)

    S. Gilardoni

    2006-10-01

    Full Text Available Recently, a novel technique to perform multiturn extraction from a circular particle accelerator was proposed. It is based on beam splitting and trapping, induced by a slow crossing of a nonlinear resonance, inside stable islands of transverse phase space. Experiments at the CERN Proton Synchrotron started in 2002 and evidence of beam splitting was obtained by summer 2004. In this paper, the measurement results achieved with both a low- and a high-intensity, single-bunch proton beam are presented.

  2. Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam

    Institute of Scientific and Technical Information of China (English)

    Qing-xu Yan; Hui-chao Zou; De-xing Feng

    2003-01-01

    In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t →∞.

  3. Nonlinear Interaction of Transversal Modes in a CO2 Laser

    OpenAIRE

    Lopez-Ruiz, Ricardo; Mindlin, G. B.; Perez-Garcia, C.; Tredicce, J. R.

    2002-01-01

    We show the possibility of achieving experimentally a Takens-Bogdanov bifurcation for the nonlinear interaction of two transverse modes ($l = \\pm 1$) in a $CO_2$ laser. The system has a basic O(2) symmetry which is perturbed by some symmetry-breaking effects that still preserve the $Z_2$ symmetry. The pattern dynamics near this codimension two bifurcation under such symmetries is described. This dynamics changes drastically when the laser properties are modified.

  4. Analysis of transverse RMS emittance growth of a beam induced by spherical and chromatic aberration in a solenoidal field

    Energy Technology Data Exchange (ETDEWEB)

    Dash, Radhakanta, E-mail: radhakanta.physics@gmail.com [Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094 (India); Accelerator and Pulse Power Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085 (India); Nayak, Biswaranjan [Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094 (India); Sharma, Archana; Mittal, Kailash C. [Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094 (India); Accelerator and Pulse Power Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085 (India)

    2016-01-21

    In a medium energy beam transport line transverse rms emittance growth associated with spherical aberration is analysed. An analytical expression is derived for beam optics in a solenoid field considering terms up to the third order in the radial displacement. Two important phenomena: effect of spherical aberrations in axial-symmetric focusing lens and influence of nonlinear space charge forces on beam emittance growth are discussed for different beam distributions. In the second part nonlinear effect associated with chromatic aberration that describes the growth of emittance and distortion of phase space area is discussed.

  5. Analysis of transverse RMS emittance growth of a beam induced by spherical and chromatic aberration in a solenoidal field

    Science.gov (United States)

    Dash, Radhakanta; Nayak, Biswaranjan; Sharma, Archana; Mittal, Kailash C.

    2016-01-01

    In a medium energy beam transport line transverse rms emittance growth associated with spherical aberration is analysed. An analytical expression is derived for beam optics in a solenoid field considering terms up to the third order in the radial displacement. Two important phenomena: effect of spherical aberrations in axial-symmetric focusing lens and influence of nonlinear space charge forces on beam emittance growth are discussed for different beam distributions. In the second part nonlinear effect associated with chromatic aberration that describes the growth of emittance and distortion of phase space area is discussed.

  6. Statistical signal processing techniques for coherent transversal beam dynamics in synchrotrons

    Energy Technology Data Exchange (ETDEWEB)

    Alhumaidi, Mouhammad

    2015-03-04

    identifying and analyzing the betatron oscillation sourced from the kick based on its mixing and temporal patterns. The accelerator magnets can generate unwanted spurious linear and non-linear fields due to fabrication errors or aging. These error fields in the magnets can excite undesired resonances leading together with the space charge tune spread to long term beam losses and reducing dynamic aperture. Therefore, the knowledge of the linear and non-linear magnets errors in circular accelerator optics is very crucial for controlling and compensating resonances and their consequent beam losses and beam quality deterioration. This is indispensable, especially for high beam intensity machines. Fortunately, the relationship between the beam offset oscillation signals recorded at the BPMs is a manifestation of the accelerator optics, and can therefore be exploited in the determination of the optics linear and non-linear components. Thus, beam transversal oscillations can be excited deliberately for purposes of diagnostics operation of particle accelerators. In this thesis, we propose a novel method for detecting and estimating the optics lattice non-linear components located in-between the locations of two BPMs by analyzing the beam offset oscillation signals of a BPMs-triple containing these two BPMs. Depending on the non-linear components in-between the locations of the BPMs-triple, the relationship between the beam offsets follows a multivariate polynomial accordingly. After calculating the covariance matrix of the polynomial terms, the Generalized Total Least Squares method is used to find the model parameters, and thus the non-linear components. A bootstrap technique is used to detect the existing polynomial model orders by means of multiple hypothesis testing, and determine confidence intervals for the model parameters.

  7. NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

    Institute of Scientific and Technical Information of China (English)

    Yang Xiaodong; Chen Li-Qun

    2006-01-01

    The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

  8. Boundary controllability for a nonlinear beam equation

    Directory of Open Access Journals (Sweden)

    Xiao-Min Cao

    2015-09-01

    Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.

  9. Nonlinear feedback control of Timoshenko beam

    Institute of Scientific and Technical Information of China (English)

    冯德兴; 张维弢

    1995-01-01

    This note is concerned with nonlinear boundary feedback control of a Timoshenko beam. Under some nonlinear boundary feedback control, first the nonlinear semigroup theory is used to show the existence and uniqueness of solution for the corresponding closed loop system. Then by using the Lyapunov method, it is proved that the vibration of the beam under the proposed control action decays in a negative power of time t as t→.

  10. Transverse beam shape measurements of intense proton beams using optical transition radiation

    Energy Technology Data Exchange (ETDEWEB)

    Scarpine, Victor E.; /Fermilab

    2012-03-01

    A number of particle physics experiments are being proposed as part of the Department of Energy HEP Intensity Frontier. Many of these experiments will utilize megawatt level proton beams onto targets to form secondary beams of muons, kaons and neutrinos. These experiments require transverse size measurements of the incident proton beam onto target for each beam spill. Because of the high power levels, most beam intercepting profiling techniques will not work at full beam intensity. The possibility of utilizing optical transition radiation (OTR) for high intensity proton beam profiling is discussed. In addition, previous measurements of OTR beam profiles from the NuMI beamline are presented.

  11. Transverse vibrations of arbitrary non-uniform beams

    Institute of Scientific and Technical Information of China (English)

    郭树起; 杨绍普

    2014-01-01

    Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.

  12. SPS transverse beam scraping and LHC injection losses

    CERN Document Server

    Drosdal, L; Bartmann, W; Bracco, C; Cornelis, K; Goddard, B; Meddahi, M; Veyrunes, E

    2012-01-01

    Machine protection sets strict requirements for the quality of the injected beam, in particular in the transverse plane. Losses at aperture restrictions and protection elements have to be kept at a minimum. Particles in the beam tails are lost at the tight transfer line collimators and can trigger the LHC beam abort system. These particles have to be removed by scrapers in the vertical and horizontal plane in the SPS. Scraping has become vital for high intensity LHC operation. This paper shows the dependence of injection quality on the SPS scraping and discusses an improved scraper setting up strategy for better reproducibility with the current scraper system.

  13. Modes and frequencies of transversely isotropic slightly curved Timoshenko beams.

    Science.gov (United States)

    Rossettos, J. N.; Squires, D. C.

    1973-01-01

    An analysis of the vibration of transversely isotropic Timoshenko beams, which have small constant initial curvature, is presented, and a closed-form general solution to the governing equations is derived. Natural modes and frequencies are determined for both clamped and simply supported end conditions, and comparisons are made. The combined effects of initial curvature, transverse shear deformation, and boundary conditions are evaluated and discussed. Specifically, it is shown in what manner the clamped beam tends to be more sensitive to shear deformation than the simply supported beam, and how initial curvature reduces the difference. Calculations also show how, in cases where shear deformation becomes more important, the initial curvature has a correspondingly smaller influence on the results.

  14. Tomography of the electron beam transverse phase space at PITZ

    Energy Technology Data Exchange (ETDEWEB)

    Asova, Galina

    2013-09-15

    The operation of a Free Elector Laser, FEL, requires high energy, high peak current electron beams with small transverse emittance. In the contemporary FELs, the electron beam is passed through a periodic magnetic structure - an undulator - which modifies the straight beam trajectory into a sinusoidal one, where FEL light is generated at each bend. According to the energy, the transverse emittance and the peak current of the beam and the parameters of the undulator, FEL radiation with wavelength in the range of nano- to micrometers can be generated. Studies and development of FELs are done all over the world. The Free electron LASer in Hamburg, FLASH, and the international European X-ray FEL, XFEL, in Hamburg, Germany, are two leading projects of the Deutsches Elektronen SYnchrotron, DESY. Part of the research program on FELs in DESY is realized in Zeuthen within the project Photo-Injector Test Facility at DESY in Zeuthen, PITZ. PITZ is an international collaboration including Germany, Russia, Italy, France, Bulgaria, Thailand, United Kingdom. The Institute of Nuclear Research and Nuclear Energy, INRNE, at the Bulgarian Academy of Sciences participates from bulgarian side. PITZ studies and optimizes the photo-injectors for FLASH and the XFEL. The research program emphasizes on detailed measurements of the transverse phase-space density distribution. Until 2010 the single slit scan technique has been used to measure the beam transverse distributions. At the end of 2010 a module for tomographic diagnostics has been installed which extends the possibilities of PITZ to measure simultaneously the two transverse planes of a single micropulse with improved signal-to-noise ratio. The difficult conditions of low emittance for high bunch charge and low energy make the operation of the module challenging. This thesis presents the design considerations for the tomography module, a number of reconstruction algorithms and their applicability to limited data sets, the influence

  15. Modulation instability of broad optical beams in nonlinear media with general nonlinearity

    Institute of Scientific and Technical Information of China (English)

    Hongcheng Wang; Weilong She

    2006-01-01

    @@ The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.

  16. Beam stability in synchrotrons with digital transverse feedback systems in dependence on beam tunes

    Science.gov (United States)

    Zhabitsky, V. M.

    2012-07-01

    The beam stability problem in synchrotrons with a digital transverse feedback system (TFS) is studied. The TFS damper kicker (DK) corrects the transverse momentum of a bunch in proportion to its displacement from the closed orbit measured at the location of the beam position monitor (BPM). It is shown that the area and configuration of the beam stability separatrix depend on the beam tune, the feedback gain, the phase balance between the phase advance from BPM to DK and the phase response of the feedback chain at the betatron frequency.

  17. Nonlinear Absolute Nodal Coordinate Formulation of a Flexible Beam Considering Shear Effect

    Institute of Scientific and Technical Information of China (English)

    LIU Jin-yang; SHEN Ling-jie; HONG Jia-zhen

    2005-01-01

    Nonlinear modeling of a flexible beam with large deformation was investigated. Absolute nodal cooridnate formulation is employed to describe the motion, and Lagrange equations of motion of a flexible beam are derived based on the geometric nonlinear theory. Different from the previous nonlinear formulation with EulerBernoulli assumption, the shear strain and transverse normal strain are taken into account. Computational example of a flexible pendulum with a tip mass is given to show the effects of the shear strain and transverse normal strain. The constant total energy verifies the correctness of the present formulation.

  18. CHAOTIC BELT PHENOMENA IN NONLINEAR ELASTIC BEAM

    Institute of Scientific and Technical Information of China (English)

    张年梅; 杨桂通

    2003-01-01

    The chaotic motions of axial compressed nonlinear elastic beam subjected totransverse load were studied. The damping force in the system is nonlinear. Consideringmaterial and geometric nonlinearity, nonlinear governing equation of the system wasderived. By use of nonlinear Galerkin method, differential dynamic system was set up.Melnikov method was used to analyze the characters of the system. The results showed thatchaos may occur in the system when the load parameters P0 and f satisfy some conditions.The zone of chaotic motion was belted. The route from subharmonic bifurcation to chaoswas analyzed. The critical conditions that chaos occurs were determined.

  19. Oscillatory Response of a Beam to a Transverse Kick

    CERN Multimedia

    1974-01-01

    When a circulating beam receives a transverse kick, it begins to perform coherent betatron oscillations. Their amplitude depends on strength, length and temporal shape of the kick, and on the Q-value (betatron tune) of the accelerator or storage ring. A calculation of a response function is shown in 3-dimensional presentation with the means of 1974: graph paper glued on cardboard stuck in a slotted base-plate.

  20. Beam dynamics experiments to study the suppression of transverse instabilities

    Science.gov (United States)

    Houck, T.; Lidia, S.

    2003-03-01

    Two-beam accelerators based upon relativistic klystron’s (RK’s) have been proposed as power sources for future generation linear electron-positron colliders. These drivers are susceptible to several transverse beam breakup (BBU) instabilities. An experiment to study a particular technique (the “betatron node scheme”) for ameliorating the high-frequency BBU has been performed at LBNL on a 1MeV, 500A induction accelerator beam. The results of this experiment are particularly important for RK, but apply to any system where the betatron phase advance between perturbing structures is an integral multiple of 180°. This phase advance is beneficial in linear accelerators as the instability growth changes from exponential to linear. In the experiment described below, the beam is contained in a solenoidal focusing channel, rf cavities are spaced every 60cm, and growth in the transverse motion was measured as a function of phase advance. Details of the experiment and results are presented.

  1. Particle-core model for transverse dynamics of beam halo

    Directory of Open Access Journals (Sweden)

    T. P. Wangler

    1998-12-01

    Full Text Available The transverse motion of beam halo particles is described by a particle-core model which uses the space-charge field of a continuous cylindrical oscillating beam core in a uniform linear focusing channel to provide the force that drives particles to large amplitudes. The model predicts a maximum amplitude for the resonantly-driven particles as a function of the initial mismatch. We have calculated these amplitude limits and have estimated the growth times for extended-halo formation as a function of both the space-charge tune-depression ratio and a mismatch parameter. We also present formulas for the scaling of the maximum amplitudes as a function of the beam parameters. The model results are compared with multiparticle simulations and we find very good agreement for a variety of initial particle distributions.

  2. Self consistent thermal wave model description of the transverse dynamics for relativistic charged particle beams in magnetoactive plasmas

    CERN Document Server

    Fedele, Renato; De Nicola, Sergio; Shukla, P K; Jovanovic, Dusan

    2011-01-01

    Thermal Wave Model is used to study the strong self-consistent Plasma Wake Field interaction (transverse effects) between a strongly magnetized plasma and a relativistic electron/positron beam travelling along the external magnetic field, in the long beam limit, in terms of a nonlocal NLS equation and the virial equation. In the linear regime, vortices predicted in terms of Laguerre-Gauss beams characterized by non-zero orbital angular momentum (vortex charge). In the nonlinear regime, criteria for collapse and stable oscillations is established and the thin plasma lens mechanism is investigated, for beam size much greater than the plasma wavelength. The beam squeezing and the self-pinching equilibrium is predicted, for beam size much smaller than the plasma wavelength, taking the aberrationless solution of the nonlocal Nonlinear Schroeding equation.

  3. Nonlinear optimization of beam lines

    CERN Document Server

    Tomás Garcia, Rogelio

    2006-01-01

    The current final focus systems of linear colliders have been designed based on the local compensation scheme proposed by P. Raimondi and A. Seryi [1]. However, there exist remaining aberrations that deteriorate the performance of the system. This paper develops a general algorithm for the optimization of beam lines based on the computation of the high orders of the transfer map using MAD-X [2] and PTC [3]. The algorithm is applied to the CLIC [4] Beam Delivery System (BDS).

  4. Nonlinear evolution of Airy-like beams generated by modulated waveguide arrays.

    Science.gov (United States)

    Cao, Zheng; Tan, Qinggui; Li, Xiaojun; Qi, Xinyuan

    2016-08-20

    We numerically study the formation of modulated waveguide generated Airy-like beams and their subsequent evolution in homogeneous medium. The results show that the Airy-like beams could be generated from narrow Gaussian beams propagating in one-dimensional transverse separation modulated unbent, cosine bent, or logarithm bent waveguide arrays, respectively. The waveguide-generated Airy-like beams maintain their characteristics when propagating without nonlinearity or under the self-defocusing nonlinearity in homogeneous medium, while the beams are distorted under the self-focusing nonlinearity. The deformation depends on the waveguide bending and the outgoing angles of the Airy-like beams. Our results provide a new way to generate and manipulate the Airy-like beam.

  5. Modeling of the vibrating beam accelerometer nonlinearities

    Science.gov (United States)

    Romanowski, P. A.; Knop, R. C.

    Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.

  6. A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches

    Science.gov (United States)

    Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.

    2013-10-01

    This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.

  7. Transverse beam diagnostics for the XUV seeding experiment at FLASH

    Energy Technology Data Exchange (ETDEWEB)

    Boedewadt, Joern

    2011-12-15

    High-gain free-electron lasers (FEL) offer intense, transversely coherent, and ultra short radiation pulses in the extreme ultraviolet, the soft- and the hard-X-ray spectral range. Undulator radiation from spontaneous emission is amplified. Due to the stochastic emission process, the radiation exhibits a low temporal coherence, and the structure of the amplified radiation in the temporal and in the spectral domain shows large shot-to-shot fluctuations. In order to improve the temporal coherence, an external radiation pulse is used to induce (or seed) the FEL process. With this, only a defined wavelength range within the FEL bandwidth is amplified provided that the irradiance of the external radiation exceeds the noise level of the FEL amplifier. In addition to the improved longitudinal coherence, a seeded FEL provides the possibility to perform pump-probe experiments with an expected temporal resolution of the order of the pulse durations. In order to experimentally proof this statement, a test experiment for direct HHG-seeding at wavelength below 40 nm was installed at the free-electron laser facility FLASH at DESY. Crucial for the seeded operation of an FEL is the six-dimensional laser-electron overlap of the seed laser pulses with the electron bunches. Hence, dedicated diagnostics to measure and mechanisms to control the overlap are essential. Within this thesis, a transport beamline for the seed laser beam and the transverse diagnostics for seed laser- and the electron-beam were developed and commissioned. Results of the performance of the seed injection beamline are presented, and first measurements of the seeded operation of the FEL are analyzed and evaluated. (orig.)

  8. Nonlinear dynamic analysis of damaged Reddy-Bickford beams supported on an elastic Pasternak foundation

    Science.gov (United States)

    Stojanović, Vladimir; Petković, Marko D.

    2016-12-01

    Geometrically nonlinear free and forced vibrations of damaged high order shear deformable beams resting on a nonlinear Pasternak foundation are investigated in this paper. Equations of motion are derived for the beam which is under subjected combined action of arbitrarily distributed or concentrated transverse loading as well as axial loading. To account for shear deformations, the concept of high order shear deformation is used in comparison with the concept of first order shear deformation theory. Analyses are performed to investigate the effects of the specific stiffness of the foundation on the damaged beam frequencies and displacements with the aim of equalising the response of a damaged and an intact beam. According to that, functions of the foundation stiffness are determined depending on the location and size of the damage as a result of the possibility for the damaged beam to behave like one that is intact. An advanced p-version of the finite element method is developed for geometrically nonlinear vibrations of damaged Reddy-Bickford beams. The present study gives a clear view of the nonlinear dynamical behaviour of four types of beams according to high order shear deformation theory - an intact beam, a damaged beam, a damaged beam on an elastic foundation and intact beam on elastic foundation. The paper also presents the derivation of a new set of two nonlinear partial differential equations where only the transverse and axial displacements figure. The forced nonlinear vibrations problem is solved in the time domain using the Newmark integration method. Free vibration analysis carried out by harmonic balance and the use of continuation methods and backbone curves are constructed.

  9. Transverse Schottky and beam transfer function measurements in space charge affected coasting ion beams

    Directory of Open Access Journals (Sweden)

    Stefan Paret

    2010-02-01

    Full Text Available Transverse Schottky spectra and beam transfer functions (BTFs of coasting ion beams were measured in the heavy ion synchrotron SIS-18 in order to study the impact of space charge on the transverse beam dynamics. The particle number in the beam was varied to investigate the intensity dependence of the space-charge effect. No cooling was applied to the beams throughout the experiment. The expected deformation of the Schottky spectra and BTFs is observed. An analytic model with linear space charge is employed to describe the deformed Schottky and BTF signals. In this model, the incoherent space-charge force and the coherent forces due to impedances are treated separately. Using the model, the space-charge induced tune shift is evaluated both from the position and the form of the signals. The data are well described by the model, only in the high-intensity BTFs deviations are observed. The stability diagrams are shifted according to the space-charge parameter obtained from the BTFs. In addition, the tune shift is estimated by virtue of measured beam profiles and particle numbers. The estimated tune shift is of the same order of magnitude but smaller than the measured one. Possible explanations for deviations between the measurements, the model, and the estimation are discussed.

  10. Chaotic motion and its control for nonlinear nonplanar oscillations of a parametrically excited cantilever beam

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Wei [College of Mechanical Engineering, Beijing University of Technology, Beijing 100022 (China)] e-mail: sandyzhang0@yahoo.com

    2005-11-01

    This paper presents an analysis of the chaotic motion and its control for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. A new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time. The governing nonlinear equations of nonplanar motion under combined parametric and external excitations are obtained. The Galerkin procedure is applied to the governing equation to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations for the in-plane and out-of-plane modes. The work is focused on the case of 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The method of multiple scales is used to transform the parametrically and externally excited system to the averaged equations which have a constant perturbation force. Based on the averaged equations obtained here, numerical simulation is utilized to discover the periodic and chaotic motions for the nonlinear nonplanar oscillations of the cantilever beam. The numerical results indicate that the transverse excitation in the z direction at the free end can control the chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam. The methodology of controlling chaotic motion by using the transverse excitation is proposed. The transverse excitation in the z direction at the free end may be thought about to be an open-loop control. For the problem investigated in this paper, this approach is an effective methodology of controlling chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam.

  11. The effect of laser beam size in a zig-zag collimator on transverse cooling of a krypton atomic beam

    Indian Academy of Sciences (India)

    Vivek Singh; V B Tiwari; S Singh; S R Mishra; H S Rawat

    2014-07-01

    The effect of size of a cooling laser beam in a zig-zag atomic beam collimator on transverse cooling of a krypton atomic beam is investigated. The simulation results show that discreteness in the interaction between the cooling laser beam and atomic beam, arising due to finite size and incidence angle of the cooling laser beam, significantly reduces the value of transverse velocity capture range of the collimator. The experimental observations show the trend similar to that obtained from simulations. Our study can be particularly useful where a small zig-zag collimator is required.

  12. Effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam

    DEFF Research Database (Denmark)

    Sorokin, Vladislav S.; Thomsen, Jon Juel

    2016-01-01

    The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli– Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature...

  13. Periodic solutions of nonlinear vibrating beams

    Directory of Open Access Journals (Sweden)

    J. Berkovits

    2003-01-01

    Full Text Available The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periods T for which the equation is solvable for any T-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable period T. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.

  14. Experimental Characterizations of 4-D Transverse Phase-Space of a Compressed Beam

    CERN Document Server

    Zhou, Feng; Andonian, Gerard; Ben-Zvi, Ilan; Cline, David B; Murokh, Alex; Rosenzweig, James E; Yakimenko, Vitaly

    2005-01-01

    Coherent synchrotron radiation can significantly distort beam phase spaces in longitudinal direction and bending plane through a bunch compressor. A tomography technique is used to reconstruct transverse phase space of electron beam. Transverse 4-D phase spaces are systematically measured at UCLA/ATF compressor and their characteristics with different bunch compression conditions are analyzed.

  15. Experimental measurement of the 4-d transverse phase space map of a heavy ion beam

    Energy Technology Data Exchange (ETDEWEB)

    Hopkins, H S

    1997-12-01

    The development and employment of a new diagnostic instrument for characterizing intense, heavy ion beams is reported on. This instrument, the ''Gated Beam Imager'' or ''GBI'' was designed for use on Lawrence Livermore National Laboratory Heavy Ion Fusion Project's ''Small Recirculator'', an integrated, scaled physics experiment and engineering development project for studying the transport and control of intense heavy ion beams as inertial fusion drivers in the production of electric power. The GBI allows rapid measurement and calculation of a heavy ion beam's characteristics to include all the first and second moments of the transverse phase space distribution, transverse emittance, envelope parameters and beam centroid. The GBI, with appropriate gating produces a time history of the beam resulting in a 4-D phase-space and time ''map'' of the beam. A unique capability of the GBI over existing diagnostic instruments is its ability to measure the ''cross'' moments between the two transverse orthogonal directions. Non-zero ''cross'' moments in the alternating gradient lattice of the Small Recirculator are indicative of focusing element rotational misalignments contributing to beam emittance growth. This emittance growth, while having the same effect on the ability to focus a beam as emittance growth caused by non-linear effects, is in principle removable by an appropriate number of focusing elements. The instrument uses the pepperpot method of introducing a plate with many pinholes into the beam and observing the images of the resulting beamlets as they interact with a detector after an appropriate drift distance. In order to produce adequate optical signal and repeatability, the detector was chosen to be a microchannel plate (MCP) with a phosphor readout screen. The heavy ions in the pepperpot beamlets are stopped in the MCP's thin

  16. Second harmonic generation of Cosh-Gaussian laser beam in collisional plasma with nonlinear absorption

    Science.gov (United States)

    Singh, Navpreet; Gupta, Naveen; Singh, Arvinder

    2016-12-01

    This paper investigates second harmonic generation (SHG) of an intense Cosh-Gaussian (ChG) laser beam propagating through a preformed underdense collisional plasma with nonlinear absorption. Nonuniform heating of plasma electrons takes place due to the nonuniform irradiance of intensity along the wavefront of laser beam. This nonuniform heating of plasma leads to the self-focusing of the laser beam and thus produces strong density gradients in the transverse direction. The density gradients so generated excite an electron plasma wave (EPW) at pump frequency that interacts with the pump beam to produce its second harmonics. To envision the propagation dynamics of the ChG laser beam, moment theory in Wentzel-Kramers-Brillouin (W.K.B) approximation has been invoked. The effects of nonlinear absorption on self-focusing of the laser beam as well as on the conversion efficiency of its second harmonics have been theoretically investigated.

  17. Efficient sub-Doppler transverse laser cooling of an indium atomic beam

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Jae-Ihn

    2009-07-23

    Laser cooled atomic gases and atomic beams are widely studied samples in experimental research in atomic and optical physics. For the application of ultra cold gases as model systems for e.g. quantum many particle systems, the atomic species is not very important. Thus this field is dominated by alkaline, earthalkaline elements which are easily accessible with conventional laser sources and have convenient closed cooling transition. On the other hand, laser cooled atoms may also be interesting for technological applications, for instance for the creation of novel materials by atomic nanofabrication (ANF). There it will be important to use technologically relevant materials. As an example, using group III atoms of the periodical table in ANF may open a route to generate fully 3D structured composite materials. The minimal requirement in such an ANF experiment is the collimation of an atomic beam which is accessible by one dimensional laser cooling. In this dissertation, I describe transverse laser cooling of an Indium atomic beam. For efficient laser cooling on a cycling transition, I have built a tunable, continuous-wave coherent ultraviolet source at 326 nm based on frequency tripling. For this purpose, two independent high power Yb-doped fiber amplifiers for the generation of the fundamental radiation at {lambda}{sub {omega}} = 977 nm have been constructed. I have observed sub-Doppler transverse laser cooling of an Indium atomic beam on a cycling transition of In by introducing a polarization gradient in the linear-perpendicular-linear configuration. The transverse velocity spread of a laser-cooled In atomic beam at full width at half maximum was achieved to be 13.5{+-}3.8 cm/s yielding a full divergence of only 0.48 {+-} 0.13 mrad. In addition, nonlinear spectroscopy of a 3-level, {lambda}-type level system driven by a pump and a probe beam has been investigated in order to understand the absorption line shapes used as a frequency reference in a previous two

  18. Nonlinear phenomena of generation of longitudinal electric current by transversal electromagnetic field in plasmas

    CERN Document Server

    Latyshev, A V

    2015-01-01

    The analysis of nonlinear interaction of transversal electromagnetic field with collisionless plasma is carried out. Formulas for calculation electric current in collisionless plasma with arbitrary degree of degeneration of electronic gas are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. This second current is orthogonal to the known transversal current, received at the classical linear analysis.

  19. Transverse beam splitting made operational: Key features of the multiturn extraction at the CERN Proton Synchrotron

    Directory of Open Access Journals (Sweden)

    A. Huschauer

    2017-06-01

    Full Text Available Following a successful commissioning period, the multiturn extraction (MTE at the CERN Proton Synchrotron (PS has been applied for the fixed-target physics programme at the Super Proton Synchrotron (SPS since September 2015. This exceptional extraction technique was proposed to replace the long-serving continuous transfer (CT extraction, which has the drawback of inducing high activation in the ring. MTE exploits the principles of nonlinear beam dynamics to perform loss-free beam splitting in the horizontal phase space. Over multiple turns, the resulting beamlets are then transferred to the downstream accelerator. The operational deployment of MTE was rendered possible by the full understanding and mitigation of different hardware limitations and by redesigning the extraction trajectories and nonlinear optics, which was required due to the installation of a dummy septum to reduce the activation of the magnetic extraction septum. This paper focuses on these key features including the use of the transverse damper and the septum shadowing, which allowed a transition from the MTE study to a mature operational extraction scheme.

  20. Beam stability & nonlinear dynamics. Formal report

    Energy Technology Data Exchange (ETDEWEB)

    Parsa, Z. [ed.

    1996-12-31

    his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.

  1. Electromagnetic beam propagation in nonlinear media

    Institute of Scientific and Technical Information of China (English)

    V.V.Semak; M.N.Shneider

    2015-01-01

    We deduce a complete wave propagation equation that includes inhomogeneity of the dielectric constant and present this propagation equation in compact vector form. Although similar equations are known in narrow fields such as radio wave propagation in the ionosphere and electromagnetic and acoustic wave propagation in stratified media, we develop here a novel approach of using such equations in the modeling of laser beam propagation in nonlinear media. Our approach satisfies the correspondence principle since in the limit of zero-length wavelength it reduces from physical to geometrical optics.

  2. Beam Combining by Phase Transition Nonlinear Media

    Science.gov (United States)

    1990-02-01

    use the Redlich Kwong equation of state for the media we consider. This equation of state can be written RT a p - -b -FT(p.-’ + b)p ; 2-I M (2-1) where...as ac 3 dg-A7 C VA/\\CIIJT (6) The Redlich - Kwong equation of state; i.e., _ RT T-1/2 v-P v(v+P) (7) can be used to compute aP/lT, where the relevant...practical the application of nonlinear phase conjugate techniques to the beam combining of multiple lasers with a coherence characteristic of a

  3. Soliton pair generation in the interactions of Airy and nonlinear accelerating beams

    CERN Document Server

    Zhang, Yiqi; Wu, Zhenkun; Zheng, Huaibin; Lu, Keqing; Li, Yuanyuan; Zhang, Yanpeng

    2013-01-01

    We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.

  4. Three-dimensional nonparaxial accelerating beams from the transverse Whittaker integral

    CERN Document Server

    Zhang, Yiqi; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Wang, Zhiguo; Zhang, Yanpeng

    2014-01-01

    We investigate three-dimensional nonparaxial linear accelerating beams arising from the transverse Whittaker integral. They include different Mathieu, Weber, and Fresnel beams, among other. These beams accelerate along a semicircular trajectory, with almost invariant nondiffracting shapes. The transverse patterns of accelerating beams are determined by their angular spectra, which are constructed from the Mathieu functions, Weber functions, and Fresnel integrals. Our results not only enrich the understanding of multidimensional nonparaxial accelerating beams, but also display their real applicative potential -- owing to the usefulness of Mathieu and Weber functions, and Fresnel integrals in describing a wealth of wave phenomena in nature.

  5. Interference of two pulse-like spatial beams with arbitrary transverse separation

    Science.gov (United States)

    Flórez, Jefferson; Álvarez, Juan-Rafael; Calderón-Losada, Omar; José Salazar-Serrano, Luis; Valencia, Alejandra

    2016-12-01

    We report the observation of interference in position and transverse momentum variables between two parallel-propagating Gaussian beams separated by an arbitrary distance. This resembles the Alford and Gold effect that has been reported for the time-frequency degree of freedom, and constitutes a method for spatial intensity shaping of light beams. We observe this interference by using a tunable beam displacer, which plays the role of a Michelson interferometer for the transverse spatial variables. Additionally, we employ the interference pattern as a function of the separation between the beams to determine the spatial coherence length of the original beam.

  6. Effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli-Euler beam.

    Science.gov (United States)

    Sorokin, Vladislav S; Thomsen, Jon Juel

    2016-02-01

    The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation.

  7. Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material

    Directory of Open Access Journals (Sweden)

    Şeref Doğuşcan Akbaş

    2013-01-01

    Full Text Available Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.

  8. Transverse Beam Halo Measurements at High Intensity Neutrino Source (HINS) using Vibrating Wire Monitor

    Energy Technology Data Exchange (ETDEWEB)

    Chung, M.; Hanna, B.; Scarpine, V.; Shiltsev, V.; Steimel, J.; Artinian, S.; Arutunian, S.

    2015-02-26

    The measurement and control of beam halos will be critical for the applications of future high-intensity hadron linacs. In particular, beam profile monitors require a very high dynamic range when used for the transverse beam halo measurements. In this study, the Vibrating Wire Monitor (VWM) with aperture 60 mm was installed at the High Intensity Neutrino Source (HINS) front-end to measure the transverse beam halo. A vibrating wire is excited at its resonance frequency with the help of a magnetic feedback loop, and the vibrating and sensitive wires are connected through a balanced arm. The sensitive wire is moved into the beam halo region by a stepper motor controlled translational stage. We study the feasibility of the vibrating wire for the transverse beam halo measurements in the low-energy front-end of the proton linac.

  9. Three-dimensional nonparaxial accelerating beams from the transverse Whittaker integral

    Science.gov (United States)

    Zhang, Yiqi; Belić, Milivoj R.; Sun, Jia; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Wang, Zhiguo; Zhang, Yanpeng

    2014-08-01

    We investigate three-dimensional nonparaxial linear accelerating beams arising from the transverse Whittaker integral. These beams accelerate along a semicircular trajectory, with almost invariant nondiffracting shapes. The transverse patterns of accelerating beams are determined by their angular spectra, which are constructed from the Mathieu functions, Weber functions, and Fresnel integrals. Our results not only enrich the understanding of multidimensional nonparaxial accelerating beams, but also display their real applicative potential —owing to the usefulness of Mathieu and Weber functions, and Fresnel integrals in describing a wealth of wave phenomena in nature.

  10. Application of Chebyshev Formalism to Identify Nonlinear Magnetic Field Components in Beam Transport Systems

    Energy Technology Data Exchange (ETDEWEB)

    Spata, Michael [Old Dominion Univ., Norfolk, VA (United States)

    2012-08-01

    An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.

  11. A viscoelastic orthotropic Timoshenko beam subjected to general transverse loading

    Directory of Open Access Journals (Sweden)

    Adámek V.

    2008-12-01

    Full Text Available The investigation of lateral vibrations of a simply supported thin beam is the aim of this work. The analytical solution of the problem is derived based on the approximate Timoshenko beam theory for a general continuous loading acting on the upper beam face over the whole beam width and perpendicular to the beam axis. The material of the beam studied is assumed linear orthotropic viscoelastic. The generalized standard viscoelastic solid is chosen for representing of viscoelastic beam behaviour. Final system of partial integro-differential equations is solved by the standard method of integral transforms and resulting relations describing beam deflection, slope of the beam and corresponding stress and strain components are presented. Moreover, the derivation of final functions of beam deflection and slope of the beam for a specific impulse loading is presented and analytical results are compared with results obtained using numerical simulation in 2D (FEM. This confrontation shows very good agreement between results obtained. Furthermore, it was shown that the measure of agreement depends not only on the beam geometry.

  12. Stress wave propagation in a composite beam subjected to transverse impact.

    Energy Technology Data Exchange (ETDEWEB)

    Lu, Wei-Yang; Song, Bo; Jin, Huiqing

    2010-08-01

    Composite materials, particularly fiber reinforced plastic composites, have been extensively utilized in many military and industrial applications. As an important structural component in these applications, the composites are often subjected to external impact loading. It is desirable to understand the mechanical response of the composites under impact loading for performance evaluation in the applications. Even though many material models for the composites have been developed, experimental investigation is still needed to validate and verify the models. It is essential to investigate the intrinsic material response. However, it becomes more applicable to determine the structural response of composites, such as a composite beam. The composites are usually subjected to out-of-plane loading in applications. When a composite beam is subjected to a sudden transverse impact, two different kinds of stress waves, longitudinal and transverse waves, are generated and propagate in the beam. The longitudinal stress wave propagates through the thickness direction; whereas, the propagation of the transverse stress wave is in-plane directions. The longitudinal stress wave speed is usually considered as a material constant determined by the material density and Young's modulus, regardless of the loading rate. By contrast, the transverse wave speed is related to structural parameters. In ballistic mechanics, the transverse wave plays a key role to absorb external impact energy [1]. The faster the transverse wave speed, the more impact energy dissipated. Since the transverse wave speed is not a material constant, it is not possible to be calculated from stress-wave theory. One can place several transducers to track the transverse wave propagation. An alternative but more efficient method is to apply digital image correlation (DIC) to visualize the transverse wave propagation. In this study, we applied three-pointbending (TPB) technique to Kolsky compression bar to facilitate

  13. Simulation study of LEBT for transversely coupled beam from an ECR ion source

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Y., E-mail: yangyao@impcas.ac.cn [Institute of Modern Physics, CAS, Lanzhou 730000 (China); University of Chinese Academy of Sciences, Beijing 100039 (China); Dou, W. P.; Sun, L. T.; Yao, Q. G.; Zhang, Z. M.; Yuan, Y. J.; He, Y.; Zh, X. Z.; Zhao, H. W. [Institute of Modern Physics, CAS, Lanzhou 730000 (China)

    2016-02-15

    A Low-Energy intense-highly charged ion Accelerator Facility (LEAF) program has been launched at Institute of Modern Physics. This accelerator facility consists of a superconducting Electron Cyclotron Resonance (ECR) ion source, a Low Energy Beam Transport (LEBT) system, and a Radio Frequency Quadrupole (RFQ). It is especially of interest for the extracted ion beam from the ECR ion source, which is transversely coupled, and this property will significantly affect the beam transmission in the LEBT line and the matching with the downstream RFQ. In the beam transport design of LEAF, beam decoupling in the LEBT is considered to lower down the projection emittances and the feasibility of the design has been verified by beam simulation with a transversely coupled beam from the ECR ion source.

  14. Transverse beams stability studies at the Large Hadron Collider

    CERN Document Server

    Buffat, Xavier; Pieloni, Tatiana

    2015-01-30

    A charged particle beam travelling at the speed of light produces large electromagnetic wake fields which, through interactions with its surroundings, act back on the particles in the beam. This coupled system may become unstable, resulting in a deterioration of the beam quality. Such effects play a major role in most existing storage rings, as they limit the maximum performance achievable. In a collider, the presence of a second beam significantly changes the dynamics, as the electromagnetic interactions of the two beams on each other are usually very strong and may, also, limit the collider performances. This thesis treats the coherent stability of the two beams in a circular collider, including the effects of the electromagnetic wake fields and of the beam-beam interactions, with particular emphasis on CERN's Large Hadron Collider. As opposed to other colliders, this machine features a large number of bunches per beam each experiencing multiple long-range and head-on beam-beam interactions. Existing models...

  15. Vibration Suppression of an Axially Moving String with Transverse Wind Loadings by a Nonlinear Energy Sink

    Directory of Open Access Journals (Sweden)

    Ye-Wei Zhang

    2013-01-01

    Full Text Available Nonlinear targeted energy transfer (TET is applied to suppress the excessive vibration of an axially moving string with transverse wind loads. The coupling dynamic equations used are modeled by a nonlinear energy sink (NES attached to the string to absorb vibrational energy. By a two-term Galerkin procedure, the equations are discretized, and the effects of vibration suppression by numerical methods are demonstrated. Results show that the NES can effectively suppress the vibration of the axially moving string with transverse wind loadings, thereby protecting the string from excessive movement.

  16. Transverse nonlinear vibrations of a circular spinning disk with a varying rotating speed

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    We analyze the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. Based on Hamilton’s principle, the nonlinear governing equations of motion (coupled equations among the radial, tangential and transverse displacements) are derived for the rotating flexible disk. When the in-plane inertia is ignored and a stress function is introduced, the three nonlinearly coupled partial differential equations are reduced to two nonlinearly coupled partial differential equations. According to Galerkin’s approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes is derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including the periodic, period-n and multi-pulse type chaotic motions for the spinning disk with a varying rotating speed. It is also found that among all parameters, the damping and excitation have great influence on the nonlinear responses of the spinning disk with a varying rotating speed.

  17. Effects of transverse electron beam size on transition radiation angular distribution

    Energy Technology Data Exchange (ETDEWEB)

    Chiadroni, E., E-mail: enrica.chiadroni@lnf.infn.it [Laboratori Nazionali di Frascati-INFN, via E. Fermi, 40, 00044 Frascati (Italy); Castellano, M. [Laboratori Nazionali di Frascati-INFN, via E. Fermi, 40, 00044 Frascati (Italy); Cianchi, A. [University of Rome ' Tor Vergata' and INFN-Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome (Italy); Honkavaara, K.; Kube, G. [Deutsches Elektronen-Synchrotron, Notkestrasse 85, 22607 Hamburg (Germany)

    2012-05-01

    In this paper we consider the effect of the transverse electron beam size on the Optical Transition Radiation (OTR) angular distribution in case of both incoherent and coherent emission. Our results confute the theoretical argumentations presented first in Optics Communications 211, 109 (2002), which predicts a dependence of the incoherent OTR angular distribution on the beam size and emission wavelength. We present here theoretical and experimental data not only to validate the well-established Ginzburg-Frank theory, but also to show the impact of the transverse beam size in case of coherent emission.

  18. Four-dimensional transverse beam matrix measurement using the multiple-quadrupole scan technique

    Directory of Open Access Journals (Sweden)

    Eduard Prat

    2014-05-01

    Full Text Available Accurate measurements of the transverse beam properties are essential to understand and optimize particle beams. We present an optimized method that uses three quadrupole magnets and one profile monitor to measure the full 4D transverse matrix of the beam. The method has been applied to the SwissFEL Injector Test Facility (SITF at the Paul Scherrer Institute (Villigen. The SITF is the principal test bed and demonstration plant for the SwissFEL project, which aims at realizing a hard-x-ray free-electron laser in 2017. Simulations, measurements, and results of cross-plane coupling correction are presented.

  19. Employing Beam-Gas Interaction Vertices for Transverse Profile Measurements

    CERN Document Server

    Rihl, Mariana; Baglin, Vincent; Barschel, Colin; Bay, Aurelio; Blanc, Frederic; Bravin, Enrico; Bregliozzi, Giuseppe; Chritin, Nicolas; Dehning, Bernd; Ferro-Luzzi, Massimiliano; Gaspar, Clara; Gianì, Sebastiana; Giovannozzi, Massimo; Greim, Roman; Haefeli, Guido; Hopchev, Plamen; Jacobsson, Richard; Jensen, Lars; Jones, Owain Rhodri; Jurado, Nicolas; Kain, Verena; Karpinski, Waclaw; Kirn, Thomas; Kuhn, Maria; Luthi, Berengere; Magagnin, Paolo; Matev, Rosen; Nakada, Tatsuya; Neufeld, Niko; Panman, Jaap; Rakotomiaramanana, Barinjaka; Salustino Guimaraes, Valdir; Salvant, Benoit; Schael, Stefan; Schneider, Olivier; Schwering, Georg; Tobin, Mark; Veness, Raymond; Veyrat, Quentin; Vlachos, Sotiris; Wlochal, Michael; Xu, Zhirui; von Dratzig, Arndt

    2016-01-01

    Interactions of high-energy beam particles with residual gas offer a unique opportunity to measure the beam profile in a non-intrusive fashion. Such a method was successfully pioneered* at the LHCb experiment using a silicon microstrip vertex detector. During the recent Large Hadron Collider shutdown at CERN, a demonstrator Beam-Gas Vertexing system based on eight scintillating-fibre modules was designed**, constructed and installed on Ring 2 to be operated as a pure beam diagnostics device. The detector signals are read out and collected with LHCb-type front-end electronics and a DAQ system consisting of a CPU farm. Tracks and vertices will be reconstructed to obtain a beam profile in real time. Here, first commissioning results are reported. The advantages and potential for future applications of this technique are discussed.

