A quantitative analysis of instabilities in the linear chiral sigma model

International Nuclear Information System (INIS)

Nemes, M.C.; Nielsen, M.; Oliveira, M.M. de; Providencia, J. da

1990-08-01

We present a method to construct a complete set of stationary states corresponding to small amplitude motion which naturally includes the continuum solution. The energy wheighted sum rule (EWSR) is shown to provide for a quantitative criterium on the importance of instabilities which is known to occur in nonasymptotically free theories. Out results for the linear σ model showed be valid for a large class of models. A unified description of baryon and meson properties in terms of the linear σ model is also given. (author)

Three caveats for linear stability theory: Rayleigh-Benard convection

International Nuclear Information System (INIS)

Greenside, H.S.

1984-06-01

Recent theories and experiments challenge the applicability of linear stability theory near the onset of buoyancy-driven (Rayleigh-Benard) convection. This stability theory, based on small perturbations of infinite parallel rolls, is found to miss several important features of the convective flow. The reason is that the lateral boundaries have a profound influence on the possible wave numbers and flow patterns even for the largest cells studied. Also, the nonlinear growth of incoherent unstable modes distorts the rolls, leading to a spatially disordered and sometimes temporally nonperiodic flow. Finally, the relation of the skewed varicose instability to the onset of turbulence (nonperiodic time dependence) is examined. Linear stability theory may not suffice to predict the onset of time dependence in large cells close to threshold

Plasma physics and instabilities

International Nuclear Information System (INIS)

Lashmore-Davies, C.N.

1981-01-01

These lectures procide an introduction to the theory of plasmas and their instabilities. Starting from the Bogoliubov, Born, Green, Kirkwood, and Yvon (BBGKY) hierarchy of kinetic equations, the additional concept of self-consistent fields leads to the fundamental Vlasov equation and hence to the warm two-fluid model and the one-fluid MHD, or cold, model. The properties of small-amplitude waves in magnetized (and unmagnetized) plasmas, and the instabilities to which they give rise, are described in some detail, and a complete chapter is devoted to Landau damping. The linear theory of plasma instabilities is illustrated by the current-driven electrostatic kind, with descriptions of the Penrose criterion and the energy principle of ideal MHD. There is a brief account of the application of feedback control. The non-linear theory is represented by three examples: quasi-linear velocity-space instabilities, three-wave instabilities, and the stability of an arbitrarily largeamplitude wave in a plasma. (orig.)

A theory for fluidelastic instability of tube-support-plate-inactive modes

International Nuclear Information System (INIS)

Cai, Y.; Chen, S.S.; Chandra, S.

1991-01-01

Fluidelastic instability of loosely supported tubes, vibrating in a tube support plate (TSP)-inactive mode, is suspected to be one of the main causes of the tube failure in some operating steam generators and heat exchangers. This paper presents a mathematical model for fluidelastic instability of loosely supported tubes exposed to nonuniform crossflow. the model incorporates all motion-dependent fluid forces based on the unsteady-flow theory. In the unstable region associated with a TSP-inactive mode, tube motion can be described by two linear models: TSP-inactive mode when tubes do not strike the TSP, and TSP-active mode when tubes do strike the TSP. The bilinear model (consisting of these linear models) presented here simulates the characteristics of fluidelastic instability of loosely supported tubes in stable and unstable regions associated with TSP-inactive modes. Analytical results obtained with the model are compared with published experimental data; they agree reasonably well. The prediction procedure presented for the fluidelastic instability response of loosely supported tubes is applicable to the stable and unstable regions of the TSP-inactive mode

Linear study of the precessional fishbone instability

Science.gov (United States)

Idouakass, M.; Faganello, M.; Berk, H. L.; Garbet, X.; Benkadda, S.

2016-10-01

The precessional fishbone instability is an m = n = 1 internal kink mode destabilized by a population of trapped energetic particles. The linear phase of this instability is studied here, analytically and numerically, with a simplified model. This model uses the reduced magneto-hydrodynamics equations for the bulk plasma and the Vlasov equation for a population of energetic particles with a radially decreasing density. A threshold condition for the instability is found, as well as a linear growth rate and frequency. It is shown that the mode frequency is given by the precession frequency of the deeply trapped energetic particles at the position of strongest radial gradient. The growth rate is shown to scale with the energetic particle density and particle energy while it is decreased by continuum damping.

Linear response in stochastic mean-field theories and the onset of instabilities

International Nuclear Information System (INIS)

Colonna, M.; Chomaz, Ph.

1993-01-01

The small amplitude response of stochastic one-body theories, such as the Boltzmann-Langevin approach is studied. Whereas the two-time correlation function only describes the propagation of fluctuations initially present, the equal-time correlation function is related to the source of stochasticity. For stable systems it yields the Einstein relation, while for unstable systems it determines the growth of the instabilities. These features are illustrated for unstable nuclear matter in two dimensions. (author) 14 refs.; 5 figs

Instability of the cored barotropic disc: the linear eigenvalue formulation

Science.gov (United States)

Polyachenko, E. V.

2018-05-01

Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of gravitational instability, but calculations of its characteristics in the gas are mostly obscured. The paper suggests a new method for finding the spiral patterns based on an expansion of small amplitude perturbations over Lagrange polynomials in small radial elements. The final matrix equation is extracted from the original hydrodynamical equations without the use of an approximate theory and has a form of the linear algebraic eigenvalue problem. The method is applied to a galactic model with the cored exponential density profile.

Bifurcation theory for toroidal MHD instabilities

International Nuclear Information System (INIS)

Maschke, E.K.; Morros Tosas, J.; Urquijo, G.

1992-01-01

Using a general representation of magneto-hydrodynamics in terms of stream functions and potentials, proposed earlier, a set of reduced MHD equations for the case of toroidal geometry had been derived by an appropriate ordering with respect to the inverse aspect ratio. When all dissipative terms are neglected in this reduced system, it has the same linear stability limits as the full ideal MHD equations, to the order considered. When including resistivity, thermal conductivity and viscosity, we can apply bifurcation theory to investigate nonlinear stationary solution branches related to various instabilities. In particular, we show that a stationary solution of the internal kink type can be found

Non-linear time series analysis on flow instability of natural circulation under rolling motion condition

International Nuclear Information System (INIS)

Zhang, Wenchao; Tan, Sichao; Gao, Puzhen; Wang, Zhanwei; Zhang, Liansheng; Zhang, Hong

2014-01-01

Highlights: • Natural circulation flow instabilities in rolling motion are studied. • The method of non-linear time series analysis is used. • Non-linear evolution characteristic of flow instability is analyzed. • Irregular complex flow oscillations are chaotic oscillations. • The effect of rolling parameter on the threshold of chaotic oscillation is studied. - Abstract: Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions were studied by the method of non-linear time series analysis. Experimental flow time series of different dimensionless power and rolling parameters were analyzed based on phase space reconstruction theory. Attractors which were reconstructed in phase space and the geometric invariants, including correlation dimension, Kolmogorov entropy and largest Lyapunov exponent, were determined. Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions was studied based on the results of the geometric invariant analysis. The results indicated that the values of the geometric invariants first increase and then decrease as dimensionless power increases which indicated the non-linear characteristics of the system first enhance and then weaken. The irregular complex flow oscillation is typical chaotic oscillation because the value of geometric invariants is at maximum. The threshold of chaotic oscillation becomes larger as the rolling frequency or rolling amplitude becomes big. The main influencing factors that influence the non-linear characteristics of the natural circulation system under rolling motion are thermal driving force, flow resistance and the additional forces caused by rolling motion. The non-linear characteristics of the natural circulation system under rolling motion changes caused by the change of the feedback and coupling degree among these influencing factors when the dimensionless power or rolling parameters changes

Linear instability and nonlinear motion of rotating plasma

International Nuclear Information System (INIS)

Liu, J.

1985-01-01

Two coupled nonlinear equations describing the flute dynamics of the magnetically confined low-β collisionless rotating plasma are derived. The linear instability and nonlinear dynamics of the rotating column are analyzed theoretically. In the linear stability analysis, a new sufficient condition of stability is obtained. From the exact solution of eigenvalue equation for Gaussian density profile and uniform rotation of the plasma, the stability of the system strongly depends on the direction of plasma rotation, FLR effect and the location of the conducting wall. An analytic expression showing the finite wall effect on different normal modes is obtained and it explains the different behavior of (1,0) normal mode from other modes. The sheared rotation driven instability is investigated by using three model equilibrium profiles, and the analytic expressions of eigenvalues which includes the wall effect are obtained. The analogy between shear rotation driven instability and the instability driven by sheared plane parallel flow in the inviscid fluid is analyzed. Applying the linear analysis to the central cell of tandem mirror system, the trapped particle instability with only passing electronics is analyzed. For uniform rotation and Gaussian density profile, an analytic expression that determines the stability boundary is found. The nonlinear analysis shows that the nonlinear equations have a solitary vortex solution which is very similar to the vortex solution of nonlinear Rossby wave equation

An exact linear dispersion relation for CRM instability

International Nuclear Information System (INIS)

Choyal, Y; Minami, K

2011-01-01

An exact self-consistent linear dispersion relation of a large orbit electron beam including two principles of cyclotron emission with oscillation frequencies above and below the relativistic electron frequency is derived and analyzed numerically for the first time in the literature. The two principles are cyclotron resonance maser (CRM) instability and Cherenkov instability in the azimuthal direction. Self-consistency in the formulation and inclusion of proper boundary conditions have removed the unphysical instability existing for infinitely large k z observed in conventional dispersion relations of CRM instability.

Waves and instabilities in plasmas

International Nuclear Information System (INIS)

Chen, L.

1987-01-01

The contents of this book are: Plasma as a Dielectric Medium; Nyquist Technique; Absolute and Convective Instabilities; Landau Damping and Phase Mixing; Particle Trapping and Breakdown of Linear Theory; Solution of Viasov Equation via Guilding-Center Transformation; Kinetic Theory of Magnetohydrodynamic Waves; Geometric Optics; Wave-Kinetic Equation; Cutoff and Resonance; Resonant Absorption; Mode Conversion; Gyrokinetic Equation; Drift Waves; Quasi-Linear Theory; Ponderomotive Force; Parametric Instabilities; Problem Sets for Homework, Midterm and Final Examinations

Theory of the current-driven ion cyclotron instability in the bottomside ionosphere

International Nuclear Information System (INIS)

Satyanarayana, P.; Chaturvedi, P.K.; Keskinen, M.J.; Huba, J.D.; Ossakow, S.L.

1985-01-01

A theory of the current-driven electrostatic ion cyclotron (EIC) instability in the collisional bottomside ionosphere is presented. It is found that electron collisions are destabilizing and are crucial for the excitation of the EIC instability in the collisional bottomside ionosphere. Furthermore, the growth rates of the ion cyclotron instability in the bottomside ionosphere maximize for k/sub perpendicular/ rho/sub i/> or =1, where 2π/k/sub perpendicular/ is the mode scale size perpendicular to the magnetic field and rho/sub i/ the ion gyroradius. Realistic plasma density and temperature profiles typical of the high-latitude ionosphere are used to compute the altitude dependence of the linear growth rate of the maximally growing modes and critical drift velocity of the EIC instability. The maximally growing modes correspond to observed tens of meter size irregularities, and the threshold drift velocity required for the excitation of EIC instability is lower for heavier ions (NO + , O + ) than that for the lighter ions (H + ). Dupree's resonance-broadening theory is used to estimate nonlinear saturated amplitudes for the ion cyclotron instability in the high-latitude ionosphere. Comparison with experimental observations is also made. It is conjectured that the EIC instability in the bottomside ionosphere could be a source of transversely accelerated heavier ions and energetic heavy-ion conic distributions at higher altitudes

Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

KAUST Repository

Bakhsh, Abeer

2016-03-09

Numerical simulations and analysis indicate that the Richtmyer-Meshkov instability(RMI) is suppressed in ideal magnetohydrodynamics(MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β=2p/B^2_r) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.

Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width

Science.gov (United States)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2018-04-01

The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number AT=1 and for sufficiently small values of AT. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

Linear predictions of supercritical flow instability in two parallel channels

International Nuclear Information System (INIS)

Shah, M.

2008-01-01

A steady state linear code that can predict thermo-hydraulic instability boundaries in a two parallel channel system under supercritical conditions has been developed. Linear and non-linear solutions of the instability boundary in a two parallel channel system are also compared. The effect of gravity on the instability boundary in a two parallel channel system, by changing the orientation of the system flow from horizontal flow to vertical up-flow and vertical down-flow has been analyzed. Vertical up-flow is found to be more unstable than horizontal flow and vertical down flow is found to be the most unstable configuration. The type of instability present in each flow-orientation of a parallel channel system has been checked and the density wave oscillation type is observed in horizontal flow and vertical up-flow, while the static type of instability is observed in a vertical down-flow for the cases studied here. The parameters affecting the instability boundary, such as the heating power, inlet temperature, inlet and outlet K-factors are varied to assess their effects. This study is important for the design of future Generation IV nuclear reactors in which supercritical light water is proposed as the primary coolant. (author)

Introduction to the linear theory of tearing instabilities

International Nuclear Information System (INIS)

Hazeltine, R.D.

1978-02-01

The reasons why tearing instabilities might bear importantly on tokamak performance are considered. The mechanism of tearing is described and the method by which this mechanism is analyzed is outlined. A survey is given of typical growth rate predictions

Perturbations of linear delay differential equations at the verge of instability.

Science.gov (United States)

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

Explore Stochastic Instabilities of Periodic Points by Transition Path Theory

Science.gov (United States)

Cao, Yu; Lin, Ling; Zhou, Xiang

2016-06-01

We consider the noise-induced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noise-induced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discrete-time continuous-space stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.

Long-wave theory for a new convective instability with exponential growth normal to the wall.

Science.gov (United States)

Healey, J J

2005-05-15

A linear stability theory is presented for the boundary-layer flow produced by an infinite disc rotating at constant angular velocity in otherwise undisturbed fluid. The theory is developed in the limit of long waves and when the effects of viscosity on the waves can be neglected. This is the parameter regime recently identified by the author in a numerical stability investigation where a curious new type of instability was found in which disturbances propagate and grow exponentially in the direction normal to the disc, (i.e. the growth takes place in a region of zero mean shear). The theory describes the mechanisms controlling the instability, the role and location of critical points, and presents a saddle-point analysis describing the large-time evolution of a wave packet in frames of reference moving normal to the disc. The theory also shows that the previously obtained numerical solutions for numerically large wavelengths do indeed lie in the asymptotic long-wave regime, and so the behaviour and mechanisms described here may apply to a number of cross-flow instability problems.

Ion-cyclotron instability in magnetic mirrors

International Nuclear Information System (INIS)

Pearlstein, L.D.

1987-01-01

This report reviews the role of ion-cyclotron frequency instability in magnetic mirrors. The modes discussed here are loss-cone or anisotropy driven. The discussion includes quasilinear theory, explosive instabilities of 3-wave interaction and non-linear Landau damping, and saturation due to non-linear orbits

Magnetohydrodynamic instability in annular linear induction pump

International Nuclear Information System (INIS)

Araseki, Hideo; Kirillov, Igor R.; Preslitsky, Gennady V.; Ogorodnikov, Anatoly P.

2006-01-01

In the previous work, the authors showed some detailed aspects of the magnetohydrodynamic instability arising in an annular linear induction pump: the instability is accompanied with a low frequency pressure pulsation in the range of 0-10 Hz when the magnetic Reynolds number is larger than unity; the low frequency pressure pulsation is produced by the sodium vortices that come from some azimuthal non-uniformity of the applied magnetic field or of the sodium inlet velocity. In the present work, an experiment and a numerical analysis are carried out to verify the pump winding phase shift that is expected as an effective way to suppress the instability. The experimental data shows that the phase shift suppresses the instability unless the slip value is so high, but brings about a decrease of the developed pressure. The numerical results indicate that the phase shift causes a local decrease of the electromagnetic force, which results in the suppression of the instability and the decrease of the developed pressure. In addition, it is exhibited that the intensity of the double-supply-frequency pressure pulsation is in nearly the same level in the case with and without the phase shift

Electromagnetic theory of the radiative Pierce instability

International Nuclear Information System (INIS)

Klochkov, D.N.; Rukhadze, A.A.

1997-01-01

A study is made of the radiative Pierce instability of a relativistic electron beam propagating in a waveguide in the presence of an infinitely strong magnetic field. The perturbation theory is used to find the growth rates and conditions of instability over a broad range of the beam current. It is shown that, under the Pierce boundary conditions, the instability is Raman in nature, and there is no current threshold for the instability. This allows the instability saturation level to be accurately determined from the condition for the violation of the Cherenkov resonance and the radiation efficiency to be estimated

Linear and non-linear calculations of the hose instability in the ion-focused regime

International Nuclear Information System (INIS)

Buchanan, H.L.

1982-01-01

A simple model is adopted to study the hose instability of an intense relativistic electron beam in a partially neutralized, low density ion channel (ion focused regime). Equations of motion for the beam and the channel are derived and linearized to obtain an approximate dispersion relation. The non-linear equations of motion are then solved numerically and the results compared to linearized data

Global Linear Instability at the Dawn of its 4th Decade: A List of Challenges (A Practical Guide on how to Contain the Euphoria and Avoid the Oversell)

OpenAIRE

Theofilis, Vassilios; Gómez, F.; Paredes Gonzalez, Pedro; Le Clainche Martínez, Soledad; Hermanns Navarro, Miguel

2011-01-01

Global linear instability theory is concerned with the temporal or spatial development of small-amplitude perturbations superposed upon laminar steady or time-periodic threedimensional flows, which are inhomogeneous in two (and periodic in one) or all three spatial directions.1 The theory addresses flows developing in complex geometries, in which the parallel or weakly nonparallel basic flow approximation invoked by classic linear stability theory does not hold. As such, global linear theory ...

Overview of nonlinear theory of kinetically driven instabilities

International Nuclear Information System (INIS)

Berk, H.L.; Breizman, B.N.

1998-09-01

An overview is presented of the theory for the nonlinear behavior of instabilities driven by the resonant wave particle interaction. The approach should be applicable to a wide variety of kinetic systems in magnetic fusion devices and accelerators. Here the authors emphasize application to Alfven were driven instability, and the principles of the theory are used to interpret experimental data

Kinetic theory of tearing instabilities

International Nuclear Information System (INIS)

Drake, J.F.; Lee, Y.C.

1977-01-01

The transition of the tearing instability from the collisional to the collisionless regime is investigated kinetically using a Fokker--Planck collision operator to represent electron-ion collisions. As a function of the collisionality of the plasma, the tearing instability falls into three regions, which are referred to as collisionless, semi-collisional, and collisional. The width Δ of the singular layer around kxB 0 =0 is limited by electron thermal motion along B 0 in the collisional and semi-collisional regimes and is typically smaller than rho/sub i/, the ion Larmor radius. Previously accepted theories, which are based on the assumption Δvery-much-greater-thanrho/sub i/, are found to be valid only in the collisional regime. The effects of density and temperature gradients on the instabilities are also studied. The tearing instability is only driven by the temperature gradient in the collisional and semi-collisional regimes. Numerical calculations indicate that the semi-collisional tearing instability is particularly relevant to present day high temperature tokamak discharges

Electromagnetic theory of the radiative Pierce instability

International Nuclear Information System (INIS)

Klochkov, D.N.; Rukhadze, A.A.

1997-01-01

The radiative Pierce instability of a relativistic electron beam in a waveguide stabilized by an infinite strong magnetic field is considered. the increment and conditions for instability development in a wide interval of the beam currents are determined on the basis of the perturbation theory. It is shown that the instability has always the Raman character and is threshold less in current for the Pierce boundary conditions. It permits sufficiently strictly to define the instability saturation level from breaking the resonance condition and to estimate the radiation efficiency

Solar Wind Proton Temperature Anisotropy: Linear Theory and WIND/SWE Observations

Science.gov (United States)

Hellinger, P.; Travnicek, P.; Kasper, J. C.; Lazarus, A. J.

2006-01-01

We present a comparison between WIND/SWE observations (Kasper et al., 2006) of beta parallel to p and T perpendicular to p/T parallel to p (where beta parallel to p is the proton parallel beta and T perpendicular to p and T parallel to p are the perpendicular and parallel proton are the perpendicular and parallel proton temperatures, respectively; here parallel and perpendicular indicate directions with respect to the ambient magnetic field) and predictions of the Vlasov linear theory. In the slow solar wind, the observed proton temperature anisotropy seems to be constrained by oblique instabilities, by the mirror one and the oblique fire hose, contrary to the results of the linear theory which predicts a dominance of the proton cyclotron instability and the parallel fire hose. The fast solar wind core protons exhibit an anticorrelation between beta parallel to c and T perpendicular to c/T parallel to c (where beta parallel to c is the core proton parallel beta and T perpendicular to c and T parallel to c are the perpendicular and parallel core proton temperatures, respectively) similar to that observed in the HELIOS data (Marsch et al., 2004).

Linear theory of the tearing instability in axisymmetric toroidal devices

International Nuclear Information System (INIS)

Rogister, A.; Singh, R.

1988-08-01

We derive a very general kinetic equation describing the linear evolution of low m/l modes in axisymmetric toroidal plasmas with arbitrary cross sections. Included are: Ion sound, inertia, diamagnetic drifts, finite poloidal beta, and finite ion Larmor radius effects. Assuming the magnetic surfaces to form a set of nested tori with circular cross sections of shifted centers, and introducing adequate simplifications justified by our knowledge of experimental tokamak plasmas, we then obtain explicitely the sets of equations describing the coupling of the quasimodes 0/1, 1/1, 2/1, and, for m≥2, m/1, (m+1)/1. By keeping finite aspect ratio effects into account when calculating the jump of the derivative of the eigenfunction, it is shown that the theory can explain the rapid evolution, within one sawtooth period, of the growth rate of the sawteeth precursors from resistive values to magnetohydrodynamic ones. The characteristics thus theoretically required from current profiles in sawtoothing discharges have clearly been observed. Other aspects of the full theory could be relevant to the phenomenon of major disruptions. (orig.)

Anomalous electron transport in Hall-effect thrusters: Comparison between quasi-linear kinetic theory and particle-in-cell simulations

Science.gov (United States)

Lafleur, T.; Martorelli, R.; Chabert, P.; Bourdon, A.

2018-06-01

Kinetic drift instabilities have been implicated as a possible mechanism leading to anomalous electron cross-field transport in E × B discharges, such as Hall-effect thrusters. Such instabilities, which are driven by the large disparity in electron and ion drift velocities, present a significant challenge to modelling efforts without resorting to time-consuming particle-in-cell (PIC) simulations. Here, we test aspects of quasi-linear kinetic theory with 2D PIC simulations with the aim of developing a self-consistent treatment of these instabilities. The specific quantities of interest are the instability growth rate (which determines the spatial and temporal evolution of the instability amplitude), and the instability-enhanced electron-ion friction force (which leads to "anomalous" electron transport). By using the self-consistently obtained electron distribution functions from the PIC simulations (which are in general non-Maxwellian), we find that the predictions of the quasi-linear kinetic theory are in good agreement with the simulation results. By contrast, the use of Maxwellian distributions leads to a growth rate and electron-ion friction force that is around 2-4 times higher, and consequently significantly overestimates the electron transport. A possible method for self-consistently modelling the distribution functions without requiring PIC simulations is discussed.

A general theory for dynamic instability of tube arrays in crossflow

Science.gov (United States)

Chen, S. S.

1987-01-01

A general theory of fluidelastic instability for a tube array in crossflow is presented. Various techniques to obtain the motion-dependent fluid-force coefficients are discussed and the general instability characteristics are summarized. The theory is also used to evaluate the results of other mathematical models for crossflow-induced instability.

Linear Analyses of Magnetohydrodynamic Richtmyer-Meshkov Instability in Cylindrical Geometry

KAUST Repository

Bakhsh, Abeer

2018-05-13

We investigate the Richtmyer-Meshkov instability (RMI) that occurs when an incident shock impulsively accelerates the interface between two different fluids. RMI is important in many technological applications such as Inertial Confinement Fusion (ICF) and astrophysical phenomena such as supernovae. We consider RMI in the presence of the magnetic field in converging geometry through both simulations and analytical means in the framework of ideal magnetohydrodynamics (MHD). In this thesis, we perform linear stability analyses via simulations in the cylindrical geometry, which is of relevance to ICF. In converging geometry, RMI is usually followed by the Rayleigh-Taylor instability (RTI). We show that the presence of a magnetic field suppresses the instabilities. We study the influence of the strength of the magnetic field, perturbation wavenumbers and other relevant parameters on the evolution of the RM and RT instabilities. First, we perform linear stability simulations for a single interface between two different fluids in which the magnetic field is normal to the direction of the average motion of the density interface. The suppression of the instabilities is most evident for large wavenumbers and relatively strong magnetic fields strengths. The mechanism of suppression is the transport of vorticity away from the density interface by two Alfv ́en fronts. Second, we examine the case of an azimuthal magnetic field at the density interface. The most evident suppression of the instability at the interface is for large wavenumbers and relatively strong magnetic fields strengths. After the shock interacts with the interface, the emerging vorticity breaks up into waves traveling parallel and anti-parallel to the magnetic field. The interference as these waves propagate with alternating phase causing the perturbation growth rate of the interface to oscillate in time. Finally, we propose incompressible models for MHD RMI in the presence of normal or azimuthal magnetic

Simulation and quasilinear theory of proton firehose instability

Energy Technology Data Exchange (ETDEWEB)

Seough, Jungjoon [Korean Astronomy and Space Science Institute, Daejeon (Korea, Republic of); Faculty of Human Development, University of Toyama, 3190, Gofuku, Toyama City, Toyama, 930-8555 (Japan); Yoon, Peter H. [University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of); Hwang, Junga [Korean Astronomy and Space Science Institute, Daejeon (Korea, Republic of); Korea, University of Science and Technology, Daejeon (Korea, Republic of)

2015-01-15

The electromagnetic proton firehose instability is driven by excessive parallel temperature anisotropy, T{sub ∥} > T{sub ⊥} (or more precisely, parallel pressure anisotropy, P{sub ∥} > P{sub ⊥}) in high-beta plasmas. Together with kinetic instabilities driven by excessive perpendicular temperature anisotropy, namely, electromagnetic proton cyclotron and mirror instabilities, its role in providing the upper limit for the temperature anisotropy in the solar wind is well-known. A recent Letter [Seough et al., Phys. Rev. Lett. 110, 071103 (2013)] employed quasilinear kinetic theory for these instabilities to explain the observed temperature anisotropy upper bound in the solar wind. However, the validity of quasilinear approach has not been rigorously tested until recently. In a recent paper [Seough et al., Phys. Plasmas 21, 062118 (2014)], a comparative study is carried out for the first time in which quasilinear theory of proton cyclotron instability is tested against results obtained from the particle-in-cell simulation method, and it was demonstrated that the agreement was rather excellent. The present paper addresses the same issue involving the proton firehose instability. Unlike the proton cyclotron instability, however, it is found that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime. Possible causes and mechanisms responsible for the discrepancies are speculated and discussed.

The portrait of eikonal instability in Lovelock theories

Energy Technology Data Exchange (ETDEWEB)

Konoplya, R.A. [Theoretical Astrophysics, Eberhard-Karls University of Tübingen, Tübingen 72076 (Germany); Zhidenko, A., E-mail: roman.konoplya@gmail.com, E-mail: olexandr.zhydenko@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), Rua Abolição, CEP: 09210-180, Santo André, SP (Brazil)

2017-05-01

Perturbations and eikonal instabilities of black holes and branes in the Einstein-Gauss-Bonnet theory and its Lovelock generalization were considered in the literature for several particular cases, where the asymptotic conditions (flat, dS, AdS), the number of spacetime dimensions D , non-vanishing coupling constants (α{sub 1}, α{sub 2}, α{sub 3} etc.) and other parameters have been chosen in a specific way. Here we give a comprehensive analysis of the eikonal instabilities of black holes and branes for the most general Lovelock theory, not limited by any of the above cases. Although the part of the stability analysis is performed here purely analytically and formulated in terms of the inequalities for the black hole parameters, the most general case is treated numerically and the accurate regions of instabilities are presented. The shared Mathematica® code allows the reader to construct the regions of eikonal instability for any desired values of the parameters.

The portrait of eikonal instability in Lovelock theories

Science.gov (United States)

Konoplya, R. A.; Zhidenko, A.

2017-05-01

Perturbations and eikonal instabilities of black holes and branes in the Einstein-Gauss-Bonnet theory and its Lovelock generalization were considered in the literature for several particular cases, where the asymptotic conditions (flat, dS, AdS), the number of spacetime dimensions D, non-vanishing coupling constants (α1, α2, α3 etc.) and other parameters have been chosen in a specific way. Here we give a comprehensive analysis of the eikonal instabilities of black holes and branes for the most general Lovelock theory, not limited by any of the above cases. Although the part of the stability analysis is performed here purely analytically and formulated in terms of the inequalities for the black hole parameters, the most general case is treated numerically and the accurate regions of instabilities are presented. The shared Mathematica® code allows the reader to construct the regions of eikonal instability for any desired values of the parameters.

Velocity space ring-plasma instability, magnetized, Part I: Theory

International Nuclear Information System (INIS)

Lee, J.K.; Birdsall, C.K.

1979-01-01

The interaction of magnetized monoenergetic ions (a ring in velocity space) with a homogeneous Maxwellian target plasma is studied numerically using linear Vlasov theory. The ring may be produced when an energetic beam is injected perpendicular to a uniform magnetic field. In addition to yielding the previously known results, the present study classifies this flute-like instability into three distinct regimes based on the beam density relative to the plasma density, where many features such as physical mechanisms, dispersion diagrams, and maximum growth rates are quite different. The effects of electron dynamics, plasma or ring thermal spread, the ratio of ω/sub p//ω/sub c/ for plasma ions, and electromagnetic modifications are also considered

Instability of black strings in the third-order Lovelock theory

Science.gov (United States)

Giacomini, Alex; Henríquez-Báez, Carla; Lagos, Marcela; Oliva, Julio; Vera, Aldo

2016-05-01

We show that homogeneous black strings of third-order Lovelock theory are unstable under s-wave perturbations. This analysis is done in dimension D =9 , which is the lowest dimension that allows the existence of homogeneous black strings in a theory that contains only the third-order Lovelock term in the Lagrangian. As is the case in general relativity, the instability is produced by long wavelength perturbations and it stands for the perturbative counterpart of a thermal instability. We also provide a comparative analysis of the instabilities of black strings at a fixed radius in general relativity, Gauss-Bonnet, and third-order Lovelock theories. We show that the minimum critical wavelength that triggers the instability grows with the power of the curvature defined in the Lagrangian. The maximum exponential growth during the time of the perturbation is the largest in general relativity and it decreases with the number of curvatures involved in the Lagrangian.

3D Relativistic Magnetohydrodynamic Simulations of Current-Driven Instability. 1; Instability of a Static Column

Science.gov (United States)

Mizuno, Yosuke; Lyubarsky, Yuri; ishikawa, Ken-Ichi; Hardee, Philip E.

2010-01-01

We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.

Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD

KAUST Repository

Gao, Song

2013-05-01

The Richtmyer-Meshkov instability occurs when density-stratified interfaces are impulsively accelerated, typically by a shock wave. We present a numerical method to simulate the Richtmyer-Meshkov instability in cylindrical geometry. The ideal MHD equations are linearized about a time-dependent base state to yield linear partial differential equations governing the perturbed quantities. Convergence tests demonstrate that second order accuracy is achieved for smooth flows, and the order of accuracy is between first and second order for flows with discontinuities. Numerical results are presented for cases of interfaces with positive Atwood number and purely azimuthal perturbations. In hydrodynamics, the Richtmyer-Meshkov instability growth of perturbations is followed by a Rayleigh-Taylor growth phase. In MHD, numerical results indicate that the perturbations can be suppressed for sufficiently large perturbation wavenumbers and magnetic fields.

Use of one-dimensional Cosserat theory to study instability in a viscous liquid jet

International Nuclear Information System (INIS)

Bogy, D.B.

1978-01-01

The problem of the instability of an incompressible viscous liquid jet is considered within the context of one-dimensional Cosserat equations. Linear stability analyses are performed for both the infinite and semi-infinite jets. The results obtained for the inviscid case are compared with the corresponding results derived from ideal fluid equations. They are also compared with recent results by other authors obtained from a different set of one-dimensional jet equations. Solutions are also obtained, within the framework of the linearized theory, to the jet break-up problems formulated as an initial-value problem for the infinite jet and as a boundary-value problem for the semi-infinite jet

Wavelength dependence of the linear growth rate of the Es layer instability

Directory of Open Access Journals (Sweden)

R. B. Cosgrove

2007-06-01

Full Text Available It has recently been shown, by computation of the linear growth rate, that midlatitude sporadic-E (Es layers are subject to a large scale electrodynamic instability. This instability is a logical candidate to explain certain frontal structuring events, and polarization electric fields, which have been observed in Es layers by ionosondes, by coherent scatter radars, and by rockets. However, the original growth rate derivation assumed an infinitely thin Es layer, and therefore did not address the short wavelength cutoff. Also, the same derivation ignored the effects of F region loading, which is a significant wavelength dependent effect. Herein is given a generalized derivation that remedies both these short comings, and thereby allows a computation of the wavelength dependence of the linear growth rate, as well as computations of various threshold conditions. The wavelength dependence of the linear growth rate is compared with observed periodicities, and the role of the zeroth order meridional wind is explored. A three-dimensional paper model is used to explain the instability geometry, which has been defined formally in previous works.

Theory of the rippling instability in toroidal devices

International Nuclear Information System (INIS)

Rogister, A.

1985-04-01

The theory of the rippling instability is developed for axisymmetric toroidal plasmas including ion viscosity and parallel electron heat conduction, but assuming that the growth rate is small compared to the wave angular frequency. Parallel electron heat conduction is stabilizing but ion viscosity broadens the instability domain. Under certain conditions, an important top-bottom asymmetry of the density fluctuation spectrum may arise. (orig./GG)

Vacuum instability in scalar field theories

International Nuclear Information System (INIS)

McKane, A.J.

1978-09-01

Scalar field theories with an interaction of the form gphisup(N) have no stable vacuum state for some range of values of their coupling constant, g. This thesis reports calculations of vacuum instability in such theories. Using the idea that the tunnelling out of the vacuum state is described by the instanton solutions of the theory, the imaginary part of the vertex functions is calculated for the massless theory in the one-loop approximation, near the dimension dsub(c) = 2N/N-2, where the theory is just renormalisable. The calculation differs from previous treatments in that dimensional regularisation is used to control the ultra-violet divergences of the theory. In this way previous analytic calculations in conformally invariant field theories are extended to the case where the theory is almost conformally invariant, since it is now defined in dsub(c) - epsilon dimensions (epsilon > 0). (author)

The linear electric motor: Instability at 1,000 g's

International Nuclear Information System (INIS)

Hunter, S.

1997-01-01

When fluid of high density is supported against gravity by a less dense liquid, the system is unstable, and microscopic perturbations grow at the interface between the fluids. This phenomenon, called the Rayleigh-Taylor instability, also occurs when a bottle of oil-and-vinegar salad dressing is turned upside down. The instability causes spikes of the dense fluid to penetrate the light fluid, while bubbles of the lighter fluid rise into the dense fluid. The same phenomenon occurs when a light fluid is used to accelerate a dense fluid, causing the two fluids to mix at a very high rate. For example, during the implosion of an ICF capsule, this instability can cause enough mixing to contaminate, cool, and degrade the yield of the thermonuclear fuel. The LEM is an excellent tool for studying this instability, but what is it? Think of a miniature high-speed electric train (the container) hurtling down a track (the electrodes) while diagnostic equipment (optical and laser) photographs it. The LEM, consists of four linear electrodes, or rails, that carry an electrical current to a pair of sliding armatures on the container. A magnetic field is produced that works in concert with the rail-armature current to accelerate the container--just as in an electric motor, but in a linear fashion rather than in rotation. The magnetic field is augmented with elongated coils just as in a conventional electric motor. This configuration also helps hold the armatures against the electrodes to prevent arcing. The electrical energy (0.6 megajoules) is provided by 16 capacitor banks that can be triggered independently to produce different acceleration profiles (i.e., how the acceleration varies with time)

Linear theory of a cold relativistic beam in a strongly magnetized finite-geometry plasma

International Nuclear Information System (INIS)

Gagne, R.R.J.; Shoucri, M.M.

1976-01-01

The linear theory of a finite-geometry cold relativistic beam propagating in a cold homogeneous finite-geometry plasma, is investigated in the case of a strongly magnetized plasma. The beam is assumed to propagate parallel to the external magnetic field. It is shown that the instability which takes place at the Cherenkov resonance ωapprox. =k/subz/v/subb/ is of the convective type. The effect of the finite geometry on the instability growth rate is studied and is shown to decrease the growth rate, with respect to the infinite geometry, by a factor depending on the ratio of the beam-to-plasma radius

Electromagnetic ion beam instability upstream of the earth's bow shock

International Nuclear Information System (INIS)

Gary, S.P.; Gosling, J.T.; Forslund, D.W.

1981-01-01

The linear theory of the electromagnetic ion beam instability for arbitrary angles of propagation has been studied. The parameters considered in the theory are typical of the solar wind upstream of the earth's bow shock when a 'reflected' proton beam is present. Maximum growth occurs for propagation parallel to the ambient field B, but this instability also displays significant growth at wave-vectors oblique to B, Oblique, unstable modes seem to be the likely source of the compressive magnetic fluctuations recently observed in conjunction with 'diffuse' ion population. An energetic ion beam does not directly give rise to linear growth of either ion acoustic or whistler mode instabilities

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

Science.gov (United States)

Hall, P.; Malik, M. R.

1984-01-01

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

Science.gov (United States)

Hall, P.; Malik, M. R.

1986-01-01

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

The Theory of Linear Prediction

CERN Document Server

Vaidyanathan, PP

2007-01-01

Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vecto

Electron heat flux instabilities in the solar wind

International Nuclear Information System (INIS)

Gary, S.P.; Feldman, W.C.; Forslund, D.W.; Montgomery, M.D.

