Nonlinear dynamo action in a precessing cylindrical container.
Nore, C; Léorat, J; Guermond, J-L; Luddens, F
2011-07-01
It is numerically demonstrated by means of a magnetohydrodynamics code that precession can trigger the dynamo effect in a cylindrical container. When the Reynolds number, based on the radius of the cylinder and its angular velocity, increases, the flow, which is initially centrosymmetric, loses its stability and bifurcates to a quasiperiodic motion. This unsteady and asymmetric flow is shown to be capable of sustaining dynamo action in the linear and nonlinear regimes. The magnetic field thus generated is unsteady and quadrupolar. These numerical evidences of dynamo action in a precessing cylindrical container may be useful for an experiment now planned at the Dresden sodium facility for dynamo and thermohydraulic studies in Germany.
A magnetic betelgeuse? Numerical simulations of non-linear dynamo action
DEFF Research Database (Denmark)
Dorch, S. B. F.
2004-01-01
question regarding the nature of Betelgeuse and supergiants in general is whether these stars may be magnetically active. If so, that may in turn also contribute to their variability. By performing detailed numerical simulations, I find that both linear kinematic and non-linear dynamo action are possible...... and that the non-linear magnetic field saturates at a value somewhat below equipartition: in the linear regime there are two modes of dynamo action....
Herault, J; Rincon, F; Cossu, C; Lesur, G; Ogilvie, G I; Longaretti, P-Y
2011-09-01
The nature of dynamo action in shear flows prone to magnetohydrodynamc instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and nonaxisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large-scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understanding the transitional and statistical properties of subcritical magnetorotational turbulence.
A magnetic betelgeuse? Numerical simulations of non-linear dynamo action
DEFF Research Database (Denmark)
Dorch, S. B. F.
2004-01-01
Betelgeuse is an example of a cool super-giant displaying brightness fluctuations and irregular surface structures. Simulations by Freytag et al. (2002) of the convective envelope of the star have shown that the fluctuations in the star's luminosity may be caused by giant cell convection. A related...... question regarding the nature of Betelgeuse and supergiants in general is whether these stars may be magnetically active. If so, that may in turn also contribute to their variability. By performing detailed numerical simulations, I find that both linear kinematic and non-linear dynamo action are possible...... and that the non-linear magnetic field saturates at a value somewhat below equipartition: in the linear regime there are two modes of dynamo action....
Properties of Nonlinear Dynamo Waves
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Nonlinear MHD dynamo operating at equipartition
DEFF Research Database (Denmark)
Archontis, V.; Dorch, Bertil; Nordlund, Åke
2007-01-01
Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......-equipartition and a turbulent state. The generation and evolution of such strong magnetic fields is relevant for the understanding of dynamo action that occurs in stars and other astrophysical objects. Aims.We study the mode of operation of this dynamo, in the linear and non-linear saturation regimes. We also consider...... the effect of varying the magnetic and fluid Reymolds number on the non-linear behaviour of the system. Methods.We perform three-dimensional non-linear MHD simulations and visualization using a high resolution numerical scheme. Results.We find that this dynamo has a high growth rate in the linear regime...
Axial dipolar dynamo action in the Taylor-Green vortex.
Krstulovic, Giorgio; Thorner, Gentien; Vest, Julien-Piera; Fauve, Stephan; Brachet, Marc
2011-12-01
We present a numerical study of the magnetic field generated by the Taylor-Green vortex. We show that periodic boundary conditions can be used to mimic realistic boundary conditions by prescribing the symmetries of the velocity and magnetic fields. This gives insight into some problems of central interest for dynamos: the possible effect of velocity fluctuations on the dynamo threshold, and the role of boundary conditions on the threshold and on the geometry of the magnetic field generated by dynamo action. In particular, we show that an axial dipolar dynamo similar to the one observed in a recent experiment can be obtained with an appropriate choice of the symmetries of the magnetic field. The nonlinear saturation is studied and a simple model explaining the magnetic Prandtl number dependence of the super- and subcritical nature of the dynamo transition is given.
Bifurcations and dynamo action in a Taylor Green flow
Dubrulle, B.; Blaineau, P.; Mafra Lopes, O.; Daviaud, F.; Laval, J.-P.; Dolganov, R.
2007-08-01
We report successive bifurcations in direct numerical simulations (DNSs) of a Taylor-Green flow, in both a hydro- and a magneto-hydrodynamic case. Hydrodynamic bifurcations occur in between different metastable states with different dynamo action, and are triggered by the numerical noise. The various states encountered range from stationary to chaotic or turbulent through possible oscillatory states. The corresponding sequence of bifurcations is reminiscent of the sequence obtained in the von Karman (VK) flow, at aspect ratio Γ=2 (Nore et al 2003 J. Fluid Mech. 477 51). We then use kinematic simulations to compute the dynamo thresholds of the different metastable states. A more detailed study of the turbulent state reveals the existence of two windows of dynamo action. Stochastic numerical simulations are then used to mimic the influence of turbulence on the dynamo threshold of the turbulent state. We show that the dynamo threshold is increased (respectively decreased) by the presence of large scale (resp. small scale) turbulent velocity fluctuations. Finally, DNSs of the magneto-hydrodynamic equations are used to explore the linear and nonlinear stage of the dynamo instability. In the linear stage, we show that the magnetic field favours the bifurcation from the basic state directly towards the turbulent or chaotic stable state. The magnetic field can also temporarily stabilize a metastable state, resulting in cycles of dynamo action, with different Lyapunov exponents. The critical magnetic Reynolds number for dynamo action is found to increase strongly with the Reynolds number. Finally, we provide a preliminary study of the saturation regime above the dynamo threshold. At large magnetic Prandtl number, we have observed two main types of saturations, in agreement with an analytical prediction of Leprovost and Dubrulle (2005 Eur. Phys. J. B 44 395): (i) intermittent dynamo, with vanishing most probable value of the magnetic energy; (ii) dynamo with non vanishing
Magnetic Helicities and Dynamo Action in Magneto-rotational Turbulence
Bodo, G.; Cattaneo, F.; Mignone, A.; Rossi, P.
2017-07-01
We examine the relationship between magnetic flux generation, taken as an indicator of large-scale dynamo action, and magnetic helicity, computed as an integral over the dynamo volume, in a simple dynamo. We consider dynamo action driven by magneto-rotational turbulence (MRT) within the shearing-box approximation. We consider magnetically open boundary conditions that allow a flux of helicity in or out of the computational domain. We circumvent the problem of the lack of gauge invariance in open domains by choosing a particular gauge—the winding gauge—that provides a natural interpretation in terms of the average winding number of pairwise field lines. We use this gauge precisely to define and measure the helicity and the helicity flux for several realizations of dynamo action. We find in these cases that the system as a whole does not break reflectional symmetry and that the total helicity remains small even in cases when substantial magnetic flux is generated. We find no particular connection between the generation of magnetic flux and the helicity or the helicity flux through the boundaries. We suggest that this result may be due to the essentially nonlinear nature of the dynamo processes in MRT.
Universal nonlinear small-scale dynamo.
Beresnyak, A
2012-01-20
We consider astrophysically relevant nonlinear MHD dynamo at large Reynolds numbers (Re). We argue that it is universal in a sense that magnetic energy grows at a rate which is a constant fraction C(E) of the total turbulent dissipation rate. On the basis of locality bounds we claim that this "efficiency of the small-scale dynamo", C(E), is a true constant for large Re and is determined only by strongly nonlinear dynamics at the equipartition scale. We measured C(E) in numerical simulations and observed a value around 0.05 in the highest resolution simulations. We address the issue of C(E) being small, unlike the Kolmogorov constant which is of order unity.
Experimental realization of dynamo action: present status and prospects
Giesecke, Andre; Gundrum, Thomas; Gerbeth, Gunter; Nore, Caroline; Leorat, Jacques
2012-01-01
In the last decades, the experimental study of dynamo action has made great progress. However, after the dynamo experiments in Karlsruhe and Riga, the von-Karman-Sodium (VKS) dynamo is only the third facility that has been able to demonstrate fluid flow driven self-generation of magnetic fields in a laboratory experiment. Further progress in the experimental examination of dynamo action is expected from the planned precession driven dynamo experiment that will be designed in the framework of the liquid sodium facility DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies). In this paper, we briefly present numerical models of the VKS dynamo that demonstrate the close relation between the axisymmetric field observed in that experiment and the soft iron material used for the flow driving impellers. We further show recent results of preparatory water experiments and design studies related to the precession dynamo and delineate the scientific prospects for the final set-up.
Constraints on dynamo action in plasmas
Helander, P.; Strumik, M.; Schekochihin, A. A.
2016-12-01
Upper bounds are derived on the amount of magnetic energy that can be generated by dynamo action in collisional and collisionless plasmas with and without external forcing. A hierarchy of mathematical descriptions is considered for the plasma dynamics: ideal magnetohydrodynamics (MHD), visco-resistive MHD, the double-adiabatic theory of Chew, Goldberger and Low (CGL), kinetic MHD and other kinetic models. It is found that dynamo action is greatly constrained in models where the magnetic moment of any particle species is conserved. In the absence of external forcing, the magnetic energy then remains small at all times if it is small in the initial state. In other words, a small `seed' magnetic field cannot be amplified significantly, regardless of the nature of flow, as long as the collision frequency and gyroradius are small enough to be negligible. A similar conclusion also holds if the system is subject to external forcing as long as this forcing conserves the magnetic moment of at least one plasma species and does not greatly increase the total energy of the plasma (i.e. in practice, is subsonic). Dynamo action therefore always requires collisions or some small-scale kinetic mechanism for breaking the adiabatic invariance of the magnetic moment.
Kinematic dynamo action in square and hexagonal patterns.
Favier, B; Proctor, M R E
2013-11-01
We consider kinematic dynamo action in rapidly rotating Boussinesq convection just above onset. The velocity is constrained to have either a square or a hexagonal pattern. For the square pattern, large-scale dynamo action is observed at onset, with most of the magnetic energy being contained in the horizontally averaged component. As the magnetic Reynolds number increases, small-scale dynamo action becomes possible, reducing the overall growth rate of the dynamo. For the hexagonal pattern, the breaking of symmetry between up and down flows results in an effective pumping velocity. For intermediate rotation rates, this additional effect can prevent the growth of any mean-field dynamo, so that only a small-scale dynamo is eventually possible at large enough magnetic Reynolds number. For very large rotation rates, this pumping term becomes negligible, and the dynamo properties of square and hexagonal patterns are qualitatively similar. These results hold for both perfectly conducting and infinite magnetic permeability boundary conditions.
Constraints on dynamo action in plasmas
Helander, P; Schekochihin, A A
2016-01-01
Upper bounds are derived on the amount of magnetic energy that can be generated by dynamo action in collisional and collisionless plasmas with and without external forcing. A hierarchy of mathematical descriptions is considered for the plasma dynamics: ideal MHD, visco-resistive MHD, the double-adiabatic theory of Chew, Goldberger and Low (CGL), kinetic MHD, and other kinetic models. It is found that dynamo action is greatly constrained in models where the magnetic moment of any particle species is conserved. In the absence of external forcing, the magnetic energy then remains small at all times if it is small in the initial state. In other words, a small "seed" magnetic field cannot be amplified significantly, regardless of the nature of flow, as long as the collision frequency and gyroradius are small enough to be negligible. A similar conclusion also holds if the system is subject to external forcing as long as this forcing conserves the magnetic moment of at least one plasma species and does not greatly i...
Magnetic dynamo action at low magnetic Prandtl numbers.
Malyshkin, Leonid M; Boldyrev, Stanislav
2010-11-19
Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid-metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum.
Nonlinear regimes in mean-field full-sphere dynamo
Pipin, V V
2016-01-01
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\\odot}$ rotating with period of 10 days. The differential rotation law was estimated using the mean-field hydrodynamic and heat transport equations. For the intermediate parameter of the turbulent magnetic Reynolds number, $Pm_{T}=3$ we found the oscillating dynamo regimes with period about 40Yr. The higher $Pm_{T}$ results to longer dynamo periods. The meridional circulation has one cell per hemisphere. It is counter-clockwise in the Northen hemisphere. The amplitude of the flow at the surface around 1 m/s. Tne models with regards for meridional circulation show the anti-symmetric relative to equator magnetic field. If the large-scale flows is fixed we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the $\\alpha$effect. The change of dynamo regime occurs because of the non-axisymmetric non-linear $\\alpha$-effect. The situation pe...
Nonlinear Magnetic Diffusion and Magnetic Helicity Transport in Galactic Dynamos
Kleeorin, N; Rogachevskii, I; Sokoloff, D D
2003-01-01
We have extended our previous mean-field galactic dynamo model which included algebraic and dynamic alpha nonlinearities (Kleeorin et al., A&A, v. 387, 453, 2002), to include also a quenching of turbulent diffusivity. We readily obtain equilibrium states for the large-scale magnetic field in the local disc dynamo model, and these fields have strengths that are comparable to the equipartition field strength. We find that the algebraic nonlinearity alone (i.e. quenching of both the alpha effect and turbulent magnetic diffusion) cannot saturate the growth of the mean magnetic field; only the combined effect of algebraic and dynamic nonlinearities can limit the growth of the mean magnetic field. However, in contrast to our earlier work without quenching of the turbulent diffusivity, we cannot now find satisfactory solutions in the no-z approximation to the axisymmetric galactic dynamo problem.
Towards understanding dynamo action in M dwarfs
Shulyak, D; Kitchatinov, L; Moss, D
2015-01-01
Recent progress in observational studies of magnetic activity in M dwarfs urgently requires support from ideas of stellar dynamo theory. We propose a strategy to connect observational and theoretical studies. In particular, we suggest four magnetic configurations that appear relevant to dwarfs from the viewpoint of the most conservative version of dynamo theory, and discuss observational tests to identify the configurations observationally. As expected, any such identification contains substantial uncertainties. However the situation in general looks less pessimistic than might be expected. Several identifications between the phenomenology of individual stars and dynamo models are suggested. Remarkably, all models discussed predict substantial surface magnetic activity at rather high stellar latitudes. This prediction looks unexpected from the viewpoint of our experience observing the Sun (which of course differs in some fundamental ways from these late-type dwarfs). We stress that a fuller understanding of t...
Direct numerical simulations of helical dynamo action: MHD and beyond
Directory of Open Access Journals (Sweden)
D. O. Gómez
2004-01-01
Full Text Available Magnetohydrodynamic dynamo action is often invoked to explain the existence of magnetic fields in several astronomical objects. In this work, we present direct numerical simulations of MHD helical dynamos, to study the exponential growth and saturation of magnetic fields. Simulations are made within the framework of incompressible flows and using periodic boundary conditions. The statistical properties of the flow are studied, and it is found that its helicity displays strong spatial fluctuations. Regions with large kinetic helicity are also strongly concentrated in space, forming elongated structures. In dynamo simulations using these flows, we found that the growth rate and the saturation level of magnetic energy and magnetic helicity reach an asymptotic value as the Reynolds number is increased. Finally, extensions of the MHD theory to include kinetic effects relevant in astrophysical environments are discussed.
Mean-field dynamo action in renovating shearing flows.
Kolekar, Sanved; Subramanian, Kandaswamy; Sridhar, S
2012-08-01
We study mean-field dynamo action in renovating flows with finite and nonzero correlation time (τ) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and nonhelical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly nonhelical, then such mean-field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval τ. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the α(2)Ω dynamo, in the small τ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean-field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.
Dynamo Action and Magnetic Cycles in F-type Stars
Augustson, Kyle C.; Brun, Allan Sacha; Toomre, Juri
2013-11-01
Magnetic activity and differential rotation are commonly observed features on main-sequence F-type stars. We seek to make contact with such observations and to provide a self-consistent picture of how differential rotation and magnetic fields arise in the interiors of these stars. The three-dimensional magnetohydrodynamic anelastic spherical harmonic code is employed to simulate global-scale convection and dynamo processes in a 1.2 M ⊙ F-type star at two rotation rates. The simulations are carried out in spherical shells that encompass most of the convection zone and a portion of the stably stratified radiative zone below it, allowing us to explore the effects a stable zone has upon the morphology of the global-scale magnetic fields. We find that dynamo action with a high degree of time variation occurs in the star rotating more rapidly at 20 Ω⊙, with the polarity of the mean field reversing on a timescale of about 1600 days. Between reversals, the magnetic energy rises and falls with a fairly regular period, with three magnetic energy cycles required to complete a reversal. The magnetic energy cycles and polarity reversals arise due to a linking of the polar-slip instability in the stable region and dynamo action present in the convection zone. For the more slowly rotating case (10 Ω⊙), persistent wreaths of magnetism are established and maintained by dynamo action. Compared to their hydrodynamic progenitors, the dynamo states here involve a marked reduction in the exhibited latitudinal differential rotation, which also vary during the course of a cycle.
On the saturation of astrophysical dynamos
DEFF Research Database (Denmark)
Dorch, Bertil; Archontis, Vasilis
2004-01-01
In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo's mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate in the li......In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo's mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate...
Buoyant Magnetic Loops Generated by Global Convective Dynamo Action
Nelson, Nicholas J; Brun, A Sacha; Miesch, Mark S; Toomre, Juri
2012-01-01
Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much larger values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength o...
On dynamo action in the giant star Pollux : first results
Palacios, A
2013-01-01
We present preliminary results of a 3D MHD simulation of the convective envelope of the giant star Pollux for which the rotation period and the magnetic ?eld intensity have been measured from spectroscopic and spectropolarimetric observations. This giant is one of the ?rst single giants with a detected magnetic ?eld, and the one with the weakest ?eld so far. Our aim is to understand the development and the action of the dynamo in its extended convective envelope.
Numerical studies of dynamo action in a turbulent shear flow
Singh, Nishant K
2013-01-01
We perform numerical experiments to study the shear dynamo problem where we look for the growth of large-scale magnetic field due to non-helical stirring at small scales in a background linear shear flow, in previously unexplored parameter regimes. We demonstrate the large-scale dynamo action in the limit when the fluid Reynolds number (Re) is below unity whereas the magnetic Reynolds number (Rem) is above unity; the exponential growth rate scales linearly with shear, which is consistent with earlier numerical works. The limit of low Re is particularly interesting, as seeing the dynamo action in this limit would provide enough motivation for further theoretical investigations, which may focus the attention to this analytically more tractable limit of Re 1. We also perform simulations in the limits when, (i) both (Re, Rem) 1 & Rem < 1, and compute all components of the turbulent transport coefficients (\\alpha_{ij} and \\eta_{ij}) using the test-field method. A reasonably good agreement is seen between ...
Convective dynamo action in a spherical shell: symmetries and modulation
Raynaud, Raphaël
2016-01-01
We consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, Type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude, for other parameters, the modulation is of Type 2, where the amplitude is significantly affected (leading to grand minima in activity) without significant changes in symmetry. Most importantly, we identify the presence of "supermodulation" in the solutions, where the activity switches chaotically between Type 1 and Type 2 modulation, this is believed to be an important process in solar activity.
Bhat, Pallavi; Blackman, Eric G
2016-01-01
We study the dynamo generation (exponential growth) of large scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal ($x$-$y$) averaging, we demonstrate the presence of large scale fields when either horizontal or vertical ($y$-$z$) averaging is employed. By computing planar averaged fields and power spectra, we find large scale dynamo action in the early MRI growth phase---a previously unidentified feature. Fast growing horizontal low modes and fiducial vertical modes over a narrow range of wave numbers amplify these planar averaged fields in the MRI growth phase, before turbulence sets in. The large scale field growth requires linear fluctuations but not nonlinear turbulence (as defined by mode-mode coupling) and grows as a direct global mode of the MRI. Only by vertical averaging, can it be shown that the growth of horizontal low wavenumber MRI modes directly feed-back to the initial vertica...
Simulations of core convection in rotating A-type stars: Magnetic dynamo action
Brun, A S; Toomre, J; Brun, Allan Sacha; Browning, Matthew K.; Toomre, Juri
2005-01-01
Core convection and dynamo activity deep within rotating A-type stars of 2 solar masses are studied with 3--D nonlinear simulations. Our modeling considers the inner 30% by radius of such stars, thus capturing within a spherical domain the convective core and a modest portion of the surrounding radiative envelope. The MHD equations are solved using the ASH code to examine turbulent flows and magnetic fields, both of which exhibit intricate time dependence. By introducing small seed magnetic fields into our progenitor hydrodynamic models rotating at one and four times the solar rate, we assess here how the vigorous convection can amplify those fields and sustain them against ohmic decay. Dynamo action is indeed realized, ultimately yielding magnetic fields that are in energy equipartion with the flow. Such magnetism reduces the differential rotation obtained in the progenitors, partly by Maxwell stresses that transport angular momentum poleward and oppose the Reynolds stresses in the latitudinal balance. In co...