  20. Quantumlike description of the nonlinear and collective effects on relativistic electron beams in strongly magnetized plasmas

    CERN Document Server

    Tanjia, Fatema; Fedele, Renato; Shukla, P K; Jovanovic, Dusan

    2011-01-01

    A numerical analysis of the self-interaction induced by a relativistic electron/positron beam in the presence of an intense external longitudinal magnetic field in plasmas is carried out. Within the context of the Plasma Wake Field theory in the overdense regime, the transverse beam-plasma dynamics is described by a quantumlike Zakharov system of equations in the long beam limit provided by the Thermal Wave Model. In the limiting case of beam spot size much larger than the plasma wavelength, the Zakharov system is reduced to a 2D Gross-Pitaevskii-type equation, where the trap potential well is due to the external magnetic field. Vortices, "beam halos" and nonlinear coherent states (2D solitons) are predicted.

  1. Deflection and Supporting Force Analysis of a Slender Beam under Combined Transverse and Tensile Axial Loads

    Science.gov (United States)

    2016-05-01

    facility. The static pressure pipe was modelled as a slender propped cantilever beam (fixed at one end and roller-supported at the other) that is...Technology Group Transonic Wind Tunnel test facility. The static pressure pipe analysed herein was modelled as a slender propped cantilever beam...25 APPENDIX B: VBA FUNCTIONS FOR STATIC SOLUTION OF PROPPED CANTILEVER BEAM SUBJECTED TO COMBINED TRANSVERSE AND AXIAL LOADING

  2. A Nonlinear Observer for Estimating Transverse Stability Parameters of Marine Surface Vessels

    DEFF Research Database (Denmark)

    Galeazzi, Roberto; Perez, Tristan

    2011-01-01

    This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel’s centre of gravity due...

  3. Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions

    Institute of Scientific and Technical Information of China (English)

    郭强; 刘曦; 钟宏志

    2004-01-01

    This paper is concerned with the effects of boundary conditions on the large-amplitude free vibrations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a specific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curvature and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.

  4. A transverse emittance and acceptance measurement system in a low-energy beam transport line

    Energy Technology Data Exchange (ETDEWEB)

    Kashiwagi, H., E-mail: kashiwagi.hirotsugu@jaea.go.jp; Miyawaki, N.; Kurashima, S.; Okumura, S. [Department of Advanced Radiation Technology, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292 (Japan)

    2014-02-15

    A transverse beam emittance and acceptance measurement system has been developed to visualize the relationship between the injected beam emittance and the acceptance of a cyclotron. The system is composed of a steering magnet, two pairs of slits to limit the horizontal and vertical phase-space, a beam intensity detector just behind the slits for the emittance measurement, and a beam intensity detector in the cyclotron for the acceptance measurement. The emittance is obtained by scanning the slits and measuring the beam intensity distribution. The acceptance is obtained by measuring the distribution of relative beam transmission by injecting small emittance beams at various positions in a transverse phase-space using the slits. In the acceptance measurement, the beam from an ion source is deflected to the defined region by the slits using the steering magnet so that measurable acceptance area covers a region outside the injection beam emittance. Measurement tests were carried out under the condition of accelerating a beam of {sup 16}O{sup 6+} from 50.2 keV to 160 MeV. The emittance of the injected beam and the acceptance for accelerating and transporting the beam to the entrance of the extraction deflector were successfully measured. The relationship between the emittance and acceptance is visualized by displaying the results in the same phase-plane.

  5. Measurement of nonlinear observables in the Large Hadron Collider using kicked beams

    Science.gov (United States)

    Maclean, E. H.; Tomás, R.; Schmidt, F.; Persson, T. H. B.

    2014-08-01

    The nonlinear dynamics of a circular accelerator such as the Large Hadron Collider (LHC) may significantly impact its performance. As the LHC progresses to more challenging regimes of operation it is to be expected that the nonlinear single particle dynamics in the transverse planes will play an increasing role in limiting the reach of the accelerator. As such it is vital that the nonlinear sources are well understood. The nonlinear fields of a circular accelerator may be probed through measurement of the amplitude detuning: the variation of tune with single particle emittance. This quantity may be assessed experimentally by exciting the beam to large amplitudes with kicks, and obtaining the tunes and actions from turn-by-turn data at Beam Position Monitors. The large amplitude excitations inherent to such a measurement also facilitate measurement of the dynamic aperture from an analysis of beam losses following the kicks. In 2012 these measurements were performed on the LHC Beam 2 at injection energy (450 GeV) with the nominal magnetic configuration. Nonlinear coupling was also observed. A second set of measurements were performed following the application of corrections for b4 and b5 errors. Analysis of the experimental results, and a comparison to simulation are presented herein.

  6. Transverse beam motion on the second axis of the dual axis radiographic hydrodynamic test facility

    Energy Technology Data Exchange (ETDEWEB)

    Caporaso, G J; Chen, Y J; Fawley, W M; Paul, A C

    1999-03-23

    The accelerator on the second-axis of the Dual-Axis Radiographic Hydrodynamic Test (DARHT-II) facility will generate a 20 MeV, 2-4 kA, 2 µs long electron beam with an energy variation {<=} ± 0.5%. Four short current pulses with various lengths will be selected out of this 2 µs long current pulse and delivered to an x-ray converter target. The DARHT-II radiographic resolution requires these electron pulses to be focused to sub-millimeter spots on Bremsstrahlung targets with peak-to-peak transverse beam motion less than a few hundred microns. We have modeled the transverse beam motion, including the beam breakup instability, corkscrew motion, transverse resistive wall instability and beam induced transverse deflection in the kicker system, from the DARHT-II injector exit to the x-ray converter target. Simulations show that the transverse motion at the x-ray converters satisfies the DARHT-II radiographic requirements.

  7. Two-dimensional nonlinear dynamics of bidirectional beam-plasma instability

    Science.gov (United States)

    Pavan, J.; Ziebell, L. F.; Gaelzer, R.; Yoon, P. H.

    2009-01-01

    Solar wind electrons near 1 AU feature wide-ranging asymmetries in the superthermal tail distribution. Gaelzer et al. (2008) recently demonstrated that a wide variety of asymmetric distributions results if one considers a pair of counterstreaming electron beams interacting with the core solar wind electrons. However, the nonlinear dynamics was investigated under the simplifying assumption of one dimensionality. In the present paper, this problem is revisited by extending the analysis to two dimensions. The classic bump-on-tail instability involves a single electron beam interacting with the background population. The bidirectional or counterstreaming beams excite Langmuir turbulence initially propagating in opposite directions. It is found that the nonlinear mode coupling leads to the redistribution of wave moments along concentric arcs in wave number space, somewhat similar to the earlier findings by Ziebell et al. (2008) in the case of one beam-plasma instability. However, the present result also shows distinctive features. The similarities and differences in the nonlinear wave dynamics are discussed. It is also found that the initial bidirectional beams undergo plateau formation and broadening in perpendicular velocity space. However, the anisotropy persists in the nonlinear stage, implying that an additional pitch angle scattering by transverse electromagnetic fluctuations is necessary in order to bring the system to a truly isotropic state.

  8. Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

    Directory of Open Access Journals (Sweden)

    W. Gafsi

    2014-01-01

    Full Text Available In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

  9. Numerical Simulations of Transverse Beam Diffusion Enhancement by the Use of Electron Lens in the Tevatron Collider

    Energy Technology Data Exchange (ETDEWEB)

    Previtali, V.; Stancari, G.; Valishev, A.; /Fermilab; Shatilov, D.N.; /Novosibirsk, IYF

    2012-05-01

    Transverse beam diffusion for the Tevatron machine has been calculated using the Lifetrac code. The following effects were included: random noise (representing residual gas scattering, voltage noise in the accelerating cavities) lattice nonlinearities and beam-beam interactions. The time evolution of particle distributions with different initial amplitudes in Hamiltonian action has been simulated for 6 million turns, corresponding to a time of about 2 minutes. For each particle distribution, several cases have been considered: a single beam in storage ring mode, the collider case and the effects of a hollow electron beam collimator. The diffusion coefficient for some representative points in the amplitude space has been calculated by fitting the time evolution of delta-like particle distributions using the diffusion equation, for different machine conditions. The results confirm a strong efficiency of the electron lens as an halo diffusive enhancer, leading to diffusion coefficients which are at least a factor 10K higher than the values obtained for the collision case. This result is confirmed by the Frequency Map Analysis, which shows a clear intensification of resonance lines for particle amplitudes larger than the electron lens inner radius. If compared with past experiments, the simulations successfully reproduce the diffusion coefficients for the beam core, but still present a large discrepancy for halo particles, still under investigation.

  10. PRINCIPAL RESONANCE IN TRANSVERSE NONLINEAR PARAMETRIC VIBRATION OF AN AXIALLY ACCELERATING VISCOELASTIC STRING

    Institute of Scientific and Technical Information of China (English)

    CHEN Liqun; Jean W.ZU; WU Jun

    2004-01-01

    To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string, the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string. To derive the governing equation, Newton's second law, Lagrangean strain, and Kelvin's model are respectively used to account the dynamical relation, geometric nonlinearity and the viscoelasticity of the string material.Based on the solvability condition of eliminating the secular terms, closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance. The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance. Some numerical examples are presented to show the effects of the mean transport speed, the amplitude and the frequency of speed variation.

  11. Interferences in the transverse profile of a toluene beam induced by a resonant RF electric field.

    Science.gov (United States)

    Morato, M; Cáceres, J O; Gonzálvez, A G; González Ureña, A

    2009-12-31

    In this work, the interaction of a supersonic beam of toluene diluted in He with a resonant oscillating RF field is investigated both experimental and theoretically. It is shown how the resonant field induces a peak structure in the transverse beam profile which can be explained by the onset of molecular interferences. Specifically, the interaction of a toluene beam of 0.12 eV of translational energy with a resonant RF field of 1.12 kV/m amplitude, and -610 kV/m(2) of gradient at the horizontal plane, during 160 micros produces a series of maxima in the transverse beam profile. The observed structure was satisfactorily reproduced by a quantum interference model based on the interaction of two coherent superpositions induced by the resonant RF field. It appears the present experimental technique could be useful to investigate the spectroscopy and dynamical behavior of coherent beams of polar molecules.

  12. Transverse Vibration of Axially Moving Functionally Graded Materials Based on Timoshenko Beam Theory

    Directory of Open Access Journals (Sweden)

    Suihan Sui

    2015-01-01

    Full Text Available The transverse free vibration of an axially moving beam made of functionally graded materials (FGM is investigated using a Timoshenko beam theory. Natural frequencies, vibration modes, and critical speeds of such axially moving systems are determined and discussed in detail. The material properties are assumed to vary continuously through the thickness of the beam according to a power law distribution. Hamilton’s principle is employed to derive the governing equation and a complex mode approach is utilized to obtain the transverse dynamical behaviors including the vibration modes and natural frequencies. Effects of the axially moving speed and the power-law exponent on the dynamic responses are examined. Some numerical examples are presented to reveal the differences of natural frequencies for Timoshenko beam model and Euler beam model. Moreover, the critical speed is determined numerically to indicate its variation with respect to the power-law exponent, axial initial stress, and length to thickness ratio.

  13. Transverse Beam Emittance Measurements of a 16 MeV Linac at the Idaho Accelerator Center

    Energy Technology Data Exchange (ETDEWEB)

    S. Setiniyaz, T.A. Forest, K. Chouffani, Y. Kim, A. Freyberger

    2012-07-01

    A beam emittance measurement of the 16 MeV S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). The HRRL linac structure was upgraded beyond the capabilities of a typical medical linac so it can achieve a repetition rate of 1 kHz. Measurements of the HRRL transverse beam emittance are underway that will be used to optimize the production of positrons using HRRL's intense electron beam on a tungsten converter. In this paper, we describe a beam imaging system using on an OTR screen and a digital CCD camera, a MATLAB tool to extract beamsize and emittance, detailed measurement procedures, and the measured transverse emittances for an arbitrary beam energy of 15 MeV.

  14. Experimental characterization of X-ray transverse coherence in the presence of beam transport optics

    DEFF Research Database (Denmark)

    Chubar, O.; Fluerasu, A.; Chu, Y.S.

    2013-01-01

    be significantly affected by the new shape of the focused beam phase-space. At the same time, optical element imperfections still have a negative impact on the transverse coherence. In such situations, which are frequently encountered in experiments at beamlines, the quantitative interpretation of a measured...... propagation based simulations show, in particular, that new generation 1D Beryllium Compound Refractive Lenses [3, 4] do not reduce the X-ray transverse coherence in any significant manner. © 2013 IOP Publishing Ltd....

  15. Controlled Transverse Blow-up of Highenergy Proton Beams for Aperture Measurements and Loss Maps

    CERN Document Server

    Hӧfle, W; Redaelli, S; Schmidt, R; Valuch, D; Wollmann, D; Zerlauth, M

    2012-01-01

    A technique was developed to blow-up transversely in a controlled way high energy proton beams in the LHC. The technique is based on band limited white noise excitation that is injected into the transverse damper feedback loop. The injected signal can be gated to selectively blow-up individual trains of bunches. The speed of transverse blow-up can be precisely controlled. This opens the possibility to perform safely and efficiently aperture measurements and loss maps with high intensity bunch trains well above stored beam energies that are considered to be safe. In particular, lengthy procedures for measurements at top energy, otherwise requiring multiple fills of individual bunches, can be avoided. In this paper, the method is presented and results from beam measurements are discussed and compared with alternative blowup methods.

  16. Statistical signal processing techniques for coherent transversal beam dynamics in synchrotrons

    Energy Technology Data Exchange (ETDEWEB)

    Alhumaidi, Mouhammad

    2015-03-04

    Transversal coherent beam oscillations can occur in synchrotrons directly after injection due to errors in position and angle, which stem from inaccurate injection kicker reactions. Furthermore, the demand for higher beam intensities is always increasing in particle accelerators. The wake fields generated by the traveling particles will be increased by increasing the beam intensity. This leads to a stronger interaction between the beam and the different accelerator components, which increases the potential of coherent instabilities. Thus, undesired beam oscillations will occur when the natural damping is not enough to attenuate the oscillations generated by the coherent beam-accelerator interactions. The instabilities and oscillations can be either in transversal or longitudinal direction. In this work we are concerned with transversal beam oscillations only. In normal operation, transversal beam oscillations are undesired since they lead to beam quality deterioration and emittance blow up caused by the decoherence of the oscillating beam. This decoherence is caused by the tune spread of the beam particles. The emittance blow up reduces the luminosity of the beam, and thus the collision quality. Therefore, beam oscillations must be suppressed in order to maintain high beam quality during acceleration. A powerful way to mitigate coherent instabilities is to employ a feedback system. A Transversal Feedback System (TFS) senses instabilities of the beam by means of Pickups (PUs), and acts back on the beam through actuators, called kickers. In this thesis, a novel concept to use multiple PUs for estimating the beam displacement at the position with 90 phase advance before the kicker is proposed. The estimated values should be the driving feedback signal. The signals from the different PUs are delayed such that they correspond to the same bunch. Subsequently, a weighted sum of the delayed signals is suggested as an estimator of the feedback correction signal. The

  17. Nonlinear Strain Measures, Shape Functions and Beam Elements for Dynamics of Flexible Beams

    Energy Technology Data Exchange (ETDEWEB)

    Sharf, I. [University of Victoria, Department of Mechanical Engineering (Canada)

    1999-05-15

    In this paper, we examine several aspects of the development of an explicit geometrically nonlinear beam element. These are: (i) linearization of the displacement field; (ii) the effect of a commonly adopted approximation for the nonlinear Lagrangian strain; and (iii) use of different-order shape functions for discretization. The issue of rigid-body check for a nonlinear beam element is also considered. An approximate check is introduced for an element based on an (approximate) intermediate strain measure. Several numerical examples are presented to support the analysis. The paper concludes with a discussion on the use of explicit nonlinear beam elements for multibody dynamics simulation.

  18. Transverse and longitudinal characterization of electron beams using interaction with optical near-fields

    CERN Document Server

    Kozák, Martin; Leedle, Kenneth J; Deng, Huiyang; Schönenberger, Norbert; Ruehl, Axel; Hartl, Ingmar; Hoogland, Heinar; Holzwarth, Ronald; Harris, James S; Byer, Robert L; Hommelhoff, Peter

    2016-01-01

    We demonstrate an experimental technique for both transverse and longitudinal characterization of bunched femtosecond free electron beams. The operation principle is based on monitoring of the current of electrons that obtained an energy gain during the interaction with the synchronized optical near-field wave excited by femtosecond laser pulses. The synchronous accelerating/decelerating fields confined to the surface of a silicon nanostructure are characterized using a highly focused sub-relativistic electron beam. Here the transverse spatial resolution of 450 nm and femtosecond temporal resolution achievable by this technique are demonstrated.

  19. Analysis of the transverse kick to beams in low-frequency photoinjectors due to wakefield effects

    Science.gov (United States)

    Salah, Wa'el; Jones, Roger M.; Coacolo, J.-L.

    2009-04-01

    A time domain analysis of the normal modes in a cavity is used to obtain an analytical expression for the transverse momentum imparted to particles within an accelerated electron beam in a low frequency photoinjector. These analytical expressions form the basis of detailed simulations on the transverse momentum imparted to an accelerated beam. This analysis of the wakefields employs a modified form of the Panofsky-Wenzel theorem in which additional velocity dependent effects are taken into account. Simulations are presented for parameters of the ELSA photocathode.

  20. ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

    Institute of Scientific and Technical Information of China (English)

    FuYiming; LiPing'en; ZhengYufang

    2004-01-01

    Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional fibre reinforced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are established. By applying the finite difference method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial differential governing equations are solved. Some examples are given and the results are compared with available data.

  1. Solution and Positive Solution to Nonlinear Cantilever Beam Equations

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of the elastic beam with a fixed end and a free end. The main results show that the equation has at least one solution or positive solution, provided that the "height" of nonlinear term is appropriate on a bounded set.

  2. Homogeneous shear turbulence - bypass concept via interplay of linear transient growth and nonlinear transverse cascade

    Science.gov (United States)

    Mamatsashvili, George; Dong, Siwei; Khujadze, George; Chagelishvili, George; Jiménez, Javier; Foysi, Holger

    2016-04-01

    We performed direct numerical simulations of homogeneous shear turbulence to study the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows. For this purpose, we analyzed the turbulence dynamics in Fourier/wavenumber/spectral space based on the simulation data for the domain aspect ratio 1 : 1 : 1. Specifically, we examined the interplay of linear transient growth of Fourier harmonics and nonlinear processes. The transient growth of harmonics is strongly anisotropic in spectral space. This, in turn, leads to anisotropy of nonlinear processes in spectral space and, as a result, the main nonlinear process appears to be not a direct/inverse, but rather a transverse/angular redistribution of harmonics in Fourier space referred to as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by the interplay of the linear transient, or nonmodal growth and the transverse cascade. This course of events reliably exemplifies the wellknown bypass scenario of subcritical turbulence in spectrally stable shear flows. These processes mainly operate at large length scales, comparable to the box size. Consequently, the central, small wavenumber area of Fourier space (the size of which is determined below) is crucial in the self-sustenance and is labeled the vital area. Outside the vital area, the transient growth and the transverse cascade are of secondary importance - Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. The number of harmonics actively participating in the self-sustaining process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) is quite large - it is equal to 36 for the considered box aspect ratio - and obviously cannot be described by low-order models.

  3. Generation of optical vortex dipole from superposition of two transversely scaled Gaussian beams.

    Science.gov (United States)

    Naik, Dinesh N; Pradeep Chakravarthy, T; Viswanathan, Nirmal K

    2016-04-20

    We propose a distinct concept on the generation of optical vortex through coupling between the amplitude and phase differences of the superposing beams. For the proof-of-concept demonstration, we propose a simple free-space optics recipe for the controlled synthesis of an optical beam with a vortex dipole by superposing two transversely scaled Gaussian beams. The experimental demonstration using a Sagnac interferometer introduces the desired amount of radial shear and linear phase difference between the two out-of-phase Gaussian beams to create a vortex pair of opposite topological charge in the superposed beam. Flexibility to tune their location and separation using the choice of direction of the linear phase difference and the amount of amplitude difference between the superposing beams has potential applications in optical tweezers and traps utilizing the local variation in angular momentum across the beam cross section.

  4. Experimental damage detection of cracked beams by using nonlinear characteristics of forced response

    Science.gov (United States)

    Andreaus, U.; Baragatti, P.

    2012-08-01

    Experimental evaluation of the flexural forced vibrations of a steel cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed, where an actual fatigue crack was introduced instead - as usual - of a narrow slot. The nonlinear aspects of the dynamic response of the beam under harmonic excitation were considered and the relevant quantitative parameters were evaluated, in order to relate the nonlinear resonances to the presence and size of the crack. To this end, the existence of sub- and super-harmonic components in the Fourier spectra of the acceleration signals was evidenced, and their amplitudes were quantified. In particular, the acceleration signals were measured in different positions along the beam axis and under different forcing levels at the beam tip. The remarkable relevance of the above mentioned nonlinear characteristics, and their substantial independence on force magnitude and measurement point were worthily noted in comparison with the behavior of the intact beam. Thus, a reliable method of damage detection was proposed which was based on simple tests requiring only harmonically forcing and acceleration measuring in any point non-necessarily near the crack. Then, the time-history of the acceleration recorded at the beam tip was numerically processed in order to obtain the time-histories of velocity and displacement. The nonlinear features of the forced response were described and given a physical interpretation in order to define parameters suitable for damage detection. The efficiency of such parameters was discussed with respect to the their capability of detecting damage and a procedure for damage detection was proposed which was able to detect even small cracks by using simple instruments. A finite element model of the cantilever beam was finally assembled and tuned in order to numerically simulate the results of the experimental tests.

  5. Analytical treatment of the nonlinear electron cloud effect and the combined effects with beam-beam and space charge nonlinear forces in storage rings

    Institute of Scientific and Technical Information of China (English)

    GAO Jie

    2009-01-01

    In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC Ⅱ. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.

  6. Optical Beams in Nonlocal Nonlinear Media

    DEFF Research Database (Denmark)

    Królikowski, W.; Bang, Ole; Wyller, J.

    2003-01-01

    We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons.......We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons....

  7. Study of transverse beam splitting for multi-turn extraction for the CERN PS2 ring

    CERN Document Server

    Giovannozzi, Massimo; CERN. Geneva. ATS Department

    2011-01-01

    In this paper a layout for the elements needed to split transversely the beam for a multi-turn extraction system in the PS2 ring is proposed and discussed. Additional sextupoles and octupoles are installed in one of the straight sections to generate the stable islands in the horizontal phase space. Scans over various beam dynamics quantities were performed to provide hints for an optimisation of the scheme. The results are presented and discussed in details.

  8. ON THE NONLINEAR TIMOSHENKO-KIRCHHOFF BEAM EQUATION

    Institute of Scientific and Technical Information of China (English)

    A.AROSIO

    1999-01-01

    When an elastic string with fixed ends is subjected to transverse vibrations, its length vaxiewith the time: this introduces chvages of the tension in the string. Thls induced Kirchoffto propose a nonlinear correction of the classical D'Alembert equation. Later on, Wolnowsky-

  9. Solution of Contact Problems for Nonlinear Gao Beam and Obstacle

    Directory of Open Access Journals (Sweden)

    J. Machalová

    2015-01-01

    Full Text Available Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.

  10. Study of the transverse beam motion in the DARHT Phase II accelerator

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Yu-Jiuan; Fawley, W M; Houck, T L

    1998-08-20

    The accelerator for the second-axis of the Dual Axis Radiographic Hydrodynamic Test (DARHT) facility will accelerate a 4-kA, 3-MeV, 2--µs long electron current pulse to 20 MeV. The energy variation of the beam within the flat-top portion of the current pulse is (plus or equal to) 0.5%. The performance of the DARHT Phase II radiographic machine requires the transverse beam motion to be much less than the beam spot size which is about 1.5 mm diameter on the x-ray converter. In general, the leading causes of the transverse beam motion in an accelerator are the beam breakup instability (BBU) and the corkscrew motion. We have modeled the transverse beam motion in the DARHT Phase II accelerator with various magnetic tunes and accelerator cell configurations by using the BREAKUP code. The predicted sensitivity of corkscrew motion and BBU growth to different tuning algorithms will be presented.

  11. Generation and focusing of electron beams with initial transverse-longitudinal correlation

    Energy Technology Data Exchange (ETDEWEB)

    Harris, J. R. [Colorado State Univ., Fort Collins, CO (United States) Dept. of Electrical and Computer Engineering.; Lewellen, J. W. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Poole, B. R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2014-10-07

    In charged particle beams, one of the roles played by space charge is to couple the transverse and longitudinal dynamics of the beam. This can lead to very complex phenomena which are generally studied using computer simulations. However, in some cases models based on phenomenological or analytic approximations can provide valuable insight into the system behavior. In this paper, we employ such approximations to investigate the conditions under which all the slices of a space charge dominated electron beam with slowly varying current could be focused to a waist with the same radius and at the same location, independent of slice current, and show that this can be accomplished approximately if the initial transverse-longitudinal correlation introduced onto the beam by the electron gun is chosen to compensate for the transverse-longitudinal correlation introduced onto the beam in the drift section. The validity of our approximations is assessed by use of progressively more realistic calculations. We also consider several design elements of electron guns that affect the initial correlations in the beams they generate.

  12. Differential equation of transverse vibrations of a beam with local stroke change of stiffness

    Directory of Open Access Journals (Sweden)

    Stanisław Kasprzyk

    2007-01-01

    Full Text Available The aim of this paper is to derive a differential equation of transverse vibrations of a beam with a local, stroke change of stiffness, and to solve it. The presented method is based on the theory of distributions.

  13. The Nature of Transverse Beam Instabilities at Injection in the Fermilab Main Ring

    Energy Technology Data Exchange (ETDEWEB)

    Chou, Ping Jung [Northwestern Univ., Evanston, IL (United States)

    1996-12-01

    Transverse beam instabilities have been observed in the Fermilab Main Ring since 1972. It was well controlled by two active feedback systems until the last fix target run in 1991. The current upgrade of accelerator facilities, where the replacement of the Main Ring by the Main Injector will allow acceleration of higher proton intensities, makes the importance of this issue surface again. Experimental studies were conducted to understand the nature and the cause of these transverse beam instabilities. The interplay between accelerator parameters and the growth rate of transverse beam oscillations is investigated. Some previously puzzling behavior of the Main Ring is now understood because of the knowledge gained from these studies. Experimental techniques were implemented to measure some important parameters of the Main Ring, such as the vertical impedance, bunch form factor, and the wake f~nction. Empirical theory is devised to understand the coupled bunch instability with many distributed gaps, and a satisfactory agreement is obtained between the analysis and the measured data. The cause of the transverse beam instabilities is identified to be the resistive wall impedance. Anomalous behavior in the frequency dependence of the impedance below the MHz range suggests that impedance sources other than the resistive wall also exist in the Main Ring. The performance of two active feedback systems is found to be inadequate to meet the goal of the Main Injector accelerator upgrade. Suggestions for hardware improvements and the choice of accelerator parameters are given.

  14. General description of transverse mode Bessel beams and construction of basis Bessel fields

    Science.gov (United States)

    Wang, Jia Jie; Wriedt, Thomas; Lock, James A.; Jiao, Yong Chang

    2017-07-01

    Based on an analysis of polarized Bessel beams using the Hertz vector potentials and the angular spectrum representation (ASR), a general description of transverse mode Bessel beams is proposed. As opposed to the cases of linearly and circularly polarized Bessel beams, the magnetic and electric fields of a Bessel beam in a transverse mode are orthogonal to each other. Both sets of fields together form a complete set of basis Bessel fields, in terms of which an arbitrary Bessel beam can be regarded as a linear combination. The completeness of the basis Bessel fields is analyzed from the perspectives of waveguide theory and vector wave functions. Decompositions of linearly polarized, circularly polarized, and circularly symmetric n-order Bessel beams in terms of basis Bessel fields are given. The results presented in this paper provide a fresh perspective on the description of Bessel beams, which are useful in casting insights into the experimental generation of Bessel beams and the interpretation of light scattering-related problems in practice.

  15. Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

    Institute of Scientific and Technical Information of China (English)

    Hu Ding; Li-Qun Chen

    2011-01-01

    Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation.It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same, but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.

  16. Methodology for nonlinear quantification of a flexible beam with a local, strong nonlinearity

    Science.gov (United States)

    Herrera, Christopher A.; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

    2017-02-01

    This study presents a methodology for nonlinear quantification, i.e., the identification of the linear and nonlinear regimes and estimation of the degree of nonlinearity, for a cantilever beam with a local, strongly nonlinear stiffness element. The interesting feature of this system is that it behaves linearly in the limits of extreme values of the nonlinear stiffness. An Euler-Bernoulli cantilever beam with two nonlinear configurations is used to develop and demonstrate the methodology. One configuration considers a cubic spring attached at a distance from the beam root to achieve a smooth nonlinear effect. The other configuration considers a vibro-impact element that generates non-smooth effects. Both systems have the property that, in the limit of small and large values of a configuration parameter, the system is almost linear and can be modeled as such with negligible error. For the beam with a cubic spring attachment, the forcing amplitude is the varied parameter, while for the vibro-impact beam, this parameter is the clearance between the very stiff stops and the beam at static equilibrium. Proper orthogonal decomposition is employed to obtain an optimal orthogonal basis used to describe the nonlinear system dynamics for varying parameter values. The frequencies of the modes that compose the basis are then estimated using the Rayleigh quotient. The variations of these frequencies are studied to identify parameter values for which the system behaves approximately linearly and those for which the dynamical response is highly nonlinear. Moreover, a criterion based on the Betti-Maxwell reciprocity theorem is used to verify the existence of nonlinear behavior for the set of parameter values suggested by the described methodology. The developed methodology is general and applicable to discrete or continuous systems with smooth or nonsmooth nonlinearities.

  17. Nonlinear images of scatterers in chirped pulsed laser beams

    Institute of Scientific and Technical Information of China (English)

    Hu Yong-Hua; Wang You-Wen; Wen Shuang-Chun; Fan Dian-Yuan

    2010-01-01

    The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer.It is found that the initially positive chirp-type bandwidth can suppress the nonlinear image,while the negative one can enhance it,and that both effects are inversely proportional to the incident pulse duration.Numerical simulations further demonstrate that the location of nonlinear image is at the conjugate plane of the scatterer and that,for negatively pre-chirped pulsed beam,the nonlinear image peak intensity can be higher than that in the corresponding monochromatic case under certain conditions.Moreover the effect of group velocity dispersion on nonlinear image is found to be similar to that of chirp-type bandwidth.

  18. Beam Position Monitor and Kicker for the SPring-8 Transverse Bunch-by-bunch Feedback

    CERN Document Server

    Nakamura, T

    2005-01-01

    Beam position monitor and kicker for the SPring-8 transverse bunch-by-bunch feedback system are developed. The beam of the SPring-8 storage ring is micro-meter size and the residual motion driven by the noise in the position signal should be suppressed to be submicro-meters. To meet this requirement, we developed shorted stripline type position monitor that produces one order higher position signal at 509MHz than button type BPM. In this paper, we describe design, simulation and beam test of the BPM and the kicker and the experience with the feedback system.

  19. Source-to-target simulation of simultaneous longitudinal and transverse focusing of heavy ion beams

    Directory of Open Access Journals (Sweden)

    D. R. Welch

    2008-06-01

    Full Text Available Longitudinal bunching factors in excess of 70 of a 300-keV, 27-mA K^{+} ion beam have been demonstrated in the neutralized drift compression experiment [P. K. Roy et al., Phys. Rev. Lett. 95, 234801 (2005PRLTAO0031-900710.1103/PhysRevLett.95.234801] in rough agreement with particle-in-cell source-to-target simulations. A key aspect of these experiments is that a preformed plasma provides charge neutralization of the ion beam in the last one meter drift region where the beam perveance becomes large. The simulations utilize the measured ion source temperature, diode voltage, and induction-bunching-module voltage waveforms in order to determine the initial beam longitudinal phase space which is critical to accurate modeling of the longitudinal compression. To enable simultaneous longitudinal and transverse compression, numerical simulations were used in the design of the solenoidal focusing system that compensated for the impact of the applied velocity tilt on the transverse phase space of the beam. Complete source-to-target simulations, that include detailed modeling of the diode, magnetic transport, induction bunching module, and plasma neutralized transport, were critical to understanding the interplay between the various accelerator components in the experiment. Here, we compare simulation results with the experiment and discuss the contributions to longitudinal and transverse emittance that limit the final compression.

  20. Employing Twin Crabbing Cavities to Address Variable Transverse Coupling of Beams in the MEIC

    Energy Technology Data Exchange (ETDEWEB)

    Castilla, Alejandro [ODU; Delayen, Jean R. [ODU, JLAB; Morozov, Vasiliy [JLAB; Satogata, Todd [JLAB

    2014-07-01

    The design strategy of the Medium Energy Electron-Ion Collider (MEIC) at Jefferson Lab contemplates both matching of the emittance aspect ratios and a 50 mrad crossing angle along with crab crossing scheme for both electron and ion beams over the energy range (√s=20-70 GeV) to achieve high luminosities at the interaction points (IPs). However, the desired locations for placing the crabbing cavities may include regions where the transverse degrees of freedom of the beams are coupled with variable coupling strength that depends on the collider rings’ magnetic elements (solenoids and skew quadrupoles). In this work we explore the feasibility of employing twin rf dipoles that produce a variable direction crabbing kick to account for a range of transverse coupling of both beams.

  1. CSR Effects in a Bunch Compressor influence of the Beam Frame Transverse Force

    CERN Document Server

    Bassi, G

    2005-01-01

    We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates (shielding) with a Vlasov approach. [1] The fields excited by the bunch are computed in the lab frame using a formula simpler than that based on retarded potentials. The Vlasov equation is solved in the beam frame interaction picture. In recent numerical investigations we solved the Vlasov equation for a bunch compressor using the Liouville-Maxwell approximation (LMA), where the bunch density is evolved under the fields produced by the unperturbed density (subject to external fields only), neglecting the beam frame transverse force. [2] Here we report on the influence of the beam frame transverse force on the equations of motion.

  2. A Fast Switchyard for the TESLA FEL-Beam Using a Superconducting Transverse Mode Cavity

    CERN Document Server

    Wanzenberg, R

    2000-01-01

    In the present design of the TESLA Linear Collider with integrated X-ray Laser Facility it is necessary that 1 ms long bunch trains with about 10000 bunches are generated and distributed to several free electron laser (FEL) beam lines. The different scientific applications of the X-ray FELs need specific filling patterns of the bunches in the bunch train. It is shown that a fast switch-yard based on a superconducting transverse mode cavity can be used to generate the required bunch pattern in a flexible way while keeping the beam loading in the main linear accelerator constant. The conceptual design of the beam optics and the transverse mode cavity are presented.

  3. Longitudinal and transverse cooling of relativistic electron beams in intense laser pulses

    CERN Document Server

    Yoffe, Samuel R; Noble, Adam; Jaroszynski, Dino A

    2015-01-01

    With the emergence in the next few years of a new breed of high power laser facilities, it is becoming increasingly important to understand how interacting with intense laser pulses affects the bulk properties of a relativistic electron beam. A detailed analysis of the radiative cooling of electrons indicates that, classically, equal contributions to the phase space contraction occur in the transverse and longitudinal directions. In the weakly quantum regime, in addition to an overall reduction in beam cooling, this symmetry is broken, leading to significantly less cooling in the longitudinal than the transverse directions. By introducing an efficient new technique for studying the evolution of a particle distribution, we demonstrate the quantum reduction in beam cooling, and find that it depends on the distribution of energy in the laser pulse, rather than just the total energy as in the classical case.

  4. Dynamics analysis of microsphere in a dual-beam fiber-optic trap with transverse offset.

    Science.gov (United States)

    Chen, Xinlin; Xiao, Guangzong; Luo, Hui; Xiong, Wei; Yang, Kaiyong

    2016-04-04

    A comprehensive dynamics analysis of microsphere has been presented in a dual-beam fiber-optic trap with transverse offset. As the offset distance between two counterpropagating beams increases, the motion type of the microsphere starts with capture, then spiral motion, then orbital rotation, and ends with escape. We analyze the transformation process and mechanism of the four motion types based on ray optics approximation. Dynamic simulations show that the existence of critical offset distances at which different motion types transform. The result is an important step toward explaining physical phenomena in a dual-beam fiber-optic trap with transverse offset, and is generally applicable to achieving controllable motions of microspheres in integrated systems, such as microfluidic systems and lab-on-a-chip systems.

  5. Transverse Laser Beam Shaping in High Brightness Electron Gun at ATF

    CERN Document Server

    Roychowdhury, S

    2005-01-01

    The brightness of electron beams from a photo injector is influenced by the transverse and longitudinal distribution of the laser beam illuminating the cathode. Previous studies at Brookhaven Accelerator Test Facility have shown that formation of an ideal e-beam with lowest transverse emittance requires uniform circular distribution of the emitted electrons. The use of the uniformly distributed power of the laser beam may not lead to that of the emitted electrons because of the non-uniform quantum efficiency. A proper shaping of the laser beam can compensate for this non-uniformity. In this paper we describe the use of digital light processing (DLP) technique based on digital mirror device (DMD) for spatial modulation of the laser beam, for measurements of the quantum efficiency map, and for creating the desirable e-beam density profiles. A DMD is aμelectronic mechanical system (MEMS) comprising of millions of highly reflectiveμmirrors controlled by underlying electronics. We present exper...

  6. Transverse phase space mapping of relativistic electron beams using optical transition radiation

    Directory of Open Access Journals (Sweden)

    G. P. Le Sage

    1999-12-01

    Full Text Available Optical transition radiation (OTR has proven to be a versatile and effective diagnostic for measuring the profile, divergence, and emittance of relativistic electron beams with a wide range of parameters. Diagnosis of the divergence of modern high brightness beams is especially well suited to OTR interference (OTRI techniques, where multiple dielectric or metal foils are used to generate a spatially coherent interference pattern. Theoretical analysis of measured OTR and OTRI patterns allows precise measurement of electron beam emittance characteristics. Here we describe an extension of this technique to allow mapping of divergence characteristics as a function of transverse coordinates within a measured beam. We present the first experimental analysis of the transverse phase space of an electron beam using all optical techniques. Comparing an optically masked portion of the beam to the entire beam, we measure different angular spread and average direction of the particles. Direct measurement of the phase-space ellipse tilt angle has been demonstrated using this optical masking technique.

  7. LEADS-DC: A computer code for intense dc beam nonlinear transport simulation

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    An intense dc beam nonlinear transport code has been developed. The code is written in Visual FORTRAN 6.6 and has ~13000 lines. The particle distribution in the transverse cross section is uniform or Gaussian. The space charge forces are calculated by the PIC (particle in cell) scheme, and the effects of the applied fields on the particle motion are calculated with the Lie algebraic method through the third order approximation. Obviously,the solutions to the equations of particle motion are self-consistent. The results obtained from the theoretical analysis have been put in the computer code. Many optical beam elements are contained in the code. So, the code can simulate the intense dc particle motions in the beam transport lines, high voltage dc accelerators and ion implanters.

  8. Influence of conducting plate boundary conditions on the transverse envelope equations describing intense ion beam transport

    Directory of Open Access Journals (Sweden)

    Steven M. Lund

    2004-06-01

    Full Text Available In typical diagnostic applications, intense ion beams are intercepted by a conducting plate associated with devices used to measure beam phase-space projections. This results in the transverse space-charge field near the plate being shorted out, rendering simple envelope models with constant space-charge strength inaccurate. Here we develop corrected envelope models based on analytical calculations to account for this effect on the space-charge term of the envelope equations, thereby removing a systematic source of error in the equations and enabling more accurate comparisons with experiment. For common intense beam parameters, we find that the envelope correction occurs primarily in the envelope angles near the plate and that the effect can be large enough to degrade precision beam matching in periodic transport lattices. Results are verified with 3D self-consistent particle-in-cell simulations based on intense beam experiments associated with driver development for heavy-ion fusion.

  9. Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers

    DEFF Research Database (Denmark)

    Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.

    of nonlinear beam reshaping occurring on a short time scale before the establishment of a steady state regime. In experiment, a 532nm laser beam can be injected into a single hole of an infiltrated PCF cladding structure, and the temporal dynamics of the nonlinear response is measured by monitoring......Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio......-sensing as well as active devices for all-optical switching at low (mW) laser powers. Commercially available PCFs infiltrated with liquids also provide a versatile and compact tool for exploration of the fundamentals of nonlinear beam propagation in periodic photonic structures. To explore the full scientific...

  10. Transverse to longitudinal phase space coupling in an electron beam for suppression of microbunching instability

    Science.gov (United States)

    Huang, Dazhang; Feng, Chao; Deng, Haixiao; Gu, Qiang; Zhao, Zhentang

    2016-10-01

    The microbunching instability developed during the beam compression process in the linear accelerator (LINAC) of a free-electron laser (FEL) facility has always been a problem that degrades the lasing performance, and even no FEL is able to be produced if the beam quality is destroyed too much by the instability. A common way to suppress the microbunching instability is to introduce extra uncorrelated energy spread by the laser heater that heats the beam through the interaction between the electron and laser beam, as what has been successfully implemented in the Linac Coherent Light Source and Fermi@Elettra. In this paper, a simple and effective scheme is proposed to suppress the microbunching instability by adding two transverse gradient undulators (TGU) before and after the magnetic bunch compressor. The additional uncorrelated energy spread and the density mixing from the transverse spread brought up by the first TGU results in significant suppression of the instability. Meanwhile, the extra slice energy spread and the transverse emittance can also be effectively recovered by the second TGU. The magnitude of the suppression can be easily controlled by varying the strength of the magnetic fields of the TGUs. Theoretical analysis and numerical simulations demonstrate the capability of the proposed technique in the LINAC of an x-ray free-electron laser facility.

  11. Transverse to longitudinal phase space coupling in an electron beam for suppression of microbunching instability

    Directory of Open Access Journals (Sweden)

    Dazhang Huang

    2016-10-01

    Full Text Available The microbunching instability developed during the beam compression process in the linear accelerator (LINAC of a free-electron laser (FEL facility has always been a problem that degrades the lasing performance, and even no FEL is able to be produced if the beam quality is destroyed too much by the instability. A common way to suppress the microbunching instability is to introduce extra uncorrelated energy spread by the laser heater that heats the beam through the interaction between the electron and laser beam, as what has been successfully implemented in the Linac Coherent Light Source and Fermi@Elettra. In this paper, a simple and effective scheme is proposed to suppress the microbunching instability by adding two transverse gradient undulators (TGU before and after the magnetic bunch compressor. The additional uncorrelated energy spread and the density mixing from the transverse spread brought up by the first TGU results in significant suppression of the instability. Meanwhile, the extra slice energy spread and the transverse emittance can also be effectively recovered by the second TGU. The magnitude of the suppression can be easily controlled by varying the strength of the magnetic fields of the TGUs. Theoretical analysis and numerical simulations demonstrate the capability of the proposed technique in the LINAC of an x-ray free-electron laser facility.

  12. A high repetition rate transverse beam profile diagnostic for laser-plasma proton sources

    Science.gov (United States)

    Dover, Nicholas; Nishiuchi, Mamiko; Sakaki, Hironao; Kando, Masaki; Nishitani, Keita

    2016-10-01

    The recently upgraded J-KAREN-P laser can provide PW peak power and intensities approaching 1022 Wcm-2 at 0.1 Hz. Scaling of sheath acceleration to such high intensities predicts generation of protons to near 100 MeV, but changes in electron heating mechanisms may affect the emitted proton beam properties, such as divergence and pointing. High repetition rate simultaneous measurement of the transverse proton distribution and energy spectrum are therefore key to understanding and optimising the source. Recently plastic scintillators have been used to measure online proton beam transverse profiles, removing the need for time consuming post-processing. We are therefore developing a scintillator based transverse proton beam profile diagnostic for use in ion acceleration experiments using the J-KAREN-P laser. Differential filtering provides a coarse energy spectrum measurement, and time-gating allows differentiation of protons from other radiation. We will discuss the design and implementation of the diagnostic, as well as proof-of-principle results from initial experiments on the J-KAREN-P system demonstrating the measurement of sheath accelerated proton beams up to 20 MeV.