1975-01-01

There are at least three plasma instabilities associated with the electron heat flux in the solar wind. This letter reports the study of the unstable fast magnetosonic, Alfven and whistler modes via a computer code which solves the full electromagnetic, linear, Vlasov dispersion relation. Linear theory demonstrates that both the magnetosonic and Alfven instabilities are candidates for turbulent limitation of the heat flux in the solar wind at 1 A.U

Plasma instabilities and turbulence in non-Abelian gauge theories

Energy Technology Data Exchange (ETDEWEB)

Scheffler, Sebastian Herwig Juergen

2010-02-17

Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (instabilities in an idealised setup is investigated. In the second part, the

Plasma instabilities and turbulence in non-Abelian gauge theories

International Nuclear Information System (INIS)

Scheffler, Sebastian Herwig Juergen

2010-01-01

Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (< or similar 1 GeV). Essential results can be translated from the gauge group SU(2) to SU(3) by a simple rescaling procedure. Finally, the role of Nielsen-Olesen instabilities in an idealised setup is investigated. In the second part, the quasi

Some effects of horizontal discretization on linear baroclinic and symmetric instabilities

Science.gov (United States)

Barham, William; Bachman, Scott; Grooms, Ian

2018-05-01

The effects of horizontal discretization on linear baroclinic and symmetric instabilities are investigated by analyzing the behavior of the hydrostatic Eady problem in ocean models on the B and C grids. On the C grid a spurious baroclinic instability appears at small wavelengths. This instability does not disappear as the grid scale decreases; instead, it simply moves to smaller horizontal scales. The peak growth rate of the spurious instability is independent of the grid scale as the latter decreases. It is equal to cf /√{Ri} where Ri is the balanced Richardson number, f is the Coriolis parameter, and c is a nondimensional constant that depends on the Richardson number. As the Richardson number increases c increases towards an upper bound of approximately 1/2; for large Richardson numbers the spurious instability is faster than the Eady instability. To suppress the spurious instability it is recommended to use fourth-order centered tracer advection along with biharmonic viscosity and diffusion with coefficients (Δx) 4 f /(32√{Ri}) or larger where Δx is the grid scale. On the B grid, the growth rates of baroclinic and symmetric instabilities are too small, and converge upwards towards the correct values as the grid scale decreases; no spurious instabilities are observed. In B grid models at eddy-permitting resolution, the reduced growth rate of baroclinic instability may contribute to partially-resolved eddies being too weak. On the C grid the growth rate of symmetric instability is better (larger) than on the B grid, and converges upwards towards the correct value as the grid scale decreases.

Secular instabilities of Keplerian stellar discs

Science.gov (United States)

Kaur, Karamveer; Kazandjian, Mher V.; Sridhar, S.; Touma, Jihad R.

2018-05-01

We present idealized models of a razor-thin, axisymmetric, Keplerian stellar disc around a massive black hole, and study non-axisymmetric secular instabilities in the absence of either counter-rotation or loss cones. These discs are prograde mono-energetic waterbags, whose phase-space distribution functions are constant for orbits within a range of eccentricities (e) and zero outside this range. The linear normal modes of waterbags are composed of sinusoidal disturbances of the edges of distribution function in phase space. Waterbags that include circular orbits (polarcaps) have one stable linear normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive pattern speed and, for polarcaps consisting of orbits with e normal modes for each m, which can be stable or unstable. We derive analytical expressions for the instability condition, pattern speeds, growth rates, and normal mode structure. Narrow bands are unstable to modes with a wide range in m. Numerical simulations confirm linear theory and follow the non-linear evolution of instabilities. Long-time integration suggests that instabilities of different m grow, interact non-linearly, and relax collisionlessly to a coarse-grained equilibrium with a wide range of eccentricities.

Linear contextual modal type theory

DEFF Research Database (Denmark)

Schack-Nielsen, Anders; Schürmann, Carsten

Abstract. When one implements a logical framework based on linear type theory, for example the Celf system [?], one is immediately con- fronted with questions about their equational theory and how to deal with logic variables. In this paper, we propose linear contextual modal type theory that gives...... a mathematical account of the nature of logic variables. Our type theory is conservative over intuitionistic contextual modal type theory proposed by Nanevski, Pfenning, and Pientka. Our main contributions include a mechanically checked proof of soundness and a working implementation....

General theory of the plasmoid instability

International Nuclear Information System (INIS)

Comisso, L.; Lingam, M.; Huang, Y.-M.; Bhattacharjee, A.

2016-01-01

In a general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. We derive and show the scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of plasmoids that depend on the initial perturbation amplitude (ŵ_0), the characteristic rate of current sheet evolution (1/τ), and the Lundquist number (S). They are not simple power laws, and are proportional to S"ατ"β[ln f(S,τ,ŵ_0)]"σ. Finally, the detailed dynamics of the instability is also elucidated, and shown to comprise of a period of quiescence followed by sudden growth over a short time scale.

Employing Theories Far beyond Their Limits - Linear Dichroism Theory.

Science.gov (United States)

Mayerhöfer, Thomas G

2018-05-15

Using linear polarized light, it is possible in case of ordered structures, such as stretched polymers or single crystals, to determine the orientation of the transition moments of electronic and vibrational transitions. This not only helps to resolve overlapping bands, but also assigning the symmetry species of the transitions and to elucidate the structure. To perform spectral evaluation quantitatively, a sometimes "Linear Dichroism Theory" called approach is very often used. This approach links the relative orientation of the transition moment and polarization direction to the quantity absorbance. This linkage is highly questionable for several reasons. First of all, absorbance is a quantity that is by its definition not compatible with Maxwell's equations. Furthermore, absorbance seems not to be the quantity which is generally compatible with linear dichroism theory. In addition, linear dichroism theory disregards that it is not only the angle between transition moment and polarization direction, but also the angle between sample surface and transition moment, that influences band shape and intensity. Accordingly, the often invoked "magic angle" has never existed and the orientation distribution influences spectra to a much higher degree than if linear dichroism theory would hold strictly. A last point that is completely ignored by linear dichroism theory is the fact that partially oriented or randomly-oriented samples usually consist of ordered domains. It is their size relative to the wavelength of light that can also greatly influence a spectrum. All these findings can help to elucidate orientation to a much higher degree by optical methods than currently thought possible by the users of linear dichroism theory. Hence, it is the goal of this contribution to point out these shortcomings of linear dichroism theory to its users to stimulate efforts to overcome the long-lasting stagnation of this important field. © 2018 Wiley-VCH Verlag GmbH & Co. KGa

Beam-beam instability driven by wakefield effects in linear colliders

CERN Document Server

Brinkmann, R; Schulte, Daniel

2002-01-01

The vertical beam profile distortions induced by wakefield effects in linear colliders (the so-called ``banana effect'') generate a beam-beam instability at the collision point when the vertical disruption parameter is large. We illustrate this effect in the case of the TESLA linear collider project. We specify the tolerance on the associated emittance growth, which translates into tolerances on injection jitter and, for a given tuning procedure, on structure misalignments. We look for possible cures based on fast orbit correction at the interaction point and using a fast luminosity monitor.

Linear Gain for the Microbunching Instability in an RF Compressor

International Nuclear Information System (INIS)

Venturini, M.; Migliorati, M.; Ronsivalle, C.; Vaccarezza, C.

2009-01-01

Velocity (or rf) compression has been suggested as a technique for bunch compression complementary to the more established technique involving magnetic chicanes and represents an important research item being investigated at the SPARC test facility. One of the aspects of this technique still not sufficiently understood is its possible impact on the microbunching instability. The purpose of this report is to present the analytical framework for investigating this instability in rf compressors. We use methods similar to those successfully applied to magnetic compressors and derive some integral equations yielding the gain for the instability in linear approximation. The focus here is on the derivation of the relevant equations. Although examples of solutions to these equations are provided we defer a more comprehensive discussion of their implication to a future report. The present study is part of a larger effort for a more comprehensive investigation that eventually will include macroparticle simulations and experiments.

Ionospheric modification and parametric instabilities

International Nuclear Information System (INIS)

Fejer, J.A.

1979-01-01

Thresholds and linear growth rates for stimulated Brillouin and Raman scattering and for the parametric decay instability are derived by using arguments of energy transfer. For this purpose an expression for the ponderomotive force is derived. Conditions under which the partial pressure force due to differential dissipation exceeds the ponderomotive force are also discussed. Stimulated Brillouin and Raman scattering are weakly excited by existing incoherent backscatter radars. The parametric decay instability is strongly excited in ionospheric heating experiments. Saturation theories of the parametric decay instability are therefore described. After a brief discussion of the purely growing instability the effect of using several pumps is discussed as well as the effects of inhomogenicity. Turning to detailed theories of ionospheric heating, artificial spread F is discussed in terms of a purely growing instability where the nonlinearity is due to dissipation. Field-aligned short-scale striations are explained in terms of dissipation of the parametrically excited Langmuir waves (plasma oscillations): they might be further amplified by an explosive instability (except the magnetic equator). Broadband absorption is probably responsible for the 'overshoot' effect: the initially observed level of parametrically excited Langmuir waves is much higher than the steady state level

Quasilinear theory and simulation of Buneman instability

International Nuclear Information System (INIS)

Pavan, J.; Yoon, P. H.; Umeda, T.

2011-01-01

In a recently developed nonlinear theory of Buneman instability, a simplifying assumption of self-similarity was imposed for the electron distribution function, based upon which, a set of moment kinetic equations was derived and solved together with nonlinear wave kinetic equation [P. H. Yoon and T. Umeda, Phys. Plasmas 17, 112317 (2010)]. It was found that the theoretical result compared reasonably against one-dimensional electrostatic Vlasov simulation. In spite of this success, however, the simulated distribution deviated appreciably from the assumed self-similar form during the late stages of nonlinear evolution. In order to rectify this shortcoming, in this paper, the distribution function is computed on the basis of rigorous velocity space diffusion equation. A novel theoretical scheme is developed so that both the quasilinear particle diffusion equation and the adiabatic dispersion relation can be solved for an arbitrary particle distribution function. Comparison with Vlasov simulation over relatively early quasilinear phase of the instability shows a reasonable agreement, despite the fact that quasilinear theory lacks coherent nonlinear effects as well as mode-mode coupling effects.

Linear theory period ratios for surface helium enhanced double-mode Cepheids

International Nuclear Information System (INIS)

Cox, A.N.; Hodson, S.W.; King, D.S.

1979-01-01

Linear nonadiabatic theory period ratios for models of double-mode Cepheids with their two periods between 1 and 7 days have been computed, assuming differing amounts and depths of surface helium enhancement. Evolution theory masses and luminosities are found to be consistent with the observed periods. All models give Pi 1 /Pi 0 approx. =0.70 as observed for the 11 known variables, contrary to previous theoretical conclusions. The composition structure that best fits the period ratios has the helium mass fraction in the outer 10 -3 of the stellar mass (T< or =250,000 K) as 0.65, similar to a previous model for the triple-mode pulsator AC And. This enrichment can be established by a Cepheid wind and downward inverted μ gradient instability mixing in the lifetime of these low-mass classical Cepheids

Wiebel instability of microwave gas discharge in strong linear and circular pulsed fields

International Nuclear Information System (INIS)

Shokri, B.; Ghorbanalilu, M.

2004-01-01

Being much weaker than the atomic fields, the gas breakdown produced by high-power pulsed microwave fields is investigated in the nonrelativistic case. The distribution function of the electrons produced by the interaction with intense linearly and circularly polarized microwave fields is obtained and it is shown that it is in a nonequilibrium state and anisotropic. The discharge mechanism for the gas atoms is governed by electron-impact avalanche ionization. By analyzing the instability of the system and by finding its growth rate, it is shown that the instability which is governed by the anisotropic property of the distribution function is Wiebel instability

Instability in relativistic mean-field theories of nuclear matter

International Nuclear Information System (INIS)

Friman, B.L.; Henning, P.A.

1988-01-01

We investigate the stability of the nuclear matter ground state with respect to small-perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion-collisions are discussed briefly. (orig.)

Instability in relativistic mean-field theories of nuclear matter

International Nuclear Information System (INIS)

Friman, B.L.; Henning, P.A.

1988-01-01

We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly. (orig.)

Nonlinear turbulence theory and simulation of Buneman instability

International Nuclear Information System (INIS)

Yoon, P. H.; Umeda, T.

2010-01-01

In the present paper, the weak turbulence theory for reactive instabilities, formulated in a companion paper [P. H. Yoon, Phys. Plasmas 17, 112316 (2010)], is applied to the strong electron-ion two-stream (or Buneman) instability. The self-consistent theory involves quasilinear velocity space diffusion equation for the particles and nonlinear wave kinetic equation that includes quasilinear (or induced emission) term as well as nonlinear wave-particle interaction term (or a term that represents an induced scattering off ions). We have also performed one-dimensional electrostatic Vlasov simulation in order to benchmark the theoretical analysis. Under the assumption of self-similar drifting Gaussian distribution function for the electrons it is shown that the current reduction and the accompanying electron heating as well as electric field turbulence generation can be discussed in a self-consistent manner. Upon comparison with the Vlasov simulation result it is found that quasilinear wave kinetic equation alone is insufficient to account for the final saturation amplitude. Upon including the nonlinear scattering term in the wave kinetic equation, however, we find that a qualitative agreement with the simulation is recovered. From this, we conclude that the combined quasilinear particle diffusion plus induced emission and scattering (off ions) processes adequately account for the nonlinear development of the Buneman instability.

THREE-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF CURRENT-DRIVEN INSTABILITY. I. INSTABILITY OF A STATIC COLUMN

International Nuclear Information System (INIS)

Mizuno, Yosuke; Nishikawa, Ken-Ichi; Lyubarsky, Yuri; Hardee, Philip E.

2009-01-01

We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic magnetohydrodynamic simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the nonlinear regime, the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depend moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and reaches the nonlinear regime at a later time than the case with constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the nonlinear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the nonlinear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the nonlinear regime nearly ceases for increasing magnetic pitch.

Computer simulations of electromagnetic cool ion beam instabilities. [in near earth space

Science.gov (United States)

Gary, S. P.; Madland, C. D.; Schriver, D.; Winske, D.

1986-01-01

Electromagnetic ion beam instabilities driven by cool ion beams at propagation parallel or antiparallel to a uniform magnetic field are studied using computer simulations. The elements of linear theory applicable to electromagnetic ion beam instabilities and the simulations derived from a one-dimensional hybrid computer code are described. The quasi-linear regime of the right-hand resonant ion beam instability, and the gyrophase bunching of the nonlinear regime of the right-hand resonant and nonresonant instabilities are examined. It is detected that in the quasi-linear regime the instability saturation is due to a reduction in the beam core relative drift speed and an increase in the perpendicular-to-parallel beam temperature; in the nonlinear regime the instabilities saturate when half the initial beam drift kinetic energy density is converted to fluctuating magnetic field energy density.

Linear system theory

Science.gov (United States)

Callier, Frank M.; Desoer, Charles A.

1991-01-01

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

Nonlinear theory for the parametric instability with comparable electron and ion temperatures

International Nuclear Information System (INIS)

Oberman, C.

1972-01-01

The basic linear theory of the parametric instability driven by a pump E 0 sin ω 0 t oscillating near the electron plasma frequency is reviewed. An expression is derived for the temporal nonlinear development of the fluctuation spectrum of the excited waves. For plasma with comparable electron and ion temperatures nonlinear Landau damping of electron plasma waves on ions provides the dominant nonlinearity. The steady state solutions are examined both analytically and numerically in the limit when the spontaneous emission term is small. The characteristics of the plasma wave spectrum agrees well with the general features of ionospheric observations. The enhanced dissipation rate of the pump due to the presence of the fluctuations agrees with laboratory observations. (U.S.)

Rotational instability in a linear theta pinch

International Nuclear Information System (INIS)

Ekdahl, C.; Bartsch, R.R.; Commisso, R.J.; Gribble, R.F.; McKenna, K.F.; Miller, G.; Siemon, R.E.

1980-01-01

The m=1 ''wobble'' instability of the plasma column in a 5-m linear theta pinch has been studied using an axial array of orthogonally viewing position detectors to resolve the wavelength and frequency of the column motion. The experimental results are compared with recent theoretical predictions that include finite Larmor orbit effects. The frequency and wavelength characteristics at saturation agree with the predicted dispersion relation for a plasma rotating faster than the diamagnetic drift speed. Measurements of the magnetic fields at the ends of the pinch establish the existence of currents flowing in such a way that they short out the radial electric fields in the plasma column. The magnitude of rotation, the observed delay in the onset of m=1 motion, and the magnitude of end-shorting currents can all be understood in terms of the torsional Alfven waves that communicate to the central plasma column the information that the ends have been shorted. The same waves are responsible for the torque which rotates the plasma and leads to the observed m=1 instability. Observations of the plasma in the presence of solid end plugs indicate a stabilization of high-m number modes and a reduction of the m=1 amplitude

RELATIVISTIC CYCLOTRON INSTABILITY IN ANISOTROPIC PLASMAS

Energy Technology Data Exchange (ETDEWEB)

López, Rodrigo A.; Moya, Pablo S.; Muñoz, Víctor; Valdivia, J. Alejandro [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago (Chile); Navarro, Roberto E.; Araneda, Jaime A. [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Viñas, Adolfo F., E-mail: rlopez186@gmail.com [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, MD 20771 (United States)

2016-11-20

A sufficiently large temperature anisotropy can sometimes drive various types of electromagnetic plasma micro-instabilities, which can play an important role in the dynamics of relativistic pair plasmas in space, astrophysics, and laboratory environments. Here, we provide a detailed description of the cyclotron instability of parallel propagating electromagnetic waves in relativistic pair plasmas on the basis of a relativistic anisotropic distribution function. Using plasma kinetic theory and particle-in-cell simulations, we study the influence of the relativistic temperature and the temperature anisotropy on the collective and noncollective modes of these plasmas. Growth rates and dispersion curves from the linear theory show a good agreement with simulations results.

Small amplitude waves and linear firehose and mirror instabilities in rotating polytropic quantum plasma

Science.gov (United States)

Bhakta, S.; Prajapati, R. P.; Dolai, B.

2017-08-01

The small amplitude quantum magnetohydrodynamic (QMHD) waves and linear firehose and mirror instabilities in uniformly rotating dense quantum plasma have been investigated using generalized polytropic pressure laws. The QMHD model and Chew-Goldberger-Low (CGL) set of equations are used to formulate the basic equations of the problem. The general dispersion relation is derived using normal mode analysis which is discussed in parallel, transverse, and oblique wave propagations. The fast, slow, and intermediate QMHD wave modes and linear firehose and mirror instabilities are analyzed for isotropic MHD and CGL quantum fluid plasmas. The firehose instability remains unaffected while the mirror instability is modified by polytropic exponents and quantum diffraction parameter. The graphical illustrations show that quantum corrections have a stabilizing influence on the mirror instability. The presence of uniform rotation stabilizes while quantum corrections destabilize the growth rate of the system. It is also observed that the growth rate stabilizes much faster in parallel wave propagation in comparison to the transverse mode of propagation. The quantum corrections and polytropic exponents also modify the pseudo-MHD and reverse-MHD modes in dense quantum plasma. The phase speed (Friedrichs) diagrams of slow, fast, and intermediate wave modes are illustrated for isotropic MHD and double adiabatic MHD or CGL quantum plasmas, where the significant role of magnetic field and quantum diffraction parameters on the phase speed is observed.

Kinematics of Nonlinearly Interacting MHD Instabilities in a Plasma

International Nuclear Information System (INIS)

Hansen, Alexander K.

2000-01-01

Plasmas play host to a wide variety of instabilities. For example, tearing instabilities use finite plasma resistivity to exploit the free energy provided by plasma currents parallel to the magnetic field to alter the magnetic topology of the plasma through a process known as reconnection. These instabilities frequently make themselves known in magnetic confinement experiments such as tokamaks and reversed field pinches (RFPs). In RFP plasmas, in fact, several tearing instabilities (modes) are simultaneously active, and are of large amplitude. Theory predicts that in addition to interacting linearly with magnetic perturbations from outside the plasma, such as field errors or as resistive wall, the modes in the RFP can interact nonlinearly with each other through a three-wave interaction. In the current work investigations of both the linear (external) and nonlinear contributions to the kinematics of the tearing modes in the Madison Symmetric Torus (MST) RFP are reported Theory predicts that tearing modes will respond only to magnetic perturbations that are spatially resonant with them, and was supported by experimental work done on tokamak devices. The results in this work verified that the theory is still applicable to the RFP, in spite of its more complicated magnetic mode structure, involving perturbations of a single poloidal mode number

Theory and Observations of Microbunching Instability in Electron Machines

International Nuclear Information System (INIS)

Stupakov, Gennady V.

2003-01-01

For not very short bunches, the coherent synchrotron radiation (CSR) is usually suppressed by the shielding effect of the conducting walls of the vacuum chamber. However an initial density fluctuation in the beam with a characteristic length much shorter than the bunch length can radiate coherently. If the radiation-reaction force drives growth of the initial fluctuation, one can expect an instability which leads to micro-bunching of the beam and increased coherent radiation at short wavelengths. It has recently been realized that such an instability can play an important role in electron/positron rings where it often manifests itself as a bursting of radiation in the range of hundreds of gigahertz or terahertz. This instability can also be a source of an undesirable emittance growth in bunch compressors used in the next generation short-wavelength FELs. In this paper, we review progress in theoretical studies and numerical simulations of the microbunching instability and show connection of the theory to recent observations in electron machines

Instability in dynamic fracture

Science.gov (United States)

Fineberg, J.; Marder, M.

1999-05-01

The fracture of brittle amorphous materials is an especially challenging problem, because the way a large object shatters is intimately tied to details of cohesion at microscopic scales. This subject has been plagued by conceptual puzzles, and to make matters worse, experiments seemed to contradict the most firmly established theories. In this review, we will show that the theory and experiments fit within a coherent picture where dynamic instabilities of a crack tip play a crucial role. To accomplish this task, we first summarize the central results of linear elastic dynamic fracture mechanics, an elegant and powerful description of crack motion from the continuum perspective. We point out that this theory is unable to make predictions without additional input, information that must come either from experiment, or from other types of theories. We then proceed to discuss some of the most important experimental observations, and the methods that were used to obtain the them. Once the flux of energy to a crack tip passes a critical value, the crack becomes unstable, and it propagates in increasingly complicated ways. As a result, the crack cannot travel as quickly as theory had supposed, fracture surfaces become rough, it begins to branch and radiate sound, and the energy cost for crack motion increases considerably. All these phenomena are perfectly consistent with the continuum theory, but are not described by it. Therefore, we close the review with an account of theoretical and numerical work that attempts to explain the instabilities. Currently, the experimental understanding of crack tip instabilities in brittle amorphous materials is fairly detailed. We also have a detailed theoretical understanding of crack tip instabilities in crystals, reproducing qualitatively many features of the experiments, while numerical work is beginning to make the missing connections between experiment and theory.

Linear network theory

CERN Document Server

Sander, K F

1964-01-01

Linear Network Theory covers the significant algebraic aspect of network theory, with minimal reference to practical circuits. The book begins the presentation of network analysis with the exposition of networks containing resistances only, and follows it up with a discussion of networks involving inductance and capacity by way of the differential equations. Classification and description of certain networks, equivalent networks, filter circuits, and network functions are also covered. Electrical engineers, technicians, electronics engineers, electricians, and students learning the intricacies

Linear spaces: history and theory

OpenAIRE

Albrecht Beutelspracher

1990-01-01

Linear spaces belong to the most fundamental geometric and combinatorial structures. In this paper I would like to give an onerview about the theory of embedding finite linear spaces in finite projective planes.

Fluid aspects of electron streaming instability in electron-ion plasmas

International Nuclear Information System (INIS)

Jao, C.-S.; Hau, L.-N.

2014-01-01

Electrons streaming in a background electron and ion plasma may lead to the formation of electrostatic solitary wave (ESW) and hole structure which have been observed in various space plasma environments. Past studies on the formation of ESW are mostly based on the particle simulations due to the necessity of incorporating particle's trapping effects. In this study, the fluid aspects and thermodynamics of streaming instabilities in electron-ion plasmas including bi-streaming and bump-on-tail instabilities are addressed based on the comparison between fluid theory and the results from particle-in-cell simulations. The energy closure adopted in the fluid model is the polytropic law of d(pρ −γ )/dt=0 with γ being a free parameter. Two unstable modes are identified for the bump-on-tail instability and the growth rates as well as the dispersion relation of the streaming instabilities derived from the linear theory are found to be in good agreement with the particle simulations for both bi-streaming and bump-on-tail instabilities. At the nonlinear saturation, 70% of the electrons are trapped inside the potential well for the drift velocity being 20 times of the thermal velocity and the pρ −γ value is significantly increased. Effects of ion to electron mass ratio on the linear fluid theory and nonlinear simulations are also examined

Theory of linear operations

CERN Document Server

Banach, S

1987-01-01

This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'''') complements this important monograph.

E × B electron drift instability in Hall thrusters: Particle-in-cell simulations vs. theory

Science.gov (United States)

Boeuf, J. P.; Garrigues, L.

2018-06-01

The E × B Electron Drift Instability (E × B EDI), also called Electron Cyclotron Drift Instability, has been observed in recent particle simulations of Hall thrusters and is a possible candidate to explain anomalous electron transport across the magnetic field in these devices. This instability is characterized by the development of an azimuthal wave with wavelength in the mm range and velocity on the order of the ion acoustic velocity, which enhances electron transport across the magnetic field. In this paper, we study the development and convection of the E × B EDI in the acceleration and near plume regions of a Hall thruster using a simplified 2D axial-azimuthal Particle-In-Cell simulation. The simulation is collisionless and the ionization profile is not-self-consistent but rather is given as an input parameter of the model. The aim is to study the development and properties of the instability for different values of the ionization rate (i.e., of the total ion production rate or current) and to compare the results with the theory. An important result is that the wavelength of the simulated azimuthal wave scales as the electron Debye length and that its frequency is on the order of the ion plasma frequency. This is consistent with the theory predicting destruction of electron cyclotron resonance of the E × B EDI in the non-linear regime resulting in the transition to an ion acoustic instability. The simulations also show that for plasma densities smaller than under nominal conditions of Hall thrusters the field fluctuations induced by the E × B EDI are no longer sufficient to significantly enhance electron transport across the magnetic field, and transit time instabilities develop in the axial direction. The conditions and results of the simulations are described in detail in this paper and they can serve as benchmarks for comparisons between different simulation codes. Such benchmarks would be very useful to study the role of numerical noise (numerical

Simulating plasma instabilities in SU(3) gauge theory

International Nuclear Information System (INIS)

Berges, Juergen; Gelfand, Daniil; Scheffler, Sebastian; Sexty, Denes

2009-01-01

We compute nonequilibrium dynamics of plasma instabilities in classical-statistical lattice gauge theory in 3+1 dimensions. The simulations are done for the first time for the SU(3) gauge group relevant for quantum chromodynamics. We find a qualitatively similar behavior as compared to earlier investigations in SU(2) gauge theory. The characteristic growth rates are about 25% lower for given energy density, such that the isotropization process is slower. Measured in units of the characteristic screening mass, the primary growth rate is independent of the number of colors.

An Electromagnetic Drift Instability in the Magnetic Reconnection Experiment (MRX) and its Importance for Magnetic Reconnection

International Nuclear Information System (INIS)

Russell Kulsrud; Hantao Ji; Will Fox; Masaaki Yamada

2005-01-01

The role which resistivity plays in breaking magnetic field lines, heating the plasma, and plasma field slippage during magnetic reconnection is discussed. Magnetic fluctuations are observed in the MRX (Magnetic Reconnection Experiment) that are believed to provide resistive friction or wave resistivity. A localized linear theory has been proposed for their origin as an obliquely propagating Lower Hybrid Drift Instability. In this paper, the linear theory of the instability is summarized, and the resulting heating and slippage are calculated from quasi-linear theory. Making use of measured amplitudes of the magnetic fluctuations in the MRX the amount of these effects is estimated. Within the experimental uncertainties they are shown to be quite important for the magnetic reconnection process

Theory of 'strong' turbulence - Application to the ion acoustic instability

International Nuclear Information System (INIS)

Abdel-Gawad, Hamdy Ibrahim

1984-01-01

In this thesis, we apply the techniques recently developed in the theory of turbulence to study the evolution of the current-driven ion acoustic instability. We present a method allow to describe analytically and with a self-coherent manner the dynamic of the deformation of the distribution function of particles in the same time as the evolution of the turbulent energy. We have also discerned the saturation mechanisms of the instability as well as their domain of validity. (author) [fr

Novel features of non-linear Raman instability in a laser plasma

Czech Academy of Sciences Publication Activity Database

Mašek, Martin; Rohlena, Karel

2010-01-01

Roč. 56, č. 1 (2010), s. 79-90 ISSN 1434-6060 R&D Projects: GA MŠk(CZ) 7E08099; GA MŠk(CZ) LC528; GA ČR GA202/05/2475 Institutional research plan: CEZ:AV0Z10100523 Keywords : laser plasma * non-linear Raman instability Subject RIV: BH - Optics, Masers, Lasers Impact factor: 1.513, year: 2010

Exponential Growth of Nonlinear Ballooning Instability

International Nuclear Information System (INIS)

Zhu, P.; Hegna, C. C.; Sovinec, C. R.

2009-01-01

Recent ideal magnetohydrodynamic (MHD) theory predicts that a perturbation evolving from a linear ballooning instability will continue to grow exponentially in the intermediate nonlinear phase at the same linear growth rate. This prediction is confirmed in ideal MHD simulations. When the Lagrangian compression, a measure of the ballooning nonlinearity, becomes of the order of unity, the intermediate nonlinear phase is entered, during which the maximum plasma displacement amplitude as well as the total kinetic energy continues to grow exponentially at the rate of the corresponding linear phase.

Prediction and discovery of extremely strong hydrodynamic instabilities due to a velocity jump: theory and experiments

International Nuclear Information System (INIS)

Fridman, A M

2008-01-01

The theory and the experimental discovery of extremely strong hydrodynamic instabilities are described, viz. the Kelvin-Helmholtz, centrifugal, and superreflection instabilities. The discovery of the last two instabilities was predicted and the Kelvin-Helmholtz instability in real systems was revised by us. (reviews of topical problems)

Nonlinear theory of the collisional Rayleigh-Taylor instability in equatorial spread F

International Nuclear Information System (INIS)

Chaturvedi, P.K.; Ossakow, S.L.

1977-01-01

The nonlinear behavior of the collisional Rayleigh-Taylor instability is studied in equatorial Spread F by including a dominant two-dimensional nonlinearity. It is found that on account of this nonlinearity the instability saturates by generating damped higher spatial harmonics. The saturated power spectrum for the density fluctuations is discussed. A comparison between experimental observations and theory is presented

Comment on the drift mirror instability

Czech Academy of Sciences Publication Activity Database

Hellinger, Petr

2008-01-01

Roč. 15, č. 5 (2008), 054502/1-054502/2 ISSN 1070-664X R&D Projects: GA AV ČR IAA300420702 Institutional research plan: CEZ:AV0Z30420517 Keywords : drift mirror instability * linear theory Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.427, year: 2008

On the kinetic theory of QPEMIC instabilities in weakly ionized plasmas placed in non-parallel fields

International Nuclear Information System (INIS)

Milic, B.S.; Gajic, D.Z.

1994-01-01

Quasi-perpendicular electromagnetic ion-cyclotron (QPEMIC) modes and instabilities are studied, on the ground of linear theory of perturbations and kinetic equations with BGK collision integrals, in weakly ionized, low-β and moderately non-isothermal plasmas placed in non-parallel electric and magnetic fields. The magnetization is assumed to be sufficiently high to cut off the perpendicular steady-state current. Special attention is given to evaluation of magnitudes of the threshold drifts required for the onset of instabilities. It is found that these drifts are smaller than those for the corresponding quasi-perpendicular electrostatic ion-cyclotron (QPESIC) instabilities studied previously for the same type of plasmas. Both QPEMIC and QPESIC threshold drifts exhibit the same behavioural pattern if the order of harmonic, magnetization, non-isothermality or the angle between the fields are varied. An increase of the angle between the fields lowers the threshold drifts, which means that the presence of u perpendicular to (or E perpendicular to ) facilitates the excitation of both QPEMIC and QPESIC instabilities. The QPEMIC threshold drifts are found to depend on the overall gas pressure, and to decrease as the pressure is lowered, which is a feature not found in the QPESIC case. The discrepancies between the QPEMIC and QPESIC threshold drifts increase if the pressure decreases, or if magnetization, degree of ionization or ion charge number increase. (orig.)

Plasma instabilities multifrequency study in equatorial electrojet

International Nuclear Information System (INIS)

Hanuise, C.

1983-01-01

In this thesis, multifrequential HF coherent radar results are presented, in the field plasma instabilities in equatorial electrojet. In a first part, characteristics of the irregularities observed either at the 3 meter wavelength by VHF radars, either at other wavelengths during pinpoint experiments, or in-situ by probe rockets are recalled. Theoretical studies progressed and are presented, at the same time with these experimental observations: instability linear theory, non linear theories, HF radar specificity, and problems associated to HF waves propagation and refraction in ionosphere. Original experimental results from Ethiopia are gathered in the second part. Plasma instability has been studied in different geophysical conditions and Doppler spectra characteristics are presented for each one of them. These characteristics are completely different according to the various cases; they are also different according to wether observations are made during the day in normal conditions (electric field pointed to the east at the equator) or in counter-electrojet conditions (electric field pointed to the west). The last part is concerned with theoretical interpretation of the previous results. A comprehensive view of the instability physical mechanisms, according to the geophysical conditions encountered, has been allowed by our results, VHF radar measurements at Jicamarca, or in situ probe measurements on the whole. Irregularities study has been limited to the E region [fr

Universal instability of hairy black holes in Lovelock-Galileon theories in D dimensions

Science.gov (United States)

Takahashi, Kazufumi; Suyama, Teruaki; Kobayashi, Tsutomu

2016-03-01

We analyze spherically symmetric black hole solutions with time-dependent scalar hair in a class of Lovelock-Galileon theories, which are the scalar-tensor theories with second-order field equations in arbitrary dimensions. We first show that known black hole solutions in five dimensions are always plagued by the ghost/gradient instability in the vicinity of the horizon. We then generalize such black hole solutions to higher dimensions and show that the same instability found in five dimensions appears universally in any number of dimensions.

Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

Science.gov (United States)

Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

1992-01-01

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

Experiments and theory in non-linear thermal transport, heat flow instabilities and plasma jet formation in inertial confinement

International Nuclear Information System (INIS)

Haines, M.G.; Bond, D.J.; Chuaqui, H.H.

1983-01-01

The paper reports experimental and theoretical contributions to the understanding of non-linear heat flow and the phenomenon of jet-like filamentary structures in inertial-confinement fusion. When lateral heat flow is minimized, through applying more carefully a radially symmetric irradiation at 1.05 and 0.53 μm on a spherical target, it is found that a heat flux in excess of 10% of the free-streaming limit is consistent with simulations and experimental measurements with particle and X-ray diagnostics. A similar result has been found in a scaled experiment in a plasma of electron density 4x10 16 cm - 3 when the condition Tsub(e) approx.=Tsub(i) is satisfied. These results are in marked contrast to earlier assertions, mainly from plane-target measurements, that the flux limiter is 3%, but in agreement with theoretical calculations of steady non-linear heat flow using a discrete-ordinate method. Thus, no anomalous inhibition of heat flow is found, consistent with theoretical predictions that ion-acoustic turbulence is of no importance in dense (n>=10 21 cm - 3 , T approx.= 1 keV) plasmas. However, in the low-density scaled experiment, under conditions where Tsub(e)>>Tsub(i) is found that ion-acoustic turbulence is present, and the flux limiter is 4%. By using shadowgraphic and schlieren techniques with an optical diagnostic probe, fine-scale jet-like structures have been observed on a scale-length of approx. 10 μm on spherical targets. They occur even outside the laser-irradiated region, and are not connected with irregularities in the laser beam; they are more pronounced with higher-Z materials and with shorter-wavelength lasers, and have megagauss magnetic fields associated with them. Electromagnetic instabilities driven by heat flow are the probable cause of the jets, and of the three known modes the thermal instability, enhanced by radiation loss, agrees more closely with the experiments than the Weibel and thermomagnetic modes, since the latter only occur

Instabilities and vortex dynamics in shear flow of magnetized plasmas

International Nuclear Information System (INIS)

Tajima, T.; Horton, W.; Morrison, P.J.; Schutkeker, J.; Kamimura, T.; Mima, K.; Abe, Y.

1990-03-01

Gradient-driven instabilities and the subsequent nonlinear evolution of generated vortices in sheared E x B flows are investigated for magnetized plasmas with and without gravity (magnetic curvature) and magnetic shear by using theory and implicit particle simulations. In the linear eigenmode analysis, the instabilities considered are the Kelvin-Helmholtz (K-H) instability and the resistive interchange instability. The presence of the shear flow can stabilize these instabilities. The dynamics of the K-H instability and the vortex dynamics can be uniformly described by the initial flow pattern with a vorticity localization parameter ε. The observed growth of the K-H modes is exponential in time for linearly unstable modes, secular for marginal mode, and absent until driven nonlinearly for linearly stable modes. The distance between two vortex centers experiences rapid merging while the angle θ between the axis of vortices and the external shear flow increases. These vortices proceed toward their overall coalescence, while shedding small-scale vortices and waves. The main features of vortex dynamics of the nonlinear coalescence and the tilt or the rotational instabilities of vortices are shown to be given by using a low dimension Hamiltonian representation for interacting vortex cores in the shear flow. 24 refs., 19 figs., 1 tab

Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

Science.gov (United States)

Wienkers, A. F.; Ogilvie, G. I.

2018-04-01

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalises the often-used cartesian shearing box model. The numerical method is an overall second order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localise the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of "bursty" dynamics such as the superhump phenomenon.

Compressional effects in nonneutral plasmas, a shallow water analogy and m=1 instability

International Nuclear Information System (INIS)

Finn, J.M.; Del-Castillo-Negrete, D.; Barnes, D.C.

1999-01-01

Diocotron instabilities form an important class of ExB shear flow instabilities which occur in nonneutral plasmas. The case of a single-species plasma confined in a cylindrical Penning trap, with an axisymmetric, hollow (nonmonotonic) density profile is studied. According to the standard linear theory, the m=1, k z =0 diocotron mode is always stable. On the other hand, experiments by Driscoll [Phys. Rev. Lett. 64, 645 (1990)] show a robust exponential growth of m=1 diocotron perturbations in hollow density profiles. The apparent contradiction between these experimental results and linear theory has been an outstanding problem in the theory of nonneutral plasmas. A new instability mechanism due to the radial variation of the equilibrium plasma length is proposed in this paper. This mechanism involves the compression of the plasma parallel to the magnetic field and implies the conservation of the line integrated density. The predicted growth rate, frequency, and mode structure are in reasonable agreement with the experiment. The effect of a linear perturbation of the plasma length is also shown to give instability with a comparable growth rate. The conservation of the line integrated density in the plasma is analogous to the conservation of the potential vorticity in the shallow water equations used in geophysical fluid dynamics. In particular, there is an analog of Rossby waves in nonneutral plasmas. copyright 1999 American Institute of Physics

Stochastic modeling of mode interactions via linear parabolized stability equations

Science.gov (United States)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Linearized potential vorticity mode and its role in transition to baroclinic instability

International Nuclear Information System (INIS)

Pieri, Alexandre; Salhi, Aziz; Cambon, Claude; Godeferd, Fabien

2011-01-01

Stratified shear flows have been studied using Rapid Distortion Theory (RDT) and DNS. If this flow is in addition subjected to vertical rotation, a slaved horizontal stratification is forced and baroclinic instability can occur. In this context, the RDT analysis shows an extention of the unstable domain up to a Richardson number Ri of 1. This work is completed here with new results on transition to baroclinic instability. Especially, the role of k x ≈ 0 modes (small streamwise wavenumbers) and the importance of coupling with the potential vorticity mode u (Ω pot ) is shown to be determinant for dramatic transient growth at intermediate times.