Dynamo action at low magnetic Prandtl numbers: mean flow versus fully turbulent motions
Energy Technology Data Exchange (ETDEWEB)
Ponty, Y [CNRS UMR6202, Laboratoire Cassiopee, Observatoire de la Cote d' Azur, BP 4229, Nice Cedex 04 (France); Mininni, P D [NCAR, P O Box 3000, Boulder Colorado 80307-3000 (United States); Pinton, J-F [CNRS UMR5672, Laboratoire de Physique, Ecole Normale Superieure de Lyon, 46 Allee d' Italie, 69007 Lyon (France); Politano, H [CNRS UMR6202, Laboratoire Cassiopee, Observatoire de la Cote d' Azur, BP 4229, Nice Cedex 04 (France); Pouquet, A [NCAR, P O Box 3000, Boulder Colorado 80307-3000 (United States)
2007-08-15
We compute numerically the threshold for dynamo action in Taylor-Green (TG) swirling flows. Kinematic dynamo calculations, for which the flow field is fixed to its time average, are compared to dynamical runs, with the Navier-Stokes and induction equations jointly solved. The dynamo instability for the kinematic calculations is found to have two branches. The dynamical dynamo threshold at low Reynolds numbers lies within the low branch, while at high Reynolds numbers it gets closer to the high branch. Based on these results, the effect of the mean flow and of the turbulent fluctuations in TG dynamos are discussed.
Bhat, Pallavi; Ebrahimi, Fatima; Blackman, Eric G.
2016-10-01
We study the dynamo generation (exponential growth) of large-scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal (x-y) averaging, we also demonstrate the presence of large-scale fields when vertical (y-z) averaging is employed instead. By computing space-time planar averaged fields and power spectra, we find large-scale dynamo action in the early MRI growth phase - a previously unidentified feature. Non-axisymmetric linear MRI modes with low horizontal wavenumbers and vertical wavenumbers near that of expected maximal growth, amplify the large-scale fields exponentially before turbulence and high wavenumber fluctuations arise. Thus the large-scale dynamo requires only linear fluctuations but not non-linear turbulence (as defined by mode-mode coupling). Vertical averaging also allows for monitoring the evolution of the large-scale vertical field and we find that a feedback from horizontal low wavenumber MRI modes provides a clue as to why the large-scale vertical field sustains against turbulent diffusion in the non-linear saturation regime. We compute the terms in the mean field equations to identify the individual contributions to large-scale field growth for both types of averaging. The large-scale fields obtained from vertical averaging are found to compare well with global simulations and quasi-linear analytical analysis from a previous study by Ebrahimi & Blackman. We discuss the potential implications of these new results for understanding the large-scale MRI dynamo saturation and turbulence.
Effect of small scale motions on dynamo actions generated by the Beltrami-like flows
Energy Technology Data Exchange (ETDEWEB)
Xu, Mingtian, E-mail: mingtian@sdu.edu.cn
2016-08-12
The geodynamo and solar dynamo are driven by the turbulent flows which involve motions of various scales. Of particular interest is what role is played by the small scale motions in these dynamos. In this paper, the integral equation approach is employed to investigate the effect of the small scale motions on dynamo actions driven by multiscale Beltrami-like flows in a cylindrical vessel. The result shows that some small scale motions can trigger a transition of a dynamo from a steady to an unsteady state. Our results also show that when the poloidal components of the small and large scale flows share the same direction in the equatorial plane, the small scale flows have more positive or less detrimental effect on the onsets of the dynamo actions in comparison with the case that the poloidal components have different directions. These findings shed light on the effect of the small scale turbulence on dynamo actions. - Highlights: • Dynamo actions driven by multiscale Beltrami-like flows are investigated. • Some small scale motions induce transition of dynamo from steady to unsteady state. • Direction of small scale poloidal flow has a significant effect on dynamo threshold.
Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo
Directory of Open Access Journals (Sweden)
R. Hide
1997-01-01
Full Text Available In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions. New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenching by nonlineax effects of current fluctuations in a self-exciting homopolar dynamo with its single Faraday disk driven into rotation with angular speed y(τ (where τ denotes time by a steady applied couple. The armature of an electric motor connected in series with the coil of the dynamo is driven into rotation' with angular speed z(τ by a torque xf (x due to Lorentz forces associated with the electric current x(τ in the system (just as certain parts of the spectrum of eddies within the liquid outer core are generated largely by Lorentz forces associated with currents generated by the self-exciting magnetohydrodynamic (MHD geodynamo. The discovery is based on bifurcation analysis supported by computational studies of the following (mathematically novel autonomous set of nonlinear ordinary differential equations: dx/dt = x(y - 1 - βzf(x, dy/dt = α(1 - x² - κy, dz/dt = xf (x -λz, where f (x = 1 - ε + εσx, in cases when the dimensionless parameters (α, β, κ, λ, σ are all positive and 0 ≤ ε ≤ 1. Within those regions of (α, β, κ, λ, σ parameter space where the applied couple, as measured by α, is strong enough for persistent dynamo action (i.e. x ≠ 0 to occur at all, there are in general extensive regions where x(τ exhibits large amplitude regular or irregular (chaotic fluctuations. But these fluctuating r
Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo
Hide, R.
In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions. New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenching by nonlineax effects of current fluctuations in a self-exciting homopolar dynamo with its single Faraday disk driven into rotation with angular speed y(τ) (where τ denotes time) by a steady applied couple. The armature of an electric motor connected in series with the coil of the dynamo is driven into rotation' with angular speed z(τ) by a torque xf (x) due to Lorentz forces associated with the electric current x(τ) in the system (just as certain parts of the spectrum of eddies within the liquid outer core are generated largely by Lorentz forces associated with currents generated by the self-exciting magnetohydrodynamic (MHD) geodynamo). The discovery is based on bifurcation analysis supported by computational studies of the following (mathematically novel) autonomous set of nonlinear ordinary differential equations: dx/dt = x(y - 1) - βzf(x), dy/dt = α(1 - x²) - κy, dz/dt = xf (x) -λz, where f (x) = 1 - ɛ + ɛσx, in cases when the dimensionless parameters (α, β, κ, λ, σ) are all positive and 0 ≤ ɛ ≤ 1. Within those regions of (α, β, κ, λ, σ) parameter space where the applied couple, as measured by α, is strong enough for persistent dynamo action (i.e. x ≠ 0) to occur at all, there are in general extensive regions where x(τ) exhibits large amplitude regular or irregular (chaotic) fluctuations. But these fluctuating régimes shrink in size as increases
Large-scale dynamo action driven by velocity shear and rotating convection.
Hughes, David W; Proctor, Michael R E
2009-01-30
By incorporating a large-scale shear flow into turbulent rotating convection, we show that a sufficiently strong shear can promote dynamo action in flows that are otherwise nondynamos. Our results are consistent with a dynamo driven either by the shear-current effect or by a fluctuating alpha effect interacting with the shear, but not with either a classical alpha(2) or alpha omega dynamo.
Dynamo action in dissipative, forced, rotating MHD turbulence
Shebalin, John V.
2016-06-01
Magnetohydrodynamic (MHD) turbulence is an inherent feature of large-scale, energetic astrophysical and geophysical magnetofluids. In general, these are rotating and are energized through buoyancy and shear, while viscosity and resistivity provide a means of dissipation of kinetic and magnetic energy. Studies of unforced, rotating, ideal (i.e., non-dissipative) MHD turbulence have produced interesting results, but it is important to determine how these results are affected by dissipation and forcing. Here, we extend our previous work and examine dissipative, forced, and rotating MHD turbulence. Incompressibility is assumed, and finite Fourier series represent turbulent velocity and magnetic field on a 643 grid. Forcing occurs at an intermediate wave number by a method that keeps total energy relatively constant and allows for injection of kinetic and magnetic helicity. We find that 3-D energy spectra are asymmetric when forcing is present. We also find that dynamo action occurs when forcing has either kinetic or magnetic helicity, with magnetic helicity injection being more important. In forced, dissipative MHD turbulence, the dynamo manifests itself as a large-scale coherent structure that is similar to that seen in the ideal case. These results imply that MHD turbulence, per se, may play a fundamental role in the creation and maintenance of large-scale (i.e., dipolar) stellar and planetary magnetic fields.
A simplified model of collision-driven dynamo action in small bodies
Wei, Xing
2013-01-01
We investigate numerically the self-sustained dynamo action in a spinning sphere whose sense of rotation reverses periodically. This system serves as a simple model of a dynamo in small bodies powered by frequent collisions. It is found that dynamo action is possible in some intervals of collision rates. At high Ekman numbers the laminar spin-up flow is helical in the boundary layers and the Ekman circulation together with the azimuthal shear powers the dynamo action. At low Ekman number a non-axisymmetric instability helps the dynamo action. The intermittency of magnetic field occurs at low Ekman number. A lower bound of magnetic energy is numerically obtained, and the space-averaged field in the fluid core and the surface field of a small body are roughly estimated.
Numerical insights into magnetic dynamo action in a turbulent regime
Kenjeres, S.; Hanjalic, K.
2007-01-01
We report on hybrid numerical simulations of a turbulent magnetic dynamo. The simulated set-up mimics the Riga dynamo experiment characterized by Re ≈ 3.5 × 106 and (Gailitis et al 2000 Phys. Rev. Lett. 84 4365–8). The simulations were performed by a simultaneous fully coupled solution of the trans
Facilitating dynamo action via control of large-scale turbulence.
Limone, A; Hatch, D R; Forest, C B; Jenko, F
2012-12-01
The magnetohydrodynamic dynamo effect is considered to be the major cause of magnetic field generation in geo- and astrophysical systems. Recent experimental and numerical results show that turbulence constitutes an obstacle to dynamos; yet its role in this context is not totally clear. Via numerical simulations, we identify large-scale turbulent vortices with a detrimental effect on the amplification of the magnetic field in a geometry of experimental interest and propose a strategy for facilitating the dynamo instability by manipulating these detrimental "hidden" dynamics.
The combined effect of precession and convection on the dynamo action
Wei, Xing
2016-01-01
To understand the generation of the Earth's and planetary magnetic fields, we investigate numerically the combined effect of precession and convection on the dynamo action in a spherical shell. The convection alone, the precession alone and the combined effect of convection and precession are studied at the low Ekman number at which the precessing flow is already unstable. The key result is that although the precession or convection alone is not strong to support the dynamo action the combined effect of precession and convection can support the dynamo action because of the resonance of precessional and convective instabilities. This result may interpret why the geodynamo maintains for such a long history compared to the Martian dynamo.
Wave-driven dynamo action in spherical magnetohydrodynamic systems.
Reuter, K; Jenko, F; Tilgner, A; Forest, C B
2009-11-01
Hydrodynamic and magnetohydrodynamic numerical studies of a mechanically forced two-vortex flow inside a sphere are reported. The simulations are performed in the intermediate regime between the laminar flow and developed turbulence, where a hydrodynamic instability is found to generate internal waves with a characteristic m=2 zonal wave number. It is shown that this time-periodic flow acts as a dynamo, although snapshots of the flow as well as the mean flow are not dynamos. The magnetic fields' growth rate exhibits resonance effects depending on the wave frequency. Furthermore, a cyclic self-killing and self-recovering dynamo based on the relative alignment of the velocity and magnetic fields is presented. The phenomena are explained in terms of a mixing of nonorthogonal eigenstates of the time-dependent linear operator of the magnetic induction equation. The potential relevance of this mechanism to dynamo experiments is discussed.
Directory of Open Access Journals (Sweden)
A. D. Pataraya
Full Text Available Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.
Coherent structures and the saturation of a nonlinear dynamo
Rempel, Erico L; Brandenburg, Axel; Muñoz, Pablo R
2012-01-01
Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean--field dynamo, produced by direct numerical simulations of the three--dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied, the kinematic stage, where a seed magnetic field undergoes exponential growth, and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, besides providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite--time Lyapunov exponents is compared with a recently developed method called function M. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced.
Small-Scale Dynamo Action in Primordial Halos
Schober, Jennifer; Klessen, Ralf S; Federrath, Christoph; Bovino, Stefano; Glover, Simon; Banerjee, Robi
2012-01-01
The first galaxies form due to gravitational collapse of primordial halos. During this collapse, weak magnetic seed fields get amplified exponentially by the small-scale dynamo - a process converting kinetic energy from turbulence into magnetic energy. We use the Kazantsev theory, which describes the small-scale dynamo analytically, to study magnetic field amplification for different turbulent velocity correlation functions. For incompressible turbulence (Kolmogorov turbulence), we find that the growth rate is proportional to the square root of the hydrodynamic Reynolds number, Re^(1/2). In the case of highly compressible turbulence (Burgers turbulence) the growth rate increases proportional to Re^(1/3). With a detailed chemical network we are able to follow the chemical evolution and determine the kinetic and magnetic viscosities (due to Ohmic and ambipolar diffusion) during the collapse of the halo. This way, we can calculate the growth rate of the small-scale dynamo quantitatively and predict the evolution...
Hide, Raymond; Moroz, Irene M.
1999-10-01
two limiting cases of ɛ=0 and ɛ=1 in the 4-mode dynamo when azimuthal eddy currents are allowed to flow i.e. cases when ρ -1=0 ; in a companion paper [I.M. Moroz, R. Hide, Effects due to induced azimuthal eddy currents in the Faraday disk self-exciting homopolar dynamo with a nonlinear series motor: II The general case, 1999, submitted] we extend the present analysis to the general case of 0≤ɛ≤1. When ɛ=0, chaotic behaviour occurs even more extensively in parameter space in the presence of azimuthal eddy currents than in their absence. When ɛ=1, the quenching of chaotic and all other non-steady dynamo action is no longer complete, for aperiodic solutions are found within limited regions of parameter space where β is very small and α is very large.
Magnetic dynamo action in random flows with zero and finite correlation times
Mason, Joanne; Boldyrev, Stanislav; Cattaneo, Fausto
2011-01-01
Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible, non-helical, homogeneous and isotropic flow. In the Kazantsev dynamo model the statistics of the driving flow are assumed to be instantaneously correlated in time. Here we compare the results of the model with the dynamo properties of a simulated flow that has equivalent spatial characteristics as the Kazantsev flow but different temporal statistics. In particular, the simulated flow is a solution of the forced Navier-Stokes equations and hence has a finite correlation time. We find that the Kazantsev model typically predicts a larger magnetic growth rate and a magnetic spectrum that peaks at smaller scales. However, we show that by filtering the diffusivity spectrum at small scales it is possible to bring the growth rates into agreement and simultaneously align the magnetic spectr...
National Research Council Canada - National Science Library
de Paor, A. M
1998-01-01
Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field...
Hide, Raymond
1997-02-01
This paper discusses the derivation of the autonomous sets of dimensionless nonlinear ordinary differential equations (ODE's) that govern the behaviour of a hierarchy of related electro-mechanical self-exciting Faraday-disk homopolar dynamo systems driven by steady mechanical couples. Each system comprises N interacting units which could be arranged in a ring or lattice. Within each unit and connected in parallel or in series with the coil are electric motors driven into motion by the dynamo, all having linear characteristics, so that nonlinearity arises entirely through the coupling between components. By introducing simple extra terms into the equations it is possible to represent biasing effects arising from impressed electromotive forces due to thermoelectric or chemical processes and from the presence of ambient magnetic fields. Dissipation in the system is due not only to ohmic heating but also to mechanical friction in the disk and the motors, with the latter agency, no matter how weak, playing an unexpectedly crucial rôle in the production of régimes of chaotic behaviour. This has already been demonstrated in recent work on a case of a single unit incorporating just one series motor, which is governed by a novel autonomous set of nonlinear ODE's with three time-dependent variables and four control parameters. It will be of mathematical as well as geophysical and astrophysical interest to investigate systematically phase and amplitude locking and other types of behaviour in the more complicated cases that arise when N > 1, which can typically involve up to 6 N dependent variables and 19 N-5 control parameters. Even the simplest members of the hierarchy, with N as low as 1, 2 or 3, could prove useful as physically-realistic low-dimensional models in theoretical studies of fluctuating stellar and planetary magnetic fields. Geomagnetic polarity reversals could be affected by the presence of the Earth's solid metallic inner core, driven like an electric motor
Plasmoid ejections driven by dynamo action underneath a spherical surface
Warnecke, Jörn; Mitra, Dhrubaditya
2010-01-01
We present a unified three-dimensional model of the convection zone and upper atmosphere of the Sun in spherical geometry. In this model, magnetic fields, generated by a helically forced dynamo in the convection zone, emerge without the assistance of magnetic buoyancy. We use an isothermal equation of state with gravity and density stratification. Recurrent plasmoid ejections, which rise through the outer atmosphere, is observed. In addition, the current helicity of the small--scale field is transported outwards and form large structures like magnetic clouds.
Dynamo action in turbulent accretion discs around black holes. 2. The mean magnetic field
Energy Technology Data Exchange (ETDEWEB)
Pudritz, R.E. (British Columbia Univ., Vancouver (Canada). Dept. of Physics)
1981-06-01
The presence of strong differential rotation and vertical density gradients in thin accretion discs allows the generation of a large-scale, mean magnetic field by ..cap alpha.. ..omega.. dynamo action. Analytic expressions for the preferred steady-state solutions are found, which when matched on to an exterior vacuum field show that the class of quadrupole modes (Bsub(phi) and Bsub(r) even, and Bsub(z) odd functions of z) are most easily excited. The critical dynamo number of this mode is Qsub(e,c)sup(1/3) = 2.4, corresponding to a turbulent Mach number of Msub(t)sup(e) = 0.19.
Energy ﬂuxes in helical magnetohydrodynamics and dynamo action
Indian Academy of Sciences (India)
Mahendra K Verma
2003-10-01
Renormalized viscosity, renormalized resistivity, and various energy ﬂuxes are calculated for helical magnetohydrodynamics using perturbative ﬁeld theory. The calculation is of ﬁrst-order in perturbation. Kinetic and magnetic helicities do not affect the renormalized parameters, but they induce an inverse cascade of magnetic energy. The sources for the large-scale magnetic ﬁeld have been shown to be (1) energy ﬂux from large-scale velocity ﬁeld to large-scale magnetic ﬁeld arising due to non-helical interactions and (2) inverse energy ﬂux of magnetic energy caused by helical interactions. Based on our ﬂux results, a primitive model for galactic dynamo has been constructed. Our calculations yield dynamo time-scale for a typical galaxy to be of the order of 108 years. Our ﬁeld-theoretic calculations also reveal that the ﬂux of magnetic helicity is backward, consistent with the earlier observations based on absolute equilibrium theory.
On magnetic instabilities and dynamo action in stellar radiation zones
Zahn, J -P; Mathis, S
2007-01-01
We examine the MHD instabilities arising in the radiation zone of a differentially rotating star, in which a poloidal field of fossil origin is sheared into a toroidal field. We focus on the non-axisymmetric instability that affects the toroidal magnetic field in a rotating star, which was first studied by Pitts and Tayler in the non-dissipative limit. According to Spruit, it could also drive a dynamo. The Pitts & Tayler instability is manifestly present in our simulations, with its conspicuous m=1 dependence in azimuth. But its analytic treatment used so far is too simplified to be applied to the real stellar situation. Although the instability generated field reaches an energy comparable to that of the mean poloidal field, that field seems unaffected by the instability: it undergoes Ohmic decline, and is neither eroded nor regenerated by the instability. The toroidal field is produced by shearing the poloidal field and it draws its energy from the differential rotation. The small scale motions behave as...
New results on an equipartition dynamo
DEFF Research Database (Denmark)
Dorch, S. B. F.; Archontis, V.
2006-01-01
This contribution presents results from numerical computer experiments with a 3-d steady sine flow (with zero mean helicity) that drives fast dynamo action. The mode of operation of this so-called ``no-cosines" dynamo (recently dubbed ``the Archontis dynamo"" by David Galloway) was studied during...... linear and non-linear saturation regimes. The means were 3-d non-linear MHD simulations and visualization using the high resolution numerical scheme by Nordlund, Galsgaard and others. We have found that the dynamo has a high growth rate in the linear regime, and that it can saturate at a level...... significantly higher that intermittent turbulent dynamos: Namely very close to energy equipartition for high Reynolds numbers. The equipartition solution however is not turbulent but a laminar solution that acts as an attractor to other modes. Similarities and differences, in the way the magnetic field...
Strong field dynamo action in rapidly rotating convection with no inertia
Hughes, David W
2015-01-01
The Earth's magnetic field is generated by dynamo action driven by convection in the outer core. Owing to the rapid rotation and small viscosity, the dynamical balance is believed to be between buoyancy, Coriolis and magnetic forces; inertial forces play no role. It is thus extremely important to produce explicit solutions with these features. However, from the traditional approach of solving the full governing equations at low Ekman numbers, it is not clear that the asymptotic regime has been captured. Here we adopt a complementary approach consisting of a model of rapidly rotating convection in which inertial forces are neglected from the outset. Within this framework we are able to construct a new branch of solutions in which the dynamo generates a strong magnetic field that satisfies the expected force balance. The resulting strongly magnetised convection is dramatically different to the corresponding solutions in which the magnetic field is weak.