  13. Direction-sensitive transverse velocity measurement by phase-modulated structured light beams.

    Science.gov (United States)

    Rosales-Guzmán, Carmelo; Hermosa, Nathaniel; Belmonte, Aniceto; Torres, Juan P

    2014-09-15

    The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge because detection is usually done by means of an interferometric setup, which only provides an absolute value of the frequency shift. In this Letter, we present a novel method that addresses this issue. It uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced. This is done by noting the change in the magnitude of the frequency shift as the transverse phase of the structured light is moved appropriately. We demonstrate our method with rotating microparticles that are illuminated by a Laguerre-Gaussian beam with a rotating phase about its propagation axis. Our method, which only requires a dynamically configurable optical beam generator, can easily be used with other types of motion by appropriate engineering and dynamic modulation of the phase of the light beam.

  14. Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com [Department of Physics, National Institute of Technology Jalandhar (India); Singh, Navpreet, E-mail: navpreet.nit@gmail.com [Guru Nanak Dev University College, Kapurthala, Punjab (India)

    2015-11-15

    This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on a numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.

  15. Behavior of Uniform Anisotropic Beams of Rectangular Section under Transverse Impact of a Mass

    Directory of Open Access Journals (Sweden)

    Lu Chun

    1997-01-01

    Full Text Available A numerical method is presented to investigate the dynamic response of uniform orthotropic beams subjected to an impact of a mass. Higher order shear deformation and rotary inertia are included in the analysis of the beams. The impactor and laminated composite beam are treated as a system. The nonlinear differential governing equations of motion are then derived based on the Lagrange principle and modified nonlinear contact law, and solved numerically. The solution procedure is applicable to arbitrary boundary conditions. Numerical results are compared with those available in the literature to demonstrate the validity of the method, and very good agreement is achieved. The effects of boundary conditions on the contact force, contact duration, stress distributions, and beam deflection are discussed.

  16. A nonlinear mathematical model for large deflection of incompressible saturated poroelastic beams

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Nonlinear governing equations are established for large deflection of incompressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams. Then, the nonlinear bending of a saturated poroelastic cantilever beam with fixed end impermeable and free end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, is examined with the Galerkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are compared, and the differences between them are revealed. It is shown that the results of the large deflection theory are less than those of the corresponding small deflection theory, and the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.

  17. Formation of compressed flat electron beams with high transverse-emittance ratios

    Energy Technology Data Exchange (ETDEWEB)

    Zhu, J. [Fermilab; Institute of Fluid Physics, CAEP, China; Piot, P. [Northern Illinois University; Fermilab; Mihalcea, D. [Northern Illinois University; Prokop, C. R. [Northern Illinois University

    2014-08-01

    Flat beams—beams with asymmetric transverse emittances—have important applications in novel light-source concepts and advanced-acceleration schemes and could possibly alleviate the need for damping rings in lepton colliders. Over the last decade, a flat beam generation technique based on the conversion of an angular-momentum-dominated beam was proposed and experimentally tested. In this paper we explore the production of compressed flat beams. We especially investigate and optimize the flat beam transformation for beams with substantial fractional energy spread. We use as a simulation example the photoinjector of Fermilab’s Advanced Superconducting Test Accelerator. The optimizations of the flat beam generation and compression at Advanced Superconducting Test Accelerator were done via start-to-end numerical simulations for bunch charges of 3.2 nC, 1.0 nC, and 20 pC at ~37 MeV. The optimized emittances of flat beams with different bunch charges were found to be 0.25 μm (emittance ratio is ~400), 0.13 μm, 15 nm before compression, and 0.41 μm, 0.20 μm, 16 nm after full compression, respectively, with peak currents as high as 5.5 kA for a 3.2-nC flat beam. These parameters are consistent with requirements needed to excite wakefields in asymmetric dielectric-lined waveguides or produce significant photon flux using small-gap micro-undulators.

  18. Possibilities and limitations of rod-beam theories. [nonlinear distortion tensor and nonlinear stress tensors

    Science.gov (United States)

    Peterson, D.

    1979-01-01

    Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.

  19. Non-Linear Vibration of Euler-Bernoulli Beams

    DEFF Research Database (Denmark)

    Barari, Amin; Kaliji, H. D.; Domairry, G.

    2011-01-01

    In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....

  20. Reflection of a Gaussian beam from a nonlinear interface.

    Science.gov (United States)

    Marcuse, D

    1980-09-15

    A numerical analysis of the reflection of a two dimensional Gaussian beam from the interface between a linear and a nonlinear medium is presented. The refractive index of the nonlinear medium is a function of the intensity of the radiation field, having a smaller value than the linear refractive index for zero field intensity. The Gaussian beam is incident from the linear medium and suffers total reflection at low intensity. At sufficiently high intensity nonlinear effects are observed. Above a threshold value the incident beam breaks up into a reflected wave and a surface wave. Once the beam is sufficiently strong for a surface wave to form, its interaction with the boundary becomes surprisingly independent of field intensity; but for very strong fields the reflectivity is increased at the expense of the surface wave. A very different behavior is observed when the refractive index is constrained to remain below a certain maximum value. Now the field detaches itself from the surface and penetrates into the nonlinear medium forming one or more distinct beams. The plane wave theory predicts the existence of hysteresis so that two different solutions should exist for the same physical parameters. A second solution was indeed found in one case with constrained refractive index, but its validity is somewhat uncertain at this time.

  1. Intense DC beam nonlinear transport-analysis & simulation

    Institute of Scientific and Technical Information of China (English)

    L(U) Jian-Qin; ZHAO Xiao-Song

    2009-01-01

    The intense dc beam nonlinear transport was analyzed with the Lie algebraic method,and the particle trajectories of the second order approximation were obtained.Based on the theoretical analysis a computer code was designed.To get self-consistent solutions,iteration procedures were used in the code.As an example,we calculated a beam line(drift-electrostatic quadrupole doublet-drift).The results agree to the results calculated by using the PIC method.

  2. Finite rotation and nonlinear beam kinematics

    Science.gov (United States)

    Hodges, Dewey H.

    1987-01-01

    Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.

  3. Nonlinear analysis of lipid tubules by nonlocal beam model.

    Science.gov (United States)

    Shen, Hui-Shen

    2011-05-07

    Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for lipid tubules. The lipid tubule is modeled as a nonlocal micro/nano-beam which contains small scale effect. The material properties are assumed to be size-dependent. The governing equation is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of lipid tubules. In contrast, it increases the nonlinear to linear frequency ratios slightly for the lipid tubule with immovable end conditions.

  4. A novel method for sub-micrometer transverse electron beam size measurements using optical transition radiation

    Energy Technology Data Exchange (ETDEWEB)

    Aryshev, A; Boogert, S T; Karataev, P [John Adams Institute at Royal Holloway, Egham, Surrey, TW20 0EX (United Kingdom); Howell, D [John Adams Institute at Oxford University, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH (United Kingdom); Terunuma, N; Urakawa, J, E-mail: alar@post.kek.j [KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)

    2010-06-01

    Optical Transition Radiation (OTR) appearing when a charged particle crosses a boundary between two media with different dielectric properties has widely been used as a tool for transverse profile measurements of charged particle beams in various facilities worldwide. The resolution of the monitor is defined by so-called Point Spread Function (PSF), source distribution generated by a single electron and projected by an optical system onto a screen. In this paper we represent the development of a novel sub-micrometre electron beam profile monitor based on the measurements of the PSF structure. The first experimental results are presented and future plans on the optimization of the monitor are discussed

  5. Crack detection in a beam with an arbitrary number of transverse cracks using genetic algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Khaji, N. [Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Mehrjoo, M. [Islamic Azad University, Tehran (Iran, Islamic Republic of)

    2014-03-15

    In this paper, a crack detection approach is presented for detecting depth and location of cracks in beam-like structures. For this purpose, a new beam element with an arbitrary number of embedded transverse edge cracks, in arbitrary positions of beam element with any depth, is derived. The components of the stiffness matrix for the cracked element are computed using the conjugate beam concept and Betti's theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain precise natural frequencies and mode shapes of the beam knowing the cracks' characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results and available experimental measurements. Moreover, by knowing the natural frequencies and mode shapes, an inverse problem is established in which the location and depth of cracks are determined. In the inverse approach, an optimization problem based on the new finite element and genetic algorithms (GAs) is solved to search the solution. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam. The proposed approach is verified through a cracked beam containing various cracks with different depths.

  6. Direction-sensitive transverse velocity measurement by phase-modulated structured light beams

    CERN Document Server

    Rosales-Guzmán, Carmelo; Belmonte, Aniceto; Torres, Juan P

    2014-01-01

    The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge since detection is usually done by means of an interferometric setup which only provides an absolute value of the frequency shift. Here, we put forward a novel method that addresses this issue. It uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced. This is done by noting the change in the magnitude of the frequency shift as the transverse phase of the structured light is moved appropriately. We demonstrate our method with rotating micro-particles that are illuminated by a Laguerre-Gaussian beam with a rotating phase about its propagation axis. Our method, which only requires a dynamically configurable optical beam generator, can easily be used with other types of motion b...

  7. Precision measurement of transverse velocity distribution of a strontium atomic beam

    OpenAIRE

    Gao, F.; H. Liu; Xu, P.; X. Tian; Y. Wang; Ren, J; Haibin Wu; Hong Chang

    2014-01-01

    We measure the transverse velocity distribution in a thermal Sr atomic beam precisely by velocity-selective saturated fluorescence spectroscopy. The use of an ultrastable laser system and the narrow intercombination transition line of Sr atoms mean that the resolution of the measured velocity can reach 0.13 m/s, corresponding to 90$\\mu K$ in energy units. The experimental results are in very good agreement with the results of theoretical calculations. Based on the spectroscopic techniques use...

  8. Electron beam based transversal profile measurements of intense ion beams; Elektronenstrahl-Diagnostik zur Bestimmung vom transversalen Profil intensiver Ionenstrahlen

    Energy Technology Data Exchange (ETDEWEB)

    El Moussati, Said

    2014-11-03

    A non-invasive diagnostic method for the experimental determination of the transverse profile of an intense ion beam has been developed and investigated theoretically as well as experimentally within the framework of the present work. The method is based on the deflection of electrons when passing the electromagnetic field of an ion beam. To achieve this an electron beam is employed with a specifically prepared transversal profile. This distinguish this method from similar ones which use thin electron beams for scanning the electromagnetic field [Roy et al. 2005; Blockland10]. The diagnostic method presented in this work will be subsequently called ''Electron-Beam-Imaging'' (EBI). First of all the influence of the electromagnetic field of the ion beam on the electrons has been theoretically analyzed. It was found that the magnetic field causes only a shift of the electrons along the ion beam axis, while the electric field only causes a shift in a plane transverse to the ion beam. Moreover, in the non-relativistic case the magnetic force is significantly smaller than the Coulomb one and the electrons suffer due to the magnetic field just a shift and continue to move parallel to their initial trajectory. Under the influence of the electric field, the electrons move away from the ion beam axis, their resulting trajectory shows a specific angle compared to the original direction. This deflection angle practically depends just on the electric field of the ion beam. Thus the magnetic field has been neglected when analysing the experimental data. The theoretical model provides a relationship between the deflection angle of the electrons and the charge distribution in the cross section of the ion beam. The model however only can be applied for small deflection angles. This implies a relationship between the line-charge density of the ion beam and the initial kinetic energy of the electrons. Numerical investigations have been carried out to clarify the

  9. Turn-by-Turn Imaging of the Transverse Beam Profile in PEP-II

    Energy Technology Data Exchange (ETDEWEB)

    Fisher, Alan A.; Petree, Mark; /SLAC

    2006-12-18

    During injection or instability, the transverse profile of an individual bunch in a storage ring can change significantly in a few turns. However, most synchrotron-light imaging techniques are not designed for this time scale. We have developed a novel diagnostic that enhances the utility of a fast gated camera by adding, inexpensively, some features of a dual-axis streak camera, in order to watch the turn-by-turn evolution of the transverse profile, in both x and y. The beam's elliptical profile is reshaped using cylindrical lenses to form a tall and narrow ellipse--essentially the projection of the full ellipse onto one transverse axis. We do this projection twice, by splitting the beam into two paths at different heights, and rotating the ellipse by 90{sup o} on one path. A rapidly rotating mirror scans these vertical ''pencils'' of light horizontally across the photocathode of the camera, which is gated for 3 ns on every Nth ring turn. A single readout of the camera captures 100 images, looking like a stroboscopic photograph of a moving object. We have observed the capture of injected charge into a bunch and the rapid change of beam size at the onset of a fast instability.

  10. Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass

    Science.gov (United States)

    Malaeke, Hasan; Moeenfard, Hamid

    2016-03-01

    The objective of this paper is to study large amplitude flexural-extensional free vibration of non-uniform cantilever beams carrying a both transversely and axially eccentric tip mass. The effects of variable axial force is also taken into account. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. A numerical finite difference scheme is proposed to find the natural frequencies and mode shapes of the system which is validated specifically for a beam with linearly varying cross section. Using a single mode approximation in conjunction with the Lagrange method, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. These temporal coupled equations are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The qualitative and quantitative knowledge resulting from this research is expected to enable the study of the effects of eccentric tip mass and non-uniformity on the large amplitude flexural-extensional vibration of beams for improved dynamic performance.

  11. Laser beam propagation in non-linearly absorbing media

    CSIR Research Space (South Africa)

    Forbes, A

    2006-08-01

    Full Text Available Many analytical techniques exist to explore the propagation of certain laser beams in free space, or in a linearly absorbing medium. When the medium is nonlinearly absorbing the propagation must be described by an iterative process using the well...

  12. Non-Linear Vibration of Euler-Bernoulli Beams

    DEFF Research Database (Denmark)

    Barari, Amin; Kaliji, H. D.; Domairry, G.

    2011-01-01

    In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...

  13. Bending of a nonlinear beam reposing on an unilateral foundation

    Directory of Open Access Journals (Sweden)

    Machalová J.

    2011-06-01

    Full Text Available This article is going to deal with bending of a nonlinear beam whose mathematical model was proposed by D. Y. Gao in (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches,Mech. Research Communication, 23 (1 1996. The model is based on the Euler-Bernoulli hypothesis and under assumption of nonzero lateral stress component enables moderately large deflections but with small strains. This is here extended by the unilateralWinkler foundation. The attribution unilateral means that the foundation is not connected with the beam. For this problem we demonstrate a mathematical formulation resulting from its natural decomposition which leads to a saddle-point problem with a proper Lagrangian. Next we are concerned with methods of solution for our problem by means of the finite element method as the paper (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech. Research Communication, 23 (1 1996 has no mention of it. The main alternatives are here the solution of a system of nonlinear nondifferentiable equations or finding of a saddle point through the use of the augmented Lagrangian method. This is illustrated by an example in the final part of the article.

  14. Effect of Physical Nonlinearity on Local Buckling in Sandwich Beams

    NARCIS (Netherlands)

    Koissin, Vitaly; Shipsha, Andrey; Skvortsov, Vitaly

    2010-01-01

    This article deals with experimental, theoretical, and FE characterization of the local buckling in foam-core sandwich beams. In the theoretical approach, this phenomena is considered in a periodic formulation (unbounded wrinkle wave); a nonlinear stress—strain response of the face material is accou

  15. Nonlinear Evolution of the Ion-Ion Beam Instability

    DEFF Research Database (Denmark)

    Pécseli, Hans; Trulsen, J.

    1982-01-01

    The criterion for the existence of vortexlike ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates...

  16. Effect of Physical Nonlinearity on Local Buckling in Sandwich Beams

    NARCIS (Netherlands)

    Koysin, V.; Shipsha, Andrey; Skvortsov, Vitaly

    2010-01-01

    This article deals with experimental, theoretical, and FE characterization of the local buckling in foam-core sandwich beams. In the theoretical approach, this phenomena is considered in a periodic formulation (unbounded wrinkle wave); a nonlinear stress—strain response of the face material is accou

  17. Measurement of the transverse four-dimensional beam rms-emittance of an intense uranium beam at 11.4 MeV/u

    Science.gov (United States)

    Xiao, C.; Groening, L.; Gerhard, P.; Maier, M.; Mickat, S.; Vormann, H.

    2016-06-01

    Knowledge of the transverse four-dimensional beam rms-parameters is essential for applications that involve lattice elements that couple the two transverse degrees of freedom (planes). Usually pepper-pots are used for measuring these beam parameters. However, for ions their application is limited to energies below 150 keV/u. This contribution is on measurements of the full transverse four-dimensional second-moments beam matrix of high intensity uranium ions at an energy of 11.4 MeV/u. The combination of skew quadrupoles with a slit/grid emittance measurement device has been successfully applied.

  18. The X-Ray Beam Imager for Transversal Profiling of Low-Emittance Electron Beam at the SPring-8

    CERN Document Server

    Takano, S; Ohkuma, H

    2005-01-01

    We have developed the X-ray beam imager (XBI) at the accelerator diagnostics beamline I of the SPring-8 to observe transverse profiles of small electron beam of a low-emittance synchrotron light source. The XBI is based on a single Fresnel zone plate (FZP) and an X-ray zooming tube (XZT). The electron beam moving in a bending magnet is imaged by the FZP. Monochromatic X-ray is selected by a double crystal monochromator to avoid the effect of chromatic aberration of the FZP. The X-ray images of the electron beam obtained are converted by the XZT to enlarged images in visible light. The XBI has achieved a superior 1 σ spatial resolution in the micron range, and a fast time resolution of 1 ms. It has also realized a vignetting-free field of view larger than 1.5 mm in diameter on the coordinates of the electron beam, which is not easily obtained by imaging optics using two FZPs. With the XBI, we have successfully measured the profiles of the small electron beam having low vertical emittance in the pm ra...

  19. Nonlinear analysis of concrete beams strengthened by date palm fibers

    Science.gov (United States)

    Bouzouaid, Samia; Kriker, Abdelouahed

    2017-02-01

    The behaviour of concrete beams strengthened with date palm fibers was studied by Nonlinear Finite Element Analysis using ANSYS software. Five beams that were experimentally tested in a previous research were considered. The results obtained from the ANSYS finite element analysis are compared with the experimental data for the five beams with different amounts of fibres, ranging from 0.2% to 0.5% by a step equal to 0.1% and with a fibre length of 0.04 m. The results obtained by FEA showed good agreement with those obtained by the experimental program. This research demonstrates the ability of FEA in predicting the behaviour of beams strengthened with Date Palm fibers. It will help researchers in studying beams with different configurations without the need to go through the lengthy experimental testing programs.

  20. Transverse superresolution technique involving rectified Laguerre-Gaussian LG(p)⁰ beams.

    Science.gov (United States)

    Cagniot, Emmanuel; Fromager, Michael; Godin, Thomas; Passilly, Nicolas; Aït-Ameur, Kamel

    2011-08-01

    A promising technique has been proposed recently [Opt. Commun. 284, 1331 (2011), Opt. Commun. 284, 4107 (2011)] for breaking the diffraction limit of light. This technique consists of transforming a symmetrical Laguerre-Gaussian LG(p)⁰ beam into a near-Gaussian beam at the focal plane of a thin converging lens thanks to a binary diffractive optical element (DOE) having a transmittance alternatively equal to -1 or +1, transversely. The effect of the DOE is to convert the alternately out-of-phase rings of the LG(p)⁰ beam into a unified phase front. The benefits of the rectified beam at the lens focal plane are a short Rayleigh range, which is very useful for many laser applications, and a focal volume much smaller than that obtained with a Gaussian beam. In this paper, we demonstrate numerically that the central lobe's radius of the rectified beam at the lens focal plane depends exclusively on the dimensionless radial intensity vanishing factor of the incident beam. Consequently, this value can be easily predicted.

  1. Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads

    Directory of Open Access Journals (Sweden)

    A. Bellino

    2012-01-01

    Full Text Available It is well known that nonlinear systems, as well as linear time-varying systems, are characterized by non-stationary response signals. In this sense, they both show natural frequencies that are not constant over time; this variation has however different origins: for a time-varying system the mass, and possibly the stiffness distributions, are changing over time, while for a nonlinear system the natural frequencies are amplitude-dependent. An interesting case of time-varying system occurs when analyzing the transit of a train over a railway bridge, easily simulated by the crossing of a moving load over a beam. In this case, the presence of a nonlinearity in the beam behaviour can cause a significant alteration of the modal parameters extracted from the linearized model, such that the contributions of the two effects are no more distinguishable.

  2. A Simple Model for Nonlinear Confocal Ultrasonic Beams

    Institute of Scientific and Technical Information of China (English)

    ZHANG Dong; ZHOU Lin; SI Li-Sheng; GONG Xiu-Fen

    2007-01-01

    @@ A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented.Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

  3. Stability of an ion beam in synchrotrons with digital filters in the feedback loop of a transverse damper

    Science.gov (United States)

    Zhabitsky, V. M.

    2010-12-01

    The stability of an ion beam in synchrotrons with digital filters in the feedback loop of a transverse damper is treated. A transverse feedback system (TFS) is required in synchrotrons to stabilize the high intensity ion beams against transverse instabilities and to damp the beam injection errors. The TFS damper kicker (DK) corrects the transverse momentum of a bunch in proportion to its displacement from the closed orbit at the location of the beam position monitor (BPM). The digital signal processing unit in the feedback loop between BPM and DK ensures a condition to achieve optimal damping. Damping rates of the feedback systems with digital filters are analysed in comparison with those in an ideal feedback system.

  4. Applications of electron lenses: scraping of high-power beams, beam-beam compensation, and nonlinear optics

    Energy Technology Data Exchange (ETDEWEB)

    Stancari, Giulio

    2014-09-11

    Electron lenses are pulsed, magnetically confined electron beams whose current-density profile is shaped to obtain the desired effect on the circulating beam. Electron lenses were used in the Fermilab Tevatron collider for bunch-by-bunch compensation of long-range beam-beam tune shifts, for removal of uncaptured particles in the abort gap, for preliminary experiments on head-on beam-beam compensation, and for the demonstration of halo scraping with hollow electron beams. Electron lenses for beam-beam compensation are being commissioned in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Hollow electron beam collimation and halo control were studied as an option to complement the collimation system for the upgrades of the Large Hadron Collider (LHC) at CERN; a conceptual design was recently completed. Because of their electric charge and the absence of materials close to the proton beam, electron lenses may also provide an alternative to wires for long-range beam-beam compensation in LHC luminosity upgrade scenarios with small crossing angles. At Fermilab, we are planning to install an electron lens in the Integrable Optics Test Accelerator (IOTA, a 40-m ring for 150-MeV electrons) as one of the proof-of-principle implementations of nonlinear integrable optics to achieve large tune spreads and more stable beams without loss of dynamic aperture.

  5. Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances

    Directory of Open Access Journals (Sweden)

    Ali H. Nayfeh

    1998-01-01

    Full Text Available The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.

  6. Electron beam based transversal profile measurements of intense ion beams; Elektronenstrahl-Diagnostik zur Bestimmung vom transversalen Profil intensiver Ionenstrahlen

    Energy Technology Data Exchange (ETDEWEB)

    El Moussati, Said

    2014-11-03

    A non-invasive diagnostic method for the experimental determination of the transverse profile of an intense ion beam has been developed and investigated theoretically as well as experimentally within the framework of the present work. The method is based on the deflection of electrons when passing the electromagnetic field of an ion beam. To achieve this an electron beam is employed with a specifically prepared transversal profile. This distinguish this method from similar ones which use thin electron beams for scanning the electromagnetic field [Roy et al. 2005; Blockland10]. The diagnostic method presented in this work will be subsequently called ''Electron-Beam-Imaging'' (EBI). First of all the influence of the electromagnetic field of the ion beam on the electrons has been theoretically analyzed. It was found that the magnetic field causes only a shift of the electrons along the ion beam axis, while the electric field only causes a shift in a plane transverse to the ion beam. Moreover, in the non-relativistic case the magnetic force is significantly smaller than the Coulomb one and the electrons suffer due to the magnetic field just a shift and continue to move parallel to their initial trajectory. Under the influence of the electric field, the electrons move away from the ion beam axis, their resulting trajectory shows a specific angle compared to the original direction. This deflection angle practically depends just on the electric field of the ion beam. Thus the magnetic field has been neglected when analysing the experimental data. The theoretical model provides a relationship between the deflection angle of the electrons and the charge distribution in the cross section of the ion beam. The model however only can be applied for small deflection angles. This implies a relationship between the line-charge density of the ion beam and the initial kinetic energy of the electrons. Numerical investigations have been carried out to clarify the

  7. Accurate investigation of lateral vibrations of a quintic nonlinear beam on an elastic foundation: Using an exact formulation of the beam curvature

    Science.gov (United States)

    Sedighi, H. M.; Shirazi, K. H.

    2014-11-01

    This article attains a new formulation of beam vibrations on an elastic foundation with quintic nonlinearity, including exact expressions for the beam curvature. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode, which, in turn, yields the natural frequency of the system. In this direction, a powerful analytical method called the parameter expansion method is employed to obtain the exact solution of the frequency-amplitude relationship. It is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of the above-mentioned system. Finally, the accuracy of the present analytic procedure is evaluated through comparisons with numerical calculations.

  8. Reversible beam heater for suppression of microbunching instability by transverse gradient undulators

    Directory of Open Access Journals (Sweden)

    Tao Liu

    2017-08-01

    Full Text Available The microbunching instability driven by beam collective effects in a linear accelerator of a free-electron laser (FEL facility significantly degrades the electron beam quality and FEL performance. A conventional method to suppress this instability is to introduce an additional uncorrelated energy spread by laser-electron interaction, which has been successfully operated in the Linac Coherent Light Source and Fermi@Elettra, etc. Some other ideas are recently proposed to suppress the instability without increasing energy spread, which could benefit the seeded FEL schemes. In this paper, we propose a reversible electron beam heater using two transverse gradient undulators to suppress the microbunching instability. This scheme introduces both an energy spread increase and a transverse-to-longitudinal phase space coupling, which suppress the microbunching instabilities driven by both longitudinal space charge and coherent synchrotron radiation before and within the system. Finally the induced energy spread increase and emittance growth are reversed. Theoretical analysis and numerical simulations are presented to verify the feasibility of the scheme and indicate the capability to improve the seeded FEL radiation performance.

  9. Reversible beam heater for suppression of microbunching instability by transverse gradient undulators

    Science.gov (United States)

    Liu, Tao; Qin, Weilun; Wang, Dong; Huang, Zhirong

    2017-08-01

    The microbunching instability driven by beam collective effects in a linear accelerator of a free-electron laser (FEL) facility significantly degrades the electron beam quality and FEL performance. A conventional method to suppress this instability is to introduce an additional uncorrelated energy spread by laser-electron interaction, which has been successfully operated in the Linac Coherent Light Source and Fermi@Elettra, etc. Some other ideas are recently proposed to suppress the instability without increasing energy spread, which could benefit the seeded FEL schemes. In this paper, we propose a reversible electron beam heater using two transverse gradient undulators to suppress the microbunching instability. This scheme introduces both an energy spread increase and a transverse-to-longitudinal phase space coupling, which suppress the microbunching instabilities driven by both longitudinal space charge and coherent synchrotron radiation before and within the system. Finally the induced energy spread increase and emittance growth are reversed. Theoretical analysis and numerical simulations are presented to verify the feasibility of the scheme and indicate the capability to improve the seeded FEL radiation performance.

  10. Nonlinear perturbative particle simulation studies of the electron-proton two-stream instability in high intensity proton beams

    Directory of Open Access Journals (Sweden)

    Hong Qin

    2003-01-01

    Full Text Available Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.

  11. Nonlinear flexural waves and chaos behavior in finite-deflection Timoshenko beam

    Institute of Scientific and Technical Information of China (English)

    Shan-yuan ZHANG; Zhi-fang LIU

    2010-01-01

    Based on the Timoshenko beam theory,the finite-deflection and the axial inertia are taken into account,and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills,the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case,a shock wave solution is given. The small perturbations are further introduced,arising from the damping and the external load to an original Hamilton system,and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov's method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform.

  12. Errors in Measuring Transverse and Energy Jitter by Beam Position Monitors

    CERN Document Server

    Balandin, V; Golubeva, N

    2010-01-01

    The problem of errors, arising due to finite BPM resolution, in the difference orbit parameters, which are found as a least squares fit to the BPM data, is one of the standard and important problems of accelerator physics. Even so for the case of transversely uncoupled motion the covariance matrix of reconstruction errors can be calculated "by hand", the direct usage of obtained solution, as a tool for designing of a "good measurement system", does not look to be fairly straightforward. It seems that a better understanding of the nature of the problem is still desirable. We make a step in this direction introducing dynamic into this problem, which at the first glance seems to be static. We consider a virtual beam consisting of virtual particles obtained as a result of application of reconstruction procedure to "all possible values" of BPM reading errors. This beam propagates along the beam line according to the same rules as any real beam and has all beam dynamical characteristics, such as emittances, energy ...

  13. Understanding transverse tune spectrum for high intensity ions beams at GSI SIS-18

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Rahul; Boine-Frankenheim, Oliver [GSI, Darmstadt (Germany); TEMF, TU Darmstadt (Germany); Forck, Peter; Kowina, Piotr; Kaufmann, Wolfgang; Lang, Kevin; Haseitl, Rainer [GSI, Darmstadt (Germany); Weiland, Thomas [TEMF, TU Darmstadt (Germany)

    2013-07-01

    Several experiments involving transverse tune spectra measurements were performed at GSI SIS-18 with various beam intensities to understand the effect of intensity on tune spectra. Besides the machine tune, the spectra provides information about the intensity dependent coherent and the incoherent space charge tune shift. The space charge tune shift is measured from a fit of the observed shifted positions of the measured head tail modes to the predictions of an analytic model. Additionally, each mode is temporally identified by using a novel excitation mechanism and fast sampling ADCs. The longitudinal structure of each head tail mode gives a direct measurement of chromaticity.

  14. Precision measurement of transverse velocity distribution of a Strontium atomic beam

    CERN Document Server

    Gao, F; Xu, P; Tian, X; Wang, Y; Ren, J; Wu, Haibin; Chang, Hong

    2013-01-01

    We measure precisely the transverse velocity distribution in a thermal Sr atomic beam with a velocity selective saturated fluorescence spectroscopy. By using the ultrastable laser system and narrow intercombination transition line of Sr atoms, the resolution of the velocity measured can be reached 0.13m/s, corresponding to 90$\\mu K$ in energy unit. The experimental results are agreement very well with a theoretical calculation. With the spectroscopic techniques, the absolute frequency of the intercombination transition of $^{88}$Sr is measured by an optical-frequency comb generator referenced to the SI second through an H maser, which is given by 434 829 121 318(10)kHz.

  15. Probing the transverse coherence of an undulator x-ray beam using brownian particles.

    Science.gov (United States)

    Alaimo, M D; Potenza, M A C; Manfredda, M; Geloni, G; Sztucki, M; Narayanan, T; Giglio, M

    2009-11-06

    We present a novel method to map the two-dimensional transverse coherence of an x-ray beam using the dynamical near-field speckles formed by scattering from colloidal particles. Owing to the statistical nature of the method, the coherence properties of synchrotron radiation from an undulator source is obtained with high accuracy. The two-dimensional complex coherence function is determined at the sample position and the imaging optical scheme further allowed us to evaluate the coherence factor at the undulator output despite the aberrations introduced by the focusing optics.

  16. Measurement of the transverse target and beam-target asymmetries in $\\eta$ meson photoproduction at MAMI

    CERN Document Server

    Akondi, C S; Arends, H J; Beck, R; Bernstein, A; Borisov, N; Braghieri, A; Briscoe, W J; Cherepnya, S; Collicott, C; Costanza, S; Downie, E J; Dieterle, M; Fix, A; Fil'kov, L V; Garni, S; Glazier, D I; Gradl, W; Gurevich, G; Barrientos, P Hall; Hamilton, D; Hornidge, D; Howdle, D; Huber, G M; Kashevarov, V L; Keshelashvili, I; Kondratiev, R; Korolija, M; Krusche, B; Lazarev, A; Lisin, V; Livingston, K; MacGregor, I J D; Mancel, J; Manley, D M; Martel, P; McNicoll, E F; Meyer, W; Middleton, D; Miskimen, R; Mushkarenkov, A; Nefkens, B M K; Neganov, A; Nikolaev, A; Oberle, M; Ostrick, M; Ortega, H; Ott, P; Otte, P B; Oussena, B; Pedroni, P; Polonski, A; Polyanski, V V; Prakhov, S; Reicherz, G; Rostomyan, T; Sarty, A; Schumann, S; Steffen, O; Strakovsky, I I; Strub, Th; Supek, I; Tiator, L; Thomas, A; Unverzagt, M; Usov, Yu A; Watts, D P; Werthmüller, D; Witthauer, L; Wolfes, M

    2014-01-01

    We present new data for the transverse target asymmetry T and the very first data for the beam-target asymmetry F in the $\\vec \\gamma \\vec p\\to\\eta p$ reaction up to a center-of-mass energy of W=1.9 GeV. The data were obtained with the Crystal-Ball/TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. All existing model predictions fail to reproduce the new data indicating a significant impact on our understanding of the underlying dynamics of $\\eta$ meson photoproduction. The peculiar nodal structure observed in existing T data close to threshold is not confirmed.

  17. Beam position monitor and kicker for the SPring-8 transverse bunch-by-bunch feedback

    Energy Technology Data Exchange (ETDEWEB)

    Nakamura, T. [JASRI/SPrig-8, Mikazuki-cho, Hyogo (Japan)

    2005-07-01

    A high-resolution beam position monitor and a wideband kicker for the SPring-8 transverse bunch-by-bunch feedback system are developed. To avoid the increase of effective emittance by unwanted kicks by a feedback driven by noise, the monitor is designed to have high position resolution of the order of micro meters for single pass of 0.25 nC bunch by adopting shorted stripline structure. Also a kicker for the feedback and the experience of those are described. (author)

  18. Nonlinear longitudinal current in degenerate plasma, arising under the influence of the transversal electromagnetic field

    CERN Document Server

    Latyshev, A V

    2015-01-01

    Kinetic Vlasov-Boltzmann equation for degenerate collisional plasmas with integral of collisions of relaxation type BGK (Bhatnagar, Gross and Krook) is used. Square-law expansion on size of intensity of electric field for kinetic equation, Lorentz's force and integral of collisions is considered. It is shown, that nonlinearity leads to generation of the longitudinal electric current directed along a wave vector. Longitudinal current is perpendicular to the known transversal classical current received at the linear analysis. The case of small values of wave number is considered. When frequency of collisions tends to the zero, all received results for collisional pass plasmas in corresponding results for collisionless plasmas. Graphic research of the real and imaginary part current density is carried out.

  19. Non-Linear Piezoelectric Actuator with a Preloaded Cantilever Beam

    OpenAIRE

    Yue Wu; Jingshi Dong; Xinbo Li; Zhigang Yang; Qingping Liu

    2015-01-01

    Piezoelectric actuation is widely used for the active vibration control of smart structural systems, and corresponding research has largely focused on linear electromechanical devices. This paper investigates the design and analysis of a novel piezoelectric actuator that uses a piezoelectric cantilever beam with a loading spring to produce displacement outputs. This device has a special nonlinear property relating to converting between kinetic energy and potential energy, and it can be used t...

  20. Tracking control of a flexible beam by nonlinear boundary feedback

    Directory of Open Access Journals (Sweden)

    Bao-Zhu Guo

    1995-01-01

    Full Text Available This paper is concerned with tracking control of a dynamic model consisting of a flexible beam rotated by a motor in a horizontal plane at the one end and a tip body rigidly attached at the free end. The well-posedness of the closed loop systems considering the dissipative nonlinear boundary feedback is discussed and the asymptotic stability about difference energy of the hybrid system is also investigated.

  1. Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities

    Science.gov (United States)

    Tokluoglu, Erinc K.

    fields generated by beam-plasma instabilities can be responsible for defocusing and distorting beams propagating in background plasma. This can be problematic in inertial fusion applications where the beam is intended to propagate ballistically as the background plasma neutralizes the beam space charge and current. We used particle-in-cell (PIC) code LSP to numerically investigate the defocusing effects in an ion beam propagating in background plasma experiences as it is exposed to the non-linear fields generated by Two-Stream instability between beam ions and plasma electrons. Supported by theory and benchmarked by the numerical solutions of governing E&M equations, the simulations were used to find and check scaling laws for the defocusing forces in the parameter space of beam and plasma density as well as the beam ion mass. A transition region where the defocusing fields peak has been identified, which should be avoided in the design of experimental devices. We further proposed a diagnostic tool to identify the presence of the two-stream instability in a system with parameters similar to the National Drift Compression Experiment II (NDCX-II) and conducted proof-of concept simulations. In the case of electron beam propagating in background plasma instability driven collisionless scattering and plasma heating is observed. 1-D simulations conducted in EDIPIC were benchmarked in LSP to study the excitation and time-evolution of electron-electron Two-Stream instability. Coupling of electron dynamics via non-linear ponderomotive force created by instability generated fields with ion cavities and Ion-Acoustic mode excitation was observed. Furthermore 2-D simulations of an electron-beam in a background plasma was performed. Many of the effects in observed in 1-D simulations were replicated. Morever generation of oblique modes with transverse wave numbers were observed in the simulations, which resulted in significant transverse scattering of beam electrons and the time

  2. Top-spin analysis of new scalar and tensor interactions in + - collisions with transverse beam polarization

    Indian Academy of Sciences (India)

    B Ananthanarayan; Monalisa Patra; Saurabh D Rindani

    2012-11-01

    The top polarization at the International Linear Collider (ILC) with transverse beam polarization is utilized in the + - → $t\\bar{t}$ process to probe interactions of the scalar and tensor type beyond the Standard Model and to disentangle their individual contributions. Confidence level limits of 90% are presented on the interactions with realistic integrated luminosity and are found to improve by an order of magnitude compared to the case when the spin of the top quark is not measured. Sensitivities of the order of a few times 10−3 TeV-2 for real and imaginary parts of both scalar and tensor couplings at $\\sqrt{s} = 500$ and 800 GeV with an integrated luminosity of 500 fb-1 and completely polarized beams are shown to be possible.

  3. Transverse circular-polarized Bessel beam generation by inward cylindrical aperture distribution.

    Science.gov (United States)

    Pavone, S C; Ettorre, M; Casaletti, M; Albani, M

    2016-05-16

    In this paper the focusing capability of a radiating aperture implementing an inward cylindrical traveling wave tangential electric field distribution directed along a fixed polarization unit vector is investigated. In particular, it is shown that such an aperture distribution generates a non-diffractive Bessel beam whose transverse component (with respect to the normal of the radiating aperture) of the electric field takes the form of a zero-th order Bessel function. As a practical implementation of the theoretical analysis, a circular-polarized Bessel beam launcher, made by a radial parallel plate waveguide loaded with several slot pairs, arranged on a spiral pattern, is designed and optimized. The proposed launcher performance agrees with the theoretical model and exhibits an excellent polarization purity.

  4. Transversal symmetry breaking and axial spreading modification for Gaussian optical beams

    CERN Document Server

    Araujo, Manoel; Lima, Marina

    2016-01-01

    For a long time it was believed there was no reason to include the geometrical phase in studying the propagation of gaussian optical beams through dielectric blocks. This can be justified by the fact that the first order term in the Taylor expansion of this phase is responsible for the lateral shift of the optical beam which is also predicted by ray optics. From this point of view, the geometrical phase can be seen as a purely auxiliary concept. In this paper, we show how the second order term in the Taylor expansion accounts for the symmetry breaking of the transversal spatial distribution and acts as an axial spreading modifier. These new effects clearly shows the importance of the geometrical phase in describing the correct behavior of light. To test our theoretical predictions, we briefly discuss a possible experimental implementation.

  5. Effect of a transverse magnetic field on the generation of electron beams in the gas-filled diode

    Science.gov (United States)

    Baksht, E. H.; Burachenko, A. G.; Erofeev, M. V.; Kostyrya, I. D.; Lomaev, M. I.; Rybka, D. V.; Tarasenko, V. F.

    2008-06-01

    The effect of a transverse magnetic field (0.080 and 0.016 T) on generation of an electron beam in the gas-filled diode is experimentally investigated. It is shown that, at voltage U = 25 kV across the diode and a low helium pressure (45 Torr), the transverse magnetic field influences the beam current amplitude behind a foil and its distribution over the foil cross section. At elevated pressures and under the conditions of ultrashort avalanche electron beam formation in helium, nitrogen, and air, the transverse magnetic field (0.080 and 0.016 T) has a minor effect on the amplitude and duration of the beam behind the foil. It is established that, when the voltage of the pulse generator reaches several hundreds of kilovolts, some runaway electrons (including the electrons from the discharge plasma near the cathode) are incident on the side walls of the diode.

  6. Nonlinear transverse cascade and two-dimensional magnetohydrodynamic subcritical turbulence in plane shear flows.

    Science.gov (United States)

    Mamatsashvili, G R; Gogichaishvili, D Z; Chagelishvili, G D; Horton, W

    2014-04-01

    We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity), and threaded by a parallel uniform background magnetic field. This flow is spectrally stable, so the turbulence is subcritical by nature and hence it can be energetically supported just by a transient growth mechanism due to shear flow non-normality. This mechanism appears to be essentially anisotropic in the spectral (wave-number) plane and operates mainly for spatial Fourier harmonics with streamwise wave numbers less than the ratio of flow shear to Alfvén speed, kymagnetohydrodynamic (MHD) turbulence research. We find similarity of the nonlinear dynamics to the related dynamics in hydrodynamic flows: to the bypass concept of subcritical turbulence. The essence of the analyzed nonlinear MHD processes appears to be a transverse redistribution of kinetic and magnetic spectral energies in the wave-number plane [as occurs in the related hydrodynamic flow; see Horton et al., Phys. Rev. E 81, 066304 (2010)] and differs fundamentally from the existing concepts of (anisotropic direct and inverse) cascade processes in MHD shear flows.

  7. Experimental observations of nonlinearly enhanced 2omega-UH electromagnetic radiation excited by steady-state colliding electron beams

    Science.gov (United States)

    Intrator, T.; Hershkowitz, N.; Chan, C.

    1984-01-01

    Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.

  8. Transverse Free Vibration of Axially Moving Stepped Beam with Different Length and Tip Mass

    Directory of Open Access Journals (Sweden)

    Guoliang Ma

    2015-01-01

    Full Text Available Axially moving stepped beam (AMSB with different length and tip mass is represented by adopting Euler-Bernoulli beam theory, and its characteristics and displacements of transverse free vibration are calculated by using semianalytical method. Firstly, the governing equation of the transverse free vibration is established based on Hamilton’s principle. The equation is cast into eigenvalue equation through the complex modal analysis. Then, a scheme is proposed to derive the continuous condition accordingly as the displacement, rotation, bending moment, and shear force are all equal at the connections of any two segments. Another scheme is to derive frequency equation from the given boundary conditions which contain a tip mass in the last segment. Finally, the natural frequency and modal function are calculated by using numerical method according to the eigenvalue equation and frequency equation. Due to the introduction of modal truncation, displacement and, the free vibration solution can be obtained by adopting modal superposition after Hilbert transform. The numerical examples illustrate that length, velocity, mass, and geometry affect characteristics and displacements significantly; the series of methods are effective and accurate to investigate the vibration of the AMSB with different length and tip mass after comparing several results.