Low-frequency linear waves and instabilities in uniform and stratified plasmas: the role of kinetic effects

Directory of Open Access Journals (Sweden)

K. M. Ferrière

2004-01-01

Full Text Available We review the basic approximations underlying magnetohydrodynamic (MHD theory, with special emphasis on the closure approximations, i.e. the approximations used in any fluid approach to close the hierarchy of moment equations. We then present the main closure models that have been constructed for collisionless plasmas in the large-scale regime, and we describe our own mixed MHD-kinetic model, which is designed to study low-frequency linear waves and instabilities in collisionless plasmas. We write down the full dispersion relation in a new, general form, which gathers all the specific features of our MHD-kinetic model into four polytropic indices, and which can be applied to standard adiabatic MHD and to double-adiabatic MHD through a simple change in the expressions of the polytropic indices. We study the mode solutions and the stability properties of the full dispersion relation in each of these three theories, first in the case of a uniform plasma, and then in the case of a stratified plasma. In both cases, we show how the results are affected by the collisionless nature of the plasma.

Instabilities and chaos in a kinetic equation for active nematics

International Nuclear Information System (INIS)

Shi, Xia-qing; Ma, Yu-qiang; Chaté, Hugues

2014-01-01

We study dry active nematics at the kinetic equation level, stressing the differences with the well-known Doi theory for non-active rods near thermal equilibrium. By deriving hydrodynamic equations from the kinetic equation, we show analytically that these two description levels share the same qualitative phase diagram, as defined by the linear instability limits of spatially-homogeneous solutions. In particular, we show that the ordered, homogeneous state is unstable in a region bordering the linear onset of nematic order, and is only linearly stable deeper in the ordered phase. Direct simulations of the kinetic equation reveal that its solutions are chaotic in the region of linear instability of the ordered homogeneous state. The local mechanisms for this large-scale chaos are discussed. (paper)

Electron beam instabilities in unmagnetized plasmas via the Stieltjes transform (linear theory and nonlinear mode coupling)

International Nuclear Information System (INIS)

Krishan, S.

2007-01-01

The Stieltjes transform has been used in place of a more common Laplace transform to determine the time evolution of the self-consistent field (SCF) of an unmagnetized semi-infinite plasma, where the plasma electrons together with a primary and a low-density secondary electron beam move perpendicular to the boundary surface. The secondary beam is produced when the primary beam strikes the grid. Such a plasma system has been investigated by Griskey and Stanzel [M. C. Grisky and R. L. Stenzel, Phys. Rev. Lett. 82, 556 (1999)]. The physical phenomenon, observed in their experiment, has been named by them as ''secondary beam instability.'' The character of the instability observed in the experiment is not the same as predicted by the conventional treatments--the field amplitude does not grow with time. In the frequency spectrum, the theory predicts peak values in the amplitude of SCF at the plasma frequency of plasma and secondary beam electrons, decreasing above and below it. The Stieltjes transform for functions, growing exponentially in the long time limit, does not exist, while the Laplace transform technique gives only exponentially growing solutions. Therefore, it should be interesting to know the kind of solutions that an otherwise physically unstable plasma will yield. In the high-frequency limit, the plasma has been found to respond to any arbitrary frequency of the initial field differentiated only by the strength of the resulting SCF. The condition required for exponential growth in the conventional treatments, and the condition for maximum amplitude (with respect to frequency) in the present treatment, have been found to be the same. Nonlinear mode coupling between the modes excited by the plasma electrons and the low-density secondary beam gives rise to two frequency-dependent peaks in the field amplitude, symmetrically located about the much stronger peak due to the plasma electrons, as predicted by the experiment

A theory of two-stream instability in two hollow relativistic electron beams

International Nuclear Information System (INIS)

Uhm, H.S.

1993-01-01

Stability properties of two-stream instability of two hollow electron beams are investigated. The equilibrium configuration consists of two intense relativistic hollow electron beams propagating through a grounded conducting cylinder. Analysis of the longitudinal two-stream instability is carried out within the framework of the linearized Vlasov--Maxwell equations for the equilibrium distribution function, in which beam electrons have a Lorentzian distribution in the axial momentum. Dispersion relation of the longitudinal two-stream instability is derived. Stability criteria from this dispersion relation indicate that the normalized velocity difference Δβ between the beams should be within a certain range of value to be unstable. Growth rate of the instability is a substantial fraction of the real frequency, thereby indicating that the longitudinal two-stream instability is an effective means of beam current modulation. Transverse instability of hollow electron beams is also investigated. Dispersion relation of the coupled transverse oscillation of the beams is derived and numerical investigation of this dispersion relation is carried out. Growth rate of the kink instability is a substantial fraction of the diocotron frequency, which may pose a serious threat to the two-stream klystron

Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

Science.gov (United States)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Linear analysis of the Richtmyer-Meshkov instability in shock-flame interactions

Science.gov (United States)

Massa, L.; Jha, P.

2012-05-01

Shock-flame interactions enhance supersonic mixing and detonation formation. Therefore, their analysis is important to explosion safety, internal combustion engine performance, and supersonic combustor design. The fundamental process at the basis of the interaction is the Richtmyer-Meshkov instability supported by the density difference between burnt and fresh mixtures. In the present study we analyze the effect of reactivity on the Richtmyer-Meshkov instability with particular emphasis on combustion lengths that typify the scaling between perturbation growth and induction. The results of the present linear analysis study show that reactivity changes the perturbation growth rate by developing a pressure gradient at the flame surface. The baroclinic torque based on the density gradient across the flame acts to slow down the instability growth of high wave-number perturbations. A gasdynamic flame representation leads to the definition of a Peclet number representing the scaling between perturbation and thermal diffusion lengths within the flame. Peclet number effects on perturbation growth are observed to be marginal. The gasdynamic model also considers a finite flame Mach number that supports a separation between flame and contact discontinuity. Such a separation destabilizes the interface growth by augmenting the tangential shear.

On the stimulated Raman sidescattering in inhomogeneous plasmas: revisit of linear theory and three-dimensional particle-in-cell simulations

Science.gov (United States)

Xiao, C. Z.; Zhuo, H. B.; Yin, Y.; Liu, Z. J.; Zheng, C. Y.; Zhao, Y.; He, X. T.

2018-02-01

Stimulated Raman sidescattering (SRSS) in inhomogeneous plasma is comprehensively revisited on both theoretical and numerical aspects due to the increasing concern of its detriments to inertial confinement fusion. Firstly, two linear mechanisms of finite beam width and collisional effects that could suppress SRSS are investigated theoretically. Thresholds for the eigenmode and wave packet in a finite-width beam are derived as a supplement to the theory proposed by Mostrom and Kaufman (1979 Phys. Rev. Lett. 42 644). Collisional absorption of SRSS is efficient at high-density plasma and high-Z material, otherwise, it allows emission of sidescattering. Secondly, we have performed the first three-dimensional particle-in-cell simulations in the context of SRSS to investigate its linear and nonlinear effects. Simulation results are qualitatively agreed with the linear theory. SRSS with the maximum growth gain is excited at various densities, grows to an amplitude that is comparable with the pump laser, and evolutes to lower densities with a large angle of emergence. Competitions between SRSS and other parametric instabilities such as stimulated Raman backscattering, two-plasmon decay, and stimulated Brillouin scattering are discussed. These interaction processes are determined by gains, occurrence sites, scattering geometries of each instability, and will affect subsequent evolutions. Nonlinear effects of self-focusing and azimuthal magnetic field generation are observed to be accompanied with SRSS. In addition, it is found that SRSS is insensitive to ion motion, collision (low-Z material), and electron temperature.

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Linear and Weakly Nonlinear Instability of Shallow Mixing Layers with Variable Friction

Directory of Open Access Journals (Sweden)

Irina Eglite

2018-01-01

Full Text Available Linear and weakly nonlinear instability of shallow mixing layers is analysed in the present paper. It is assumed that the resistance force varies in the transverse direction. Linear stability problem is solved numerically using collocation method. It is shown that the increase in the ratio of the friction coefficients in the main channel to that in the floodplain has a stabilizing influence on the flow. The amplitude evolution equation for the most unstable mode (the complex Ginzburg–Landau equation is derived from the shallow water equations under the rigid-lid assumption. Results of numerical calculations are presented.

Linear theory of plasma filled backward wave oscillator

Indian Academy of Sciences (India)

An analytical and numerical study of backward wave oscillator (BWO) in linear regime is presented to get an insight into the excitation of electromagnetic waves as a result of the interaction of the relativistic electron beam with a slow wave structure. The effect of background plasma on the BWO instability is also presented.

Siemens experience on linear and nonlinear analyses of out-of-phase BWR instabilities

International Nuclear Information System (INIS)

Kreuter, D.; Wehle, F.

1995-01-01

The Siemens design code STAIF has been applied extensively for linear analysis of BWR instabilities. The comparison between measurements and STAIF calculations for different plants under various conditions has shown good agreement for core-wide and regional instabilities. Based on the high quality of STAIF, the North German TUeV has decided to replace the licensing requirement of extensive stability measurements by predictive analyses with the code STAIF. Nonlinear stability analysis for beyond design boundary conditions with RAMONA has shown dryout during temporarily reversed flow at core inlet in case of core-wide oscillations. For large out-of-phase oscillations, dryout occurs already for small, still positive channel inlet flow. (orig.)

Linear and nonlinear analysis of density wave instability phenomena

International Nuclear Information System (INIS)

Ambrosini, Walter

1999-01-01

In this paper the mechanism of density-wave oscillations in a boiling channel with uniform and constant heat flux is analysed by linear and nonlinear analytical tools. A model developed on the basis of a semi-implicit numerical discretization of governing partial differential equations is used to provide information on the transient distribution of relevant variables along the channel during instabilities. Furthermore, a lumped parameter model and a distributed parameter model developed in previous activities are also adopted for independent confirmation of the observed trends. The obtained results are finally put in relation with the picture of the phenomenon proposed in classical descriptions. (author)

Linear stability analysis of supersonic axisymmetric jets

Directory of Open Access Journals (Sweden)

Zhenhua Wan

2014-01-01

Full Text Available Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory (LST. It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.

Algebraic Theory of Linear Viscoelastic Nematodynamics

International Nuclear Information System (INIS)

Leonov, Arkady I.

2008-01-01

This paper consists of two parts. The first one develops algebraic theory of linear anisotropic nematic 'N-operators' build up on the additive group of traceless second rank 3D tensors. These operators have been implicitly used in continual theories of nematic liquid crystals and weakly elastic nematic elastomers. It is shown that there exists a non-commutative, multiplicative group N 6 of N-operators build up on a manifold in 6D space of parameters. Positive N-operators, which in physical applications hold thermodynamic stability constraints, do not generally form a subgroup of group N 6 . A three-parametric, commutative transversal-isotropic subgroup S 3 subset of N 6 of positive symmetric nematic operators is also briefly discussed. The special case of singular, non-negative symmetric N-operators reveals the algebraic structure of nematic soft deformation modes. The second part of the paper develops a theory of linear viscoelastic nematodynamics applicable to liquid crystalline polymer. The viscous and elastic nematic components in theory are described by using the Leslie-Ericksen-Parodi (LEP) approach for viscous nematics and de Gennes free energy for weakly elastic nematic elastomers. The case of applied external magnetic field exemplifies the occurrence of non-symmetric stresses. In spite of multi-(10) parametric character of the theory, the use of nematic operators presents it in a transparent form. When the magnetic field is absent, the theory is simplified for symmetric case with six parameters, and takes an extremely simple, two-parametric form for viscoelastic nematodynamics with possible soft deformation modes. It is shown that the linear nematodynamics is always reducible to the LEP-like equations where the coefficients are changed for linear memory functionals whose parameters are calculated from original viscosities and moduli

Experiment of ablative Rayleigh-Taylor instability in a strongly non linear regime on the National Ignition Facility

International Nuclear Information System (INIS)

Casner, A.; Masse, L.; Liberatore, S.; Delorme, B.; Jacquet, L.; Loiseau, P.; Smalyuk, V. A.; Martinez, D.; Remington, B. A.

2012-01-01

As the control of the development of Rayleigh-Taylor-type hydrodynamic instabilities is crucial to achieve efficient implosions on the Laser Megajoule, and as the complexity of these instabilities requires an experimental validation of theoretical models and of the associated numerical simulations, the authors briefly present a proposition of experiments aimed at studying the strongly non linear Rayleigh-Taylor instability on the National Ignition Facility (NIF). This should allow a regime of competition between bubbles to be achieved for the first time in direct attack. They evoke the first experiment performed in March 2013

Solution strategies for linear and nonlinear instability phenomena for arbitrarily thin shell structures

International Nuclear Information System (INIS)

Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.

1983-01-01

In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)

Pion condensation and instabilities: current theory and experiment

International Nuclear Information System (INIS)

Gyulassy, M.

1980-05-01

Current calculations of pion condensation phenomena in symmetric nuclear matter are reviewed. The RPA and MFA methods are compared. Latest results [LBL-10572] with a relativistic MFA theory constrained by bulk nuclear properties are presented. The differences between equilibrium (condensation) and nonequilibrium (dynamic) instabilities are discussed. Finally, two-proton correlation experiments aimed at looking for critical scattering phenomena and two-pion correlation experiments aimed at looking for pion field coherence are analyzed. 10 figures, 2 tables

Canonical perturbation theory in linearized general relativity theory

International Nuclear Information System (INIS)

Gonzales, R.; Pavlenko, Yu.G.

1986-01-01

Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field

Gravitational instability of thermally anisotropic plasma

International Nuclear Information System (INIS)

Singh, B.; Kalra, G.L.

1986-01-01

The equations of Chew, Goldberger, and Low (1956) modified to include the heat flux vector and self-gravitation are used to study the gravitational instability of unbounded plasma placed in a uniform static magnetic field. The linear stability analysis shows that some of the additional terms which arise as a result of higher moments are of the same order of magnitude as the terms in the original Chew, Goldberger, and Low theory. The influence of these terms on the gravitational instability has been specially examined. It is found that the gravitational instability sets in at a comparatively shorter wavelength and the growth rate is enhanced owing to the inclusion of these terms in the case where the propagation vector is along the magnetic field. The condition for instability is, however, unaltered when the direction of propagation is transverse to the direction of magnetic field. 19 references

High-Speed Linear Raman Spectroscopy for Instability Analysis of a Bluff Body Flame

Science.gov (United States)

Kojima, Jun; Fischer, David

2013-01-01

We report a high-speed laser diagnostics technique based on point-wise linear Raman spectroscopy for measuring the frequency content of a CH4-air premixed flame stabilized behind a circular bluff body. The technique, which primarily employs a Nd:YLF pulsed laser and a fast image-intensified CCD camera, successfully measures the time evolution of scalar parameters (N2, O2, CH4, and H2O) in the vortex-induced flame instability at a data rate of 1 kHz. Oscillation of the V-shaped flame front is quantified through frequency analysis of the combustion species data and their correlations. This technique promises to be a useful diagnostics tool for combustion instability studies.

Gravitational instability theory of galaxy formation and clustering - Some recent developments

International Nuclear Information System (INIS)

Fall, S.M.; Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass.)

1980-01-01

Some recent developments in the gravitational instability theory of galaxy formation and clustering are discussed including a comparison with observational data. On the theoretical side, N-body computer simulations have helped to sharpen the predictions of the theory and several new ideas have emerged on the roles of dissipation in protogalactic fragmentation and in galaxy collisions. On the observational side, the clustering properties of galaxies have been analyzed in new ways that demand a detailed comparison with theory. More and better measurements of the sizes, masses, and rotations of galaxies continue to accumulate

Linear programming mathematics, theory and algorithms

CERN Document Server

1996-01-01

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

Linear theory radial and nonradial pulsations of DA dwarf stars

International Nuclear Information System (INIS)

Starrfield, S.; Cox, A.N.; Hodson, S.; Pesnell, W.D.

1982-01-01

The Los Alamos stellar envelope and radial linear non-adiabatic computer code, along with a new Los Alamos non-radial code are used to investigate the total hydrogen mass necessary to produce the non-radial instability of DA dwarfs

Modulational Instability in Linearly Coupled Asymmetric Dual-Core Fibers

Directory of Open Access Journals (Sweden)

Arjunan Govindarajan

2017-06-01

Full Text Available We investigate modulational instability (MI in asymmetric dual-core nonlinear directional couplers incorporating the effects of the differences in effective mode areas and group velocity dispersions, as well as phase- and group-velocity mismatches. Using coupled-mode equations for this system, we identify MI conditions from the linearization with respect to small perturbations. First, we compare the MI spectra of the asymmetric system and its symmetric counterpart in the case of the anomalous group-velocity dispersion (GVD. In particular, it is demonstrated that the increase of the inter-core linear-coupling coefficient leads to a reduction of the MI gain spectrum in the asymmetric coupler. The analysis is extended for the asymmetric system in the normal-GVD regime, where the coupling induces and controls the MI, as well as for the system with opposite GVD signs in the two cores. Following the analytical consideration of the MI, numerical simulations are carried out to explore nonlinear development of the MI, revealing the generation of periodic chains of localized peaks with growing amplitudes, which may transform into arrays of solitons.

A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam

International Nuclear Information System (INIS)

Uhm, H.S.

1994-01-01

A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall klystron, in which a relativistic electron beam is modulated at the first cavity and propagates downstream through the resistive wall. Because of the self-excitation of the space charge waves by the resistive-wall instability, a highly nonlinear current modulation of the electron beam is accomplished as the beam propagates downstream. A partial integrodifferential equation is obtained in terms of the initial energy modulation (ε), the self-field effects (h), and the resistive-wall effects (κ). Analytically investigating the partial integrodifferential equation, a scaling law of the propagation distance z m at which the maximum current modulation occurs is obtained. It is found in general that the self-field effects dominate over the resistive-wall effects at the beginning of the propagation. As the beam propagates farther downstream, the resistive-wall effects dominate. Because of a relatively large growth rate of the instability, the required tube length of the klystron is short for most applications

Linear radial pulsation theory. Lecture 5

International Nuclear Information System (INIS)

Cox, A.N.

1983-01-01

We describe a method for getting an equilibrium stellar envelope model using as input the total mass, the envelope mass, the surface effective temperature, the total surface luminosity, and the composition of the envelope. Then wih the structure of the envelope model known, we present a method for obtaining the raidal pulsation periods and growth rates for low order modes. The large amplitude pulsations observed for the yellow and red giants and supergiants are always these radial models, but for the stars nearer the main sequence, as for all of our stars and for the white dwarfs, there frequently are nonradial modes occuring also. Application of linear theory radial pulsation theory is made to the giant star sigma Scuti variables, while the linear nonradial theory will be used for the B stars in later lectures

Effects of mass transfer on a resonance instability in the laminar ...

Indian Academy of Sciences (India)

pressible boundary layer flow due to a rotating-disk is investigated in this paper based on the linear stability theory. The possible .... Reynolds number limit to the inviscid modes strongly suggests that the resonance instability identified here ...

Problems of linear electron (polaron) transport theory in semiconductors

CERN Document Server

Klinger, M I

1979-01-01

Problems of Linear Electron (Polaron) Transport Theory in Semiconductors summarizes and discusses the development of areas in electron transport theory in semiconductors, with emphasis on the fundamental aspects of the theory and the essential physical nature of the transport processes. The book is organized into three parts. Part I focuses on some general topics in the theory of transport phenomena: the general dynamical theory of linear transport in dissipative systems (Kubo formulae) and the phenomenological theory. Part II deals with the theory of polaron transport in a crystalline semicon

Non-linear 3D simulations of current-driven instabilities in jets

International Nuclear Information System (INIS)

Ivanovski, S.; Bonanno, A.

2009-01-01

We present global 3D nonlinear simulations of the Taylor instability in the presence of vertical fields. The initial configuration is in equilibrium, which is achieved by a pressure gradient or an external potential force. The non linear evolution of the system leads to a stable equilibrium with a current free toroidal field. We find the that presence of a vertical poloidal field stabilize the system if B φ ∼B z . The implication of our findings for the physics of astrophysical jets are discussed.

Rayleigh-Taylor instability in accelerated elastic-solid slabs

Science.gov (United States)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2017-12-01

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ2, shear modulus G , and thickness h , placed over a semi-infinite ideal fluid of density ρ110.1007/s000330050121] to arbitrary values of AT and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ2g h /G ≤2 (1 -AT) /AT .

Linear theory of plasma Čerenkov masers

Science.gov (United States)

Birau, M.

1996-11-01

A different theoretical model of Čerenkov instability in the linear amplification regime of plasma Čerenkov masers is developed. The model assumes a cold relativistic annular electron beam propagating through a column of cold dense plasma, the two bodies being immersed in an infinite magnetic guiding field inside a perfect cylindrical waveguide. In order to simplify the calculations, a radial rectangular distribution of plasma and beam density is assumed and only azimuthal symmetric modes are under investigation. The model's difference consists of taking into account the whole plasma and beam electromagnetic structures in the interpretation of the Čerenkov instability. This model leads to alternative results such as the possibility of emission at several frequencies. In addition, the electric field is calculated taking into account its radial phase dependence, so that a map of the field in the interaction region can be presented.

Linear and nonlinear studies of velocity shear driven three dimensional electron-magnetohydrodynamics instability

International Nuclear Information System (INIS)

Gaur, Gurudatt; Das, Amita

2012-01-01

The study of electron velocity shear driven instability in electron magnetohydrodynamics (EMHD) regime in three dimensions has been carried out. It is well known that the instability is non-local in the plane defined by the flow direction and that of the shear, which is the usual Kelvin-Helmholtz mode, often termed as the sausage mode in the context of EMHD. On the other hand, a local instability with perturbations in the plane defined by the shear and the magnetic field direction exists which is termed as kink mode. The interplay of these two modes for simple sheared flow case as well as that when an external magnetic field exists has been studied extensively in the present manuscript in both linear and nonlinear regimes. Finally, these instability processes have been investigated for the exact 2D dipole solutions of EMHD equations [M. B. Isichenko and A. N. Marnachev, Sov. Phys. JETP 66, 702 (1987)] for which the electron flow velocity is sheared. It has been shown that dipoles are very robust and stable against the sausage mode as the unstable wavelengths are typically longer than the dipole size. However, we observe that they do get destabilized by the local kink mode.

Game Theory and its Relationship with Linear Programming Models ...

African Journals Online (AJOL)

Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.

Single-mode coherent synchrotron radiation instability

Directory of Open Access Journals (Sweden)

S. Heifets

2003-06-01

Full Text Available The microwave instability driven by the coherent synchrotron radiation (CSR has been previously studied [S. Heifets and G. V. Stupakov, Phys. Rev. ST Accel. Beams 5, 054402 (2002] neglecting effect of the shielding caused by the finite beam pipe aperture. In practice, the unstable mode can be close to the shielding threshold where the spectrum of the radiation in a toroidal beam pipe is discrete. In this paper, the CSR instability is studied in the case when it is driven by a single synchronous mode. A system of equations for the beam-wave interaction is derived and its similarity to the 1D free-electron laser theory is demonstrated. In the linear regime, the growth rate of the instability is obtained and a transition to the case of continuous spectrum is discussed. The nonlinear evolution of the single-mode instability, both with and without synchrotron damping and quantum diffusion, is also studied.

Solar wind heat flux regulation by the whistler instability

International Nuclear Information System (INIS)

Gary, S.P.; Feldman, W.C.

1977-01-01

This paper studies the role of the whistler instability in the regulation of the solar wind heat flux near 1 AU. A comparison of linear and second-order theory with experimental results provides strong evidence that the whistler may at times contribute to the limitation of this heat flux

Anisotropy-Driven Instability in Intense Charged Particle Beams

CERN Document Server

Startsev, Edward; Qin, Hong

2005-01-01

In electrically neutral plasmas with strongly anisotropic distribution functions, free energy is available to drive different collective instabilities such as the electrostatic Harris instability and the transverse electromagnetic Weibel instability. Such anisotropies develop naturally in particle accelerators and may lead to a detoriation of beam quality. We have generalized the analysis of the classical Harris and Weibel instabilities to the case of a one-component intense charged particle beam with anisotropic temperature including the important effects of finite transverse geometry and beam space-charge. For a long costing beam, the delta-f particle-in-cell code BEST and the eighenmode code bEASt have been used to determine detailed 3D stability properties over a wide range of temperature anisotropy and beam intensity. A theoretical model is developed which describes the essential features of the linear stage of these instabilities. Both, the simulations and analytical theory, clearly show that moderately...

Experimental study of linear and nonlinear regimes of density-driven instabilities induced by CO2 dissolution in water

International Nuclear Information System (INIS)

Outeda, R.; D'Onofrio, A.; El Hasi, C.; Zalts, A.

2014-01-01

Density driven instabilities produced by CO 2 (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO 2 pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a color indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO 2 pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm −1 ) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO 2 pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator

Unitary theory of xenon instability in nuclear thermal reactors - 1. Reactor at 'zero power'

International Nuclear Information System (INIS)

Novelli, A.

1982-01-01

The question of nuclear thermal-reactor instability against xenon oscillations is widespread in the literature, but most theories, concerned with such an argument, contradict each other and, above all, they conflict with experimentally-observed instability at very low reactor power, i.e. without any power feedback. It is shown that, in any nuclear thermal reactor, xenon instability originates at very low power levels, and a very general stability condition is deduced by an extension of the rigorous, simple and powerful reduction of the Nyquist criterion, first performed by F. Storrer. (author)

The non-linear growth of the magnetic Rayleigh-Taylor instability

Science.gov (United States)

Carlyle, Jack; Hillier, Andrew

2017-09-01

This work examines the effect of the embedded magnetic field strength on the non-linear development of the magnetic Rayleigh-Taylor instability (RTI) (with a field-aligned interface) in an ideal gas close to the incompressible limit in three dimensions. Numerical experiments are conducted in a domain sufficiently large so as to allow the predicted critical modes to develop in a physically realistic manner. The ratio between gravity, which drives the instability in this case (as well as in several of the corresponding observations), and magnetic field strength is taken up to a ratio which accurately reflects that of observed astrophysical plasma, in order to allow comparison between the results of the simulations and the observational data which served as inspiration for this work. This study finds reduced non-linear growth of the rising bubbles of the RTI for stronger magnetic fields, and that this is directly due to the change in magnetic field strength, rather than the indirect effect of altering characteristic length scales with respect to domain size. By examining the growth of the falling spikes, the growth rate appears to be enhanced for the strongest magnetic field strengths, suggesting that rather than affecting the development of the system as a whole, increased magnetic field strengths in fact introduce an asymmetry to the system. Further investigation of this effect also revealed that the greater this asymmetry, the less efficiently the gravitational energy is released. By better understanding the under-studied regime of such a major phenomenon in astrophysics, deeper explanations for observations may be sought, and this work illustrates that the strength of magnetic fields in astrophysical plasmas influences observed RTI in subtle and complex ways.

Non-linear development of secular gravitational instability in protoplanetary disks

Science.gov (United States)

Tominaga, Ryosuke T.; Inutsuka, Shu-ichiro; Takahashi, Sanemichi Z.

2018-01-01

We perform non-linear simulation of secular gravitational instability (GI) in protoplanetary disks, which has been proposed as a mechanism of planetesimal and multiple ring formation. Since the timescale of the growth of the secular GI is much longer than the Keplerian rotation period, we develop a new numerical scheme for a long-term calculation utilizing the concept of symplectic integration. With our new scheme, we first investigate the non-linear development of the secular GI in a disk without a pressure gradient in the initial state. We find that the surface density of dust increases by more than a factor of 100 while that of gas does not increase even by a factor of 2, which results in the formation of dust-dominated rings. A line mass of the dust ring tends to be very close to the critical line mass of a self-gravitating isothermal filament. Our results indicate that the non-linear growth of the secular GI provides a powerful mechanism to concentrate the dust. We also find that the dust ring formed via the non-linear growth of the secular GI migrates inward with a low velocity, which is driven by the self-gravity of the ring. We give a semi-analytical expression for the inward migration speed of the dusty ring.

Linear and nonlinear development of m=0 instability in a diffuse Bennett Z-pinch equilibrium with sheared axial flow

International Nuclear Information System (INIS)

Paraschiv, I.; Bauer, B. S.; Lindemuth, I. R.; Makhin, V.

2010-01-01

The effect of sheared axial flow on the Z-pinch sausage instability has been examined with two-dimensional magnetohydrodynamic simulations. Diffuse Bennett equilibria in the presence of axial flows with parabolic and linear radial profiles have been considered, and a detailed study of the linear and nonlinear development of small perturbations from these equilibria has been performed. The consequences of both single-wavelength and random-seed perturbations were calculated. It was found that sheared flows changed the internal m=0 mode development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. High spatial frequency modes were stabilized to small amplitudes and only long wavelengths continued to grow. Full stability was obtained for supersonic plasma flows.

Role of secondary instability theory and parabolized stability equations in transition modeling

Science.gov (United States)

El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.

1993-01-01

In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.

Single-Bunch Instability Driven by the Electron Cloud Effect in the Positron Damping Ring of the International Linear Collider

International Nuclear Information System (INIS)

Pivi, Mauro; Raubenheimer, Tor O.; Ghalam, Ali; Harkay, Katherine; Ohmi, Kazuhito; Wanzenberg, Rainer; Wolski, Andrzej; Zimmermann, Frank

2005-01-01

Collective instabilities caused by the formation of an electron cloud (EC) are a potential limitation to the performances of the damping rings for a future linear collider. In this paper, we present recent simulation results for the electron cloud build-up in damping rings of different circumferences and discuss the single-bunch instabilities driven by the electron cloud

Analytical theory and nonlinear δf perturbative simulations of temperature anisotropy instability in intense charged particle beams

Directory of Open Access Journals (Sweden)

Edward A. Startsev

2003-08-01

Full Text Available In plasmas with strongly anisotropic distribution functions (T_{∥b}/T_{⊥b}≪1 a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy (T_{⊥b}≫T_{∥b} to allow for nonaxisymmetric perturbations with ∂/∂θ≠0. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with s_{b}=ω[over ^]_{pb}^{2}/2γ_{b}^{2}ω_{β⊥}^{2}≳0.5 are linearly unstable to short-wavelength perturbations with k_{z}^{2}r_{b}^{2}≳1, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ω[over ^]_{pb}^{2}=4πn[over ^]_{b}e_{b}^{2}/γ_{b}m_{b} is the relativistic plasma frequency squared, and ω_{β⊥} is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number m=1 is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.

An electromagnetic drift instability in the magnetic reconnection experiment and its importance for magnetic reconnection

International Nuclear Information System (INIS)

Kulsrud, Russell; Ji Hantao; Fox, William; Yamada, Masaaki

2005-01-01

The role which resistivity plays in breaking magnetic field lines, heating the plasma, and plasma-field slippage during magnetic reconnection is discussed. Magnetic fluctuations are observed in the MRX (magnetic reconnection experiment) [M. Yamada, H. Ji, S. Hsu, T. Carter, R. Kulsrud, N. Bertz, F. Jobes, Y. Ono, and F. Perkins, Phys. Plasmas 4, 1936 (1997)] that are believed to provide resistive friction or wave resistivity. A localized linear theory has been proposed for their origin as an obliquely propagating lower hybrid drift instability. In this paper, the linear theory of the instability is summarized, and the resulting heating and slippage are calculated from quasilinear theory. Making use of measured amplitudes of the magnetic fluctuations in the MRX, the amount of these effects is estimated. Within the experimental uncertainties they are shown to be quite important for the magnetic reconnection process

The linearized pressure Poisson equation for global instability analysis of incompressible flows

Science.gov (United States)

Theofilis, Vassilis

2017-12-01

The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.

The Experimental Study of Rayleigh-Taylor Instability using a Linear Induction Motor Accelerator

Science.gov (United States)

Yamashita, Nicholas; Jacobs, Jeffrey

2009-11-01

The experiments to be presented utilize an incompressible system of two stratified miscible liquids of different densities that are accelerated in order to produce the Rayleigh-Taylor instability. Three liquid combinations are used: isopropyl alcohol with water, a calcium nitrate solution or a lithium polytungstate solution, giving Atwood numbers of 0.11, 0.22 and 0.57, respectively. The acceleration required to drive the instability is produced by two high-speed linear induction motors mounted to an 8 m tall drop tower. The motors are mounted in parallel and have an effective acceleration length of 1.7 m and are each capable of producing 15 kN of thrust. The liquid system is contained within a square acrylic tank with inside dimensions 76 x76x184 mm. The tank is mounted to an aluminum plate, which is driven by the motors to create constant accelerations in the range of 1-20 g's, though the potential exists for higher accelerations. Also attached to the plate are a high-speed camera and an LED backlight to provide continuous video of the instability. In addition, an accelerometer is used to provide acceleration measurements during each experiment. Experimental image sequences will be presented which show the development of a random three-dimensional instability from an unforced initial perturbation. Measurements of the mixing zone width will be compared with traditional growth models.

Diffuse ions produced by electromagnetic ion beam instabilities

International Nuclear Information System (INIS)

Winske, D.; Leroy, M.M.

1984-01-01

The evolution of the electromagnetic ions beam instability driven by the reflected ion component backstreaming away from the earth's how shock into the foreshock region is studied by means computer simulation. The linear the quasi-linear states of the instability are found to be in good agreement with known results for the resonant model propagating parallel to the beam along the magnetic field and with theory developed in this paper for the nonresonant mode, which propagates antiparallel to the beam direction. The quasi-linear stage, which produces large amplitude 8Bapprox.B, sinusoidal transverse waves and ''intermediate'' ion distribution, is terminated by a nonlinear phase in which strongly nonlinear, compressive waves and ''diffuse'' ion distributions are produced. Additional processes by which the diffuse ions are accelerated to observed high energies are not addressed. The results are discussed in terms of the ion distributions and hydromagnetic waves observed in the foreshock of the earth's bow shock and of interplanetary shocks

Scattering theory of the linear Boltzmann operator

International Nuclear Information System (INIS)

Hejtmanek, J.

1975-01-01

In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.) [de

Kinetic-MHD simulations of gyroresonance instability driven by CR pressure anisotropy

Science.gov (United States)

Lebiga, O.; Santos-Lima, R.; Yan, H.

2018-05-01

The transport of cosmic rays (CRs) is crucial for the understanding of almost all high-energy phenomena. Both pre-existing large-scale magnetohydrodynamic (MHD) turbulence and locally generated turbulence through plasma instabilities are important for the CR propagation in astrophysical media. The potential role of the resonant instability triggered by CR pressure anisotropy to regulate the parallel spatial diffusion of low-energy CRs (≲100 GeV) in the interstellar and intracluster medium of galaxies has been shown in previous theoretical works. This work aims to study the gyroresonance instability via direct numerical simulations, in order to access quantitatively the wave-particle scattering rates. For this, we employ a 1D PIC-MHD code to follow the growth and saturation of the gyroresonance instability. We extract from the simulations the pitch-angle diffusion coefficient Dμμ produced by the instability during the linear and saturation phases, and a very good agreement (within a factor of 3) is found with the values predicted by the quasi-linear theory (QLT). Our results support the applicability of the QLT for modelling the scattering of low-energy CRs by the gyroresonance instability in the complex interplay between this instability and the large-scale MHD turbulence.

Linear response theory for quantum open systems

OpenAIRE

Wei, J. H.; Yan, YiJing

2011-01-01

Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.

Spectral theories for linear differential equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

A theory for the Langmuir waves in the electron foreshock

International Nuclear Information System (INIS)

Cairns, I.H.

1987-01-01

A theory for the Langmuir (L) waves observed in the electron foreshock is suggested. Free energy for the Langmuir wave growth is contained in cutoff distributions of energetic electrons streaming from the bow shock. These cutoff distributions drive Langmuir wave growth primarily by the kinetic version of the beam instability, and wave growth is limited by quasi-linear relaxation. The observed bump-on-tail electron distributions are interpreted as the remnants of cutoff distributions after quasi-linear relaxation has limited the wave growth. Only plausibility arguments for this theory are given since suitable treatments of quasi-linear relaxation are not presently available. However, it is shown that the wave processes L ± S → L' and L ± S → T (where S and T denote ion sound and transverse waves, respectively), refraction in steady-state density structures, diffusion due to interactions with ion sound turbulence, and effects due to wave convection and spatial gradients in the beam velocity, are unable to suppress the beam instability. The theory leads to natural interpretations of the Langmuir electric field waveforms observed and of the decrease in the Langmuir wave electric fields with increasing distance from the foreshock boundary. The theory for the beam instability is reviewed, and previous analytic and numerical treatments of the beam instability are related

Theory of the corrugation instability of a piston-driven shock wave.

Science.gov (United States)

Bates, J W

2015-01-01

We analyze the two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state. For h≤-1 or h>h(c), where h is the D'yakov parameter and h(c) is the Kontorovich limit, we find that small perturbations on the shock front are unstable and grow--at first quadratically and later linearly--with time. Such instabilities are associated with nonequilibrium fluid states and imply a nonunique solution to the hydrodynamic equations. The above criteria are consistent with instability limits observed in shock-tube experiments involving ionizing and dissociating gases and may have important implications for driven shocks in laser-fusion, astrophysical, and/or detonation studies.

Cosmic ray driven instability

International Nuclear Information System (INIS)

Dorfi, E.A.; Drury, L.O.

1985-01-01

The interaction between energetic charged particles and thermal plasma, which forms the basis of diffusive shock acceleration, leads also to interesting dynamical phenomena. For a compressional mode propagating in a system with homoeneous energetic particle pressure it is well known that friction with the energetic particles leads to damping. The linear theory of this effect has been analyzed in detail by Ptuskin. Not so obvious is that a non-uniform energetic particle pressure can in addition amplify compressional disturbances. If the pressure gradient is sufficiently steep this growth can dominate the frictional damping and lead to an instability. It is important to not that this effect results from the collective nature of the interaction between the energetic particles and the gas and is not connected with the Parker instability, nor with the resonant amplification of Alfven waves

Hydrodynamic instabilities in inertial fusion

International Nuclear Information System (INIS)

Hoffman, N.M.