Turbulence and small scale dynamo action in population III star formation
Oishi, Jeffrey S.; Turk, Matthew J.; Abel, Tom; Bryan, Greg
2012-09-01
We discuss some results from a recent set of magnetohydrodynamic simulations of the formation of the first stars, including cosmological initial conditions and a full treatment of primordial chemistry. These simulations follow the exponential amplification of seed magnetic fields by small-scale dynamo action, and we explore some of the details of the turbulence that leads to this behavior. The key to understanding the growth of magnetic fields is the growth of vorticity, and we focus on its generation and dissipation in simulations of varying resolution. We show that the production and amplification of vorticity changes with increasing resolution, leading to the previous observations of dynamo growth rates and late time field strengths increasing with increased resolution.
Kinematic dynamo induced by helical waves
Wei, Xing
2014-01-01
We investigate numerically the kinematic dynamo induced by the superposition of two helical waves in a periodic box as a simplified model to understand the dynamo action in astronomical bodies. The effects of magnetic Reynolds number, wavenumber and wave frequency on the dynamo action are studied. It is found that this helical-wave dynamo is a slow dynamo. There exists an optimal wavenumber for the dynamo growth rate. A lower wave frequency facilitates the dynamo action and the oscillations o...
A. M. de Paor
1998-01-01
International audience; Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ? has the value 1 is proved via ...
de Paor, A. M.
Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.
Large-scale weakly nonlinear perturbations of convective magnetic dynamos in a rotating layer
Chertovskih, Roman
2015-01-01
We present a new mechanism for generation of large-scale magnetic field by thermal convection which does not involve the alpha-effect. We consider weakly nonlinear perturbations of space-periodic steady convective magnetic dynamos in a rotating layer that were identified in our previous work. The perturbations have a spatial scale in the horizontal direction that is much larger than the period of the perturbed convective magnetohydrodynamic state. Following the formalism of the multiscale stability theory, we have derived the system of amplitude equations governing the evolution of the leading terms in expansion of the perturbations in power series in the scale ratio. This asymptotic analysis is more involved than in the cases considered earlier, because the kernel of the operator of linearisation has zero-mean neutral modes whose origin lies in the spatial invariance of the perturbed regime, the operator reduced on the generalised kernel has two Jordan normal form blocks of size two, and simplifying symmetri...
An integrated model for Jupiter's dynamo action and mean jet dynamics
Gastine, Thomas; Wicht, Johannes; Duarte, Lucia; Heimpel, Moritz
2014-05-01
Data from various space crafts revealed that Jupiter's large scale interior magnetic field is very Earth-like. This is surprising since numerical simulations have demonstrated that, for example, the radial dependence of density, electrical conductivity and other physical properties, which is only mild in the iron cores of terrestrial planets but very drastic in gas planets, can significantly affect the interior dynamics. Jupiter's dynamo action is thought to take place in the deeper envelope where hydrogen, the main constituent of Jupiter's atmosphere, assumes metallic properties. The potential interaction between the observed zonal jets and the deeper dynamo region is an unresolved problem with important consequences for the magnetic field generation. Here we present the first numerical simulation that is based on recent interior models and covers 99% of the planetary radius (below the 1 bar level). A steep decease in the electrical conductivity over the outer 10% in radius allowed us to model both the deeper metallic region and the outer molecular layer in an integrated approach. The magnetic field very closely reproduces Jupiter's known large scale field. A strong equatorial zonal jet remains constrained to the molecular layer while higher latitude jets are suppressed by Lorentz forces. This suggests that Jupiter's higher latitude jets remain shallow and are driven by an additional effect not captured in our deep convection model. The dynamo action of the equatorial jet produces a band of magnetic field located around the equator. The unprecedented magnetic field resolution expected from the Juno mission will allow to resolve this feature allowing a direct detection of the equatorial jet dynamics at depth. Typical secular variation times scales amount to around 750 yr for the dipole contribution but decrease to about 5 yr at the expected Juno resolution (spherical harmonic degree 20). At a nominal mission duration of one year Juno should therefore be able to
Strong-field dynamo action in rapidly rotating convection with no inertia.
Hughes, David W; Cattaneo, Fausto
2016-06-01
The earth's magnetic field is generated by dynamo action driven by convection in the outer core. For numerical reasons, inertial and viscous forces play an important role in geodynamo models; however, the primary dynamical balance in the earth's core is believed to be between buoyancy, Coriolis, and magnetic forces. The hope has been that by setting the Ekman number to be as small as computationally feasible, an asymptotic regime would be reached in which the correct force balance is achieved. However, recent analyses of geodynamo models suggest that the desired balance has still not yet been attained. Here we adopt a complementary approach consisting of a model of rapidly rotating convection in which inertial forces are neglected from the outset. Within this framework we are able to construct a branch of solutions in which the dynamo generates a strong magnetic field that satisfies the expected force balance. The resulting strongly magnetized convection is dramatically different from the corresponding solutions in which the field is weak.
Directory of Open Access Journals (Sweden)
A. M. de Paor
1998-01-01
Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.
Kinematic Dynamo Action in the Presence of a Large Scale Velocity
Carvalho, J. C.
1990-11-01
RESUMEN. Se investiga la influencia de Un campo de velocidades de ran escala sobre la acci6n del tur bulento. Usando Un proceso de expansi6n, las soluciones se encuentran en el del movimiento lobal y de cizalla pequeflo y para randes de Reynolds. Se calcula la re jeneraci6n tica hasta un orden en el de expansi6n usando convectivas ciclotr6nicas para el campo turbulento de velocidad. ABSTRACT. The influence a scale velocity field upon the kinernatic turbulent dynamo action is . Usinj an expansion process, the solutions are found in the limit of small bulk motion and shear, and for Reynolds number. The majnetic is calculated up to second order in the expansion parameter usin cyclonic convective cells for the turbulent velocity field. Key o'td : HYDROMAGNETICS
Dynamo action in turbulent accretion discs around black holes. 1. The fluctuations
Energy Technology Data Exchange (ETDEWEB)
Pudritz, R.E. (British Columbia Univ., Vancouver (Canada). Dept. of Physics)
1981-06-01
The magnetic field in a turbulent accretion disc is decomposed into large-scale, mean and microscale, fluctuating fields. It is shown that a rather strong, mean magnetic field can be generated by turbulent dynamo action on time-scales of order M/sup -2/sub(t) tsub(k) in the small Mach number regime Msub(t)<1. Magnetic fluctuations much more energetic than the mean magnetic field will occur and will ultimately draw their energy from the turbulence. When the mean field is of strength B/sup 2/sub(c)/8..pi.. = (3/4)csub(u)M/sup 2/sub(t)P, where csub(u) less than approximately 1/2 and P is the gas pressure, the magnetic fluctuations shut down the turbulence altogether. An explicit expression for the Maxwell stress, arising from these intense fluctuations, is given.
Higher helicity invariants and solar dynamo
Sokolov, D. D.; Illarionov, E. A.; Akhmet'ev, P. M.
2017-01-01
Modern models of nonlinear dynamo saturation in celestial bodies (specifically, on the Sun) are largely based on the consideration of the balance of magnetic helicity. This physical variable has also a topological meaning: it is associated with the linking coefficient of magnetic tubes. In addition to magnetic helicity, magnetohydrodynamics has a number of topological integrals of motion (the so-called higher helicity moments). We have compared these invariants with magnetic helicity properties and concluded that they can hardly serve as nonlinear constraints on dynamo action.
HYSTERESIS BETWEEN DISTINCT MODES OF TURBULENT DYNAMOS
Energy Technology Data Exchange (ETDEWEB)
Karak, Bidya Binay; Brandenburg, Axel [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm (Sweden); Kitchatinov, Leonid L., E-mail: bbkarak@nordita.org [Institute of Solar-Terrestrial Physics, P.O. Box 291, Irkutsk 664033 (Russian Federation)
2015-04-20
Nonlinear mean-field models of the solar dynamo show long-term variability, which may be relevant to different states of activity inferred from long-term radiocarbon data. This paper is aimed at probing the dynamo hysteresis predicted by the recent mean-field models of Kitchatinov and Olemskoy with direct numerical simulations. We perform three-dimensional (3D) simulations of large-scale dynamos in a shearing box with helically forced turbulence. As an initial condition, we either take a weak random magnetic field or we start from a snapshot of an earlier simulation. Two quasi-stable states are found to coexist in a certain range of parameters close to the onset of the large-scale dynamo. The simulations converge to one of these states depending on the initial conditions. When either the fractional helicity or the magnetic Prandtl number is increased between successive runs above the critical value for onset of the dynamo, the field strength jumps to a finite value. However, when the fractional helicity or the magnetic Prandtl number is then decreased again, the field strength stays at a similar value (strong field branch) even below the original onset. We also observe intermittent decaying phases away from the strong field branch close to the point where large-scale dynamo action is just possible. The dynamo hysteresis seen previously in mean-field models is thus reproduced by 3D simulations. Its possible relation to distinct modes of solar activity such as grand minima is discussed.
Dynamo action due to alpha fluctuations in a shear flow: mean--field theory
Sridhar, S
2013-01-01
We present an analytical theory of the growth of a large-scale mean magnetic field in a linear shear flow with fluctuations in time of the alpha parameter (equivalently, kinetic helicity). Using shearing coordinates and Fourier variables we derive a set of coupled integro-differential equations, governing the dynamics of the mean magnetic field, that are non perturbative in the rate of shear. When the alpha fluctuations are of white-noise form, the mean electromotive force (EMF) is identical to the negative diffusive form derived by Kraichnan for the case of no shear; the physical reason is that shear takes time to act, and white-noise fluctuations have zero correlation time. We demonstrate that the white-noise case does not allow for large-scale dynamo action. We then allow for a small but non zero correlation time and show that, for a slowly varying mean magnetic field, the mean EMF has additional terms that depend on a combination of shear and alpha fluctuations; the mean-field equations now reduce to a se...
Dynamo action in thick disks around Kerr black holes: high-order resistive GRMHD simulations
Bugli, M; Bucciantini, N
2014-01-01
We present the first kinematic study of an $\\alpha\\Omega$-dynamo in the General Relativistic Magneto-HydroDynamics (GRMHD) regime, applied to thick disks orbiting around Kerr black holes and using a fully covariant mean field dynamo closure for the Ohm law. We show that the $\\alpha\\Omega$-dynamo mechanism leads to a continuous exponential growth of the magnetic field within the disk and to the formation of dynamo waves drifting away or toward the equatorial plane. Since the evolution of the magnetic field occurs qualitatively in the same fashion as in the Sun, we present also butterfly diagrams that characterize our models and show the establishment of an additional timescale, which depends on the microscopic properties of the turbulent motions, possibly providing an alternative explanation to periodicities observed in many high-energy astrophysical sources where accretion onto a rotating black hole is believed to operate.
Giesecke, André; Stefani, Frank; Burguete, Javier
2012-12-01
We present numerical simulations of the kinematic induction equation in order to examine the dynamo efficiency of an axisymmetric von Kármán-like flow subject to time-dependent nonaxisymmetric velocity perturbations. The numerical model is based on the setup of the French von Kármán-sodium dynamo (VKS) and on the flow measurements from a water experiment conducted at the University of Navarra in Pamplona, Spain. The principal experimental observations that are modeled in our simulations are nonaxisymmetric vortexlike structures which perform an azimuthal drift motion in the equatorial plane. Our simulations show that the interactions of these periodic flow perturbations with the fundamental drift of the magnetic eigenmode (including the special case of nondrifting fields) essentially determine the temporal behavior of the dynamo state. We find two distinct regimes of dynamo action that depend on the (prescribed) drift frequency of an (m=2) vortexlike flow perturbation. For comparatively slowly drifting vortices we observe a narrow window with enhanced growth rates and a drift of the magnetic eigenmode that is synchronized with the perturbation drift. The resonance-like enhancement of the growth rates takes place when the vortex drift frequency roughly equals the drift frequency of the magnetic eigenmode in the unperturbed system. Outside of this small window, the field generation is hampered compared to the unperturbed case, and the field amplitude of the magnetic eigenmode is modulated with approximately twice the vortex drift frequency. The abrupt transition between the resonant regime and the modulated regime is identified as a spectral exceptional point where eigenvalues (growth rates and frequencies) and eigenfunctions of two previously independent modes collapse. In the actual configuration the drift frequencies of the velocity perturbations that are observed in the water experiment are much larger than the fundamental drift frequency of the magnetic
Giesecke, André; Stefani, Frank; Burguete, Javier
2012-12-01
We present numerical simulations of the kinematic induction equation in order to examine the dynamo efficiency of an axisymmetric von Kármán-like flow subject to time-dependent nonaxisymmetric velocity perturbations. The numerical model is based on the setup of the French von Kármán-sodium dynamo (VKS) and on the flow measurements from a water experiment conducted at the University of Navarra in Pamplona, Spain. The principal experimental observations that are modeled in our simulations are nonaxisymmetric vortexlike structures which perform an azimuthal drift motion in the equatorial plane. Our simulations show that the interactions of these periodic flow perturbations with the fundamental drift of the magnetic eigenmode (including the special case of nondrifting fields) essentially determine the temporal behavior of the dynamo state. We find two distinct regimes of dynamo action that depend on the (prescribed) drift frequency of an (m=2) vortexlike flow perturbation. For comparatively slowly drifting vortices we observe a narrow window with enhanced growth rates and a drift of the magnetic eigenmode that is synchronized with the perturbation drift. The resonance-like enhancement of the growth rates takes place when the vortex drift frequency roughly equals the drift frequency of the magnetic eigenmode in the unperturbed system. Outside of this small window, the field generation is hampered compared to the unperturbed case, and the field amplitude of the magnetic eigenmode is modulated with approximately twice the vortex drift frequency. The abrupt transition between the resonant regime and the modulated regime is identified as a spectral exceptional point where eigenvalues (growth rates and frequencies) and eigenfunctions of two previously independent modes collapse. In the actual configuration the drift frequencies of the velocity perturbations that are observed in the water experiment are much larger than the fundamental drift frequency of the magnetic
A global galactic dynamo with a corona constrained by relative helicity
Prasad, A
2015-01-01
We present a model for a global axisymmetric turbulent dynamo operating in a galaxy with a corona which treats the supernovae (SNe) and magneto-rotational instability (MRI) driven turbulence parameters under a common formalism. The nonlinear quenching of the dynamo is alleviated by inclusion of small-scale advective and diffusive magnetic helicity fluxes, which allow the gauge invariant magnetic helicity to be transferred outside the disk and consequently build up a corona during the course of dynamo action. The time-dependent dynamo equations are expressed in a separable form and solved through an eigenvector expansion constructed using the steady-state solutions of the dynamo equation. The parametric evolution of the dynamo solution allows us to estimate the final structure of the global magnetic field and the saturated value of the turbulence parameter $\\alpha_m$, even before solving the dynamical equations for evolution of magnetic fields in the disk and the corona, along with $\\alpha$-quenching. We then ...
Schober, Jennifer; Federrath, Christoph; Klessen, Ralf; Banerjee, Robi
2011-01-01
The small-scale dynamo is a process by which turbulent kinetic energy is converted into magnetic energy, and thus is expected to depend crucially on the nature of turbulence. In this work, we present a model for the small-scale dynamo that takes into account the slope of the turbulent velocity spectrum v(l) ~ l^theta, where l and v(l) are the size of a turbulent fluctuation and the typical velocity on that scale. The time evolution of the fluctuation component of the magnetic field, i.e., the small-scale field, is described by the Kazantsev equation. We solve this linear differential equation for its eigenvalues with the quantum-mechanical WKB-approximation. The validity of this method is estimated as a function of the magnetic Prandtl number Pm. We calculate the minimal magnetic Reynolds number for dynamo action, Rm_crit, using our model of the turbulent velocity correlation function. For Kolmogorov turbulence (theta=1/3), we find that the critical magnetic Reynolds number is approximately 110 and for Burger...
Quasi-cyclic behaviour in non-linear simulations of the shear dynamo
Teed, Robert J.; Proctor, Michael R. E.
2017-06-01
The solar magnetic field displays features on a wide range of length-scales including spatial and temporal coherence on scales considerably larger than the chaotic convection that generates the field. Explaining how the Sun generates and sustains such large-scale magnetic field has been a major challenge of dynamo theory for many decades. Traditionally, the 'mean-field' approach, utilizing the well-known α-effect, has been used to explain the generation of large-scale field from small-scale turbulence. However, with the advent of increasingly high-resolution computer simulations there is doubt as to whether the mean-field method is applicable under solar conditions. Models such as the 'shear dynamo' provide an alternative mechanism for the generation of large-scale field. In recent work, we showed that while coherent magnetic field was possible under kinematic conditions (where the kinetic energy is far greater than magnetic energy), the saturated state typically displayed a destruction of large-scale field and a transition to a small-scale state. In this paper, we report that the quenching of large-scale field in this way is not the only regime possible in the saturated state of this model. Across a range of simulations, we find a quasi-cyclic behaviour where a large-scale field is preserved and oscillates between two preferred length-scales. In this regime, the kinetic and magnetic energies can be of a similar order of magnitude. These results demonstrate that there is mileage in the shear dynamo as a model for the solar dynamo.
Heimpel, M.; Gomez Perez, N.
2009-05-01
The surface winds and magnetic fields of Jupiter and Saturn are observed to be broadly comparable. Both planets have strong and prograde equatorial jet and weaker jets, flowing in alternating directions at higher latitudes. Also, both planets exhibit relatively strong, dipolar magnetic fields. Saturn's magnetic field is weaker and more axisymmetric than that of Jupiter. In addition, Saturn's equatorial jet is broader and stronger than that of Jupiter. We have performed a set of numerical simulations of rotating convection and dynamo action in spherical shells. The model fluid is Boussinesq with radially varying electrical conductivity. The electrical conductivity, which is nearly constant in the deeper parts of the shell, exponentially decreases outward, starting at a chosen radius parameter. We find that the character of the dynamo-generated magnetic field, and the fluid flow structure are strongly affected by the afore-mentioned radius parameter, as well as by the size of the inner boundary radius and the temperature boundary conditions. In some of the simulations a strong, magnetostrophic, mainly dipolar dynamo develops in the deeper region of high electrical conductivity. In most cases, a strong zonal flow with an equatorial jet develops near the low-conductivity, free slip outer surface, and penetrates to a depth associated with the conductivity profile. The zonal flow is attenuated by Lorentz forces at depth and is, in some cases, greatly diminished in the dynamo region. The relationship between the structure of equatorial jets and the magnetic fields generated in our models implies that major differences between the surface zonal flow and magnetic fields of Jupiter and Saturn can arise from the presence of a rocky core, and the depth of transition from their low-conductivity molecular envelopes to their liquid metal interiors.
Schober, Jennifer; Schleicher, Dominik; Federrath, Christoph; Klessen, Ralf; Banerjee, Robi
2012-02-01
The small-scale dynamo is a process by which turbulent kinetic energy is converted into magnetic energy, and thus it is expected to depend crucially on the nature of the turbulence. In this paper, we present a model for the small-scale dynamo that takes into account the slope of the turbulent velocity spectrum v(ℓ)proportional ℓ([symbol see text])V}, where ℓ and v(ℓ) are the size of a turbulent fluctuation and the typical velocity on that scale. The time evolution of the fluctuation component of the magnetic field, i.e., the small-scale field, is described by the Kazantsev equation. We solve this linear differential equation for its eigenvalues with the quantum-mechanical WKB approximation. The validity of this method is estimated as a function of the magnetic Prandtl number Pm. We calculate the minimal magnetic Reynolds number for dynamo action, Rm_{crit}, using our model of the turbulent velocity correlation function. For Kolmogorov turbulence ([symbol see text] = 1/3), we find that the critical magnetic Reynolds number is Rm(crit) (K) ≈ 110 and for Burgers turbulence ([symbol see text] = 1/2) Rm(crit)(B) ≈ 2700. Furthermore, we derive that the growth rate of the small-scale magnetic field for a general type of turbulence is Γ proportional Re((1-[symbol see text])/(1+[symbol see text])) in the limit of infinite magnetic Prandtl number. For decreasing magnetic Prandtl number (down to Pm >/~ 10), the growth rate of the small-scale dynamo decreases. The details of this drop depend on the WKB approximation, which becomes invalid for a magnetic Prandtl number of about unity.
Warnecke, Jörn
2013-01-01
We report on turbulent dynamo simulations in a spherical wedge with an outer coronal layer. We apply a two-layer model where the lower layer represents the convection zone and the upper layer the solar corona. This setup is used to study the coronal influence on the dynamo action beneath the surface. Increasing the radial coronal extent gradually to three times the solar radius and changing the magnetic Reynolds number, we find that dynamo action benefits from the additional coronal extent in terms of higher magnetic energy in the saturated stage. The flux of magnetic helicity can play an important role in this context.