  9. The transversal creeping vibrations of a fractional derivative order constitutive relation of nonhomogeneous beam

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available We considered the problem on transversal oscillations of two-layer straight bar, which is under the action of the lengthwise random forces. It is assumed that the layers of the bar were made of nonhomogenous continuously creeping material and the corresponding modulus of elasticity and creeping fractional order derivative of constitutive relation of each layer are continuous functions of the length coordinate and thickness coordinates. Partial fractional differential equation and particular solutions for the case of natural vibrations of the beam of creeping material of a fractional derivative order constitutive relation in the case of the influence of rotation inertia are derived. For the case of natural creeping vibrations, eigenfunction and time function, for different examples of boundary conditions, are determined. By using the derived partial fractional differential equation of the beam vibrations, the almost sure stochastic stability of the beam dynamic shapes, corresponding to the n th shape of the beam elastic form, forced by a bounded axially noise excitation, is investigated. By the use of S. T. Ariaratnam's idea, as well as of the averaging method, the top Lyapunov exponent is evaluated asymptotically when the intensity of excitation process is small.

  10. Fast Transverse Beam Instability Caused by Electron Cloud Trapped in Combined Function Magnets

    Energy Technology Data Exchange (ETDEWEB)

    Antipov, Sergey [Univ. of Chicago, IL (United States)

    2017-03-01

    Electron cloud instabilities affect the performance of many circular high-intensity particle accelerators. They usually have a fast growth rate and might lead to an increase of the transverse emittance and beam loss. A peculiar example of such an instability is observed in the Fermilab Recycler proton storage ring. Although this instability might pose a challenge for future intensity upgrades, its nature had not been completely understood. The phenomena has been studied experimentally by comparing the dynamics of stable and unstable beam, numerically by simulating the build-up of the electron cloud and its interaction with the beam, and analytically by constructing a model of an electron cloud driven instability with the electrons trapped in combined function dipoles. Stabilization of the beam by a clearing bunch reveals that the instability is caused by the electron cloud, trapped in beam optics magnets. Measurements of microwave propagation confirm the presence of the cloud in the combined function dipoles. Numerical simulations show that up to 10$^{-2}$ of the particles can be trapped by their magnetic field. Since the process of electron cloud build-up is exponential, once trapped this amount of electrons significantly increases the density of the cloud on the next revolution. In a combined function dipole this multi-turn accumulation allows the electron cloud reaching final intensities orders of magnitude greater than in a pure dipole. The estimated fast instability growth rate of about 30 revolutions and low mode frequency of 0.4 MHz are consistent with experimental observations and agree with the simulations. The created instability model allows investigating the beam stability for the future intensity upgrades.

  11. On the weakly nonlinear, transversal vibrations of a conveyor belt with a low and time-varying velocity

    NARCIS (Netherlands)

    Suweken, G.; van Horssen, W.T.

    2002-01-01

    In this paper the weakly nonlinear, transversal vibrations of a conveyor belt will be considered. The belt is assumed to move with a low and time-varying speed. Using Kirchhoff's approach a single equation of motion will be derived from a coupled system of partial differential equations describing

  12. Quasi-periodic solutions of nonlinear beam equations with quintic quasi-periodic nonlinearities

    Directory of Open Access Journals (Sweden)

    Qiuju Tuo

    2015-01-01

    Full Text Available In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities $$ u_{tt}+u_{xxxx}+(B+ \\varepsilon\\phi(tu^5=0 $$ under periodic boundary conditions, where B is a positive constant, $\\varepsilon$ is a small positive parameter, $\\phi(t$ is a real analytic quasi-periodic function in t with frequency vector $\\omega=(\\omega_1,\\omega_2,\\dots,\\omega_m$. It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form.

  13. The effect of transverse shear on the face sheets failure modes of sandwich beams loaded in three points bending

    Directory of Open Access Journals (Sweden)

    BOUROUIS FAIROUZ

    2012-04-01

    Full Text Available Sandwich beams loaded in three points bending may fail in several ways including tension or compression failure of facings. In this paper , The effect of the transverse shear on the face yielding and face wrinkling failure modes of sandwich beams loaded in three points bending have been studied, the beams were made of various composites materials carbon/epoxy, kevlar/epoxy, glass/epoxy at sequence [+θ/-θ]3s, [0°/90°]3s. . The stresses in the face were calculated using maximum stress criterion and the simple beam theory. The obtained different results show that the sandwich beams with carbon/epoxy, and glass/epoxy face sheets are the best materials, inreturn the kevlar /epoxy facing characterised by low resistance of transverse shear in compression and tensile.

  14. Non-Linear Piezoelectric Actuator with a Preloaded Cantilever Beam

    Directory of Open Access Journals (Sweden)

    Yue Wu

    2015-08-01

    Full Text Available Piezoelectric actuation is widely used for the active vibration control of smart structural systems, and corresponding research has largely focused on linear electromechanical devices. This paper investigates the design and analysis of a novel piezoelectric actuator that uses a piezoelectric cantilever beam with a loading spring to produce displacement outputs. This device has a special nonlinear property relating to converting between kinetic energy and potential energy, and it can be used to increase the output displacement at a lower voltage. The system is analytically modeled with Lagrangian functional and Euler–Lagrange equations, numerically simulated with MATLAB, and experimentally realized to demonstrate its enhanced capabilities. The model is validated using an experimental device with several pretensions of the loading spring, therein representing three interesting cases: a linear system, a low natural frequency system with a pre-buckled beam, and a system with a buckled beam. The motivating hypothesis for the current work is that nonlinear phenomena could be exploited to improve the effectiveness of the piezoelectric actuator’s displacement output. The most practical configuration seems to be the pre-buckled case, in which the proposed system has a low natural frequency, a high tip displacement, and a stable balanced position.

  15. Single-particle And Collective Effects Of Cubic Nonlinearity In The Beam Dynamics Of Proton Synchrotrons

    CERN Document Server

    Tran Hy, J

    1998-01-01

    This thesis describes some new studies of the effects of cubic nonlinearities arising from image-charge forces and octupole magnets on the transverse beam dynamics of proton synchrotrons and storage rings, and also a study of the damping of coherent oscillations using a feed-back damper. In the latter case, various corrective algorithms were modeled using linear one-turn maps. Kicks of fixed amplitude but appropriate sign were shown to provide linear damping and no coherent tune shift, though the rate predicted analytically was somewhat higher than that observed in simulations. This algorithm gave much faster damping (for equal power) than conventional proportional kicks, which damp exponentially. Two single-particle effects of the image-change force were investigated: distortion of the momentum dispersion function and amplitude dependence of the betatron tunes (resulting in tune spread). The former is calculated using transfer maps and the method of undetermined coefficients, the latter by solving the cubic ...

  16. Generation of non-classical optical fields by a beam splitter with second-order nonlinearity

    CERN Document Server

    Prakash, Hari

    2016-01-01

    We propose quantum-mechanical model of a beam splitter with second-order nonlinearity and show that non-classical features such as squeezing and sub-Poissonian photon statistics of optical fields can be generated in output fundamental and second harmonic modes when we mix coherent light beams via such a nonlinear beam splitter.

  17. Localization of Transversal Cracks in Sandwich Beams and Evaluation of Their Severity

    Directory of Open Access Journals (Sweden)

    G. R. Gillich

    2014-01-01

    Full Text Available An algorithm to assess transversal cracks in composite structures based on natural frequency changes due to damage is proposed. The damage assessment is performed in two steps; first the crack location is found, and afterwards an evaluation of its severity is performed. The technique is based on a mathematical relation that provides the exact solution for the frequency changes of bending vibration modes, considering two terms. The first term is related to the strain energy stored in the beam, while the second term considers the increase of flexibility due to damage. Thus, it is possible to separate the problems of localization and severity assessment, which makes the localization process independent of the beams cross-section shape and boundary conditions. In fact, the process consists of comparing vectors representing the measured frequency shifts with patterns constructed using the mode shape curvatures of the undamaged beam. Once the damage is localized, the evaluation of its severity is made taking into account the global rigidity reduction. The damage identification algorithm was validated by experiments performed on numerous sandwich panel specimens.

  18. Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.

    Science.gov (United States)

    Shemer, Keren; Voloch-Bloch, Noa; Shapira, Asia; Libster, Ana; Juwiler, Irit; Arie, Ady

    2013-12-15

    We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump's radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new "virtual beam" having multiple values of OAM that are determined by the nonlinear process.

  19. Quasi-periodic Solutions of the General Nonlinear Beam Equations

    Institute of Scientific and Technical Information of China (English)

    GAO YI-XIAN

    2012-01-01

    In this paper,one-dimensional (1D) nonlinear beam equations of the form utt - uxx + uxxxx + mu = f(u)with Dirichlet boundary conditions are considered,where the nonlinearity f is an analytic,odd function and f(u) = O(u3).It is proved that for all m ∈ (0,M*] (∈) R(M* is a fixed large number),but a set of small Lebesgue measure,the above equations admit small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system.The proof is based on an infinite dimensional KAM theory and a partial Birkhoff normal form technique.

  20. Transverse Beam Spin Asymmetries in Forward-Angle Elastic Electron-Proton Scattering

    CERN Document Server

    Armstrong, D S; Asaturyan, R; Averett, T; Bailey, S L; Batigne, G; Beck, D H; Beise, E J; Benesch, J; Bimbot, L; Birchall, J; Biselli, A; Bosted, P; Boukobza, E; Breuer, H; Carlini, R; Carr, R; Chant, N; Chao, Y C; Chattopadhyay, S; Clark, R; Covrig, S; Cowley, A; Dale, D; Davis, C; Falk, W; Finn, J M; Forest, T; Franklin, G; Furget, C; Gaskell, D; Grames, J; Griffioen, K A; Grimm, K; Guillon, B; Guler, H; Hannelius, L; Hasty, R; Hawthorne Allen, A; Horn, T; Johnston, K; Jones, M; Kammel, P; Kazimi, R; King, P M; Kolarkar, A; Korkmaz, E; Korsch, W; Kox, S; Kühn, J; Lachniet, J; Lee, L; Lenoble, J; Liatard, E; Liu, J; Loupias, B; Lung, A; Marchand, D; Martin, J W; McFarlane, K W; McKee, D W; McKeown, R D; Merchez, F; Mkrtchyan, H; Moffit, B; Morlet, M; Nakagawa, I; Nakahara, K; Neveling, R; Niccolai, S; Ong, S; Page, S; Papavassiliou, V; Pate, S F; Phillips, S K; Pitt, M L; Poelker, M; Porcelli, T A; Quéméner, G; Quinn, B; Ramsay, W D; Rauf, A W; Real, J S; Roche, J; Roos, P; Rutledge, G A; Secrest, J; Simicevic, N; Smith, G R; Spayde, D T; Stepanyan, S; Stutzman, M; Sulkosky, V; Tadevosyan, V; Tieulent, R; Van de Wiele, J; Van Oers, W T H; Voutier, E; Vulcan, W; Warren, G; Wells, S P; Williamson, S E; Wood, S A; Yan, C; Yun, J; Zeps, V

    2007-01-01

    We have measured the beam-normal single-spin asymmetry in elastic scattering of transversely-polarized 3 GeV electrons from unpolarized protons at Q^2 values of 0.15 and 0.25 (GeV/c)^2 with results of A_n = -4.06 +- 0.99 (stat) +- 0.63 (syst) and A_n = -4.82 +- 1.87 (stat) +- 0.98 (syst) ppm. These results are inconsistent with calculations solely using the elastic nucleon intermediate state, and generally agree with calculations with significant inelastic hadronic intermediate state contributions. A_n provides a direct probe of the imaginary component of the 2-gamma exchange amplitude, the complete description of which is important in the interpretation of data from precision electron-scattering experiments.

  1. New Measurements of the Transverse Beam Asymmetry for Elastic Electron Scattering from Selected Nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Abrahamyan, S; Afanasev, A; Ahmed, Z; Albataineh, H; Aniol, K; Armstrong, D S; Armstrong, W; Arrington, J; Averett, T; Babineau, B; Bailey, S L; Barber, J; Barbieri, A; Beck, A; Bellini, V; Beminiwattha, R; Benaoum, H; Benesch, J; Benmokhtar, F; Bertin, P; Bielarski, T; Boeglin, W; Bosted, P; Butaru, F; Burtin, E; Cahoon, J; Camsonne, A; Canan, M; Carter, P; Chang, C C; Cates, G D; Chao, Y -C; Chen, C; Chen, J -P; Choi, Seonho; Chudakov, E; Cisbani, E; Craver, B; Cusanno, F; Dalton, M M; De Leo, R; de Jager, K; Deconinck, W; Decowski, P; Deepa, D; Deng, X; Dutta, D; Etile, A; Ferdi, C; Feuerbach, J; Finn, J M; Flay, D; Franklin, G B; Friend, M; Frullani, S; Fuchey, E; Fuchs, S A; Fuoti, K; Garibaldi, F; Gasser, E; Gilman, R; Guisa, A; Glamazdin, A; Glesener, L E; Gomez, J; Gorchtein, M; Grames, J; Grimm, K; Gu, C; Hansen, O; Hansknecht, J; Hen, O; Higinbotham, D W; Holmes, R S; Holmstrom, T; Horowitz, C J; Hoskins, J; Huang, J; Humensky, T B; Hyde, C E; Ibrahim, H; Itard, F; Jen, C -M; Jensen, E; Jiang, X; Jin, G; Johnston, S; Katich, J; Kaufman, L J; Kelleher, A; Kliakhandler, K; King, P M; Kolarkar, A; Kowalski, S; Kuchina, E; Kumar, K S; Lagamba, L; Lambert, D; LaViolette, P; Leacock, J; Leckey IV, J; Lee, J H; LeRose, J J; Lhuillier, D; Lindgren, R; Liyanage, N; Lubinsky, N; Mammei, J; Mammoliti, F; Margaziotis, D J; Markowitz, P; Mazouz, M; McCormick, K; McCreary, A; McNulty, D; Meekins, D G; Mercado, L; Meziani, Z -E; Michaels, R W; Mihovilovic, M; Moffit, B; Monaghan, P; Muangma, N; Munoz-Camacho, C; Nanda, S; Nelyubin, V; Neyret, D; Nuruzzaman,; Oh, Y; Otis, K; Palmer, A; Parno, D; Paschke, K D; Phillips, S K; Poelker, M; Pomatsalyuk, R; Posik, M; Potokar, M; Prok, K; Puckett, A.J.R.; Qian, X; Qiang, Y; Quinn, B; Rakhman, A; Reimer, P E; Reitz, B; Riordan, S; Roche, J; Rogan, P; Ron, G; Russo, G; Saenboonruang, K; Saha, A; Sawatzky, B; Shahinyan, A; Silwal, R; Singh, J; Sirca, S; Slifer, K; Snyder, R; Solvignon, P; Souder, P A; Sperduto, M L; Subedi, R; Stutzman, M L; Suleiman, R; Sulkosky, V; Sutera, C M; Tobias, W A; Troth, W; Urciuoli, G M; Ulmer, P; Vacheret, A; Voutier, A; Waidyawansa, B; Wang, D; Wang, K; Wexler, J; Whitbeck, A; Wilson, R; Wojtsekhowski, B; Yan, X; Yao, H; Ye, Y; Ye, Z; Yim, V; Zana, L; Zhan, X; Zhang, J; Zhang, Y; Zheng, X; Ziskin, V; Zhu, P

    2012-11-05

    Here we have measured the beam-normal single-spin asymmetry A{sub n} in the elastic scattering of 1-3 GeV transversely polarized electrons from 1H and for the first time from 4He, 12C, and 208Pb. For 1H, 4He and 12C, the measurements are in agreement with calculations that relate An to the imaginary part of the two-photon exchange amplitude including inelastic intermediate states. Surprisingly, the 208Pb result is significantly smaller than the corresponding prediction using the same formalism. Our results suggest that a systematic set of new An measurements might emerge as a new and sensitive probe of the structure of heavy nuclei.

  2. Precision measurement of transverse velocity distribution of a strontium atomic beam

    Science.gov (United States)

    Gao, F.; Liu, H.; Xu, P.; Tian, X.; Wang, Y.; Ren, J.; Wu, Haibin; Chang, Hong

    2014-02-01

    We measure the transverse velocity distribution in a thermal Sr atomic beam precisely by velocity-selective saturated fluorescence spectroscopy. The use of an ultrastable laser system and the narrow intercombination transition line of Sr atoms mean that the resolution of the measured velocity can reach 0.13 m/s, corresponding to 90 μK in energy units. The experimental results are in very good agreement with the results of theoretical calculations. Based on the spectroscopic techniques used here, the absolute frequency of the intercombination transition of 88Sr is measured using an optical-frequency comb generator referenced to the SI second through an H maser, and is given as 434 829 121 318(10) kHz.

  3. Precision measurement of transverse velocity distribution of a strontium atomic beam

    Directory of Open Access Journals (Sweden)

    F. Gao

    2014-02-01

    Full Text Available We measure the transverse velocity distribution in a thermal Sr atomic beam precisely by velocity-selective saturated fluorescence spectroscopy. The use of an ultrastable laser system and the narrow intercombination transition line of Sr atoms mean that the resolution of the measured velocity can reach 0.13 m/s, corresponding to 90 μK in energy units. The experimental results are in very good agreement with the results of theoretical calculations. Based on the spectroscopic techniques used here, the absolute frequency of the intercombination transition of 88Sr is measured using an optical-frequency comb generator referenced to the SI second through an H maser, and is given as 434 829 121 318(10 kHz.

  4. Transverse Beam Spin Asymmetries in Forward-Angle Elastic Electron-Proton Scattering

    Energy Technology Data Exchange (ETDEWEB)

    David Armstrong; Francois Arvieux; Razmik Asaturyan; Todd Averett; Stephanie Bailey; Guillaume Batigne; Douglas Beck; Elizabeth Beise; Jay Benesch; Louis Bimbot; James Birchall; Angela Biselli; Peter Bosted; Elodie Boukobza; Herbert Breuer; Roger Carlini; Robert Carr; Nicholas Chant; Yu-Chiu Chao; Swapan Chattopadhyay; Russell Clark; Silviu Covrig; Anthony Cowley; Daniel Dale; Charles Davis; Willie Falk; John Finn; Tony Forest; Gregg Franklin; Christophe Furget; David Gaskell; Joseph Grames; Keith Griffioen; Klaus Grimm; Benoit Guillon; Hayko Guler; Lars Hannelius; Richard HASTY; Alice Hawthorne Allen; Tanja Horn; Kathleen Johnston; Mark Jones; Peter Kammel; Reza Kazimi; Paul King; Ameya Kolarkar; Elie Korkmaz; Wolfgang Korsch; Serge Kox; Joachim Kuhn; Jeff Lachniet; Lawrence Lee; Jason Lenoble; Eric Liatard; Jianglai Liu; Berenice Loupias; Allison Lung; Dominique Marchand; Jeffery Martin; Kenneth McFarlane; David McKee; Robert McKeown; Fernand Merchez; Hamlet Mkrtchyan; Bryan Moffit; M. Morlet; Itaru Nakagawa; Kazutaka Nakahara; Retief Neveling; Silvia Niccolai; S. Ong; Shelley Page; Vassilios Papavassiliou; Stephen Pate; Sarah Phillips; Mark Pitt; Benard Poelker; Tracy Porcelli; Gilles Quemener; Brian Quinn; William Ramsay; Aamer Rauf; Jean-Sebastien Real; Julie Roche; Philip Roos; Gary Rutledge; Jeffery Secrest; Neven Simicevic; Gregory Smith; Damon Spayde; Samuel Stepanyan; Marcy Stutzman; Vince Sulkosky; Vincent Sulkosky; Vince Sulkosky; Vincent Sulkosky; Vardan Tadevosyan; Raphael Tieulent; Jacques Van de Wiele; Willem van Oers; Eric Voutier; William Vulcan; Glen Warren; Steven Wells; Steven Williamson; Stephen Wood; Chen Yan; Junho Yun; Valdis Zeps

    2007-08-01

    We have measured the beam-normal single-spin asymmetry in elastic scattering of transversely-polarized 3 GeV electrons from unpolarized protons at Q^2 values of 0.15 and 0.25 (GeV/c)^2 with results of A_n = -4.06 +- 0.99(stat) +- 0.63(syst) and A_n = -4.82 +- 1.87(stat) +- 0.98(syst) ppm. These results are inconsistent with calculations solely using the elastic nucleon intermediate state, and generally agree with calculations with significant inelastic hadronic intermediate state contributions. A_n provides a direct probe of the imaginary component of the two-photon exchange amplitude, the complete description of which is important in the interpretation of data from precision electron-scattering experiments.

  5. Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Alex J. Dragt; Filippo Neri; Govindan Rangarajan; David Douglas; Liam M. Healy; Robert D. Ryne

    1988-12-01

    The purpose of this paper is to present a summary of new methods, employing Lie algebraic tools, for characterizing beam dynamics in charged-particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics, by a certain operator. The operators for the various elements can then be concatenated, following well-defined rules, to obtain a resultant operator that characterizes the entire system. This paper deals mostly with accelerator design and charged-particle beam transport. The application of Lie algebraic methods to light optics and electron microscopes is described elsewhere (1, see also 44). To keep its scope within reasonable bounds, they restrict their treatment of accelerator design and charged-particle beam transport primarily to the use of Lie algebraic methods for the description of particle orbits in terms of transfer maps. There are other Lie algebraic or related approaches to accelerator problems that the reader may find of interest (2). For a general discussion of linear and nonlinear problems in accelerator physics see (3).

  6. Effect of nonlinear radiofrequency electromagnetic fields on the emittance of bunched beams

    Science.gov (United States)

    Phadte, D. S.; Patidar, C. B.

    2013-07-01

    Gap transformations are frequently used in ion Linac codes, to efficiently describe the particle dynamics. Using similar approach, we analyze the uniformly bunched beam passing through an axis-symmetric radiofrequency (RF) cavity. The method can be used for other distributions as well using a similar six dimensional analysis. The effect of non-linear RF field in radial and axial directions in an RF cavity and the finite phase width of the bunch, on the transverse and longitudinal emittance growth have been studied. The expressions obtained have been verified for the two types of cavity cells namely the zero mode DTL and pi mode CCL type used frequently in ion linacs. The results are seen to be valid for the entire maximum phase acceptance up to 360 degrees. Simulations with the equivalent beams of non-uniform distributions namely Waterbag and Gaussian show that at synchronous phases closer to the wave crest, the results give a good approximation of emittance growth in both planes for non-uniform beams.

  7. Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient.

    Science.gov (United States)

    Xiao, Fajun; Li, Baoran; Wang, Meirong; Zhu, Weiren; Zhang, Peng; Liu, Sheng; Premaratne, Malin; Zhao, Jianlin

    2014-09-22

    We theoretically report the existence of optical Bloch oscillations (BO) of an Airy beam in a one-dimensional optically induced photonic lattice with a linear transverse index gradient. The Airy beam experiencing optical BO shows a more robust non-diffracting feature than its counterparts in free space or in a uniform photonic lattice. Interestingly, a periodical recurrence of Airy shape accompanied with constant alternation of its acceleration direction is also found during the BO. Furthermore, we demonstrate that the period and amplitude of BO of an Airy beam can be readily controlled over a wide range by varying the index gradient and/or the lattice period. Exploiting these features, we propose a scheme to rout an Airy beam to a predefined output channel without losing its characteristics by longitudinally modulating the transverse index gradient.

  8. Nonlinear dynamics for charges particle beams with a curved axis in the matrix - recursive model

    Energy Technology Data Exchange (ETDEWEB)

    Dymnikov, A.D. [University of St Petersburg, (Russian Federation). Institute of Computational Mathematics and Control Process

    1993-12-31

    In this paper a new matrix and recursive approach has been outlined for treating nonlinear optics of charged particle beams. This approach is a new analytical and computational tool for designers of optimal beam control systems. 9 refs.

  9. Transverse Emittance reconstruction in presence of space charge and application to the 50 MeV beam of Linac4

    CERN Document Server

    Garcia Tudela, M; Posocco, P A

    2011-01-01

    During the commissioning stage of Linac4 a test bench is planned to be used in order to characterize the 50 MeV beam after the DTL. Among other parameters, it will be possible to measure the transverse emittance using both the 3 monitors and the quadrupole scan method. As the space charge effects are not negligible at this energy, classical techniques of emittance reconstruction become questionable and a different approach based on recursive beam dynamics simulations must be applied.

  10. Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources

    CERN Document Server

    Geloni, Gianluca; Schneidmiller, Evgeni; Yurkov, Mikhail

    2008-01-01

    This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert-Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical(geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude (from 0.1 Angstrom up to 10^3 Angstrom). Sometimes, the so-called Gaussian-Schell model, that is widely used in statistical optics in the description of partially-coherent sources, is applied as an alternative to the quasi-homogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of X-ray beams from non-homogeneous undulator sources. As a result, a more...

  11. Evaluation and Correction of the Non-linear Distortion of CEBAF Beam Position Monitors

    Energy Technology Data Exchange (ETDEWEB)

    M. Spata, T.L. Allison, K.E. Cole, J. Musson, J. Yan

    2011-09-01

    The beam position monitors at CEBAF have four antenna style pickups that are used to measure the location of the beam. There is a strong nonlinear response when the beam is far from the electrical center of the device. In order to conduct beam experiments at large orbit excitation we need to correct for this nonlinearity. The correction algorithm is presented and compared to measurements from our stretched wire BPM test stand.

  12. Transverse (lateral) instantaneous force of an acoustical first-order Bessel vortex beam centered on a rigid sphere.

    Science.gov (United States)

    Mitri, F G; Fellah, Z E A

    2012-01-01

    In a recent report [F.G. Mitri, Z.E.A. Fellah, Ultrasonics 51 (2011) 719-724], it has been found that the instantaneous axial force (i.e. acting along the axis of wave propagation) of a Bessel acoustic beam centered on a sphere is only determined for the fundamental order (i.e. m=0) but vanishes when the beam is of vortex type (i.e. m>0, where m is the order (or helicity) of the beam). It has also been recognized that for circularly symmetric beams (such as Bessel beams of integer order), the transverse (lateral) instantaneous force should vanish as required by symmetry. Nevertheless, in this commentary, the present analysis unexpectedly reveals the existence of a transverse instantaneous force on a rigid sphere centered on the axis of a Bessel vortex beam of unit magnitude order (i.e. |m|=1) not reported in [F.G. Mitri, Z.E.A. Fellah, Ultrasonics 51 (2011) 719-724]. The presence of the transverse instantaneous force components of a first-order Bessel vortex beam results from mathematical anti-symmetry in the surface integrals, but vanishes for the fundamental (m=0) and higher-order Bessel (vortex) beams (i.e. |m|>1). Here, closed-form solutions for the instantaneous force components are obtained and examples for the transverse components for progressive waves are computed for a fixed and a movable rigid sphere. The results show that only the dipole (n=1) mode in the scattering contributes to the instantaneous force components, as well as how the transverse instantaneous force per unit cross-sectional surface varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere's radius), and the half-cone angle β of the beam. Moreover, the velocity of the movable sphere is evaluated based on the concept of mechanical impedance. The proposed analysis may be of interest in the analysis of transverse instantaneous forces on spherical particles for particle manipulation and rotation in drug delivery and other biomedical or

  13. Nonlinear Dynamic Analysis of an Inclined Timoshenko Beam Subjected to a Moving Mass/Force with Beam’s Weight Included

    Directory of Open Access Journals (Sweden)

    Ahmad Mamandi

    2011-01-01

    Full Text Available In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the outcome results have been compared to the results with those obtained from linear solution. The influence of the large deflections caused by a stretching effect due to the beam's fixed ends is captured. It was seen that existence of quadratic-cubic nonlinear terms in the nonlinear governing coupled PDEs of motion causes stiffening (hardening behavior of the dynamic responses of the self-weight beam under the act of a traveling mass as well as equivalent concentrated moving force. Furthermore, in a case where the object leaves the beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption.

  14. Beam Stability in Synchrotrons with Notch and All-Pass Filters in the Feedback Loop of a Transverse Damper

    CERN Document Server

    Zhabitsky, V M; Kotzian, G

    2009-01-01

    The stability of a beam in synchrotrons with digital filters in the feedback loop of a transverse damper is treated. A transverse feedback system (TFS) is required in synchrotrons to stabilize the high intensity beams against transverse instabilities and to damp the beam injection errors. The TFS damper kicker (DK) corrects the transverse momentum of a bunch in proportion to its displacement from the closed orbit at the location of the beam position monitor (BPM). The digital signal processor in the feedback loop between BPM and DK ensures the adjustment of the phase advance and the correction of the time of flight for optimum damping. Digital FIR (finite impulse response) and IIR (infinite impulse response) filters are used commonly for the signal processing. A notch filter with zeros at the revolution frequency is required to remove the closed orbit content of the signal and correct for the imperfect electric centre of the BPM. Further processing is required to adjust for the betatron phase advance between ...

  15. Laser based stripping system for measurement of the transverse emittance of H-beams at the CERN Linac4

    CERN Document Server

    Hofmann, T; Raich, U; Roncarolo, F; Cheymol, B

    2013-01-01

    The new LINAC4 at CERN will accelerate H- particles to 160 MeV and allow high brightness proton beam transfers to the Proton Synchrotron Booster, via a charge-exchange injection scheme. This paper describes the conceptual design of a laser system proposed for transverse profile and emittance measurements based on photon detachment of electrons from the H- ions. The binding energy of the outer electron is only 0.75 eV and can easily be stripped with a laser beam. Measuring the electron signal as function of the laser position allows the transverse beam profile to be reconstructed. A downstream dipole can also be used to separate the laser neutralized H0 atoms from the main H- beam. By imaging these H0 atoms as a function of laser position the transverse emittance can be reconstructed in the same way as in traditional slit-and-grid systems. By properly dimensioning the laser power and spot size, this method results in negligible beam losses and is therefore non-destructive. In addition, the absence of material ...

  16. Analysis of a Beam Made of Physical Nonlinear Material on Nonlinear Elastic Foundation under a Moving Concentrated Load

    Directory of Open Access Journals (Sweden)

    E. Mardani

    2008-01-01

    Full Text Available A prismatic beam made of a behaviorally nonlinear material was analyzed under a concentrated load moving with a known velocity on a nonlinear elastic foundation with a reaction the vibration equation of motion was derived using Hamilton principle and Euler Lagrange equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculated by the presented solution. Considering the response of the beam, in the sense of its resonance, it was found that there is no critical velocity when the behavior of the beam and foundation material is assumed to be physically nonlinear and there are finite values for the deflection, stress and bending moment of the beam when

  17. FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA

    Institute of Scientific and Technical Information of China (English)

    文双春; 范滇元

    2001-01-01

    The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.

  18. Finite Element Solution: Nonlinear Flapping Beams for Use with Micro Air Vehicle Design

    Science.gov (United States)

    2007-03-01

    used to approximate the nonlinearity in a beam is the SDOF Duffing Oscillator ӱ + C ẏ + ω0 2 y + βy3 = P sin(ωt...Hilbert Transform.......................................................................................................19 Duffing Equation...Amplitude vs Nonlinear Frequency: Fixed-Fixed Steel................................. 36 Figure 26. Duffing Equation Plot: Fixed-Fixed Steel Beam

  19. Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing

    DEFF Research Database (Denmark)

    Karamehmedovic, Emir; Pedersen, Christian; Jensen, Ole Bjarlin;

    2009-01-01

    We investigate the possibility of improving the beam quality and obtaining high conversion efficiency in nonlinear sum-frequency generation. A 765 nm beam from an external cavity tapered diode laser is single-passed through a nonlinear crystal situated in the high intracavity field of a 1342 nm Nd...

  20. Modulation instability, solitons and beam propagation in spatially nonlocal nonlinear media

    DEFF Research Database (Denmark)

    Krolikowski, Wieslaw; Bang, Ole; Nikolov, Nikola Ivanov

    2004-01-01

    We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction...

  1. Experimental nonlinear beam dynamics studies with turn- by-turn phase space monitors

    Science.gov (United States)

    Terebilo, Andrei Gennadyevich

    1999-10-01

    This thesis presents an experimental study of single particle and collective beam dynamics undertaken by the author in SPEAR electron storage ring. The technique used for measurement consists of exciting transverse oscillations of a bunch circulating in the ring with a fast kicker and observing the center of mass oscillations every turn for several thousand turns. The goal of this study was to develop new applications of the turn-by-turn technique to accelerator diagnostics. One innovation introduced is the use of a collective mode of the beam motion as a phase space probe. When in this mode the bunch behaves similar to a macroparticle and oscillates coherently. It is possible to control the growth/damping rate of this oscillation by adjusting the accelerator parameters. Another new tool proposed is the analysis of phase space trajectories in the time-frequency domain. This technique makes it possible to conduct nonlinear dynamics experiments such as observation of high order resonances in the frequency map and single-kick measurement of the tune dependence on the amplitude of oscillations.

  2. Single Shot Measurements of the 4-Dimensional Transverse Phase Space Distribution of Intense Ion Beams at the UNILAC at GSI

    CERN Document Server

    Groening, L

    2003-01-01

    The UNILAC is used as an injector for the synchrotron SIS. It is designed to fill the synchrotron up to its space charge limit. The upper limit for the useful beam emittance of the UNILAC is given by the finite acceptance of the SIS during the injection process. In order to remain within this acceptance the emittance growth during beam acceleration and transportation due to space charge effects must be minimized by applying an appropriate beam focusing. Therefore, the influence of the magnetic focusing strength on the beam emittance growth was investigated experimentally for different beam currents. Measurements of transverse phase space distributions were performed before and after the Alvarez accelerator with a periodic focusing channel, respectively. In order to perform such a wide parameter scan within a reasonable time with respect to machine stability, the pepper pot technique was applied. The pepper pot method allows for single-pulse measurements. For comparison several measurements using the slit-grid...

  3. Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept

    Science.gov (United States)

    Mamatsashvili, G.; Khujadze, G.; Chagelishvili, G.; Dong, S.; Jiménez, J.; Foysi, H.

    2016-08-01

    To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies

  4. Orbital angular momentum of helical necklace beams in colloid-based nonlinear optical metamaterials (Conference Presentation)

    Science.gov (United States)

    Walasik, Wiktor T.; Silahli, Salih Z.; Litchinitser, Natalia M.

    2016-09-01

    Colloidal metamaterials are a robust and flexible platform for engineering of optical nonlinearities and studies of light filamentation. To date, nonlinear propagation and modulation instability of Gaussian beams and optical vortices carrying orbital angular momentum were studied in such media. Here, we investigate the propagation of necklace beams and the conservation of the orbital angular momentum in colloidal media with saturable nonlinearity. We study various scenarios leading to generation of helical necklace beams or twisted beams, depending on the radius, power, and charge of the input vortex beam. Helical beams are build of two separate solitary beams with circular cross-sections that spiral around their center of mass as a result of the equilibrium between the attraction force of in-phase solitons and the centrifugal force associated with the rotational movement. A twisted beam is a single beam with an elliptical cross-section that rotates around it's own axis. We show that the orbital angular momentum is converted into the rotational motion at different rates for helical and twisted beams. While earlier studies reported that solitary beams are expelled form the initial vortex ring along straight trajectories tangent to the vortex ring, we show that depending on the charge and the power of the initial beam, these trajectories can diverge from the tangential direction and may be curvilinear. These results provide a detailed description of necklace beam dynamics in saturable nonlinear media and may be useful in studies of light filamentation in liquids and light propagation in highly scattering colloids and biological samples.

  5. Instability and dynamics of two nonlinearly coupled laser beams in a plasma

    CERN Document Server

    Shukla, P K; Marklund, M; Stenflo, L; Kourakis, I; Parviainen, M; Dieckmann, M E

    2006-01-01

    We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.

  6. Effects of initial stress on transverse wave propagation in carbon nanotubes based on Timoshenko laminated beam models

    Science.gov (United States)

    Cai, H.; Wang, X.

    2006-01-01

    Based on Timoshenko laminated beam models, this paper investigates the influence of initial stress on the vibration and transverse wave propagation in individual multi-wall carbon nanotubes (MWNTs) under ultrahigh frequency (above 1 THz), in which the initial stress in the MWNTs can occur due to thermal or lattice mismatch between different materials. Considering van der Waals force interaction between two adjacent tubes and effects of rotary inertia and shear deformation, results show that the initial stress in individual multi-wall carbon nanotubes not only affects the number of transverse wave speeds and the magnitude of transverse wave speeds, but also terahertz critical frequencies at which the number of wave speeds changes. When the initial stress in individual multi-wall carbon nanotubes is the compressive stress, transverse wave speeds decrease and the vibration amplitude ratio of two adjacent tubes increases. When the initial stress in individual multi-wall carbon nanotubes is the tensile stress, transverse wave speeds increase and the vibration amplitude ratio of two adjacent tubes decreases. The investigation of the effects of initial stress on transverse wave propagation in carbon nanotubes may be used as a useful reference for the application and the design of nanoelectronic and nanodrive devices, nano-oscillators, and nanosensors, in which carbon nanotubes act as basic elements.

  7. 低能离子束横向发射度的测量及分析%Measuring and Analyzing Transverse Low-Energy Ion Beam Emittances

    Institute of Scientific and Technical Information of China (English)

    M.P.Stockli

    2007-01-01

    The transverse emittance of an ion beam describes its transverse size as the particles are transported from a source to a target.It allows for predicting beam losses in limiting apertures and the beam focus size at the target.Various definitions and issues are discussed.The most common and emerging measuring techniques are presented,including their advantages.Several methods of emittance data analysis,their accuracy and trustworthiness,are discussed.

  8. Suppression of space charge induced beam halo in nonlinear focusing channel

    Science.gov (United States)

    Batygin, Yuri K.; Scheinker, Alexander; Kurennoy, Sergey; Li, Chao

    2016-04-01

    An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.

  9. Suppression of Space Charge Induced Beam Halo in Nonlinear Focusing Channel

    CERN Document Server

    Batygin, Yuri K; Kurennoy, Sergey; Li, Chao

    2016-01-01

    An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.

  10. Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media

    Science.gov (United States)

    Qiu, Yunli; Chen, Zhaoxi; He, Yingji

    2017-04-01

    Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.

  11. A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

    Science.gov (United States)

    Nemeth, Michael P.

    2013-01-01

    A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

  12. On the non-linear high-order theory of unidirectional sandwich panels with a transversely flexible core

    Energy Technology Data Exchange (ETDEWEB)

    Frostig, Yeoshua; Sheinman, Izhak [Technion-Israel Inst. of Technology, Faculty of Civil and Environmental Engineering, Haifa (Israel); Thomsen, Ole Thybo [Aalborg Univ., Inst. of Mechanical Engineering, Aalborg (Denmark)

    2005-03-01

    The paper presents a general geometrically non-linear high-order theory of sandwich panels that takes into account the high-order geometrical non-linearities in the core as well as in the face sheets and is based on a variational approach. The formulation, which yields a set of rather complicated governing equations, has been simplified in two different approaches and has been compared with FEA results for verification. The first formulation uses the kinematic relations of large displacements with moderate rotations for the face sheets, non-linear kinematic relations for the core and it assumes that the distribution of the vertical normal stresses through the depth of the core are linear. The second approach uses the general formulation to the non-linear high-order theory of sandwich panels (HSAPT) that considers geometrical non-linearities in the face sheets and only linear high-order effects in the core. The numerical results of the two formulations are presented for a three point bending loading scheme, which is associated with a limit point behavior. The results of the two formulations are compared in terms of displacements, bending moments and shear stresses and transverse (vertical) normal stresses at the face-core interfaces on one hand, and load versus these structural quantities on the other hand. The results have compared well with FEA results obtained using the commercial codes ADINA and ANSYS. (Author)

  13. Excitation of Large Transverse Beam Oscillations without Emittance Blow-up using the AC-Dipole Principle

    CERN Document Server

    Berrig, O E; Jones, R; Koopman, J; Koutchouk, Jean-Pierre; Schmickler, Hermann; Schmidt, F

    2001-01-01

    The so-called "AC-Dipole" principle allows the excitation of transverse oscillations to large (several sigma) excursions without emittance blow-up. The idea was originally proposed and tested at BNL for resonance crossing with polarized beams, using an orbit corrector dipole with an excitation frequency close to the betatron tune, hence "AC-Dipole". This method of beam excitation has several potential applications in teh LHC, such as phase advance and beta-measurements, dynamic aperture studies and the investigation of resonance strengths. The technique was recently tested in the CERN SPS using the transverse damper as an "AC-Dipole" providing the fixed frequency excitation. Results from this experiment are presented, along with an explanation of the underlying principle.

  14. A fast wire scanner, used to measure the transverse density distribution of beams circulating in an accelerator or storage ring.

    CERN Multimedia

    Maximilien Brice

    2002-01-01

    Fast wire scanners are used to measure the transverse density distribution of beams circulating in an accelerator or storage ring. In order to minimize blow-up of the beam through multiple Coulomb scattering, the wires are very thin (in the version shown here it is actually a twisted strand of carbon fibres with a total diameter of about 25 microns) and are swept through the beam at high speed (a linear motor, not mounted here, accelerates the wires to up to 20 m/s). One measures either the secondary emission current from the wire, or the signal from a scintillator/photomultiplier combination downstream from the wire scanner receiving the shower from nuclear reactions of beam particles with the wire nuclei. There are four such fast wire scanners in the 26 GeV PS and eight in the 1.4 GeV Booster.

  15. Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections

    Science.gov (United States)

    Atilgan, Ali R.; Hodges, Dewey H.

    1991-01-01

    A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.

  16. Transverse Field Dispersion in the Generalized Nonlinear Schrödinger Equation: Four Wave Mixing in a Higher Order Mode Fiber

    DEFF Research Database (Denmark)

    Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris

    2013-01-01

    An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...

  17. Intermittent Giant Goos-Hanchen shifts from Airy beams at nonlinear interfaces

    CERN Document Server

    Chamorro-Posada, Pedro; Aceves, Alejandro B; McDonald, Graham S

    2013-01-01

    We study the giant Goos-Hanchen shift obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the numerical solution of the nonlinear Helmholtz equation. We report the existence of non-standard intermittent and oscillatory regimes for the nonlinear Goos-Hanchen shifts which can be explained in terms of the competition between the critical coupling to a surface mode of the reflected component of the Airy beam and the soliton emission from the refracted beam component.

  18. Reciprocity breaking during nonlinear propagation of adapted beams through random media.

    Science.gov (United States)

    Palastro, J P; Peñano, J; Nelson, W; DiComo, G; Helle, M; Johnson, L A; Hafizi, B

    2016-08-22

    Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate phase aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown, providing the first analysis of AO applied to high peak power laser beams. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.

  19. Widely varying giant Goos-Hänchen shifts from Airy beams at nonlinear interfaces.

    Science.gov (United States)

    Chamorro-Posada, Pedro; Sánchez-Curto, Julio; Aceves, Alejandro B; McDonald, Graham S

    2014-03-15

    We present a numerical study of the giant Goos-Hänchen shifts (GHSs) obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the nonlinear Helmholtz equation. We report the existence of nonstandard nonlinear GHSs displaying an extreme sensitivity to the input intensity and the existence of multiple critical values. These intermittent and oscillatory regimes can be explained in terms of competition between critical coupling to a surface mode and soliton emission from the refracted beam component and how this interplay varies with localization of the initial Airy beam.

  20. Nonlinear Stability of Intense Mismatched Beams in a Uniform Focusing Field

    CERN Document Server

    Pakter, Renato; Simeoni, Wilson

    2005-01-01

    We investigate the nonlinear coupling between axisymmetric and elliptic oscillations in the dynamics of intense beams propagating in a uniform magnetic focusing field. It is shown that finite amplitude mismatched oscillations of an initially round beam may destabilize elliptic oscillations, heavily affecting stability and the shape of the beam. This is a potential mechanics for beam particle loss in such systems. Self consistent simulations are performed to verify the findings.

  1. Localized Effects in the Nonlinear Behavior of Sandwich Panels with a Transversely Flexible Core

    DEFF Research Database (Denmark)

    Frostig, Y.; Thomsen, Ole Thybo

    2005-01-01

    nonlinear analysis approach incorporates the effects of the vertical flexibility of the core, and it is based on the approach of the High-order Sandwich Panel Theory (HSAPT). The results demonstrate that the effects of localized loads, when taken into the geometrically nonlinear domain, change the response...