1994-01-01

This report discusses topics on hydrodynamics instabilities in inertial confinement: linear analysis of Rayleigh-Taylor instability; ablation-surface instability; bubble rise in late-stage Rayleigh-Taylor instability; and saturation and multimode interactions in intermediate-stage Rayleigh-Taylor instability

An analytic study of the perpendicularly propagating electromagnetic drift instabilities in the Magnetic Reconnection Experiment

International Nuclear Information System (INIS)

Wang Yansong; Kulsrud, Russell; Ji, Hantao

2008-01-01

A local linear theory is proposed for a perpendicularly propagating drift instability driven by relative drifts between electrons and ions. The theory takes into account local cross-field current, pressure gradients, and modest collisions as in the Magnetic Reconnection Experiment [M. Yamada et al., Phys. Plasmas 4, 1936 (1997)]. The unstable waves have very small group velocities in the direction of the pressure gradient, but have a large phase velocity near the relative drift velocity between electrons and ions in the direction of the cross-field current. By taking into account the electron-ion collisions and applying the theory in the Harris sheet, we establish that this instability could be excited near the center of the Harris sheet and have enough e-foldings to grow to large amplitude before it propagates out of the unstable region. Comparing with the other magnetic reconnection related instabilities (lower-hybrid-drift instability, modified two-stream instability, etc.) studied previously, we believe the instability we found is a favorable candidate to produce anomalous resistivity because of its unique wave characteristics, such as electromagnetic component, large phase velocity, and small group velocity in the cross-current-layer direction.

Laser driven hydrodynamic instability experiments

International Nuclear Information System (INIS)

Remington, B.A.; Weber, S.V.; Haan, S.W.; Kilkenny, J.D.; Glendinning, S.G.; Wallace, R.J.; Goldstein, W.H.; Wilson, B.G.; Nash, J.K.

1992-01-01

We have conducted an extensive series of experiments on the Nova laser to measure hydrodynamic instabilities in planar foils accelerated by x-ray ablation. Single mode experiments allow a measurement of the fundamental growth rates from the linear well into the nonlinear regime; multimode foils allow an assessment of the degree of mode coupling; and surface-finish experiments allow a measurement of the evolution of a broad spectrum of random initial modes. Experimental results and comparisons with theory and simulations are presented

Unified theory of ballooning instabilities and temperature gradient driven trapped ion modes

International Nuclear Information System (INIS)

Xu, X.Q.

1990-08-01

A unified theory of temperature gradient driven trapped ion modes and ballooning instabilities is developed using kinetic theory in banana regimes. All known results, such as electrostatic and purely magnetic trapped particle modes and ideal MHD ballooning modes (or shear Alfven waves) are readily derived from our single general dispersion relation. Several new results from ion-ion collision and trapped particle modification of ballooning modes are derived and discussed and the interrelationship between those modes is established. 24 refs

Hosing Instability of the Drive Electron Beam in the E157 Plasma-Wakefield Acceleration Experiment at the Stanford Linear Accelerator

International Nuclear Information System (INIS)

Blue, Brent Edward

2005-01-01

In the plasma-wakefield experiment at SLAC, known as E157, an ultra-relativistic electron beam is used to both excite and witness a plasma wave for advanced accelerator applications. If the beam is tilted, then it will undergo transverse oscillations inside of the plasma. These oscillations can grow exponentially via an instability know as the electron hose instability. The linear theory of electron-hose instability in a uniform ion column predicts that for the parameters of the E157 experiment (beam charge, bunch length, and plasma density) a growth of the centroid offset should occur. Analysis of the E157 data has provided four critical results. The first was that the incoming beam did have a tilt. The tilt was much smaller than the radius and was measured to be 5.3 (micro)m/(delta) z at the entrance of the plasma (IP1.) The second was the beam centroid oscillates in the ion channel at half the frequency of the beam radius (betatron beam oscillations), and these oscillations can be predicted by the envelope equation. Third, up to the maximum operating plasma density of E157 (∼2 x 10 14 cm -3 ), no growth of the centroid offset was measured. Finally, time-resolved data of the beam shows that up to this density, no significant growth of the tail of the beam (up to 8ps from the centroid) occurred even though the beam had an initial tilt

Hosing Instability of the Drive Electron Beam in the E157 Plasma-Wakefield Acceleration Experiment at the Stanford Linear Accelerator

Energy Technology Data Exchange (ETDEWEB)

Blue, Brent Edward; /SLAC /UCLA

2005-10-10

In the plasma-wakefield experiment at SLAC, known as E157, an ultra-relativistic electron beam is used to both excite and witness a plasma wave for advanced accelerator applications. If the beam is tilted, then it will undergo transverse oscillations inside of the plasma. These oscillations can grow exponentially via an instability know as the electron hose instability. The linear theory of electron-hose instability in a uniform ion column predicts that for the parameters of the E157 experiment (beam charge, bunch length, and plasma density) a growth of the centroid offset should occur. Analysis of the E157 data has provided four critical results. The first was that the incoming beam did have a tilt. The tilt was much smaller than the radius and was measured to be 5.3 {micro}m/{delta}{sub z} at the entrance of the plasma (IP1.) The second was the beam centroid oscillates in the ion channel at half the frequency of the beam radius (betatron beam oscillations), and these oscillations can be predicted by the envelope equation. Third, up to the maximum operating plasma density of E157 ({approx}2 x 10{sup 14} cm{sup -3}), no growth of the centroid offset was measured. Finally, time-resolved data of the beam shows that up to this density, no significant growth of the tail of the beam (up to 8ps from the centroid) occurred even though the beam had an initial tilt.

Jeans instability of magnetized quantum plasma: Effect of viscosity, rotation and finite Larmor radius corrections

International Nuclear Information System (INIS)

Jain, Shweta; Sharma, Prerana; Chhajlani, R. K.

2015-01-01

The Jeans instability of self-gravitating quantum plasma is examined considering the effects of viscosity, finite Larmor radius (FLR) corrections and rotation. The analysis is done by normal mode analysis theory with the help of relevant linearized perturbation equations of the problem. The general dispersion relation is obtained using the quantum magneto hydrodynamic model. The modified condition of Jeans instability is obtained and the numerical calculations have been performed to show the effects of various parameters on the growth rate of Jeans instability

Curvature-Induced Instabilities of Shells

Science.gov (United States)

Pezzulla, Matteo; Stoop, Norbert; Steranka, Mark P.; Bade, Abdikhalaq J.; Holmes, Douglas P.

2018-01-01

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities, and their dependence on geometry, are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.

Kinetic theory of tearing instability

International Nuclear Information System (INIS)

Hazeltine, R.D.; Dobrott, D.; Wang, T.S.

1975-01-01

The guiding-center kinetic equation with Fokker-Planck collision term is used to study, in cylindrical geometry, a class of dissipative instabilities of which the classical tearing mode is an archetype. Variational solution of the kinetic equation obviates the use of an approximate Ohm's law or adiabatic assumption, as used in previous studies, and it provides a dispersive relation which is uniformly valid for any ratio of wave frequency to collision frequency. One result of using the rigorous collision operator is the prediction of a new instability. This instability, driven by the electron temperature gradient, is predicted to occur under the long mean-free path conditions of present tokamak experiments, and has significant features in common with the kink-like oscillations observed in such experiments

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Studies of the trapped particle and ion temperature gradient instabilities in the Columbia Linear Machine

International Nuclear Information System (INIS)

Mathey, O.H.

1989-01-01

In the first part of the work, the effects of weak Coulomb and neutral collisions on the collisionless curvature driven trapped particle mode are studied in the Columbia Linear Machine (CLM) [Phys. Rev. Lett. 57, 1729, (1986)]. Low Coulomb collisionality yields a small stabilizing correction to the magnetohydrodynamic (MHD) collisionless mode, which scales as v, using the Krook model, and ν ec 1/2 using a Lorentz pitch angle operator. In higher collisionality regimes, both models tend to yield similar scalings. In view of relative high neutral collisionality in CLM, both types of collisionality are then combined, modeling neutral collisions with the conserving Krook and Coulomb collisions with a Lorentz model. The dispersion relation is then integrated over velocity space. This combination yields results in very good accord with the available experimental data. The Ion Temperature Gradient Instability is then investigated. It is shown that anisotropy in gradient has a substantial effect on the ion temperature gradient driven mode. A gradient in the parallel temperature is needed for an instability to occur, and a gradient in the perpendicular temperature gradient further enhances the instability indirectly as long as the frequency of the mode is near ion resonance. The physical reason for this important role difference is presented. The Columbia Linear Machine is being redesigned to produce and identify the ion temperature gradient driven η i mode. Using the expected parameters, the author has developed detailed predictions of the mode characteristics in the CLM. Strong multi mode instabilities are expected. As the ion parallel and perpendicular ion temperature gradients are expected to differ significantly, we differentiate between η i parallel and ν i perpendicular and explore the physical differences between them, which leads to a scheme for stabilization of the mode

Laboratory beam-plasma interactions linear and nonlinear

International Nuclear Information System (INIS)

Christiansen, P.J.; Bond, J.W.; Jain, V.K.

1982-01-01

This chapter attempts to demonstrate that despite unavoidable scaling limitations, laboratory experiments can uncover details of beam plasma interaction processes which could never be revealed through space plasma physics. Topics covered include linear theory, low frequency couplings, indirect effects, nonlinear effects, quasi-linear effects, trapping effects, nonlinear wave-wave interactions, and self modulation and cavitation. Unstable electrostatic waves arising from an exchange of energy with the ''free energy'' beam features are considered as kinetic and as hydrodynamic, or fluid, instabilities. The consequences of such instabilities (e.g. when the waves have grown to a finite level) are examined and some studies are reviewed which have attempted to understand how the free energy originally available in the beam is redistributed to produce a final state of equilibrium turbulence

Methods in half-linear asymptotic theory

Directory of Open Access Journals (Sweden)

Pavel Rehak

2016-10-01

Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.

Two-dimensional Nonlinear Simulations of Temperature-anisotropy Instabilities with a Proton-alpha Drift

Science.gov (United States)

Markovskii, S. A.; Chandran, Benjamin D. G.; Vasquez, Bernard J.

2018-04-01

We present two-dimensional hybrid simulations of proton-cyclotron and mirror instabilities in a proton-alpha plasma with particle-in-cell ions and a neutralizing electron fluid. The instabilities are driven by the protons with temperature perpendicular to the background magnetic field larger than the parallel temperature. The alpha particles with initially isotropic temperature have a nonzero drift speed with respect to the protons. The minor ions are known to influence the relative effect of the proton-cyclotron and mirror instabilities. In this paper, we show that the mirror mode can dominate the power spectrum at the nonlinear stage even if its linear growth rate is significantly lower than that of the proton-cyclotron mode. The proton-cyclotron instability combined with the alpha-proton drift is a possible cause of the nonzero magnetic helicity observed in the solar wind for fluctuations propagating nearly parallel to the magnetic field. Our simulations generally confirm this concept but reveal a complex helicity spectrum that is not anticipated from the linear theory of the instability.

Parametric dependence of density limits in the Tokamak Experiment for Technology Oriented Research (TEXTOR): Comparison of thermal instability theory with experiment

International Nuclear Information System (INIS)

Kelly, F.A.; Stacey, W.M.; Rapp, J.

2001-01-01

The observed dependence of the TEXTOR [Tokamak Experiment for Technology Oriented Research: E. Hintz, P. Bogen, H. A. Claassen et al., Contributions to High Temperature Plasma Physics, edited by K. H. Spatschek and J. Uhlenbusch (Akademie Verlag, Berlin, 1994), p. 373] density limit on global parameters (I, B, P, etc.) and wall conditioning is compared with the predicted density limit parametric scaling of thermal instability theory. It is necessary first to relate the edge parameters of the thermal instability theory to n(bar sign) and the other global parameters. The observed parametric dependence of the density limit in TEXTOR is generally consistent with the predicted density limit scaling of thermal instability theory. The observed wall conditioning dependence of the density limit can be reconciled with the theory in terms of the radiative emissivity temperature dependence of different impurities in the plasma edge. The thermal instability theory also provides an explanation of why symmetric detachment precedes radiative collapse for most low power shots, while a multifaceted asymmetric radiation from the edge MARFE precedes detachment for most high power shots

Laboratory beam-plasma interactions: linear and nonlinear

International Nuclear Information System (INIS)

Christiansen, P.J.; Jain, V.K.; Bond, J.W.

1982-01-01

The present investigation is concerned with the configuration of a cool plasma (often magnetized axially) penetrated by an injected electron beam. The attempt is made to demonstrate that despite unavoidable scaling limitations, laboratory experiments can illuminate, in a controlled fashion, details of beam plasma interaction processes in a way which will never be possible in the space plasma physics. In view of the increasing interest in high frequency instabilities in the auroral zone, the possibilities for interesting cross fertilizations of the two fields appear to be extensive. The linear theory is considered along with low frequency couplings and indirect effects. Attention is given to the evidence for the existence of exponentially growing instabilities in beam plasma interactions. The consequences of such instabilities are also explored and some processes of nonlinear processes are discussed, taking into account quasi-linear effects, trapping effects, nonlinear effects, trapping effects, nonlinear wave-wave interactions, and self-modulation and cavitation. 80 references

Temporal instability of viscous liquid microjets with spatially varying surface tension

Energy Technology Data Exchange (ETDEWEB)

Furlani, E P [Integrated Materials and Microstructures Laboratory, Electronic Imaging Products, Eastman Kodak Company, Rochester, NY 14650-2121 (United States)

2005-01-07

A linear theory is developed for the temporal instability of a viscous liquid microjet of Newtonian fluid with a spatially periodic variation of surface tension imposed along its length. The variation of surface tension induces Marangoni flow within the jet that leads to breakup and drop formation. An analytical expression is derived for the behaviour of the free surface of the microjet. This expression is useful for parametric analysis of jet instability and breakup as a function of jet radius, wavelength and fluid properties.

Temporal instability of viscous liquid microjets with spatially varying surface tension

International Nuclear Information System (INIS)

Furlani, E P

2005-01-01

A linear theory is developed for the temporal instability of a viscous liquid microjet of Newtonian fluid with a spatially periodic variation of surface tension imposed along its length. The variation of surface tension induces Marangoni flow within the jet that leads to breakup and drop formation. An analytical expression is derived for the behaviour of the free surface of the microjet. This expression is useful for parametric analysis of jet instability and breakup as a function of jet radius, wavelength and fluid properties

Experimental study of linear and nonlinear regimes of density-driven instabilities induced by CO{sub 2} dissolution in water

Energy Technology Data Exchange (ETDEWEB)

Outeda, R.; D' Onofrio, A. [Grupo de Medios Porosos, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, C1063ACV Buenos Aires (Argentina); El Hasi, C.; Zalts, A. [Instituto de Ciencias, Universidad Nacional General Sarmiento, J. M. Gutiérrez 1150, B1613GSX, Los Polvorines, Provincia de Buenos Aires (Argentina)

2014-03-15

Density driven instabilities produced by CO{sub 2} (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO{sub 2} pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a color indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO{sub 2} pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm{sup −1}) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO{sub 2} pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator.

Detection and control of combustion instability based on the concept of dynamical system theory

Science.gov (United States)

Gotoda, Hiroshi; Shinoda, Yuta; Kobayashi, Masaki; Okuno, Yuta; Tachibana, Shigeru

2014-02-01

We propose an online method of detecting combustion instability based on the concept of dynamical system theory, including the characterization of the dynamic behavior of combustion instability. As an important case study relevant to combustion instability encountered in fundamental and practical combustion systems, we deal with the combustion dynamics close to lean blowout (LBO) in a premixed gas-turbine model combustor. The relatively regular pressure fluctuations generated by thermoacoustic oscillations transit to low-dimensional intermittent chaos owing to the intermittent appearance of burst with decreasing equivalence ratio. The translation error, which is characterized by quantifying the degree of parallelism of trajectories in the phase space, can be used as a control variable to prevent LBO.

Detection and control of combustion instability based on the concept of dynamical system theory.

Science.gov (United States)

Gotoda, Hiroshi; Shinoda, Yuta; Kobayashi, Masaki; Okuno, Yuta; Tachibana, Shigeru

2014-02-01

We propose an online method of detecting combustion instability based on the concept of dynamical system theory, including the characterization of the dynamic behavior of combustion instability. As an important case study relevant to combustion instability encountered in fundamental and practical combustion systems, we deal with the combustion dynamics close to lean blowout (LBO) in a premixed gas-turbine model combustor. The relatively regular pressure fluctuations generated by thermoacoustic oscillations transit to low-dimensional intermittent chaos owing to the intermittent appearance of burst with decreasing equivalence ratio. The translation error, which is characterized by quantifying the degree of parallelism of trajectories in the phase space, can be used as a control variable to prevent LBO.

Linear {GLP}-algebras and their elementary theories

Science.gov (United States)

Pakhomov, F. N.

2016-12-01

The polymodal provability logic {GLP} was introduced by Japaridze in 1986. It is the provability logic of certain chains of provability predicates of increasing strength. Every polymodal logic corresponds to a variety of polymodal algebras. Beklemishev and Visser asked whether the elementary theory of the free {GLP}-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable [1]. For every positive integer n we solve the corresponding question for the logics {GLP}_n that are the fragments of {GLP} with n modalities. We prove that the elementary theory of the free {GLP}_n-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable for all n. We introduce the notion of a linear {GLP}_n-algebra and prove that all free {GLP}_n-algebras generated by the constants \\mathbf{0}, \\mathbf{1} are linear. We also consider the more general case of the logics {GLP}_α whose modalities are indexed by the elements of a linearly ordered set α: we define the notion of a linear algebra and prove the latter result in this case.

Buneman instability and Pierce instability in a collisionless bounded plasma

International Nuclear Information System (INIS)

Iizuka, Satoru; Saeki, Koichi; Sato, Noriyoshi; Hatta, Yoshisuke

1983-01-01

A systematic experiment is performed on the Buneman instability and the Pierce instability in a bounded plasma consisting of beam electrons and stationary ions. Current fluctuations are confirmed to be induced by the Buneman instability. On the other hand, the Pierce instability gives rise to a current limitation. The phenomena are well explained by Mikhailovskii's theory taking account of ion motion in a bounded plasma. (author)

Linear stability analysis of flow instabilities with a nodalized reduced order model in heated channel

International Nuclear Information System (INIS)

Paul, Subhanker; Singh, Suneet

2015-01-01

The prime objective of the presented work is to develop a Nodalized Reduced Order Model (NROM) to carry linear stability analysis of flow instabilities in a two-phase flow system. The model is developed by dividing the single phase and two-phase region of a uniformly heated channel into N number of nodes followed by time dependent spatial linear approximations for single phase enthalpy and two-phase quality between the consecutive nodes. Moving boundary scheme has been adopted in the model, where all the node boundaries vary with time due to the variation of boiling boundary inside the heated channel. Using a state space approach, the instability thresholds are delineated by stability maps plotted in parameter planes of phase change number (N pch ) and subcooling number (N sub ). The prime feature of the present model is that, though the model equations are simpler due to presence of linear-linear approximations for single phase enthalpy and two-phase quality, yet the results are in good agreement with the existing models (Karve [33]; Dokhane [34]) where the model equations run for several pages and experimental data (Solberg [41]). Unlike the existing ROMs, different two-phase friction factor multiplier correlations have been incorporated in the model. The applicability of various two-phase friction factor multipliers and their effects on stability behaviour have been depicted by carrying a comparative study. It is also observed that the Friedel model for friction factor calculations produces the most accurate results with respect to the available experimental data. (authors)

An Analysis of Dynamic Instability on TC-Like Vortex Using the Regularization-Based Eigenmode Linear Superposition Method

Directory of Open Access Journals (Sweden)

Shuang Liu

2018-01-01

Full Text Available In this paper, the eigenmode linear superposition (ELS method based on the regularization is used to discuss the distributions of all eigenmodes and the role of their instability to the intensity and structure change in TC-like vortex. Results show that the regularization approach can overcome the ill-posed problem occurring in solving mode weight coefficients as the ELS method are applied to analyze the impacts of dynamic instability on the intensity and structure change of TC-like vortex. The Generalized Cross-validation (GCV method and the L curve method are used to determine the regularization parameters, and the results of the two approaches are compared. It is found that the results based on the GCV method are closer to the given initial condition in the solution of the inverse problem of the vortex system. Then, the instability characteristic of the hollow vortex as the basic state are examined based on the linear barotropic shallow water equations. It is shown that the wavenumber distribution of system instability obtained from the ELS method is well consistent with that of the numerical analysis based on the norm mode. On the other hand, the evolution of the hollow vortex are discussed using the product of each eigenmode and its corresponding weight coefficient. Results show that the intensity and structure change of the system are mainly affected by the dynamic instability in the early stage of disturbance development, and the most unstable mode has a dominant role in the growth rate and the horizontal distribution of intense disturbance in the near-core region. Moreover, the wave structure of the most unstable mode possesses typical characteristics of mixed vortex Rossby-inertio-gravity waves (VRIGWs.

Gravitational Instabilities in Circumstellar Disks

Science.gov (United States)

Kratter, Kaitlin; Lodato, Giuseppe

2016-09-01

Star and planet formation are the complex outcomes of gravitational collapse and angular momentum transport mediated by protostellar and protoplanetary disks. In this review, we focus on the role of gravitational instability in this process. We begin with a brief overview of the observational evidence for massive disks that might be subject to gravitational instability and then highlight the diverse ways in which the instability manifests itself in protostellar and protoplanetary disks: the generation of spiral arms, small-scale turbulence-like density fluctuations, and fragmentation of the disk itself. We present the analytic theory that describes the linear growth phase of the instability supplemented with a survey of numerical simulations that aim to capture the nonlinear evolution. We emphasize the role of thermodynamics and large-scale infall in controlling the outcome of the instability. Despite apparent controversies in the literature, we show a remarkable level of agreement between analytic predictions and numerical results. In the next part of our review, we focus on the astrophysical consequences of the instability. We show that the disks most likely to be gravitationally unstable are young and relatively massive compared with their host star, Md/M*≥0.1. They will develop quasi-stable spiral arms that process infall from the background cloud. Although instability is less likely at later times, once infall becomes less important, the manifestations of the instability are more varied. In this regime, the disk thermodynamics, often regulated by stellar irradiation, dictates the development and evolution of the instability. In some cases the instability may lead to fragmentation into bound companions. These companions are more likely to be brown dwarfs or stars than planetary mass objects. Finally, we highlight open questions related to the development of a turbulent cascade in thin disks and the role of mode-mode coupling in setting the maximum angular

Bayes linear statistics, theory & methods

CERN Document Server

Goldstein, Michael

2007-01-01

Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...

LONGITUDINAL AND TRANSVERSAL PLASMA WAVE INSTABILITIES IN TWO COUNTERSTREAMING PLASMAS WITHOUT EXTERNAL FIELDS

Energy Technology Data Exchange (ETDEWEB)

Buenemann, D

1963-03-15

Some aspects of the theory of longitudinal and transversal waves in a collisionless nonrelativistic plasma are treated. A dispersion relation for multicomponent plasmas is derived from the linearized Boltzmann-Vlasov equation using the full set of Maxwell's equations without an external field. The velocity distributions of the plasma streams are assumed to be Maxwellian. For the particular case of two counterstreaming plasmas it is shown that there exists transversal instabilities for all counterstreaming velocities whereas the well known two stream instabilities only exist for velocities greater than a critical velocity. Exact solutions for the onset of the instabilities can be given. This kind of instability may occur for any nonisotropic velocity distribution in a collisionless plasma. (auth)

Unitary theory of xenon instability in nuclear thermal reactors - 1. Reactor at 'zero power'

Energy Technology Data Exchange (ETDEWEB)

Novelli, A. (Politecnico di Milano (Italy). Centro Studi Nucleari E. Fermi)

1982-01-01

The question of nuclear thermal-reactor instability against xenon oscillations is widespread in the literature, but most theories, concerned with such an argument, contradict each other and, above all, they conflict with experimentally-observed instability at very low reactor power, i.e. without any power feedback. It is shown that, in any nuclear thermal reactor, xenon instability originates at very low power levels, and a very general stability condition is deduced by an extension of the rigorous, simple and powerful reduction of the Nyquist criterion, first performed by F. Storrer.

Instabilities in inhomogeneous plasma

International Nuclear Information System (INIS)

Mikhailovsky, A.B.

1983-01-01

The plasma inhomogeneity across the magnetic field causes a wide class of instabilities which are called instabilities of an inhomogeneous plasma or gradient instabilities. The instabilities that can be studied in the approximation of a magnetic field with parallel straight field lines are treated first, followed by a discussion of the influence of shear on these instabilities. The instabilities of a weakly inhomogeneous plasma with the Maxwellian velocity distribution of particles caused by the density and temperature gradients are often called drift instabilities, and the corresponding types of perturbations are the drift waves. An elementary theory of drift instabilities is presented, based on the simplest equations of motion of particles in the field of low-frequency and long-wavelength perturbations. Following that is a more complete theory of inhomogeneous collisionless plasma instabilities which uses the permittivity tensor and, in the case of electrostatic perturbations, the scalar of permittivity. The results are used to study the instabilities of a strongly inhomogeneous plasma. The instabilities of a plasma in crossed fields are discussed and the electromagnetic instabilities of plasma with finite and high pressure are described. (Auth.)

Graph-based linear scaling electronic structure theory

Energy Technology Data Exchange (ETDEWEB)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.; Swart, Pieter J.; Germann, Timothy C.; Bock, Nicolas [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mniszewski, Susan M.; Mohd-Yusof, Jamal; Wall, Michael E.; Djidjev, Hristo [Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Rubensson, Emanuel H. [Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala (Sweden)

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Linear circuits, systems and signal processing: theory and application

International Nuclear Information System (INIS)

Byrnes, C.I.; Saeks, R.E.; Martin, C.F.

1988-01-01

In part because of its universal role as a first approximation of more complicated behaviour and in part because of the depth and breadth of its principle paradigms, the study of linear systems continues to play a central role in control theory and its applications. Enhancing more traditional applications to aerospace and electronics, application areas such as econometrics, finance, and speech and signal processing have contributed to a renaissance in areas such as realization theory and classical automatic feedback control. Thus, the last few years have witnessed a remarkable research effort expended in understanding both new algorithms and new paradigms for modeling and realization of linear processes and in the analysis and design of robust control strategies. The papers in this volume reflect these trends in both the theory and applications of linear systems and were selected from the invited and contributed papers presented at the 8th International Symposium on the Mathematical Theory of Networks and Systems held in Phoenix on June 15-19, 1987

A cosmic ray driven instability

Science.gov (United States)

Dorfi, E. A.; Drury, L. O.

1985-01-01

The interaction between energetic charged particles and thermal plasma which forms the basis of diffusive shock acceleration leads also to interesting dynamical phenomena. For a compressional mode propagating in a system with homogeneous energetic particle pressure it is well known that friction with the energetic particles leads to damping. The linear theory of this effect has been analyzed in detail by Ptuskin. Not so obvious is that a non-uniform energetic particle pressure can addition amplify compressional disturbances. If the pressure gradient is sufficiently steep this growth can dominate the frictional damping and lead to an instability. It is important to not that this effect results from the collective nature of the interaction between the energetic particles and the gas and is not connected with the Parker instability, nor with the resonant amplification of Alfven waves.

Onset of Darrieus-Landau Instability in Expanding Flames

Science.gov (United States)

Mohan, Shikhar; Matalon, Moshe

2017-11-01

The effect of small amplitude perturbations on the propagation of circular flames in unconfined domains is investigated, computationally and analytically, within the context of the hydrodynamic theory. The flame, treated as a surface of density discontinuity separating fresh combustible mixture from the burnt gas, propagates at a speed dependent upon local curvature and hydrodynamic strain. For mixtures with Lewis numbers above criticality, thermodiffusive effects have stabilizing influences which largely affect the flame at small radii. The amplitude of these disturbances initially decay and only begin to grow once a critical radius is reached. This instability is hydrodynamic in nature and is a consequence of thermal expansion. Through linear stability analysis, predictions of critical flame radius at the onset of instability are obtained as functions of Markstein length and thermal expansion coefficients. The flame evolution is also examined numerically where the motion of the interface is tracked via a level-set method. Consistent with linear stability results, simulations show the flame initially remaining stable and the existence of a particular mode that will be first to grow and later determine the cellular structure observed experimentally at the onset of instability.

Turbulence closure for mixing length theories

Science.gov (United States)

Jermyn, Adam S.; Lesaffre, Pierre; Tout, Christopher A.; Chitre, Shashikumar M.

2018-05-01

We present an approach to turbulence closure based on mixing length theory with three-dimensional fluctuations against a two-dimensional background. This model is intended to be rapidly computable for implementation in stellar evolution software and to capture a wide range of relevant phenomena with just a single free parameter, namely the mixing length. We incorporate magnetic, rotational, baroclinic, and buoyancy effects exactly within the formalism of linear growth theories with non-linear decay. We treat differential rotation effects perturbatively in the corotating frame using a novel controlled approximation, which matches the time evolution of the reference frame to arbitrary order. We then implement this model in an efficient open source code and discuss the resulting turbulent stresses and transport coefficients. We demonstrate that this model exhibits convective, baroclinic, and shear instabilities as well as the magnetorotational instability. It also exhibits non-linear saturation behaviour, and we use this to extract the asymptotic scaling of various transport coefficients in physically interesting limits.

Influence of gradual density transition and nonlinear saturation on Rayleigh-Taylor instability growth

International Nuclear Information System (INIS)

Jacobs, H.

1984-08-01

Linear theory of Rayleigh-Taylor instability growth at a density profile which varies exponentially between regions of constant density is discussed in detail. The exact theory provides an approximate but conservative simple formula for the growth constant and it shows that a hitherto widely used theory erroneously underestimates the growth constant. A simple but effective ''synthetical model'' of nonlinear bubble growth is obtained from a synthesis of linear theory and constant terminal bubble speed. It is applied to pusher shell break-up in an inertial confinement fusion pellet to determine the maximum allowable initial perturbations and the most dangerous wavelength. In a situation typical of heavy ion drivers it is found that the allowable initial perturbations are increased by a few orders of magnitude by the gradual density transition and another order of magnitude by nonlinear saturation of the bubble speed. The gradual density transition also shifts the most dangerous wavelength from about once to about four times the minimum pusher shell thickness. The following topics are treated briefly: Reasons conflicting with use of the synthetical model to decide whether the pusher shell in a certain simulation will be broken up; other nonlinear theories available in the literature; further realistic effects that might aggravate instability growth. (orig.) [de

An Analytic Study of the Perpendicularly Propagating Electromagnetic Drift Instabilities in the Magnetic Reconnection Experiment

International Nuclear Information System (INIS)

Wang, Y.; Kulsrud, R.; Ji, H.

2008-01-01

A local linear theory is proposed for a perpendicularly propagating drift instability driven by relative drifts between electrons and ions. The theory takes into account local cross-field current, pressure gradients and modest collisions as in the Magnetic Reconnection Experiment (MRX) (10). The unstable waves have very small group velocities in the direction of the pressure gradient, but have a large phase velocity near the relative drift velocity between electrons and ions in the direction of cross-field current. By taking into account the electron-ion collisions and applying the theory in the Harris sheet, we establish that this instability could be excited near the center of the Harris sheet and have enough efoldings to grow to large amplitude before it propagates out of the unstable region. Comparing with the other magnetic reconnection related instabilities (LHDI, MTSI et.) studied previously, we believe the instability we find is a favorable candidate to produce anomalous resistivity because of its unique wave characteristics, such as electromagnetic component, large phase velocity, and small group velocity in the cross current layer direction

Numerical study of jets secondary instabilities

International Nuclear Information System (INIS)

Brancher, Pierre

1996-01-01

The work presented in this dissertation is a contribution to the study of the transition to turbulence in open shear flows. Results from direct numerical simulations are interpreted within the framework of hydrodynamic stability theory. The first chapter is an introduction to the primary and secondary instabilities observed in jets and mixing layers. The numerical method used in the present study is detailed in the second chapter. The dynamics of homogeneous circular jets subjected to stream wise and azimuthal perturbations are investigated in the third chapter. A complete scenario describing the evolution of the jet is proposed with emphasis on the dynamics of vorticity within the flow. In the fourth chapter a parametric study reveals a three-dimensional secondary instability mainly controlled in the linear regime by the Strouhal number of the primary instability. In the nonlinear regime the dynamics of the azimuthal harmonies are described by means of model equations and are linked to the formation of stream wise vortices in the braid. The fifth chapter is dedicated to the convective or absolute nature of the secondary instabilities in plane shear layers. It is shown that there are flow configurations for which the two-dimensional secondary instability (pairing) is absolute even though the primary instability (Kelvin-Helmholtz) is convective. Some preliminary results concerning the three-dimensional secondary instabilities arc presented at the end of this chapter. The last chapter summarizes the main results and examines possible extensions of this work. (author) [fr

Localized modelling and feedback control of linear instabilities in 2-D wall bounded shear flows

Science.gov (United States)

Tol, Henry; Kotsonis, Marios; de Visser, Coen

2016-11-01

A new approach is presented for control of instabilities in 2-D wall bounded shear flows described by the linearized Navier-Stokes equations (LNSE). The control design accounts both for spatially localized actuators/sensors and the dominant perturbation dynamics in an optimal control framework. An inflow disturbance model is proposed for streamwise instabilities that drive laminar-turbulent transition. The perturbation modes that contribute to the transition process can be selected and are included in the control design. A reduced order model is derived from the LNSE that captures the input-output behavior and the dominant perturbation dynamics. This model is used to design an optimal controller for suppressing the instability growth. A 2-D channel flow and a 2-D boundary layer flow over a flat plate are considered as application cases. Disturbances are generated upstream of the control domain and the resulting flow perturbations are estimated/controlled using wall shear measurements and localized unsteady blowing and suction at the wall. It will be shown that the controller is able to cancel the perturbations and is robust to unmodelled disturbances.

Linear algebra and group theory for physicists

CERN Document Server

Rao, K N Srinivasa

2006-01-01

Professor Srinivasa Rao's text on Linear Algebra and Group Theory is directed to undergraduate and graduate students who wish to acquire a solid theoretical foundation in these mathematical topics which find extensive use in physics. Based on courses delivered during Professor Srinivasa Rao's long career at the University of Mysore, this text is remarkable for its clear exposition of the subject. Advanced students will find a range of topics such as the Representation theory of Linear Associative Algebras, a complete analysis of Dirac and Kemmer algebras, Representations of the Symmetric group via Young Tableaux, a systematic derivation of the Crystallographic point groups, a comprehensive and unified discussion of the Rotation and Lorentz groups and their representations, and an introduction to Dynkin diagrams in the classification of Lie groups. In addition, the first few chapters on Elementary Group Theory and Vector Spaces also provide useful instructional material even at an introductory level. An author...

A local homology theory for linearly compact modules

International Nuclear Information System (INIS)

Nguyen Tu Cuong; Tran Tuan Nam

2004-11-01

We introduce a local homology theory for linearly modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties of local homology modules are shown such as: the vanishing and non-vanishing, the noetherianness of local homology modules. By using duality, we extend some well-known results in theory of local cohomology of A. Grothendieck. (author)

Linear and nonlinear physics of the magnetoacoustic cyclotron instability of fusion-born ions in relation to ion cyclotron emission

Energy Technology Data Exchange (ETDEWEB)

Carbajal, L., E-mail: L.Carbajal-Gomez@warwick.ac.uk; Cook, J. W. S. [Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Dendy, R. O. [EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB, Oxfordshire (United Kingdom); Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Chapman, S. C. [Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Department of Mathematics and Statistics, University of Tromsø, N-9037, Tromsø (Norway); Max Planck Institute for the Physics of Complex Systems, D-01187, Dresden (Germany)

2014-01-15

The magnetoacoustic cyclotron instability (MCI) probably underlies observations of ion cyclotron emission (ICE) from energetic ion populations in tokamak plasmas, including fusion-born alpha-particles in JET and TFTR [Dendy et al., Nucl. Fusion 35, 1733 (1995)]. ICE is a potential diagnostic for lost alpha-particles in ITER; furthermore, the MCI is representative of a class of collective instabilities, which may result in the partial channelling of the free energy of energetic ions into radiation, and away from collisional heating of the plasma. Deep understanding of the MCI is thus of substantial practical interest for fusion, and the hybrid approximation for the plasma, where ions are treated as particles and electrons as a neutralising massless fluid, offers an attractive way forward. The hybrid simulations presented here access MCI physics that arises on timescales longer than can be addressed by fully kinetic particle-in-cell simulations and by analytical linear theory, which the present simulations largely corroborate. Our results go further than previous studies by entering into the nonlinear stage of the MCI, which shows novel features. These include stronger drive at low cyclotron harmonics, the re-energisation of the alpha-particle population, self-modulation of the phase shift between the electrostatic and electromagnetic components, and coupling between low and high frequency modes of the excited electromagnetic field.

Wakefields and Instabilities in Linear Accelerators

CERN Document Server

Ferrario, M.; Palumbo, L.

2014-12-19

When a charged particle travels across the vacuum chamber of an accelerator, it induces electromagnetic fields, which are left mainly behind the generating particle. These electromagnetic fields act back on the beam and influence its motion. Such an interaction of the beam with its surro undings results in beam energy losses, alters the shape of the bunches, and shifts the betatron and synchrotron frequencies. At high beam current the fields can even lead to instabilities, thus limiting the performance of the accelerator in terms of beam quality and current intensity. We discuss in this lecture the general features of the electromagnetic fields, introducing the concepts of wakefields and giving a few simple examples in cylindrical geometry. We then show the effect of the wakefields on the dynamics of a beam in a linac, dealing in particular with the beam breakup instability and how to cure it.

Lattice instability and martensitic transformation in LaAg predicted from first-principles theory

DEFF Research Database (Denmark)

Vaitheeswaran, G.; Kanchana, V.; Zhang, X.

2012-01-01

The electronic structure, elastic constants and lattice dynamics of the B2 type intermetallic compound LaAg are studied by means of density functional theory calculations with the generalized gradient approximation for exchange and correlation. The calculated equilibrium properties and elastic......, calculated using density functional perturbation theory, are in good agreement with available inelastic neutron scattering data. Under pressure, the phonon dispersions develop imaginary frequencies, starting at around 2.3 GPa, in good accordance with the martensitic instability observed above 3.4 GPa...