The Kinematic Theory of Solar Dynamo
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Generation of the Sun's magnetic fields by self-inductive processes inthe solar electrically conducting interior, the solar dynamo theory, is a fundamen-tally important subject in astrophysics. The kinematic dynamo theory concernshow the magnetic fields are produced by kinematically possible flows without beingconstrained by the dynamic equation. We review a number of basic aspects of thekinematic dynamo theory, including the magnetohydrodynamic approximation forthe dynamo equation, the impossibility of dynamo action with the solar differentialrotation, the Cowling's anti-dynamo theorem in the solar context, the turbulent al-pha effect and recently constructed three-dimensional interface dynamos controlledby the solar tachocline at the base of the convection zone.
Mesogranulation and small-scale dynamo action in the quiet Sun
Bushby, Paul J
2014-01-01
Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is probable that some of these magnetic fields are generated locally by a convective dynamo mechanism. In addition to the well-known granular and supergranular convective scales, various observations have indicated that there is an intermediate scale of convection, known as mesogranulation, with vertical magnetic flux concentrations accumulating preferentially at mesogranular boundaries. Our aim is to investigate the small-scale dynamo properties of a convective flow that exhibits both granulation and mesogranulation, comparing our findings with solar observations. Adopting an idealised model for a localised region of quiet Sun, we use numerical simulations of compressible magnetohydrodynamics, in a 3D Cartesian domain, to investigate the parametric dependence of this system (focusing particularly upon the effects of varying ...
Dynamo action and magnetic buoyancy in convection simulations with vertical shear
Guerrero, G
2011-01-01
A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the whole convection zone. We follow the evolution of a random seed magnetic field with the aim of study under what conditions it is possible to excite the dynamo instability and whether the dynamo generated magnetic field becomes buoyantly unstable and emerges to the surface as expected in the flux-tube context. We perform numerical simulations of compressible turbulent convection that include a vertical shear layer. Like the solar tachocline, the shear is located at the interface between convective and stable layers. We find that shear and convection are able to amplify the initial magnetic field and form large-scale elongated magnetic structures. The magnetic field strength depends on several parameters such as the shear amplitude, the thickness and location ...
Fluctuation dynamo based on magnetic reconnections
Baggaley, A. W.; Shukurov, A.; Barenghi, C. F.; Subramanian, K.
2010-01-01
We develop a new model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multi-scale flow which models turbulence. Magnetic dissipation occurs only via reconnections of flux ropes. The model is particularly suitable for rarefied plasma, such as the solar corona or galactic halos. We investigate the kinetic energy release into heat, mediated by dynamo action, both in our model and by solving the induction equation with the same flow. We find that the flux rope dynamo is more than an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy released during reconnections has a power-law form with the slope -3, consistent with the solar corona heating by nanoflares. We also present a nonlinear extension of the model. This shows that a plausible saturation mechanism of the fluctuation dynamo is the suppression of turbulent magnetic diffusivity, due to suppression of random stretching at the location of the flux ropes. We confirm that the probability distribution function of the magnetic line curvature has a power-law form suggested by \\citet{Sheck:2002b}. We argue, however, using our results that this does not imply a persistent folded structure of magnetic field, at least in the nonlinear stage.
Indian Academy of Sciences (India)
Mahendra K Verma; Bidya Binay Karak; Rohit Kumar
2013-12-01
In this paper, we estimate the magnetic Reynolds number of a typical protostar before and after deuterium burning, and claim for the existence of dynamo process in both the phases, because the magnetic Reynolds number of the protostar far exceeds the critical magnetic Reynolds number for dynamo action. Using the equipartition of kinetic and magnetic energies, we estimate the steady-state magnetic field of the protostar to be of the order of kilogauss, which is in good agreement with observations.
Galactic dynamos supported by magnetic helicity fluxes
Sur, S; Subramanian, K; Sur, Sharanya; Shukurov, Anvar; Subramanian, Kandaswamy
2006-01-01
We present a simple semi-analytical model of nonlinear, mean-field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the `no-$z$' approximation to a nonlinear system of ordinary differential equations in time; we demonstrate that the model reproduces accurately earlier results, including those where nonlinear behaviour is driven by a magnetic helicity flux. We discuss the implications and interplay of two types of magnetic helicity flux, one produced by advection (e.g., due to the galactic fountain or wind) and the other, arising from anisotropy of turbulence as suggested by Vishniac & Cho(2001). We argue that the latter is significant if the galactic differential rotation is strong enough: in our model, for $\\Rw\\la-10$ in terms of the corresponding turbulent magnetic Reynolds number. We confirm that the intensity of gas outflow from the galactic disc optimal for the dynamo action is close to that expected for normal spiral galaxie...
Fluctuation dynamo based on magnetic reconnections
Baggaley, Andrew W; Shukurov, Anvar; Subramanian, Kandaswamy
2009-01-01
We develop a new model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multi-scale flow which models turbulence. Magnetic dissipation occurs only via reconnections of flux ropes. The model is particularly suitable for rarefied plasma, such as the Solar corona or galactic halos. We investigate the kinetic energy release into heat, mediated by dynamo action, both in our model and by solving the induction equation with the same flow. We find that the flux rope dynamo is more than an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy released during reconnections has a power-law form with the slope -3, consistent with the Solar corona heating by nanoflares. We also present a nonlinear extension of the model. This shows that a plausible saturation mechanism of the fluctuation dynamo is the suppression of turbulent magnetic diffusivity, due to suppression of random stretching at the location o...
Intermittency in spherical Couette dynamos
Raynaud, Raphaël; 10.1103/PhysRevE.87.033011
2013-01-01
We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.
Small-scale dynamo action during the formation of the first stars and galaxies
Schleicher, Dominik R G; Sur, Sharanya; Arshakian, Tigran G; Klessen, Ralf S; Beck, Rainer; Spaans, Marco
2010-01-01
We explore the implications of the small-scale dynamo on the formation of the first stars and galaxies. During the formation of the first stars, the presence of sub-sonic turbulence leads to the rapid build-up of magnetic fields until a saturation value of B n^{-0.5} \\sim10^{-7} G cm^{1.5}, with n the number density. The magnetic pressure is thus still considerably smaller than the thermal pressure, and we do not expect a strong influence of magnetic fields during the collapse phase. In the protostellar disk, they may however have profound implications on fragmentation and binary formation. In the first galaxies, we expect the presence of supersonic turbulence, leading to a more rapid amplification of the magnetic field on even larger scales and saturation values that are increased by an order of magnitude. The magnetic pressure comes close to the thermal pressure, with only half an order of magnitude difference. Due to the intrinsic inhomogeneities of the magnetic field, the magnetic field may then be locall...
Giesecke, Andre; Burguete, Javier
2012-01-01
We have performed numerical simulations of the kinematic induction equation in order to examine the dynamo efficiency of an axisymmetric von-K\\'arm\\'an-like flow subject to time-dependent non-axisymmetric velocity perturbations. The numerical model is based on the setup of the French Von-K\\'arm\\'an-Sodium dynamo (VKS) and on the flow measurements from a model water experiment conducted at the University of Navarra in Pamplona, Spain. Our simulations show that the interactions of azimuthally drifting flow perturbations with the fundamental drift of the magnetic eigenmode (caused by the inevitable equatorial symmetry breaking of the basic flow) essentially determine the temporal behavior of the dynamo state. We find two distinct regimes of dynamo action that depend on the (prescribed) drift frequency of an ($m=2$) vortex-like flow perturbation. For comparatively slowly drifting vortices we observe a narrow window with enhanced growth-rates and a drift of the magnetic eigenmode that is synchronized with the pert...
Dynamo effect in a driven helical flow.
Feudel, F; Gellert, M; Rüdiger, S; Witt, A; Seehafer, N
2003-10-01
The Roberts flow, a helical flow in the form of convectionlike rolls, is known to be capable of both kinematic and nonlinear dynamo action. We study the Roberts dynamo with particular attention being paid to the spatial structure of the generated magnetic field and its back-reaction on the flow. The dynamo bifurcation is decisively determined by the symmetry group of the problem, which is given by a subgroup of discrete transformations and a continuous translational invariance of the flow. In the bifurcation the continuous symmetry is broken while the discrete subgroup symmetry completely survives. Its actions help in understanding the spatial structures of the magnetic field and of the modified flow. In accordance with experimental observations, the magnetic field component perpendicular to the originally invariant direction is much stronger than the component in this direction. Furthermore, the magnetic field is largely concentrated in layers separating the convectionlike rolls of the flow and containing, in particular, its stagnation points, which are isolated for the modified flow while they are line filling for the original Roberts flow. The magnetic field is strongest near beta-type stagnation points, with a two-dimensional unstable and a one-dimensional stable manifold, and is weak near alpha-type stagnation points, with a two-dimensional stable and a one-dimensional unstable manifold. This contrasts with the usual picture that dynamo action is promoted at the alpha points and impeded at the beta points. Both the creation of isolated stagnation points and the concentration of strong fields at the beta points may be understood as a result of the way in which the Roberts dynamo saturates. It is also found that, while the original Roberts flow is regular, the modified flow is chaotic in the layers between the convectionlike rolls where the magnetic field is concentrated. This chaoticity, which results from the back-reaction of the magnetic field on the flow
A Reconnecting Flux Rope Dynamo
Baggaley, Andrew W.; Barenghi, Carlo F.; Shukurov, Anvar; Subramanian, Kandaswamy
2009-01-01
We develop a new model of the fluctuation dynamo in which the magnetic field is confined in thin flux ropes advected by a multi-scale flow modeling turbulence. Magnetic dissipation occurs only via reconnection of the flux ropes. We investigate the kinetic energy release into heat, mediated by the dynamo action, both in our model and by solving the induction equation with the same flow. We find that a flux rope dynamo is an order of magnitude more efficient at converting mechanical energy into...
The Karlsruhe Dynamo Experiment
Directory of Open Access Journals (Sweden)
2002-01-01
Full Text Available It has been shown theoretically in the past that homogeneous dynamos may occur in electrically conducting fluids for various vortical velocity fields. Roberts (1972 investigated spatially periodic, infinitely extended fields of vortices which Busse (1978, 1992 confined to a finite cylindrical domain. Based on Busse's vortex arrangement a conceptual design for an experimental homogeneous dynamo has been developed and a test facility was setup at the Forschungszentrum Karlsruhe. The first experiments demonstrated that permanent dynamo action can be generated in a cylindrical container filled with liquid sodium in which by means of guide tubes counterrotating and countercurrent spiral vortices are established. The dynamo is self-exciting and the magnetic field saturates at a mean value for fixed super-critical flow rates. The instantaneous magnetic field fluctuates around this mean value by an order of about 5%. As predicted by theory the mode of the observed magnetic field is non-axisymmetric. In a series of experiments a phase- and a bifurcation diagram has been derived as a function of the spiral and axial flow rates.
Statistical simulation of the magnetorotational dynamo
Energy Technology Data Exchange (ETDEWEB)
Squire, J. [PPPL; Bhattacharjee, A. [PPPL
2014-08-01
We analyze turbulence and dynamo induced by the magnetorotational instability (MRI) using quasi-linear statistical simulation methods. We find that homogenous turbulence is unstable to a large scale dynamo instability, which saturates to an inhomogenous equilibrium with a very strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the quasi-linear model exhibits the same qualitative scaling of angular momentum transport with Pm as fully nonlinear turbulence. This demonstrates the relationship of recent convergence problems to the large scale dynamo and suggests possible methods for studying astrophysically relevant regimes at very low or high Pm.
Statistical Simulation of the Magnetorotational Dynamo
Energy Technology Data Exchange (ETDEWEB)
Squire, Jonathan [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Bhattacharjee, Amitava [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Max Planck Society, Garching (Germany). Max Planck Inst. for Astrophysik
2015-02-01
Turbulence and dynamo induced by the magnetorotational instability (MRI) are analyzed using quasilinear statistical simulation methods. It is found that homogenous turbulence is unstable to a large-scale dynamo instability, which saturates to an inhomogenous equilibrium with a strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the dependence of the angular momentum transport on Pm in the quasilinear model is qualitatively similar to that of nonlinear MRI turbulence. This demonstrates the importance of the large-scale dynamo and suggests how dramatically simplified models may be used to gain insight into the astrophysically relevant regimes of very low or high Pm.
Statistical simulation of the magnetorotational dynamo.
Squire, J; Bhattacharjee, A
2015-02-27
Turbulence and dynamo induced by the magnetorotational instability (MRI) are analyzed using quasilinear statistical simulation methods. It is found that homogenous turbulence is unstable to a large-scale dynamo instability, which saturates to an inhomogenous equilibrium with a strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the dependence of the angular momentum transport on Pm in the quasilinear model is qualitatively similar to that of nonlinear MRI turbulence. This demonstrates the importance of the large-scale dynamo and suggests how dramatically simplified models may be used to gain insight into the astrophysically relevant regimes of very low or high Pm.
Dietrich, Wieland; Hori, Kumiko
2015-01-01
Within the fluid iron cores of terrestrial planets, convection and the resulting generation of global magnetic fields are controlled by the overlying rocky mantle. The thermal structure of the lower mantle determines how much heat is allowed to escape the core. Hot lower mantle features, such as the thermal footprint of a giant impact or hot mantle plumes, will locally reduce the heat flux through the core mantle boundary (CMB), thereby weakening core convection and affecting the magnetic field generation process. In this study, we numerically investigate how parametrised hot spots at the CMB with arbitrary sizes, amplitudes, and positions affect core convection and hence the dynamo. The effect of the heat flux anomaly is quantified by changes in global flow symmetry properties, such as the emergence of equatorial antisymmetric, axisymmetric (EAA) zonal flows. For purely hydrodynamic models, the EAA symmetry scales almost linearly with the CMB amplitude and size, whereas self-consistent dynamo simulations typ...
Plunian, F.; Marty, P.; Alemany, A.
1999-03-01
Most of the studies concerning the dynamo effect are motivated by astrophysical and geophysical applications. The dynamo effect is also the subject of some experimental studies in fast breeder reactors (FBR) for they contain liquid sodium in motion with magnetic Reynolds numbers larger than unity. In this paper, we are concerned with the flow of sodium inside the core of an FBR, characterized by a strong helicity. The sodium in the core flows through a network of vertical cylinders. In each cylinder assembly, the flow can be approximated by a smooth upwards helical motion with no-slip conditions at the boundary. As the core contains a large number of assemblies, the global flow is considered to be two-dimensionally periodic. We investigate the self-excitation of a two-dimensionally periodic magnetic field using an instability analysis of the induction equation which leads to an eigenvalue problem. Advantage is taken of the flow symmetries to reduce the size of the problem. The growth rate of the magnetic field is found as a function of the flow pitch, the magnetic Reynolds number (Rm) and the vertical magnetic wavenumber (k). An [alpha]-effect is shown to operate for moderate values of Rm, supporting a mean magnetic field. The large-Rm limit is investigated numerically. It is found that [alpha]=O(Rm[minus sign]2/3), which can be explained through appropriate dynamo mechanisms. Either a smooth Ponomarenko or a Roberts type of dynamo is operating in each periodic cell, depending on k. The standard power regime of an industrial FPBR is found to be subcritical.
Emeriau-Viard, Constance; Brun, Allan Sacha
2017-10-01
During the PMS, structure and rotation rate of stars evolve significantly. We wish to assess the consequences of these drastic changes on stellar dynamo, internal magnetic field topology and activity level by mean of HPC simulations with the ASH code. To answer this question, we develop 3D MHD simulations that represent specific stages of stellar evolution along the PMS. We choose five different models characterized by the radius of their radiative zone following an evolutionary track, from 1 Myr to 50 Myr, computed by a 1D stellar evolution code. We introduce a seed magnetic field in the youngest model and then we spread it through all simulations. First of all, we study the consequences that the increase of rotation rate and the change of geometry of the convective zone have on the dynamo field that exists in the convective envelop. The magnetic energy increases, the topology of the magnetic field becomes more complex and the axisymmetric magnetic field becomes less predominant as the star ages. The computation of the fully convective MHD model shows that a strong dynamo develops with a ratio of magnetic to kinetic energy reaching equipartition and even super-equipartition states in the faster rotating cases. Magnetic fields resulting from our MHD simulations possess a mixed poloidal-toroidal topology with no obvious dominant component. We also study the relaxation of the vestige dynamo magnetic field within the radiative core and found that it satisfies stability criteria. Hence it does not experience a global reconfiguration and instead slowly relaxes by retaining its mixed poloidal-toroidal topology.
Two spinning ways for precession dynamo.
Cappanera, L; Guermond, J-L; Léorat, J; Nore, C
2016-04-01
It is numerically demonstrated by means of a magnetohydrodynamic code that precession can trigger dynamo action in a cylindrical container. Fixing the angle between the spin and the precession axis to be 1/2π, two limit configurations of the spinning axis are explored: either the symmetry axis of the cylinder is parallel to the spin axis (this configuration is henceforth referred to as the axial spin case), or it is perpendicular to the spin axis (this configuration is referred to as the equatorial spin case). In both cases, the centro-symmetry of the flow breaks when the kinetic Reynolds number increases. Equatorial spinning is found to be more efficient in breaking the centro-symmetry of the flow. In both cases, the average flow in the reference frame of the mantle converges to a counter-rotation with respect to the spin axis as the Reynolds number grows. We find a scaling law for the average kinetic energy in term of the Reynolds number in the axial spin case. In the equatorial spin case, the unsteady asymmetric flow is shown to be capable of sustaining dynamo action in the linear and nonlinear regimes. The magnetic field is mainly dipolar in the equatorial spin case, while it is is mainly quadrupolar in the axial spin case.
Nonlinear signal-based control with an error feedback action for nonlinear substructuring control
Enokida, Ryuta; Kajiwara, Koichi
2017-01-01
A nonlinear signal-based control (NSBC) method utilises the 'nonlinear signal' that is obtained from the outputs of a controlled system and its linear model under the same input signal. Although this method has been examined in numerical simulations of nonlinear systems, its application in physical experiments has not been studied. In this paper, we study an application of NSBC in physical experiments and incorporate an error feedback action into the method to minimise the error and enhance the feasibility in practice. Focusing on NSBC in substructure testing methods, we propose nonlinear substructuring control (NLSC), that is a more general form of linear substructuring control (LSC) developed for dynamical substructured systems. In this study, we experimentally and numerically verified the proposed NLSC via substructuring tests on a rubber bearing used in base-isolated structures. In the examinations, NLSC succeeded in gaining accurate results despite significant nonlinear hysteresis and unknown parameters in the substructures. The nonlinear signal feedback action in NLSC was found to be notably effective in minimising the error caused by nonlinearity or unknown properties in the controlled system. In addition, the error feedback action in NLSC was found to be essential for maintaining stability. A stability analysis based on the Nyquist criterion, which is used particularly for linear systems, was also found to be efficient for predicting the instability conditions of substructuring tests with NLSC and useful for the error feedback controller design.
Rincon, F; Schekochihin, A A; Valentini, F
2015-01-01
Magnetic fields pervade the entire Universe and, through their dynamical interactions with matter, affect the formation and evolution of astrophysical systems from cosmological to planetary scales. How primordial cosmological seed fields arose and were further amplified to $\\mu$Gauss levels reported in nearby galaxy clusters, near equipartition with kinetic energy of plasma motions and on scales of at least tens of kiloparsecs, is a major theoretical puzzle still largely unconstrained by observations. Extragalactic plasmas are weakly collisional (as opposed to collisional magnetohydrodynamic fluids), and whether magnetic-field growth and its sustainment through an efficient dynamo instability driven by chaotic motions is possible in such plasmas is not known. Fully kinetic numerical simulations of the Vlasov equation in a six-dimensional phase space necessary to answer this question have until recently remained beyond computational capabilities. Here, we show by means of such simulations that magnetic-field a...
A Reconnecting Flux Rope Dynamo
Baggaley, Andrew W; Shukurov, Anvar; Subramanian, Kandaswamy
2009-01-01
We develop a new model of the fluctuation dynamo in which the magnetic field is confined in thin flux ropes advected by a multi-scale flow modeling turbulence. Magnetic dissipation occurs only via reconnection of the flux ropes. We investigate the kinetic energy release into heat, mediated by the dynamo action, both in our model and by solving the induction equation with the same flow. We find that a flux rope dynamo is an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy release in reconnections has a power-law form with the slope -3, consistent with the Solar corona heating by nanoflares.
Baggaley, Andrew W.; Barenghi, Carlo F.; Shukurov, Anvar; Subramanian, Kandaswamy
2009-11-01
We develop a model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multiscale model of turbulence. Magnetic dissipation occurs only via reconnection of the flux ropes. This model can be viewed as an implementation of the asymptotic limit Rm→∞ for a continuous magnetic field, where magnetic dissipation is strongly localized to small regions of strong-field gradients. We investigate the kinetic-energy release into heat mediated by the dynamo action, both in our model and by solving the induction equation with the same flow. We find that a flux-rope dynamo is an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy release in reconnections has a power-law form with the slope -3 , consistent with the solar corona heating by nanoflares.
Reconnecting flux-rope dynamo.