  2. Application of Metal-Semiconductor-Metal (MSM) Photodetectors for Transverse and Longitudinal Intra-Bunch Beam Diagnostics

    CERN Document Server

    Steinhagen, R J; Boland, M J; Lucas, T G; Rassool, R P

    2013-01-01

    The performance reach of modern accelerators is often governed by the ability to reliably measure and control the beam stability. In high-brightness lepton and high-energy hadron accelerators, the use of optical diagnostic techniques is becoming more widespread as the required bandwidth, resolution and high RF beam power level involved limit the use of traditional electro-magnetic RF pick-up based methods. This contribution discusses the use of fibre-coupled ultra-fast Metal-Semiconductor-Metal Photodetectors (MSM-PD) as an alternative, dependablemeans to measure signals derived from electro-optical and synchrotron-light based diagnostics systems. It describes the beam studies performed at CERN’s CLIC Test Facility (CTF3) and the Australian Synchrotron to assess the feasibility of this technology as a robust, wide-band and sensitive technique for measuring transverse intra-bunch and bunch-by-bunch beam oscillations, longitudinal beam profiles, un-bunched beam population and beam-halo profiles. The amplifica...

  3. Tunable nonlinear beam defocusing in infiltrated photonic crystal fibers

    DEFF Research Database (Denmark)

    Rosberg, Christian Romer; Bennet, Francis H; Neshev, Dragomir N.;

    2007-01-01

    We demonstrate a novel experimental platform for discrete nonlinear optics based on infiltrated photonic crystal fibers. We observe tunable discrete diffraction and nonlinear self-defocusing, and apply the effects to realize a compact all-optical power limiter....

  4. Suppression of beam halo-chaos using nonlinear feedback discrete control method

    CERN Document Server

    Fang Jin Qing; Chen Guan Rong; Luo Xiao Shu; Weng Jia Qiang

    2002-01-01

    Based on nonlinear feedback control method, wavelet-based feedback controller as a especial nonlinear feedback function is designed for controlling beam halo-chaos in high-current accelerators of driven clean nuclear power system. PIC simulations show that suppression of beam halo-chaos are realized effectively after discrete control of wavelet-based feed-back is applied to five kinds of the initial proton beam distributions, respectively. The beam halo strength factor is quickly reduced to zero, and other statistical physical quantities of beam halo-chaos are more than doubly reduced. These performed PIC simulation results demonstrate that the developed methods are very effective for control of beam halo-chaos. Potential application of the beam halo-chaos control methods is discussed finally

  5. Two-dimensional simulations of nonlinear beam-plasma interaction in isotropic and magnetized plasmas

    CERN Document Server

    Timofeev, I V

    2012-01-01

    Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide two-dimensional wave spectrum is driven unstable, and we also study how nonlinear evolution of these structures is affected by the external magnetic field. In the case of isotropic plasma, nonlinear buildup of filamentation modes due to the combined effects of two-stream and oblique instabilities is found to exist and growth mechanisms of secondary instabilities destroying the BGK--type nonlinear wave are identified. In the weak magnetic field, the energy of beam-excited plasma waves at the nonlinear stage of beam-plasma interaction goes predominantly to the short-wavelength upper-hybrid waves propagating parallel to the magnetic field, whereas in the strong magnetic field the spectral energy is transferred to the electrostatic whistlers with oblique propagation.

  6. The effects of transverse plasma flow on laser beam deflection and of ultra-intense laser beam filamentation on channel formation

    Science.gov (United States)

    Hinkel, D. E.

    1997-11-01

    Recent experiments conducted at Lawrence Livermore National Laboratory (LLNL) with the Nova and Janus lasers demonstrate deflection of the laser beam in plasma with flow transverse to the beam. In gas-filled hohlraum experiments(S. G. Glendinning et al.), the laser spot on the hohlraum wall is ~ 100 μm closer to the laser entrance hole (LEH) than in empty hohlraum experiments, which degrades drive symmetry. In a series of exploding foil experiments(J. D. Moody et al.), Phys. Rev. Lett. 77, 1294 (1996)., intensity dependent deflection of the transmitted beam is observed, and interferometric measurements of laser-produced channels in preformed plasma(P. E. Young et al.), to be submitted to Phys. Rev. Lett., 1997. show beam deflection in the presence of near-sonic transverse flow. Theoretical analysis(D. E. Hinkel et al.), Phys. Rev. Lett. 77, 1298 (1996). yields simple scaling laws for the formation of ponderomotively (or thermally) created density depressions downstream from the laser beam's high intensity regions, into which the light is refracted. An integrated approach that utilizes plasma parameters from the hydrocode Lasnex, detailed knowledge of the beam structure, and plasma physics analysis and modelling with F3D(R. L. Berger et al.), Phys. Fluids B 5, 2243 (1993)., has been used to develop a predictive capability that successfully quantifies the amount of beam deflection occurring in experiments. Related physics of beam self-focussing and filamentation is of relevance to the Fast Ignitor(M. Tabak et al.), Phys. Plasmas 1, 1626 (1994).. In channeling experiments performed on the 100 TW laser at LLNL, the f/3 laser beam, which has a 15 μm waist at best focus, has intensities in excess of IL = 1 × 10^17 W/cm^2. Modelling of these high intensity experiments indicates that channel formation occurs over a wide range of cone angles for an idealized (Gaussian) beam. However, when beam structure is taken into consideration, channel formation in the underdense

  7. APLICACIÓN DEL TEST DE LA BARRA TRANSVERSAL MODIFICADO PARA EVALUAR RATAS HEMIPARKINSONIZADAS. Modify Beam Transversal Test to Evauate Hemiparkinsonian Rats.

    Directory of Open Access Journals (Sweden)

    LISETTE BLANCO LEZCANO

    Full Text Available La degeneración nigroestriatal que caracteriza a la enfermedad de Parkinson (EP es estudiada en modelos experimentales en roedores por inyección de 6-hidroxidopamina (6-OHDA. El presente estudio presenta una versión modificada del test de la barra transversal (TBT que permite la cuantificación del déficit motor a través de: tiempo que demora la rata en alcanzar una de las plataformas (latencia de escape, LE; tiempo que demora en caer de la barra (latencia de caída, LC; número total de errores cometidos durante la ejecución en cada barra (número de errores, NE. La forma y el diámetro de la sección transversal de la barra se modificaron desde barras rectangulares y circulares de 2,5 cm de diámetro hasta barras con esta misma forma y 1 cm de diámetro respectivamente lo cual impuso la mayor dificultad a la ejecución del test. Tres grupos de ratas Wistar fueron evaluados: no tratadas (n=15, lesionadas con 6-OHDA (n=14 y falsas operadas (n=14. Todas las variables estudiadas mostraron diferencias signifi-cativas entre ratas controles y hemiparkinsonizadas. Para todos los tipos de barras, las variables LE y NE se incrementaron mientras que la LC disminuyó significativamente en las ratas hemiparkinsonizadas en comparación con las ratas controles. La LC mostró diferencias altamente significativas (pThe nigrostriatal degeneration underlying Parkinson’s disease (PD is commonly studied in experimental animals by injection of the neurotoxin 6-hydroxydopamine. The present study describes a modified version of a beam traversal test which allows the quantification of the motor deficit through the time spent to arrive to the platform once all four paws of the animals are in contact with the beam (escape latency, EL, the time spent before falling (tumbled down latency, TDL and the number of errors (NE committed for the animals in each beam. The shape and the diameter of the cross section of the beams were modified from rectangular and circular

  8. AN ELASTIC STRESS ANALYSIS FOR A POLYMER MATRIX COMPOSITE CANTILEVER BEAM SUBJECTED TO A SINGLE TRANSVERSE FORCE

    Directory of Open Access Journals (Sweden)

    Ayla TEKİN

    2004-03-01

    Full Text Available In this study, elasto-plastic stress analysis is carried out in a polymer matrix composite cantilever beam of arbitrary fiber orientation subjected to a single transverse force applied to the free end by using the anisotropic elasticity theory. The residual stress component of ?x and yield points are determined for 0°, 30°, 45°, 60° and 90° fiber orientation angles. The yielding begins for 0° and 90° fiber orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. It is seen that the yielding begins for 30°, 45° and 60° fiber orientation angles at the upper surface of the beam. The intensity of the residual stress component of ?x is maximum at the upper and lower surfaces of the beam. In this study, the residual stress component of ?x obtained for the polymer matrix composite thermoplastic cantilever beam reinforced by reinforced unidirectional fibers is compared with that of the thermoplastic cantilever beam reinforced by woven Cr-Ni steel fibers.

  9. Notes on the nonlinear beam dynamics with strong damping in the CLIC Damping Ring

    CERN Document Server

    Levichev, Eugene; Shatilov, Dmitry

    2010-01-01

    The beam is injected into the CLIC damping ring with the relatively large emittance and energy spread and then is damped to the extremely low phase volume. During the damping process the betatron frequency of each particle changes due to the space charge tune shift and nonlinear dependence of the betatron tune on the amplitude. This nonlinearity is produced by the strong chromatic sextupoles, wiggler nonlinear field components and, again, by the space charge force. During the damping, the particle cross resonances, which can trap some fraction of the beam, cause the loss of intensity, the beam blow up and degrade the beam quality. In this paper we study the evolution of the beam distribution in time during the damping for the original lattice of the CLIC DR (May 2005). Geneva, Switzerland June 2010 CLIC – Note – 850

  10. Hollow Gaussian beam generation through nonlinear interaction of photons with orbital-angular-momemtum

    CERN Document Server

    Chaitanya, N Apurv; Banerji, J; Samanta, G K

    2016-01-01

    Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.

  11. Dynamic Nonlinear Focal Shift in Amplitude Modulated Moderately Focused Acoustic Beams

    CERN Document Server

    Jiménez, Noé; González-Salido, Nuria

    2016-01-01

    The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25 kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behaviour, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both, for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by ...

  12. Hollow Gaussian beam generation through nonlinear interaction of photons with orbital angular momentum

    Science.gov (United States)

    Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.

    2016-09-01

    Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.

  13. Beam Tests and Plans for the CERN PS Transverse Damper System

    CERN Document Server

    Blas, A; Sterbini, G

    2013-01-01

    The CERN Proton Synchrotron (CPS) has been running without any transverse damping equipment since 1998, thanks to the stabilizing effect of the linear coupling applied between horizontal and vertical planes. \

  14. Numerical study for beam loss occurring for wide-ranging transverse injection painting and its mitigation scenario in the J-PARC 3-GeV RCS

    Science.gov (United States)

    Hotchi, Hideaki; Tani, Norio; Watanabe, Yasuhiro

    2015-04-01

    In the J-PARC 3-GeV Rapid Cycling Synchrotron (RCS), transverse injection painting is utilized to manipulate the transverse beam profile according to the requirements from the downstream facilities as well as to mitigate the space-charge induced beam loss in RCS. Therefore, a flexible control is required for the transverse painting area. But now the available range of transverse painting is limited to small area due to beta function beating caused by the edge focus of injection bump magnets which operate during the beam injection period. This beta function beating additionally excites various random betatron resonances through a distortion of the lattice super-periodicity, causing a shrinkage of the dynamic aperture during the injection period. This decrease of the dynamic aperture leads to extra beam loss at present when applying large transverse painting. For beta function beating caused by the edge focus, we proposed a correction scheme with additional pulse-type quadrupole correctors. In this paper, we will discuss the feasibility and effectiveness of this correction scheme for expanding the transverse injection painting area with no extra beam loss, while considering the beam loss and its mitigation mechanisms, based on numerical simulations.

  15. CLIC spectrometer magnet interference computation of transversal B-field on primary beam

    CERN Document Server

    Swoboda, Detlef; Tomas, Rogelio

    2009-01-01

    A 3-D FE model with the present spectrometer magnet concept has been built to compute the interference of the spectrometer field with the primary beam. Screening of the primary beam and Final Focus magnets (FF) is achieved by an “Anti-solenoid” close to the beam trajectory.

  16. Nonlinear dynamic characteristic analysis of jointed beam with clearance

    Science.gov (United States)

    Zhang, Jing; Guo, Hong-Wei; Liu, Rong-Qiang; Wu, Juan; Kou, Zi-Ming; Deng, Zong-Quan

    2016-12-01

    The impact and elasticity of discontinuous beams with clearance frequently affect the dynamic response of structures used in space missions. This study investigates the dynamic response of jointed beams which are the periodic units of deployable structures. The vibration process of jointed beams includes free-play and impact stages. A method for the dynamic analysis of jointed beams with clearance is proposed based on mode superposition and instantaneous static deformation. Transfer matrix, which expresses the relationship of the responses before and after the impact of jointed beams, is derived to calculate the response of the jointed beams after a critical position. The dynamic responses of jointed beams are then simulated. The effects of various parameters on the displacement and velocity of beams are investigated.

  17. Effect of magnetic field on the propagation of quasi-transverse waves in a nonhomogeneous conducting medium under the theory of nonlinear elasticity

    Indian Academy of Sciences (India)

    D P Acharya; Asit Kumar Mondal

    2006-06-01

    The object of the present paper is to investigate the propagation of quasi-transverse waves in a nonlinear perfectly conducting nonhomogeneous elastic medium in the presence of a uniform magnetic field transverse to the direction of wave propagation. Different types of figures have been drawn to exhibit the distortion of waves due to the presence of magnetic field and the nonhomogeneous nature of the medium. Formation of shocks has also been numerically discussed.

  18. Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX

    Science.gov (United States)

    Belova, E. V.; Gorelenkov, N. N.; Crocker, N. A.; Lestz, J. B.; Fredrickson, E. D.; Tang, S.; Tritz, K.

    2017-04-01

    Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n =4 -9 , and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfvén wave (KAW) that occurs on the high-field side at the Alfvén resonance location. High-frequency Alfvén eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam-driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.

  19. Management of the orbital angular momentum of vortex beams in a quadratic nonlinear interaction

    CERN Document Server

    Bovino, Fabio A; Bertolotti, Mario; Sibilia, Concita

    2011-01-01

    Light intensity control of the orbital angular momentum of the fundamental beam in a quadratic nonlinear process is theoretically and numerically presented. In particular we analyzed a seeded second harmonic generation process in presence of orbital angular momentum of the interacting beams due both to on axis and off axis optical vortices. Examples are proposed and discussed.

  20. Port-Hamiltonian Modeling of a Nonlinear Timoshenko Beam with Piezo Actuation

    NARCIS (Netherlands)

    Voss, Thomas; Scherpen, Jacquelien M. A.

    2014-01-01

    In this paper we develop a mathematical model for the dynamics of a nonlinear Timoshenko beam with piezoelectric actuation. This model can then be used to design controllers with the goal of achieving a desired shape of the beam. The control scheme can be used for several applications, e. g., vibrat

  1. Transverse beam splitting made operational: Recent progress of the multi-turn extraction at the CERN proton synchrotron

    CERN Document Server

    AUTHOR|(CDS)2082016; Borburgh, Jan; Damjanovic, Sanja; Gilardoni, Simone; Giovannozzi, Massimo; Hourican, Michael; Kahle, Karsten; Michels, Olivier; Sterbini, Guido; Hernalsteens, Cedric; Le Godec, Gilles

    2016-01-01

    Following a successful commissioning period, the Multi-Turn Extraction (MTE) at the CERN Proton Synchrotron (PS) has been applied for the fixed-target physics programme at the Super Proton Synchrotron (SPS) since September 2015. This exceptional extraction technique was proposed to replace the long-serving Continuous Transfer (CT) extraction, which has the drawback of inducing high activation in the ring. MTE exploits the principles of non-linear beam dynamics to perform loss-free beam splitting in the horizontal phase space. Over multiple turns, the resulting beamlets are then transferred to the downstream accelerator. The operational deployment of MTE was rendered possible by the full understanding and mitigation of different hardware limitations and by redesigning the extraction trajectories and non-linear optics, which was required due to the installation of a dummy septum to reduce the activation of the magnetic extraction septum. The results of the related experimental and simulation studies, a summary ...

  2. SOME PROBLEMS CONCERNING FREE NON-LINEAR VIBRATIONS OF BEAM STRUCTURES

    Directory of Open Access Journals (Sweden)

    S. V. Bosakov

    2008-01-01

    Full Text Available The paper analyzes an influence of physical non-linearity material account on vibrations of single beams with various support fixing. The authors also analyze power criteria for existing stable periodic vibrations and dependence of vibration period on initial power is determined in the paper. Accurate values of an amplitude and non-linear bending vibration period of beams have been also determined as a conservative system with due account of initial conditions. A number of examples are given that clearly illustrate the obtained solutions and show an influence rate of the mentioned effects on amplitude-frequency characteristics of non-linear systems. 

  3. Reciprocity breaking during nonlinear propagation of adapted beams through random media

    CERN Document Server

    Palastro, J P; Nelson, W; DiComo, G; Johnson, L A; Helle, M H; Hafizi, B

    2016-01-01

    Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate profile aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.

  4. Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

    Directory of Open Access Journals (Sweden)

    Peng Liu

    2016-01-01

    Full Text Available A new model for the free transverse vibration of axially functionally graded (FG tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved.

  5. Study of Slow Beam Extraction Through the Third Order Resonance with Transverse Phase Space Manipulation by a Mono-Frequency RFKO

    CERN Document Server

    Miyamoto, Atsushi; Hinode, Fujio; Kawai, Masayuki; Shinto, Katsuhiro; Tanaka, Takumi

    2005-01-01

    An electron pulse-stretcher ring (STB ring) has a function which converts a pulse beam generated by RF linac into a quasi-continuous beam. Circulating beam in the ring is extracted by the third order resonance. Since there is no accelerating field in the ring, the beam approaches a transverse resonance condition due to synchrotron radiation loss with finite chromaticity. The extracted beam from the ring has some spread in time and space corresponding to injected beam from linac even if the injected beam is perfectly matched to the ring optics. However, the extracted beam emittance can be reduced by applying a phase space manipulation using an RF shaker. Under the influence of perturbation using an RF shaker driven by a mono-frequency, the betatron amplitude of circulating beam can be controlled in order to reduce the extracted beam emittance. The experimental results will be reported in this conference.

  6. Lie algebraic analysis for the nonlinear transport of intense bunched beam in electrostatic quadrupoles

    Institute of Scientific and Technical Information of China (English)

    ZHANG Zhuo; L(U) Jian-Qin

    2008-01-01

    In this paper, the nonlinear transport of intense bunched beams in electrostatic quadrupoles is analyzed using the Lie algebraic method, and the results are briefly presented of the linear matrix approximation and the second order correction of particle trajectory in the state space. Beam having K-V distribution and Gaussian distribution approximation are respectively considered. A brief discussion is also given of the total effects of the quadrupole and the space charge forces on the evolution of the beam envelope.

  7. Plasmon beams interaction at interface between metal and dielectric with saturable Kerr nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Ignatyeva, Daria O.; Sukhorukov, Anatoly P. [Lomonosov Moscow State University, Moscow (Russian Federation)

    2012-12-15

    We present a novel theory of surface plasmon polariton interaction on the surface of dielectric with saturable Kerr nonlinearity. The effect of the total internal reflection of a weak signal plasmon beam from a high-power reference beam is discussed. Both ray and wave theories are used to describe signal propagation. The effect of the signal tunneling through the narrow inhomogeneity induced by the reference beam is considered. (orig.)

  8. Measurement of azimuthal asymmetries with respect of both beam charge and transverse target polarization in exclusive electroproduction of real photons

    Energy Technology Data Exchange (ETDEWEB)

    Airapetian, A. [DESY Hamburg (Germany); Akopov, N.; Akopov, Z. [Yerevan Physics Institute (AR)] (and others)

    2008-02-15

    Azimuthal asymmetries in exclusive electroproduction of real photons are measured for the first time with respect to transverse target polarisation, providing new constraints on Generalized Parton Distributions. From the same data set on a hydrogen target, new results for the beam-charge asymmetry are also extracted with better precision than those previously reported. By comparing model calculations with measured asymmetries attributed to the interference between the deeply virtual Compton scattering and Bethe-Heitler processes, a model-dependent constraint is obtained on the total angular momenta carried by up and down quarks in the nucleon. (orig.)

  9. Measurement of Azimuthal Asymmetries With Respect To Both Beam Charge and Transverse Target Polarization in Exclusive Electroproduction of Real Photons

    CERN Document Server

    Airapetian, A; Akopov, Z; Andrus, A; Aschenauer, E C; Augustyniak, W; Avakian, R; Avetisian, A; Avetisyan, E; Barion, L; Belostotskii, S; Bianchi, N; Blok, H P; Bttcher, H; Bonomo, C; Borisov, A; Brüll, A; Bryzgalov, V; Burns, J; Capiluppi, M; Capitani, G P; Cisbani, E; Ciullo, G; Contalbrigo, M; Dalpiaz, P F; Deconinck, W; De Leo, R; Demey, M; De Nardo, L; De Sanctis, E; Diefenthaler, M; Di Nezza, P; Dreschler, J; Düren, M; Ehrenfried, M; Elbakian, G; Ellinghaus, F; Elschenbroich, U; Fabbri, R; Fantoni, A; Felawka, L; Frullani, S; Funel, A; Gabbert, D; Gapienko, G; Gapienko, V; Garibaldi, F; Gavrilov, G; Karibian, V; Giordano, F; Gliske, S; Guler, H; Hadjidakis, C; Hasch, D; Hasegawa, T; Hill, G; Hillenbrand, A; Hoek, M; Holler, Y; Hristova, I; Iarygin, G; Imazu, Y; Ivanilov, A; Izotov, A; Jackson, H E; Jgoun, A; Joosten, S; Kaiser, R; Keri, T; Kinney, E; Kiselev, A; Kopytin, M; Korotkov, V; Kozlov, V; Kravchenko, P; Krivokhizhin, V G; Lagamba, L; Lamb, R; Lapiks, L; Lehmann, I; Lenisa, P; Linden-Levy, L A; Lorenzon, W; Lu, S; Lü, X; Ma, B Q; Mahon, D; Maiheu, B; Makins, N C R; Mao, Y; Marianski, B; Marukyan, H; Miller, C A; Miyachi, Y; Muccifora, V; Murray, M; Mussgiller, A; Nagaitsev, A; Nappi, E; Naryshkin, Yu; Nass, A; Negodaev, M; Nowak, W D; Osborne, A; Pappalardo, L L; Perez-Benito, R; Pickert, N; Raithel, M; Reimer, P E; Reischl, A; Reolon, A R; Riedl, C; Rith, K; Rock, S E; Rosner, G; Rostomyan, A; Rubacek, L; Rubin, J; Ruiz, A L; Ryckbosch, D; Salomatin, Y; Sanjiev, I; Schäfer, A; Schnell, G; Schüler, K P; Seitz, B

    2008-01-01

    Azimuthal asymmetries in exclusive electroproduction of real photons are measured for the first time with respect to transverse target polarisation, providing new constraints on Generalized Parton Distributions. From the same data set on a hydrogen target, new results for the beam-charge asymmetry are also extracted with better precision than those previously reported. By comparing model calculations with measured asymmetries attributed to the interference between the deeply virtual Compton scattering and Bethe-Heitler processes, a model-dependent constraint is obtained on the total angular momenta carried by up and down quarks in the nucleon.

  10. Propagation of Gaussian beam in longitudinally inhomogeneous nonlinear graded index waveguides with gain and losses

    CERN Document Server

    Yesayan, G L

    2001-01-01

    The equations for the width and curvature radius of the wave front for a Gaussian beam of light propagating along the axis of the longitudinally inhomogeneous graded index waveguide with gain and losses in the presence of third-order nonlinearity are obtained. By means of numerical calculations it is shown that in such waveguides the mode of stabilization of the beam width is possible, when the absorption of radiation on the edges of the beam compensates its spreading caused by the longitudinal inhomogeneity and nonlinearity of the waveguide

  11. Determining critical load in the multispan beams with the nonlinear model

    Science.gov (United States)

    DemÑ-r, D. Dönmez; Sinir, B. G.; Usta, L.

    2017-01-01

    The beams which are one of the most commonly used structural members are quite important for many researchers. Mathematical models determining the response of beams under external loads are concluded from elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. In this study, the derivation of the nonlinear model is introduced to determine the critical load in the multispan beams. Since the engineering practice of this kind of problems is very common, determining the critical load is quite important. For this purpose, the nonlinear mathematical model of the multispan Euler-Bernoulli beam is firstly obtained. To be able to obtain the independent of the material and the geometry, the present model are became dimensionless. Then, the critical axial load can be determined via the nonlinear solution of the governing equation.

  12. A simple numerical model of a geometrically nonlinear Timoshenko beam

    NARCIS (Netherlands)

    Keijdener, C.; Metrikine, A.

    2015-01-01

    In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and tran

  13. Free vibration analysis of pre-stressed FGM Timoshenko beams under large transverse deflection by a variational method

    Directory of Open Access Journals (Sweden)

    Amlan Paul

    2016-06-01

    Full Text Available A theoretical study on free vibration behavior of pre-stressed functionally graded material (FGM beam is carried out. Power law variation of volume fraction along the thickness direction is considered. Geometric non-linearity is incorporated through von Kármán non-linear strain–displacement relationship. The governing equation for the static problem is obtained using minimum potential energy principle. The dynamic problem for the pre-stressed beam is formulated as an eigenvalue problem using Hamilton's principle. Three classical boundary conditions with immovable ends are considered for the present work, namely clamped–clamped, simply supported–simply supported and clamped–simply supported. Four different FGM beams, namely Stainless Steel–Silicon Nitride, Stainless Steel–Zirconia, Stainless Steel–Alumina and Titanium alloy–Zirconia, are considered for generation of results. Numerical results for non-dimensional frequency parameters of undeformed beam are presented. The results are presented in non-dimensional pressure-displacement plane for the static problem and in non-dimensional frequency-displacement plane for the dynamic problem. Comparative frequency-displacement plots are presented for different FGMs and also for different volume fraction indices.

  14. Controlling Beam Halo-chaos Using a Special Nonlinear Method

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power

  15. Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beams with Damage on a Viscoelastic Foundation

    Institute of Scientific and Technical Information of China (English)

    盛冬发; 张燕; 程昌钧

    2004-01-01

    Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.

  16. Efficiency of feedbacks for suppression of transverse instabilities of bunched beams

    CERN Document Server

    Burov, Alexey

    2016-01-01

    Which gain and phase have to be set for a bunch-by-bunch transverse damper, and at which chromaticity it is better to stay? These questions are considered for three models: the two-particle model with possible quadrupole wake, the author's Nested Head-Tail Vlasov solver with a broadband impedance, and the same with the LHC impedance model.

  17. Nonlinear dynamic response of beam and its application in nanomechanical resonator

    Institute of Scientific and Technical Information of China (English)

    Yin Zhang; Yun Liu; Kevin D. Murphy

    2012-01-01

    Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application.Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed.The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach.The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity,its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects.However,for the nanomechanical resonator of the curvature-dominant nonlinearity,its dynamic nonlinearity is only dependent on axial loading.Compared with the tension-dominant nonlinearity,the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects.The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.

  18. Nonlinear Dynamic Analysis of Functionally Graded Timoshenko Beam fixed to a Rotating Hub

    Science.gov (United States)

    Panigrahi, B.; Pohit, G.

    2016-08-01

    The present work accounts centrifugal stiffening effect on the nonlinear vibration response of an FGM Timoshenko beam. Analysis is carried out for a cantilever beam fixed with a rotating hub. Material is assumed to have a gradation relation along the depth of the beam. Centrifugal force and axial displacement raised due to the rotating hub is incorporated in the strain energy equations. Subsequent to this, an iterative technique is employed to obtain amplitude dependent vibration response of a rotating Timoshenko beam while material follows a gradation relation along the beam depth. Main objective of the work is to obtain the effects of rotational speeds, hub radius, and different gradation relations on the linear as well as nonlinear frequencies and mode shapes.

  19. Three-dimensional multispecies nonlinear perturbative particle simulations of collective processes in intense particle beams

    Directory of Open Access Journals (Sweden)

    Hong Qin

    2000-08-01

    Full Text Available Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment. Detailed simulations in a parameter regime characteristic of the PSR experiment show that the dipole-mode two-stream instability is stabilized by a modest spread (about 0.1% in axial momentum of the beam particles.

  20. Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams

    CERN Document Server

    Porras, Miguel A; Losada, Juan Carlos

    2015-01-01

    In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward H\\"ankel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines de NL-UBB attractor is given. Steady or unsteady propagation depends on whether the attracting NL-UBB has a small, exponentially growing, unstable mode. In case of unsteady propagation, periodic, quasi-periodic or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.

  1. Nonlinear Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System

    Institute of Scientific and Technical Information of China (English)

    FANG JinQing; CHEN GuanRong; ZHOU LiuLai; WENG JiaQiang

    2002-01-01

    Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry, medicine, and national defense. Some general engineering methods for chaos control have been developed in recent years, but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints. Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator. In this paper, some efficient nonlinear control methods, including wavelet function feedback control as a special nonlinear control method, are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e., Kapchinsky-Vladimirsky, full Gauss,3-sigma Gauss, water-bag, and parabola distributions) respectively. Particles-in-cell simulations show that after control of beam halo-chaos, the beam halo strength factor is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator. Some potential application of the beam halo-chaos control in experiments is finally pointed out.

  2. Transverse vibrations of a linearly tapered cantilever beam with constraining springs

    Science.gov (United States)

    Craver, W. L., Jr.; Jampala, P.

    1993-09-01

    The free vibrations of a linearly tapered cantilever beam, elastically constrained at an arbitrary position along the length of the beam, have been investigated using the Bernoulli-Euler equation. The beam has a rectangular cross-section with equal taper in the horizontal and vertical planes, and the constraint is a translational spring. The characteristic determinant is derived in terms of dimensionless spring constant, and the eigenfrequencies are determined using a straight search and bisection method. The results are presented in tabular and graphical form.

  3. RTA beam dynamics experiments: Limiting cumulative transverse instability growth in a linear periodic system

    Science.gov (United States)

    Houck, Tim; Lidia, Steve; Westenskow, Glen

    2001-05-01

    A critical issue for a Two-Beam accelerator based upon extended relativistic klystrons is controlling the cumulative dipole instability growth. We describe a theoretical scheme to reduce the growth from an exponential to a more manageable linear rate, and a new experiment to test this concept. The experiment utilizes a 1-MeV, 600-Amp, 200-ns electron beam and a short beamline of periodically spaced RF dipole pillbox cavities and solenoid magnets for transport. Descriptions of the RTA injector and the planned beamline are presented, followed by theoretical studies of the beam transport and dipole mode growth.

  4. Generation of High Brightness Electron Beams via Ionization Induced Injection by Transverse Colliding Lasers in a Beam-Driven Plasma Wakefield Accelerator

    CERN Document Server

    Li, F; Xu, X L; Zhang, C J; Yan, L X; Du, Y C; Huang, W H; Cheng, H B; Tang, C X; Lu, W; Joshi, C; Mori, W B; Gu, Y Q

    2013-01-01

    The production of ultra-bright electron bunches using ionization injection triggered by two transversely colliding laser pulses inside a beam-driven plasma wake is examined via three-dimensional (3D) particle-in-cell (PIC) simulations. The relatively low intensity lasers are polarized along the wake axis and overlap with the wake for a very short time. The result is that the residual momentum of the ionized electrons in the transverse plane of the wake is much reduced and the injection is localized along the propagation axis of the wake. This minimizes both the initial 'thermal' emittance and the emittance growth due to transverse phase mixing. 3D PIC simulations show that ultra-short (around 8 fs) high-current (0.4 kA) electron bunches with a normalized emittance of 8.5 and 6 nm in the two planes respectively and a brightness greater than 1.7*10e19 A rad-2 m-2 can be obtained for realistic parameters.

  5. Polarization of a probe laser beam due to nonlinear QED effects

    Science.gov (United States)

    Shakeri, Soroush; Kalantari, Seyed Zafarollah; Xue, She-Sheng

    2017-01-01

    Nonlinear QED interactions induce different polarization properties on a given probe beam. We consider the polarization effects caused by the photon-photon interaction in laser experiments, when a laser beam propagates through a constant magnetic field or collides with another laser beam. We solve the quantum Boltzmann equation within the framework of the Euler-Heisenberg Lagrangian for both time-dependent and constant background field to explore the time evolution of the Stokes parameters Q, U, and V describing polarization. Assuming an initially linearly polarized probe laser beam, we also calculate the induced ellipticity and rotation of the polarization plane.

  6. Nonlinear delta f Simulations of Collective Effects in Intense Charged Particle Beams

    CERN Document Server

    Hong Qi

    2003-01-01

    A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, ...

  7. Estimation of blood velocity vectors using transverse ultrasound beam focusing and cross-correlation

    DEFF Research Database (Denmark)

    Jensen, Jørgen Arendt; Lacasa, Isabel Rodriguez

    1999-01-01

    Modern ultrasound scanners estimate the blood velocity by tracking the movement of the blood scatterers along the ultrasound beam. This is done by emitting pulsed ultrasound fields and finding the shift in position from pulse to pulse by correlating the received signals. Only the velocity component...... along the beam direction is found, and this is a serious limitation in the current scanners, since most blood vessels are parallel to the skin surface. A method to find the velocity across the vessel has been suggested by Bonnefous (1988). Here a number of parallel receive beams are measured and used...... or across it or in any direction to the beam. The focused lines, thus, follow the flow and a cross-correlation of lines from different pulses can find the movement of the blood particles between pulse emissions and, thus, the blood velocity. The new approach is investigated using the Field II simulation...

  8. Direction-sensitive transverse velocity measurement by phase-modulated structured light beams

    OpenAIRE

    2014-01-01

    The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge because detection is usually done by means of an interferometric setup, which only provides an absolute value of the frequency shift. In this Letter, we present a novel method that addresses this issue. It uses dynamic control of the phase in the transv...

  9. Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators.

    Science.gov (United States)

    Nourmohammadi, Zahra; Joshi, Surabhi; Vengallatore, Srikar

    2016-01-01

    The linear theory of thermoelastic damping (TED) has been extensively developed over the past eight decades, but relatively little is known about the different types of nonlinearities that are associated with this fundamental mechanism of material damping. Here, we initiate the study of a dissipative nonlinearity (also called thermomechanical nonlinearity) whose origins reside at the heart of the thermomechanical coupling that gives rise to TED. The finite difference method is used to solve the nonlinear governing equation and estimate nonlinear TED in Euler-Bernoulli beams. The maximum difference between the nonlinear and linear estimates ranges from 0.06% for quartz and 0.3% for silicon to 7% for aluminum and 28% for zinc.

  10. Nonlinear generation of whistler waves by an ion beam

    Science.gov (United States)

    Akimoto, K.; Winske, D.

    1989-01-01

    An electromagnetic hybrid code is used to simulate a new mechanism for whistler wave generation by an ion beam. First, a field-aligned ion beam becomes unstable to the electromagnetic ion/ion right-hand resonant instability which generates large amplitude MHD-like waves. These waves then trap the ion beam and increase its effective temperature anisotropy. As a result, the growth rates of the electron/whistler instability are significantly enhanced, and whistlers start to grow above the noise level. At the same time, because of the reduced parallel drift speed of the ion beam, the frequencies of the whistlers are also downshifted. Full simulations were performed to isolate and separately investigate the electron/ion whistler instability. The results are in agreement with the assumption of fluid electrons in the hybrid simulations and with the linear theory of the instability.

  11. Free-Space Nonlinear Beam Combining Towards Filamentation

    CERN Document Server

    Rostami, Shermineh; Kepler, Daniel; Baudelet, Matthieu; Litchinitser, Natalia M; Richardson, Martin

    2016-01-01

    Multi-filamentation opens new degrees of freedom for manipulating electromagnetic waves in air. However, without control, multiple filament interactions, including attraction, repulsion or fusion often result in formation of complex disordered filament distributions. Moreover, high power beams conventionally used in multi-filament formation experiments often cause significant surface damage. The growing number of applications for laser filaments requires fine control of their formation and propagation. We demonstrate, experimentally and theoretically, that the attraction and fusion of ultrashort beams with initial powers below the critical value enable the eventual formation of a filament downstream. Filament formation is delayed to a predetermined distance in space, avoiding optical damage to external beam optics while still enabling robust filaments with controllable properties as if formed from a single high power beam. This paradigm introduces new opportunities for filament engineering eliminating the nee...

  12. Nonlinear interaction of intense hypergeometric Gaussian subfamily laser beams in plasma

    Science.gov (United States)

    Sobhani, H.; Vaziri (Khamedi), M.; Rooholamininejad, H.; Bahrampour, A. R.

    2016-07-01

    Propagation of Hypergeometric-Gaussian laser beam in a nonlinear plasma medium is investigated by considering the Source Dependent Expansion method. A subfamily of Hypergeometric-Gaussian beams with a non-negative, even and integer radial index, can be expressed as the linear superposition of finite number of Laguerre-Gaussian functions. Propagation of Hypergeometric-Gaussian beams in a nonlinear plasma medium depends on the value of radial index. The bright rings' number of these beams is changed during the propagation in plasma medium. The effect of beam vortex charge number l and initial (input) beam intensity on the self-focusing of Hypergeometric-Gaussian beams is explored. Also, by choosing the suitable initial conditions, Hypergeometric-Gaussian subfamily beams can be converted to one or more mode components that a typical of mode conversion may be occurred. The self-focusing of these winding beams can be used to control the focusing force and improve the electron bunch quality in laser plasma accelerators.

  13. A theoretical and experimental study on geometric nonlinearity of initially curved cantilever beams

    Directory of Open Access Journals (Sweden)

    Sushanta Ghuku

    2016-03-01

    Full Text Available This paper presents a theoretical and experimental study on large deflection behavior of initially curved cantilever beams subjected to various types of loadings. The physical system as a straight cantilever beam subjected to a tip concentrated load is considered in this study. Nonlinear differential equations are obtained for large deflection analysis of such a straight cantilever beam, and this problem is known to involve geometrical nonlinearity. The equations are solved numerically with the help of MATLAB® computational platform to get deflection profiles of the concerned problem. These results are imposed subsequently on the center line of an initially curved beam to get theoretical load-deflection behavior of curved beam problems. To verify the theoretical model, experiment is carried out with the master leaf of a leaf spring bundle by modeling it as an initially curved cantilever beam. The effects of initial clamping and geometry variations in the eye-region are observed from experimental investigation which is commonly neglected in the mathematical formulation. Comparisons of the theoretical results with the experimental results are quite good, but the avenues for further improvement are also reported. The proposed approach is further extended to study large deflection behavior of an initially curved cantilever beam subjected to distributed and combined load. These results are successfully validated with existing results for straight beams and some new results are furnished for initially curved cantilever beams.

  14. Simulation of transverse beam splitting using time-dependent dipolar or quadrupolar kicks

    CERN Document Server

    Capoani, Federico

    2017-01-01

    Two simple systems with high relevance for accelerator physics have been studied in detail in the context of this Summer Student Project. These systems describe the motion under the influence of detuning with amplitude due to non-linear magnets and an external, time-dependent force of dipolar or quadrupolar nature.Two simple systems with high relevance for accelerator physics have been studied in detail in the context of this Summer Student Project. These systems describe the motion under the influence of detuning with amplitude due to non-linear magnets and an external, time-dependent force of dipolar or quadrupolar nature.

  15. Efficiency enhancement of a two-beam free-electron laser using a nonlinearly tapered wiggler

    Institute of Scientific and Technical Information of China (English)

    Maryam Zahedian; B.Maraghechi; M.H.Rouhani

    2012-01-01

    A nonlinear and non-averaged model of a two-beam free-electron laser (FEL) wiggler that is tapered nonlinearly in the absence of slippage is presented.The two beams are assumed to have different energies,and the fundamental resonance of the higher energy beam is at the third harmonic of the lower energy beam.By using Maxwell's equations and the full Lorentz force equation of motion for the electron beams,coupled differential equations are derived and solved numerically by the fourth-order Runge-Kutta method.The amplitude of the wiggler field is assumed to decrease nonlinearly when the saturation of the third harmonic occurs.By simulation,the optimum starting point of the tapering and the slopes for reducing the wiggler amplitude are found.This technique can be applied to substantially improve the efficiency of the two-beam FEL in the XUV and X-ray regions.The effect of tapering on the dynamical stability of the fast electron beam is also studied.

  16. An efficient and accurate method for calculating nonlinear diffraction beam fields

    Energy Technology Data Exchange (ETDEWEB)

    Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)

    2016-04-15

    This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.

  17. Active suppression of nonlinear composite beam vibrations by selected control algorithms

    Science.gov (United States)

    Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal

    2011-05-01

    This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.

  18. Nonlinear features identified by Volterra series for damage detection in a buckled beam

    Directory of Open Access Journals (Sweden)

    Shiki S. B.

    2014-01-01

    Full Text Available The present paper proposes a new index for damage detection based on nonlinear features extracted from prediction errors computed by multiple convolutions using the discrete-time Volterra series. A reference Volterra model is identified with data in the healthy condition and used for monitoring the system operating with linear or nonlinear behavior. When the system has some structural change, possibly associated with damage, the index metrics computed could give an alert to separate the linear and nonlinear contributions, besides provide a diagnostic about the structural state. To show the applicability of the method, an experimental test is performed using nonlinear vibration signals measured in a clamped buckled beam subject to different levels of force applied and with simulated damages through discontinuities inserted in the beam surface.

  19. Diffraction corrections for second harmonic beam fields and effects on the nonlinearity parameter evaluation

    Energy Technology Data Exchange (ETDEWEB)

    Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)

    2016-04-15

    The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter β. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of β on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved β values can be obtained by considering the diffraction effects.

  20. Role of Density Profiles for the Nonlinear Propagation of Intense Laser Beam through Plasma Channel

    OpenAIRE

    Sonu Sen; Meenu Asthana Varshney; Dinesh Varshney

    2014-01-01

    In this work role of density profiles for the nonlinear propagation of intense laser beam through plasma channel is analyzed. By employing the expression for the dielectric function of different density profile plasma, a differential equation for beamwidth parameter is derived under WKB and paraxial approximation. The laser induces modifications of the dielectric function through nonlinearities. It is found that density profiles play vital role in laser-plasma interaction studies. To have num...

  1. A new solution procedure for a nonlinear infinite beam equation of motion

    Science.gov (United States)

    Jang, T. S.

    2016-10-01

    Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

  2. The Nonlinear Interaction of Two-Crossed Focussed Ultrasonic Beams in the Presence of Turbulence

    Science.gov (United States)

    1988-06-10

    in water or any fluid medium can be obtained by the vibration of a solid body in the fluid, such as the vibration of a vocal chord or guitar string . In... physical phenomenon due to the nonlinearity of sound arises from the interaction of two sound beams. Nonlinear acoustic theory predictions by Westervelt in...known experimental data for the turbulent velocity field. Goals of this research include mapping out the turbulence and studying the physical

  3. Coupled transverse and torsional vibrations in a mechanical system with two identical beams

    Science.gov (United States)

    Vlase, S.; Marin, M.; Scutaru, M. L.; Munteanu, R.

    2017-06-01

    The paper aims to study a plane system with bars, with certain symmetries. Such problems can be encountered frequently in industry and civil engineering. Considerations related to the economy of the design process, constructive simplicity, cost and logistics make the use of identical parts a frequent procedure. The paper aims to determine the properties of the eigenvalues and eigenmodes for transverse and torsional vibrations of a mechanical system where two of the three component bars are identical. The determination of these properties allows the calculus effort and the computation time and thus increases the accuracy of the results in such matters.

  4. Efficiency of feedbacks for suppression of transverse instabilities of bunched beams

    Science.gov (United States)

    Burov, Alexey

    2016-08-01

    Which gain and phase have to be set for a bunch-by-bunch transverse damper, and at which chromaticity is it better to stay? These questions are considered for three models: the two-particle model with possible quadrupole wake, the author's nested head-tail (NHT) model with the broadband impedance, and the NHT with the LHC impedance model. Details of 2D areas of stability in the chromaticity-intensity and chromaticity-gain planes and possibilities to use them are discussed. It is shown that resistive feedbacks may generate asymmetry of the tune shift distribution, which requires positively-shifted stability diagrams.

  5. Operational performance of the CERN injector complex with transversely split beams

    Science.gov (United States)

    Abernethy, S.; Akroh, A.; Bartosik, H.; Blas, A.; Bohl, T.; Cettour-Cave, S.; Cornelis, K.; Damerau, H.; Gilardoni, S.; Giovannozzi, M.; Hernalsteens, C.; Huschauer, A.; Kain, V.; Manglunki, D.; Métral, G.; Mikulec, B.; Salvant, B.; Sanchez Alvarez, J.-L.; Steerenberg, R.; Sterbini, G.; Wu, Y.