Coarse-graining free theories with gauge symmetries: the linearized case

International Nuclear Information System (INIS)

Bahr, Benjamin; Dittrich, Bianca; He Song

2011-01-01

Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties in both canonical and covariant quantization approaches. We discuss here the method of perfect actions, which attempts to restore gauge symmetries by mirroring exactly continuum physics on a lattice via a coarse graining process. Analytical results can only be obtained via a perturbative approach, for which we consider the first step, namely the coarse graining of the linearized theory. The linearized gauge symmetries are exact also in the discretized theory; hence, we develop a formalism to deal with gauge systems. Finally, we provide a discretization of linearized gravity as well as a coarse graining map and show that with this choice the three-dimensional (3D) linearized gravity action is invariant under coarse graining.

Renormalization, averaging, conservation laws and AdS (in)stability

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg; Vanhoof, Joris

2015-01-01

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

Linear Analysis of Converging Richtmyer-Meshkov Instability in the Presence of an Azimuthal Magnetic Field

KAUST Repository

Bakhsh, Abeer; Samtaney, Ravindra

2017-01-01

We investigate the linear stability of both positive and negative Atwood ratio interfaces accelerated either by a fast magnetosonic or hydrodynamic shock in cylindrical geometry. For the magnetohydrodynamic (MHD) case, we examine the role of an initial seed azimuthal magnetic field on the growth rate of the perturbation. In the absence of a magnetic field, the Richtmyer-Meshkov growth is followed by an exponentially increasing growth associated with the Rayleigh-Taylor instability. In the MHD case, the growth rate of the instability reduces in proportion to the strength of the applied magnetic field. The suppression mechanism is associated with the interference of two waves running parallel and anti-parallel to the interface that transport of vorticity and cause the growth rate to oscillate in time with nearly a zero mean value.

Linear Analysis of Converging Richtmyer-Meshkov Instability in the Presence of an Azimuthal Magnetic Field

KAUST Repository

Bakhsh, Abeer

2017-11-17

We investigate the linear stability of both positive and negative Atwood ratio interfaces accelerated either by a fast magnetosonic or hydrodynamic shock in cylindrical geometry. For the magnetohydrodynamic (MHD) case, we examine the role of an initial seed azimuthal magnetic field on the growth rate of the perturbation. In the absence of a magnetic field, the Richtmyer-Meshkov growth is followed by an exponentially increasing growth associated with the Rayleigh-Taylor instability. In the MHD case, the growth rate of the instability reduces in proportion to the strength of the applied magnetic field. The suppression mechanism is associated with the interference of two waves running parallel and anti-parallel to the interface that transport of vorticity and cause the growth rate to oscillate in time with nearly a zero mean value.

Analysis of two-phase flow instability in vertical boiling channels I: development of a linear model for the inlet velocity perturbation

International Nuclear Information System (INIS)

Hwang, D.H.; Yoo, Y.J.; Kim, K.K.

1998-08-01

A linear model, named ALFS, is developed for the analysis of two-phase flow instabilities caused by density wave oscillation and flow excursion in a vertical boiling channel with constant pressure drop conditions. The ALFS code can take into account the effect of the phase velocity difference and the thermally non-equilibrium phenomena, and the neutral boundary of the two-phase flow instability was analyzed by D-partition method. Three representative two-phase flow models ( i.e. HEM, DEM, and DNEM) were examined to investigate the effects on the stability analysis. As the results, it reveals that HEM shows the most conservative prediction of heat flux at the onset of flow instability. three linear models, Ishiis DEM, Sahas DNEM, and ALFS model, were applied to Sahas experimental data of density wave oscillation, and as the result, the mean and standard deviation of the predicted-to-measured heat flux at the onset of instability were calculated as 0.93/0.162, 0.79/0.112, and 0.95/0.143, respectively. For the long test section, however, ALFS model tends to predict the heat fluxes about 30 % lower than the measured values. (author). 14 refs

Formulated linear programming problems from game theory and its ...

African Journals Online (AJOL)

Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.

Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method

International Nuclear Information System (INIS)

Zhang Xu; Tan Duowang

2009-01-01

A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)

A general theory of electronic parametric instability of relativistically intense laser light in plasma

International Nuclear Information System (INIS)

Parr, D.M.

2000-04-01

This thesis studies the propagation and stability of ultraintense laser light in plasma. A new method is devised, both general and inclusive yet requiring only modest computational effort. The exact anharmonic waveforms for laser light are established. An examination of their stability extends the theory of electron parametric instabilities to relativistic regimes in plasmas of any density including classically overdense plasma accessible by self-induced transparency. Such instabilities can rapidly degrade intense pulses, but can also be harnessed, for example in the self-resonant laser wakefield accelerator. Understanding both the new and established regimes is thus basic to the success of many applications arising in high-field science, including novel x-ray sources and ignition of laser fusion targets, as well as plasma-based accelerator schemes. A covariant formulation of a cold electron fluid plasma is Lorentz transformed to the laser group velocity frame; this is the essence of the method and produces a very simple final model. Then, first, the zero-order laser 'driver' model is developed, in this frame representing a spatially homogeneous environment and thus soluble numerically as ordinary differential equations. The linearised first-order system leads to a further set of differential equations, whose solution defines the growth and other characteristics of an instability. The method is exact, rugged and flexible, avoiding the many approximations and restrictions previously necessary. This approach unifies all theory on purely electronic parametric instabilities over the last 30 years and, for the first time in generality, extends it into the ultrahigh relativistic regime. Besides extensions to familiar parametric instabilities, such as Stimulated Raman Scattering and Two-Plasmon Decay, strong stimulated harmonic generation emerges across a wide range of harmonics with high growth rates, presenting a varied and complex physical entity

Mitigating of modal instabilities in linearly-polarized fiber amplifiers by shifting pump wavelength

International Nuclear Information System (INIS)

Tao, Rumao; Ma, Pengfei; Wang, Xiaolin; Zhou, Pu; Liu, Zejin

2015-01-01

We investigated the effect of pump wavelength on the modal instabilities (MI) in high-power linearly polarized Yb-doped fiber amplifiers. We built a novel semi-analytical model to determine the frequency coupling characteristics and power threshold of MI, which indicates promising MI suppression through pumping at an appropriate wavelength. By pumping at 915 nm, the threshold can be enhanced by a factor of 2.1 as compared to that pumped at 976 nm. Based on a high-power linearly polarized fiber amplifier platform, we studied the influence of pump wavelength experimentally. A maximal enhancement factor of 1.9 has been achieved when pumped at 915 nm, which agrees with the theoretical calculation and verified our theoretical model. Furthermore, we show that MI suppression by detuning the pump wavelength is weakened for fiber with a large core-to-cladding ratio. (paper)

Kelvin-Helmholtz instability and kinetic internal kink modes in tokamaks

International Nuclear Information System (INIS)

Naitou, H.; Kobayashi, T.; Yagi, M.; Matsumoto, T.; Tokuda, S.; Kishimoto, Y.

2003-01-01

The m=1 (poloidal mode number) and n=1 (toroidal mode number) kinetic internal kink (KIK) mode in the presence of a density gradient is studied with the cylindrical version of the gyro-reduced MHD code, which is one of the extended MHD codes being able to treat the physics beyond resistive MHD. Electron inertia and electron finite temperature effects are included. The unstable KIK mode is observed in the parameter range in which the linear theory predicts complete stabilization due to the electron diamagnetic effect. The electrostatic potential profile in the linear stage of the KIK instability has the sheared poloidal flow with the m=1 mode structure. The vortexes are generated due to the Kelvin-Helmholtz (K-H) instability. The KIK is stabilized when the vortexes are formed, but it is destabilized again as the vortexes diminish due to the charge neutralizing electron motion along the magnetic field. These phenomena are observed in the early nonlinear stage of the KIK instability in which the width of the m=1 magnetic island is sufficiently small compared with the radial extent of the vortexes. The strong coupling between the vortexes and the KIK instability can be one of the candidates explaining the sudden onset of the sawtooth crash. (author)

One-loop dimensional reduction of the linear σ model

International Nuclear Information System (INIS)

Malbouisson, A.P.C.; Silva-Neto, M.B.; Svaiter, N.F.

1997-05-01

We perform the dimensional reduction of the linear σ model at one-loop level. The effective of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum instability of the model for large N. (author)

Nonlinear Development and Secondary Instability of Traveling Crossflow Vortices

Science.gov (United States)

Li, Fei; Choudhari, Meelan M.; Duan, Lian; Chang, Chau-Lyan

2014-01-01

Transition research under NASA's Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable "sufficiently" accurate transition prediction and practical transition control for future vehicle concepts. This paper builds upon prior effort targeting the laminar breakdown mechanisms associated with stationary crossflow instability over a swept-wing configuration relevant to subsonic aircraft with laminar flow technology. Specifically, transition via secondary instability of traveling crossflow modes is investigated as an alternate scenario for transition. Results show that, for the parameter range investigated herein, secondary instability of traveling crossflow modes becomes insignificant in relation to the secondary instability of the stationary modes when the relative initial amplitudes of the traveling crossflow instability are lower than those of the stationary modes by approximately two orders of magnitudes or more. Linear growth predictions based on the secondary instability theory are found to agree well with those based on PSE and DNS, with the most significant discrepancies being limited to spatial regions of relatively weak secondary growth, i.e., regions where the primary disturbance amplitudes are smaller in comparison to its peak amplitude. Nonlinear effects on secondary instability evolution is also investigated and found to be initially stabilizing, prior to breakdown.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

International Nuclear Information System (INIS)

Hack, Thomas-Paul; Schenkel, Alexander

2012-05-01

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Hack, Thomas-Paul [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Physik

2012-05-15

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

Linear theory of drift-tearing and interchange modes in a screw pinch

International Nuclear Information System (INIS)

Copenhaver, C.

1978-04-01

A drift dispersion relation, as applied to a resistive incompressible plasma in a screw pinch, is derived. This dispersion relation incorporates both drift-tearing and drift-interchange modes and is valid throughout the collisional regime by including kinetic theory factors. The dispersion relation reduces to the drift-tearing dispersion relation in the zero pressure gradient limit, and to the classical resistive dispersion relation in the zero drift limit. The electron temperature gradient instability is still present. Now, however, the introduction of the interchange-drift instability increases the growth rate further above the tearing-drift case. (orig.) [de

Fire Hose Instability in the Multiple Magnetic Reconnection

Science.gov (United States)

Alexandrova, A.; Retino, A.; Divin, A. V.; Le Contel, O.; Matteini, L.; Breuillard, H.; Deca, J.; Catapano, F.; Cozzani, G.; Nakamura, R.; Panov, E. V.; Voros, Z.

2017-12-01

We present observations of multiple reconnection in the Earth's magnetotail. In particular, we observe an ion temperature anisotropy characterized by large temperature along the magnetic field, between the two active X-lines. The anisotropy is associated with right-hand polarized waves at frequencies lower than the ion cyclotron frequency and propagating obliquely to the background magnetic field. We show that the observed anisotropy and the wave properties are consistent with linear kinetic theory of fire hose instability. The observations are in agreement with the particle-in-cell simulations of multiple reconnection. The results suggest that the fire hose instability can develop during multiple reconnection as a consequence of the ion parallel anisotropy that is produced by counter-streaming ions trapped between the X-lines.

Electron-acoustic Instability Simulated By Modified Zakharov Equations

Science.gov (United States)

Jásenský, V.; Fiala, V.; Vána, O.; Trávnícek, P.; Hellinger, P.

We present non-linear equations describing processes in plasma when electron - acoustic waves are excited. These waves are present for instance in the vicinity of Earth's bow shock and in the polar ionosphere. Frequently they are excited by an elec- tron beam in a plasma with two electron populations, a cold and hot one. We derive modified Zakharov equations from kinetic theory for such a case together with numer- ical method for solving of this type of equations. Bispectral analysis is used to show which non-linear wave processes are of importance in course of the instability. Finally, we compare these results with similar simulations using Vlasov approach.

Modeling hydrodynamic instabilities of double ablation fronts in inertial confinement fusion

International Nuclear Information System (INIS)

Yanez, C.; Sanz, J.; Olazabal-Loume, M.; Ibanez, L. F.

2013-01-01

A linear Rayleigh-Taylor instability theory of double ablation (DA) fronts is developed for direct-drive inertial confinement fusion. Two approaches are discussed: an analytical discontinuity model for the radiation dominated regime of very steep DA front structure, and a numerical self-consistent model that covers more general hydrodynamic profiles behaviours. Dispersion relation results are compared to 2D simulations. (authors)

Direct Numerical Simulation of the Rayleigh−Taylor Instability with the Spectral Element Method

International Nuclear Information System (INIS)

Xu, Zhang; Duo-Wang, Tan

2009-01-01

A novel method is proposed to simulate Rayleigh−Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier–Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh−Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh–Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh−Taylor instabilities of turbulent flows. (fundamental areas of phenomenology (including applications))

Edge localized linear ideal magnetohydrodynamic instability studies in an extended-magnetohydrodynamic code

International Nuclear Information System (INIS)

Burke, B. J.; Kruger, S. E.; Hegna, C. C.; Zhu, P.; Snyder, P. B.; Sovinec, C. R.; Howell, E. C.

2010-01-01

A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition to instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1-20). The results use the compressible MHD model and depend on a precise representation of 'ideal-like' and 'vacuumlike' or 'halo' regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 10 8 and 10 3 for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 10 5 , which is much larger than experimentally measured values using T e values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.

MHD instabilities in astrophysical plasmas: very different from MHD instabilities in tokamaks!

Science.gov (United States)

Goedbloed, J. P.

2018-01-01

The extensive studies of MHD instabilities in thermonuclear magnetic confinement experiments, in particular of the tokamak as the most promising candidate for a future energy producing machine, have led to an ‘intuitive’ description based on the energy principle that is very misleading for most astrophysical plasmas. The ‘intuitive’ picture almost directly singles out the dominant stabilizing field line bending energy of the Alfvén waves and, consequently, concentrates on expansion schemes that minimize that contribution. This happens when the wave vector {{k}}0 of the perturbations, on average, is perpendicular to the magnetic field {B}. Hence, all macroscopic instabilities of tokamaks (kinks, interchanges, ballooning modes, ELMs, neoclassical tearing modes, etc) are characterized by satisfying the condition {{k}}0 \\perp {B}, or nearly so. In contrast, some of the major macroscopic instabilities of astrophysical plasmas (the Parker instability and the magneto-rotational instability) occur when precisely the opposite condition is satisfied: {{k}}0 \\parallel {B}. How do those instabilities escape from the dominance of the stabilizing Alfvén wave? The answer to that question involves, foremost, the recognition that MHD spectral theory of waves and instabilities of laboratory plasmas could be developed to such great depth since those plasmas are assumed to be in static equilibrium. This assumption is invalid for astrophysical plasmas where rotational and gravitational accelerations produce equilibria that are at best stationary, and the associated spectral theory is widely, and incorrectly, believed to be non-self adjoint. These complications are addressed, and cured, in the theory of the Spectral Web, recently developed by the author. Using this method, an extensive survey of instabilities of astrophysical plasmas demonstrates how the Alfvén wave is pushed into insignificance under these conditions to give rise to a host of instabilities that do not

Alfven wave. [Book on linear and nonlinear properties for fusion applications

Energy Technology Data Exchange (ETDEWEB)

Hasegawa, A.; Uberoi, C.

1978-11-01

Seven chapters are included. Chapters 1 and 2 introduce the Alfven wave and describe its linear properties in a homogeneous medium. Chapters 3 and 4 cover the effects of inhomogeneities on these linear properties. Particular emphasis is placed on the appearance of a continuum spectrum and the associated absorption of the Alfven wave which arise due to the inhomogeneity. The explanation of the physical origin of absorption is given using kinetic theory. Chapter 5 is devoted to the associated plasma instabilities. Nonlinear effects discussed in Chapter 6 include quasilinear diffusion, decay, a solitary wave, and a modulational instability. The principles of Alfven wave heating, a design example and present-day experimental results are described in Chapter 7.

Simulation studies of plasma waves in the electron foreshock - The transition from reactive to kinetic instability

Science.gov (United States)

Dum, C. T.

1990-01-01

Particle simulation experiments were used to analyze the electron beam-plasma instability. It is shown that there is a transition from the reactive state of the electron beam-plasma instability to the kinetic instability of Langmuir waves. Quantitative tests, which include an evaluation of the dispersion relation for the evolving non-Maxwellian beam distribution, show that a quasi-linear theory describes the onset of this transition and applies again fully to the kinetic stage. This stage is practically identical to the late stage seen in simulations of plasma waves in the electron foreshock described by Dum (1990).

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

Science.gov (United States)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Effective collision frequency due to ion-acoustic instability: Theory and simulations

Czech Academy of Sciences Publication Activity Database

Hellinger, Petr; Trávníček, Pavel; Menietti, J. D.

2004-01-01

Roč. 31, č. 10 (2004), L10806 ISSN 0094-8276 R&D Projects: GA MŠk ME 500; GA AV ČR IAA3042403 Grant - others:ESA PRODEX(XE) 14529/00/NL/SFe; NASA (US) NAG5-11942 Institutional research plan: CEZ:AV0Z3042911 Keywords : Magnetospheric Physics: Plasma waves and instabilities * Space Plasma Physics: Kinetic and MHD theory * Space Plasma Physics: Magnetic reconnection Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.378, year: 2004

Size effects on cavitation instabilities

DEFF Research Database (Denmark)

Niordson, Christian Frithiof; Tvergaard, Viggo

2006-01-01

growth is here analyzed for such cases. A finite strain generalization of a higher order strain gradient plasticity theory is applied for a power-law hardening material, and the numerical analyses are carried out for an axisymmetric unit cell containing a spherical void. In the range of high stress...... triaxiality, where cavitation instabilities are predicted by conventional plasticity theory, such instabilities are also found for the nonlocal theory, but the effects of gradient hardening delay the onset of the instability. Furthermore, in some cases the cavitation stress reaches a maximum and then decays...... as the void grows to a size well above the characteristic material length....

Recent progresses in relativistic beam-plasma instability theory

Directory of Open Access Journals (Sweden)

A. Bret

2010-11-01

Full Text Available Beam-plasma instabilities are a key physical process in many astrophysical phenomena. Within the fireball model of Gamma ray bursts, they first mediate a relativistic collisionless shock before they produce upstream the turbulence needed for the Fermi acceleration process. While non-relativistic systems are usually governed by flow-aligned unstable modes, relativistic ones are likely to be dominated by normally or even obliquely propagating waves. After reviewing the basis of the theory, results related to the relativistic kinetic regime of the poorly-known oblique unstable modes will be presented. Relevant systems besides the well-known electron beam-plasma interaction are presented, and it is shown how the concept of modes hierarchy yields a criterion to assess the proton to electron mass ratio in Particle in cell simulations.

Kinetic theory of the sausage instability of a z-pinch

International Nuclear Information System (INIS)

Isichenko, M.B.; Kulyabin, K.L.; Yan'kov, V.V.

1989-01-01

A linear problem of z-pinch sausage development is considered taking into account the influence of kinetic effects for ideal scanning current. Plasma electrons are considered to be cold and ions - collisionless. It is also supposed that the magnetic field inside a pinch doesn't affect the motion of ions, which are reflected like in a mirror from a jump of an electric potential arising on the plasma boundary. In case of long-wave perturbations ka >1 the acount of kinetics leads to considerable decrease of the increment [(ka) 1/2 times] in comparison with the hydrodynamic description, that permits to explain the increased instability of z-pinches observed in experiments

High-pressure melting curve of KCl: Evidence against lattice-instability theories of melting

International Nuclear Information System (INIS)

Ross, M.; Wolf, G.

1986-01-01

We show that the large curvature in the T-P melting curve of KCl is the result of a reordering of the liquid to a more densely packed arrangement. As a result theories of melting, such as the instability model, which do not take into account the structure of the liquid fail to predict the correct pressure dependence of the melting curve

Collective processes in a tokamak with high-energy particles: general problems of the linear theory of Alfven instabilities of a tokamak with high-energy ions

International Nuclear Information System (INIS)

Mikhailovskii, A.B.

1986-01-01

Some general problems of the theory of Alfven instabilities of a tokamak with high-energy ions are considered. It is assumed that such ions are due to either ionization of fast neutral atoms, injected into the tokamak, or production of them under thermo-nuclear conditions. Small-oscillation equations are derived for the Alfven-type waves, which allow for both destabilizing effects, associated with the high-energy particles, and stabilizing ones, such as effects of shear and bulk-plasm dissipation. A high-energy ion contribution is calculated into the growth rate of the Alfven waves. The author considers the role of trapped-electron collisional dissipation

Kelvin-Helmholtz instability in a weakly ionized layer

OpenAIRE

Shadmehri, Mohsen; Downes, Turlough P.

2007-01-01

We study the linear theory of Kelvin-Helmholtz instability in a layer of ions and neutrals with finite thickness. In the short wavelength limit the thickness of the layer has a negligible effect on the growing modes. However, perturbations with wavelength comparable to layer's thickness are significantly affected by the thickness of the layer. We show that the thickness of the layer has a stabilizing effect on the two dominant growing modes. Transition between the modes not only depends on th...

Linear stability analysis and nonlinear simulation of the channeling effect on viscous fingering instability in miscible displacement

Science.gov (United States)

Shahnazari, M. R.; Maleka Ashtiani, I.; Saberi, A.

2018-03-01

In this paper, the effect of channeling on viscous fingering instability of miscible displacement in porous media is studied. In fact, channeling is introduced as a solution to stabilize the viscous fingering instability. In this solution, narrow channels were placed next to the walls, and by considering an exponential function to model the channeling effect, a heterogeneous media is assumed. In linear stability analysis, the governing equations are transferred to Fourier space, and by introducing a novel numerical method, the transferred equations are analyzed. The growth rate based on the wave number diagram has been drawn up in three sections of the medium. It is found that the flow becomes more stable at the center and unstable along the walls when the permeability ratio is increased. Also when the permeability ratio is approximately equal to one, the channeling has no significant effect. In nonlinear simulations, by using stream function and vortices, new equations have been rewritten and it is shown that channeling has a profound effect on the growth of the fingers and mechanisms. In addition to the superposition of velocity vectors and concentration contours, the development of instability is investigated using the mixing length and sweep efficiency diagram. The results show that although channeling reduces instability, it increases the displacement process time.

Resonant Drag Instabilities in protoplanetary disks: the streaming instability and new, faster-growing instabilities

Science.gov (United States)

Squire, Jonathan; Hopkins, Philip F.

2018-04-01

We identify and study a number of new, rapidly growing instabilities of dust grains in protoplanetary disks, which may be important for planetesimal formation. The study is based on the recognition that dust-gas mixtures are generically unstable to a Resonant Drag Instability (RDI), whenever the gas, absent dust, supports undamped linear modes. We show that the "streaming instability" is an RDI associated with epicyclic oscillations; this provides simple interpretations for its mechanisms and accurate analytic expressions for its growth rates and fastest-growing wavelengths. We extend this analysis to more general dust streaming motions and other waves, including buoyancy and magnetohydrodynamic oscillations, finding various new instabilities. Most importantly, we identify the disk "settling instability," which occurs as dust settles vertically into the midplane of a rotating disk. For small grains, this instability grows many orders of magnitude faster than the standard streaming instability, with a growth rate that is independent of grain size. Growth timescales for realistic dust-to-gas ratios are comparable to the disk orbital period, and the characteristic wavelengths are more than an order of magnitude larger than the streaming instability (allowing the instability to concentrate larger masses). This suggests that in the process of settling, dust will band into rings then filaments or clumps, potentially seeding dust traps, high-metallicity regions that in turn seed the streaming instability, or even overdensities that coagulate or directly collapse to planetesimals.

Effect of Compliant Walls on Secondary Instabilities in Boundary-Layer Transition

Science.gov (United States)

Joslin, Ronald D.; Morris, Philip J.

1991-01-01

For aerodynamic and hydrodynamic vehicles, it is highly desirable to reduce drag and noise levels. A reduction in drag leads to fuel savings. In particular for submersible vehicles, a decrease in noise levels inhibits detection. A suggested means to obtain these reduction goals is by delaying the transition from laminar to turbulent flow in external boundary layers. For hydrodynamic applications, a passive device which shows promise for transition delays is the compliant coating. In previous studies with a simple mechanical model representing the compliant wall, coatings were found that provided transition delays as predicted from the semi-empirical e(sup n) method. Those studies were concerned with the linear stage of transition where the instability of concern is referred to as the primary instability. For the flat-plate boundary layer, the Tollmien-Schlichting (TS) wave is the primary instability. In one of those studies, it was shown that three-dimensional (3-D) primary instabilities, or oblique waves, could dominate transition over the coatings considered. From the primary instability, the stretching and tilting of vorticity in the shear flow leads to a secondary instability mechanism. This has been theoretical described by Herbert based on Floquet theory. In the present study, Herbert's theory is used to predict the development of secondary instabilities over isotropic and non-isotropic compliant walls. Since oblique waves may be dominant over compliant walls, a secondary theory extention is made to allow for these 3-D primary instabilities. The effect of variations in primary amplitude, spanwise wavenumber, and Reynolds number on the secondary instabilities are examined. As in the rigid wall case, over compliant walls the subharmonic mode of secondary instability dominates for low-amplitude primary disturbances. Both isotropic and non-isotropic compliant walls lead to reduced secondary growth rates compared to the rigid wall results. For high frequencies

Azerbaijan Technical University’s Experience in Teaching Linear Electrical Circuit Theory

Directory of Open Access Journals (Sweden)

G. A. Mamedov

2006-01-01

Full Text Available An experience in teaching linear electrical circuit theory at the Azerbaijan Technical University is presented in the paper. The paper describes structure of the Linear Electrical Circuit Theory course worked out by the authors that contains a section on electrical calculation of track circuits, information on electro-magnetic compatibility and typical tests for better understanding of the studied subject.

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

Science.gov (United States)

Freed, Alan D.; Leonov, Arkady I.

2002-01-01

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Dynamical instabilities in magnetohydrodynamic wind-cloud interactions

Science.gov (United States)

Banda-Barragan, Wladimir Eduardo; Parkin, Elliot Ross; Crocker, Roland M.; Federrath, Christoph; Bicknell, Geoffrey Vincent

2015-08-01

We report the results from a comprehensive numerical study that investigates the role of dynamical instabilities in magnetohydrodynamic interactions between winds and spherical clouds in the interstellar medium. The growth of Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilities at interfaces between wind and cloud material is responsible for the disruption of clouds and the formation of filamentary tails. We show how different strengths and orientations of the initial magnetic field affect the development of unstable modes and the ultimate morphology of these filaments. In the weak field limit, for example, KH instabilities developing at the flanks of clouds are dominant, whilst they are suppressed when stronger fields are considered. On the other hand, perturbations that originate RT instabilities at the leading edge of clouds are enhanced when fields are locally stronger. The orientation of the field lines also plays an important role in the structure of filaments. Magnetic ropes are key features of systems in which fields are aligned with the wind velocity, whilst current sheets are favoured when the initial field is preferentially transverse to the wind velocity. We compare our findings with analytical predictions obtained from the linear theory of hydromagnetic stability and provide a classification of filamentary tails based on their morphology.

Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

International Nuclear Information System (INIS)

Marcos, B.

2008-01-01

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.

Feasibility of combining linear theory and impact theory methods for the analysis and design of high speed configurations

Science.gov (United States)

Brooke, D.; Vondrasek, D. V.

1978-01-01

The aerodynamic influence coefficients calculated using an existing linear theory program were used to modify the pressures calculated using impact theory. Application of the combined approach to several wing-alone configurations shows that the combined approach gives improved predictions of the local pressure and loadings over either linear theory alone or impact theory alone. The approach not only removes most of the short-comings of the individual methods, as applied in the Mach 4 to 8 range, but also provides the basis for an inverse design procedure applicable to high speed configurations.

The Velikhov and anti-Velikhov effects in the theory of magnetorotational instability

International Nuclear Information System (INIS)

Mikhailovskii, A. B.; Lominadze, J. G.; Churikov, A. P.; Pustovitov, V. D.; Kharshiladze, O. A.

2008-01-01

A theory of magnetorotational instability (MRI) allowing an equilibrium plasma pressure gradient and nonaxisymmetry of perturbations is developed. This approach reveals that in addition to the Velikhov effect driving the MRI due to negative rotation frequency profile, dΘ 2 /dr < 0, there is an opposite effect (the anti-Velikhov effect) weakening this driving (here, Θ is the rotation frequency and r is the radial coordinate). It is shown that in addition to the Velikhov mechanism, two new mechanisms of MRI driving are possible, one of which is due to the pressure gradient squared and the other is due to the product of the pressure and density gradients. The analysis includes both the one-fluid magnetohydrodynamic plasma model and the kinetics allowing collisionless effects. In addition to the pure plasma containing ions and electrons, the dusty plasma is considered. The charged dust effect on stability is analyzed using the approximation of immobile dust. In the presence of dust, a term with the electric field appears in the one-fluid equation of plasma motion. This electric field affects the equilibrium plasma rotation and also gives rise to a family of instabilities of the rotating plasma, called the dust-induced rotational instabilities

Secondary Instability of Second Modes in Hypersonic Boundary Layers

Science.gov (United States)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

2012-01-01

Second mode disturbances dominate the primary instability stage of transition in a number of hypersonic flow configurations. The highest amplification rates of second mode disturbances are usually associated with 2D (or axisymmetric) perturbations and, therefore, a likely scenario for the onset of the three-dimensionality required for laminar-turbulent transition corresponds to the parametric amplification of 3D secondary instabilities in the presence of 2D, finite amplitude second mode disturbances. The secondary instability of second mode disturbances is studied for selected canonical flow configurations. The basic state for the secondary instability analysis is obtained by tracking the linear and nonlinear evolution of 2D, second mode disturbances using nonlinear parabolized stability equations. Unlike in previous studies, the selection of primary disturbances used for the secondary instability analysis was based on their potential relevance to transition in a low disturbance environment and the effects of nonlinearity on the evolution of primary disturbances was accounted for. Strongly nonlinear effects related to the self-interaction of second mode disturbances lead to an upstream shift in the upper branch neutral location. Secondary instability computations confirm the previously known dominance of subharmonic modes at relatively small primary amplitudes. However, for the Purdue Mach 6 compression cone configuration, it was shown that a strong fundamental secondary instability can exist for a range of initial amplitudes of the most amplified second mode disturbance, indicating that the exclusive focus on subharmonic modes in the previous applications of secondary instability theory to second mode primary instability may not have been fully justified.

Solar Wind Electron Scattering by Kinetic Instabilities and Whistler Turbulence

Science.gov (United States)

Gary, S. P.

2015-12-01

The expansion of the solar wind away from the Sun drives electron velocity distributions away from the thermal Maxwellian form, yielding distributions near 1 AU which typically can be characterized as consisting of three anisotropic components: a more dense, relatively cool core, a relatively tenuous , relatively warm halo and a similarly tenuous, warm strahl. Each of these nonthermal components are potential sources of kinetic plasma instabilities; the enhanced waves from each instability can scatter the electrons, acting to reduce the various anisotropies and making their overall velocity distribution more nearly (but not completely) thermal. In contrast, simulations are demonstrating that the forward decay of whistler turbulence can lead to the development of a T||> T_perp electron anisotropy. This presentation will review linear theories of electron-driven kinetic instabilities (following the presentation by Daniel Verscharen at the 2015 SHINE Workshop), and will further consider the modification of electron velocity distributions as obtained from particle-in-cell simulations of such instabilities as well as from the decay of whistler turbulence.

Tunnelling instability via perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Graffi, S. (Bologna Univ. (Italy). Dip. di Matematica); Grecchi, V. (Moderna Univ. (Italy). Dip. di Matematica); Jona-Lasinio, G. (Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique et Hautes Energies)

1984-10-21

The semiclassical limit of low lying states in a multiwell potential is studied by rigorous perturbative techniques. In particular tunnelling instability and localisation of wave functions is obtained in a simple way under small deformations of symmetric potentials.

Boosted quantum black hole and black string in M-theory, and quantum correction to Gregory-Laflamme instability

Energy Technology Data Exchange (ETDEWEB)

Hyakutake, Yoshifumi [Faculty of Science, Ibaraki University,Bunkyo 2-1-1, Mito, Ibaraki, 310-8512 (Japan)

2015-09-11

We take into account higher derivative R{sup 4} corrections in M-theory and construct quantum black hole and black string solutions in 11 dimensions up to the next leading order. The quantum black string is stretching along the 11th direction and the Gregory-Laflamme instability is examined at the quantum level. Thermodynamics of the boosted quantum black hole and black string are also discussed. Especially we take the near horizon limit of the quantum black string and investigate its instability quantitatively.

Eikonal instability of Gauss-Bonnet-(anti-)-de Sitter black holes

Science.gov (United States)

Konoplya, R. A.; Zhidenko, A.

2017-05-01

Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, [J. High Energy Phys. 07 (2016) 151, 10.1007/JHEP07(2016)151] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown [Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), 10.1103/PhysRevLett.114.071102], that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [Frolov, Phys. Rev. Lett. 115, 051102 (2015), 10.1103/PhysRevLett.115.051102]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.

When is quasi-linear theory exact. [particle acceleration

Science.gov (United States)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Kinetic theory of Jeans instability

NARCIS (Netherlands)

Trigger, S.A.; Ershkovic, A.I.; Heijst, van G.J.F.; Schram, P.P.J.M.

2004-01-01

Kinetic treatment of the Jeans gravitational instability, with collisions taken into account, is presented. The initial-value problem for the distribution function which obeys the kinetic equation, with the collision integral conserving the number of particles, is solved. Dispersion relation is

Wigner's little group as a gauge generator in linearized gravity theories

International Nuclear Information System (INIS)

Scaria, Tomy; Chakraborty, Biswajit

2002-01-01

We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory

Suhl instabilities for spin waves in ferromagnetic nanostripes and ultrathin films

Energy Technology Data Exchange (ETDEWEB)

Haghshenasfard, Zahra, E-mail: zhaghshe@uwo.ca; Nguyen, Hoa T.; Cottam, Michael G., E-mail: cottam@uwo.ca

2017-03-15

A microscopic (or Hamiltonian-based) theory is employed for the spin-wave instability thresholds of nonlinear processes in ultrathin ferromagnetic stripes and films under perpendicular pumping with an intense microwave field. The spatially-quantized linear spin waves in these nanostructures may participate in parametric processes through the three-magnon interactions (the first-order Suhl process) and the four-magnon interactions (the second-order Suhl process) when pumped. By contrast with most previous studies of spin-wave instabilities made for larger samples, where macroscopic (or continuum) theories involving Maxwell's equations for magnetic dipolar effects are used, a discrete lattice of effective spins is employed. Then a dipole-exchange spin Hamiltonian is employed to investigate the behavior of the quantized spin waves under perpendicular pumping, when modifications due to the more extensive spatial confinement and edges effects in these nanostructures become pronounced. The instability thresholds versus applied magnetic field are calculated, with emphasis on the size effects and geometries of the nanostructures and on the different relative strengths of the magnetic dipole-dipole and exchange interactions in materials. Numerical results are presented using parameters for Permalloy, YIG, and EuS. - Highlights: • Suhl instabilities for spin waves in magnetic stripes and films are investigated. • Three- and four-magnon processes in perpendicular pumping are taken into account. • Numerical applications are made to Permalloy, YIG, and EuS.

A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories

Directory of Open Access Journals (Sweden)

V. V. Zozulya

2013-01-01

Full Text Available A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.

Numerical simulation of anisotropic preheating ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Wang Lifeng; Ye Wenhua; Li Yingjun

2010-01-01

The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability (ARTI) is studied by numerical simulations. The preheating model κ(T)=κ SH [1+f(T)] is applied, where f(T) is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse. (authors)

Modified ocean circulation, albedo instability and ice-flow instability. Risks of non-linear climate change

Energy Technology Data Exchange (ETDEWEB)

Ham, J. van; Beer, R.J. van; Builtjes, P.J.H.; Roemer, M.G.M. [TNO Inst. of Environmental Sciences, Delft (Netherlands); Koennen, G.P. [KNMI, Royal Netherlands Meteorological Inst., de Bilt (Netherlands); Oerlemans, J. [Utrecht Univ. (Netherlands). Inst. for Meteorological and Atmospheric Research

1995-12-31

In this presentation part of an investigation is described into risks for climate change which are presently not adequately covered in General Circulation Models. In the concept of climate change as a result of the enhanced greenhouse effect it is generally assumed that the radiative forcings from increased concentrations of greenhouse gases (GHG) will result in a proportional or quasilinear global warming. Though correlations of this kind are known from palaeoclimate research, the variability of the climate seems to prevent the direct proof of a causal relation between recent greenhouse gas concentrations and temperature observations. In order to resolve the issue the use of General Circulation Models (GCMs), though still inadequate at present, is indispensable. Around the world some 10 leading GCMs exist which have been the subject of evaluation and intercomparison in a number of studies. Their results are regularly assessed in the IPCC process. A discussion on their performance in simulating present or past climates and the causes of their weak points shows that the depiction of clouds is a major weakness of GCMs. A second element which is virtually absent in GCMs are the feedbacks from natural biogeochemical cycles. These cycles are influenced by man in a number of ways. GCMs have a limited performance in simulating regional effects on climate. Moreover, albedo instability, in part due to its interaction with cloudiness, is only roughly represented. Apparently, not all relevant processes have been included in the GCMs. That situation constitutes a risk, since it cannot be ruled out that a missing process could cause or trigger a non-linear climate change. In the study non-linear climate change is connected with those processes which could provide feedbacks with a risk for non-monotonous or discontinuous behaviour of the climate system, or which are unpredictable or could cause rapid transitions

Modified ocean circulation, albedo instability and ice-flow instability. Risks of non-linear climate change

Energy Technology Data Exchange (ETDEWEB)

Ham, J van; Beer, R.J. van; Builtjes, P J.H.; Roemer, M G.M. [TNO Inst. of Environmental Sciences, Delft (Netherlands); Koennen, G P [KNMI, Royal Netherlands Meteorological Inst., de Bilt (Netherlands); Oerlemans, J [Utrecht Univ. (Netherlands). Inst. for Meteorological and Atmospheric Research

1996-12-31

In this presentation part of an investigation is described into risks for climate change which are presently not adequately covered in General Circulation Models. In the concept of climate change as a result of the enhanced greenhouse effect it is generally assumed that the radiative forcings from increased concentrations of greenhouse gases (GHG) will result in a proportional or quasilinear global warming. Though correlations of this kind are known from palaeoclimate research, the variability of the climate seems to prevent the direct proof of a causal relation between recent greenhouse gas concentrations and temperature observations. In order to resolve the issue the use of General Circulation Models (GCMs), though still inadequate at present, is indispensable. Around the world some 10 leading GCMs exist which have been the subject of evaluation and intercomparison in a number of studies. Their results are regularly assessed in the IPCC process. A discussion on their performance in simulating present or past climates and the causes of their weak points shows that the depiction of clouds is a major weakness of GCMs. A second element which is virtually absent in GCMs are the feedbacks from natural biogeochemical cycles. These cycles are influenced by man in a number of ways. GCMs have a limited performance in simulating regional effects on climate. Moreover, albedo instability, in part due to its interaction with cloudiness, is only roughly represented. Apparently, not all relevant processes have been included in the GCMs. That situation constitutes a risk, since it cannot be ruled out that a missing process could cause or trigger a non-linear climate change. In the study non-linear climate change is connected with those processes which could provide feedbacks with a risk for non-monotonous or discontinuous behaviour of the climate system, or which are unpredictable or could cause rapid transitions

Long wavelength limit of the current convective instability

International Nuclear Information System (INIS)

Huba, J.D.