Baggaley, Andrew W; Barenghi, Carlo F; Shukurov, Anvar; Subramanian, Kandaswamy
2009-11-01
We develop a model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multiscale model of turbulence. Magnetic dissipation occurs only via reconnection of the flux ropes. This model can be viewed as an implementation of the asymptotic limit R_{m}-->infinity for a continuous magnetic field, where magnetic dissipation is strongly localized to small regions of strong-field gradients. We investigate the kinetic-energy release into heat mediated by the dynamo action, both in our model and by solving the induction equation with the same flow. We find that a flux-rope dynamo is an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy release in reconnections has a power-law form with the slope -3 , consistent with the solar corona heating by nanoflares.
On Magnetic Dynamos in Thin Accretion Disks around Compact and Young Stars
Stepinski, T. F.
1993-01-01
A variety of geometrically thin accretion disks commonly associated with such astronomical objects as X-ray binaries, cataclysmic variables, and protostars are likely to be seats of MHD dynamo actions. Thin disk geometry and the particular physical environment make accretion disk dynamos different from stellar, planetary, or even galactic dynamos. We discuss those particular features of disk dynamos with emphasis on the difference between protoplanetary disk dynamos and those associated with compact stars. We then describe normal mode solutions for thin disk dynamos and discuss implications for the dynamical behavior of dynamo-magnetized accretion disks.
A GLOBAL GALACTIC DYNAMO WITH A CORONA CONSTRAINED BY RELATIVE HELICITY
Energy Technology Data Exchange (ETDEWEB)
Prasad, A.; Mangalam, A., E-mail: avijeet@iiap.res.in, E-mail: mangalam@iiap.res.in [Indian Institute of Astrophysics, Sarjapur Road, Koramangala, Bangalore, 560034 (India)
2016-01-20
We present a model for a global axisymmetric turbulent dynamo operating in a galaxy with a corona that treats the parameters of turbulence driven by supernovae and by magneto-rotational instability under a common formalism. The nonlinear quenching of the dynamo is alleviated by the inclusion of small-scale advective and diffusive magnetic helicity fluxes, which allow the gauge-invariant magnetic helicity to be transferred outside the disk and consequently to build up a corona during the course of dynamo action. The time-dependent dynamo equations are expressed in a separable form and solved through an eigenvector expansion constructed using the steady-state solutions of the dynamo equation. The parametric evolution of the dynamo solution allows us to estimate the final structure of the global magnetic field and the saturated value of the turbulence parameter α{sub m}, even before solving the dynamical equations for evolution of magnetic fields in the disk and the corona, along with α-quenching. We then solve these equations simultaneously to study the saturation of the large-scale magnetic field, its dependence on the small-scale magnetic helicity fluxes, and the corresponding evolution of the force-free field in the corona. The quadrupolar large-scale magnetic field in the disk is found to reach equipartition strength within a timescale of 1 Gyr. The large-scale magnetic field in the corona obtained is much weaker than the field inside the disk and has only a weak impact on the dynamo operation.
Simulations of galactic dynamos
Brandenburg, Axel
2014-01-01
We review our current understanding of galactic dynamo theory, paying particular attention to numerical simulations both of the mean-field equations and the original three-dimensional equations relevant to describing the magnetic field evolution for a turbulent flow. We emphasize the theoretical difficulties in explaining non-axisymmetric magnetic fields in galaxies and discuss the observational basis for such results in terms of rotation measure analysis. Next, we discuss nonlinear theory, the role of magnetic helicity conservation and magnetic helicity fluxes. This leads to the possibility that galactic magnetic fields may be bi-helical, with opposite signs of helicity and large and small length scales. We discuss their observational signatures and close by discussing the possibilities of explaining the origin of primordial magnetic fields.
Solar Dynamo Near Tachocline and Magnetic Monopoly
Kryvodubskyj, Valery N.
To explain the observed magnetic anomaly of the polar Sun's field the turbulent dynamo mechanism based on the joint action of mean helical turbulence and differential rotation (alpha-omega-dynamo) was used near tachocline in the solar convection zone (SCZ). The global magnetic field modes (odd or even ones) excited by dynamo depend on the eigenvalue Kh for a Parker dynamo-wave (K is the wave number of the dynamo-wave and h is the extent of the dynamo region). Estimations of the helicity-parameter and radial angular-velocity gradient based on the most recent helioseismological measurements at the growth phase of solar cycle 23 were obtained using the mixing-length approximation. For the SCZ model by Stix (1989) these estimations indicate that the alpha-omega-dynamo mechanism near the tachocline most efficiency excites the poloidal field main odd mode dipole (Kh ~ -7); while the physical conditions at latitudes above 50 degrees are more favourable for the exitation of the lowest even mode quadrupole (Kh ~ +8). The resulting north-south magnetic asymmetry of the poloidal field can explain the magnetic anomaly (""monopoly"" structure) of the polar fields observed near solar-cycle maxima.
Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?
Riols, A.; Rincon, F.; Cossu, C.; Lesur, G.; Ogilvie, G. I.; Longaretti, P.-Y.
2017-02-01
In Keplerian accretion disks, turbulence and magnetic fields may be jointly excited through a subcritical dynamo mechanisminvolving magnetorotational instability (MRI). This dynamo may notably contribute to explaining the time-variability of various accreting systems, as high-resolution simulations of MRI dynamo turbulence exhibit statistical self-organization into large-scale cyclic dynamics. However, understanding the physics underlying these statistical states and assessing their exact astrophysical relevance is theoretically challenging. The study of simple periodic nonlinear MRI dynamo solutions has recently proven useful in this respect, and has highlighted the role of turbulent magnetic diffusion in the seeming impossibility of a dynamo at low magnetic Prandtl number (Pm), a common regime in disks. Arguably though, these simple laminar structures may not be fully representative of the complex, statistically self-organized states expected in astrophysical regimes. Here, we aim at closing this seeming discrepancy by reporting the numerical discovery of exactly periodic, yet semi-statistical "chimeral MRI dynamo states" which are the organized outcome of a succession of MRI-unstable, non-axisymmetric dynamical stages of different forms and amplitudes. Interestingly, these states, while reminiscent of the statistical complexity of turbulent simulations, involve the same physical principles as simpler laminar cycles, and their analysis further confirms the theory that subcritical turbulent magnetic diffusion impedes the sustainment of an MRI dynamo at low Pm. Overall, chimera dynamo cycles therefore offer an unprecedented dual physical and statistical perspective on dynamos in rotating shear flows, which may prove useful in devising more accurate, yet intuitive mean-field models of time-dependent turbulent disk dynamos. Movies associated to Fig. 1 are available at http://www.aanda.org
Stretch-Twist-Fold and slow filamentary dynamos in liquid sodium Madison Dynamo Experiments
de Andrade, Garcia
2009-01-01
Recently Ricca and Maggione [MHD (2008)] have presented a very simple and interesting model of stretch-twist-fold dynamo in diffusive media based on numerical simulations of Riemannian flux tubes. In this paper we present a yet simpler way of analytically obtaining fast and slow dynamo, generated by by the curvature energy of magnetic filaments in diffusive media. geometrical model for the galactic or accretion disk dynamo in shear flows is presented. In the fast dynamo case it is shown that the absence of stretching leads to the absence of fast dynamos and when torsion of filaments vanishes the dynamo action cannot be support as well. This is the Cowling-Zeldovich theorem for planar flows. Isotropy of the magnetic fields hypothesis is used to compute the fast nature of dynamo. A similar result using non-holonomic Frenet frame has been recently obtained for filamentary dynamos [Garcia de Andrade, AN (2008)]. The stretch-twist-fold (STF) filamented models discussed here may serve to formulate future experiment...
Subcritical dynamo bifurcation in the Taylor-Green flow.
Ponty, Y; Laval, J-P; Dubrulle, B; Daviaud, F; Pinton, J-F
2007-11-30
We report direct numerical simulations of dynamo generation for flow generated using a Taylor-Green forcing. We find that the bifurcation is subcritical and show its bifurcation diagram. We connect the associated hysteretic behavior with hydrodynamics changes induced by the action of the Lorentz force. We show the geometry of the dynamo magnetic field and discuss how the dynamo transition can be induced when an external field is applied to the flow.
Wang, Z; Barnes, C W; Barnes, D C; Wang, Zhehui; Pariev, Vladimir I.; Barnes, Cris W.; Barnes, Daniel C.
2002-01-01
A new kind of dynamo utilizing flowing laboratory plasmas has been identified. Conversion of plasma kinetic energy to magnetic energy is verified numerically by kinematic dynamo simulations for magnetic Reynolds numbers above 210. As opposed to intrinsically-turbulent liquid-sodium dynamos, the proposed plasma dynamos correspond to laminar flow topology. Modest plasma parameters, 1-20 eV temperatures, 10^{19}-10^{20} m^{-3} densities in 0.3-1.0 m scale-lengths driven by velocities on the order of the Alfven Critical Ionization Velocity (CIV), self-consistently satisfy the conditions needed for the magnetic field amplication. Growth rates for the plasma dynamos are obtained numerically with different geometry and magnetic Reynolds numbers. Magnetic-field-free coaxial plasma guns can be used to sustain the plasma flow and the dynamo.
2012-09-30
1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Ocean Dynamics: Dynamo Robert Pinkel Marine Physical...execution of the Dynamo Leg IV Experiment in December 2011. Our objective was to document the development of the diurnal surface layer and its...2. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Ocean Dynamics: Dynamo 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM
Bistability and chaos in the Taylor-Green dynamo.
Yadav, Rakesh K; Verma, Mahendra K; Wahi, Pankaj
2012-03-01
Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.
Effective action and vacuum expectations in nonlinear $\\sigma$ model
Fayzullaev, B A
2015-01-01
The equations for effective action for nonlinear $\\sigma$ model are derived using DeWitt method in two forms - for generator of vertex parts $\\Gamma$ and for generator of weakly connected parts $W$. Loop-expansion solutions to these equations are found. It is shown that vacuum expectation values for various quantities including divergence of a N\\"{o}ther current, trace of the energy-momentum tensor and so on, can be calculated by this method. Also it is shown that vacuum expectation to the sigma-field is determined by an explicit combination of tree Green function and classical solution. It is shown that the limit when coupling constant tends to zero is singular one.
Nigro, G.; Pongkitiwanichakul, P.; Cattaneo, F.; Tobias, S. M.
2017-01-01
We consider kinematic dynamo action in a sheared helical flow at moderate to high values of the magnetic Reynolds number (Rm). We find exponentially growing solutions which, for large enough shear, take the form of a coherent part embedded in incoherent fluctuations. We argue that at large Rm large-scale dynamo action should be identified by the presence of structures coherent in time, rather than those at large spatial scales. We further argue that although the growth rate is determined by small-scale processes, the period of the coherent structures is set by mean-field considerations.
Weiss, Benjamin P; Tikoo, Sonia M
2014-12-05
The inductive generation of magnetic fields in fluid planetary interiors is known as the dynamo process. Although the Moon today has no global magnetic field, it has been known since the Apollo era that the lunar rocks and crust are magnetized. Until recently, it was unclear whether this magnetization was the product of a core dynamo or fields generated externally to the Moon. New laboratory and spacecraft measurements strongly indicate that much of this magnetization is the product of an ancient core dynamo. The dynamo field persisted from at least 4.25 to 3.56 billion years ago (Ga), with an intensity reaching that of the present Earth. The field then declined by at least an order of magnitude by ∼3.3 Ga. The mechanisms for sustaining such an intense and long-lived dynamo are uncertain but may include mechanical stirring by the mantle and core crystallization.
The Turbulent Dynamo in Highly Compressible Supersonic Plasmas
Federrath, Christoph; Bovino, Stefano; Schleicher, Dominik R G
2014-01-01
The turbulent dynamo may explain the origin of cosmic magnetism. While the exponential amplification of magnetic fields has been studied for incompressible gases, little is known about dynamo action in highly-compressible, supersonic plasmas, such as the interstellar medium of galaxies and the early Universe. Here we perform the first quantitative comparison of theoretical models of the dynamo growth rate and saturation level with three-dimensional magnetohydrodynamical simulations of supersonic turbulence with grid resolutions of up to 1024^3 cells. We obtain numerical convergence and find that dynamo action occurs for both low and high magnetic Prandtl numbers Pm = nu/eta = 0.1-10 (the ratio of viscous to magnetic dissipation), which had so far only been seen for Pm >= 1 in supersonic turbulence. We measure the critical magnetic Reynolds number, Rm_crit = 129 (+43, -31), showing that the compressible dynamo is almost as efficient as in incompressible gas. Considering the physical conditions of the present a...
Shear dynamo problem: Quasilinear kinematic theory.
Sridhar, S; Subramanian, Kandaswamy
2009-04-01
Large-scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is nonperturbative in the shear strength. We derive the integrodifferential equation for the evolution of the mean magnetic field by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. For nonhelical turbulence the time evolution of the cross-shear components of the mean field does not depend on any other components excepting themselves. This is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence the shear-current assisted dynamo is essentially absent, although large-scale nonhelical dynamo action is not ruled out.
The Shear Dynamo: quasilinear kinematic theory
Sridhar, S
2008-01-01
Large--scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is non perturbative in the strength of the background shear. We derive expressions for the turbulent transport coefficients of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. We prove that, for non helical turbulence, the equation governing the time evolution of the cross shear component of the mean magnetic field is closed, in the sense that it is independent of the other two components. This result is valid for any Galilean--invariant velocity field, independent of its dynamics. Thus we find the shear--current assisted dynamo is essentially absent, although large--scale non helical dynamo action is not ruled out.
The Magnetic Furnace: Intense Core Dynamos in B Stars
Augustson, Kyle C.; Brun, Allan Sacha; Toomre, Juri
2016-10-01
The dynamo action achieved in the convective cores of main-sequence massive stars is explored here through three-dimensional (3D) global simulations of convective core dynamos operating within a young 10 {M}⊙ B-type star, using the anelastic spherical harmonic code. These simulations capture the inner 65% of this star by radius, encompassing the convective nuclear-burning core (about 23% by radius) and a portion of the overlying radiative envelope. Eight rotation rates are considered, ranging from 0.05% to 16% of the surface breakup velocity, thereby capturing both convection that barely senses the effects of rotation and other situations in which the Coriolis forces are prominent. The vigorous dynamo action realized within all of these turbulent convective cores builds magnetic fields with peak strengths exceeding a megagauss, with the overall magnetic energy (ME) in the faster rotators reaching super-equipartition levels compared to the convective kinetic energy (KE). The core convection typically involves turbulent columnar velocity structures roughly aligned with the rotation axis, with magnetic fields threading through these rolls and possessing complex linkages throughout the core. The very strong fields are able to coexist with the flows without quenching them through Lorentz forces. The velocity and magnetic fields achieve such a state by being nearly co-aligned, and with peak magnetic islands being somewhat displaced from the fastest flows as the intricate evolution proceeds. As the rotation rate is increased, the primary force balance shifts from nonlinear advection balancing Lorentz forces to a magnetostrophic balance between Coriolis and Lorentz forces.
Magnetized Turbulent Dynamo in Protogalaxies
Malyshkin, L M; Malyshkin, Leonid; Kulsrud, Russell
2002-01-01
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of this theory to protogalaxies is rather limited. The reason is that in protogalaxies the temperature is very high, and the viscosity is dominated by magnetized ions. As the magnetic field strength grows in time, the ion cyclotron time becomes shorter than the ion collision time, and the plasma becomes strongly magnetized. As a result, the ion viscosity becomes the Braginskii viscosity. Thus, in protogalaxies the back reaction sets in much earlier, at field strengths much lower than those which correspond...
Galactic dynamo and helicity losses through fountain flow
Shukurov, A; Subramanian, K; Brandenburg, A; Shukurov, Anvar; Sokoloff, Dmitry; Subramanian, Kandaswamy; Brandenburg, Axel
2006-01-01
Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.
Fluctuation dynamo based on magnetic reconnections
Baggaley, Andrew W.; Barenghi, Carlo F.; Shukurov, Anvar; Subramanian, Kandaswamy
2009-01-01
We develop a new model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multi-scale flow which models turbulence. Magnetic dissipation occurs only via reconnections of flux ropes. The model is particularly suitable for rarefied plasma, such as the Solar corona or galactic halos. We investigate the kinetic energy release into heat, mediated by dynamo action, both in our model and by solving the induction equation with the same flow. We find tha...
Waves, Coriolis force and the dynamo effect
Mahajan, S M; Gómez, D O
2004-01-01
Dynamo activity caused by waves in a rotating magneto-plasma is investigated. In astrophysical environments such as accretion disks and at sufficiently small spatial scales, the Hall effect is likely to play an important role. It is shown that a combination of the Coriolis force and Hall effect can produce a finite $\\alpha$-effect by generating net helicity in the small scales. The shear/ion-cyclotron normal mode of the Hall plasma is the dominant contributor to the dynamo action for short scale motions.
Turbulence and dynamo interlinks
de Gouveia Dal Pino, E. M.; Santos-Lima, R.; Kowal, G.; Falceta-Gonçalves, D.
2013-07-01
The role of turbulence in astrophysical environments and its interplay with magnetic fields is still highly debated. In this lecture, we will discuss this issue in the framework of dynamo processes. We will first present a very brief summary of turbulent dynamo theories, then will focus on small scale turbulent dynamos and their particular relevance on the origin and maintenance of magnetic fields in the intra-cluster media (ICM) of galaxies. In these environments, the very low density of the flow requires a collisionless-MHD treatment. We will show the implications of this approach in the turbulent amplification of the magnetic fields in these environments. To finalize, we will also briefly address the connection between MHD turbulence and fast magnetic reconnection and its possible implications in the diffusion of magnetic flux in the dynamo process.
Turbulence and Dynamo Interlinks
Pino, E M de Gouveia Dal
2013-01-01
The role of turbulence in astrophysical environments and its interplay with magnetic fields is still highly debated. In this lecture, we will discuss this issue in the framework of dynamo processes. We will first present a very brief summary of turbulent dynamo theories, then will focus on small scale turbulent dynamos and their particular relevance on the origin and maintenance of magnetic fields in the intra-cluster media (ICM) of galaxies. In these environments, the very low density of the flow requires a collisionless-MHD treatment. We will show the implications of this approach in the turbulent amplification of the magnetic fields in these environments. To finalize, we will also briefly address the connection between MHD turbulence and fast magnetic reconnection and its possible implications in the diffusion of magnetic flux in the dynamo process.
Transition from large-scale to small-scale dynamo.
Ponty, Y; Plunian, F
2011-04-15
The dynamo equations are solved numerically with a helical forcing corresponding to the Roberts flow. In the fully turbulent regime the flow behaves as a Roberts flow on long time scales, plus turbulent fluctuations at short time scales. The dynamo onset is controlled by the long time scales of the flow, in agreement with the former Karlsruhe experimental results. The dynamo mechanism is governed by a generalized α effect, which includes both the usual α effect and turbulent diffusion, plus all higher order effects. Beyond the onset we find that this generalized α effect scales as O(Rm(-1)), suggesting the takeover of small-scale dynamo action. This is confirmed by simulations in which dynamo occurs even if the large-scale field is artificially suppressed.
Generation of dynamo magnetic fields in thin Keplerian disks
Stepinski, T. F.; Levy, E. H.
1990-01-01
The combined action of nonuniform rotation and helical convection in protoplanetary disks, in the Galaxy, or in accretion disks surrounding black holes and other compact objects, enables an alpha-omega dynamo to generate a large-scale magnetic field. In this paper, the properties of such magnetic fields are investigated using a two-dimensional, partially numerical method. The structures of the lowest-order steady state and oscillatory modes are calculated for two kinds of external boundary conditions. A quadruple, steady state, highly localized mode is the most easily excited for low values of the dynamo number. The results indicate that, except under special conditions, disk dynamo modes tend to consist of relatively localized rings structures. For large values of the dynamo number, the magnetic field consists of a number of quasi-independent, spatially localized modes generated in various concentric rings filling the disk inward of a dynamo generation 'front'.
Generation of dynamo magnetic fields in thin Keplerian disks
Energy Technology Data Exchange (ETDEWEB)
Stepinski, T.F.; Levy, E.H. (Arizona Univ., Tucson (USA))
1990-10-01
The combined action of nonuniform rotation and helical convection in protoplanetary disks, in the Galaxy, or in accretion disks surrounding black holes and other compact objects, enables an alpha-omega dynamo to generate a large-scale magnetic field. In this paper, the properties of such magnetic fields are investigated using a two-dimensional, partially numerical method. The structures of the lowest-order steady state and oscillatory modes are calculated for two kinds of external boundary conditions. A quadruple, steady state, highly localized mode is the most easily excited for low values of the dynamo number. The results indicate that, except under special conditions, disk dynamo modes tend to consist of relatively localized rings structures. For large values of the dynamo number, the magnetic field consists of a number of quasi-independent, spatially localized modes generated in various concentric rings filling the disk inward of a dynamo generation front. 36 refs.