    2017-01-01

    With the progress made in 2015, the beams produced by the CERN Proton Synchrotron using multiturn extraction (MTE) have been delivered to the Super Proton Synchrotron (SPS) for the fixed-target physics run. Operation successfully started in the second half of September 2015 and continued until the end of the proton physics program by mid November. In this paper the overall performance and beam quality is discussed in detail considering the complete chain of accelerators, from the PS-Booster to the SPS. Moreover, a thorough comparison of the global performance of the MTE scheme against the previously used technique, the so-called continuous transfer (CT), is also carried out.

  6. NONLINEAR ANALYSIS OF CFRP- PRESTRESSED CONCRETE BEAMS SUBJECTED TO INCREMENTAL STATIC LOADING BY FINITE ELEMENTS

    Directory of Open Access Journals (Sweden)

    Husain M. Husain

    2013-05-01

    Full Text Available In this work a program is developed to carry out the nonlinear analysis (material nonlinearity of prestressed concrete beams using tendons of carbon fiber reinforced polymer (CFRP instead of steel. The properties of this material include high strength, light weight, and insusceptibility to corrosion and magnetism. This material is still under investigation, therefore it needs continuous work to make it beneficial in concrete design. Four beams which are tested experimentally by Yan et al. are examined by the developed computer program to reach a certain analytical approach of the design and analysis of such beams because there is no available restrictions or recommendations covering this material in the codes. The program uses the finite element analysis by dividing the beams into isoparametric 20-noded brick elements. The results obtained are good in comparison with experimental results.

  7. Numerical simulation of nonlinear processes in a beam-plasma system

    Energy Technology Data Exchange (ETDEWEB)

    Efimova, A. A., E-mail: anna.an.efimova@gmail.com; Berendeev, E. A.; Vshivkov, V. A. [Institute of Computational Mathematics and Mathematical Geophysics SB RAS 6 Acad. Lavrentyev Ave., Novosibirsk 630090 (Russian Federation); Dudnikova, G. I. [University of Maryland, College Park, MD 20742 (United States); Institute of Computational Technologies SB RAS, 6 Acad. Lavrentyev Ave., Novosibirsk 630090 (Russian Federation)

    2015-10-28

    In the present paper we consider the efficiency of the electromagnetic radiation generation due to various nonlinear processes in the beam-plasma system. The beam and plasma parameters were chosen close to the parameters in the experiment on the GOL-3 facility (BINP SB RAS). The model of the collisionless plasma is described by system of the Vlasov-Maxwell equations with periodic boundary conditions. The parallel numerical algorithm is based on the particles-in-cell method (PIC) with mixed Euler-Lagrangian domain decomposition. Various scenarios of nonlinear evolution in the beam-plasma system under the influence of an external magnetic field in case of a low density beam were studied. The energy transfer from one unstable mode to the others modes was observed.

  8. Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media

    Science.gov (United States)

    Wu, Zhen-Kun; Li, Peng; Gu, Yu-Zong

    2017-10-01

    We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.

  9. Active Vibration Control of a Nonlinear Beam with Self- and External Excitations

    Directory of Open Access Journals (Sweden)

    J. Warminski

    2013-01-01

    Full Text Available An application of the nonlinear saturation control (NSC algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.

  10. Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices

    DEFF Research Database (Denmark)

    Mamaev, A.V.; Saffman, M.; Zozulya, A.A.

    1996-01-01

    We analyze the evolution of (1+1) dimensional dark stripe beams in bulk media with a photorefractive nonlinear response. These beams, including solitary wave solutions, are shown to be unstable with respect to symmetry breaking and formation of structure along the initially homogeneous coordinate....... Experimental results show the complete sequence of events starting from self-focusing of the stripe, its bending due to the snake instability, and subsequent decay into a set of optical vortices....

  11. Interactions between self-channeled optical beams in soft-matter systems with artificial nonlinearities.

    Science.gov (United States)

    Fardad, Shima; Mills, Matthew S; Zhang, Peng; Man, Weining; Chen, Zhigang; Christodoulides, D N

    2013-09-15

    We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions.

  12. EFFECTS OF TRANSFERSE BEAM SIZE IN BEAM POSITIONS MONITORS

    Energy Technology Data Exchange (ETDEWEB)

    S.S. KURENNOY

    2001-06-01

    The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by the displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those from a pencil beam. The non-linearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.

  13. Tunable strong nonlinearity of a micromechanical beam embedded in a dc-superconducting quantum interference device

    Energy Technology Data Exchange (ETDEWEB)

    Ella, Lior, E-mail: lior.ella@weizmann.ac.il; Yuvaraj, D.; Suchoi, Oren; Shtempluk, Oleg; Buks, Eyal [Faculty of Electrical Engineering, Technion, Haifa 32000 (Israel)

    2015-01-07

    We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.

  14. Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems

    Energy Technology Data Exchange (ETDEWEB)

    Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics

    2017-06-01

    Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

  15. Analytic Approximations to Nonlinear Boundary Value Problems Modeling Beam-Type Nano-Electromechanical Systems

    Science.gov (United States)

    Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.

    2017-03-01

    Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

  16. On the Possibility of Using Nonlinear Elements for Landau Damping in High-Intensity Beams

    Energy Technology Data Exchange (ETDEWEB)

    Alexahin, Y. [Fermilab; Gianfelice-Wendt, E. [Fermilab; Lebedev, V. [Fermilab; Valishev, A. [Fermilab

    2016-09-30

    Direct space-charge force shifts incoherent tunes downwards from the coherent ones breaking the Landau mechanism of coherent oscillations damping at high beam intensity. To restore it nonlinear elements can be employed which move back tunes of large amplitude particles. In the present report we consider the possibility of creating a “nonlinear integrable optics” insertion in the Fermilab Recycler to host either octupoles or hollow electron lens for this purpose. For comparison we also consider the classic scheme with distributed octupole families. It is shown that for the Proton Improvement Plan II (PIP II) parameters the required nonlinear tune shift can be created without destroying the dynamic aperture.

  17. Comparison between Laboratory Measurements, Simulations and Analytical Predictions of the Resistive Wall Transverse Beam Impedance at low frequencies

    CERN Document Server

    Roncarolo, F; Kroyer, T; Métral, E; Salvant, B

    2008-01-01

    The prediction of the resistive wall transverse beam impedance at the first unstable betatron line (8 kHz) of the CERN Large Hadron Collider (LHC) is of paramount importance for understanding and controlling the related coupled-bunch instability. Until now only novel analytical formulas were available at this frequency. Recently, laboratory measurements and numerical simulations were performed to crosscheck the analytical predictions. The experimental results based on the measurement of the variation of a probe coil inductance in the presence of i) sample graphite plates, ii) stand-alone LHC collimator jaws and iii) a full LHC collimator assembly are presented in detail. The measurement results are compared to both analytical theories and simulations. In addition, the consequences for the understanding of the LHC impedance are discussed.

  18. Analysis of residual stresses on the transverse beam of a casting stand by means of drilling method

    Directory of Open Access Journals (Sweden)

    P. Frankovský

    2014-10-01

    Full Text Available The presented paper demonstrates the application of drilling method in the analysis of residual stresses on the transverse beam of a casting stand. In the initial stage of the analysis the determination of strains was done for individual steps of drilling in the area which was determined by means of numerical analysis. The drilling was carried out gradually by 0,5 mm up to the depth of 5 mm, while the diameter of the drilled hole was 3,2 mm. During the analysis we used the drilling device RS-200, strain indicator P3 and SGD 1-RY21-3/120. The paper presents the development of residual stresses throughout the depth of the drilled hole which were determined according to standard ASTM E837-01, by means of integral method, power series method and by means of Power Series method.

  19. Optimizing nonlinear beam coupling in low-symmetry crystals.

    Science.gov (United States)

    Shumelyuk, A; Volkov, A; Odoulov, S; Grabar, A; Stoyka, I; Evans, D R

    2014-10-01

    The purpose of this paper is to find the polarizations and spatial orientations of the two interacting counterpropagating coherent light waves which ensure the largest beam coupling in monoclinic photorefractive crystal. The results of calculations are presented that are verified experimentally with Sn₂P₂S₆.

  20. Nonlinear Vibration of an Elastically Restrained Tapered Beam

    DEFF Research Database (Denmark)

    Karimpour, S; Ganji, S.S; Barari, Amin;

    2012-01-01

    This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method (EBM) and the iteration perturbation method (IPM). To assess the accuracy of solutions, we compare the results with the harmonic balance method (HBM). The obtained re...

  1. Non-Linear Beam Transport System for the LENS 7 MeV Proton Beam

    CERN Document Server

    Jones, William P; Derenchuk, Vladimir Peter; Rinckel, Thomas; Solberg, Keith

    2005-01-01

    A beam transport system has been designed to carry a high-intensity low-emittance proton beam from the exit of the RFQ-DTL acceleration system of the Indiana University Low Energy Neutron System (LENS)* to the neutron production target. The goal of the design was to provide a beam of uniform density over a 3cm by 3cm area at the target. Two octupole magnets** are employed in the beam line to provide the necessary beam phase space manipulations to achieve this goal. First order calculations were done using TRANSPORT and second order calculations have been performed using TURTLE. Second order simulations have been done using both a Gaussian beam distribution and a particle set generated by calculations of beam transport through the RFQ-DTL using PARMILA. Comparison of the design characteristics with initial measurements from the LENS commissioning process will be made.

  2. Nonlinear dynamics and chaos in an optomechanical beam

    CERN Document Server

    Navarro-Urrios, D; Colombano, M F; Garcia, P D; Sledzinska, M; Alzina, F; Griol, A; Martinez, A; Sotomayor-Torres, C M

    2016-01-01

    Optical non-linearities, such as thermo-optic effects and free-carrier-dispersion, are often considered as undesired effects in silicon-based resonators and, more specifically, optomechanical (OM) cavities, affecting the relative detuning between an optical resonance and the excitation laser. However, the interplay between such mechanisms could also enable unexpected physical phenomena to be used in new applications. In the present work, we exploit those non-linearities and their intercoupling with the mechanical degrees of freedom of a silicon OM nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser, namely its power and wavelength, we demonstrate accurate control for activating bi-dimensional and tetra-dimensional limit-cycles, a period doubling route and chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between bi-dimensional and tetra-dimensional limit-cycles, be...

  3. Transverse self-modulation of ultra-relativistic lepton beams in the plasma wakefield accelerator

    CERN Document Server

    Vieira, J; Mori, W B; Silva, L O; Muggli, P

    2015-01-01

    The transverse self-modulation of ultra-relativistic, long lepton bunches in high-density plasmas is explored through full-scale particle-in-cell simulations. We demonstrate that long SLAC-type electron and positron bunches can become strongly self-modulated over centimeter distances, leading to wake excitation in the blowout regime with accelerating fields in excess of 20 GV/m. We show that particles energy variations exceeding 10 GeV can occur in meter-long plasmas. We find that the self-modulation of positively and negatively charged bunches differ when the blowout is reached. Seeding the self-modulation instability suppresses the competing hosing instability. This work reveals that a proof-of-principle experiment to test the physics of bunch self-modulation can be performed with available lepton bunches and with existing experimental apparatus and diagnostics.

  4. Gaussian-Schell analysis of the transverse spatial properties of high-harmonic beams

    CERN Document Server

    Lloyd, David T; Anderson, Patrick N; Hooker, Simon M

    2016-01-01

    High harmonic generation (HHG) is an established means of producing coherent, short wavelength, ultrafast pulses from a compact set-up. Table-top high-harmonic sources are increasingly being used to image physical and biological systems using emerging techniques such as coherent diffraction imaging and ptychography. These novel imaging methods require coherent illumination, and it is therefore important to both characterize the spatial coherence of high-harmonic beams and understand the processes which limit this property. Here we investigate the near- and far-field spatial properties of high-harmonic radiation generated in a gas cell. The variation with harmonic order of the intensity profile, wavefront curvature, and complex coherence factor is measured in the far-field by the SCIMITAR technique. Using the Gaussian-Schell model, the properties of the harmonic beam in the plane of generation are deduced. Our results show that the order-dependence of the harmonic spatial coherence is consistent with partial c...

  5. MEASUREMENT OF THE TRANSVERSE BEAM DYNAMICS IN A TESLA-TYPE SUPERCONDUCTING CAVITY

    Energy Technology Data Exchange (ETDEWEB)

    Halavanau, A. [NICADD, DeKalb; Eddy, N. [Fermilab; Edstrom, D. [Fermilab; Lunin, A. [Fermilab; Piot, P. [NICADD, DeKalb; Ruan, J. [Fermilab; Solyak, N. [Fermilab

    2016-09-26

    Superconducting linacs are capable of producing intense, ultra-stable, high-quality electron beams that have widespread applications in Science and Industry. Many project are based on the 1.3-GHz TESLA-type superconducting cavity. In this paper we provide an update on a recent experiment aimed at measuring the transfer matrix of a TESLA cavity at the Fermilab Accelerator Science and Technology (FAST) facility. The results are discussed and compared with analytical and numerical simulations.

  6. Variational principles for transversely vibrating multiwalled carbon nanotubes based on nonlocal Euler-Bernoulli beam model.

    Science.gov (United States)

    Adali, Sarp

    2009-05-01

    Variational principles are derived for multiwalled carbon nanotubes undergoing vibrations. Derivations are based on the continuum modeling with the Euler-Bernoulli beam representing the nanotubes and small scale effects taken into account via the nonlocal elastic theory. Hamilton's principle for multiwalled nanotubes is given and Rayleigh's quotient for the frequencies is derived for nanotubes undergoing free vibrations. Natural and geometric boundary conditions are derived which lead to a set of coupled boundary conditions due to nonlocal effects.

  7. The transverse and longitudinal beam characteristics of the PHIN photo-injector at CERN

    CERN Document Server

    Mete, Ö; Dabrowski, A; Divall, M; Döbert, S; Egger, D; Elsener, K; Fedosseev, V; Lefèvre, T; Petrarca, M

    2010-01-01

    A new photo-injector, capable to deliver a long pulse train with a high charge per bunch for CTF3, has been designed and installed by a collaboration between LAL, CCLRC and CERN within the framework of the second Joint Research Activity PHIN of the European CARE program. The demonstration of the high charge and the stability along the pulse train are the important goals for CTF3 and the CLIC drive beam. The nominal beam for CTF3 has an average current of 3.5 A, a 1.5 GHz bunch repetation frequency and a pulse length of 1.27 μs (1908 bunches). The existing CTF3 injector consists of a thermionic gun and a subharmonic bunching system. The PHIN photo-injector is being tested in a dedicated test-stand at CERN to replace the existing CTF3 injector that is producing unwanted satellite bunches during the bunching process. A phase-coding scheme is planned to be implemented to the PHIN laser system providing the required beam temporal structure by CTF3. RF photo-injectors are high-brightness, low-emittance electron so...

  8. Large deflections and vibrations of a tip pulled beam with variable transversal section

    Science.gov (United States)

    Kurka, P.; Izuka, J.; Gonzalez, P.; Teixeira, L. H.

    2016-10-01

    The use of long flexible probes in outdoors exploration vehicles, as opposed to short and rigid arms, is a convenient way to grant easier access to regions of scientific interest such as terrain slopes and cliff sides. Longer and taller arms can also provide information from a wider exploration horizon. The drawback of employing long and flexible exploration probes is the fact that its vibration is not easily controlled in real time operation by means of a simple analytic linear dynamic model. The numerical model required to describe the dynamics of a very long and flexible structure is often very large and of slow computational convergence. The present work proposes a simplified numerical model of a long flexible beam with variable cross section, which is statically deflected by a pulling cable. The paper compares the proposed simplified model with experimental data regarding the static and dynamic characteristics of a beam with variable cross section. The simulations show the effectiveness of the simplified dynamic model employed in an active control loop to suppress tip vibrations of the beam.

  9. A mixed finite element formulation for a non-linear, transversely isotropic material model for the cardiac tissue.

    Science.gov (United States)

    Thorvaldsen, Tom; Osnes, Harald; Sundnes, Joakim

    2005-12-01

    In this paper we present a mixed finite element method for modeling the passive properties of the myocardium. The passive properties are described by a non-linear, transversely isotropic, hyperelastic material model, and the myocardium is assumed to be almost incompressible. Single-field, pure displacement-based formulations are known to cause numerical difficulties when applied to incompressible or slightly compressible material cases. This paper presents an alternative approach in the form of a mixed formulation, where a separately interpolated pressure field is introduced as a primary unknown in addition to the displacement field. Moreover, a constraint term is included in the formulation to enforce (almost) incompressibility. Numerical results presented in the paper demonstrate the difficulties related to employing a pure displacement-based method, applying a set of physically relevant material parameter values for the cardiac tissue. The same problems are not experienced for the proposed mixed method. We show that the mixed formulation provides reasonable numerical results for compressible as well as nearly incompressible cases, also in situations of large fiber stretches. There is good agreement between the numerical results and the underlying analytical models.

  10. Applications of electron lenses: scraping of high-power beams, beam-beam compensation, and nonlinear optics

    CERN Document Server

    Stancari, Giulio

    2014-01-01

    Electron lenses are pulsed, magnetically confined electron beams whose current-density profile is shaped to obtain the desired effect on the circulating beam. Electron lenses were used in the Fermilab Tevatron collider for bunch-by-bunch compensation of long-range beam-beam tune shifts, for removal of uncaptured particles in the abort gap, for preliminary experiments on head-on beam-beam compensation, and for the demonstration of halo scraping with hollow electron beams. Electron lenses for beam-beam compensation are being commissioned in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Hollow electron beam collimation and halo control were studied as an option to complement the collimation system for the upgrades of the Large Hadron Collider (LHC) at CERN; a conceptual design was recently completed. Because of their electric charge and the absence of materials close to the proton beam, electron lenses may also provide an alternative to wires for long-range beam-beam compens...

  11. Concatenated beam splitters, optical feed-forward and the nonlinear sign gate

    CERN Document Server

    Jacobs, K; Jacobs, Kurt; Dowling, Jonathan P.

    2006-01-01

    We consider a nonlinear sign gate implemented using a sequence of two beam splitters, and consider the use of further sequences of beam splitters to implement feed-forward so as to correct an error resulting from the first beam splitter. We obtain similar results to Scheel et al. [Scheel et al., Phys. Rev. A 73, 034301 (2006)], in that we also find that our feed-forward procedure is only able to produce a very minor improvement in the success probability of the original gate.

  12. Compensating the Electron Beam Energy Spread by the Natural Transverse Gradient of Laser Undulator in All-Optical X-ray Sources

    CERN Document Server

    Zhang, Tong; Deng, Haixiao; Wang, Dong; Dai, Zhimin; Zhao, Zhentang

    2013-01-01

    All-optical schemes provide a potential to dramatically cut off the size and cost of x-ray light sources to the university-laboratory scale, with the combination of the laser-plasma accelerator and the laser undulator. However, the large longitudinal energy spread of the electron beam from laser-plasma accelerator may hinder the way to high brightness of these all-optical light sources. In this letter, the beam energy spread effect is proposed to be significantly compensated by the natural transverse gradient of a laser undulator when properly dispersing the electron beam transversely. Theoretical analysis and numerical simulations on conventional laser-Compton scattering sources and high-gain all-optical x-ray free-electron lasers with the electron beams from laser-plasma accelerators are presented.

  13. Compensating the electron beam energy spread by the natural transverse gradient of laser undulator in all-optical x-ray light sources.

    Science.gov (United States)

    Zhang, Tong; Feng, Chao; Deng, Haixiao; Wang, Dong; Dai, Zhimin; Zhao, Zhentang

    2014-06-02

    All-optical ideas provide a potential to dramatically cut off the size and cost of x-ray light sources to the university-laboratory scale, with the combination of the laser-plasma accelerator and the laser undulator. However, the large longitudinal energy spread of the electron beam from laser-plasma accelerator may hinder the way to high brightness of these all-optical light sources. In this paper, the beam energy spread effect is proposed to be significantly compensated by the natural transverse gradient of a laser undulator when properly transverse-dispersing the electron beam. Theoretical analysis and numerical simulations on conventional laser-Compton scattering sources and high-gain all-optical x-ray free-electron lasers with the electron beams from laser-plasma accelerators are presented.

  14. Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

    Directory of Open Access Journals (Sweden)

    Donald Mark Santee

    2006-01-01

    Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

  15. Nonlinear free vibrations of beams in space due to internal resonance

    Science.gov (United States)

    Stoykov, S.; Ribeiro, P.

    2011-08-01

    The geometrically nonlinear free vibrations of beams with rectangular cross section are investigated using a p-version finite element method. The beams may vibrate in space, hence they may experience longitudinal, torsional and non-planar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The geometrical nonlinearity is taken into account by considering Green's nonlinear strain tensor. Isotropic and elastic beams are investigated and generalised Hooke's law is used. The equation of motion is derived by the principle of virtual work. Mostly clamped-clamped beams are investigated, although other boundary conditions are considered for validation purposes. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. One constant term, odd and even harmonics are assumed in the Fourier series and convergence with the number of harmonics is analysed. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of backbone curves. Coupling between modes is investigated, internal resonances are found and the ensuing multimodal oscillations are described. Some of the couplings discovered lead from planar oscillations to oscillations in the three dimensional space.

  16. Beam-Based Nonlinear Optics Corrections in Colliders

    CERN Document Server

    Pilat, Fulvia Caterina; Malitsky, Nikolay; Ptitsyn, Vadim

    2005-01-01

    A method has been developed to measure and correct operationally the non-linear effects of the final focusing magnets in colliders, which gives access to the effects of multi-pole errors by applying closed orbit bumps, and analyzing the resulting tune and orbit shifts. This technique has been tested and used during 3 years of RHIC (the Relativistic Heavy Ion Collider at BNL) operations. I will discuss here the theoretical basis of the method, the experimental set-up, the correction results, the present understanding of the machine model, the potential and limitations of the method itself as compared with other non linear correction techniques.

  17. Nonlinear analysis of the progressive collapse of reinforced concrete plane frames using a multilayered beam formulation

    Directory of Open Access Journals (Sweden)

    C. E. M. Oliveira

    Full Text Available This work investigates the response of two reinforced concrete (RC plane frames after the loss of a column and their potential resistance for progressive collapse. Nonlinear dynamic analysis is performed using a multilayered Euler/Bernoulli beam element, including elasto-viscoplastic effects. The material nonlinearity is represented using one-dimensional constitutive laws in the material layers, while geometrical nonlinearities are incorporated within a corotational beam formulation. The frames were designed in accordance with the minimum requirements proposed by the reinforced concrete design/building codes of Europe (fib [1-2], Eurocode 2 [3] and Brazil (NBR 6118 [4]. The load combinations considered for PC analysis follow the prescriptions of DoD [5]. The work verifies if the minimum requirements of the considered codes are sufficient for enforcing structural safety and robustness, and also points out the major differences in terms of progressive collapse potential of the corresponding designed structures.

  18. Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Danxia Wang

    2015-01-01

    Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l‍(ux2dxuxx-ϕ(∫0l‍(ux2dxuxxt=q(x, in  [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.

  19. Rematching AGS Booster synchrotron injection lattice for smaller transverse beam emittances

    Energy Technology Data Exchange (ETDEWEB)

    Liu, C. [Brookhaven National Lab. (BNL), Upton, NY (United States); Beebe-Wang, J. [Brookhaven National Lab. (BNL), Upton, NY (United States); Brown, K. [Brookhaven National Lab. (BNL), Upton, NY (United States); Gardner, C. [Brookhaven National Lab. (BNL), Upton, NY (United States); Huang, H. [Brookhaven National Lab. (BNL), Upton, NY (United States); Minty, M. [Brookhaven National Lab. (BNL), Upton, NY (United States); Schoefer, V. [Brookhaven National Lab. (BNL), Upton, NY (United States); Zeno, K. [Brookhaven National Lab. (BNL), Upton, NY (United States)

    2017-01-25

    The polarized proton beam is injected into the booster via the charge-exchange (H- to H+) scheme. The emittance growth due to scattering at the stripping foil is proportional to the beta functions at the foil. It was demonstrated that the current scheme of reducing the beta functions at the stripping foil preserves the emittance better; however the betatron tunes are above but very close to half integer. Due to concern of space charge and half integer in general, options of lattice designs aimed towards reducing the beta functions at the stripping foil with tunes at more favorable places are explored.

  20. Dynamic nonlinear focal shift in amplitude modulated moderately focused acoustic beams.

    Science.gov (United States)

    Jiménez, Noé; Camarena, Francisco; González-Salido, Nuria

    2017-03-01

    The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behavior, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by using a focused mono-element transducer excited by an amplitude modulated signal.

  1. Nonlinear targeted energy transfer of two coupled cantilever beams coupled to a bistable light attachment

    Science.gov (United States)

    Mattei, P.-O.; Ponçot, R.; Pachebat, M.; Côte, R.

    2016-07-01

    In order to control the sound radiation by a structure, one aims to control vibration of radiating modes of vibration using "Energy Pumping" also named "Targeted Energy Transfer". This principle is here applied to a simplified model of a double leaf panel. This model is made of two beams coupled by a spring. One of the beams is connected to a nonlinear absorber. This nonlinear absorber is made of a 3D-printed support on which is clamped a buckled thin small beam with a small mass fixed at its centre having two equilibrium positions. The experiments showed that, once attached onto a vibrating system to be controlled, under forced excitation of the primary system, the light bistable oscillator allows a reduction of structural vibration up to 10 dB for significant amplitude and frequency range around the first two vibration modes of the system.

  2. Relativistic nonlinearity and wave-guide propagation of rippled laser beam in plasma

    Indian Academy of Sciences (India)

    R K Khanna; K Baheti

    2001-06-01

    In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the WKB and paraxial-ray approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focusing of laser beam has been studied for arbitrary large magnitude of nonlinearity. Results indicate that the medium behaves as an oscillatory wave-guide. The self-focusing is found to depend on the position parameter of ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple. Effects of axially and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.

  3. Nonlinear Analysis of External Prestressed Reinforced Concrete Beams with BFRP and CFRP

    Directory of Open Access Journals (Sweden)

    Haleem K. Hussain

    2017-05-01

    Full Text Available The traditional strengthening methods for concrete structure (girders, beams, columns…. consuming time and could be an economical, a new modern repair methods using the Carbon Fiber Reinforced Polymers (CFRP and Basalt Fiber Reinforced Polymer (BFRP as a laminate strips or bars,and considered a competitive solution that will increase the life-cycle of repaired structures. This study investigated the strengthen reinforced concrete girder. Nonlinear analysis have been adopted to the models using FEM analysis (ANSYS to simulate the theoretical results compared with experimental results.Using finite element packages, more efficient and better analyses can be made to fully understand the response of individual structural components and their contribution to a structure as a whole.Three type of material are used in this study as an external prestressed wire (steel, CFRP and BFRP. The prestressed beam is modeled as simply supported beam with two concentrated point load. The results showed that all tested strengthening beam increased the load carryingcapacity of the beams depend on prestressing force. Obtained Result was compared for different type of beam.This study also was enlarged to include using CFRP and BFRPbarwhich are light weight and moredurable, lead to ease of handling and maintenance. The research conducted analytical work to evaluate the effectiveness of concrete beams reinforced normally by the use of CFRP and BFRP bars. The results showed a significant gain in the beam’s ultimate capacities using CFRP bars comparing with beam reinforced with BFRP bar and reference beam

  4. Fast IR Array Detector for Transverse Beam Diagnostics at DA{\\Phi}NE

    CERN Document Server

    Bocci, A; Clozza, A; Drago, A; Grilli, A; Marcelli, A; Raco, A; Sorchetti, R; Gambicorti, L; De Sio, A; Pace, E; Piotrowski, J

    2010-01-01

    At the Laboratori Nazionali di Frascati of the National Institute of Nuclear Physics (INFN) an infrared (IR) array detector with fast response time has been built and assembled in order to collect the IR image of e-/e+ sources of the DA{\\Phi}NE collider. Such detector is made by 32 bilinear pixels with an individual size of 50x50 {\\mu}m2 and a response time of ~1 ns. In the framework of an experiment funded by the INFN Vth Committee dedicated to beam diagnostics, the device with its electronic board has been tested and installed on the DA{\\Phi}NE positron ring. A preliminary characterization of few pixels of the array and of the electronics has been carried out at the IR beamline SINBAD at DA{\\Phi}NE. In particular the detection of the IR source of the e- beam has been observed using four pixels of the array acquiring signals simultaneously with a four channels scope at 1 GHz and at 10 Gsamples/s. The acquisition of four pixels allowed monitoring in real time differences in the bunch signals in the vertical d...

  5. Nonlinear Dynamical analysis of an AFM tapping mode microcantilever beam

    Directory of Open Access Journals (Sweden)

    Choura S.

    2012-07-01

    Full Text Available We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM microcantilever beam. This latter is subjected to a harmonic excitation of its base displacement and to Van der Waals and DMT contact forces at its free end. For AFM design purposes, we derive a mathematical model for accurate description of the AFM microbeam dynamics. We solve the resulting equations of motions and associated boundary conditions using the Galerkin method. We find that using one-mode approximation in tapping mode operating in the neighborhood of the contact region one-mode approximation may lead to erroneous results.

  6. Simulation of Transverse Multi-Bunch Instabilities of Proton Beams in LHC

    CERN Document Server

    Koschik, Alexander; Zotter, Bruno

    The CERN Large Hadron Collider (LHC) is designed for highest luminosity and therefore requires operation with a large number of bunches and high intensities. Its performance could be limited by the electromagnetic interaction between the charged particle beam and its surroundings which cause collective instabilities. This thesis describes methods of simulating and analyzing multi-bunch instabilities in circular accelerators and storage rings. The simulation models as well as analyzing tools presented here, also facilitate the interpretation of measurements in multi-bunch machines. The 3-dimensional, multi-bunch tracking program MultiTRISIM was developed, based on its single-bunch predecessor TRISIM3D. It allows the exploration of longrange effects in round or flat vacuum chambers for equidistant or uneven filling schemes. Previous computer simulations of collective effects concentrated mainly on instabilities of single or few bunches in electron storage rings. There, the strong radiation damping reduces the r...

  7. Nonlinear dynamics of a sliding beam on two supports under sinusoidal excitation

    Indian Academy of Sciences (India)

    R J Somnay; R A Ibrahim

    2006-08-01

    This study deals with the nonlinear dynamics associated with large deformation of a beam sliding on two-knife edge supports under external excitation. The beam is referred to as a Gospodnetic–Frisch-Fay beam, after the researchers who reported its static deformation in closed form. The freedom of the beam to slide on its supports imparts a nonlinear characteristic to the force-deflection response. The restoring elastic force of the beam possesses characteristics similar to those of the roll-restoring moment of ships. The Gospodnetic–Frisch-Fay exact solution is given in terms of elliptic functions. A curve fit of the exact solution up to eleventh-order is constructed to establish the governing equation of motion under external excitation. The dynamic stability of the unperturbed beam is examined for the damped and undamped cases. The undamped case reveals periodic orbits and one homoclinic orbit depending on the value of the initial conditions. The response to a sinusoidal excitation at a frequency below the linear natural frequency is numerically estimated for different excitation amplitude and different values of initial conditions covered by the area of the homoclinic orbit. The safe basins of attraction are plotted for different values of excitation amplitude. It is found that the safe region of operation is reduced as the excitation amplitude increases.

  8. Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity

    Science.gov (United States)

    Bekhoucha, F.; Rechak, S.; Duigou, L.; Cadou, J. M.

    2016-09-01

    In this paper, we study the bending nonlinear free vibrations of a centrifugally stiffened beam with uniform cross-section and constant angular velocity. The nonlinear intrinsic equations of motion used here are geometrically exact and specific to beams exhibiting large amplitude displacements and rotations associated with small strains. Based on the Timoshenko beam model, these equations are derived from Hamilton's principle, in which the warping is considered. All coupling terms are considered including Coriolis terms. The studied beams are isotropic with clamped-free boundary conditions. By combining the Galerkin method with the harmonic balance method, the equations of motion are converted into a quadratic function treated with a continuation method: the Asymptotic Numerical Method, where the generalized displacement vector is presented as a series expansion. While analysing the effect of the angular velocity, we determine the amplitude versus frequency variations which are plotted as backbone curves. Considering the first lagging and flapping modes, the changes in beam behaviour from hardening to softening are investigated and identified as a function of the angular velocity and the effect of shear. Particular attention is paid to high angular velocities for both Euler-Bernoulli and Timoshenko beams and the natural frequencies so obtained are compared with the results available in the literature.

  9. Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

    Science.gov (United States)

    Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

    2016-06-27

    We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

  10. Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum

    Directory of Open Access Journals (Sweden)

    H. Vázquez-Leal

    2013-01-01

    Full Text Available In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to 179.99999999∘ yielding a relative error of 0.01222747.

  11. Beam manipulation techniques, nonlinear beam dynamics, and space charge effect in high energy high power accelerators

    Energy Technology Data Exchange (ETDEWEB)

    Lee, S. Y.

    2014-04-07

    We had carried out a design of an ultimate storage ring with beam emittance less than 10 picometer for the feasibility of coherent light source at X-ray wavelength. The accelerator has an inherent small dynamic aperture. We study method to improve the dynamic aperture and collective instability for an ultimate storage ring. Beam measurement and accelerator modeling are an integral part of accelerator physics. We develop the independent component analysis (ICA) and the orbit response matrix method for improving accelerator reliability and performance. In collaboration with scientists in National Laboratories, we also carry out experimental and theoretical studies on beam dynamics. Our proposed research topics are relevant to nuclear and particle physics using high brightness particle and photon beams.

  12. Nonlinear physics and energetic particle transport features of the beam-plasma instability

    CERN Document Server

    Carlevaro, Nakia; Montani, Giovanni; Zonca, Fulvio

    2015-01-01

    In this paper, we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume $n$ cold supra-thermal beams and investigate the self-consistent evolution in the presence of the complete spectrum of nearly degenerate Langmuir modes. A qualitative transport estimation is obtained by computing the Lagrangian Coherent Structures of the system on given temporal scales. This leads to the splitting of the phase space into regions where the local transport processes are relatively faster. The general theoretical framework is applied to the case of the nonlinear dynamics of two cold beams, for which numerical simulation results are illustrated and analyzed.

  13. The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities

    CERN Document Server

    Chang, Philip; Lamberts, Astrid

    2014-01-01

    Very-high energy gamma-rays from extragalactic sources pair-produce off of the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the "oblique" instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here, we show with numerical calculations that the effective damping rate is $8\\times 10^{-4}$ of the growth rate of the linear instability, which is sufficient for the "oblique" instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wavenumber and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to ap...

  14. Nonlinear dynamics and bifurcation mechanisms in intense electron beam with virtual cathode

    Science.gov (United States)

    Frolov, Nikita S.; Kurkin, Semen A.; Koronovskii, Alexey A.; Hramov, Alexander E.

    2017-07-01

    In this paper we report on the results of investigations of nonlinear dynamics and bifurcation mechanisms in intense electron beam with virtual cathode in micrometer-scaled source of sub-THz electromagnetic radiation. The numerical analysis is provided by means of 3D electromagnetic particle-in-cell (PIC) simulation. We have studied evolution of the system dynamics with the change of beam current value by means of Fourier and bifurcation analysis. The bifurcation diagram has identified a number of the alternating regions of beam current with regular or chaotic regimes of system dynamics. The study of spatiotemporal dynamics of formed electron structures in the beam has revealed the physical mechanisms responsible for the regimes switchings in the system.

  15. Analytical and Experimental Assessment of Seismic Vulnerability of Beam-Column Joints without Transverse Reinforcement in Concrete Buildings

    Science.gov (United States)

    Hassan, Wael Mohammed

    Beam-column joints in concrete buildings are key components to ensure structural integrity of building performance under seismic loading. Earthquake reconnaissance has reported the substantial damage that can result from inadequate beam-column joints. In some cases, failure of older-type corner joints appears to have led to building collapse. Since the 1960s, many advances have been made to improve seismic performance of building components, including beam-column joints. New design and detailing approaches are expected to produce new construction that will perform satisfactorily during strong earthquake shaking. Much less attention has been focused on beam-column joints of older construction that may be seismically vulnerable. Concrete buildings constructed prior to developing details for ductility in the 1970s normally lack joint transverse reinforcement. The available literature concerning the performance of such joints is relatively limited, but concerns about performance exist. The current study aimed to improve understanding and assessment of seismic performance of unconfined exterior and corner beam-column joints in existing buildings. An extensive literature survey was performed, leading to development of a database of about a hundred tests. Study of the data enabled identification of the most important parameters and the effect of each parameter on the seismic performance. The available analytical models and guidelines for strength and deformability assessment of unconfined joints were surveyed and evaluated. In particular, The ASCE 41 existing building document proved to be substantially conservative in joint shear strength estimation. Upon identifying deficiencies in these models, two new joint shear strength models, a bond capacity model, and two axial capacity models designed and tailored specifically for unconfined beam-column joints were developed. The proposed models strongly correlated with previous test results. In the laboratory testing phase of

  16. Role of Density Profiles for the Nonlinear Propagation of Intense Laser Beam through Plasma Channel

    Directory of Open Access Journals (Sweden)

    Sonu Sen

    2014-01-01

    Full Text Available In this work role of density profiles for the nonlinear propagation of intense laser beam through plasma channel is analyzed. By employing the expression for the dielectric function of different density profile plasma, a differential equation for beamwidth parameter is derived under WKB and paraxial approximation. The laser induces modifications of the dielectric function through nonlinearities. It is found that density profiles play vital role in laser-plasma interaction studies. To have numerical appreciation of the results the propagation equation for plasma is solved using the fourth order Runge-Kutta method for the initial plane wave front of the beam, using boundary conditions. The spot size of the laser beam decreases as the beam penetrates into the plasma and significantly adds self-focusing in plasma. This causes the laser beam to become more focused by reduction of diffraction effect, which is an important phenomenon in inertial confinement fusion and also for the understanding of self-focusing of laser pulses. Numerical computations are presented and discussed in the form of graphs for typical parameters of laser-plasma interaction.

  17. Propagation characteristics of a high-power broadband laser beam passing through a nonlinear optical medium with defects

    Institute of Scientific and Technical Information of China (English)

    Xueqiong; Chen; Xiaoyan; Li; Ziyang; Chen; Jixiong; Pu; Guowen; Zhang; Jianqiang; Zhu

    2013-01-01

    The intensity distributions of a high-power broadband laser beam passing through a nonlinear optical medium with defects and then propagating in free space are investigated based on the general nonlinear Schr¨odinger equation and the split-step Fourier numerical method. The influences of the bandwidth of the laser beam, the thickness of the medium,and the defects on the light intensity distribution are revealed. We find that the nonlinear optical effect can be suppressed and that the uniformity of the beam can be improved for a high-power broadband laser beam with appropriate wide bandwidth. It is also found that, under the same incident light intensity, a thicker medium will lead to a stronger self-focusing intensity, and that the influence of defects in the optical elements on the intensity is stronger for a narrowband beam than for a broadband beam.

  18. Rapidity and transverse momentum dependence of pion-pion Bose-Einstein correlations measured at 20, 30, 40, 80, and 158 AGeV beam energy

    CERN Document Server

    Kniege, S; Anticic, T; Baatar, B; Barna, D; Bartke, Jerzy; Betev, L; Bialkowska, H; Billmeier, A; Blume, C; Boimska, B; Botje, M; Bracinik, J; Bramm, R; Brun, R; Buncic, P; Cerny, V; Christakoglou, P; Chvala, O; Cramer, J G; Csató, P; Darmenov, N; Dimitrov, A; Dinkelaker, P; Eckardt, V; Farantatos, G; Filip, P; Flierl, D; Fodor, Z; Foka, P Y; Freund, P; Friese, V; Gál, J; Gazdzicki, M; Georgopoulos, G; Gladysz-Dziadus, E; Grebieszkow, K; Hegyi, S; Höhne, C; Kadija, K; Karev, A; Kliemant, M; Kolesnikov, V I; Kollegger, T; Kornas, E; Korus, R; Kowalski, M; Kraus, I; Kreps, M; Van Leeuwen, M; Lévai, Peter; Litov, L; Lungwitz, B; Makariev, M; Malakhov, A I; Markert, C; Mateev, M; Mayes, B W; Melkumov, G L; Meurer, C; Mischke, A; Mitrovski, M; Molnár, J; Mrówczynski, S; Pálla, G; Panagiotou, A D; Panayotov, D; Petridis, A; Pikna, M; Pinsky, L; Pühlhofer, F; Reid, J G; Renfordt, R E; Richard, A; Roland, C; Roland, G; Rybczynski, M; Rybicki, A; Sandoval, A; Sann, H; Schmitz, N; Seyboth, P; Siklér, F; Sitár, B; Skrzypczak, E; Stefanek, G; Stock, R; Ströbele, H; Susa, T; Szentpétery, I; Sziklai, J; Trainor, T A; Varga, D; Vassiliou, Maria; Veres, G I; Vesztergombi, G; Vranic, D; Wetzler, A; Wlodarczyk, Z; Yoo, I K; Zaranek, J; Zimányi, J; Kniege, Stefan

    2004-01-01

    Preliminary results on pion-pion Bose-Einstein correlations in central Pb+Pb collisions measured by the NA49 experiment are presented. Rapidity as well as transverse momentum dependence of the HBT-radii are shown for collisions at 20, 30, 40, 80, and 158 AGeV beam energy. Including results from AGS and RHIC experiments only a weak energy dependence of the radii is observed. Based on hydrodynamical models parameters like lifetime and geometrical radius of the source are derived from the dependence of the radii on transverse momentum.

  19. Crack modelling and detection in Timoshenko FGM beam under transverse vibration using frequency contour and response surface model with GA

    Science.gov (United States)

    Banerjee, Amit; Panigrahi, Brajesh; Pohit, G.

    2016-04-01

    In the present work, dynamic response of cracked Timoshenko beam with functionally graded material properties are obtained by a numerical technique using Ritz approximation. In order to verify the applicability and performance of the formulation, comparisons of the present numerical method with three-dimensional FEM models are made. Crack is assumed to be transverse and open throughout the vibration cycle. Two different crack detection techniques have been proposed. Results obtained by the numerical technique are used in both of the crack detection techniques. In the first technique, the frequency contours with respect to crack location and size are plotted and the intersection of contours of different modes helps in the prediction of crack location and size. In the second technique, crack is modelled using response surface methodology (RSM). The sum of the squared errors between the numerical and RSM regression model natural frequencies is used as the objective function. This objective function is minimised using genetic algorithm optimisation technique. Both the crack detection techniques and the numerical analysis have shown good agreement with each other.

  20. Investigations on nonlinear optical properties of electron beam treated Gd:ZnO thin films for photonic device applications

    Science.gov (United States)

    Spoorthi, K.; Pramodini, S.; Kityk, I. V.; Abd-Lefdil, M.; Sekkati, M.; El Fakir, A.; Rao, Ashok; Sanjeev, Ganesh; Poornesh, P.

    2017-06-01

    In this article, we report the third-order nonlinear optical properties of electron beam irradiated gadolinium-doped zinc oxide (GZO) thin films prepared using the spray pyrolysis deposition technique. GZO thin films were treated with an electron beam from a variable energy microtron accelerator at dose rates ranging from 1-5 kGy. Nonlinear optical measurements were conducted by employing the single beam Z-scan technique. A continuous wave He-Ne laser operating at 633 nm was used as the source of excitation. Closed aperture Z-scan results reveal that the films exhibit self-defocusing nonlinearity. Open aperture Z-scan results exhibit a switching over phenomena of reverse saturable absorption to saturable absorption for thin film irradiated at 3 kGy, indicating the influence of electron beams on optical nonlinearity. The significant change in third-order nonlinear optical susceptibility χ (3) ranging from 2.14  ×  10-3 to 3.12  ×  10-3 esu is attributed to the effect of electron beam irradiation. The study shows that the nonlinear coefficients of GZO films can be tuned by electron beams for use in nonlinear optical device applications.