1984-01-01

A linear theory is presented of the current convective instability in the long wavelength limit, i.e., kL >ω) and inertial (ν/sub i/n>>ω) limits where ω is the wave frequency and ν/sub i/n is the ion-neutral collision frequency. It is shown that the growth rate scales as k in the collisional limit and as k/sup 2/3/ in the inertial limit. The analytical solutions are compared to exact numerical solutions, and very good agreement is found. Applications to the auroral ionosphere are discussed

SATURATION OF MAGNETOROTATIONAL INSTABILITY THROUGH MAGNETIC FIELD GENERATION

International Nuclear Information System (INIS)

Ebrahimi, F.; Prager, S. C.; Schnack, D. D.

2009-01-01

The saturation mechanism of magnetorotational instability (MRI) is examined through analytical quasi-linear theory and through nonlinear computation of a single mode in a rotating disk. We find that large-scale magnetic field is generated through the α-effect (the correlated product of velocity and magnetic field fluctuations) and causes the MRI mode to saturate. If the large-scale plasma flow is allowed to evolve, the mode can also saturate through its flow relaxation. In astrophysical plasmas, for which the flow cannot relax because of gravitational constraints, the mode saturates through field generation only.

Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

CERN Document Server

Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

2016-01-01

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...

A Study of Current Driven Electrostatic Instability on the Auroral Zone

Directory of Open Access Journals (Sweden)

S. Y. Kim

1986-12-01

Full Text Available According to recent satellite observations, strong ion transverse acceleration to the magnetic field(ion conics has been known. The ion conics may be a result of electrostatic waves frequently observed on the auroral zone. Both linear and nonlinear theory of electrostatic instability driven by an electron current based on 1-dimenstional particle simulation experiment have been considered. From the results of simulation strong ion transverse acceleration has been shown.

Linear control theory for gene network modeling.

Science.gov (United States)

Shin, Yong-Jun; Bleris, Leonidas

2010-09-16

Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

An experimental test of the linear no-threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1990-01-01

There is a substantial body of quantitative information on radiation-induced cancer at high dose, but there are no data at low dose. The usual method for estimating effects of low-level radiation is to assume a linear no-threshold dependence. if this linear no-threshold assumption were not used, essentially all fears about radiation would disappear. Since these fears are costing tens of billions of dollars, it is most important that the linear no-threshold theory be tested at low dose. An opportunity for possibly testing the linear no-threshold concept is now available at low dose due to radon in homes. The purpose of this paper is to attempt to use this data to test the linear no-threshold theory

Saturation of equatorial inertial instability

NARCIS (Netherlands)

Kloosterziel, R.C.; Orlandi, P.; Carnevale, G.F.

2015-01-01

Inertial instability in parallel shear flows and circular vortices in a uniformly rotating system ( $f$f-plane) redistributes absolute linear momentum or absolute angular momentum in such a way as to neutralize the instability. In previous studies we showed that, in the absence of other

Mass-induced instability of SAdS black hole in Einstein-Ricci cubic gravity

Science.gov (United States)

Myung, Yun Soo

2018-05-01

We perform the stability analysis of Schwarzschild-AdS (SAdS) black hole in the Einstein-Ricci cubic gravity. It shows that the Ricci tensor perturbations exhibit unstable modes for small black holes. We call this the mass-induced instability of SAdS black hole because the instability of small black holes arises from the massiveness in the linearized Einstein-Ricci cubic gravity, but not a feature of higher-order derivative theory giving ghost states. Also, we point out that the correlated stability conjecture holds for the SAdS black hole by computing the Wald entropy of SAdS black hole in Einstein-Ricci cubic gravity.

Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents

International Nuclear Information System (INIS)

Hoelzl, M; Merkel, P; Lackner, K; Strumberger, E; Huijsmans, G T A; Aleynikova, K; Liu, F; Atanasiu, C; Nardon, E; Fil, A; McAdams, R; Chapman, I

2014-01-01

The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described

Normal mode analysis for linear resistive magnetohydrodynamics

International Nuclear Information System (INIS)

Kerner, W.; Lerbinger, K.; Gruber, R.; Tsunematsu, T.

1984-10-01

The compressible, resistive MHD equations are linearized around an equilibrium with cylindrical symmetry and solved numerically as a complex eigenvalue problem. This normal mode code allows to solve for very small resistivity eta proportional 10 -10 . The scaling of growthrates and layer width agrees very well with analytical theory. Especially, both the influence of current and pressure on the instabilities is studied in detail; the effect of resistivity on the ideally unstable internal kink is analyzed. (orig.)

Parametric plasma surface instabilities with s-polarized radiation

International Nuclear Information System (INIS)

Rappaport, H.L.

1994-01-01

The authors argue that parametric plasma surface mode excitation is a viable broadband instability mechanism in the microwave regime since the wavelength of incident radiation ca be large compared to plasma ion density gradient scale lengths. They restrict their attention to plasmas which are uniform in the planes perpendicular to the density gradients. The boundary is characterized by three parameters: (1) the ion density gradient scale length, (2) the electron Debye length, and (3) the excursion of boundary electrons as they move in response to monochromatic radiation. For s-polarized radiation, equilibrium fluid motion is parallel to the boundary when the ratio of the pump quiver velocity to the speed of light is small. In this case, an abruptly bounded plasma may be modeled with no transition width. If in this case the cold fluid approximation is used as well, the specular and diffuse boundary approximations become the same. A new formation is presented in which pump induced perturbations are expressed as an explicit superposition of linear and non-linear plasma half-space modes. A four-wave interaction is found to produce instability as well as surface wave frequency-shift. This mode is compared against other modes known to exist in this geometry. The theory of surface wave linear mode conversion is reviewed with special attention paid to power flow and energy conservation in this system

Effect of feedback and noise on fast ion instability

International Nuclear Information System (INIS)

Chao, A.W.; Stupakov, G.V.

1997-07-01

One can use a feedback system to suppress the fast ion instability. However, the feedback noise (and also other sources of noise in the machine) continuously excites the transient oscillations in the electron beam that are amplified through the electron interaction with the ions. We calculate the equilibrium level of these oscillations under the influence of the feedback and show how they grow exponentially from the head to the tail of the bunch train in a linear theory. Nonlinear saturation effects are assume negligible

Collisionless two-fluid theory of toroidal ηi stability

International Nuclear Information System (INIS)

Mondt, J.; Weiland, J.

1989-01-01

A collisionless two-fluid theory based on a fourteen-moment generalization of the 'double-adiabatic' equations is developed to lowest order in the Larmor radius parameter, and applied to derive the toroidal η i stability boundary for all values of the ratio of the density gradient scale length divided by the field curvature length. The present model is an improvement over existing collisional two-fluid models in view of the collisionless nature of the η i instability, while retaining the advantage over kinetic theory of the practability of mode-coupling simulations. The linear stability boundary, linear growth rate and real frequency agree fairly accurately with draft-kinetic theory

Hydrodynamic theory for quantum plasmonics: Linear-response dynamics of the inhomogeneous electron gas

DEFF Research Database (Denmark)

Yan, Wei

2015-01-01

We investigate the hydrodynamic theory of metals, offering systematic studies of the linear-response dynamics for an inhomogeneous electron gas. We include the quantum functional terms of the Thomas-Fermi kinetic energy, the von Weizsa¨cker kinetic energy, and the exchange-correlation Coulomb...... energies under the local density approximation. The advantages, limitations, and possible improvements of the hydrodynamic theory are transparently demonstrated. The roles of various parameters in the theory are identified. We anticipate that the hydrodynamic theory can be applied to investigate the linear...... response of complex metallic nanostructures, including quantum effects, by adjusting theory parameters appropriately....

Nonlinear features of the energy beam-driven instability

International Nuclear Information System (INIS)

Lesur, M.; Idomura, Y.; Garbet, X.

2009-01-01

Full text: A concern with ignited fusion plasmas is that, as a result of the instabilities they trigger, the high-energy particles eject themselves before they could give their energy to the core to sustain the reaction. Similarities between this class of instabilities and the so-called Berk-Breizman problem motivate us to study a single-mode instability driven by an energetic particle beam. For this purpose, a one dimensional Vlasov simulation is extended to include a Krook collision operator and external damping processes. The code is benchmarked with previous work. The fully nonlinear behavior is recovered in the whole parameter space characterized by an effective relaxation rate ν a and an external damping rate γ d . Steady state, periodic and chaotic behaviors are observed in nonlinear solutions. In the regime above marginal stability where both ν a and γ d are smaller than the linear drive γ L , we observe a good agreement of steady saturation levels between the simulation and theory. Near marginal stability, the role of the normalized relaxation rate ν a /(γ L -γ d ), which is a key parameter to predict the behavior of the solution, is investigated for an initial distribution with relatively small γ L , which correspond to the situation considered in the theory. In the low relaxation rate regime, frequency sweeping events are observed, and the time-evolution of such event is investigated. (author)

Transition from convective to absolute Raman instability via the longitudinal relativistic effect by using Vlasov-Maxwell simulations

Science.gov (United States)

Wang, Q.; Liu, Z. J.; Zheng, C. Y.; Xiao, C. Z.; Feng, Q. S.; Zhang, H. C.; He, X. T.

2018-01-01

The longitudinal relativistic effect on stimulated Raman backscattering (SRBS) is investigated by using one-dimensional (1D) Vlasov-Maxwell simulations. Using a short backscattered light seed pulse with a very small amplitude, the linear gain spectra of SRBS in the strongly convective regime is presented by combining the relativistic and non-relativistic 1D Vlasov-Maxwell simulations, which is in agreement with the steady-state linear theory. More interestingly, by considering transition from convective to absolute instability due to electron trapping, we successfully predict the critical duration of the seed which can just trigger the kinetic inflation of the excited SRBS after the seed leaves the simulation box. The critical duration in the relativistic case is much shorter than that in the nonrelativistic case, which indicates that the kinetic inflation more easily occurs in the relativistic case than in the nonrelativistic case. In the weakly convective regime, the transition from convective to absolute instability for SRBS can directly occur in the linear regime due to the longitudinal relativistic modification. For the same pump, our simulations first demonstrate that the SRBS excited by a short and small seed pulse is a convective instability in the nonrelativistic case but becomes an absolute instability due to the decrease of the linear Landau damping from the longitudinal relativistic modification in the relativistic case. In more detail, the growth rate of the backscattered light is also in excellent agreement with theoretical prediction.

Study of flow instability in a centrifugal fan based on energy gradient theory

International Nuclear Information System (INIS)

Xiao, Meina; Dou, Hua-Shu; Ma, Xiaoyang; Xiao, Qing; Chen, Yongning; He, Haijiang; Ye, Xinxue

2016-01-01

Flow instability in a centrifugal fan was studied using energy gradient theory. Numerical simulation was performed for the three dimensional turbulent flow field in a centrifugal fan. The flow is governed by the three-dimensional incompressible Navier-Stokes equations coupled with the RNG k-ε turbulent model. The finite volume method was used to discretize the governing equations and the Semiimplicit method for pressure linked equation (SIMPLE) algorithm is employed to iterate the system of the equations. The interior flow field in the centrifugal fan and the distribution of the energy gradient function K are obtained at different flow rates. According to the energy gradient method, the area with larger value of K is the place where the flow loses stability easier. The results show that instability is easier to generate in the regions of impeller outlet and volute tongue. The air flow near the hub is more stable than that near the shroud. That is due to the influences of variations of the velocity and the inlet angle along the axial direction. With the decrease of the flow rate, instability zone in a blade channel moves to the impeller inlet from the outlet and the unstable regions in different channels develop in opposite direction to the rotation of impeller

Multitrace Deformations of Vector and Adjoint Theories and their Holographic Duals

CERN Document Server

Elitzur, S; Porrati, M; Rabinovici, Eliezer

2006-01-01

We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV com...

Clifford Algebras and Spinorial Representation of Linear Canonical Transformations in Quantum Theory

International Nuclear Information System (INIS)

Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.

2017-11-01

This work is a continuation of previous works that we have done concerning linear canonical transformations and a phase space representation of quantum theory. It is mainly focused on the description of an approach which permits to establish spinorial representation of linear canonical transformations. It begins with an introduction section in which the reason and context of the content are discussed. The introduction section is followed by a brief recall about Clifford algebra and spin group. The description of the approach is started with the presentation of an adequate parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operators space. The establishment of the spinorial representation is deduced using relation between special pseudo-orthogonal groups and spin groups. The cases of one dimension quantum mechanics and general multidimensional theory are both studied. The case of linear canonical transformation related to Minkowski space is particularly studied and it is shown that Lorentz transformation may be considered as particular case of linear canonical transformation. Some results from the spinorial representation are also exploited to define operators which may be used to establish equations for fields if one considers the possibility of envisaging a field theory which admits as main symmetry group the group constituted by linear canonical transformations.

Linear control theory for gene network modeling.

Directory of Open Access Journals (Sweden)

Yong-Jun Shin

Full Text Available Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain and linear state-space (time domain can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

Science.gov (United States)

Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

2018-05-01

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

Cyclic and seasonal features in the behaviour of linear growth increment of Rayleigh-Taylor instability in equatorial F-region

International Nuclear Information System (INIS)

Farkullin, M.N.; Nikitin, M.A.; Kashchenko, N.M.

1989-01-01

Calculations of linear increment of the Rayleigh-Taylor instability for various geophysical conditions are presented. It is shwn that space-time characteristics of increment depend strongly on conditions of solar activity and seasons. The calculation results are in a good agreement with statistical regularities of F-scattering observation in equatorial F-area, which points to the Rayleigh-Taylor natur of the penomena

Non-linear Q-clouds around Kerr black holes

International Nuclear Information System (INIS)

Herdeiro, Carlos; Radu, Eugen; Rúnarsson, Helgi

2014-01-01

Q-balls are regular extended ‘objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family

Plane answers to complex questions the theory of linear models

CERN Document Server

Christensen, Ronald

1987-01-01

This book was written to rigorously illustrate the practical application of the projective approach to linear models. To some, this may seem contradictory. I contend that it is possible to be both rigorous and illustrative and that it is possible to use the projective approach in practical applications. Therefore, unlike many other books on linear models, the use of projections and sub­ spaces does not stop after the general theory. They are used wherever I could figure out how to do it. Solving normal equations and using calculus (outside of maximum likelihood theory) are anathema to me. This is because I do not believe that they contribute to the understanding of linear models. I have similar feelings about the use of side conditions. Such topics are mentioned when appropriate and thenceforward avoided like the plague. On the other side of the coin, I just as strenuously reject teaching linear models with a coordinate free approach. Although Joe Eaton assures me that the issues in complicated problems freq...

Numerical Simulation of Anisotropic Preheating Ablative Rayleigh–Taylor Instability

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Ying-Jun, Li

2010-01-01

The linear growth rate of the anisotropic preheating ablative Rayleigh–Taylor instability (ARTI) is studied by numerical simulations. The preheating model κ(T) = κ SH [1 + f(T)] is applied, where f(T) is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse [Phys. Rev. Lett. 98 (2007) 245001]. (physics of gases, plasmas, and electric discharges)

Instabilities in the 'on' phase of the plasma focus

International Nuclear Information System (INIS)

Kaeppeler, H.J.

1990-07-01

In the operation of large plasma focus devices, e.g. POSEIDON, there appear saturation phenomena in the neutron production when the charging energy of the condensor bank approaches its nominal value. This saturation is attributed to the action of impurities. It is assumed that there appear instabilities which are in part caused by impurities. In order to be able to answer this question, the linear dispersion relation was derived from a three-fluid theory (electrons, ions and neutrals) with the aid of the computer algebra (CA) code MACSYMA. The inversion of the 17x17 matrix (it is assumed that v a =v i and T a =T i ) and solution of the determinant was carried out on a CONVEX C 120 computer using the CA code MAPLE. The calculation of the zeros was done with a modified CPZERO program from the SLATEC library. There appear four instabilities in the rundown phase of the plasma focus, two of them gradient driven. The first two are unstable electrostatic waves with very high phase velocities, thus they do not contribute to anomalous dissipation. The third is identified as a gradient driven space charge instability which may possibly lead to current chopping. The electron acoustic wave instability, here gradient driven, is the fourth. It was found in a previous study of MPD thruster instabilities. (orig.)

Triclade: influence of a sinuous secondary instability on the Richtmyer-Meshkov instabilities

International Nuclear Information System (INIS)

Boulet, M.; Griffond, J.

2004-01-01

Occurrence of a secondary instability developing after the Richtmyer-Meshkov (primary) instability is emphasized thanks to numerical simulations with the TRICLADE code. We are mainly considering 2D perturbations describes by trigonometric function cosine or [cosine]. However, the 3D case is also tackled. The sinuous secondary instability is characterized by the loss of the symmetries in the direction normal to the interface at its crests. It reduces the late time growing rate of the 'mushrooms' formed by the Richtmyer-Meshkov instability. Related simplified problems, like symmetrical Riemann problems or the Mallier-Maslowe array of counter-rotating vortices, allow us to perform 2D linear stability analysis. Thus, we show that the sinuous secondary instability is not a numerical artifact and that is comes from the continuous incompressible velocity field in the interface region. This instability implies temporal limitations for the validity of single mode simulations; therefore multimode simulations are necessary to study the ]ate-time behaviour of interfaces bitted by shocks. (authors)

A simple theory of linear mode conversion

International Nuclear Information System (INIS)

Cairns, R.A.; Lashmore-Davies, C.N.; Woods, A.M.

1984-01-01

A summary is given of the basic theory of linear mode conversion involving the construction of differential equations for the mode amplitudes based on the properties of the dispersion relation in the neighbourhood of the mode conversion point. As an example the transmission coefficient for tunneling from the upper hybrid resonance through the evanescent region to the adjacent cut-off is treated. 7 refs, 3 figs

A quantum-mechanical perspective on linear response theory within polarizable embedding

DEFF Research Database (Denmark)

List, Nanna Holmgaard; Norman, Patrick; Kongsted, Jacob

2017-01-01

We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole...

A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs

OpenAIRE

Giang, Phan H.; Shenoy, Prakash P.

2013-01-01

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize "qualitative expected utility." Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic l...

Linear analysis of sheared flow stabilization of global magnetohydrodynamic instabilities based on the Hall fluid model

International Nuclear Information System (INIS)

Sotnikov, V.I.; Paraschiv, I.; Makhin, V.; Bauer, B.S.; Leboeuf, J.N.; Dawson, J.M.

2002-01-01

A systematic study of the linear stage of sheared flow stabilization of Z-pinch plasmas based on the Hall fluid model with equilibrium that contains sheared flow and an axial magnetic field is presented. In the study we begin with the derivation of a general set of equations that permits the evaluation of the combined effect of sheared flow and axial magnetic field on the development of the azimuthal mode number m=0 sausage and m=1 kink magnetohydrodynamic (MHD) instabilities, with the Hall term included in the model. The incorporation of sheared flow, axial magnetic field, and the Hall term allows the Z-pinch system to be taken away from the region in parameter space where ideal MHD is applicable to a regime where nonideal effects tend to govern stability. The problem is then treated numerically by following the linear development in time of an initial perturbation. The numerical results for linear growth rates as a function of axial sheared flow, an axial magnetic field, and the Hall term are reported

The equatorial E-region and its plasma instabilities: a tutorial

Directory of Open Access Journals (Sweden)

D. T. Farley

2009-04-01

Full Text Available In this short tutorial we first briefly review the basic physics of the E-region of the equatorial ionosphere, with emphasis on the strong electrojet current system that drives plasma instabilities and generates strong plasma waves that are easily detected by radars and rocket probes. We then discuss the instabilities themselves, both the theory and some examples of the observational data. These instabilities have now been studied for about half a century (!, beginning with the IGY, particularly at the Jicamarca Radio Observatory in Peru. The linear fluid theory of the important processes is now well understood, but there are still questions about some kinetic effects, not to mention the considerable amount of work to be done before we have a full quantitative understanding of the limiting nonlinear processes that determine the details of what we actually observe. As our observational techniques, especially the radar techniques, improve, we find some answers, but also more and more questions. One difficulty with studying natural phenomena, such as these instabilities, is that we cannot perform active cause-and-effect experiments; we are limited to the inputs and responses that nature provides. The one hope here is the steadily growing capability of numerical plasma simulations. If we can accurately simulate the relevant plasma physics, we can control the inputs and measure the responses in great detail. Unfortunately, the problem is inherently three-dimensional, and we still need somewhat more computer power than is currently available, although we have come a long way.

Primer on theory and operation of linear accelerators in radiation therapy

International Nuclear Information System (INIS)

Karzmark, C.J.; Morton, R.J.

1981-12-01

This primer is part of an educational package that also includes a series of 3 videotapes entitled Theory and Operation of Linear Accelerators in Radiation Therapy, Parts I, II, and III. This publication provides an overview of the components of the linear accelerator and how they function and interrelate. The auxiliary systems necessary to maintain the operation of the linear accelerator are also described

Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids.

Science.gov (United States)

Merli, Marcello; Pavese, Alessandro

2018-03-01

The critical points analysis of electron density, i.e. ρ(x), from ab initio calculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points, i.e. such that ∇ρ(x c ) = 0 and λ 1 , λ 2 , λ 3 ≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) at x c ], towards degenerate critical points, i.e. ∇ρ(x c ) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood of x c and allows one to rationalize the occurrence of instability in terms of electron-density topology and Gibbs energy. The phase/state transitions that TiO 2 (rutile structure), MgO (periclase structure) and Al 2 O 3 (corundum structure) undergo because of pressure and/or temperature are here discussed. An agreement of 3-5% is observed between the theoretical model and experimental pressure/temperature of transformation.

Energy of linear quasineutral electrostatic drift waves

International Nuclear Information System (INIS)

Pfirsch, D.; Correa-Restrepo, D.

1993-01-01

Certain kinds of nonlinear instabilities are related to the existence of negative-energy perturbations. In this paper, an exact energy expression for linear quasineutral electrostatic perturbations is derived within the framework of dissipationless multifluid theory that is valid for any geometry. Taking the mass formally as a tensor with, in general, different masses parallel and perpendicular to an ambient magnetic field allows one to treat in a convenient way different approximations such as the full dynamics and restriction to parallel dynamics or the completely adiabatic case. Application to slab configurations yields the result that the adiabatic approximation does not allow negative energy for perturbations which are perfectly localized at a mode resonant surface, whereas inclusion of the parallel dynamics does. This is in agreement with a recent numerical study of drift-wave turbulence within the framework of collisional two-fluid theory by B. Scott [Phys. Rev. Lett. 65, 3289 (1990); Phys. Fluids B 4, 2468 (1992)]. A dissipationless theory can be formulated in terms of a Lagrangian, from which the energy is immediately obtained. We start with the nonlinear theory. The theory is formulated via a Lagrangian which is written in terms of displacement vectors ξ ν (x,t) such that all constraints are taken into account. The nonlinear energy is obtained from the Lagrangian by standard methods. The procedure used is the same as that developed in a forthcoming paper by Pfirsch and Sudan [Phys. Fluids B (to be published)] for ideal nonlinear magnetohydrodynamics theory. From the exact Lagrangian one obtains the Lagrangian of the linearized theory by simple expansion to second order in ξ ν . This Lagrangian then yields the energy of the linearized theory

Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

Science.gov (United States)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

2017-01-01

The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

Science.gov (United States)

Rogers, Barrett N.; Zhu, Ben; Francisquez, Manaure

2018-05-01

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on k∥=0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k⊥ρi˜1 and vanish in the long wavelength k⊥→0 limit. This work also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ=√{β/[2 (1 +β)] }Cs/|Lp| with Cs2=p0/ρ0 for k⊥→0 and is universally unstable for 1 /Lp≠0 . We show that the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p0+B02/(8 π)=constant , which renders the assumption B0'=0 inconsistent if p0'≠0 .

Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory

International Nuclear Information System (INIS)

Soda, Jiro.

1989-08-01

On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)

S- and T-self-dualities in dilatonic f(R) theories

Energy Technology Data Exchange (ETDEWEB)

Rador, Tonguc [Bogazici University, Department of Physics, Istanbul (Turkey); Izmir Institute of Technology, Department of Physics, Izmir (Turkey)

2017-12-15

We search for theories, in general spacetime dimensions, that would incorporate a dilaton and higher powers of the scalar Ricci curvature such that they have exact S- or T-self-dualities. The theories we find are free of Ostrogradsky instabilities. We also show that within the framework we are confining ourselves, a theory of the form mentioned above cannot have both T- and S-dualities except for the case where the action is linear in the scalar curvature. (orig.)

A non-linear theory of strong interactions

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs

CHF Enhancement by Surface Patterning based on Hydrodynamic Instability Model

Energy Technology Data Exchange (ETDEWEB)

Seo, Han; Bang, In Cheol [UNIST, Ulsan (Korea, Republic of)

2015-05-15

If the power density of a device exceeds the CHF point, bubbles and vapor films will be covered on the whole heater surface. Because vapor films have much lower heat transfer capabilities compared to the liquid layer, the temperature of the heater surface will increase rapidly, and the device could be damaged due to the heater burnout. Therefore, the prediction and the enhancement of the CHF are essential to maximizing the efficient heat removal region. Numerous studies have been conducted to describe the CHF phenomenon, such as hydrodynamic instability theory, macrolayer dryout theory, hot/dry spot theory, and bubble interaction theory. The hydrodynamic instability model, proposed by Zuber, is the predominant CHF model that Helmholtz instability attributed to the CHF. Zuber assumed that the Rayleigh-Taylor (RT) instability wavelength is related to the Helmholtz wavelength. Lienhard and Dhir proposed a CHF model that Helmholtz instability wavelength is equal to the most dangerous RT wavelength. In addition, they showed the heater size effect using various heater surfaces. Lu et al. proposed a modified hydrodynamic theory that the Helmholtz instability was assumed to be the heater size and the area of the vapor column was used as a fitting factor. The modified hydrodynamic theories were based on the change of Helmholtz wavelength related to the RT instability wavelength. In the present study, the change of the RT instability wavelength, based on the heater surface modification, was conducted to show the CHF enhancement based on the heater surface patterning in a plate pool boiling. Sapphire glass was used as a base heater substrate, and the Pt film was used as a heating source. The patterning surface was based on the change of RT instability wavelength. In the present work the study of the CHF was conducted using bare Pt and patterned heating surfaces.

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Directory of Open Access Journals (Sweden)

Ali Koochi

Full Text Available It is well recognized that size dependency of materials characteristics, i.e. size-effect, often plays a significant role in the performance of nano-structures. Herein, strain gradient continuum theory is employed to investigate the size dependent pull-in instability of beam-type nano-electromechanical systems (NEMS. Two most common types of NEMS i.e. nano-bridge and nano-cantilever are considered. Effects of electrostatic field and dispersion forces i.e. Casimir and van der Waals (vdW attractions have been considered in the nonlinear governing equations of the systems. Two different solution methods including numerical and Rayleigh-Ritz have been employed to solve the constitutive differential equations of the system. Effect of dispersion forces, the size dependency and the importance of coupling between them on the instability performance are discussed.

Microbunch Instability Theory and Simulations

Energy Technology Data Exchange (ETDEWEB)

Stupakov, G.

2005-01-26

Over the last years there have been several reports of quasiperiodic bursts of coherent synchrotron radiation (CSR) in electron rings in the microwave and far-infrared range. The observations were made on synchrotron radiation light sources which include the Synchrotron Ultraviolet Radiation Facility SURF II [1], the VUV ring at the National Synchrotron Light Source at BNL [2, 3], second generation light sources MAX-I [4], BESSY II [5], and ALS [6]. General features of those observations can be summarized as follows. Above a threshold current, there is a strongly increased radiation of the beam in the range of wavelengths shorter than the bunch length, {lambda} < {sigma}{sub 2}. At large currents, this radiation is observed as a sequence of random bursts. In the bursting regime, intensity of the radiation scales approximately as square of the number of particles in the bunch, indicating a coherent nature of the phenomenon. It is generally accepted that the source of this radiation is related to the microbunching of the beam arising from development of a microwave instability caused by the coherent synchrotron radiation of the beam. A relativistic electron beam moving in a circular orbit in free space can radiate coherently if the wavelength of the synchrotron radiation exceeds the length of the bunch. In accelerators coherent radiation of the bunch is usually suppressed by the shielding effect of the conducting walls of the vacuum chamber [7-9], which gives an exponential cutoff of wavelengths greater than a certain threshold. However, an initial density fluctuation with a characteristic length much shorter than the shielding threshold would radiate coherently. If the radiation reaction force is such that it results in the growth of the initial fluctuation one can expect an instability that leads to micro-bunching of the beam and an increased coherent radiation at short wavelengths. A possibility of CSR instability was pointed out in Refs. [10, 11].

Accurate electrostatic and van der Waals pull-in prediction for fully clamped nano/micro-beams using linear universal graphs of pull-in instability

Science.gov (United States)

Tahani, Masoud; Askari, Amir R.

2014-09-01

In spite of the fact that pull-in instability of electrically actuated nano/micro-beams has been investigated by many researchers to date, no explicit formula has been presented yet which can predict pull-in voltage based on a geometrically non-linear and distributed parameter model. The objective of present paper is to introduce a simple and accurate formula to predict this value for a fully clamped electrostatically actuated nano/micro-beam. To this end, a non-linear Euler-Bernoulli beam model is employed, which accounts for the axial residual stress, geometric non-linearity of mid-plane stretching, distributed electrostatic force and the van der Waals (vdW) attraction. The non-linear boundary value governing equation of equilibrium is non-dimensionalized and solved iteratively through single-term Galerkin based reduced order model (ROM). The solutions are validated thorough direct comparison with experimental and other existing results reported in previous studies. Pull-in instability under electrical and vdW loads are also investigated using universal graphs. Based on the results of these graphs, non-dimensional pull-in and vdW parameters, which are defined in the text, vary linearly versus the other dimensionless parameters of the problem. Using this fact, some linear equations are presented to predict pull-in voltage, the maximum allowable length, the so-called detachment length, and the minimum allowable gap for a nano/micro-system. These linear equations are also reduced to a couple of universal pull-in formulas for systems with small initial gap. The accuracy of the universal pull-in formulas are also validated by comparing its results with available experimental and some previous geometric linear and closed-form findings published in the literature.

Effect of accelerating gap geometry on the beam breakup instability in linear induction accelerators

International Nuclear Information System (INIS)

Miller, R.B.; Marder, B.M.; Coleman, P.D.; Clark, R.E.

1988-01-01

The electron beam in a linear induction accelerator is generally susceptible to growth of the transverse beam breakup instability. In this paper we analyze a new technique for reducing the transverse coupling between the beam and the accelerating cavities, thereby reducing beam breakup growth. The basic idea is that the most worrisome cavity modes can be cutoff by a short section of coaxial transmission line inserted between the cavity structure and the accelerating gap region. We have used the three-dimensional simulation code SOS to analyze this problem. In brief, we find that the technique works, provided that the lowest TE mode cutoff frequency in the coaxial line is greater than the frequency of the most worrisome TM mode of the accelerating cavity

Luminosity Loss due to Beam Distortion and the Beam-Beam Instability

CERN Document Server

Wu, Juhao; Raubenheimer, Tor O; Seryi, Andrei; Sramek, Christopher K

2005-01-01

In a linear collider, sources of emittance dilution such as transverse wakefields or dispersive errors will couple the vertical phase space to the longitudinal position within the beam (the so-called ‘banana effect'). When the Intersection Point (IP) disruption parameter is large, these beam distortions will be amplified by a single bunch kink instability which will lead to luminosity loss. We study this phenomena both analytically using linear theory and via numerical simulation. In particular, we examine the dependence of the luminosity loss on the wavelength of the beam distortions and the disruption parameter. This analysis may prove useful when optimizing the vertical disruption parameter for luminosity operation with given beam distortions.

Comparison of Linear Induction Motor Theories for the LIMRV and TLRV Motors

Science.gov (United States)

1978-01-01

The Oberretl, Yamamura, and Mosebach theories of the linear induction motor are described and also applied to predict performance characteristics of the TLRV & LIMRV linear induction motors. The effect of finite motor width and length on performance ...

Asymptotic solutions and spectral theory of linear wave equations

International Nuclear Information System (INIS)

Adam, J.A.

1982-01-01

This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

Theory of elementary excitations in unstable Bose-Einstein condensates and the instability of sonic horizons

International Nuclear Information System (INIS)

Leonhardt, U.; Kiss, T.; Oehberg, P.

2003-01-01

Like classical fluids, quantum gases may suffer from hydrodynamic instabilities. Our paper develops a quantum version of the classical stability analysis in fluids, the Bogoliubov theory of elementary excitations in unstable Bose-Einstein condensates. In unstable condensates the excitation modes have complex frequencies. We derive the normalization conditions for unstable modes such that they can serve in a mode decomposition of the noncondensed component. Furthermore, we develop approximative techniques to determine the spectrum and the mode functions. Finally, we apply our theory to sonic horizons - sonic black and white holes. For sonic white holes the spectrum of unstable modes turns out to be intrinsically discrete, whereas black holes may be stable

Stability of non-linear constitutive formulations for viscoelastic fluids

CERN Document Server

Siginer, Dennis A

2014-01-01

Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.

New macroscopic theory of anamalous diffusion induced by the dissipative trapped-ion instability

International Nuclear Information System (INIS)

Wimmel, H.K.

1975-03-01

For an axisymmetric toroidal plasma of the TOKAMAK type a new set of dissipative trapped-fluid equations is established. In addition to E vector x B vector drifts and collisions of the trapped particles, these equations take full account of the effect of Esub(//) (of the trapped ion modes) on free and trapped particles, and of the effect of grad delta 0 (delta 0 = equilibrium fraction of trapped particles). From the new equations the linear-mode properties of the dissipative trapped-ion instability and the anomalous diffusion flux of the trapped particles are derived. (orig.) [de

Effect of plasma instability on F region photoelectron distributions

International Nuclear Information System (INIS)

Bloomberg, H.W.

1975-01-01

Ionospheric suprathermal photoelectrons have relatively large cross sections for selected energies. In particular, electrons with energies of about 2.5 eV strongly excite nitrogen vibrational modes, while metastable states of oxygen are excited at about 5 eV. Thus an energy distribution based on chemical kinetic considerations give rise to a maximum at around 4 eV in the F region below 250 km. However, rocket experiments have shown that the expected peaks in the flux spectrum are relatively weak. This discrepancy is explained by the development of a linear instability leading to a wave-particle interaction. The linear mode is driven by the photoelectrons near the 4-eV maximum in the presence of a magnetic field. The effect is shown to be ineffective at sufficiently low altitudes, where collisionless theory fails. (auth)

Effect of plasma instability on F region photoelectron distributions

International Nuclear Information System (INIS)

Bloomberg, H.W.

1975-01-01

Ionospheric suprathermal photoelectrons have relatively large cross sections for selected energies. In particular, electrons with energies of about 2.5 eV strongly excite nitrogen vibrational modes, while metastable states of oxygen are excited at about 5 eV. Thus an energy distribution based on chemical kinetic considerations gives rise to a maximum at around 4 eV in the F region below 250 km. However, rocket experiments have shown that the expected peaks in the flux spectrum are relatively weak. This discrepancy is explained by the development of a linear instability leading to a wave-particle interaction. the linear mode is driven by the photoelectrons near the 4-eV maximum in the presence of a magnetic field. The effect is shown to be ineffective at sufficiently low altitudes, where collisionless theory fails

Present status of mirror stability theory

International Nuclear Information System (INIS)

Baldwin, D.E.; Berk, H.L.; Byers, J.A.

1976-01-01

A status report of microinstability as it applies to 2XIIB and MX theory for mirror machines is presented. It is shown that quasilinear computations reproduce many of the parameters observed in the 2XIIB experiment. In regard to large mirror machines, there are presented detailed calculations of the linear theory of the drift cyclotron loss-cone mode, with inhomogeneous geometry and nonlinear diffusive effects. Further, the stability of a mirror machine to the Alfven ion-cyclotron instability is assessed, and the Baldwin-Callen diffusion is estimated for a spatially varying plasma

The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.; Morrison, P.J.; Texas Univ., Austin

1990-02-01

A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any kind of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated - which need not be the same for all particle species in a plasma - are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. (orig.)

The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.; Morrison, P.J.

1990-02-01

A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any king of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated --- which need not be the same for all particle species in a plasma --- are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. 11 refs

Nonlinear theory of the free-electron laser

International Nuclear Information System (INIS)

Chian, A.C.-L.; Padua Brito Serbeto, A. de.

1984-01-01

A theory of Raman free-electron laser using a circularly polarized electromagnetic pump is investigated. Coupled wave equations that describe both linear and nonlinear evolution of stimulated Raman scattering are derived. The dispersion relation and the growth rate for the parametric instability are obtained. Nonlinear processes that may lead to saturation of the free-electron laser are discussed. (Author) [pt

Linear kinetic theory and particle transport in stochastic mixtures

Energy Technology Data Exchange (ETDEWEB)

Pomraning, G.C. [Univ. of California, Los Angeles, CA (United States)

1995-12-31

We consider the formulation of linear transport and kinetic theory describing energy and particle flow in a random mixture of two or more immiscible materials. Following an introduction, we summarize early and fundamental work in this area, and we conclude with a brief discussion of recent results.

Modification of linear response theory for mean-field approximations

NARCIS (Netherlands)

Hütter, M.; Öttinger, H.C.

1996-01-01

In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the

Linear response theory an analytic-algebraic approach

CERN Document Server

De Nittis, Giuseppe

2017-01-01

This book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3–5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about...

Adiabatic instability in coupled dark energy/dark matter models

International Nuclear Information System (INIS)

Bean, Rachel; Flanagan, Eanna E.; Trodden, Mark

2008-01-01

We consider theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the Universe. Such theories can possess an adiabatic regime in which the quintessence field always sits at the minimum of its effective potential, which is set by the local dark matter density. We show that if the coupling strength is much larger than gravitational, then the adiabatic regime is always subject to an instability. The instability, which can also be thought of as a type of Jeans instability, is characterized by a negative sound speed squared of an effective coupled dark matter/dark energy fluid, and results in the exponential growth of small scale modes. We discuss the role of the instability in specific coupled cold dark matter and mass varying neutrino models of dark energy and clarify for these theories the regimes in which the instability can be evaded due to nonadiabaticity or weak coupling.