Problems and Progress in Astrophysical Dynamos
Vishniac, E T; Cho, J
2002-01-01
Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux threading a fluid element, or the field topology. Classical dynamo theory evades this limit by assuming that magnetic reconnection is fast, even for vanishing resistivity, and that the large scale field can be generated by the action of kinetic helicity. Both these claims have been severely criticized, and the latter appears to conflict with strong theoretical arguments based on magnetic helicity conservation and a series of numerical simulations. Here we discuss recent efforts to explain fast magnetic reconnection through the topological effects of a weak stochastic magnetic field component. We also show how mean-field dynamo theory can be recast in a form which respects magnetic helicity conservation, and how this changes our understanding of astrophysical dynamos. Finally, we ...
The Magnetic Furnace: Examining Fully Convective Dynamos And The Influence Of Rotation
Augustson, Kyle; Mathis, S.; Brun, A. S.; Toomre, J.
2016-08-01
The dynamo action likely present within fully convective regions is explored through global-scale 3-D simulations. These simulations provide a contextual analog for the convective dynamos that are likely operating deep within the interiors of fully convective low mass stars. A logarithmic range of rotation rates is considered, thereby capturing both convection barely sensing the effects of rotation to others in which the Coriolis forces are prominent. The vigorous dynamo action realized within all of these turbulent convective cores builds magnetic fields with peak strengths exceeding a megagauss, with the overall magnetic energy (ME) in the faster rotators reaching super-equipartition levels compared to the convective kinetic energy (KE). Such strong fields are able to coexist with the flows without quenching them through Lorentz forces. This state is achieved due to the velocity and magnetic fields being nearly co-aligned, and with peak magnetic islands being somewhat displaced from the fastest flows as the intricate evolution of these MHD structures proceeds. As the rotation rate is increased, the primary force balance shifts from nonlinear advection balancing Lorentz forces to a magnetostrophic balance between Coriolis and Lorentz forces.
Turbulent dynamos in spherical shell segments of varying geometrical extent
Mitra, Dhrubaditya; Brandenburg, Axel; Moss, David
2008-01-01
We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We use perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic fields at scales larger than the characteristic scale of the forcing. The magnetic energy exceeds the kinetic energy over dissipative time scales, similar to that seen earlier in Cartesian simulations in periodic boxes. As we increase the size of the domain in the azimuthal direction we find that the nonlinearly saturated magnetic field organizes itself in long-lived cellular structures with aspect ratios close to unity....
Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?
Riols, A; Cossu, C; Lesur, G; Ogilvie, G I; Longaretti, P-Y
2016-01-01
In Keplerian accretion disks, turbulence and magnetic fields may be jointly excited through a subcritical dynamo process involving the magnetorotational instability (MRI). High-resolution simulations exhibit a tendency towards statistical self-organization of MRI dynamo turbulence into large-scale cyclic dynamics. Understanding the physical origin of these structures, and whether they can be sustained and transport angular momentum efficiently in astrophysical conditions, represents a significant theoretical challenge. The discovery of simple periodic nonlinear MRI dynamo solutions has recently proven useful in this respect, and has notably served to highlight the role of turbulent magnetic diffusion in the seeming decay of the dynamics at low magnetic Prandtl number Pm (magnetic diffusivity larger than viscosity), a common regime in accretion disks. The connection between these simple structures and the statistical organization reported in turbulent simulations remained elusive, though. Here, we report the n...
Magnetic Helicity and Planetary Dynamos
Shebalin, John V.
2012-01-01
A model planetary dynamo based on the Boussinesq approximation along with homogeneous boundary conditions is considered. A statistical theory describing a large-scale MHD dynamo is found, in which magnetic helicity is the critical parameter
Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes
Gorban, A N
2015-01-01
The nonlinear Markov processes are the measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic equations allow Lyapunov functionals (entropy, free energy, etc.). This may be considered as a sort of inheritance of the Lyapunov functionals from the microscopic master equations. We study nonlinear Markov processes that inherit thermodynamic properties from the microscopic linear Markov processes. We develop the thermodynamics of nonlinear Markov processes and analyze the asymptotic assumption, which are sufficient for this inheritance.
Stochastic flux freezing and magnetic dynamo.
Eyink, Gregory L
2011-05-01
Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered.
Hathaway, David H.
1998-01-01
The solar dynamo is the process by which the Sun's magnetic field is generated through the interaction of the field with convection and rotation. In this, it is kin to planetary dynamos and other stellar dynamos. Although the precise mechanism by which the Sun generates its field remains poorly understood despite decades of theoretical and observational work, recent advances suggest that solutions to this solar dynamo problem may be forthcoming. Two basic processes are involved in dynamo activity. When the fluid stresses dominate the magnetic stresses (high plasma beta = 8(pi)rho/B(sup 2)), shear flows can stretch magnetic field lines in the direction of the shear (the "alpha effect") and helical flows can lift and twist field lines into orthogonal planes (the "alpha effect"). These two processes can be active anywhere in the solar convection zone but with different results depending upon their relative strengths and signs. Little is known about how and where these processes occur. Other processes, such as magnetic diffusion and the effects of the fine scale structure of the solar magnetic field, pose additional problems.
Kinetic Magnetorotational Turbulence and Dynamo
Kunz, Matthew; Stone, James; Quataert, Eliot
2016-10-01
Low-luminosity black-hole accretion flows, such as that at the Galactic center, are collisionless. A kinetic approach is thus necessary to understand the transport of heat and angular momentum, the acceleration of particles, and the growth and structure of the magnetic field in these systems. We present results from the first 6D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model. Special attention will be paid to the enhanced transport of angular momentum by field-aligned pressure anisotropies, as well as to the ion-Larmor-scale kinetic instabilities (firehose, mirror, ion-cyclotron) which regulate those anisotropies. Energy spectra and phase-space evolution will be discussed. Time permitting, dedicated nonlinear studies of firehose and mirror instabilities in a shearing plasma will also be presented as a complement to the study of the magnetorotational instability. The profits, perils, and price of using a kinetic approach will be briefly mentioned.
Sharp magnetic structures from dynamos with density stratification
Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Rogachevskii, Igor
2017-01-01
Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and might be driven in nonlinear stage of evolution by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 2.5 times supercritical.
Strong Field Spherical Dynamos
Dormy, Emmanuel
2014-01-01
Numerical models of the geodynamo are usually classified in two categories: those denominated dipolar modes, observed when the inertial term is small enough, and multipolar fluctuating dynamos, for stronger forcing. I show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong field limit. This solution co-exists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set the dominant length scale, and the strong field branch in which viscous and inertial effects are largely negligible. These results indicate that a distinguished limit needs to be sought to produce numerical models relevant to the geodynamo and that the usual approach of minimizing the magnetic Prandtl number (ratio of the fluid kinematic viscosity to its magnetic diffusivity) at a given Ekman number is mi...
Cameron, R. H.; Dikpati, M.; Brandenburg, A.
2017-09-01
A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property has been identified with the decline of large-scale magnetic fields found in direct numerical simulations at large magnetic Reynolds numbers. However, magnetic helicity fluxes through the solar surface can alleviate this problem and connect theory with observations, as will be discussed.
Cameron, R H; Brandenburg, A
2016-01-01
A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property has been identified with the decline of large-scale magnetic fields found in direct numerical simulations at large magnetic Reynolds numbers. However, magnetic helicity fluxes through the solar surface can alleviate this problem and connect theory with observations, as will be discussed.
Busse, F H; 10.1017/S1743921307000920
2009-01-01
Possibilities and difficulties of applying the theory of magnetic field generation by convection flows in rotating spherical fluid shells to the Giant Planets are outlined. Recent progress in the understanding of the distribution of electrical conductivity in the Giant Planets suggests that the dynamo process occurs predominantly in regions of semiconductivity. In contrast to the geodynamo the magnetic field generation in the Giant Planets is thus characterized by strong radial conductivity variations. The importance of the constraint on the Ohmic dissipation provided by the planetary luminosity is emphasized. Planetary dynamos are likely to be of an oscillatory type, although these oscillations may not be evident from the exterior of the planets.
Stone, James
2011-04-01
Numerical methods have proved crucial for the study of the nonlinear regime of the magnetorotational instability (MRI) and resulting dynamo action. After a brief introduction to the methods, a variety of results from new simulations of the MRI in both local (shearing box approximation) and global domains will be presented. Previous work on the saturation level and numerical convergence in both stratified and unstratified domains with no net flux (both with and without explicit dissipation) will be described, and the connection to dynamo theory will be mentioned. Results from several groups in which the size of the computational domain, and the vertical boundary conditions, are varied will be discussed. Finally, new work on the direct comparison between high-resolution global and shearing box simulations will be presented, and new studies of stratified disks with radiative transfer will be introduced.
Solar and Stellar Dynamos Saas-Fee Advanced Course 39 Swiss Society for Astrophysics and Astronomy
2013-01-01
Astrophysical dynamos are at the heart of cosmic magnetic fields of a wide range of scales, from planets and stars to entire galaxies. This book presents a thorough, step-by-step introduction to solar and stellar dynamos. Looking first at the ultimate origin of cosmic seed magnetic fields, the antagonists of field amplification are next considered: resistive decay, flux expulsion, and flows ruled out by anti-dynamo theorems. Two kinematic flows that can act as dynamos are then studied: the Roberts cell and the CP-flow. Mean-field electrodynamics and derivation of the mean-field dynamo equations lead to the alpha Omega-dynamo, the flux transport dynamo, and dynamos based on the Babcock-Leighton mechanism. Alternatives to the mean-field theory are also presented, as are global MHD dynamo simulations. Fluctuations and grand minima in the solar cycle are discussed in terms of dynamo modulations through stochastic forcing and nonlinear effects. The book concludes with an overview of the major challenges in underst...
Naso, L; Bonanno, A; Paternò, L
2007-01-01
During the first 40 s after their birth, proto-neutron stars are expected to be subject to at least two types of instability: the convective instability and the neutron-finger one. Both instabilities involve convective motions and hence can trigger dynamo actions which may be responsible for the large magnetic fields in neutron stars and magnetars. We have solved the mean-field induction equation in a simplified one-dimensional model of both the convective and the neutron-finger instability zones. Although very idealized, the model includes the nonlinearities introduced by the feedback processes which tend to saturate the growth of the magnetic field (alpha-quenching) and suppress its turbulent diffusion (eta-quenching). The possibility of a dynamo action is studied within a dynamical model of turbulent diffusivity where the boundary of the unstable zone is allowed to move. We show that the dynamo action can be operative and that the amplification of the magnetic field can still be very effective. Furthermore...
Azimuthal dynamo wave in spherical shell convection
Cole, Elizabeth; Mantere, Maarit J; Brandenburg, Axel
2013-01-01
We report the finding of an azimuthal dynamo wave of a low-order (m=1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean field dynamo theory and have been obtained previously in mean-field models. Observational results both from photometry and Doppler imaging have revealed persistent drifts of spots for several rapidly rotating stars, but, although an azimuthal dynamo wave has been proposed as a possible mechanism responsible for this behavior, it has been judged as unlikely, as practical evidence for such waves from DNS has been lacking. The large-scale magnetic field in our DNS, which is due to self-consistent dynamo action, is dominated by a retrograde m=1 mode. Its pattern speed is nearly independent of latitude and does not reflect the speed of the differential rotation at any depth. The extrema of magnetic m=1 structures coincide reasonably with the maxima of m=2 structures of the temperature. These results provide direct support for...
Fluctuation dynamos and their Faraday rotation signatures
Bhat, Pallavi
2012-01-01
Turbulence is ubiquitous in many astrophysical systems like galaxies, galaxy clusters and possibly even the IGM filaments. We study fluctuation dynamo action in turbulent systems focusing on one observational signature; the Faraday rotation measure (RM) from background radio sources seen through the magnetic field generated by such a dynamo. We simulate the fluctuation dynamo (FD) in periodic boxes up to resolutions of 512^3, with varying fluid and magnetic Reynolds numbers, and measure the resulting random RMs. We show that the resulting rms value of RM is quite significant, given that the FD produces intermittent fields. When the dynamo saturates, it is of order 40%-50% of the value expected in a model where fields of strength B_rms uniformly fill cells of the largest turbulent eddy but are randomly oriented from one cell to another. This level of RM dispersion obtains across different values of magnetic Reynolds number and Prandtl number explored. We also use the random RMs to probe the structure of the ge...
Invisible dynamo in mean-field models
Reshetnyak, M. Yu.
2016-07-01
The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.
NONLINEAR FREE SURFACE ACTION WITH AN ARRAY OF VERTICAL CYLINDERS
Institute of Scientific and Technical Information of China (English)
HUANG J. B.
2004-01-01
Nonlinear diffraction of regular waves by an array of bottom-seated circular cylinders is investigated in frequency domain, based on a Stokes expansion approach. A complete semi-analytical solution is developed which allows an efficient evaluation of the second-order potentials in the entire fluid domain, and the wave forces on the structure. Expressions are derived for the second-order potential in the vicinity of individual cylinders. These expressions have a simple form, thus providing an effective means for investigating the wave enhancement due to nonlinear interactions with multiple cylinders. Based on the present method, the wave run-up and free-surface elevations around an array of two, three and four cylinders are investigated numerically.
Planetary Dynamos: Investigations of Saturn and Ancient Mars
Energy Technology Data Exchange (ETDEWEB)
Stanley, Sabine [University of Toronto
2012-04-18
Magnetic field observations by spacecraft missions have provided vital information on planetary dynamos. The four giant planets as well as Earth, Mercury and Ganymede have observable magnetic fields generated by active dynamos. In contrast, Moon and Mars only have remanent crustal fields from dynamo action in their early histories. A variety of magnetic field morphologies and intensities can be found in the solar system. We have found that some of the differences between planetary magnetic fields can be explained as the result of the presence of boundary thermal variations or stably-stratified layers. In this talk, I will discuss how dynamos are affected by these complications and discuss the implications for Mars’ magnetic dichotomy and Saturn’s extremely axisymmetric magnetic field.
Generation of dynamo magnetic fields in the primordial solar nebula
Stepinski, Tomasz F.
1992-01-01
The present treatment of dynamo-generated magnetic fields in the primordial solar nebula proceeds in view of the ability of the combined action of Keplerian rotation and helical convention to generate, via alpha-omega dynamo, large-scale magnetic fields in those parts of the nebula with sufficiently high, gas-and magnetic field coupling electrical conductivity. Nebular gas electrical conductivity and the radial distribution of the local dynamo number are calculated for both a viscous-accretion disk model and the quiescent-minimum mass nebula. It is found that magnetic fields can be easily generated and maintained by alpha-omega dynamos occupying the inner and outer parts of the nebula.
Experimental demonstration of a homogeneous two-scale dynamo
Stieglitz, R.; Muller, U.
2002-06-01
It has been shown theoretically in the past that homogeneous dynamos may occur for various velocity fields. G.O. Roberts investigated spatially periodic velocity fields, which Busse confined to a finite cylindrical domain. Using a mean field approach he derived an approximate condition for the onset of dynamo action. Based on Busse's idea at the Forschungszentrum Karlsruhe a conceptual design for an experimental homogeneous dynamo was developed, and a test facility was set up. The first experiments demonstrated that a permanent dynamo can exist in a cylindrical container filled with liquid sodium in which by means of guide vanes counter rotating and counter current spiral vortices are arranged. The dynamo is self-exciting at sufficiently high flow rates, and the magnetic field saturates at a mean value. The instantaneous magnetic field fluctuates around this mean value by about 5%. As predicted by theory the mode of the observed magnetic field is strongly non-axisymmetric. In a series of experiments a phase and a bifurcation diagramm for dynamo action was derived which depend on the spiral and axial flow rates. Figs 5, Refs 14.
Parker's dynamo and geomagnetic reversals
Reshetnyak, M
2011-01-01
Fluctuations of the alpha-effect which break equatorial symmetry of the flow in the kinematic Parker's dynamo are considered. We show, that even small (a few percents) fluctuation can leed to the substantial assymmetry of the magnetic field in the hemispheres as well as the propagation of the dynamo wave through the equator plane. We also consider how change of the dynamo number can be used to explain different regimes of magnetic field generation in geodynamo.
Mars' paleomagnetic field as the result of a single-hemisphere dynamo.
Stanley, Sabine; Elkins-Tanton, Linda; Zuber, Maria T; Parmentier, E Marc
2008-09-26
Mars' crustal magnetic field was most likely generated by dynamo action in the planet's early history. Unexplained characteristics of the field include its strength, concentration in the southern hemisphere, and lack of correlation with any surface features except for the hemispheric crustal dichotomy. We used numerical dynamo modeling to demonstrate that the mechanisms proposed to explain crustal dichotomy formation can result in a single-hemisphere dynamo. This dynamo produces strong magnetic fields in only the southern hemisphere. This magnetic field morphology can explain why Mars' crustal magnetic field intensities are substantially stronger in the southern hemisphere without relying on any postdynamo mechanisms.
Resonant oscillations in ${\\alpha}^{2}$-dynamos on a closed, twisted Riemannian 2D flux tubes
de Andrade, Garcia
2009-01-01
Chicone et al [CMP (1995)] have shown that, kinematic fast dynamos in diffusive media, could exist only on a closed, 2D Riemannian manifold of constant negative curvature. This report, shows that their result cannot be extended to oscillatory ${\\alpha}^{2}$-dynamos, when there are resonance modes, between toroidal and poloidal frequencies of twisted magnetic flux tubes. Thus, dynamo action can be supported in regions, where Riemannian curvature is positive. For turbulent dynamos, this seems physically reasonable, since recently, [Shukurov et al PRE (2008)] have obtained a Moebius flow strip in sodium liquid, torus Perm dynamo where curvature is also connected to the magnetic fields via diffusion. This could be done, by adjusting the corresponding frequencies till they achieved resonance. Actually 2D torus, is a manifold of zero mean curvature, where regions of positive and negative curvatures exist. It is shown that, Riemannian solitonic surface, endowed with a steady ${\\alpha}^{2}$-dynamo from magnetic filam...
Dynamo onset as a first-order transition: lessons from a shell model for magnetohydrodynamics.
Sahoo, Ganapati; Mitra, Dhrubaditya; Pandit, Rahul
2010-03-01
We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number PrM and the magnetic Reynolds number ReM. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (PrM-1,ReM) plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain a hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.
Turbulent ${\\alpha}$-effect in twisted magnetic flux tubes dynamos in Riemannian space
de Andrade, Garcia
2007-01-01
Analytical solution of first order torsion ${\\alpha}$-effect in twisted magnetic flux tubes representing a flux tube dynamo in Riemannian space is presented. Toroidal and poloidal component of the magnetic field decays as $r^{-1}$, while grow exponentially in time. The rate of speed of the helical dynamo depends upon the value of Frenet curvature of the tube. The $\\alpha$ factor possesses a fundamental contribution from constant torsion tube approximation. It is also assumed that the curvature of the magnetic axis of the tube is constant. Though ${\\alpha}$-effect dynamo equations are rather more complex in Riemann flux tube coordinates, a simple solution assuming force-free magnetic fields is shown to be possible. Dynamo solutions are possible if the dynamo action is able to change the signs of torsion and curvature of the dynamo flux tube simultaneously.
Radiative transfer dynamo effect
Munirov, Vadim R.; Fisch, Nathaniel J.
2017-01-01
Magnetic fields in rotating and radiating astrophysical plasma can be produced due to a radiative interaction between plasma layers moving relative to each other. The efficiency of current drive, and with it the associated dynamo effect, is considered in a number of limits. It is shown here, however, that predictions for these generated magnetic fields can be significantly higher when kinetic effects, previously neglected, are taken into account.
Mathematical aspects of natural dynamos
Dormy, Emmanuel
2007-01-01
Although the origin of Earth's and other celestial bodies' magnetic fields remains unknown, we do know that the motion of electrically conducting fluids generates and maintains these fields, forming the basis of magnetohydrodynamics (MHD) and, to a larger extent, dynamo theory. Answering the need for a comprehensive, interdisciplinary introduction to this area, ""Mathematical Aspects of Natural Dynamos"" provides a foundation in dynamo theory before moving on to modeling aspects of natural dynamos.Bringing together eminent international contributors, the book first introduces governing equatio
Comparison of terrestrial and solar dynamos
Energy Technology Data Exchange (ETDEWEB)
Zhang, Keke [Center for Geophysical and Astrophysical Fluid Dynamics, Department of Mathematical Sciences, University of Exeter, EX4 4QE (United Kingdom); Schubert, Gerald [Department of Earth and Space Sciences, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095-1567 (United States)
2006-05-01
also discuss why different approaches have been employed in the numerical modelling of the geodynamo and solar dynamo and what are the major difficulties in simulating both dynamos. We employ two spherical non-linear dynamo models to illustrate how the observed geomagnetic or solar magnetic fields can be controlled by the effect of the radial shear layers which exist in the Sun's interior and might exist in the Earth's core.0.