  1. Higher order mode spectra and the dependence of localized dipole modes on the transverse beam position in third harmonic superconducting cavities at FLASH

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Pei [Manchester Univ. (United Kingdom); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Baboi, Nicoleta [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Jones, Roger M. [The Cockcroft Institute, Daresbury (United Kingdom)

    2012-06-15

    An electron beam entering an accelerating cavity excites a wakefield. This wakefield can be decomposed into a series of multi-poles or modes. The dominant component of the transverse wakefield is dipole. This report summarizes the higher order mode (HOM) signals of the third harmonic cavities of FLASH measured at various stages: transmission measurements in the single cavity test stand at Fermilab, at CMTB (Cryo- Module Test Bench) and at FLASH, and beam-excited measurements at FLASH. Modes in the first two dipole bands and the fifth dipole band have been identified using a global Lorentzian fit technique. The beam-pipe modes at approximately 4 GHz and some modes in the fifth dipole band have been observed as localized modes, while the first two dipole bands, containing some strong coupling cavity modes, propagate. This report also presents the dependence of the localized dipole modes on the transverse beam position. Linear dependence for various modes has been observed. This makes them suitable for beam position diagnostics. These modes, together with some propagating, strong coupling modes, have been considered in the design of a dedicated electronics for beam diagnostics with HOMs for the third harmonic cavities.

  2. Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

    Science.gov (United States)

    Subrahmanyam, K. B.; Kaza, K. R. V.

    1985-01-01

    The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.

  3. New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

    Science.gov (United States)

    Rahman, Md. Saifur; Lee, Yiu-Yin

    2017-10-01

    In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.

  4. THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Philip; Lamberts, Astrid [Department of Physics, University of Wisconsin-Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, WI 53211 (United States); Broderick, Avery E.; Shalaby, Mohamad [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5 (Canada); Pfrommer, Christoph [Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg (Germany); Puchwein, Ewald, E-mail: chang65@uwm.edu [Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA (United Kingdom)

    2014-12-20

    Very high energy gamma-rays from extragalactic sources produce pairs from the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the ''oblique'' instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here we show with numerical calculations that the effective damping rate is 8 × 10{sup –4} the growth rate of the linear instability, which is sufficient for the ''oblique'' instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wave numbers and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long-wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long-wavelength modes, this scenario represents the ''worst case'' scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the ''oblique'' instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.

  5. Numerical Simulations of Nonlinear Dynamics of Electron Cyclotron Maser with a Straight Beam

    Institute of Scientific and Technical Information of China (English)

    KONG Ling-Bao; HOU Zhi-Ling

    2011-01-01

    An electron cyclotron maser based on anomalous Doppler effect (ADECM) with an initially axial beam velocity is considered,and the nonlinear equation of beam-wave interaction is presented.With the numerical methods,the nonlinear dynamics of the ADECM is investigated.It is shown that the saturated interaction efficiency of the ADECM approaches 90% and the interaction length for the saturated efficiency spans about 5-20cm.The results may be of importance for designing a compact device in applications in microwave generations or microwave heating of ceramic laminates.In the late 1950s,the theoretical studies on the instability of electron cyclotron maser based on normal Doppler effect (NDECM) were performed almost simultaneously by Gaponov,[1] Twiss,[2] and Schneider.[3] Their discoveries have resulted in the most successful fast-wave devices such as the gyrotron and variants.[4,5] The possible applications of microwaves span a wide range of technologies such as in thermonuclear fusion energy,charged particle accelerations,radar systems,and processing of advanced ceramics.[6-16]%An electron cyclotron maser based on anomalous Doppler effect (ADECM) with an initially axial beam velocity is considered, and the nonlinear equation of beam-wave interaction is presented. With the numerical methods, the nonlinear dynamics of the ADECM is investigated. It is shown that the saturated interaction efficiency of the ADECM approaches 90% and the interaction length for the saturated efficiency spans about 5-20 cm. The results may be of importance for designing a compact device in applications in microwave generations or microwave heating of ceramic laminates.

  6. Advances in nonlinear vibration analysis of structures. Part-I. Beams

    Indian Academy of Sciences (India)

    Sudhakar R Marur

    2001-06-01

    The development of nonlinear vibration formulations for beams in the literature can be seen to have gone through distinct phases — earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the process of evolution of this field. This paper attempts to achieve precisely this objective.

  7. Non-linearity of Beam Halo-Chaos in the ADS

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applicationsin industry, medicine, and national defense. This latter reviews some general features of complexities and their expressions in accelerator-driven clean nuclear power system (ADS).Complexity has become an important subject for study, especially in the field of nonlinear

  8. 非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams

    Institute of Scientific and Technical Information of China (English)

    陈立群; 程昌; 张能辉

    2000-01-01

    The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.

  9. 非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams

    Institute of Scientific and Technical Information of China (English)

    陈立群; 程昌; 张能辉

    2001-01-01

    The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.

  10. Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.

    Science.gov (United States)

    Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor

    2013-08-01

    The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation.

  11. Nonlinear self-focus of pulsed-wave beams in Kerr media

    Energy Technology Data Exchange (ETDEWEB)

    Judkins, J.B.

    1992-12-31

    A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.

  12. Stimulated Raman Scattering and Nonlinear Focusing of High-Power Laser Beams Propagating in Water

    CERN Document Server

    Hafizi, B; Penano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D

    2015-01-01

    The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. While discussed here in the context of propagation in water, the gain-focusing phenomenon is general to any medium supporting nonlinear focusing and stimulated forward Raman scattering.

  13. Extreme events induced by self-action of laser beams in dynamic nonlinear liquid crystal cells

    Science.gov (United States)

    Bugaychuk, S.; Iljin, A.; Chunikhina, K.

    2017-06-01

    Optical extreme events represent a feature of nonlinear systems where there may emerge individual pulses possessing very high (or very low) intensity hardly probable statistically. Such property is being connected with the generation of solitons in the nonlinear systems. We carry out the first experiments for detection of extreme events during two-wave mixing with nonlinear dynamical liquid crystal (LC) cells. We investigate the statistics of the extreme events in dependence on relation between the duration of a laser pulse and the time characteristic of dynamic grating relaxation in LC cell. Our research shows that the self-diffraction of laser beams with a dynamical grating support the generation of envelope solitons in this system.

  14. Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks.

    Science.gov (United States)

    Mangussi, Franco; Zanette, Damián H

    2016-01-01

    In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined.

  15. Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks

    Science.gov (United States)

    Mangussi, Franco

    2016-01-01

    In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined. PMID:27648829

  16. Analysis of Retrofitting Non-Linear Finite Element Of RCC Beam And Column Using Ansys

    Directory of Open Access Journals (Sweden)

    T. Subramani

    2014-12-01

    Full Text Available Many of the existing reinforced concrete structures throughout the world are in urgent need of strengthening, repair or reconstruction because of deterioration due to various factors like corrosion, lack of detailing, failure of bonding between beam-column joints, increase in service loads, etc., leading to cracking, spalling, loss of strength, deflection, etc., Direct observation of these damaged structures has shown that damage occurs usually at the beam-column joints, with failure in bending or shear, depending on geometry and reinforcement distribution type.A nonlinear finite element analysis that is a simulation technique is used in this work to evaluate the effectiveness of retrofitting technique called “wrapping technique” for using carbon fibres (FRP for strengthening of RC beam-column connections damaged due to various reasons. After carrying out a nonlinear finite element analysis of a reinforced concrete frame (Controlled Specimen and reinforced concrete frame where carbon fibres are attached to the beam column joint portion in different patterns ,the measured response histories of the original and strengthened specimens are then subsequently compared. It is seen that the strengthened specimens exhibit significant increase in strength, stiffness, and stability as compared to controlled specimens. It appears that the proposed simulation technique will have a significant impact in engineering practice in the near future.

  17. Nonlinear dynamics of beam-plasma instability in a finite magnetic field

    Science.gov (United States)

    Bogdankevich, I. L.; Goncharov, P. Yu.; Gusein-zade, N. G.; Ignatov, A. M.

    2017-06-01

    The nonlinear dynamics of beam-plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam-plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B 0 = 4.5 kG (Ω ω B p ) and 20 kG (Ω B ≫ ωp). For B 0 = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.

  18. 3D Nonlinear Numerical Simulation of Intact and Debonded Reinforced Concrete Beams

    Institute of Scientific and Technical Information of China (English)

    Chen Quan(陈权); Marcus L.

    2004-01-01

    To study the behaviour of reinforced concrete (RC) structures with sections of concrete removed and the reinforcement exposed, 3D nonlinear numerical analysis was performed upon both intact and debonded RC beams by using finite element techniques. The deformational characteristics and the ultimate loads were obtained through numerical models, as well as crack and stress distributions. The failure modes can also be deduced from computational results. Compared with intact beams, the normal assumptions of plane section behaviour is not hold true and the patterns of stress and strain are different in debonded RC beams. The numerical results show good consistency with experimental data. This kind of numerical simulation is a supplement to existing codes.

  19. Image formation by linear and nonlinear digital scanned light-sheet fluorescence microscopy with Gaussian and Bessel beam profiles

    Science.gov (United States)

    Olarte, Omar E.; Licea-Rodriguez, Jacob; Palero, Jonathan A.; Gualda, Emilio J.; Artigas, David; Mayer, Jürgen; Swoger, Jim; Sharpe, James; Rocha-Mendoza, Israel; Rangel-Rojo, Raul; Loza-Alvarez, Pablo

    2012-01-01

    We present the implementation of a combined digital scanned light-sheet microscope (DSLM) able to work in the linear and nonlinear regimes under either Gaussian or Bessel beam excitation schemes. A complete characterization of the setup is performed and a comparison of the performance of each DSLM imaging modality is presented using in vivo Caenorhabditis elegans samples. We found that the use of Bessel beam nonlinear excitation results in better image contrast over a wider field of view. PMID:22808423

  20. Effect of electron beam on structural, linear and nonlinear properties of nanostructured Fluorine doped ZnO thin films

    Science.gov (United States)

    Antony, Albin; Pramodini, S.; Kityk, I. V.; Abd-Lefdil, M.; Douayar, A.; Cherkaoui El Moursli, F.; Sanjeev, Ganesh; Manjunatha, K. B.; Poornesh, P.

    2017-10-01

    Electron beam induced effects on Fluorine doped ZnO thin films (FZO) grown by chemical spray pyrolysis deposition technique were studied. The samples were exposed to 8 MeV electron beam at different dose rate ranging from 1 kGy to 4 kGy. All films exhibit a polycrystalline nature which shows an increase in crystallanity with irradiation dosages. The electron beam irradiation effectively controls the films surface morphology and its linear optical characteristics. Z-Scan technique was employed to evaluate the sign and magnitude of nonlinear refractive index and nonlinear absorption coefficient using a continuous wave laser at 632.8 nm as light source. Enhancement in the third order nonlinear optical properties was were noted due to electron beam irradiation. Tailoring the physical and NLO properties by electron beam, the FZO thin films becomes a promising candidate for various optoelectronic applications such as phase change memory devices, optical pulse compression, optical switching and laser pulse narrowing.

  1. Opposite Goos-Hänchen shifts for transverse-electric and transverse-magnetic beams at the interface associated with single-negative materials.

    Science.gov (United States)

    Hu, Xiaolong; Huang, Yidong; Zhang, Wei; Qing, De-Kui; Peng, Jiangde

    2005-04-15

    Goos-Hänchen shifts are investigated when total reflection occurs at the interfaces associated with single-negative materials (SNMs). A general rule for judging the direction of the Goos-Hänchen lateral shift concerning lossless media is obtained: Whether the lateral shift is positive or negative depends on the sign of micro1micro2 for TE-polarized incident beams and epsilon1epsilon2 for TM-polarized incident beams. It was theoretically demonstrated that, at the interface associated with SNMs, TE- and TM-polarized incident beams experience opposite Goos-Hänchen lateral shifts. An effective and simple approach to discriminating epsilon-negative material and micro-negative material is proposed.

  2. Semi-Analytical Solution for Stresses and Displacements in a Tunnel Excavated in Transversely Isotropic Formation with Non-Linear Behavior

    Science.gov (United States)

    Vu, The Manh; Sulem, Jean; Subrin, Didier; Monin, Nathalie

    2013-03-01

    A semi-analytical solution based on the transfer matrix technique is proposed to analyze the stresses and displacements in a two-dimensional circular opening excavated in transversely isotropic formation with non-linear behavior. A non-isotropic far field can be accounted for and the process of excavation is simulated by progressive reduction of the internal radial stress. A hyperbolic stress-strain law is proposed to take into account the non-linear behavior of the rock. The model contains seven independent parameters corresponding to the five elastic constants of an elastic material with transverse isotropy and to the friction coefficient and cohesion along the parallel joints (weakness planes). This approach is based on the discretization of the space into concentric rings. It requires the establishment of elementary solutions corresponding to the stress and displacement fields inside each ring for given conditions at its boundaries. These solutions, based on complex variable theory, are obtained in the form of infinite series. The appropriate number of terms to be kept for acceptable approximation is discussed. This non-linear model is applied to back analyze the convergence measurements of Saint-Martin-la-Porte access gallery. Short-term and long-term ground parameters are evaluated.

  3. Influence of the transverse dimensions of the beams of the HERA accelerator on the cross section for the process ep. -->. ep. gamma

    Energy Technology Data Exchange (ETDEWEB)

    Kotkin, G.L.; Polityko, S.I.; Serbo, V.G.

    1985-10-01

    It is planned to measure the luminosity in the HERA accelerator by means of the reaction ep..-->..ep..gamma... One notes that in this process an important role is played by impact parameters larger than the transverse dimensions of the beams. This will lead to a decrease of the number of observed photons in comparison with a standard calculation. Calculations performed show that for E/sub ..gamma../< or =0.04E/sub e/ the difference amounts to > or =10%.

  4. Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors

    Energy Technology Data Exchange (ETDEWEB)

    Kacem, N; Hentz, S; Pinto, D; Reig, B; Nguyen, V [CEA/LETI-MINATEC, Grenoble (France)

    2009-07-08

    In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.

  5. Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors.

    Science.gov (United States)

    Kacem, N; Hentz, S; Pinto, D; Reig, B; Nguyen, V

    2009-07-08

    In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.

  6. Nonlinear and long-term beam dynamics in low energy storage rings

    Science.gov (United States)

    Papash, A. I.; Smirnov, A. V.; Welsch, C. P.

    2013-06-01

    Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF+ ions at 93keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3-30 keV ions with a gas jet target are summarized.

  7. Nonlinear and long-term beam dynamics in low energy storage rings

    Directory of Open Access Journals (Sweden)

    A. I. Papash

    2013-06-01

    Full Text Available Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF^{+} ions at 93  keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3–30 keV ions with a gas jet target are summarized.

  8. Non-Linear Beam Dynamics Studies of the Diamond Storage Ring

    CERN Document Server

    Bartolini, Riccardo; Belgroune, Mahdia; Henry Rowland, James; Jones, James; Martin, Ian; Singh, Beni

    2005-01-01

    The non-linear beam dynamics have been investigated for the non-zero dispersion lattice of the Diamond storage ring. Effects in realistic lattice configurations such as the introduction of coupling errors, beta beating, closed orbit correction, quadrupole fringe field and in-vacuum and helical insertion devices have been studied in the presence of realistic physical aperture limitations. Frequency map analysis together with 6D tracking allows identification of the limiting resonances as well as the loss locations and calculation of the influence of non-linear longitudinal motion on the Touschek lifetime. The sensitivity of the lattice to some of these effects leads to the identification of a better working point for the machine.

  9. (3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material

    Institute of Scientific and Technical Information of China (English)

    Hu Yong-Hua; Fu Xi-Quan; Wen Shuang-Chun; Su Wen-Hua; Fan Dian-Yuan

    2006-01-01

    In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized (3+1)-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material (RHM) and left-handed material (LHM) is derived. By the commonly used Drude dispersive model for LHM, a (3+1)-dimensional nonlinear Schr(o)dinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.

  10. Strong quantum squeezing near the pull-in instability of a nonlinear beam

    Science.gov (United States)

    Passian, Ali; Siopsis, George

    2016-08-01

    Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. We predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. By taking into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator. We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.

  11. Influence of the transverse dimensions of colliding beams on processes of bremsstrahlung and production of e/sup +/e/sup -/ pairs

    Energy Technology Data Exchange (ETDEWEB)

    Kotkin, G.L.; Polityko, S.I.; Serbo, V.G.

    1985-09-01

    For high energies of colliding e/sup +/e/sup -/, ep, and ..gamma..e beams in processes of bremsstrahlung and production of e/sup +/e/sup -/ pairs, an important role is played by impact parameters much greater than the transverse dimensions of the beams. This leads to a decrease of the number of observed events in comparison with the standard calculations. Exact formulas and a number of convenient approximate formulas are obtained for the number of events in an arbitrary reaction with allowance for the finite dimensions of the beams. Concrete calculations are given for production of e/sup +/e/sup -/ pairs.The deviations from the standard calculations for e/sup +/e/sup -/ collisions under the conditions of LEP, SLC, and VLEPP are 1, 4, and 15%, respectively, and for ..gamma..e collisions under the conditions of SLC and VLEPP they are 20 and 35%, respectively.

  12. On Approximate Analytical Solutions of Nonlinear Vibrations of Inextensible Beams using Parameter-Expansion Method

    DEFF Research Database (Denmark)

    Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo;

    2010-01-01

    In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which ...... is valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed....

  13. Lie algebraic analysis for the nonlinear transport of intense pulsed beams in electrostatics lenses

    Institute of Scientific and Technical Information of China (English)

    Lu Jian-Qin; Li Jin-Hai

    2004-01-01

    The Lie algebraic method is applied to the analysis of the nonlinear transport of an intense pulsed beam in cylindrically symmetrical electrostatic lenses, and particle orbits in a six-dimensional phase space (x, px, y, py, τ, pτ)are obtained in the second order approximation. They can also be acquired in the third or higher order approximation if needed. In the analysis, we divide the electrostatic lenses into several segments. Each segment is considered as a uniform accelerating field, and each dividing point is treated as a thin lens. The particle distribution in a three-dimensional ellipsoid is of Gaussian type.

  14. Two-beam nonlinear Kerr effect to stabilize laser frequency with sub-Doppler resolution

    CERN Document Server

    Martins, Weliton Soares; de Silans, Thierry Passerat; Oriá, Marcos; Chevrollier, Martine; 10.1364/AO.51.005080

    2012-01-01

    Avoiding laser frequency drifts is a key issue in many atomic physics experiments. Several techniques have been developed to lock the laser frequency using sub-Doppler dispersive atomic lineshapes as error signals in a feedback loop. We propose here a two-beam technique that uses non-linear properties of an atomic vapor around sharp resonances to produce sub-Doppler dispersive-like lineshapes that can be used as error signals. Our simple and robust technique has the advantage of not needing either modulation or magnetic fields.

  15. Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Jing [College of Information Technology, Jilin Agricultural University, Changchun 130118 (China); Gao, Yixian, E-mail: gaoyx643@nenu.edu.cn; Li, Yong [School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024 (China)

    2015-05-15

    Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. .

  16. Calibration of a Non-Linear Beam Position Monitor Electronics by Switching Electrode Signals

    CERN Document Server

    Gasior, M

    2013-01-01

    Button electrode signals from beam position monitors embedded into new LHC collimators will be individually processed with front-end electronics based on compensated diode detectors and digitized with 24-bit audio-range ADCs. This scheme allows sub-micrometre beam orbit resolution to be achieved with simple hardware and no external timing. As the diode detectors only operate in a linear regime with large amplitude signals, offset errors of the electronics cannot be calibrated in the classical way with no input. This paper describes the algorithms developed to calibrate the offset and gain asymmetry of these nonlinear electronic channels. Presented algorithm application examples are based on measurements performed with prototype diode orbit systems installed on the CERN SPS and LHC machines.

  17. Non-Linear Optical Flow Cytometry Using a Scanned, Bessel Beam Light-Sheet

    Science.gov (United States)

    Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.

    2015-01-01

    Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers. PMID:26021750

  18. Nonlinear effects in optical pumping of a cold and slow atomic beam

    KAUST Repository

    Porfido, N.

    2015-10-12

    By photoionizing hyperfine (HF) levels of the Cs state 62P3/2 in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around 180μs) spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The evolution of population within the HF structure is calculated by numerical integration of the multilevel optical Bloch equations. The agreement between numerical results and experiment outcomes is excellent. All main features in the experimental findings are explained by the occurrence of “dark” and “bright” resonances leading to power-dependent branching coefficients.

  19. Nonlinear Breit-Wheeler pair production in a tightly focused laser beam

    CERN Document Server

    Di Piazza, A

    2016-01-01

    The only available analytical framework for investigating QED processes in a strong laser field systematically relies on approximating the latter as a plane wave. However, realistic high-intensity laser beams feature much more complex space-time structures than plane waves. Here, we show the feasibility of an analytical framework for investigating strong-field QED processes in laser beams of arbitrary space-time structure by determining the energy spectrum of positrons produced via nonlinear Breit-Wheeler pair production as a function of the background field. A numerical evaluation of the angular resolved positron spectrum shows significant quantitative differences with respect to the analogous result in a plane wave, such that the present results will be also important for the design of upcoming strong laser facilities aiming at measuring this process.

  20. Nonlinear Breit-Wheeler Pair Production in a Tightly Focused Laser Beam

    Science.gov (United States)

    Di Piazza, A.

    2016-11-01

    The only available analytical framework for investigating QED processes in a strong laser field systematically relies on approximating the latter as a plane wave. However, realistic high-intensity laser beams feature much more complex space-time structures than plane waves. Here, we show the feasibility of an analytical framework for investigating strong-field QED processes in laser beams of arbitrary space-time structure by determining the energy spectrum of positrons produced via nonlinear Breit-Wheeler pair production as a function of the background field in the realistic assumption that the energy of the incoming photon is the largest dynamical energy in the problem. A numerical evaluation of the angular resolved positron spectrum shows significant quantitative differences with respect to the analogous result in a plane wave, such that the present results will be also important for the design of upcoming strong laser facilities aiming at measuring this process.

  1. THREE-BEAM INSTABILITY IN THE LHC*

    CERN Document Server

    Burov, A

    2013-01-01

    In the LHC, a transverse instability is regularly observed at 4TeV right after the beta-squeeze, when the beams are separated by about their ten transverse rms sizes [1-3], and only one of the two beams is seen as oscillating. So far only a single hypothesis is consistent with all the observations and basic concepts, one about a third beam - an electron cloud, generated by the two proton beams in the high-beta areas of the interaction regions. The instability results from a combined action of the cloud nonlinear focusing and impedance.

  2. Vibration reduction in beam bridge under moving loads using nonlinear smooth and discontinuous oscillator

    Directory of Open Access Journals (Sweden)

    Ruilan Tian

    2016-06-01

    Full Text Available The coupled system of smooth and discontinuous absorber and beam bridge under moving loads is constructed in order to detect the effectiveness of smooth and discontinuous absorber. It is worth pointing out that the coupled system contains an irrational restoring force which is a barrier for conventional nonlinear techniques. Hence, the harmonic balance method and Fourier expansion are used to obtain the approximate solutions of the system. The first and the second kind of generalized complete elliptic integrals are introduced. Furthermore, using power flow approach, the performance of smooth and discontinuous absorber in vibration reduction is estimated through the input energy, the dissipated energy, and the damping efficiency. It is interesting that only depending on the value of the smoothness parameter, the efficiency parameter of vibration reduction is optimized. Therefore, smooth and discontinuous absorber can adapt itself to effectively reducing the amplitude of the vibration of the beam bridge, which provides an insight to the understanding of the applications of smooth and discontinuous oscillator in engineering and power flow characteristics in nonlinear system.

  3. Nonlinear optical studies of inorganic nanoparticles-polymer nanocomposite coatings fabricated by electron beam curing

    Science.gov (United States)

    Misra, Nilanjal; Rapolu, Mounika; Venugopal Rao, S.; Varshney, Lalit; Kumar, Virendra

    2016-05-01

    The optical nonlinearity of metal nanoparticles in dielectrics is of special interest because of their high polarizability and ultrafast response that can be utilized in potential device applications. In this study nanocomposite thin films containing in situ generated Ag nanoparticles dispersed in an aliphatic urethane acrylate (AUA) matrix were synthesized using electron beam curing technique, in presence of an optimized concentration of diluent Trimethylolpropanetriacrylate (TMPTA). The metal nanocomposite films were characterized using UV-visible spectrophotometry, transmission electron microscope (TEM) and field emission scanning electron microscope (FE-SEM) techniques. Ag nanoparticle impregnated films demonstrated an absorption peak at ∼420 nm whose intensity increased with increase in the Ag concentration. The optical limiting property of the coatings was tested using a nanosecond Nd-YAG laser operated at third harmonic wavelength of 355 nm. For a 25 ns pulse and 10 Hz cycle, Ag-polymer coatings showed good optical limiting property and the threshold fluence for optical limiting was found to be ∼3.8×10-2 J/cm2 while the transmission decreased to 82%. The nonlinear optical coefficients were also determined using the standard Z-scan technique with picosecond (∼2 ps, 1 kHz) and femtosecond (∼150 fs, 100 MHz) pulses. Open aperture Z-scan data clearly suggested two-photon absorption as the dominant nonlinear absorption mechanism. Our detailed studies suggest these composites are potential candidates for optical limiting applications.

  4. Focused ultrasonic beam behavior at a stress-free boundary and applicability for measuring nonlinear parameter in a reflection mode

    Science.gov (United States)

    Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing

    2017-02-01

    In this work, we employ a focused beam theory to modify the phase reversal at the stress-free boundary, and consequently enhance the second harmonic generation during its back-propagation toward the initial source position. We first confirmed this concept through experiment by using a spherically focused beam at the water-air interface, and measuring the reflected second harmonic and comparing with a planar wave reflected from the same stress-free or a rigid boundary. In order to test the feasibility of this idea for measuring the nonlinearity parameter of solids in a reflection mode, a focused nonlinear ultrasonic beam is modeled for focusing at and reflection from a stress-free boundary. A nonlinearity parameter expression is then defined together with diffraction and attenuation corrections.

  5. Nonlinear Free Vibration Analysis of Thin-walled Curved Beam with Non-symmetric Open Cross Section

    Institute of Scientific and Technical Information of China (English)

    DUAN Hai-juan; SONG Zhen-sen

    2008-01-01

    A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of flexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.

  6. Influence of the transverse beam sizes on the ep -> ep. gamma. cross section at the HERA and a FUTURE CERN electron-proton collider

    Energy Technology Data Exchange (ETDEWEB)

    Kotkin, G.L.; Polityko, S.I.; Serbo, V.G.; Schiller, A.

    1988-06-01

    In the process ep -> ep..gamma.., proposed for luminosity measurements at HERA, impact parameters occur which are larger than the transverse beam sizes in the ep-colliders in HERA and a CERN option (LHC+LEP). This decreases the number of observed photons compared to the standard QED calculation. The difference is larger than 10% at photon energies E/sub ..gamma../ < 0.4E/sub e/ for the CERN option and E/sub ..gamma../ < 0.01E/sub e/ for HERA. (orig.)

  7. Beam-Beam Effect with an External Noise in LHC

    CERN Document Server

    Ohmi, K; Höfle, Wolfgang; Tomás, R; Zimmermann, F

    2007-01-01

    In absence of synchrotron radiation, proton beams do not have any damping mechanism for incoherent betatron motion. A noise, which kicks beam particles in the transverse plane, gives a coherent betatron amplitude. If the system is linear, the coherent motion is maintained in amplitude. Nonlinear force, beam-beam and beam-electron cloud interactions, cause a decoherence of the betatron motion keeping the amplitude of each beam particle, with the result that an emittance growth arises. We focus only on fast noise with a correlation time of 1-100 turns. Slower noise is less serious, because it is regarded as an adiabatic change like a closed orbit change. As sources of the noise, we consider the bunch by bunch feedback system and phase jitter of cavities which turns to transverse noise via a crab cavity.

  8. Sensitivity optimization of the one beam Z-scan technique and a Z-scan technique immune to nonlinear absorption.

    Science.gov (United States)

    Dávila Pintle, José A; Lara, Edmundo Reynoso; Iturbe Castillo, Marcelo D

    2013-07-01

    It is presented a criteria for selecting the optimum aperture radius for the one beam Z-scan technique (OBZT), based on the analysis of the transmittance of the aperture. It is also presented a modification to the OBZT by directly measuring the beam radius in the far field with a rotating disk, which allows to determine simultaneously the non-linear absorptive coefficient and non-linear refractive index, much less sensitive to wave front distortions caused by inhomogeneities of the sample with a negligible loss of signal to noise ratio. It is demonstrated its equivalence to the OBZT.

  9. CP asymmetries with Longitudinal and Transverse Beam Polarizations in Neutralino Production and Decay into the Z^0 Boson at the ILC

    CERN Document Server

    Bartl, Alfred; Kernreiter, T; Kittel, O

    2007-01-01

    We study neutralino production at the linear collider with the subsequent two-body decays ~chi^0_i -> ~chi^0_n Z^0 and Z^0 -> l^+ l^-, with l=e, mu, tau, or Z^0 -> q q- with q=c,b. We show that transverse electron and positron beam polarizations allow the definition of unique CP observables. These are azimuthal asymmetries in the distributions of the final leptons or quarks. We calculate these CP asymmetries and the cross sections in the Minimal Supersymmetric Standard Model with complex higgsino and gaugino parameters mu and M_1. For final quark pairs, we find CP asymmetries as large as 30%. We discuss the significances for observing the CP asymmetries at the International Linear Collider (ILC). Finally we compare the CP asymmetries with those asymmetries which require unpolarized and/or longitudinally polarized beams only.

  10. CP asymmetries with longitudinal and transverse beam polarizations in neutralino production and decay into the Z0 boson at the ILC

    Science.gov (United States)

    Bartl, Alfred; Hohenwarter-Sodek, Karl; Kernreiter, Thomas; Kittel, Olaf

    2007-09-01

    We study neutralino production at the linear collider with the subsequent two-body decays tilde chi0i → tilde chi0nZ0 and Z0 → ell bar-ell, with ell = e, μ, τ, or Z0 → qbar q with q = c, b. We show that transverse electron and positron beam polarizations allow the definition of unique CP observables. These are azimuthal asymmetries in the distributions of the final leptons or quarks. We calculate these CP asymmetries and the cross sections in the Minimal Supersymmetric Standard Model with complex higgsino and gaugino parameters μ and M1. For final quark pairs, we find CP asymmetries as large as 30%. We discuss the significances for observing the CP asymmetries at the International Linear Collider (ILC). Finally we compare the CP asymmetries with those asymmetries which require unpolarized and/or longitudinally polarized beams only.

  11. Physical mechanism of beam halo-chaos formation for high-current proton beam in a periodic-focusing channels and a nonlinear control strategy

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The physical mechanism of the halo-chaos formation for a high intensity proton beam in a periodic-fo cusing channel is analyzed using the transfer mahix theory and a qualiative analysis method.Particles-in-cell simula tims are further used to explore the mechanism of the beam halo-chaos fomation, which concerns not only with thc non linear effect of the beam space charge but also with the lransverse energy exchange belween the particles and the particle core. as well as the chaos generated by the nonlinear resonance ovcrlap. A nonlinear control method is proposed for con trolling tie haho-chaos. Simulation results show lhal the melhod is efhclivc. Somc potemlial applications of the halo chaos conlrol in experimenls are discussed.

  12. Single-Transverse-Spin-Asymmetry studies with a fixed-target experiment using the LHC beams (AFTER@LHC)

    CERN Document Server

    Lansberg, J P; Arnaldi, R; Brodsky, S J; Chambert, V; Da Silva, C; Didelez, J P; Echevarria, M G; Ferreiro, E G; Fleuret, F; Gao, Y; Genolini, B; Hadjidakis, C; Hřivnáčová, I; Kikola, D; Klein, A; Kurepin, A; Kusina, A; Lorcé, C; Lyonnet, F; Massacrier, L; Nass, A; Pisano, C; Robbe, P; Schienbein, I; Schlegel, M; Scomparin, E; Seixas, J; Shao, H S; Signori, A; Steffens, E; Topilskaya, N; Trzeciak, B; Uggerhøj, U I; Uras, A; Ulrich, R; Yang, Z

    2016-01-01

    We discuss the potential of AFTER@LHC to measure single-transverse-spin asymmetries in open-charm and bottomonium production. With a HERMES-like hydrogen polarised target, such measurements over a year can reach precisions close to the per cent level. This is particularly remarkable since these analyses can probably not be carried out anywhere else

  13. Transverse, normal modes of vibration of a cantilever Timoshenko beam with a mass elastically mounted at the free end

    Science.gov (United States)

    Rossit, C. A.; Laura, P. A. A.

    2001-12-01

    An exact solution for the title problem is obtained by means of the classical eigenfunction approach. The natural frequencies are computed for a wide range of the intervening mechanical and geometric parameters. Normal modes of transverse vibration are plotted for some cases of practical interest. The problem is technically important in several areas of applied science and technology.

  14. The role of nonlinear torsional contributions on the stability of flexural-torsional oscillations of open-cross section beams

    Science.gov (United States)

    Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio

    2015-12-01

    An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.

  15. Non-linear beam-beam forces in storage rings. Particular analysis for S. S. C. and L. H. C. parameters

    Energy Technology Data Exchange (ETDEWEB)

    Pusterla, M.; Servizi, G.; Turchetti, G.

    1985-10-01

    Theoretical models, suitable for description of the long behaviour of bunched and unbunched beams of particles in accelerators and storage rings, are becoming more and more appreciated by physicists that want a high luminosity joined with the stability of the beams. Such a point is going to be particulary important for the next generation machines as L.E.P., S.S.C. and L.H.C. In this note we are giving a simplified analysis of the beam-beam non-linear effects for proton colliders on the basis of the latest designs (we think of S.S.C. and L.H.C.). Before doing that, however, we like to consider the general features of the dynamical approaches that describe the beam-beam forces both for the proton proton rings (fixed angle collision) and for proton-antiproton or electronpositron rings (head-on collisions): they follow directly from the recent developments of non-linear classical mechanics, namely the K.A.M. theorem and the transition to a chaotic motion in deterministic mechanical systems.

  16. High Power Amplifiers Chain nonlinearity influence on the accelerating beam stability in free electron laser (FLASH)

    CERN Document Server

    Cichalewski, w

    2010-01-01

    The high power amplifiers transfer characteristics nonlinearities can have a negative influence on the overall system performance. This is also true for the TESLA superconducting cavities accelerating field parameters control systems. This Low Level Radio Frequency control systems uses microwave high power amplifiers (like 10 MW klystrons) as actuators in the mentioned feedback loops. The amplitude compression and phase deviations phenomena introduced to the control signals can reduce the feedback performance and cause electron beam energy instabilities. The transfer characteristics deviations in the Free Electron Laser in Hamburg experiment have been investigated. The outcome of this study together with the description of the developed linearization method based on the digital predistortion approach have been described in this paper. Additionally, the results from the linearization tool performance tests in the FLASH's RF systems have been placed.

  17. Geometric nonlinear free vibration of axially functionally graded non-uniform beams supported on elastic foundation

    Science.gov (United States)

    Lohar, Hareram; Mitra, Anirban; Sahoo, Sarmila

    2016-09-01

    In the present study non-linear free vibration analysis is performed on a tapered Axially Functionally Graded (AFG) beam resting on an elastic foundation with different boundary conditions. Firstly the static problem is carried out through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigen value problem. Minimum potential energy principle is used for the formulation of the static problem whereas for the dynamic problem Hamilton's principle is utilized. The free vibrational frequencies are tabulated for different taper profile, taper parameter and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane.

  18. Measurement of the Beam Longitudinal Profile in a Storage Ring by Non-Linear Laser Mixing

    Science.gov (United States)

    Beche, J.-F.; Byrd, J.; De Santis, S.; Denes, P.; Placidi, M.; Turner, W.; Zolotorev, M.

    2004-11-01

    We report on the development of a new technique for the measurement of the longitudinal beam profile in storage rings. This technique, which has been successfully demonstrated at the Advanced Light Source, mixes the synchrotron radiation with the light from a mode-locked solid-state laser oscillator in a non-linear crystal. The up-converted radiation is then detected with a photomultiplier and processed to extract, store, and display the required information. The available choices of laser repetition frequency, pulse width, and phase modulation give a wide range of options for matching the bunch configuration of a particular storage ring. Besides the dynamic measurement of the longitudinal profile of each bunch, the instrument can monitor the evolution of the bunch tails, the presence of un trapped particles, and their diffusion into nominally empty RF buckets ("ghost bunches").

  19. A Beam-Fourier Technique for the Numerical Investigation of 2D Nonlinear Convective Flows

    Science.gov (United States)

    Papanicolaou, N. C.

    2011-11-01

    In the current work, we develop a numerical method suitable for treating the problem of nonlinear two-dimensional flows in rectangular domains. For the spatial approximation we employ the Fourier-Galerkin approach. More specifically, our basis functions are products of trigonometric and Beam functions. This choice means that the solutions automatically satisfy the boundary and periodic conditions in the x and y directions respectively. The accuracy of the method is assessed by applying it to model problems which admit exact analytical solutions. The numerical and analytic solutions are found to be in good agreement. The convergence rate of the spectral coefficients is found to be fifth-order algebraic in the x-direction and y-direction, confirming the efficiency and speed of our technique.

  20. Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.

    Science.gov (United States)

    Akemann, Walther; Léger, Jean-François; Ventalon, Cathie; Mathieu, Benjamin; Dieudonné, Stéphane; Bourdieu, Laurent

    2015-11-01

    Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions.

  1. Z-scan theory for nonlocal nonlinear media with simultaneous nonlinear refraction and nonlinear absorption.

    Science.gov (United States)

    Rashidian Vaziri, Mohammad Reza

    2013-07-10

    In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.

  2. Nonlinear Deformation Analysis of Saturated Poroelastic Timoshenko Beam%饱和多孔弹性Timoshenko梁的非线性变形分析

    Institute of Scientific and Technical Information of China (English)

    宋少沪; 卢欣; 杨骁

    2012-01-01

    基于微观不可压饱和多孔介质理论和固相骨架有限变形假定,在孔隙流体仅沿梁轴向扩散的限定下,建立了饱和多孔弹性Timoshenko梁非线性弯曲变形的数学模型.在此基础上,利用Galerkin截断法,研究了两端可渗透简支饱和多孔Timoshenko梁在突加横向载荷作用下的拟静态弯曲,给出了饱和多孔弹性Timoshenko梁弯曲时固相挠度、弯矩和孔隙流体压力等效力偶等随时间的响应.比较了饱和多孔 Timoshenko梁和Euler-Bernoulli梁的非线性弯曲,揭示了他们间的差异,指出Timoshenko梁的挠度始终大于Euler-Bernoulli梁的挠度.但不同于Euler-Bernoulli梁,由于剪切变形产生的附加挠度,当载荷突加于梁时,Timoshenko梁挠度由零突增为非零,且随着时间的增加,其挠度逐渐增大至稳态值.同时,由于孔隙流体压力等效力偶逐渐减小至零,梁骨架逐步承担全部的外载荷.%Based on the theory of microscopic incompressible saturated porous media and the hypothesis of finite deformation solid skeleton, a mathematical model for nonlinear bending of saturated poroelastic Timoshenko beams was presented under constraint of diffusion of the pore fluid only existing in the axial direction of beams. Then, quasi-static bending of a simply-supported saturated poroelastic Timoshenko beam with two ends permeable, subjected to a step constant transverse load, was investigated with the Galerkin truncation method. The responses of deflections, bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure with respect to the time were shown in figures. The results of the nonlinear bending of the saturated poroelastic Timoshenko beam were compared with those of the saturated poroelastic Euler-Bernoulli beam, and the differences between them were revealed. It was shown that the deflection of the saturated poroelastic Timoshenko beam is larger than that of the saturated poroelastic Euler

  3. Snap-through and pull-in analysis of an electro-dynamically actuated curved micro-beam using a nonlinear beam model

    Science.gov (United States)

    Hu, Y. J.; Yang, J.; Kitipornchai, S.

    2013-07-01

    This paper presents a geometrically nonlinear micro-beam model for the electro-dynamic analysis of an initially curved micro-beam under an applied voltage, with an emphasis on its snap-through and pull-in behaviors. The governing equations of motion and the associated boundary conditions are derived in an arc coordinate system without involving any assumptions on the nonlinear deformation. Differential quadrature method (DQM) and Petzold-Gear Backward Differentiation Formulas (BDF) are employed to solve the governing equations in the space and time domains respectively to obtain the nonlinear fundamental frequency, snap-through voltage, pull-in voltage and the corresponding mode shapes of a micro-beam clamped at both ends. The present analysis is validated through a direct comparison with the published experimental and numerical results. A parametric study is conducted to investigate the influences of the initial gap, base length, arc rise, and initial curved configuration on the snap-through and pull-in behaviors of the micro-beam.

  4. Fast ion mass spectrometry and charged particle spectrography investigations of transverse ion acceleration and beam-plasma interactions

    Science.gov (United States)

    Gibson, W. C.; Tomlinson, W. M.; Marshall, J. A.

    1987-01-01

    Ion acceleration transverse to the magnetic field in the topside ionosphere was investigated. Transverse acceleration is believed to be responsible for the upward-moving conical ion distributions commonly observed along auroral field lines at altitudes from several hundred to several thousand kilometers. Of primary concern in this investigation is the extent of these conic events in space and time. Theoretical predictions indicate very rapid initial heating rates, depending on the ion species. These same theories predict that the events will occur within a narrow vertical region of only a few hundred kilometers. Thus an instrument with very high spatial and temporal resolution was required; further, since different heating rates were predicted for different ions, it was necessary to obtain composition as well as velocity space distributions. The fast ion mass spectrometer (FIMS) was designed to meet these criteria. This instrument and its operation is discussed.

  5. Transverse vibration of Bernoulli Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

    Science.gov (United States)

    Maiz, Santiago; Bambill, Diana V.; Rossit, Carlos A.; Laura, P. A. A.

    2007-06-01

    The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of the machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. An exact solution for the title problem is obtained in closed-form fashion, considering general boundary conditions by means of translational and rotatory springs at both ends. The model allows to analyze the influence of the masses and their rotatory inertia on the dynamic behavior of beams with all the classic boundary conditions, and also, as particular cases, to determine the frequencies of continuous beams.

  6. Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance

    Directory of Open Access Journals (Sweden)

    Liu-Yang Xiong

    2014-01-01

    Full Text Available Nonlinear dynamics of a viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance is investigated for the first time. For appropriate choice of system parameters, the natural frequency of the second mode is approximately twice that of the first providing the condition for 2 : 1 internal resonance. The ordinary differential equations of the two mode shapes are established using the Galerkin method. The problem is replaced by two coupled second-order differential equations with quadratic and cubic nonlinearities. The multiple scales method is applied to derive the modulation-phase equations. Steady-state solutions of the system as well as their stability are examined. The frequency-amplitude curves exhibit the steady-state response in the directly excited and indirectly excited modes due to modal interaction. The double-jump, the saturation phenomenon, and the nonperiodic region phenomena are observed illustrating the influence of internal resonance. The validity range of the analytical approximations is assessed by comparing the analytical approximate results with a numerical solution by the Runge-Kutta method. The unstable regions in the internal resonance are explored via numerical simulations.

  7. Transverse writing of three-dimensional tubular optical waveguides in glass with slit-shaped femtosecond laser beams

    CERN Document Server

    Liao, Yang; Wang, Peng; Chu, Wei; Wang, Zhaohui; Qiao, Lingling; Cheng, Ya

    2016-01-01

    We report on fabrication of tubular optical waveguides buried in ZBLAN glass based on transverse femtosecond laser direct writing. Irradiation in ZBLAN with focused femtosecond laser pulses leads to decrease of refractive index in the modified region. Tubular optical waveguides of variable mode areas are fabricated by forming the four sides of the cladding with slit-shaped femtosecond laser pulses, ensuring single mode waveguiding with a mode field dimension compatible with direct coupling to single-mode optical fibers.