Spectral theory of linear operators and spectral systems in Banach algebras

CERN Document Server

Müller, Vladimir

2003-01-01

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...

On coupled development of MHD instabilities of Rayleigh-Taylor and Kelvin-Helmholtz types in nonuniform gas-plasmas flows

International Nuclear Information System (INIS)

Likhachev, A P; Medin, S A

2010-01-01

The simultaneous development of the MHD instabilities of Raylegh-Taylor and Kelvin-Helmholtz types at the interface between high-conducting plasmoid and surrounding non- or low-conducting gas is considered. The linear stage of the RTI development is studied analytically for incompressible and compressible fluids. The nonlinear stage of the individual development of the RTI and the coupled development of both instabilities has been investigated numerically. The time-dependent two-dimensional numerical model based on the solution of the Euler gasdynamic equations with body momentum and energy sources of MHD origin has been developed and used in calculations. A disturbance introducing in the background flow has been periodic with varied assignment type and wave length. Fundamental difference between the results of linear and nonlinear analysis has been revealed. In particular, the increment of the RTI development at nonlinear stage is one-two order of magnitude less than that predicted by linear theory and rather weakly depends on initial disturbance mode. In linear analysis the coupled development of the RTI and the KHI is determined by simple summing of the two effects in the expression of wave increment, whereas in nonlinear case the mutual influence of the instabilities leads to essential alterations in their development, main of which is the intensive 'layer-by-layer' destruction of the plasmoid surface.

Theory of linear operators in Hilbert space

CERN Document Server

Akhiezer, N I

1993-01-01

This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

The theory of stability, bistability, and instability in three-mode class-A lasers

International Nuclear Information System (INIS)

Jahanpanah, J; Rahdar, A A

2014-01-01

Instability is an inevitable and common problem in all different kinds of lasers when they are oscillating in both single-and multi-mode states. Here, the stability conditions are investigated for a three-mode class-A laser. A set of linear equations is derived for the stable oscillation of the cavity central mode together with its left and right adjacent longitudinal modes. The coefficient determinant of stability equations is Hermitian and equal to zero for the roots of two diagonal arrays. In other words, the novelty of our work is to expand the stability coefficient determinant in terms of main diagonal arrays rather than for one row or one column. These diagonal roots lead to two lower and upper boundary curves in the form of a bifurcation. The lower boundary curve mimics the single-mode laser and delimits the instability region (with no above-threshold oscillating mode) from the bistability region (with two above-threshold oscillating modes). The upper boundary curve mimics the two-mode laser and delimits the bistability region from the stability region, in which all three-longitudinal modes are simultaneously oscillating in the above-threshold state. (paper)

Thermal instability in a stratified plasma

International Nuclear Information System (INIS)

Hermanns, D.F.M.; Priest, E.R.

1989-01-01

The thermal instability mechansism has been studied in connection to observed coronal features, like, e.g. prominences or cool cores in loops. Although these features show a lot of structure, most studies concern the thermal instability in an uniform medium. In this paper, we investigate the thermal instability and the interaction between thermal modes and the slow magneto-acoustic subspectrum for a stratified plasma slab. We fomulate the relevant system of equations and give some straightforward properties of the linear spectrum of a non-uniform plasma slab, i.e. the existence of continuous parts in the spectrum. We present a numerical scheme with which we can investigate the linear spectrum for equilibrium states with stratification. The slow and thermal subspectra of a crude coronal model are given as a preliminary result. (author). 6 refs.; 1 fig

Localized multi-scale energy and vorticity analysis. II. Finite-amplitude instability theory and validation

Science.gov (United States)

San Liang, X.; Robinson, Allan R.

2007-12-01

A novel localized finite-amplitude hydrodynamic stability analysis is established in a unified treatment for the study of real oceanic and atmospheric processes, which are in general highly nonlinear, and intermittent in space and time. We first re-state the classical definition using the multi-scale energy and vorticity analysis (MS-EVA) developed in Liang and Robinson [Liang, X.S., Robinson, A.R., 2005. Localized multiscale energy and vorticity analysis. I. Fundamentals. Dyn. Atmos. Oceans 38, 195-230], and then manipulate certain global operators to achieve the temporal and spatial localization. The key of the spatial localization is transfer-transport separation, which is made precise with the concept of perfect transfer, while relaxation of marginalization leads to the localization of time. In doing so the information of transfer lost in the averages is retrieved and an easy-to-use instability metric is obtained. The resulting metric is field-like (Eulerian), conceptually generalizing the classical formalism, a bulk notion over the whole system. In this framework, an instability has a structure, which is of particular use for open flow processes. We check the structure of baroclinic instability with the benchmark Eady model solution, and the Iceland-Faeroe Frontal (IFF) intrusion, a highly localized and nonlinear process occurring frequently in the region between Iceland and Faeroe Islands. A clear isolated baroclinic instability is identified around the intrusion, which is further found to be characterized by the transition from a spatially growing mode to a temporally growing mode. We also check the consistency of the MS-EVA dynamics with the barotropic Kuo model. An observation is that a local perturbation burst does not necessarily imply an instability: the perturbation energy could be transported from other processes occurring elsewhere. We find that our analysis yields a Kuo theorem-consistent mean-eddy interaction, which is not seen in a conventional

Turnpike theory of continuous-time linear optimal control problems

CERN Document Server

Zaslavski, Alexander J

2015-01-01

Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems.  The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands.  Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...

Current filamentation caused by the electrochemical instability in a fully ionized plasma

International Nuclear Information System (INIS)

Haines, M.G.; Marsh, F.

1983-01-01

This chapter is primarily concerned with the non-linear development of electrothermal instabilities in a fully ionized plasma discharge in which the current is predominantly carried parallel to an applied magnetic field, as in the Tokamak configuration. Discusses instabilities with wave-number K perpendicular to magnetic field B and current J; the non-linear steady state; amplitude of the filaments; and runaway electrons and ion acoustic instabilities. Concludes that the steady non-linear amplitude of the fully developed instability shows a spiky filamentary structure with the possibility of the generation of runaway electrons and ion acoustic turbulence in the current maxima. Finds that the addition of bremsstrahlung radiation loss enhances the instability, reducing the critical ratio of T /SUB e/ to T /SUB i/ for its onset, and yielding a maximum ion temperature attainable by Joule heating and equipartition

Experimental and numerical analysis of behavior of electromagnetic annular linear induction pump

International Nuclear Information System (INIS)

Goldsteins, Linards

2015-01-01

The research explores the issue of magnetohydrodynamic (MHD) instability in electromagnetic induction pumps with focus on the regimes of high slip Reynolds magnetic number (Rm s ) in Annular Linear Induction Pumps (ALIP) operating with liquid sodium. The context of the thesis is French GEN IV Sodium Fast Reactor research and development program for ASTRID in a framework of which the use of high discharge ALIP in the secondary cooling loops is being studied. CEA has designed, realized and will exploit PEMDYN facility, able to represent MHD instability in high discharge ALIP. In the thesis stability of an ideal ALIP is elaborated theoretically using linear stability analysis. Analysis revealed that strong amplification of perturbation is expected after convective stability threshold is reached. Theory is supported with numerical results and experiments reported in literature. Stable operation and stabilization technique operating with two frequencies in case of an ideal ALIP is discussed and necessary conditions derived. Detailed numerical models of flat linear induction pump (FLIP) taking into account effects of a real pump are developed. New technique of magnetic field measurements has been introduced and experimental results demonstrate a qualitative agreement with numerical models capturing all principal phenomena such as oscillation of magnetic field and perturbed velocity profiles. These results give significantly more profound insight in the phenomenon of MHD instability and can be used as a reference in further studies. (author) [fr

Linear conversion theory on the second harmonic emission from a plasma filament

International Nuclear Information System (INIS)

Tan Weihan; Gu Min

1989-01-01

The linear conversion theory of laser produced plasma filaments is studied. By calculations for the energy flux of the second harmonic emission on the basis of the planar wave-plasma interaction model, it has been found that there exists no 2ω 0 harmonic emission in the direction perpendicular to the incident laser, in contradiction with the experiments. A linear conversion theory is proposed on the second harmonic emission from a plasma filament and discovered the intense 2ω 0 harmonic emission in the direction perpendicular to the incident laser, which is in agreement with the experiments. (author)

Janus field theories from non-linear BF theories for multiple M2-branes

International Nuclear Information System (INIS)

Ryang, Shijong

2009-01-01

We integrate the nonpropagating B μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M IJK in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M IJK as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.

Two-dimensional simulation of the hydromagnetic Rayleigh-Taylor instability in an imploding foil plasma

International Nuclear Information System (INIS)

Roderick, N.F.; Hussey, T.W.; Faehl, R.J.; Boyd, R.W.

1978-01-01

Two-dimensional (r-z) magnetohydrodynamic simulations of the electromagnetic implosion of metallic foil plasmas show, for certain initial configurations, a tendency to develop large-amplitude perturbations characteristic of the hydromagnetic Rayleigh-Taylor instability. These perturbations develop at the plasma magnetic field interface for plasma configurations where the density gradient scale length, the characteristic dimension for the instability, is short. The effects on the plasma dynamics of the implosion will be discussed for several initial foil configurations. In general, the growth rates and linear mode structure are found to be influenced by the plasma shell thickness and density gradient scale length, in agreement with theory. The most destructive modes are found to be those with wavelengths of the order of the plasma shell thickness

Non-gaussian inflationary shapes in G3 theories beyond Horndeski

International Nuclear Information System (INIS)

Fasiello, Matteo; Renaux-Petel, Sébastien

2014-01-01

We consider the possible signatures of a recently introduced class of healthy theories beyond Horndeski models on higher-order correlators of the inflationary curvature fluctuation. Despite the apparent large number and complexity of the cubic interactions, we show that the leading-order bispectrum generated by the Generalized Horndeski (also called G 3 ) interactions can be reduced to a linear combination of two well known k-inflationary shapes. We conjecture that said behavior is not an accident of the cubic order but a consequence dictated by the requirements on the absence of Ostrogradski instability, the general covariance and the linear dispersion relation in these theories

Nonlinear Mirror and Weibel modes: peculiarities of quasi-linear dynamics

Directory of Open Access Journals (Sweden)

O. A. Pokhotelov

2010-12-01

Full Text Available A theory for nonlinear evolution of the mirror modes near the instability threshold is developed. It is shown that during initial stage the major instability saturation is provided by the flattening of the velocity distribution function in the vicinity of small parallel ion velocities. The relaxation scenario in this case is accompanied by rapid attenuation of resonant particle interaction which is replaced by a weaker adiabatic interaction with mirror modes. The saturated plasma state can be considered as a magnetic counterpart to electrostatic BGK modes. After quasi-linear saturation a further nonlinear scenario is controlled by the mode coupling effects and nonlinear variation of the ion Larmor radius. Our analytical model is verified by relevant numerical simulations. Test particle and PIC simulations indeed show that it is a modification of distribution function at small parallel velocities that results in fading away of free energy driving the mirror mode. The similarity with resonant Weibel instability is discussed.

Linearized propulsion theory of flapping airfoils revisited

Science.gov (United States)

Fernandez-Feria, Ramon

2016-11-01

A vortical impulse theory is used to compute the thrust of a plunging and pitching airfoil in forward flight within the framework of linear potential flow theory. The result is significantly different from the classical one of Garrick that considered the leading-edge suction and the projection in the flight direction of the pressure force. By taking into account the complete vorticity distribution on the airfoil and the wake the mean thrust coefficient contains a new term that generalizes the leading-edge suction term and depends on Theodorsen function C (k) and on a new complex function C1 (k) of the reduced frequency k. The main qualitative difference with Garrick's theory is that the propulsive efficiency tends to zero as the reduced frequency increases to infinity (as 1 / k), in contrast to Garrick's efficiency that tends to a constant (1 / 2). Consequently, for pure pitching and combined pitching and plunging motions, the maximum of the propulsive efficiency is not reached as k -> ∞ like in Garrick's theory, but at a finite value of the reduced frequency that depends on the remaining non-dimensional parameters. The present analytical results are in good agreement with experimental data and numerical results for small amplitude oscillations. Supported by the Ministerio de Economia y Competitividad of Spain Grant No. DPI2013-40479-P.

Symmetric linear systems - An application of algebraic systems theory

Science.gov (United States)

Hazewinkel, M.; Martin, C.

1983-01-01

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

Linear response theory of activated surface diffusion with interacting adsorbates

Energy Technology Data Exchange (ETDEWEB)

Marti' nez-Casado, R. [Department of Chemistry, Imperial College London, South Kensington, London SW7 2AZ (United Kingdom); Sanz, A.S.; Vega, J.L. [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); Rojas-Lorenzo, G. [Instituto Superior de Tecnologi' as y Ciencias Aplicadas, Ave. Salvador Allende, esq. Luaces, 10400 La Habana (Cuba); Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain); Miret-Artes, S., E-mail: s.miret@imaff.cfmac.csic.es [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain)

2010-05-12

Graphical abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed. - Abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed.

Evaporative and Convective Instabilities for the Evaporation of a Binary Mixture in a Bilayer System

Science.gov (United States)

Guo, Weidong; Narayanan, Ranga

2006-11-01

Evaporative convection in binary mixtures arises in a variety of industrial processes, such as drying of paint and coating technology. There have been theories devoted to this problem either by assuming a passive vapor layer or by isolating the vapor fluid dynamics. Previous work on evaporative and convective instabilities in a single component bilayer system suggests that active vapor layers play a major role in determining the instability of the interface. We have investigated the evaporation convection in binary mixtures taking into account the fluid dynamics of both phases. The liquid mixture and its vapor are assumed to be confined between two horizontal plates with a base state of zero evaporation but with linear vertical temperature profile. When the vertical temperature gradient reaches a critical value, the evaporative instability, Rayleigh and Marangoni convection set in. The effects of vapor and liquid depth, various wave numbers and initial composition of the mixture on the evaporative and convective instability are determined. The physics of the instability are explained and detailed comparison is made between the Rayleigh, Marangoni and evaporative convection in pure component and those in binary mixtures.

Experimental investigation of a coherent flute instability using a heavy ion beam probe

International Nuclear Information System (INIS)

Glowienka, J.C.; Jennings, W.C.; Hickok, R.L.

1988-01-01

A coherent, low-frequency instability found in a cylindrical, hollow cathode arc plasma has been investigated by using a heavy ion beam probe (HIBP). The energy density of the plasma was high enough to render it inaccessible to Langmuir probes, but the HIBP was able to provide measurements throughout the plasma cross section. The data clearly show that azimuthal symmetry does not exist. Radial profiles of steady-state density and space potential and of simultaneous n, phi amplitude and phase were obtained to allow detailed comparison between theory and experiment. Predictions from a cylindrically symmetric, small-perturbation theoretical model provide reasonably conclusive identification of the instability as a Kelvin--Helmholtz flute driven by and localized in a region of fluid shear. The most serious discrepancy was with regard to the oscillation frequency, which was consistently predicted to be three to four times lower than that observed experimentally. The reason for the discrepancy is not understood, but it is probably related to inadequacies in the theory caused by assumptions of azimuthal symmetry and of small linear perturbations

The large density electron beam-plasma Buneman instability

International Nuclear Information System (INIS)

Mantei, T.D.; Doveil, F.; Gresillon, D.

1976-01-01

The threshold conditions and growth rate of the Buneman (electron beam-stationary ion) instability are calculated with kinetic theory, including a stationary electronic population. A criteria on the wave energy sign is used to separate the Buneman hydrodynamic instability from the ion-acoustic kinetic instability. The stationary electron population raises the instability threshold and, for large beam velocities yields a maximum growth rate oblique to the beam. (author)

Ponderomotive force effects on temperature-gradient-driven instabilities

International Nuclear Information System (INIS)

Sundaram, A.K.; Hershkowitz, N.

1992-01-01

The modification of temperature-gradient-driven instabilities due to the presence of nonuniform radio-frequency fields near the ion cyclotron frequency is investigated in the linear regime. Employing the fluid theory, it is shown that the induced field line compression caused by ion cyclotron range of frequencies (ICRF) fields makes the net parallel compressibility positive, and thus provides a stabilizing influence on the ion-temperature-gradient-driven mode for an appropriately tailored profile of radio-frequency (rf) pressure. Concomitantly, the radial ponderomotive force generates an additional contribution via coupling between the perturbed fluid motion and the equilibrium ponderomotive force and this effect plays the role of dissipation to enhance or decrease the growth of temperature-gradient-driven modes depending upon the sign of rf pressure gradients. For decreased growth of temperature-gradient-driven instabilities, the plasma density gradients and rf pressure gradients must have opposite signs while enhancement in growth arises when both gradients have the same sign. Finally, the kinetic effects associated with these modes are briefly discussed

Modes of storage ring coherent instabilities

Energy Technology Data Exchange (ETDEWEB)

Wang, J.M.

1986-12-01

Longitudinal impedance in a beam and various modes of longitudinal coherent instabilities are discussed. The coasting beam coherent instability, microwave instability, and single-bunch longitudinal coherent instabilities are considered. The Vlasov equation is formulated, and a method of solving it is developed. The synchrotron modes are treated, which take the possible bunch shape distortion fully into consideration. A method of treating the synchrotron mode coupling in the case of a small bunch is discussed which takes advantage of the fact that only a few of the synchrotron modes can contribute in such a case. The effect of many bunches on the coherent motion of the beam and the longitudinal symmetric coupled bunch modes are discussed. The transverse impedance is then introduced, and the transverse coasting beam instability is discussed. Various bunched beam instabilities are discussed, including both single bunch instabilities and coupled bunch instabilities. The Vlasov equation for transverse as well as longitudinal motion of particles is introduced as well as a method of solving it within a linear approximation. Head-tail modes and short bunch instabilities and strong coupling instabilities in the long bunch case are covered. (LEW)

Modes of storage ring coherent instabilities

International Nuclear Information System (INIS)

Wang, J.M.

1986-12-01

Longitudinal impedance in a beam and various modes of longitudinal coherent instabilities are discussed. The coasting beam coherent instability, microwave instability, and single-bunch longitudinal coherent instabilities are considered. The Vlasov equation is formulated, and a method of solving it is developed. The synchrotron modes are treated, which take the possible bunch shape distortion fully into consideration. A method of treating the synchrotron mode coupling in the case of a small bunch is discussed which takes advantage of the fact that only a few of the synchrotron modes can contribute in such a case. The effect of many bunches on the coherent motion of the beam and the longitudinal symmetric coupled bunch modes are discussed. The transverse impedance is then introduced, and the transverse coasting beam instability is discussed. Various bunched beam instabilities are discussed, including both single bunch instabilities and coupled bunch instabilities. The Vlasov equation for transverse as well as longitudinal motion of particles is introduced as well as a method of solving it within a linear approximation. Head-tail modes and short bunch instabilities and strong coupling instabilities in the long bunch case are covered

Linear-response theory of Coulomb drag in coupled electron systems

DEFF Research Database (Denmark)

Flensberg, Karsten; Hu, Ben Yu-Kuang; Jauho, Antti-Pekka

1995-01-01

We report a fully microscopic theory for the transconductivity, or, equivalently, the momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear-response formalism and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which...

Excitonic bistabilities, instabilities and chaos in laser-pumped semiconductor

International Nuclear Information System (INIS)

Nguyen Ba An; Nguyen Trung Dan; Hoang Xuan Nguyen

1992-07-01

The Hurwitz criteria are used for a stability analysis of the steady state excitonic optical bistability curves in a semiconductor pumped by an external laser resonant with the exciton level. Besides the middle branch of the bistability curves which is unstable in the sense of the linear stability theory, we have found other domains of instability in the upper and lower branches of the steady state curves. Numerical results show that a possible route to chaos in the photon-exciton system is period-doubling self-oscillation process. The influence of the presence of free carriers that coexist with the excitons is also discussed. (author). 16 refs, 6 figs

Linear theory of equatorial spread F

International Nuclear Information System (INIS)

Hudson, M.K.; Kennel, C.F.

1975-01-01

A fluid dispersion relation for the drift and interchange (Rayleigh-Taylor) modes in a collisional plasma forms the basis for a linear theory of equatorial spread F. The collisional drift mode growth rate will exceed the growth rate of the Rayleigh-Taylor mode at short perpendicular wavelengths and density gradient scale lengths, and the drift mode can grow on top side as well as on bottom side density gradients. However, below the F peak, where spread F predominates, it is concluded that both the drift and the Rayleigh-Taylor modes contribute to the total spread F spectrum, the Rayleigh-Taylor mode dominating at long and the drift mode at short perpendicular wavelengths above the ion Larmor radius

Stochastic linear programming models, theory, and computation

CERN Document Server

Kall, Peter

2011-01-01

This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...

Linearly Polarized IR Spectroscopy Theory and Applications for Structural Analysis

CERN Document Server

Kolev, Tsonko

2011-01-01

A technique that is useful in the study of pharmaceutical products and biological molecules, polarization IR spectroscopy has undergone continuous development since it first emerged almost 100 years ago. Capturing the state of the science as it exists today, "Linearly Polarized IR Spectroscopy: Theory and Applications for Structural Analysis" demonstrates how the technique can be properly utilized to obtain important information about the structure and spectral properties of oriented compounds. The book starts with the theoretical basis of linear-dichroic infrared (IR-LD) spectroscop

Saturation of the ion transverse instability

International Nuclear Information System (INIS)

Heifets, S.

1997-01-01

Fast Ion Instability is studied in the nonlinear regime. It is shown that exponential growth of the linear regime is replaced in this case by the linear dependence on time. Numeric and analytical results are presented describing the beam profile and the beam spectrum in both regimes

Analysis of fluid structural instability in water

International Nuclear Information System (INIS)

Piccirillo, N.

1997-02-01

Recent flow testing of stainless steel hardware in a high pressure/high temperature water environment produced an apparent fluid-structural instability. The source of instability was investigated by studying textbook theory and by performing NASTRAN finite element analyses. The modal analyses identified the mode that was being excited, but the flutter instability analysis showed that the design is stable if minimal structural damping is present. Therefore, it was suspected that the test hardware was the root cause of the instability. Further testing confirmed this suspicion

Assessing Spontaneous Combustion Instability with Nonlinear Time Series Analysis

Science.gov (United States)

Eberhart, C. J.; Casiano, M. J.

2015-01-01

Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.

Potential Flow Model for Compressible Stratified Rayleigh-Taylor Instability

Science.gov (United States)

Rydquist, Grant; Reckinger, Scott; Owkes, Mark; Wieland, Scott

2017-11-01

The Rayleigh-Taylor Instability (RTI) is an instability that occurs when a heavy fluid lies on top of a lighter fluid in a gravitational field, or a gravity-like acceleration. It occurs in many fluid flows of a highly compressive nature. In this study potential flow analysis (PFA) is used to model the early stages of RTI growth for compressible fluids. In the localized region near the bubble tip, the effects of vorticity are negligible, so PFA is applicable, as opposed to later stages where the induced velocity due to vortices generated from the growth of the instability dominate the flow. The incompressible PFA is extended for compressibility effects by applying the growth rate and the associated perturbation spatial decay from compressible linear stability theory. The PFA model predicts theoretical values for a bubble terminal velocity for single-mode compressible RTI, dependent upon the Atwood (A) and Mach (M) numbers, which is a parameter that measures both the strength of the stratification and intrinsic compressibility. The theoretical bubble terminal velocities are compared against numerical simulations. The PFA model correctly predicts the M dependence at high A, but the model must be further extended to include additional physics to capture the behavior at low A. Undergraduate Scholars Program - Montana State University.

Diffusive instabilities in hyperbolic reaction-diffusion equations

Science.gov (United States)

Zemskov, Evgeny P.; Horsthemke, Werner

2016-03-01

We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.

Feedback stabilization of electrostatic reactive instabilities

International Nuclear Information System (INIS)

Richards, R.K.

1976-01-01

A general theory for the feedback stabilization of electrostatic reactive instabilities is developed which includes the effects of dissipation in the plasma and frequency dependence in the sensor-suppressor elements and in the external feedback circuit. This theory is compared to experiments involving particular reactive instability, an interchange mode, found in a magnetic mirror device; these results are found to be in good agreement with theory. One noteworthy result is that a frequency dependence in the overall gain and phase shift of the feedback loop can cause destabilization at large gain. Multimode feedback stabilization is studied using the spatial variation of two interchange modes to separate them such that each can be acted upon individually by the feedback system. The transfer function of the plasma is also examined. This analysis is used for mode identification and location of the pole positions. As an example of using feedback as a diagnostic tool, instability induced transport is studied. Here feedback is used to control the amplitude of fluctuations at saturation

Instabilities and prediction of the acoustic resonance of flows with wall injection; Instabilites et prevision de l'accrochage acoustique des ecoulements avec injection parietale

Energy Technology Data Exchange (ETDEWEB)

Avalon, G. [Office National d' Etudes et de Recherches Aerospatiales (ONERA), 91 - Palaiseau (France); Casalis, G. [Office National d' Etudes et de Recherches Aerospatiales (ONERA), 91 - Palaiseau (France)

1998-07-01

Aero-acoustic coupling that occurs inside solid propellant rocket engines can lead to a longitudinal acoustic mode resonance of the combustion chamber. This phenomenon, which can have various origins, in analyzed using the Vecla test facility and the theory of linear stability of flows. Different comparisons between the hot-wire measurements performed and the theory of stability confirm the presence of intrinsic instabilities for this type of flow. The instability allows to selectively amplify a given range of frequencies which depends on the injection velocity and on the conduit height. The results obtained seem to indicate that when this frequency range does not comprise the longitudinal acoustic mode or the first harmonics, the flow becomes turbulent downstream. (J.S.)

Mixed-Mode Oscillations in Complex-Plasma Instabilities

International Nuclear Information System (INIS)

Mikikian, Maxime; Cavarroc, Marjorie; Coueedel, Lenaiec; Tessier, Yves; Boufendi, Laiefa

2008-01-01

Instabilities in dusty plasmas are frequent phenomena. We show that some instabilities can be described by mixed-mode oscillations often encountered in chemical systems or neuronal dynamics and studied through dynamical system theories. The time evolution of these instabilities is studied through the change in the associated waveform. Frequency and interspike interval are analyzed and compared to results obtained in other scientific fields concerned by mixed-mode oscillations

Physics of Transitional Shear Flows Instability and Laminar–Turbulent Transition in Incompressible Near-Wall Shear Layers

CERN Document Server

Boiko, Andrey V; Grek, Genrih R; Kozlov, Victor V

2012-01-01

Starting from fundamentals of classical stability theory, an overview is given of the transition phenomena in subsonic, wall-bounded shear flows. At first, the consideration focuses on elementary small-amplitude velocity perturbations of laminar shear layers, i.e. instability waves, in the simplest canonical configurations of a plane channel flow and a flat-plate boundary layer. Then the linear stability problem is expanded to include the effects of pressure gradients, flow curvature, boundary-layer separation, wall compliance, etc. related to applications. Beyond the amplification of instability waves is the non-modal growth of local stationary and non-stationary shear flow perturbations which are discussed as well. The volume continues with the key aspect of the transition process, that is, receptivity of convectively unstable shear layers to external perturbations, summarizing main paths of the excitation of laminar flow disturbances. The remainder of the book addresses the instability phenomena found at l...

Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

International Nuclear Information System (INIS)

Zavaljevski, N.

1985-01-01

Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

Neutron star pulsations and instabilities

International Nuclear Information System (INIS)

Lindblom, L.

2001-01-01

Gravitational radiation (GR) drives an instability in certain modes of rotating stars. This instability is strong enough in the case of the r-modes to cause their amplitudes to grow on a timescale of tens of seconds in rapidly rotating neutron stars. GR emitted by these modes removes angular momentum from the star at a rate which would spin it down to a relatively small angular velocity within about one year, if the dimensionless amplitude of the mode grows to order unity. A pedagogical level discussion is given here on the mechanism of GR instability in rotating stars, on the relevant properties of the r-modes, and on our present understanding of the dissipation mechanisms that tend to suppress this instability in neutron stars. The astrophysical implications of this GR driven instability are discussed for young neutron stars, and for older systems such as low mass x-ray binaries. Recent work on the non-linear evolution of the r-modes is also presented. (author)

Electron beam instabilities in gyrotron beam tunnels

International Nuclear Information System (INIS)

Pedrozzi, M.; Alberti, S.; Hogge, J.P.; Tran, M.Q.; Tran, T.M.

1997-10-01

Electron beam instabilities occurring in a gyrotron electron beam can induce an energy spread which might significantly deteriorate the gyrotron efficiency. Three types of instabilities are considered to explain the important discrepancy found between the theoretical and experimental efficiency in the case of quasi-optical gyrotrons (QOG): the electron cyclotron maser instability, the Bernstein instability and the Langmuir instability. The low magnetic field gradient in drift tubes of QOG makes that the electron cyclotron maser instability can develop in the drift tube at very low electron beam currents. Experimental measurements show that with a proper choice of absorbing structures in the beam tunnel, this instability can be suppressed. At high beam currents, the electrostatic Bernstein instability can induce a significant energy spread at the entrance of the interaction region. The induced energy spread scales approximately linearly with the electron beam density and for QOG one observes that the beam density is significantly higher than the beam density of an equivalent cylindrical cavity gyrotron. (author) figs., tabs., refs

Helical instability in film blowing process: Analogy to buckling instability

Science.gov (United States)

Lee, Joo Sung; Kwon, Ilyoung; Jung, Hyun Wook; Hyun, Jae Chun

2017-12-01

The film blowing process is one of the most important polymer processing operations, widely used for producing bi-axially oriented film products in a single-step process. Among the instabilities observed in this film blowing process, i.e., draw resonance and helical motion occurring on the inflated film bubble, the helical instability is a unique phenomenon portraying the snake-like undulation motion of the bubble, having the period on the order of few seconds. This helical instability in the film blowing process is commonly found at the process conditions of a high blow-up ratio with too low a freezeline position and/or too high extrusion temperature. In this study, employing an analogy to the buckling instability for falling viscous threads, the compressive force caused by the pressure difference between inside and outside of the film bubble is introduced into the simulation model along with the scaling law derived from the force balance between viscous force and centripetal force of the film bubble. The simulation using this model reveals a close agreement with the experimental results of the film blowing process of polyethylene polymers such as low density polyethylene and linear low density polyethylene.

A dynamical theory for linearized massive superspin 3/2

International Nuclear Information System (INIS)

Gates, James S. Jr.; Koutrolikos, Konstantinos

2014-01-01

We present a new theory of free massive superspin Y=3/2 irreducible representation of the 4D, N=1 Super-Poincaré group, which has linearized non-minimal supergravity (superhelicity Y=3/2) as it’s massless limit. The new results will illuminate the underlying structure of auxiliary superfields required for the description of higher massive superspin systems

System theory as applied differential geometry. [linear system

Science.gov (United States)

Hermann, R.

1979-01-01

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

A review of recent results on spread F theory

International Nuclear Information System (INIS)

Ossakow, S.L.

1979-01-01

Ionospheric Spread F was discovered some four decades ago. Yet only in the past few years has significant progress been made in the theoretical explanation of such phenomena. In particular, considerable effort has been expended to explain equatorial Spread F and the attendant satellite signal propagation scintillation phenomena. The present review dwells mainly in this low latitude area. The various linear plasma instabilities thought to initiate equatorial Spread F are discussed. Recent theoretical and numerical simulation studies of the nonlinear evolution of the collisional Rayleigh-Taylor instability in equatorial Spread F are reviewed. Also, analytical studies of rising equatorial Spread F bubbles in the collisional and collisionless Rayleigh-Taylor regime are discussed, as well as the nohlinear saturation of instabilities in these two regimes. Current theories on very small scale (< approx 10 meters) size irregularities observed by radar backscatter during equatorial Spread F and their relation to the larger wavelength scintillation causing irregularities are discussed. Application of turbulence theory to equatorial Spread F phenomena is reviewed. Remaining problems to be dealt with at equatorial latitudes are summarized. (Auth.)

How does political instability affect economic growth?

OpenAIRE

Aisen, Ari; Veiga, Francisco José

2011-01-01

The purpose of this paper is to empirically determine the effects of political instability on economic growth. Using the system-GMM estimator for linear dynamic panel data models on a sample covering up to 169 countries, and 5-year periods from 1960 to 2004, we find that higher degrees of political instability are associated with lower growth rates of GDP per capita. Regarding the channels of transmission, we find that political instability adversely affects growth by lowering the rates of pr...

Refinements to longitudinal, single bunch, coherent instability theory

Energy Technology Data Exchange (ETDEWEB)

Koscielniak, S R

1995-06-01

For the case of a bunched beam confined to a quadratic potential well, we demonstrate the necessity for considering mode-coupling to correctly obtain the threshold current for the d.c. instability. Further we find the effect upon growth rate and coherent tune shift of evaluating the impedance at a complex frequency. For the case of a bunched beam confined to a cosine potential well, we give an exact analytic expression for the dispersion integral, and calculate (with no approximations), the stability diagram for the Robinson instability taking into account Landau damping. This paper comprises extracts from a lengthy internal report. (author). 2 refs., 4 figs.

Linear and nonlinear ion beam instabilities in a double plasma device

International Nuclear Information System (INIS)

Lee, S.G.; Diebold, D.; Hershkowitz, N.

1994-01-01

Ion beam instabilities in the double plasma device DOLI-1 were found to be quite sensitive to the difference between the source and target chamber plasma potentials when those potentials were within an electron temperature T e /e or so of each other. When the target chamber plasma potential of DOLI-1 was ≤ T e /e more positive than the source chamber plasma potential, a global ion beam-ion beam instability was observed. On the other hand, when the maximum target potential was between approximately 0.5 T e /e and 2.0 T e /e below the source potential, an ion-ion beam instability and a soliton associated with it were observed. This soliton is unique in that it is not launched but rather is self generated by the plasma and beam. When the target potential was less than source potential by more than two or so T e /e, the plasma was quite quiescent, which allowed small amplitude wave packet launched by Langmuir probe to be detected

Non-cooperative stochastic differential game theory of generalized Markov jump linear systems

CERN Document Server

Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning

2017-01-01

This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...

Non-linear electrodynamics in Kaluza-Klein theory

International Nuclear Information System (INIS)

Kerner, R.

1987-01-01

The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr

Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

Science.gov (United States)

Lagos, Macarena; Bellini, Emilio; Noller, Johannes; Ferreira, Pedro G.; Baker, Tessa

2018-03-01

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.

Calculation of the interfacial tension of the methane-water system with the linear gradient theory

DEFF Research Database (Denmark)

Schmidt, Kurt A. G.; Folas, Georgios; Kvamme, Bjørn

2007-01-01

The linear gradient theory (LGT) combined with the Soave-Redlich-Kwong (SRK EoS) and the Peng-Robinson (PR EoS) equations of state has been used to correlate the interfacial tension data of the methane-water system. The pure component influence parameters and the binary interaction coefficient...... for the mixture influence parameter have been obtained for this system. The model was successfully applied to correlate the interfacial tension data set to within 2.3% for the linear gradient theory and the SRK EoS (LGT-SRK) and 2.5% for the linear gradient theory and PE EoS (LGT-PR). A posteriori comparison...... of data not used in the parameterisation were to within 3.2% for the LGT-SRK model and 2.7% for the LGT-PR model. An exhaustive literature review resulted in a large database for the investigation which covers a wide range of temperature and pressures. The results support the success of the linear...

Buneman instability in hot electron plasma (Te>>Ti)

International Nuclear Information System (INIS)

Khalil, S.M.; Sayed, Y.A.; Sayed, R.A.

1986-07-01

We shall investigate the linear excitation of electrostatic current Buneman instability in both unmagnetized and magnetized homogeneous plasma. The frequency, growth rate and conditions of excitation of such instability are obtained analytically. We consider that the current velocity u (due to relative streaming of ions and electrons) slightly exceeds the instability threshold velocity u cr and that the electron temperature is much higher than the ion temperature (T e >>T i ). (author)

Gravitational instability in isotropic MHD plasma waves

Science.gov (United States)

Cherkos, Alemayehu Mengesha

2018-04-01

The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.

Theory of resistive magnetohydrodynamic instabilities excited by energetic trapped particles in large-size tokamaks

International Nuclear Information System (INIS)

Biglari, H.

1987-01-01

A theory describing excitation of resistive magnetohydrodynamic instabilities due to a population of energetic particles, trapped in region of adverse curvature on energetic particles, trapped in region of adverse curvature in tokamaks, is presented. Theory's principal motivation is observation that high magnetic-field strengths and large geometric dimensions characteristic of present-generation thermonuclear fusion devices, places them in a frequency regime whereby processional drift frequency of auxiliary hot-ion species, in order of magnitude, falls below a typical inverse resistive interchange time scale, so that inclusion of resistive dissipation effects becomes important. Destabilization of the resistive internal kink mode by these suprathermal particles is first investigated. Using variational techniques, a generalized dispersion relation governing such modes, which recovers ideal theory in its appropriate limit, is derived and analyzed using Nyquist-diagrammatic techniques. An important implication of theory for present-generation fusion devices is that they will be stable to fishbone activity. Interaction of energetic particles with resistive interchange-ballooning modes is taken up. A population of hot particles, deeply trapped on adverse curvature side in tokamaks, can resonantly destabilize resistive interchange mode, which is stable in their absence because of favorable average curvature. Both modes are different from their usual resistive magnetohydrodynamic counterparts in their destabilization mechanism

The spin polarized linear response from density functional theory: Theory and application to atoms

Energy Technology Data Exchange (ETDEWEB)

Fias, Stijn, E-mail: sfias@vub.ac.be; Boisdenghien, Zino; De Proft, Frank; Geerlings, Paul [General Chemistry (ALGC), Vrije Universiteit Brussel (Free University Brussels – VUB), Pleinlaan 2, 1050 Brussels (Belgium)

2014-11-14

Within the context of spin polarized conceptual density functional theory, the spin polarized linear response functions are introduced both in the [N, N{sub s}] and [N{sub α}, N{sub β}] representations. The mathematical relations between the spin polarized linear response functions in both representations are examined and an analytical expression for the spin polarized linear response functions in the [N{sub α}, N{sub β}] representation is derived. The spin polarized linear response functions were calculated for all atoms up to and including argon. To simplify the plotting of our results, we integrated χ(r, r′) to a quantity χ(r, r{sup ′}), circumventing the θ and ϕ dependence. This allows us to plot and to investigate the periodicity throughout the first three rows in the periodic table within the two different representations. For the first time, χ{sub αβ}(r, r{sup ′}), χ{sub βα}(r, r{sup ′}), and χ{sub SS}(r, r{sup ′}) plots have been calculated and discussed. By integration of the spin polarized linear response functions, different components to the polarisability, α{sub αα}, α{sub αβ}, α{sub βα}, and α{sub ββ} have been calculated.