MHD Turbulence, Turbulent Dynamo and Applications
Beresnyak, Andrey
2014-01-01
MHD Turbulence is common in many space physics and astrophysics environments. We first discuss the properties of incompressible MHD turbulence. A well-conductive fluid amplifies initial magnetic fields in a process called small-scale dynamo. Below equipartition scale for kinetic and magnetic energies the spectrum is steep (Kolmogorov -5/3) and is represented by critically balanced strong MHD turbulence. In this paper we report the basic reasoning behind universal nonlinear small-scale dynamo and the inertial range of MHD turbulence. We measured the efficiency of the small-scale dynamo $C_E=0.05$, Kolmogorov constant $C_K=4.2$ and anisotropy constant $C_A=0.63$ for MHD turbulence in high-resolution direct numerical simulations. We also discuss so-called imbalanced or cross-helical MHD turbulence which is relevant for in many objects, most prominently in the solar wind. We show that properties of incompressible MHD turbulence are similar to the properties of Alfv\\'enic part of MHD cascade in compressible turbul...
Convective Dynamo Simulation with a Grand Minimum
Augustson, Kyle; Miesch, Mark; Toomre, Juri
2015-01-01
The global-scale dynamo action achieved in a simulation of a Sun-like star rotating at thrice the solar rate is assessed. The 3-D MHD Anelastic Spherical Harmonic (ASH) code, augmented with a viscosity minimization scheme, is employed to capture convection and dynamo processes in this G-type star. The simulation is carried out in a spherical shell that encompasses 3.8 density scale heights of the solar convection zone. It is found that dynamo action with a high degree of time variation occurs, with many periodic polarity reversals occurring roughly every 6.2 years. The magnetic energy also rises and falls with a regular period. The magnetic energy cycles arise from a Lorentz-force feedback on the differential rotation, whereas the processes leading to polarity reversals are more complex, appearing to arise from the interaction of convection with the mean toroidal fields. Moreover, an equatorial migration of toroidal field is found, which is linked to the changing differential rotation, and potentially to a no...
Vishniac, Ethan T.
2015-01-01
We show that a differentially rotating conducting fluid automatically creates a magnetic helicity flux with components along the rotation axis and in the direction of the local vorticity. This drives a rapid growth in the local density of current helicity, which in turn drives a large scale dynamo. The dynamo growth rate derived from this process is not constant, but depends inversely on the large scale magnetic field strength. This dynamo saturates when buoyant losses of magnetic flux compete with the large scale dynamo, providing a simple prediction for magnetic field strength as a function of Rossby number in stars. Increasing anisotropy in the turbulence produces a decreasing magnetic helicity flux, which explains the flattening of the B/Rossby number relation at low Rossby numbers. We also show that the kinetic helicity is always a subdominant effect. There is no kinematic dynamo in real stars.
Effect of the Lorentz force on on-off dynamo intermittency.
Alexakis, Alexandros; Ponty, Yannick
2008-05-01
An investigation of the dynamo instability close to the threshold produced by an ABC forced flow is presented. We focus on the on-off intermittency behavior of the dynamo and the countereffect of the Lorentz force in the nonlinear stage of the dynamo. The Lorentz force drastically alters the statistics of the turbulent fluctuations of the flow and reduces their amplitude. As a result, much longer bursts (on phases) are observed than is expected based on the amplitude of the fluctuations in the kinematic regime of the dynamo. For large Reynolds numbers, the duration time of the on phase follows a power law distribution, while for smaller Reynolds numbers the Lorentz force completely kills the noise and the system transits from a chaotic state into a laminar time periodic flow. The behavior of the on-off intermittency as the Reynolds number is increased is also examined. The connections with dynamo experiments and theoretical modeling are discussed.
Kinematic dynamo simulations of von K\\'arm\\'an flows: application to the VKS experiment
Pinter, A; Daviaud, F; Leorat, J
2011-01-01
The VKS experiment has evidenced dynamo action in a highly turbulent liquid sodium von K\\'arm\\'an flow [R. Monchaux et al., Phys. Rev. Lett. {\\bf 98}, 044502 (2007)]. However, the existence and the onset of a dynamo happen to depend on the exact experimental configuration. By performing kinematic dynamo simulations on real flows, we study their influence on dynamo action, in particular the sense of rotation and the presence of an annulus in the shear layer plane. The 3 components of the mean velocity fields are measured in a water prototype for different VKS configurations through Stereoscopic Particle Imaging Velocimetry. Experimental data are then processed in order to use them in a periodic cylindrical kinematic code. Even if the kinematic predicted mode appears to be different from the experimental saturated one, the results concerning the existence of a dynamo and the thresholds are in qualitative agreement, showing the importance of the flow characteristics.
The Magnetic Furnace: Intense Core Dynamos in B-stars
Augustson, Kyle C; Toomre, Juri
2016-01-01
The dynamo action achieved in the convective cores of main-sequence massive stars is explored here through 3-D global simulations of convective core dynamos operating within a young 10$M_{\\mathrm{sun}}$ B-type star, using the anelastic spherical harmonic (ASH) code. These simulations capture the inner 65% of this star by radius, encompassing the convective nuclear-burning core (about 23% by radius) and a portion of the overlying radiative envelope. Eight rotation rates are considered, ranging from 0.05% to 16% of the surface breakup velocity, thereby capturing both convection barely sensing the effects of rotation to others in which the Coriolis forces are prominent. The vigorous dynamo action realized within all of these turbulent convective cores builds magnetic fields with peak strengths exceeding a megagauss, with the overall magnetic energy (ME) in the faster rotators reaching super-equipartition levels compared to the convective kinetic energy (KE). The core convection typically involves turbulent colum...
Hall current effects in mean-field dynamo theory
Lingam, Manasvi
2016-01-01
The role of the Hall term on large scale dynamo action is investigated by means of the First Order Smoothing Approximation. It is shown that the standard $\\alpha$ coefficient is altered, and is zero when a specific double Beltrami state is attained, in contrast to the Alfv\\'enic state for MHD dynamos. The $\\beta$ coefficient is no longer positive definite, and thereby enables dynamo action even if $\\alpha$-quenching were to operate. The similarities and differences with the (magnetic) shear-current effect are pointed out, and a mechanism that may be potentially responsible for $\\beta < 0$ is advanced. The results are compared against previous studies, and their astrophysical relevance is also highlighted.
Dynamo waves in Friedmann and Misner cosmologies
de Andrade, Garcia
2015-01-01
It is shown that Misner metric can be obtained as solution of dynamo waves equations and Friedmann hyperbolic metrics are obtained when the dynamo waves are absent. In the case of dynamo waves ICM fields are computed and galactic dynamos are obtained.
THE TURBULENT DYNAMO IN HIGHLY COMPRESSIBLE SUPERSONIC PLASMAS
Energy Technology Data Exchange (ETDEWEB)
Federrath, Christoph [Research School of Astronomy and Astrophysics, The Australian National University, Canberra, ACT 2611 (Australia); Schober, Jennifer [Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Strasse 2, D-69120 Heidelberg (Germany); Bovino, Stefano; Schleicher, Dominik R. G., E-mail: christoph.federrath@anu.edu.au [Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany)
2014-12-20
The turbulent dynamo may explain the origin of cosmic magnetism. While the exponential amplification of magnetic fields has been studied for incompressible gases, little is known about dynamo action in highly compressible, supersonic plasmas, such as the interstellar medium of galaxies and the early universe. Here we perform the first quantitative comparison of theoretical models of the dynamo growth rate and saturation level with three-dimensional magnetohydrodynamical simulations of supersonic turbulence with grid resolutions of up to 1024{sup 3} cells. We obtain numerical convergence and find that dynamo action occurs for both low and high magnetic Prandtl numbers Pm = ν/η = 0.1-10 (the ratio of viscous to magnetic dissipation), which had so far only been seen for Pm ≥ 1 in supersonic turbulence. We measure the critical magnetic Reynolds number, Rm{sub crit}=129{sub −31}{sup +43}, showing that the compressible dynamo is almost as efficient as in incompressible gas. Considering the physical conditions of the present and early universe, we conclude that magnetic fields need to be taken into account during structure formation from the early to the present cosmic ages, because they suppress gas fragmentation and drive powerful jets and outflows, both greatly affecting the initial mass function of stars.
Contributions to the theory of a two-scale homogeneous dynamo experiment.
Rädler, Karl-Heinz; Brandenburg, Axel
2003-02-01
The principle of the two-scale dynamo experiment at the Forschungszentrum Karlsruhe is closely related to that of the Roberts dynamo working with a simple fluid flow which is, with respect to proper Cartesian coordinates x, y, and z, periodic in x and y and independent of z. A modified Roberts dynamo problem is considered with a flow more similar to that in the experimental device. Solutions are calculated numerically, and on this basis an estimate of the excitation condition of the experimental dynamo is given. The modified Roberts dynamo problem is also considered in the framework of the mean-field dynamo theory, in which the crucial induction effect of the fluid motion is an anisotropic alpha effect. Numerical results are given for the dependence of the mean-field coefficients on the fluid flow rates. The excitation condition of the dynamo is also discussed within this framework. The behavior of the dynamo in the nonlinear regime, i.e., with backreaction of the magnetic field on the fluid flow, depends on the effect of the Lorentz force on the flow rates. The quantities determining this effect are calculated numerically. The results for the mean-field coefficients and the quantities describing the backreaction provide corrections to earlier results, which were obtained under simplifying assumptions.
COHERENT NONHELICAL SHEAR DYNAMOS DRIVEN BY MAGNETIC FLUCTUATIONS AT LOW REYNOLDS NUMBERS
Energy Technology Data Exchange (ETDEWEB)
Squire, J.; Bhattacharjee, A., E-mail: jsquire@caltech.edu [Department of Astrophysical Sciences and Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States)
2015-11-01
Nonhelical shear dynamos are studied with a particular focus on the possibility of coherent dynamo action. The primary results—serving as a follow up to the results of Squire and Bhattacharjee—pertain to the “magnetic shear-current effect” as a viable mechanism to drive large-scale magnetic field generation. This effect raises the interesting possibility that the saturated state of the small-scale dynamo could drive large-scale dynamo action, and is likely to be important in the unstratified regions of accretion disk turbulence. In this paper, the effect is studied at low Reynolds numbers, removing the complications of small-scale dynamo excitation and aiding analysis by enabling the use of quasi-linear statistical simulation methods. In addition to the magnetically driven dynamo, new results on the kinematic nonhelical shear dynamo are presented. These illustrate the relationship between coherent and incoherent driving in such dynamos, demonstrating the importance of rotation in determining the relative dominance of each mechanism.
Turbulent Dynamos and Magnetic Helicity
Energy Technology Data Exchange (ETDEWEB)
Ji, Hantao
1999-04-01
It is shown that the turbulent dynamo alpha-effect converts magnetic helicity from the turbulent field to the mean field when the turbulence is electromagnetic while the magnetic helicity of the mean-field is transported across space when the turbulence is elcetrostatic or due to the elcetron diamagnetic effect. In all cases, however, the dynamo effect strictly conserves the total helicity expect for a battery effect which vanishes in the limit of magnetohydrodynamics. Implications for astrophysical situations, especially for the solar dynamo, are discussed.
Turbulent dynamo in a conducting fluid and partially ionized gas
Xu, Siyao
2016-01-01
By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of turbulent dynamo, and study the dynamo process for a full range of magnetic Prandtl number Pm and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on Pm in a conducting fluid and R (a function of ionization fraction) in partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regime of dynamo characterized by linear-in-time growth of magnetic field strength, and the resulting magnetic energy is much higher than the kinetic energy carried by viscous-scale eddies. Unlike the kinematic stage, the subsequent nonlinear stage is unaffected by microscopic diffusion processes and has a universal linear-in-time growth of magnetic energy with the growth rate as a constant fraction $3/38$ of the turbulent e...
Strong horizontal photospheric magnetic field in a surface dynamo simulation
SchÜssler, M.; Vögler, A.
2008-01-01
Context. Observations with the Hinode spectro-polarimeter have revealed strong horizontal internetwork magnetic fields in the quiet solar photosphere. Aims. We aim to interpret the observations with results from numerical simulations. Methods. Radiative MHD simulations of dynamo action by near-surfa
Energy Technology Data Exchange (ETDEWEB)
Dvirny, A. I. [Hadmark University College (Norway); Slyn' ko, V. I., E-mail: dvirny@mail.ru, E-mail: vitstab@ukr.net [Timoshenko Institute of Mathematics, NAS of Ukraine, Kiev (Ukraine)
2014-06-01
Inverse theorems to Lyapunov's direct method are established for quasihomogeneous systems of differential equations with impulsive action. Conditions for the existence of Lyapunov functions satisfying typical bounds for quasihomogeneous functions are obtained. Using these results, we establish conditions for an equilibrium of a nonlinear system with impulsive action to be stable, using the properties of a quasihomogeneous approximation to the system. The results are illustrated by an example of a large-scale system with homogeneous subsystems. Bibliography: 30 titles. (paper)
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A new dynamo model based on the polarization of plasma is presented in this paper.From the Maxwell equations in a moving medium, a magnetization vector can be causedwith Rongon current. The steady solar magnetic field is solved from the equations. Onthe assumption that the meridianal flow is ignored, the distribution of magnetic field isput out. In the model, there is no additional parameter considered. The intensity ofmagnetic field inside the sun ranges from 1-6T. The surface magnetic field around thepole is in the order of 1×10-3T, at low latitude the calculated surface magnetic fieldhas the order of 1×10-2 T. The maximum magnetic field is around 30° in latitude.
Egeland, Ricky; Soon, Willie H.; Baliunas, Sallie L.; Hall, Jeffrey C.; Pevtsov, Alexei A.; Henry, Gregory W.
2016-05-01
We present composite time series of Ca II H & K line core emission indices of up to 50 years in length for a set of 27 solar-analog stars (spectral types G0-G5; within ~10% of the solar mass) and the Sun. These unique data are available thanks to the long-term dedicated efforts of the Mount Wilson Observatory HK project, the Lowell Observatory Solar-Stellar Spectrograph, and the National Solar Observatory/Air Force Research Laboratory/Sacremento Peak K-line monitoring program. The Ca II H & K emission originates in the lower chromosphere and is strongly correlated with the presence of magnetic plage regions in the Sun. These synoptic observations allow us to trace the patterns long-term magnetic variability and explore dynamo behavior over a wide range of rotation regimes and stellar evolution timescales.
Liquid Metal Dynamo Measurements
Luh, W. J.; Choi, Y. H.; Hardy, B. S.; Brown, M. R.
1997-11-01
Detection of convected magnetic fields in a small-scale liquid metal dynamo is attempted. Initial experiments will focus on the conversion of toroidal to poloidal flux (a version of the ω effect). A precision vector magnetometer will be used to measure the effect of a rotating magnetofluid on a static magnetic field. Water will be used as a control medium and effects will be compared with a conducting medium (liquid sodium or NaK). A small spherical flask (0.16 m diameter) houses 2 liters of fluid, a teflon stirrer creates an asymmetrical flow pattern, and Helmholtz coils generate a constant magnetic field on the order of 10 gauss. The Reynold's number will be of order unity.
Interface dynamos in supernova progenitors
Blackman, E G; Thomas, J H; Blackman, Eric G.; Nordhaus, Jason T.; Thomas, John H.
2004-01-01
Observational evidence for anisotropy in supernovae (SN) and their phenomenological connection to jetted sources such as gamma-ray bursts^Mhave revived considerations of the role magnetohydrodynamic outflows might play therein. Understanding the types of dynamos that might operate in supernova progenitors is therefore relevant. In contrast to previous work, here we study an ``interface dynamo'' for the conditions of a rapidly rotating neutron star surrounded by a convective envelope. Such dynamos have been studied for the Sun, naked white dwarfs,and post-AGB stars, where analogous configurations of strong shear layers surrounded by convective envelopes are present. The interface dynamo provides estimates of large-scale poloidal and toroidal fields, whose product enters the Poynting flux. Because the poloidal field is much weaker than the toroidal magnetic field, the actual average Poynting flux is lower than rough estimates which invoke the only the magnitude of the total magnetic energy. The lower value is s...
Shear-driven dynamo waves at high magnetic Reynolds number.
Tobias, S M; Cattaneo, F
2013-05-23
Astrophysical magnetic fields often display remarkable organization, despite being generated by dynamo action driven by turbulent flows at high conductivity. An example is the eleven-year solar cycle, which shows spatial coherence over the entire solar surface. The difficulty in understanding the emergence of this large-scale organization is that whereas at low conductivity (measured by the magnetic Reynolds number, Rm) dynamo fields are well organized, at high Rm their structure is dominated by rapidly varying small-scale fluctuations. This arises because the smallest scales have the highest rate of strain, and can amplify magnetic field most efficiently. Therefore most of the effort to find flows whose large-scale dynamo properties persist at high Rm has been frustrated. Here we report high-resolution simulations of a dynamo that can generate organized fields at high Rm; indeed, the generation mechanism, which involves the interaction between helical flows and shear, only becomes effective at large Rm. The shear does not enhance generation at large scales, as is commonly thought; instead it reduces generation at small scales. The solution consists of propagating dynamo waves, whose existence was postulated more than 60 years ago and which have since been used to model the solar cycle.
Numerical Simulations of Dynamos Generated in Spherical Couette Flows
Guervilly, Céline; 10.1080/03091920903550955
2010-01-01
We numerically investigate the efficiency of a spherical Couette flow at generating a self-sustained magnetic field. No dynamo action occurs for axisymmetric flow while we always found a dynamo when non-axisymmetric hydrodynamical instabilities are excited. Without rotation of the outer sphere, typical critical magnetic Reynolds numbers $Rm_c$ are of the order of a few thousands. They increase as the mechanical forcing imposed by the inner core on the flow increases (Reynolds number $Re$). Namely, no dynamo is found if the magnetic Prandtl number $Pm=Rm/Re$ is less than a critical value $Pm_c\\sim 1$. Oscillating quadrupolar dynamos are present in the vicinity of the dynamo onset. Saturated magnetic fields obtained in supercritical regimes (either $Re>2 Re_c$ or $Pm>2Pm_c$) correspond to the equipartition between magnetic and kinetic energies. A global rotation of the system (Ekman numbers $E=10^{-3}, 10^{-4}$) yields to a slight decrease (factor 2) of the critical magnetic Prandtl number, but we find a peculi...
Calkins, Michael A; Tobias, Steven M; Aurnou, Jonathan M; Marti, Philippe
2015-01-01
The onset of dynamo action is investigated within the context of a newly developed low Rossby, low magnetic Prandtl number, convection-driven dynamo model. The model represents an asymptotically exact form of an $\\alpha^2$ mean field dynamo model in which the small-scale convection is represented explicitly by the finite amplitude, single mode convective solutions first investigated by Bassom and Zhang (Geophys.~Astrophys.~Fluid Dyn., \\textbf{76}, p.223, 1994). Both steady and oscillatory convection are considered for a variety of horizontal planforms. The kinematic helicity is observed to be a monotonically increasing function of the Rayleigh number; as a result, very small magnetic Prandtl number dynamos can be found for a sufficiently large Rayleigh number. All dynamos are found to be oscillatory with an oscillation frequency that increases as the strength of the convection is increased and the magnetic Prandtl number is reduced. Single mode solutions which exhibit boundary layer behavior in the kinematic ...
Ricci dynamo stretch-shear plasma flows and magnetic energy bounds
de Andrade, Garcia
2009-01-01
Geometrical tools, used in Einstein's general relativity (GR), are applied to dynamo theory, in order to obtain fast dynamo action bounds to magnetic energy, from Killing symmetries in Ricci flows. Magnetic field is shown to be the shear flow tensor eigendirection, in the case of marginal dynamos. Killing symmetries of the Riemann metric, bounded by Einstein space, allows us to reduce the computations. Techniques used are similar to those strain decomposition of the flow in Sobolev space, recently used by Nu\\~nez [JMP \\textbf{43} (2002)] to place bounds in the magnetic energy in the case of hydromagnetic dynamos with plasma resistivity. Contrary to Nu\\~nez case, we assume that the dynamos are kinematic, and the velocity flow gradient is decomposed into expansion, shear and twist. The effective twist vanishes by considering that the frame vorticity coincides with Ricci rotation coefficients. Eigenvalues are here Lyapunov exponents. In analogy to GR, where curvature plays the role of gravity, here Ricci curvatu...
The fratricide of alpha-Omega dynamos by their alpha-squared siblings
Hubbard, Alexander; Brandenburg, Axel
2011-01-01
Context. Helically forced magneto-hydrodynamic shearing-sheet turbulence can support different large-scale dynamo modes, although the {\\alpha} - {\\Omega} mode is generally expected to dominate because it is the fastest growing. In an {\\alpha} - {\\Omega} dynamo, most of the field amplification is produced by the shear. As differential rotation is an ubiquitous source of shear in astrophysics, such dynamos are believed to be the source of most astrophysical large-scale magnetic fields. Aims. We study the stability of oscillatory migratory {\\alpha} - {\\Omega} type dynamos in turbulence simulations. Methods. We use shearing-sheet simulations of hydromagnetic turbulence that is helically forced at a wavenumber that is about three times larger than the lowest wavenumber in the domain so that both {\\alpha} - {\\Omega} and {\\alpha}2 dynamo action is possible. Results. After initial dominance and saturation, the {\\alpha} - {\\Omega} mode is found to be destroyed by an orthogonal {\\alpha}2 mode sustained by the helical t...