  8. Transverse writing of three-dimensional tubular optical waveguides in glass with slit-shaped femtosecond laser beams

    OpenAIRE

    Liao, Yang; Qi, Jia; Wang, Peng; Chu, Wei; Wang, Zhaohui; Qiao, Lingling; Cheng, Ya

    2016-01-01

    We report on fabrication of tubular optical waveguides buried in ZBLAN glass based on transverse femtosecond laser direct writing. Irradiation in ZBLAN with focused femtosecond laser pulses leads to decrease of refractive index in the modified region. Tubular optical waveguides of variable mode areas are fabricated by forming the four sides of the cladding with slit-shaped femtosecond laser pulses, ensuring single mode waveguiding with a mode field dimension as small as ~ 4 {\\mu}m.

  9. Transverse writing of three-dimensional tubular optical waveguides in glass with a slit-shaped femtosecond laser beam

    Science.gov (United States)

    Liao, Yang; Qi, Jia; Wang, Peng; Chu, Wei; Wang, Zhaohui; Qiao, Lingling; Cheng, Ya

    2016-06-01

    We report on fabrication of tubular optical waveguides buried in ZBLAN glass based on transverse femtosecond laser direct writing. Irradiation in ZBLAN with focused femtosecond laser pulses leads to decrease of refractive index in the modified region. Tubular optical waveguides of variable mode areas are fabricated by forming the four sides of the cladding with slit-shaped femtosecond laser pulses, ensuring single mode waveguiding with a mode field dimension as small as ~4 μm.

  10. Transverse writing of three-dimensional tubular optical waveguides in glass with a slit-shaped femtosecond laser beam

    OpenAIRE

    Yang Liao; Jia Qi; Peng Wang; Wei Chu; Zhaohui Wang; Lingling Qiao; Ya Cheng

    2016-01-01

    We report on fabrication of tubular optical waveguides buried in ZBLAN glass based on transverse femtosecond laser direct writing. Irradiation in ZBLAN with focused femtosecond laser pulses leads to decrease of refractive index in the modified region. Tubular optical waveguides of variable mode areas are fabricated by forming the four sides of the cladding with slit-shaped femtosecond laser pulses, ensuring single mode waveguiding with a mode field dimension as small as ~4 μm.

  11. High power microwave beam steering based on gyromagnetic nonlinear transmission lines

    Energy Technology Data Exchange (ETDEWEB)

    Romanchenko, I. V., E-mail: riv@lfe.hcei.tsc.ru; Rostov, V. V.; Gunin, A. V.; Konev, V. Yu. [Institute of high current electronics SB RAS, Akademichesky 2/3, 634055, Tomsk (Russian Federation)

    2015-06-07

    We demonstrate electronically controlled beam steering by high power RF pulses produced by two gyromagnetic nonlinear transmission lines (NLTLs) connected to a one high voltage driver. Each NLTL is capable of producing several ns RF pulses with peak power from 50 to 700 MW (6% standard deviation) at frequencies from 0.5 to 1.7 GHz (1% standard deviation) with 100 Hz repetition rate. Using a helix antenna allows irradiating of RF pulses with almost circular polarization and 350 MW maximum peak power, which corresponds to 350 kV effective potential of radiation. At the installation of two identical channels, we demonstrate the possibility of beam steering within ±15° in the horizontal plane by coherent RF pulses with circular polarization at 1.0 GHz center frequency. Fourfold increase in the power flux density for in-phase irradiation of RF pulses is confirmed by comparison with one-channel operation.

  12. A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation

    Science.gov (United States)

    Crivelli, Luis A.; Felippa, Carlos A.

    1992-01-01

    A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.

  13. Nonlinear Earthquake Analysis of Reinforced Concrete Frames with Fiber and Bernoulli-Euler Beam-Column Element

    Directory of Open Access Journals (Sweden)

    Muhammet Karaton

    2014-01-01

    Full Text Available A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.

  14. Nonlinear earthquake analysis of reinforced concrete frames with fiber and Bernoulli-Euler beam-column element.

    Science.gov (United States)

    Karaton, Muhammet

    2014-01-01

    A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.

  15. A Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory

    Science.gov (United States)

    2012-06-09

    these formulations employ some form of either the Euler-Bernoulli or Timoshenko beam theories and are mostly restricted to small strain analysis. The...and Kadioglu [1], wherein a Timoshenko beam element is de- veloped using mixed variational principles. In their work, the finite element model...method in their analysis of cylindrical helical rods (based on the Timoshenko beam hypotheses). Additional numerical formulations for viscoelastic beams

  16. The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model.

    Science.gov (United States)

    Gras, Laure-Lise; Mitton, David; Crevier-Denoix, Nathalie; Laporte, Sébastien

    2012-01-01

    Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.

  17. Vacuum channeling radiation by relativistic electrons in a transverse field of a laser-based Bessel beam.

    Science.gov (United States)

    Schächter, L; Kimura, W D

    2015-05-15

    Relativistic electrons counterpropagating through the center of a radially polarized J_{1} optical Bessel beam in vacuum will emit radiation in a manner analogous to the channeling radiation that occurs when charged particles traverse through a crystal lattice. However, since this interaction occurs in vacuum, problems with scattering of the electrons by the lattice atoms are eliminated. Contrary to inverse Compton scattering, the emitted frequency is also determined by the amplitude of the laser field, rather than only by its frequency. Adjusting the value of the laser field permits the tuning of the emitted frequency over orders of magnitude, from terahertz to soft X rays. High flux intensities are predicted (~100 MW/cm^{2}). Extended interaction lengths are feasible due to the diffraction-free properties of the Bessel beam and its radial field, which confines the electron trajectory within the center of the Bessel beam.

  18. Beam stabilization in the two-dimensional nonlinear Schrödinger equation with an attractive potential by beam splitting and radiation.

    Science.gov (United States)

    leMesurier, Brenton John; Christiansen, Peter Leth; Gaididei, Yuri B; Rasmussen, Jens Juul

    2004-10-01

    The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrödinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrödinger equation in the critical dimension 2 and can lead to a stable oscillating beam. This is observed to involve a splitting of the beam into an inner part that is oscillatory and of subcritical power and an outer dispersing part. An analysis is given in terms of the rate competition between the linear and nonlinear focusing effects, radiation losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials.

  19. Non-linear beam dynamics tests in the LHC: LHC dynamic aperture MD on Beam 2 (24th of June 2012)

    CERN Document Server

    Maclean, E H; Persson, T H B; Redaelli, S; Schmidt, F; Tomas, R; Uythoven, J

    2013-01-01

    This MD note summarizes measurements performed on LHC Beam 2 during the non-linear machine development (MD) of 24 June 2012. The aim of the measurement was to observe the dynamic aperture of LHC Beam 2, and obtain turn-by-turn (TbT) betatron oscillation data, enabling the study of amplitude detuning and resonance driving terms (RDTs). The regular injections required by the MD also represented an opportunity to test a new coupling feedback routine based on the analysis of injection oscillation data. Initial measurements were performed on the nominal state of the LHC at injection. On completion of this study the Landau octupoles were turned off and corrections for higher-order chromaticities were implemented to reduce the non-linearity of the machine as far as possible. A second set of measurements were then performed. All studies were performed using the LHC aperture kicker (MKA).

  20. The dependence of transverse and longitudinal resolutions on incident Gaussian beam widths in the illumination part of optical scanning microscopy

    CERN Document Server

    Chon, H S; Lee, S B; Yoon, S; Kim, J; Lee, J H; An, K; Chon, Hyung-Su; Park, Gisung; Lee, Sang-Bum; Yoon, Seokchan; Kim, Jaisoon; Lee, Jai-Hyung; An, Kyungwon

    2004-01-01

    We studied the intensity distribution of a Gaussian laser beam when it was focussed by an objective lens with its numerical-aperture up to 0.95. We found that the resulting full widths at half maximum (FWHM values) at the focus in the x and z directions were not much different from the ultimate FWHM values when the initial beam waist was equal to the entrance pupil radius of the objective lens. In addition, the increase in FWHM values were less than 100% even when the initial waist was further reduced to a half.

  1. Transversely Compressed Bonded Joints

    DEFF Research Database (Denmark)

    Hansen, Christian Skodborg; Schmidt, Jacob Wittrup; Stang, Henrik

    2012-01-01

    The load capacity of bonded joints can be increased if transverse pressure is applied at the interface. The transverse pressure is assumed to introduce a Coulomb-friction contribution to the cohesive law for the interface. Response and load capacity for a bonded single-lap joint was derived using...... non-linear fracture mechanics. The results indicated a good correlation between theory and tests. Furthermore, the model is suggested as theoretical base for determining load capacity of bonded anchorages with transverse pressure, in externally reinforced concrete structures....

  2. Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

    Directory of Open Access Journals (Sweden)

    Iman Eshraghi

    2016-09-01

    Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

  3. Seismic Performance of RC Beam-Column Connections with Continuous Rectangular Spiral Transverse Reinforcements for Low Ductility Classes

    Directory of Open Access Journals (Sweden)

    Mohammadamin Azimi

    2014-01-01

    Full Text Available The seismic performance of RC columns could be significantly improved by continuous spiral reinforcement as a result of its adequate ductility and energy dissipation capacity. Due to post-earthquake brittle failure observations in beam-column connections, the seismic behaviour of such connections could greatly be improved by simultaneous application of this method in both beams and columns. In this study, a new proposed detail for beam to column connection introduced as “twisted opposing rectangular spiral” was experimentally and numerically investigated and its seismic performance was compared against normal rectangular spiral and conventional shear reinforcement systems. In this study, three full scale beam to column connections were first designed in conformance with Eurocode (EC2-04 for low ductility class connections and then tested by quasistatic cyclic loading recommended by ACI Building Code (ACI 318-02. Next, the experimental results were validated by numerical methods. Finally, the results revealed that the new proposed connection could improve the ultimate lateral resistance, ductility, and energy dissipation capacity.

  4. 智能悬臂梁横向振动的行波解%WAVE PROPAGATION SOLUTION OF SMART CANTILEVER BEAMS TRANSVERSE VIBRATION

    Institute of Scientific and Technical Information of China (English)

    郭兰满; 黄迪山; 唐亮; 朱晓锦

    2011-01-01

    介绍智能梁的行波建模方法及其横向振动固有频率的计算方法.行波建模方法主要步骤包括,①求出Timoshenko梁横向振动方程的谐波解.②根据弯曲波的传播特性,给出弯曲波的传递关系;在智能梁上截面尺寸改变处和边界处,根据其连续条件和平衡条件,给出波的反射关系和透射关系.③通过联立智能梁内所有的传递、反射、透射关系,求得整体智能梁的特征方程.文中以智能悬臂梁为算例,通过解析法(包括Timoshenko梁模型和Euler-Bernoulli梁模型)与有限元法得到横向振动频率的比较,验证行波建模方法的有效性.此外,为考虑压电片材料对智能梁整体模型的影响,引入等效弹性模量.%A smart beam is modeled by a wave propagation method, and is used for computing the natural frequency and mode of transverse vibration. The wave propagating modeling contains three steps. Firstly, a general solution in the form of harmonic is given from the governing equation of Timoshenko beam vibration. Secondly, in accordance with traveling manner of elastic bending wave, transfer matrices are determined. Also, the reflection and transmission incited by harmonic disturbance on those cross-section discontinuities and boundaries are derived respectively. Finally, all of these matrices are combined into the equation reflecting the global characteristic of the smart beam. Examples of cantilever beam are presented to illustrate the valid of wave propagation modeling by comparing analytical solutions of Timosheko beam with a FEA( finite element analysis) solution. To consider different materials in the smart beam where the foundational material is mixed with some piezoelectric components, an equivalent elastic modulus was applied in the model of smart beam as a whole.

  5. Strengthening of RC Beams with Large Openings in Shear by CFRP Laminates: Experiment and 2D Nonlinear Finite Element Analysis

    Directory of Open Access Journals (Sweden)

    S.C. Chin

    2012-05-01

    Full Text Available This study presents the experimental study and numerical analysis of Reinforced Concrete (RC beams with large square openings placed in the shear region, at a distance 0.5d and d away from the support, strengthened by Carbon Fiber Reinforced Polymer (CFRP laminates. This research aims to investigate the strength losses in RC beam due to the presence of large square openings placed at two different locations in shear region. Also, in order to re-gain the beam structural capacity loss due to the openings, strengthening by CFRP laminates around the openings were studied. A total of six RC beams were tested to failure under four point loading including control beams, un-strengthened and strengthened RC beams with large square openings in shear region at a distance 0.5d and d away from the support. The CFRP strengthening configuration considered in this study was a full wrapping system around the square openings. A nonlinear finite element program, ATENA was used to validate the results of the tested beams. Comparisons between the finite element predictions and experimental results in terms of crack patterns and load deflection relationships are presented. The crack pattern results of the finite element model show good agreement with the experimental data. The load midspan deflection curves of the finite element models exhibited a stiffer result compared to the experimental beams. The possible reason may be due to the perfect bond assumption between the concrete and steel reinforcement.

  6. Collisionless damping of circularly polarized nonlinear Alfvén waves in solar wind plasmas with and without beam protons

    Energy Technology Data Exchange (ETDEWEB)

    Nariyuki, Y. [Faculty of Human Development, University of Toyama, 3190, Toyama City, Toyama 930-8555 (Japan); Hada, T. [Department of Earth System Science and Technology, Kyushu University, 6-1, Kasuga City, Fukuoka 816-8580 (Japan); Tsubouchi, K., E-mail: nariyuki@edu.u-toyama.ac.jp [Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550 (Japan)

    2014-10-01

    The damping process of field-aligned, low-frequency right-handed polarized nonlinear Alfvén waves (NAWs) in solar wind plasmas with and without proton beams is studied by using a two-dimensional ion hybrid code. The numerical results show that the obliquely propagating kinetic Alfvén waves (KAWs) excited by beam protons affect the damping of the low-frequency NAW in low beta plasmas, while the nonlinear wave-wave interaction between parallel propagating waves and nonlinear Landau damping due to the envelope modulation are the dominant damping process in high beta plasmas. The nonlinear interaction between the NAWs and KAWs does not cause effective energy transfer to the perpendicular direction. Numerical results suggest that while the collisionless damping due to the compressibility of the envelope-modulated NAW plays an important role in the damping of the field-aligned NAW, the effect of the beam instabilities may not be negligible in low beta solar wind plasmas.

  7. Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundations under a moving load

    Science.gov (United States)

    Ding, Hu; Chen, Li-Qun; Yang, Shao-Pu

    2012-05-01

    The present paper investigates the convergence of the Galerkin method for the dynamic response of an elastic beam resting on a nonlinear foundation with viscous damping subjected to a moving concentrated load. It also studies the effect of different boundary conditions and span length on the convergence and dynamic response. A train-track or vehicle-pavement system is modeled as a force moving along a finite length Euler-Bernoulli beam on a nonlinear foundation. Nonlinear foundation is assumed to be cubic. The Galerkin method is utilized in order to discretize the nonlinear partial differential governing equation of the forced vibration. The dynamic response of the beam is obtained via the fourth-order Runge-Kutta method. Three types of the conventional boundary conditions are investigated. The railway tracks on stiff soil foundation running the train and the asphalt pavement on soft soil foundation moving the vehicle are treated as examples. The dependence of the convergence of the Galerkin method on boundary conditions, span length and other system parameters are studied.

  8. Beware the two-beam coupling phase shift: Interpreting pump-probe measurements of the nonlinear refractive index

    CERN Document Server

    Wahlstrand, J K; McCole, E T; Cheng, Y -H; Palastro, J P; Levis, R J; Milchberg, H M

    2013-01-01

    Nonlinear optics experiments measuring phase shifts induced in a weak probe pulse by a strong pump pulse must account for coherent effects that only occur when the pump and probe pulses are temporally overlapped. It is well known that a weak probe beam experiences a greater phase shift from a strong pump beam than the pump beam induces on itself. The physical mechanism behind the enhanced phase shift is diffraction of pump light into the probe direction by a nonlinear refractive index grating produced by interference between the two beams. For an instantaneous third-order response, the effect of the grating is to simply double the probe phase shift, but when delayed nonlinearities are considered, the effect is more complex. A comprehensive treatment is given for both degenerate and nondegenerate pump-probe experiments in noble and diatomic gases. Results of numerical calculations are compared to a recent transient birefringence measurement [Loriot et al., Opt. Express 17, 13429 (2009)] and a recent spectral i...

  9. A Study of High Transverse Momentum Direct Photon Production in Interactions of 500 GeV/c $\\pi^{-}$ and Proton Beams on a Beryllium Target

    Energy Technology Data Exchange (ETDEWEB)

    Choudhary, Brajesh Chandra [Univ. of Delhi, New Delhi (India)

    1991-01-01

    This thesis presents the measurement of inclusive direct photon production cross section for experiment E706* for the data accumulated during 1987-88 fixed target run at Fermilab.$^{\\dagger}$ The experiment employed a large liquid argon sampling calorimeter for electromagnetic particle detection with an energy resolution of approximately 15% $\\sqrt{E}$. The spectrometer was exposed to incident $\\pi^-$ and proton beam interacting with Beryllium (Be) target. The spectrometer triggered on high transverse momentum ($P_{\\tau}$) electromagnetic showers. The incident $\\pi^-$ beam was employed to measure the inclusive direct photon production cross sections from Be target in the $P_{\\tau}$ range 3.5 < $P_{\\tau}$ < 10 GeV/c. The incident proton beam was used to measure the inclusive direct photon production cross-sections from Be target in the $P_{\\tau}$ range 4 < $P_{\\tau}$ < 8 GeV/c. The cross sections are presented as a function of $P_{\\tau}$ averaged over the rapidity ranges - .7 < y < - .2, - .2 < y < .2, .2 < y < .7 and - .7 < y < .7, as well as a function of rapidity integrated over $P_{\\tau}$ range of 4 to 8 GeV/c. The ratio of direct photon production to $\\pi^0$ production ($\\gamma/\\pi^0$ ) is also presented. The $\\gamma/\\pi^0$ ratio for $\\pi^-$ and proton beam on Beryllium target is compared to leading log Quantum Chromodynarnics ( QCD) predictions. The direct photon cross sections are compared to next to leading log QCD predictions. Results are also compared to previous experiments.

  10. Lie map for the nonlinear transport of continuous intense beams in the axial-symmetric electrostatic fields

    Institute of Scientific and Technical Information of China (English)

    Jianqin Lü; Xiaosong Zhao

    2008-01-01

    Nonlinear transport of intense continuous beam in the axial-symmetric electrostatic fields is analyzed with the Lie algebraic method.The K-V particle distribution is adopted in the analysis. The results obtained can be used in the calculations of the intense continuous beam dynamics in the beam optical systems consisting of drift spaces, electrostatic lenses, and DC electrostatic accelerating tubes. A com-puter code has been designed for practical simulations. To meet the needs of accurate calculation, all the elements are divided into many small segments, the electric fields in each segment are regarded as uniform fields, and the dividing points are treated as thin lenses. Iter-ation procedures are adopted in the code to obtain self-consistent solutions. The code can be used to design low energy dc beam transport systems, electrostatic accelerators, and ion implantation machines.

  11. Nonlinear fracture mechanics investigation on the ductility of reinforced concrete beams

    Directory of Open Access Journals (Sweden)

    A. Carpinteri

    Full Text Available In the present paper, a numerical algorithm based on the finite element method is proposed for the prediction of the mechanical response of reinforced concrete (RC beams under bending loading. The main novelty of such an approach is the introduction of the Overlapping Crack Model, based on nonlinear fracture mechanics concepts, to describe concrete crushing. According to this model, the concrete dam- age in compression is represented by means of a fictitious interpenetration. The larger is the interpenetration, the lower are the transferred forces across the damaged zone. The well-known Cohesive Crack Model in tension and an elastic-perfectly plastic stress versus crack opening displacement relationship describing the steel reinforcement behavior are also integrated into the numerical algorithm. The application of the proposed Cohesive-Overlapping Crack Model to the assessment of the minimum reinforcement amount neces- sary to prevent unstable tensile crack propagation and to the evaluation of the rotational capacity of plastic hinges, permits to predict the size-scale effects evidenced by several experimental programs available in the literature. According to the obtained numerical results, new practical design formulae and diagrams are proposed for the improvement of the current code provisions which usually disregard the size effects.

  12. Determination of the Mode I Interlaminar Fracture Toughness by Using a Nonlinear Double-Cantilever Beam Specimen

    Science.gov (United States)

    Pavelko, V.; Lapsa, K.; Pavlovskis, P.

    2016-07-01

    The aim of this study is estimation of the effect of large deflections of a double-cantilever beam (DCB) on the accuracy of determination of the mode I interlaminar fracture toughness GIc of layered composites by using the nonlinear theory of bending of beams. The differential equation of the deflection curve of arm of the DCB specimen in the natural form was used to analyze the strain energy of the specimen and its strain energy release rate GI upon propagation of delamination under the action of cleavage forces at the ends of cantilevers. An algorithm for calculating the strain energy and its release rate in the DCB specimens is realized in the form of a MATLAB code. An experimental study was carried out on DCB specimens of a highly flexible carbon/epoxy laminate. The validity of the nonlinear model developed is demonstrated. The standard methods used to determine GIc are refined for the case of highly flexible specimens.

  13. Remarks on the derivation of the governing equations for the dynamics of a nonlinear beam to a non ideal shaft coupling

    Energy Technology Data Exchange (ETDEWEB)

    Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo (Brazil); Balthazar, José M., E-mail: jmbaltha@gmail.com [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo, Brazil and Universidade Estadual Paulista, Faculdade de Engenharia Mec and #x00E (Brazil); Francisco, Cayo Prado Fernandes [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo, Brazil and Instituto de Aeronáutica e Espaço, Departamento de (Brazil)

    2014-12-10

    We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.

  14. Landau Damping of Beam Instabilities by Electron Lenses

    Energy Technology Data Exchange (ETDEWEB)

    Shiltsev, V. [Fermilab; Alexahin, Yuri; Burov, A. [Fermilab; Valishev, A. [Fermilab

    2017-06-26

    Modern and future particle accelerators employ increasingly higher intensity and brighter beams of charged particles and become operationally limited by coherent beam instabilities. Usual methods to control the instabilities, such as octupole magnets, beam feedback dampers and use of chromatic effects, become less effective and insufficient. We show that, in contrast, Lorentz forces of a low-energy, a magnetically stabilized electron beam, or "electron lens", easily introduces transverse nonlinear focusing sufficient for Landau damping of transverse beam instabilities in accelerators. It is also important that, unlike other nonlinear elements, the electron lens provides the frequency spread mainly at the beam core, thus allowing much higher frequency spread without lifetime degradation. For the parameters of the Future Circular Collider, a single conventional electron lens a few meters long would provide stabilization superior to tens of thousands of superconducting octupole magnets.

  15. Internal transport barrier triggered by non-linear lower hybrid wave deposition under condition of beam-driven toroidal rotation

    Science.gov (United States)

    Gao, Q. D.; Budny, R. V.

    2015-03-01

    By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (Vϕ) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.

  16. Nonlinear Phenomena in the Single-Mode Dynamics in an AFM Cantilever Beam

    KAUST Repository

    Ruzziconi, Laura

    2016-12-05

    This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario of the structure response in a neighborhood of the primary resonance. Extensive numerical simulations are performed when both the forcing amplitude and frequency are varied, ranging from low up to elevated excitations. The coexistence of competing attractors with different characteristics is analyzed. Both the non-resonant and the resonant behavior are observed, as well as ranges of inevitable escape. Versatility of behavior is highlighted, which may be attractive in applications. Special attention is devoted to the effects of the tip-sample separation distance, since this aspect is of fundamental importance to understand the operation of an AFM. We explore the metamorphoses of the multistability region when the tip-sample separation distance is varied. To have a complete description of the AFM response, comprehensive behavior charts are introduced to detect the theoretical boundaries of appearance and disappearance of the main attractors. Also, extensive numerical simulations investigate the AFM response when both the forcing amplitude and the tip-sample separation distance are considered as control parameters. The main features are analyzed in detail and the obtained results are interpreted in terms of oscillations of the cantilever-tip ensemble. However, we note that all the aforementioned results represent the limit when disturbances are absent, which never occurs in practice. Here comes the importance of overcoming local investigations and exploring dynamics from a global perspective, by introducing dynamical integrity concepts. To extend the AFM results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After performing a systematic basin of attraction analysis, integrity

  17. Effect of CFRP Schemes on the Flexural Behavior of RC Beams Modeled by Using a Nonlinear Finite-element Analysis

    Science.gov (United States)

    Al-Rousan, R. Z.

    2015-09-01

    The main objective of this study was to assess the effect of the number and schemes of carbon-fiber-reinforced polymer (CFRP) sheets on the capacity of bending moment, the ultimate displacement, the ultimate tensile strain of CFRP, the yielding moment, concrete compression strain, and the energy absorption of RC beams and to provide useful relationships that can be effectively utilized to determine the required number of CFRP sheets for a necessary increase in the flexural strength of the beams without a major loss in their ductility. To accomplish this, various RC beams, identical in their geometric and reinforcement details and having different number and configurations of CFRP sheets, are modeled and analyzed using the ANSYS software and a nonlinear finite-element analysis.

  18. Analytical Solutions for the Nonlinear Longitudinal Drift Compression (Expansion) of Intense Charged Particle Beams

    Energy Technology Data Exchange (ETDEWEB)

    Edward A. Startsev; Ronald C. Davidson

    2004-04-09

    To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.

  19. Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method

    Science.gov (United States)

    Mei, Chuh; Shen, Mo-How

    1987-01-01

    Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.

  20. Beam stabilization in the two-dimensional nonlinear Schrodinger equation with an attractive potential by beam splitting and radiation

    DEFF Research Database (Denmark)

    leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich

    2004-01-01

    The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...

  1. 基于梁格法的预制箱梁横向刚度模拟研究%Study of Transverse Stiffness Simulaton Based on Beam Grillage Method for Prefabricated Box Girder

    Institute of Scientific and Technical Information of China (English)

    杨圣超; 夏兴佳

    2016-01-01

    To correctly simulate the transverse stiffness of the spatial beam grillage model of the prefabricated box beam ,the right deck of the Weijiacun Zhong Bridge on the Zhunxing Heavy Load Expressway was taken as the study background ,to study the influence of the type of the vir‐tual beams in the spatial beam grillage model of a prestressed box beam on the transverse stiffness . The bridge is a 4 × 20 m prestressed concrete continuous box beam bridge ,to which full loads was applied according to the static test results gained when the bridge was completed and transferred , to test the strain and deflection of the main beam .The MIDAS Civil software was used to establish the spatial beam grillage models of the main beam with three types of virtual beams ,to calculate the main beam bending moment under the design loads and testing loads ,and the strain and deflec‐tion of the main beam under the maximum positive bending moment and the related verification co‐efficients ,and the calculated results were compared with the measured ones .The results demon‐strate that the transverse stiffness of the spatial beam grillage model show s sign of increase as the increase of the length of the rigid zone of the virtual beam and the decrease of the efficient length of the virtual beam .And when the part of the virtual beam from the center of the stringers to the in‐ner edge of the stringer webs was set as the rigid zone ,the transverse stiffness simulated by the spatial beam grillage model is the closest to the transverse stiffness of the actual bridge .%为准确模拟预制箱梁空间梁格模型的横向刚度,以准兴重载高速公路魏家村中桥右幅桥为背景,研究预制箱梁空间梁格模型中虚梁形式对横向刚度的影响。该桥为4×20 m预制混凝土连续箱梁桥,按交工静载试验满载加载,测试主梁的应变和挠度;采用M IDAS Civil软件建立3种虚梁形式的主梁空间梁格模型,计算设计荷载和试验

  2. Finite Difference Method of Free Transverse Vibration Equations of Beams%梁自由横振动方程的有限差分方法

    Institute of Scientific and Technical Information of China (English)

    杜绍洪

    2012-01-01

    以简支梁的自由横振动问题为背景,求解一个非稳态四阶线性偏微分方程的初边值问题.通过引进辅助函数组,将四阶问题转化为二阶混合初边值问题.对两个辅助函数和二阶混合初边值问题进行离散并消掉中间变量,对由简支梁两端挠度为零得来的二阶偏微分边界条件进行近似处理,构造出求解四阶非稳态线性偏微分方程的差分隐格式.数值实验表明构造的隐格式绝对稳定并且具有很高的精度阶.%A fourth order partial differential equation which originates from the free transverse vibration of beams, was changed into a second order mixed initial boundary value problem by introducing a couple of auxiliary functions. An implicit scheme of difference was constructed by discretization of two auxiliary functions and the second order mixed initial boundary value problem in which intermediate variables were eliminated and the second order boundary value conditions derived from vanishing deflection at both ends of the beam were approximated. Numerical experiments showed that the developed implicit scheme was absolutely stable and guaranteed a very high accuracy.

  3. Z-scan studies of the nonlinear optical properties of gold nanoparticles prepared by electron beam deposition.

    Science.gov (United States)

    Mezher, M H; Nady, A; Penny, R; Chong, W Y; Zakaria, R

    2015-11-20

    This paper details the fabrication process for placing single-layer gold (Au) nanoparticles on a planar substrate, and investigation of the resulting optical properties that can be exploited for nonlinear optics applications. Preparation of Au nanoparticles on the substrate involved electron beam deposition and subsequent thermal dewetting. The obtained thin films of Au had a variation in thicknesses related to the controllable deposition time during the electron beam deposition process. These samples were then subjected to thermal annealing at 600°C to produce a randomly distributed layer of Au nanoparticles. Observation from field-effect scanning electron microscope (FESEM) images indicated the size of Au nanoparticles ranges from ∼13 to ∼48  nm. Details of the optical properties related to peak absorption of localized surface plasmon resonance (LSPR) of the nanoparticle were revealed by use of UV-Vis spectroscopy. The Z-scan technique was used to measure the nonlinear effects on the fabricated Au nanoparticle layers where it strongly relates LSPR and nonlinear optical properties.

  4. THERMAL POST-BUCKLING OF FUNCTIONALLY GRADED MATERIAL TIMOSHENKO BEAMS

    Institute of Scientific and Technical Information of China (English)

    LI Shi-rong; ZHANG Jing-hua; ZHAO Yong-gang

    2006-01-01

    Analysis of thermal post-buckling of FGM (Functionally Graded Material)Timoshenko beams subjected to transversely non-uniform temperature rise is presented.By accurately considering the axial extension and transverse shear deformation in the sense of theory of Timoshenko beam, geometrical nonlinear governing equations including seven basic unknown functions for functionally graded beams subjected to mechanical and thermal loads were formulated. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using a shooting method, the obtained nonlinear boundary value problem was numerically solved and thermal buckling and post-buckling response of transversely non-uniformly heated FGM Timoshenko beams with fixed-fixed edges were obtained. Characteristic curves of the buckling deformation of the beam varying with thermal load and the power law index are plotted. The effects of material gradient property on the buckling deformation and critical temperature of beam were discussed in details. The results show that there exists the tension-bend coupling deformation in the uniformly heated beam because of the transversely non-uniform characteristic of materials.

  5. Nonlinear Dynamics of High-Brightness Electron Beams and Beam-Plasma Interactions: Theories, Simulations, and Experiments

    Energy Technology Data Exchange (ETDEWEB)

    C. L. Bohn (deceased), P. Piot and B. Erdelyi

    2008-05-31

    According to its original Statement of Work (SOW), the overarching objective of this project is: 'To enhance substantially the understanding of the fundamental dynamics of nonequilibrium high-brightness beams with space charge.' Our work and results over the past three and half years have been both intense and fruitful. Inasmuch as this project is inextricably linked to a larger, growing research program - that of the Beam Physics and Astrophysics Group (BPAG) - the progress that it has made possible cannot easily be separated from the global picture. Thus, this summary report includes major sections on 'global' developments and on those that can be regarded as specific to this project.

  6. Extension of non-linear beam models with deformable cross sections

    Science.gov (United States)

    Sokolov, I.; Krylov, S.; Harari, I.

    2015-12-01

    Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.

  7. Linear and nonlinear theory of the proton beam transit-time oscillator (TTO)

    Science.gov (United States)

    Walsh, John E.; Mostrom, Michael A.; Clark, Randy M.; Arman, M. Joseph; Campbell, Mark M.

    1989-07-01

    A theoretical characterization is presented for both the small- and large-amplitude behaviors of the intense beam-driven transit-time oscillator device which encompasses the effects of the beam self-fields and space-charge effects. The theory has been employed in the development of expressions for comparison with particle simulation results. Attention is given to the effect of beam-plasma frequency on gain, saturation growth in the monotron, the effects of space-charge depression on the transit angle, and the dependence of monotron performance on beam energy.

  8. Internal transport barrier triggered by non-linear lower hybrid wave deposition under condition of beam-driven toroidal rotation

    Energy Technology Data Exchange (ETDEWEB)

    Gao, Q. D., E-mail: qgao@swip.ac.cn [Southwestern Institute of Physics, Chengdu 610041 (China); Budny, R. V. [Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)

    2015-03-15

    By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (T{sub i,e}) and toroidal velocity (V{sub ϕ}) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.

  9. Reliability-based design optimization of a nonlinear elastic plastic thin-walled T-section beam

    Science.gov (United States)

    Ba-Abbad, Mazen A.

    A two part study is performed to investigate the application of reliability-based design optimization (RBDO) approach to design elastic-plastic stiffener beams with T-section. The objectives of this study are to evaluate the benefits of reliability-based optimization over deterministic optimization, and to illustrate through a practical design example some of the difficulties that a design engineer may encounter while performing reliability-based optimization. Other objectives are to search for a computationally economic RBDO method and to utilize that method to perform RBDO to design an elastic-plastic T-stiffener under combined loads and with flexural-torsional buckling and local buckling failure modes. First, a nonlinear elastic-plastic T-beam was modeled using a simple 6 degree-of-freedom non-linear beam element. To address the problems of RBDO, such as the high non-linearity and derivative discontinuity of the reliability function, and to illustrate a situation where RBDO fails to produce a significant improvement over the deterministic optimization, a graphical method was developed. The method started by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor (SF), and based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost for the same level of reliability as the deterministic design. Three failure modes were considered for an elastic-plastic beam of T cross-section under combined axial and bending loads. The failure modes are based on the total plastic failure in a beam section, buckling, and maximum allowable deflection. The results of the first part show that it is possible to get improved optimum designs (more reliable or lighter weight) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly non-linear with respect to

  10. Accurate determination of electronic transport properties of silicon wafers by nonlinear photocarrier radiometry with multiple pump beam sizes

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Qian [Institute of Optics and Electronics, Chinese Academy of Sciences, P. O. Box 350, Shuangliu, Chengdu 610209 (China); University of the Chinese Academy of Sciences, Beijing 100039 (China); Li, Bincheng, E-mail: bcli@uestc.ac.cn [Institute of Optics and Electronics, Chinese Academy of Sciences, P. O. Box 350, Shuangliu, Chengdu 610209 (China); School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054 (China)

    2015-12-07

    In this paper, photocarrier radiometry (PCR) technique with multiple pump beam sizes is employed to determine simultaneously the electronic transport parameters (the carrier lifetime, the carrier diffusion coefficient, and the front surface recombination velocity) of silicon wafers. By employing the multiple pump beam sizes, the influence of instrumental frequency response on the multi-parameter estimation is totally eliminated. A nonlinear PCR model is developed to interpret the PCR signal. Theoretical simulations are performed to investigate the uncertainties of the estimated parameter values by investigating the dependence of a mean square variance on the corresponding transport parameters and compared to that obtained by the conventional frequency-scan method, in which only the frequency dependences of the PCR amplitude and phase are recorded at single pump beam size. Simulation results show that the proposed multiple-pump-beam-size method can improve significantly the accuracy of the determination of the electronic transport parameters. Comparative experiments with a p-type silicon wafer with resistivity 0.1–0.2 Ω·cm are performed, and the electronic transport properties are determined simultaneously. The estimated uncertainties of the carrier lifetime, diffusion coefficient, and front surface recombination velocity are approximately ±10.7%, ±8.6%, and ±35.4% by the proposed multiple-pump-beam-size method, which is much improved than ±15.9%, ±29.1%, and >±50% by the conventional frequency-scan method. The transport parameters determined by the proposed multiple-pump-beam-size PCR method are in good agreement with that obtained by a steady-state PCR imaging technique.

  11. Observations And Measurements of Anomalous Hollow Electron Beams in a Storage Ring

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Y.K.; Li, J.; /Duke U.; Wu, J.; /SLAC

    2006-02-06

    Anomalous hollow electron beams have been recently observed in the Duke storage ring. With a single bunch beam in a lattice with a negative chromaticity, a hollow beam can be created. This beam consists of a solid core beam inside and a large ring beam outside. In this paper, we report the measurements of the hollow beam phenomenon, including its distinct image pattern and spectrum signature, and its evolution with time. By capturing the post-instability bursting beam, the hollow beam is a unique model system for studying transverse instabilities, in particular, the interplay of the wakefield and lattice nonlinearity. The hollow beam can also be used as a tool to study linear and nonlinear particle dynamics in the storage ring.

  12. MULTI-OBJECTIVE ONLINE OPTIMIZATION OF BEAM LIFETIME AT APS

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Yipeng

    2017-06-25

    In this paper, online optimization of beam lifetime at the APS (Advanced Photon Source) storage ring is presented. A general genetic algorithm (GA) is developed and employed for some online optimizations in the APS storage ring. Sextupole magnets in 40 sectors of the APS storage ring are employed as variables for the online nonlinear beam dynamics optimization. The algorithm employs several optimization objectives and is designed to run with topup mode or beam current decay mode. Up to 50\\% improvement of beam lifetime is demonstrated, without affecting the transverse beam sizes and other relevant parameters. In some cases, the top-up injection efficiency is also improved.

  13. Assessment of Two Analytical Methods in Solving the Linear and Nonlinear Elastic Beam Deformation Problems

    DEFF Research Database (Denmark)

    Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari

    2010-01-01

    Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...... and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However...

  14. Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

    Science.gov (United States)

    Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.

    2015-04-01

    In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized

  15. Nonlinear statistical reconstruction for flat-panel cone-beam CT with blur and correlated noise models

    Science.gov (United States)

    Tilley, Steven; Siewerdsen, Jeffrey H.; Zbijewski, Wojciech; Stayman, J. Webster

    2016-03-01

    Flat-panel cone-beam CT (FP-CBCT) is a promising imaging modality, partly due to its potential for high spatial resolution reconstructions in relatively compact scanners. Despite this potential, FP-CBCT can face difficulty resolving important fine scale structures (e.g, trabecular details in dedicated extremities scanners and microcalcifications in dedicated CBCT mammography). Model-based methods offer one opportunity to improve high-resolution performance without any hardware changes. Previous work, based on a linearized forward model, demonstrated improved performance when both system blur and spatial correlations characteristics of FP-CBCT systems are modeled. Unfortunately, the linearized model relies on a staged processing approach that complicates tuning parameter selection and can limit the finest achievable spatial resolution. In this work, we present an alternative scheme that leverages a full nonlinear forward model with both system blur and spatially correlated noise. A likelihood-based objective function is derived from this forward model and we derive an iterative optimization algorithm for its solution. The proposed approach is evaluated in simulation studies using a digital extremities phantom and resolution-noise trade-offs are quantitatively evaluated. The correlated nonlinear model outperformed both the uncorrelated nonlinear model and the staged linearized technique with up to a 86% reduction in variance at matched spatial resolution. Additionally, the nonlinear models could achieve finer spatial resolution (correlated: 0.10 mm, uncorrelated: 0.11 mm) than the linear correlated model (0.15 mm), and traditional FDK (0.40 mm). This suggests the proposed nonlinear approach may be an important tool in improving performance for high-resolution clinical applications.

  16. Evaluation of the Transverse Craniofacial Morphology of Adolescents With Repaired Unilateral Cleft Lip and Palate Using Cone-Beam Computed Tomography.

    Science.gov (United States)

    Buyuk, Suleyman Kutalmiş; Celikoglu, Mevlut; Benkli, Yasin Atakan; Sekerci, Ahmet Ercan

    2016-10-01

    The aim of the study was to evaluate the transverse craniofacial morphology of the adolescent patients affected by unilateral cleft lip and palate (UCLP) and to compare the findings with age- and sex-matched control group without any cleft using their cone-beam computed tomography (CBCT) images. The study sample (n = 56 patients; mean age: 14.35 ± 3.06 years) consisted of 26 UCLP (n = 26 patients; 10 women and 16 men; mean age: 13.70 ± 2.94 years) and 30 control (n = 30 patients; 19 women and 11 men; mean age: 14.90 ± 3.10 years) subjects. Twenty-five conventional skeletal and dental tissue landmarks were identified. Twenty widely used frontal cephalometric variables (14 linear distances, 3 angles, and 3 ratios) were measured. The data were analyzed using the independent t-test between the groups. Patients affected by UCLP had statistically significantly smaller interorbital width (89.83 ± 4.16 mm), maxillary width (58.02 ± 5.77 mm), maxillary intermolar width (52.83 ± 4.83 mm), and upper face height (57.64 ± 4.57 mm) (P cleft width had significant effect on Cr-ANS (r = 0.446, P = 0.022) and the ANS-isf (r = 0.459, P = 0.018) measurements. The UCLP group showed statistically significantly smaller values for interorbital width, maxillary width, maxillary intermolar width, and upper face height than the noncleft controls.

  17. Transverse wobbling

    CERN Document Server

    Frauendorf, S

    2013-01-01

    The wobbling motion of a triaxial rotor coupled to a high-j quasiparticle is treated semiclassically. Longitudinal and transverse coupling regimes can be distinguished depending on, respectively whether the quasiparticle a.m. is oriented parallel or perpendicular to the rotor axis with the largest MoI. Simple analytical expressions for the wobbling frequency and the electromagnetic E2 and M1 transition probabilites are derived assuming rigid alignment of the quasiparticle with one of the rotor axes and harmonic oscillations (HFA). Transverse wobbling is characterized by a decrease of the wobbling frequency with increasing a.m.. Two examples for transverse wobbling, $^{163}$Lu and $^{135}$Pr, are studied in the framework of the full triaxial particle-rotor model and the HFA. The signature of transverse wobbling, decreasing wobbling frequency and enhanced E2 inter-band transitions, is found in agreement with experiment.

  18. Anomalous Hollow Electron Beams in a Storage Ring

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Y.K.

    2005-04-12

    This paper reports the first observations of an anomalous hollow electron beam in the Duke storage ring. Created by exciting the single bunch beam in a lattice with a negative chromaticity, the hollow beam consists of a solid core inside and a large ring outside. We report the detailed measurements of the hollow beam phenomenon, including its distinct image pattern, spectrum signature, and its evolution with time. By capturing the post-instability bursting beam, the hollow beam is a unique model system for studying the transverse instabilities, in particular, the interplay of the wake field and the lattice nonlinearity. In addition, the hollow beam can be used as a powerful tool to study the linear and nonlinear particle dynamics in the storage ring.

  19. Modifying the optical path in a nonlinear double-slit experiment

    CERN Document Server

    Paltoglou, Vassilis

    2015-01-01

    In this letter, we study a nonlinear interferometric setup based on diffraction rather than beam combining. It consists of a nonlinear analogue of Young's double-slit experiment where a nonlinear material is placed exactly after one of the slits. The presence of nonlinearity breaks the transverse spatial symmetry of the system and thus modifies the optical path. For moderate nonlinearities this leads to a self-induced shift of the intensity pattern in the transverse plane. A simple theoretical model is developed which is surprisingly accurate in predicting the intensity profile of the main lobes for a wide range of parameters. We discuss about possible applications of our model in nonlinear interferometry, for example in measuring the nonlinearities of optical materials.

  20. Focal-Plane Imaging of Crossed Beams in Nonlinear Optics Experiments

    Science.gov (United States)

    Bivolaru, Daniel; Herring, G. C.

    2007-01-01

    An application of focal-plane imaging that can be used as a real time diagnostic of beam crossing in various optical techniques is reported. We discuss two specific versions and demonstrate the capability of maximizing system performance with an example in a combined dual-pump coherent anti-Stokes Raman scattering interferometric Rayleigh scattering experiment (CARS-IRS). We find that this imaging diagnostic significantly reduces beam alignment time and loss of CARS-IRS signals due to inadvertent misalignments.