Quantum optimal control theory in the linear response formalism

International Nuclear Information System (INIS)

Castro, Alberto; Tokatly, I. V.

2011-01-01

Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice, this normally means optimizing the value of some observable, a so-called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization: the unperturbed Hamiltonian is allowed to be time dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in terms of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for nonequilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.

Flow and instability in quantum gravity

International Nuclear Information System (INIS)

Douglas, M.R.; Seiberg, N.; Shenker, S.H.

1990-01-01

We study the flow from the m=3 multicritical matrix theory, unambiguously defined by Brezin, Marinari and Parisi, to the m=2 pure gravity theory. We find behavior in the flow indicative of a non-perturbative instability in this definition of non-perturbative pure quantum gravity. We expect a similar situation for all m even theories. Other definitions of these theories are briefly discussed. (orig.)

Thresholds of parametric instabilities near the lower hybrid frequency

International Nuclear Information System (INIS)

Berger, R.L.; Perkins, F.W.

1975-06-01

Resonant decay instabilities of a pump wave with frequency ω 0 near the lower-hybrid frequency ω/sub LH/ are analyzed with respect to the wavenumber k of the decay waves and the ratio ω 0 /ω/sub LH/ to determine the decay process with the minimum threshold. It was found that the lowest thresholds are for decay into an electron plasma (lower hybrid) wave plus either a backward ion-cyclotron wave, an ion Bernstein wave, or a low frequency sound wave. For ω 0 less than (2ω/sub LH/)/sup 1 / 2 /, it was found that these decay processes can occur and have faster growth than ion quasimodes provided the drift velocity (cE 0 /B 0 ) is much less than the sound speed. In many cases of interest, electromagnetic corrections to the lower-hybrid wave rule out decay into all but short wavelength (k rho/sub i/ greater than 1) waves. The experimental results are consistent with the linear theory of parametric instabilities in a homogeneous plasma. (U.S.)

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

Science.gov (United States)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

Generation companies decision-making modeling by linear control theory

International Nuclear Information System (INIS)

Gutierrez-Alcaraz, G.; Sheble, Gerald B.

2010-01-01

This paper proposes four decision-making procedures to be employed by electric generating companies as part of their bidding strategies when competing in an oligopolistic market: naive, forward, adaptive, and moving average expectations. Decision-making is formulated in a dynamic framework by using linear control theory. The results reveal that interactions among all GENCOs affect market dynamics. Several numerical examples are reported, and conclusions are presented. (author)

Super-Gaussian transport theory and the field-generating thermal instability in laser–plasmas

International Nuclear Information System (INIS)

Bissell, J J; Ridgers, C P; Kingham, R J

2013-01-01

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser–plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density n e , which we associate with a novel heat-flow q n ∝∇n e . Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇T e × ∇n e field generation mechanism by ∼30% (where T e is the electron temperature), and the diffusive and Righi–Leduc heat-flows by ∼80 and ∼90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux q n are checked against kinetic simulation using the Vlasov–Fokker–Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields. (paper)

Super-Gaussian transport theory and the field-generating thermal instability in laser-plasmas

Science.gov (United States)

Bissell, J. J.; Ridgers, C. P.; Kingham, R. J.

2013-02-01

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser-plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density ne, which we associate with a novel heat-flow qn∝∇ne. Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇Te × ∇ne field generation mechanism by ˜30% (where Te is the electron temperature), and the diffusive and Righi-Leduc heat-flows by ˜80 and ˜90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux qn are checked against kinetic simulation using the Vlasov-Fokker-Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields.

Instability of ties in compression

DEFF Research Database (Denmark)

Buch-Hansen, Thomas Cornelius

2013-01-01

Masonry cavity walls are loaded by wind pressure and vertical load from upper floors. These loads results in bending moments and compression forces in the ties connecting the outer and the inner wall in a cavity wall. Large cavity walls are furthermore loaded by differential movements from...... the temperature gradient between the outer and the inner wall, which results in critical increase of the bending moments in the ties. Since the ties are loaded by combined compression and moment forces, the loadbearing capacity is derived from instability equilibrium equations. Most of them are iterative, since...... exact instability solutions are complex to derive, not to mention the extra complexity introducing dimensional instability from the temperature gradients. Using an inverse variable substitution and comparing an exact theory with an analytical instability solution a method to design tie...

Curvature-driven instabilities in a hot-electron plasma: radial analysis

International Nuclear Information System (INIS)

Berk, H.L.; Van Dam, J.W.; Rosenbluth, M.N.; Spong, D.A.

1981-12-01

The theory of unfavorable curvature-driven instabilities is developed for a plasma interacting with a hot electron ring whose drift frequencies are larger than the growth rates predicted from conventional magnetohydrodynamic theory. A z-pinch model is used to emphasize the radial structure of the problem. Stability criteria are obtained for the five possible modes of instability: the conventional hot electron interchange, a high-frequency hot electron interchange (at frequencies larger than the ion cyclotron frequency), a compressional instability, a background pressure-driven interchange, and an interacting pressure-driven interchange

Corona-induced electrohydrodynamic instabilities in low conducting liquids

Energy Technology Data Exchange (ETDEWEB)

Vega, F.; Perez, A.T. [Depto. Electronica y Electromagnetismo, Facultad de Fisica, Universidad de Sevilla, Avda. Reina Mercedes, s/n. 41012, Sevilla (Spain)

2003-06-01

The rose-window electrohydrodynamic (EHD) instability has been observed when a perpendicular field with an additional unipolar ion injection is applied onto a low conducting liquid surface. This instability has a characteristic pattern with cells five to 10 times greater than those observed in volume instabilities caused by unipolar injection. We have used corona discharge from a metallic point to perform some measurements of the rose-window instability in low conducting liquids. The results are compared to the linear theoretical criterion for an ohmic liquid. They confirmed that the minimum voltage for this instability is much lower than that for the interfacial instability in high conducting liquids. This was predicted theoretically in the dependence of the critical voltage as a function of the non-dimensional conductivity. It is shown that in a non-ohmic liquid the rose window appears as a secondary instability after the volume instability. (orig.)

Non-linear general instability of ring-stiffened conical shells under external hydrostatic pressure

International Nuclear Information System (INIS)

Ross, C T F; Kubelt, C; McLaughlin, I; Etheridge, A; Turner, K; Paraskevaides, D; Little, A P F

2011-01-01

The paper presents the experimental results for 15 ring-stiffened circular steel conical shells, which failed by non-linear general instability. The results of these investigations were compared with various theoretical analyses, including an ANSYS eigen buckling analysis and another ANSYS analysis; which involved a step-by-step method until collapse; where both material and geometrical nonlinearity were considered. The investigation also involved an analysis using BS5500 (PD 5500), together with the method of Ross of the University of Portsmouth. The ANSYS eigen buckling analysis tended to overestimate the predicted buckling pressures; whereas the ANSYS nonlinear results compared favourably with the experimental results. The PD5500 analysis was very time consuming and tended to grossly underestimate the experimental buckling pressures and in some cases, overestimate them. In contrast to PD5500 and ANSYS, the design charts of Ross of the University of Portsmouth were the easiest of all these methods to use and generally only slightly underestimated the experimental collapse pressures. The ANSYS analyses gave some excellent graphical displays.

Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory

Directory of Open Access Journals (Sweden)

Hamid M. Sedighi

Full Text Available This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency- amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.

Model of oscillatory instability in vertically-homogeneous atmosphere

Directory of Open Access Journals (Sweden)

P. B. Rutkevich

2009-02-01

Full Text Available Existence and repeatability of tornadoes could be straightforwardly explained if there existed instability, responsible for their formation. However, it is well known that convection is the only instability in initially stable air, and the usual convective instability is not applicable for these phenomena. In the present paper we describe an instability in the atmosphere, which can be responsible for intense vortices. This instability appears in a fluid with Coriolis force and dissipation and has oscillatory behaviour, where the amplitude growth is accompanied by oscillations with frequency comparable to the growth rate of the instability. In the paper, both analytical analysis of the linear phase of the instability and nonlinear simulation of the developed stage of the air motion are addressed. This work was supported by the RFBR grant no. 09-05-00374-a.

TOWARD A MAGNETOHYDRODYNAMIC THEORY OF THE STATIONARY ACCRETION SHOCK INSTABILITY: TOY MODEL OF THE ADVECTIVE-ACOUSTIC CYCLE IN A MAGNETIZED FLOW

International Nuclear Information System (INIS)

Guilet, Jerome; Foglizzo, Thierry

2010-01-01

The effect of a magnetic field on the linear phase of the advective-acoustic instability is investigated as a first step toward a magnetohydrodynamic (MHD) theory of the stationary accretion shock instability taking place during stellar core collapse. We study a toy model where the flow behind a planar stationary accretion shock is adiabatically decelerated by an external potential. Two magnetic field geometries are considered: parallel or perpendicular to the shock. The entropy-vorticity wave, which is simply advected in the unmagnetized limit, separates into five different waves: the entropy perturbations are advected, while the vorticity can propagate along the field lines through two Alfven waves and two slow magnetosonic waves. The two cycles existing in the unmagnetized limit, advective-acoustic and purely acoustic, are replaced by up to six distinct MHD cycles. The phase differences among the cycles play an important role in determining the total cycle efficiency and hence the growth rate. Oscillations in the growth rate as a function of the magnetic field strength are due to this varying phase shift. A vertical magnetic field hardly affects the cycle efficiency in the regime of super-Alfvenic accretion that is considered. In contrast, we find that a horizontal magnetic field strongly increases the efficiencies of the vorticity cycles that bend the field lines, resulting in a significant increase of the growth rate if the different cycles are in phase. These magnetic effects are significant for large-scale modes if the Alfven velocity is a sizable fraction of the flow velocity.

Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

Science.gov (United States)

Jiang, Fei

2018-04-01

We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

Plasma instability of a vacuum arc centrifuge

International Nuclear Information System (INIS)

Hole, M.J.; Dallaqua, R.S.; Simpson, S.W.; Del Bosco, E.

2002-01-01

Ever since conception of the vacuum arc centrifuge in 1980, periodic fluctuations in the ion saturation current and floating potential have been observed in Langmuir probe measurements in the rotation region of a vacuum arc centrifuge. In this work we develop a linearized theoretical model to describe a range of instabilities in the vacuum arc centrifuge plasma column, and then test the validity of the description through comparison with experiment. We conclude that the observed instability is a 'universal' instability, driven by the density gradient, in a plasma with finite conductivity

Treatment of the subject of tearing instability

International Nuclear Information System (INIS)

Paris, P.C.

1977-07-01

A simple approach is taken to the mechanics of potential instability associated with the steady tearing portion of J-Integral R-curves. The analysis is developed from simple examples of structural component (or test specimen) configurations with cracks, examining their instability possibilities individually, in order to draw more general conclusions about elastic-plastic cracking instability as contrasted to linear-elastic behavior. Finally, an attempt is made to model a more local cleavage-like instability for material in the fracture process zone just ahead of a crack tip. Results are then presented of a testing program which clearly demonstrates the appropriateness of the tearing instability analysis and which illustrates its broad potential for future application, as well as presenting guidelines for its further development. The material selected for analysis was Ni-Cr-Mo-V rotor steel

Importance of Resolving the Spectral Support of Beam-plasma Instabilities in Simulations

Energy Technology Data Exchange (ETDEWEB)

Shalaby, Mohamad; Broderick, Avery E. [Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada); Chang, Philip [Department of Physics, University of Wisconsin-Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, WI 53211 (United States); Pfrommer, Christoph [Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg (Germany); Lamberts, Astrid [Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125 (United States); Puchwein, Ewald, E-mail: mshalaby@live.ca [Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge, CB3 0HA (United Kingdom)

2017-10-20

Many astrophysical plasmas are prone to beam-plasma instabilities. For relativistic and dilute beams, the spectral support of the beam-plasma instabilities is narrow, i.e., the linearly unstable modes that grow with rates comparable to the maximum growth rate occupy a narrow range of wavenumbers. This places stringent requirements on the box-sizes when simulating the evolution of the instabilities. We identify the implied lower limits on the box size imposed by the longitudinal beam plasma instability, i.e., typically the most stringent condition required to correctly capture the linear evolution of the instabilities in multidimensional simulations. We find that sizes many orders of magnitude larger than the resonant wavelength are typically required. Using one-dimensional particle-in-cell simulations, we show that the failure to sufficiently resolve the spectral support of the longitudinal instability yields slower growth and lower levels of saturation, potentially leading to erroneous physical conclusion.

Importance of Resolving the Spectral Support of Beam-plasma Instabilities in Simulations

International Nuclear Information System (INIS)

Shalaby, Mohamad; Broderick, Avery E.; Chang, Philip; Pfrommer, Christoph; Lamberts, Astrid; Puchwein, Ewald

2017-01-01

Many astrophysical plasmas are prone to beam-plasma instabilities. For relativistic and dilute beams, the spectral support of the beam-plasma instabilities is narrow, i.e., the linearly unstable modes that grow with rates comparable to the maximum growth rate occupy a narrow range of wavenumbers. This places stringent requirements on the box-sizes when simulating the evolution of the instabilities. We identify the implied lower limits on the box size imposed by the longitudinal beam plasma instability, i.e., typically the most stringent condition required to correctly capture the linear evolution of the instabilities in multidimensional simulations. We find that sizes many orders of magnitude larger than the resonant wavelength are typically required. Using one-dimensional particle-in-cell simulations, we show that the failure to sufficiently resolve the spectral support of the longitudinal instability yields slower growth and lower levels of saturation, potentially leading to erroneous physical conclusion.

Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

Science.gov (United States)

Gasbarro, Andrew

2018-03-01

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

Instabilities and nonequilibrium structures

International Nuclear Information System (INIS)

Tirapegui, E.; Villarroel, D.

1987-01-01

Physical systems can be studied both near to and far from equilibrium where instabilities appear. The behaviour in these two regions is reviewed in this book, from both the theoretical and application points of view. The influence of noise in these situations is an essential feature which cannot be ignored. It is therefore discussed using phenomenological and theoretical approaches for the numerous problems which still remain in the field. This volume should appeal to mathematicians and physicists interested in the areas of instability, bifurcation theory, dynamical systems, pattern formation, nonequilibrium structures and statistical mechanics. (Auth.)

Limit cycle behaviour of the bump-on-tail and ion-acoustic instability

International Nuclear Information System (INIS)

Janssen, P.A.E.M.; Rasmussen, J.J.

1980-12-01

The nonlinear dynamics of the bump-on-tail and current-driven ion-acoustic instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density and the electron drift velocity respectively) above its neutral stable value by a small fractional amount Δ 2 , one mode becomes unstable. The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behaviour is found. A short comparison with quasi-linear theory is given, and the results are compared with experiment. (Auth.)

Effect of hall currents on thermal instability of dusty couple stress fluid

Directory of Open Access Journals (Sweden)

Aggarwal Amrish Kumar

2016-09-01

Full Text Available In this paper, effect of Hall currents on the thermal instability of couple-stress fluid permeated with dust particles has been considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For the case of stationary convection, dust particles and Hall currents are found to have destabilizing effect while couple stresses have stabilizing effect on the system. Magnetic field induced by Hall currents has stabilizing/destabilizing effect under certain conditions. It is found that due to the presence of Hall currents (hence magnetic field, oscillatory modes are produced which were non-existent in their absence.

Transitional inertialess instabilities in driven multilayer channel flows

Science.gov (United States)

Papaefthymiou, Evangelos; Papageorgiou, Demetrios

2016-11-01

We study the nonlinear stability of viscous, immiscible multilayer flows in channels driven both by a pressure gradient and/or gravity in a slightly inclined channel. Three fluid phases are present with two internal interfaces. Novel weakly nonlinear models of coupled evolution equations are derived and we concentrate on inertialess flows with stably stratified fluids, with and without surface tension. These are 2 × 2 systems of second-order semilinear parabolic PDEs that can exhibit inertialess instabilities due to resonances between the interfaces - mathematically this is manifested by a transition from hyperbolic to elliptic behavior of the nonlinear flux functions. We consider flows that are linearly stable (i.e the nonlinear fluxes are hyperbolic initially) and use the theory of nonlinear systems of conservation laws to obtain a criterion (which can be verified easily) that can predict nonlinear stability or instability (i.e. nonlinear fluxes encounter ellipticity as they evolve spatiotemporally) at large times. In the former case the solution decays asymptotically to its base state, and in the latter nonlinear traveling waves emerge. EPSRC Grant Numbers EP/K041134 and EP/L020564.

Instabilities, turbulence and transport in a magnetized plasma

International Nuclear Information System (INIS)

Garbet, X.

2001-06-01

The purpose of this work is to introduce the main processes that occur in a magnetized plasma. During the last 2 decades, the understanding of turbulence has made great progress but analytical formulas and simulations are far to produce reliable predictions. The values of transport coefficients in a tokamak plasma exceed by far those predicted by the theory of collisional transport. This phenomenon is called abnormal transport and might be due to plasma fluctuations. An estimation of turbulent fluxes derived from the levels of fluctuations, is proposed. A flow description of plasma allows the understanding of most micro-instabilities. The ballooning representation deals with instabilities in a toric geometry. 3 factors play an important role to stabilize plasmas: density pinch, magnetic shear and speed shear. The flow model of plasma gives an erroneous value for the stability threshold, this is due to a bad description of the resonant interaction between wave and particle. As for dynamics, flow models can be improved by adding dissipative terms so that the linear response nears the kinetic response. The kinetic approach is more accurate but is complex because of the great number of dimensions involved. (A.C.)

Beam Instabilities in Circular Particle Accelerators

CERN Document Server

AUTHOR|(CDS)2067185

2017-01-01

The theory of impedance-induced bunched-beam coherent instabilities is reviewed following Laclare's formalism, adding the effect of an electronic damper in the transverse plane. Both single-bunch and coupled-bunch instabilities are discussed, both low-intensity and high-intensity regimes are analysed, both longitudinal and transverse planes are studied, and both short-bunch and long-bunch regimes are considered. Observables and mitigation measures are also examined.

The coalescence instability in solar flares

International Nuclear Information System (INIS)

Tajima, T.; Brunel, F.; Sakai, J.I.; Vlahos, L.; Kundu, M.R.

1984-01-01

The non-linear coalescence instability of current carrying solar loops can explain many of the characteristics of the solar flares such as their impulsive nature, heating and high energy particle acceleration, amplitude oscillations of electromagnetic emission as well as the characteristics of 2-D microwave images obtained during a flare. The plasma compressibility leads to the explosive phase of loop coalescence and its overshoot results in amplitude oscillations in temperatures by adiabatic compression and decompression. We note that the presence of strong electric fields and super-Alfvenic flows during the course of the instabilty paly an important role in the production of non-thermal particles. A qualitative explanation on the physical processes taking place during the non-linear stages of the instability is given. (author)

Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

International Nuclear Information System (INIS)

Sugahara, Y.; Toki, H.

1994-01-01

We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

Linear spin-wave theory of incommensurably modulated magnets

DEFF Research Database (Denmark)

Ziman, Timothy; Lindgård, Per-Anker

1986-01-01

Calculations of linearized theories of spin dynamics encounter difficulties when applied to incommensurable magnetic phases: lack of translational invariance leads to an infinite coupled system of equations. The authors resolve this for the case of a `single-Q' structure by mapping onto the problem......: at higher frequency there appear bands of response sharply defined in frequency, but broad in momentum transfer; at low frequencies there is a response maximum at the q vector corresponding to the modulation vector. They discuss generalizations necessary for application to rare-earth magnets...

Checking the foundation: recent radiobiology and the linear no-threshold theory.

Science.gov (United States)

Ulsh, Brant A

2010-12-01

The linear no-threshold (LNT) theory has been adopted as the foundation of radiation protection standards and risk estimation for several decades. The "microdosimetric argument" has been offered in support of the LNT theory. This argument postulates that energy is deposited in critical cellular targets by radiation in a linear fashion across all doses down to zero, and that this in turn implies a linear relationship between dose and biological effect across all doses. This paper examines whether the microdosimetric argument holds at the lowest levels of biological organization following low dose, low dose-rate exposures to ionizing radiation. The assumptions of the microdosimetric argument are evaluated in light of recent radiobiological studies on radiation damage in biological molecules and cellular and tissue level responses to radiation damage. There is strong evidence that radiation initially deposits energy in biological molecules (e.g., DNA) in a linear fashion, and that this energy deposition results in various forms of prompt DNA damage that may be produced in a pattern that is distinct from endogenous (e.g., oxidative) damage. However, a large and rapidly growing body of radiobiological evidence indicates that cell and tissue level responses to this damage, particularly at low doses and/or dose-rates, are nonlinear and may exhibit thresholds. To the extent that responses observed at lower levels of biological organization in vitro are predictive of carcinogenesis observed in vivo, this evidence directly contradicts the assumptions upon which the microdosimetric argument is based.

Analytic theory of the Rayleigh-Taylor instability in a uniform density plasma-filled ion diode

International Nuclear Information System (INIS)

Hussey, T.W.; Payne, S.S.

1987-04-01

The J-vector x B-vector forces associated with the surface current of a plasma-filled ion diode will accelerate this plasma fill toward the anode surface. It is well known that such a configuration with a high I is susceptible to the hydromagnetic Rayleigh-Taylor instability in certain geometries. A number of ion diode plasma sources have been proposed, most of which have a falling density going away from the wall. A somewhat more unstable case, however, is that of uniform density. In this report we attempt to establish an upper limit on this effect with a simple analytic model in which a uniform-density plasma is accelerated by the magnetic field anticipated in a PBFA-II diode. We estimate the number of linear e-foldings experienced by an unstable surface as well as the most damaging wavelength initial perturbation. This model, which accounts approximately for stabilization due to field diffusion, suggests that even with a uniform fill, densities in excess of a few 10 15 are probably not damaged by the instability. In addition, even lower densities might be tolerated if perturbations near the most damaging wavelength can be kept very small

Saturation and postsaturation phenomena of Rayleigh-Taylor instability with adjacent modes

International Nuclear Information System (INIS)

Ikegawa, Tadashi; Nishihara, Katsunobu

2003-01-01

A weakly nonlinear theory has been developed for the classical Rayleigh-Taylor instability with a finite bandwidth taken into account self-consistently. The theory includes up to third order nonlinearity, which results in the saturation of linear growth and determines subsequent weakly nonlinear growth. Analytical results are shown to agree fairly well with two-dimensional hydrodynamic simulations. There are generally many local peaks of a perturbation with a finite bandwidth due to the interference of modes. Since a local amplitude is determined from phases among the modes as well as the bandwidth, we have investigated an onset of the linear growth saturation and the subsequent weakly nonlinear growth for different bandwidths and phases. It is shown that the saturation of the linear growth occurs locally, i.e., each of the local maximum amplitudes (LMAs) grows exponentially until it reaches almost the same saturation amplitude. In the random phase case, the root mean square amplitude thus saturates with almost the same amplitude as the LMA, after most of the LMAs have saturated. The saturation amplitude of the LMA is found to be independent of the bandwidth and depends on the Atwood number. We derive a formula of the saturation amplitude of modes based on the results obtained, and discuss its relation with Haan's formula [Phys. Rev. A 39, 5812 (1989)]. The LMAs grow linearly in time after the saturation and their speeds are approximated by the product of the linear growth rate and the saturation amplitude. We investigate the Atwood number dependence of both the saturation amplitude and the weakly nonlinear growth

Damping-controlled fluidelastic instability forces in multi-span tubes with loose supports

International Nuclear Information System (INIS)

Hassan, Marwan A.; Rogers, Robert J.; Gerber, Andrew G.

2011-01-01

This paper presents simulations of a loosely supported multi-span tube subjected to turbulence and fluidelastic instability forces in order to compare several time-domain fluid force models simulating the damping-controlled fluidelastic instability mechanism in tube arrays. These models include the negative damping model based on the Connors equation, fluid force coefficient-based models (Chen; Tanaka and Takahara), and two semi-analytical models (Price and Paidoussis; and Lever and Weaver). Time domain modelling challenges for each of these theories are discussed. The implemented models are validated against available experimental data. The linear simulations (without tube/support clearance) show that the Connors-equation based model exhibits the most conservative prediction of the critical flow velocity when the recommended design values for the Connors equation are used. The models are then utilized to simulate the nonlinear response of a three-span cantilever tube in a lattice bar support subjected to air crossflow. The tube is subjected to a single-phase flow passing over the spans where the flow velocity and the support clearance are varied. Special attention is paid to the tube/support interaction parameters that affect wear, such as impact forces, contact ratio, and normal work rate. As was seen for the linear cases, the reduced flow velocity at the instability threshold differs for the fluid force models considered. The investigated models do, however, exhibit similar response characteristics for the impact force, tip lift response, and work rate, except for the Connors-based model that overestimates the response and the tube/support interaction parameters for the loose support case, especially at large clearances.

Linear canonical transforms theory and applications

CERN Document Server

Kutay, M; Ozaktas, Haldun; Sheridan, John

2016-01-01

This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

The Measurement, Nomological Net, and Theory of Perceived Self-Esteem Instability: Applying the Conservation of Resources Theory to Understand the Construct.

Science.gov (United States)

Howard, Matt C

2018-01-01

The current article performs the first focused investigation into the construct of perceived self-esteem instability (P-SEI). Four studies investigate the construct's measurement, nomological net, and theoretical dynamics. Study 1 confirms the factor structure of a P-SEI Measure, supporting that P-SEI can be adequately measured. Study 2 identifies an initial nomological net surrounding P-SEI, showing that the construct is strongly related to stable aspects of the self (i.e., neuroticism and core self-evaluations). In Studies 3 and 4, the Conservation of Resources Theory is applied to develop and test five hypotheses. These studies show that P-SEI is predicted by self-esteem level and stressors, and the relationship of certain stressors is moderated by self-esteem contingencies. P-SEI also predicts stress, depression, anxiety, and certain defensive postures. From these studies and the integration of Conservation of Resources Theory, we suggest that P-SEI emerges through an interaction between environmental influences and personal resources, and we provide a theoretical model to better understand the construct of P-SEI. We suggest that this theory-driven model can prompt the initial field of study on P-SEI.

Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes

International Nuclear Information System (INIS)

Durkee, Mark N.; Reall, Harvey S.

2011-01-01

It is shown that the equations governing linearized gravitational (or electromagnetic) perturbations of the near-horizon geometry of any known extreme vacuum black hole (allowing for a cosmological constant) can be Kaluza-Klein reduced to give the equation of motion of a charged scalar field in AdS 2 with an electric field. One can define an effective Breitenloehner-Freedman bound for such a field. We conjecture that if a perturbation preserves certain symmetries then a violation of this bound should imply an instability of the full black hole solution. Evidence in favor of this conjecture is provided by the extreme Kerr solution and extreme cohomogeneity-1 Myers-Perry solution. In the latter case, we predict an instability in seven or more dimensions and, in five dimensions, we present results for operator conformal weights assuming the existence of a conformal field theory dual. We sketch a proof of our conjecture for scalar field perturbations.

BNS damping of beam breakup instability

International Nuclear Information System (INIS)

Stupakov, G.V.

1997-08-01

The author studies BNS damping of the beam breakup instability in a simple model assuming a constant beam energy, flat bunch distribution, and a smooth transverse focusing. The model allows an analytic solution for a constant and linear wake functions. Scaling dimensionless parameters are derived and the beam dynamics is illustrated for the range of parameters relevant to the Stanford Linear Collider

Beam Instabilities in Hadron Synchrotrons

CERN Document Server

Métral, E; Bartosik, H; Biancacci, N; Buffat, X; Esteban Muller, J F; Herr, W; Iadarola, G; Lasheen, A; Li, K; Oeftiger, A; Pieloni, T; Quartullo, D; Rumolo, G; Salvant, B; Schenk, M; Shaposhnikova, E; Tambasco, C; Timko, H; Zannini, C; Burov, A; Banfi, D; Barranco, J; Mounet, N; Boine-Frankenheim, O; Niedermayer, U; Kornilov, V; White, S

2016-01-01

Beam instabilities cover a wide range of effects in particle accelerators and they have been the subjects of intense research for several decades. As the machines performance was pushed new mechanisms were revealed and nowadays the challenge consists in studying the interplays between all these intricate phenomena, as it is very often not possible to treat the different effects separately. The aim of this paper is to review the main mechanisms, discussing in particular the recent developments of beam instability theories and simulations.

Instabilities of higher dimensional compactifications

International Nuclear Information System (INIS)

Accetta, F.S.

1987-02-01

Various schemes for cosmological compactification of higher dimensional theories are considered. Possible instabilities which drive the ground state with static internal space to de Sitter-like expansion of all dimensions are discussed. These instabilities are due to semiclassical barrier penetration and classical thermal fluctuations. For the case of the ten dimensional Chapline-Manton action, it is possible to avoid such difficulties by balancing one-loop Casimir corrections against monopole contributions from the field strength H/sub MNP/ and fermionic condensates. 10 refs

Background field method in gauge theories and on linear sigma models

International Nuclear Information System (INIS)

van de Ven, A.E.M.

1986-01-01

This dissertation constitutes a study of the ultraviolet behavior of gauge theories and two-dimensional nonlinear sigma-models by means of the background field method. After a general introduction in chapter 1, chapter 2 presents algorithms which generate the divergent terms in the effective action at one-loop for arbitrary quantum field theories in flat spacetime of dimension d ≤ 11. It is demonstrated that global N = 1 supersymmetric Yang-Mills theory in six dimensions in one-loop UV-finite. Chapter 3 presents an algorithm which produces the divergent terms in the effective action at two-loops for renormalizable quantum field theories in a curved four-dimensional background spacetime. Chapter 4 presents a study of the two-loop UV-behavior of two-dimensional bosonic and supersymmetric non-linear sigma-models which include a Wess-Zumino-Witten term. It is found that, to this order, supersymmetric models on quasi-Ricci flat spaces are UV-finite and the β-functions for the bosonic model depend only on torsionful curvatures. Chapter 5 summarizes a superspace calculation of the four-loop β-function for two-dimensional N = 1 and N = 2 supersymmetric non-linear sigma-models. It is found that besides the one-loop contribution which vanishes on Ricci-flat spaces, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for superstrings are discussed. Chapters 6 and 7 treat the details of these calculations

Competing processes of whistler and electrostatic instabilities in the magnetosphere

International Nuclear Information System (INIS)

Omura, Y.; Matsumoto, H.

1987-01-01

Competing processes of whistler mode and electrostatic mode instabilities induced by an electron beam are studied by a linear growth rate analysis and by an electromagnetic particle simulation. In addition to a background cold plasma we assumed an electron beam drifting along a static magnetic field. We studied excitation of whistler and electrostatic mode waves in the direction of the static magnetic field. We first calculated linear growth rates for the whistler mode and electrostatic mode instabilities, assuming various possible parameters in the equatorial magnetosphere. We found that the growth rate for the electrostatic instability is always larger than that of the whistler mode instability. A short simulation run with a monoenergetic electron beam demonstrates that a monoenergetic beam can hardly give energy to whistler mode waves as a result of competition with faster growing electrostatic waves, because the beam electrons are trapped and diffused by the electrostatic waves, and hence the growth rates for whistler mode waves become very small. A long simulation run starting with a warm electron beam demonstrates that whistler mode waves are excited in spite of the small growth rates and the coexisting quasi-linear electrostatic diffusion process

Quantitative study of the trapped particle bunching instability in Langmuir waves

International Nuclear Information System (INIS)

Hara, Kentaro; Boyd, Iain D.; Chapman, Thomas; Joseph, Ilon; Berger, Richard L.; Banks, Jeffrey W.; Brunner, Stephan

2015-01-01

The bunching instability of particles trapped in Langmuir waves is studied using Vlasov simulations. A measure of particle bunching is defined and used to extract the growth rate from numerical simulations, which are compared with theory [Dodin et al., Phys. Rev. Lett. 110, 215006 (2013)]. In addition, the general theory of trapped particle instability in 1D is revisited and a more accurate description of the dispersion relation is obtained. Excellent agreement between numerical and theoretical predictions of growth rates of the bunching instability is shown over a range of parameters

Quantitative study of the trapped particle bunching instability in Langmuir waves

Energy Technology Data Exchange (ETDEWEB)

Hara, Kentaro, E-mail: kenhara@umich.edu; Boyd, Iain D. [Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109 (United States); Chapman, Thomas; Joseph, Ilon; Berger, Richard L. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Banks, Jeffrey W. [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States); Brunner, Stephan [Centre de Recherches en Physique des Plasmas, Association Euratom-Confederation Suisse, Ecole Polytechnique Fédérale de Lausanne, CRPP-PPB, CH-1015 Lausanne (Switzerland)

2015-02-15

The bunching instability of particles trapped in Langmuir waves is studied using Vlasov simulations. A measure of particle bunching is defined and used to extract the growth rate from numerical simulations, which are compared with theory [Dodin et al., Phys. Rev. Lett. 110, 215006 (2013)]. In addition, the general theory of trapped particle instability in 1D is revisited and a more accurate description of the dispersion relation is obtained. Excellent agreement between numerical and theoretical predictions of growth rates of the bunching instability is shown over a range of parameters.

Temperature-gradient instability induced by conducting end walls

International Nuclear Information System (INIS)

Berk, H.L.; Ryutov, D.D.; Tsidulko, Yu.A.

1990-04-01

A new rapidly growing electron temperature gradient instability is found for a plasma in contact with a conducting wall. The linear instability analysis is presented and speculations are given for its nonlinear consequences. This instability illustrates that conducting walls can produce effects that are detrimental to plasma confinement. This mode should be of importance in open-ended systems including astrophysical plasmas, mirror machines and at the edge of tokamaks where field lines are open and are connected to limiters or divertors. 16 refs., 2 figs

Lessons from non-Abelian plasma instabilities in two spatial dimensions

International Nuclear Information System (INIS)

Arnold, Peter; Leang, P.-S.

2007-01-01

Plasma instabilities can play a fundamental role in quark-gluon plasma equilibration in the high energy (weak coupling) limit. Early simulations of the evolution of plasma instabilities in non-Abelian gauge theory, performed in one spatial dimension, found behavior qualitatively similar to traditional QED plasmas. Later simulations of the fully three-dimensional theory found different behavior, unlike traditional QED plasmas. To shed light on the origin of this difference, we study the intermediate case of two spatial dimensions. Depending on how the 'two-dimensional' theory is formulated, we can obtain either behavior

Uncertainty Instability Risk Analysis of High Concrete Arch Dam Abutments

Directory of Open Access Journals (Sweden)

Xin Cao

2017-01-01

Full Text Available The uncertainties associated with concrete arch dams rise with the increased height of dams. Given the uncertainties associated with influencing factors, the stability of high arch dam abutments as a fuzzy random event was studied. In addition, given the randomness and fuzziness of calculation parameters as well as the failure criterion, hazard point and hazard surface uncertainty instability risk ratio models were proposed for high arch dam abutments on the basis of credibility theory. The uncertainty instability failure criterion was derived through the analysis of the progressive instability failure process on the basis of Shannon’s entropy theory. The uncertainties associated with influencing factors were quantized by probability or possibility distribution assignments. Gaussian random theory was used to generate random realizations for influence factors with spatial variability. The uncertainty stability analysis method was proposed by combining the finite element analysis and the limit equilibrium method. The instability risk ratio was calculated using the Monte Carlo simulation method and fuzzy random postprocessing. Results corroborate that the modeling approach is sound and that the calculation method is feasible.

Theory of resistivity-gradient-driven turbulence

International Nuclear Information System (INIS)

Garcia, L.; Carreras, B.A.; Diamond, P.H.; Callen, J.D.

1984-10-01

A theory of the nonlinear evolution and saturation of resistivity-driven turbulence, which evolves from linear rippling instabilities, is presented. The nonlinear saturation mechanism is identified both analytically and numerically. Saturation occurs when the turbulent diffusion of the resistivity is large enough so that dissipation due to parallel electron thermal conduction balances the nonlinearly modified resistivity gradient driving term. The levels of potential, resistivity, and density fluctuations at saturation are calculated. A combination of computational modeling and analytic treatment is used in this investigation

Fingerprints of dynamical instabilities

International Nuclear Information System (INIS)

Chomaz, Ph.; Colonna, M.; Guarnera, A.

1993-01-01

It is explained why any reduced descriptions, such as mean field approximation, are stochastic in nature. It is shown that the introduction of this stochastic dynamics leads to a predictive theory in a statistical sens whatever the individual trajectories are characterized by the occurrence of bifurcations, instabilities or phase transitions. Concerning nuclear matter, the spinodal instability is discussed. In such a critical situation, the possibility to replace the stochastic part of the collision integral in the Boltzmann-Langevin model by the numerical noise associated with the finite number of test particles in ordinary BUU treatment is studied. It is shown that the fingerprints of these instabilities are kept during the evolution because of the relatively long recombination time compared with the typical time scales imposed by the Coulomb repulsion and the possible collective expansion. (author) 5 refs., 12 figs

Non-linear theory of elasticity and optimal design

CERN Document Server

Ratner, LW

2003-01-01

In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

Ab initio calculations of ideal strength and lattice instability in W-Ta and W-Re alloys

Science.gov (United States)

Yang, Chaoming; Qi, Liang

2018-01-01

An important theoretical criterion to evaluate the ductility of metals with a body-centered cubic (bcc) lattice is the mechanical failure mode of their perfect crystals under tension along ; directions. When the tensile stress reaches the ideal tensile strength, the pure W crystal fails by a cleavage fracture along the {100 } plane so that it is intrinsically brittle. To discover the strategy to improve its ductility, we performed density functional theory and density functional perturbation theory calculations to study the ideal tensile strength and the lattice instability under tension for both W-Ta and W-Re alloys. Anisotropic linear elastic fracture mechanics (LEFM) theory and Rice's criterion were also applied to analyze the mechanical instability at the crack tip under tension based on the competition between cleavage propagation and dislocation emission. The results show that the intrinsic ductility can be achieved in both W-Ta and W-Re, however, by different mechanisms. Even though W-Ta alloys with low Ta concentrations are still intrinsically brittle, the intrinsic ductility of W-Ta alloys with high Ta concentrations is promoted by elastic shear instability before the cleavage failure. The intrinsic ductility of W-Re alloys is produced by unstable transverse phonon waves before the cleavage failure, and the corresponding phonon mode is related to the generation of 1/2 {2 ¯11 } dislocation in bcc crystals. The ideal tensile calculations, phonon analyses, and anisotropic LEFM examinations are mutually consistent in the evaluation of intrinsic ductility. These results bring us physical insights on the ductility-brittle mechanisms of W alloys under extreme stress conditions.

Numerical computation of linear instability of detonations