Suppression of a kinematic dynamo by large shear
Sood, Aditi; Kim, Eun-jin
2016-01-01
We numerically solve the magnetic induction equation in a spherical shell geometry, with a kinematically prescribed axisymmetric flow that consists of a superposition of a small-scale helical flow and a large-scale shear flow. The small-scale flow is chosen to be a local analog of the classical Roberts cells, consisting of strongly helical vortex rolls. The large-scale flow is a shearing motion in either the radial or the latitudinal directions. In the absence of large-scale shear, the small-scale flow is an efficient dynamo, in agreement with previous results. Adding increasingly large shear flows strongly suppresses the dynamo efficiency, indicating that shear is not always a favourable ingredient in dynamo action.
Convection-driven dynamos in the limit of rapid rotation
Calkins, Michael; Long, Louie; Nieves, David; Julien, Keith; Tobias, Steven
2016-11-01
Most large-scale planetary magnetic fields are thought to be driven by rapidly rotating convection. Direct numerical simulation (DNS) remains an important tool for investigating the physics of dynamos, but remains severely restricted in parameter space relative to geo- and astrophysical systems. Asymptotic models provide a complimentary approach to DNS that have the ability to access planetary-like magnetohydrodynamical regimes. We utilize an asymptotic dynamo model to investigate the influence of convective flow regime on dynamo action. We find that the spatial characteristics of the large-scale magnetic field are dependent only weakly on changes in flow behavior. In contrast, the behavior of the small-scale magnetic field is directly dependent on, and therefore shows significant variations with, the small-scale convective flow field. These results may suggest why many previous DNS studies, which reside in a vastly different parameter space relative to planets, are nonetheless successful in reproducing many of the observed features of planetary magnetic fields.
Kinematic Dynamo In Turbulent Circumstellar Disks
Stepinski, T.
1993-01-01
Many circumstellar disks associated with objects ranging from protoplanetary nebulae, to accretion disks around compact stars allow for the generation of magnetic fields by an (alpha)omega dynamo. We have applied kinematic dynamo formalism to geometrically thin accretion disks. We calculate, in the framework of an adiabatic approximation, the normal mode solutions for dynamos operating in disks around compact stars. We then describe the criteria for a viable dynamo in protoplanetary nebulae, and discuss the particular features that make accretion disk dynamos different from planetary, stellar, and galactic dynamos.
Solar small-scale dynamo and polarity of sunspot groups
Sokoloff, D; Abramenko, V
2015-01-01
In order to clarify a possible role of small-scale dynamo in formation of solar magnetic field, we suggest an observational test for small-scale dynamo action based on statistics of anti-Hale sunspot groups. As we have shown, according to theoretical expectations the small-scale dynamo action has to provide a population of sunspot groups which do not follow the Hale polarity law, and the density of such groups on the time-latitude diagram is expected to be independent on the phase of the solar cycle. Correspondingly, a percentage of the anti-Hale groups is expected to reach its maximum values during solar minima. For several solar cycles, we considered statistics of anti-Hale groups obtained by several scientific teams, including ours, to find that the percentage of anti-Hale groups becomes indeed maximal during a solar minimum. Our interpretation is that this fact may be explained by the small-scale dynamo action inside the solar convective zone.
Solar small-scale dynamo and polarity of sunspot groups
Sokoloff, D.; Khlystova, A.; Abramenko, V.
2015-08-01
In order to clarify a possible role of small-scale dynamo in formation of solar magnetic field, we suggest an observational test for small-scale dynamo action based on statistics of anti-Hale sunspot groups. As we have shown, according to theoretical expectations the small-scale dynamo action has to provide a population of sunspot groups which do not follow the Hale polarity law, and the density of such groups on the time-latitude diagram is expected to be independent on the phase of the solar cycle. Correspondingly, a percentage of the anti-Hale groups is expected to reach its maximum values during solar minima. For several solar cycles, we considered statistics of anti-Hale groups obtained by several scientific teams, including ours, to find that the percentage of anti-Hale groups becomes indeed maximal during a solar minimum. Our interpretation is that this fact may be explained by the small-scale dynamo action inside the solar convective zone.
Dynamos driven by poloidal flows in untwisted, curved and flat Riemannian diffusive flux tubes
de Andrade, L C Garcia
2010-01-01
Recently Vishik anti-fast dynamo theorem, has been tested against non-stretching flux tubes [Phys Plasmas 15 (2008)]. In this paper, another anti-dynamo theorem, called Cowling's theorem, which states that axisymmetric magnetic fields cannot support dynamo action, is carefully tested against thick tubular and curved Riemannian untwisted flows, as well as thin flux tubes in diffusive and diffusionless media. In the non-diffusive media the Cowling's theorem is not violated in thin Riemann-flat untwisted flux tubes, where the Frenet curvature is negative. Nevertheless the diffusion action in the thin flux tube leads to a a dynamo action driven by poloidal flows as shown by Love and Gubbins (Geophysical Res.) in the context of geodynamos. Actually it is shown that a slow dynamo action is obtained. In this case the Frenet and Riemann curvature still vanishes. In the case of magnetic filaments in diffusive media dynamo action is obtained when the Frenet scalar curvature is negative. Since the Riemann curvature tens...
Dynamo generation of magnetic field in the white dwarf GD 358
Markiel, J. Andrew; Thomas, John H.; Van Horn, H. M.
1994-01-01
On the basis of Whole Earth Telescope observations of the g-mode oscillation spectrum of the white dwarf GD 358, Winget et al. find evidence for significant differential rotation and for a time-varying magnetic field concentrated in the surface layers of this star. Here we argue on theoretical grounds that this magnetic field is produced by an alpha omega dynamo operating in the lower part of a surface convection zone in GD 358. Our argument is based on numerical solutions of the nonlinear, local dynamo equations of Robinson & Durney, with specific parameters based on our detailed models of white-dwarf convective envelopes, and universal constants determined by a calibration with the the Sun's dynamo. The calculations suggest a dynamo cycle period of about 6 years for the fundamental mode, and periods as short as 1 year for the higher-order modes that are expected to dominate in view of the large dynamo number we estimate for GD 358. These dynamo periods are consistent with the changes in the magnetic field of GD 358 over the span of 1 month inferred by Winget et. al. from their observations. Our calculations also suggest a peak dynamo magnetic field strength at the base of the surface convection zone of about 1800 G, which is consistent with the field strength inferred from the observations.
Egeland, Ricky; Soon, Willie; Baliunas, Sallie; Hall, Jeffrey C.; Pevtsov, Alexei A.; Henry, Gregory W.
2016-07-01
We present composite time series of Ca II H & K line core emission indices of up to 50 years in length for a set of 27 solar-analog stars (spectral types G0-G5; within 10% of the solar mass) and the Sun. These unique data are available thanks to the long-term dedicated efforts of the Mount Wilson Observatory HK project, the Lowell Observatory Solar-Stellar Spectrograph, and the National Solar Observatory/Air Force Research Laboratory/Sacramento Peak K-line monitoring program. The Ca II H & K emission originates in the lower chromosphere and is strongly correlated with the presence of magnetic plage regions in the Sun. These synoptic observations allow us to trace the patterns long-term magnetic variability and explore dynamo behavior over a wide range of rotation regimes and stellar evolution timescales.In this poster, the Ca HK observations are expressed using the Mount Wilson S-index. Each time series is accompanied by a Lomb-Scargle periodogram, fundemental stellar parameters derived from the Geneva-Copenhagen Survey, and statistics derived from the time series including the median S-index value and seasonal and long-term amplitudes. Statistically significant periodogram peaks are ranked according to a new cycle quality metric. We find that clear, simple, Sun-like cycles are the minority in this sample.
Ayres, Thomas R.
2016-04-01
The Dynamo Clinical Trial evaluates long-term stellar magnetic health through periodic X-ray examinations (by the Chandra Observatory). So far, there are only three subjects enrolled in the DTC: Alpha Centauri A (a solar-like G dwarf), Alpha Cen B (an early K dwarf, more active than the Sun), and Alpha Canis Majoris A (Procyon, a mid-F subgiant similar in activity to the Sun). Of these, Procyon is a new candidate, so it is too early to judge how it will fare. Of the other two, Alpha Cen B has responded well, with a steady magnetic heartbeat of about 8 years duration. The sickest of the bunch, Alpha Cen A, was in magnetic cardiac arrest during 2005-2010, but has begun responding to treatment in recent years, and seems to be successfully cycling again, perhaps achieving a new peak of magnetic health in the 2016 time frame. If this is the case, it has been 20 years since A's last healthful peak, significantly longer than the middle-aged Sun's 11-year magnetic heartbeat, but perhaps in line with Alpha Cen A's more senescent state (in terms of "relative evolutionary age," apparently an important driver of activity). (By the way, don't miss the exciting movie of the Alpha Cen stars' 20-year X-ray dance.)
Tsunami: ocean dynamo generator.
Sugioka, Hiroko; Hamano, Yozo; Baba, Kiyoshi; Kasaya, Takafumi; Tada, Noriko; Suetsugu, Daisuke
2014-01-08
Secondary magnetic fields are induced by the flow of electrically conducting seawater through the Earth's primary magnetic field ('ocean dynamo effect'), and hence it has long been speculated that tsunami flows should produce measurable magnetic field perturbations, although the signal-to-noise ratio would be small because of the influence of the solar magnetic fields. Here, we report on the detection of deep-seafloor electromagnetic perturbations of 10-micron-order induced by a tsunami, which propagated through a seafloor electromagnetometer array network. The observed data extracted tsunami characteristics, including the direction and velocity of propagation as well as sea-level change, first to verify the induction theory. Presently, offshore observation systems for the early forecasting of tsunami are based on the sea-level measurement by seafloor pressure gauges. In terms of tsunami forecasting accuracy, the integration of vectored electromagnetic measurements into existing scalar observation systems would represent a substantial improvement in the performance of tsunami early-warning systems.
Gusev, Vitalyi E; Lomonosov, Alexey M; Ni, Chenyin; Shen, Zhonghua
2017-09-01
An analytical theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous plate material on the Lamb waves near the S1 zero group velocity point is developed. The theory predicts that the main effect of the hysteretic quadratic nonlinearity consists in the modification of the frequency and the induced absorption of the Lamb modes. The effects of the nonlinear self-action in the propagating and standing Lamb waves are expected to be, respectively, nearly twice and three times stronger than those in the plane propagating acoustic waves. The theory is restricted to the simplest hysteretic nonlinearity, which is influencing only one of the Lamé moduli of the materials. However, possible extensions of the theory to the cases of more general hysteretic nonlinearities are discussed as well as the perspectives of its experimental testing. Applications include nondestructive evaluation of micro-inhomogeneous and cracked plates. Copyright © 2017 Elsevier B.V. All rights reserved.
Toward an asymptotic behaviour of the ABC dynamo
Bouya, Ismaël
2016-01-01
The ABC flow was originally introduced by Arnol'd to investigate Lagrangian chaos. It soon became the prototype example to illustrate magnetic-field amplification via fast dynamo action, i.e. dynamo action exhibiting magnetic-field amplification on a typical timescale independent of the electrical resistivity of the medium. Even though this flow is the most classical example for this important class of dynamos (with application to large-scale astrophysical objects), it was recently pointed out (Bouya Isma\\"el and Dormy Emmanuel, Phys. Fluids, 25 (2013) 037103) that the fast dynamo nature of this flow was unclear, as the growth rate still depended on the magnetic Reynolds number at the largest values available so far $(\\text{Rm} = 25000)$ . Using state-of-the-art high-performance computing, we present high-resolution simulations (up to 40963) and extend the value of $\\text{Rm}$ up to $ 5\\cdot10^5$ . Interestingly, even at these huge values, the growth rate of the leading eigenmode still depends on the controll...
Energy Technology Data Exchange (ETDEWEB)
Ruzmaikin, A.A.; Sokolov, D.D.; Turchaninov, V.I.
1980-03-01
The large-scale magnetic field in a rotating, turbulent gaseous disk will be generated by a dynamo process (the ..cap alpha omega..-dynamo) determined by the differential rotation ..omega..(r) and the spirality function ..cap alpha..(z). The generation is best described by a difference approximation to the dynamo equations, using a step greater than the turbulence correlation length and a smooth function ..cap alpha..(z). The critical dynamo-number for exciting the lowest even quadrupole mode is D/sub q/ = -8. The odd dipole mode will be excited only for large dynamo-numberabsolute value (D/sub d/) > or approx. = 500. When absolute value (D) > or approx. = 20, all modes other than the lowest quadrupole mode (for which the threshold Dapprox. =-500) are oscillatory. The results are applied to the Galaxy (D approx. = -10; characteristic growth time, 3 x 10/sup 8/ yr) and to accretion disks in binary systems containing a black hole, where several oscillatory modes can be excited.
Magnetic helicity in non-axisymmetric mean-field solar dynamo
Pipin, V V
2016-01-01
The paper address the effects of magnetic helicity conservation in a non-linear nonaxisymmetric mean-field solar dynamo model. We study the evolution of the shallow non-axisymmetric magnetic field perturbation with the strength about 10G in the solar convection zone. The dynamo evolves from the pure axisymmetric stage through the short (about 2 years) transient phase when the non-axisymmetric m=1 dynamo mode is dominant to the final stage where the axisymmetry of the dynamo is almost restored. It is found that magnetic helicity is transferred forth and back over the spectral space during the transient phase. Also our simulations shows that the non-axisymmetric distributions of magnetic helicity tend to follows the regions of the Hale polarity rule.
Moss, David; Suleimanov, Valery
2016-01-01
Magnetic fields are important for accretion disc structure. Magnetic fields in a disc system may be transported with the accreted matter. They can be associated with either the central body and/or jet, and be fossil or dynamo excited in situ. We consider dynamo excitation of magnetic fields in accretion discs of accreting binary systems in an attempt to clarify possible configurations of dynamo generated magnetic fields. We first model the entire disc with realistic radial extent and thickness using an alpha-quenching non-linearity. We then study the simultaneous effect of feedback from the Lorentz force from the dynamo-generated field. We perform numerical simulations in the framework of a relatively simple mean-field model which allows the generation of global magnetic configurations. We explore a range of possibilities for the dynamo number, and find quadrupolar-type solutions with irregular temporal oscillations that might be compared to observed rapid luminosity fluctuations. The dipolar symmetry models ...
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion
de Andrade, L Garcia
2009-01-01
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion}} Previous attempts for building a cosmic dynamo including preheating in inflationary universes [Bassett et al Phys Rev (2001)] has not included mean field or turbulent dynamos. In this paper a mean field dynamo in cosmic scales on a Riemannian spatial cosmological section background, is set up. When magnetic fields and flow velocities are parallel propagated along the Riemannian space dynamo action is obtained. Turbulent diffusivity ${\\beta}$ is coupled with the Ricci magnetic curvature, as in Marklund and Clarkson [MNRAS (2005)], GR-MHD dynamo equation. Mean electric field possesses an extra term where Ricci tensor couples with magnetic vector potential in Ohm's law. In Goedel universe induces a mean field dynamo growth rate ${\\gamma}=2{\\omega}^{2}{\\beta}$. In this frame kinetic helicity vanishes. In radiation era this yields ${\\gamma}\\approx{2{\\beta}{\\times}10^{-12}s^{-1}}$. In non-comoving the magnetic field is expressed as $B\\ap...
Helicity, Reconnection, and Dynamo Effects
Energy Technology Data Exchange (ETDEWEB)
Ji, Hantao
1998-11-01
The inter-relationships between magnetic helicity, magnetic reconnection, and dynamo effects are discussed. In laboratory experiments, where two plasmas are driven to merge, the helicity content of each plasma strongly affects the reconnection rate, as well as the shape of the diffusion region. Conversely, magnetic reconnection events also strongly affect the global helicity, resulting in efficient helicity cancellation (but not dissipation) during counter-helicity reconnection and a finite helicity increase or decrease (but less efficiently than dissipation of magnetic energy) during co-helicity reconnection. Close relationships also exist between magnetic helicity and dynamo effects. The turbulent electromotive force along the mean magnetic field (alpha-effect), due to either electrostatic turbulence or the electron diamagnetic effect, transports mean-field helicity across space without dissipation. This has been supported by direct measurements of helicity flux in a laboratory plasma. When the dynamo effect is driven by electromagnetic turbulence, helicity in the turbulent field is converted to mean-field helicity. In all cases, however, dynamo processes conserve total helicity except for a small battery effect, consistent with the observation that the helicity is approximately conserved during magnetic relaxation.
Statistical dynamo theory: Mode excitation.
Hoyng, P
2009-04-01
We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B= summation operator_{k}a;{k}(t)b;{k}(r) . The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a;{k} is governed by a stochastic differential equation from which we infer their averages a;{k} , autocorrelation functions a;{k}(t)a;{k *}(t+tau) , and an equation for the cross correlations a;{k}a;{l *} . The eigenfunctions of the dynamo equation (with eigenvalues lambda_{k} ) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Ilambda_{k} and -1/Rlambda_{k} , respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for |a;{k}|;{2}/|a;{0}|;{2} in case the fundamental mode b;{0} has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that |a;{k}|;{2}/|a;{0}|;{2} approximately 1/N , where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Rlambda_{k}<0 .
An analytical dynamo solution for large-scale magnetic fields of galaxies
Chamandy, Luke
2016-01-01
We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parameterized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the `no-$z$' approximation and the dynamical $\\alpha$-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted onto galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure (RM) datasets. Further, we explore the properties of our numerical solut...
The small scale dynamo and the amplification of magnetic fields in massive primordial haloes
Latif, M A; Schmidt, W; Niemeyer, J
2012-01-01
While our present standard model of cosmology yields no clear prediction for the initial magnetic field strength, efficient dynamo action may compensate for initially weak seed fields via rapid amplification. In particular, the small-scale dynamo is expected to exponentially amplify any weak magnetic field in the presence of turbulence. We explore whether this scenario is viable using cosmological magneto-hydrodynamics simulations modeling the formation of the first galaxies, which are expected to form in so-called atomic cooling halos with virial temperatures $\\rm T_{vir} \\geq 10^{4}$ K. As previous calculations have shown that a high Jeans resolution is needed to resolve turbulent structures and dynamo effects, our calculations employ resolutions of up to 128 cells per Jeans length. The presence of the dynamo can be clearly confirmed for resolutions of at least 64 cells per Jeans length, while saturation occurs at approximate equipartition with turbulent energy. As a result of the large Reynolds numbers in ...
Generation of Large-Scale Magnetic Fields by Small-Scale Dynamo in Shear Flows.
Squire, J; Bhattacharjee, A
2015-10-23
We propose a new mechanism for a turbulent mean-field dynamo in which the magnetic fluctuations resulting from a small-scale dynamo drive the generation of large-scale magnetic fields. This is in stark contrast to the common idea that small-scale magnetic fields should be harmful to large-scale dynamo action. These dynamos occur in the presence of a large-scale velocity shear and do not require net helicity, resulting from off-diagonal components of the turbulent resistivity tensor as the magnetic analogue of the "shear-current" effect. Given the inevitable existence of nonhelical small-scale magnetic fields in turbulent plasmas, as well as the generic nature of velocity shear, the suggested mechanism may help explain the generation of large-scale magnetic fields across a wide range of astrophysical objects.
Energy Technology Data Exchange (ETDEWEB)
Ebrahimi, Fatima [Univ. of New Hampshire, Durham, NH (United States)
2014-07-31
Large-scale magnetic fields have been observed in widely different types of astrophysical objects. These magnetic fields are believed to be caused by the so-called dynamo effect. Could a large-scale magnetic field grow out of turbulence (i.e. the alpha dynamo effect)? How could the topological properties and the complexity of magnetic field as a global quantity, the so called magnetic helicity, be important in the dynamo effect? In addition to understanding the dynamo mechanism in astrophysical accretion disks, anomalous angular momentum transport has also been a longstanding problem in accretion disks and laboratory plasmas. To investigate both dynamo and momentum transport, we have performed both numerical modeling of laboratory experiments that are intended to simulate nature and modeling of configurations with direct relevance to astrophysical disks. Our simulations use fluid approximations (Magnetohydrodynamics - MHD model), where plasma is treated as a single fluid, or two fluids, in the presence of electromagnetic forces. Our major physics objective is to study the possibility of magnetic field generation (so called MRI small-scale and large-scale dynamos) and its role in Magneto-rotational Instability (MRI) saturation through nonlinear simulations in both MHD and Hall regimes.
Optical diode action from axially asymmetric nonlinearity in an all-carbon solid-state device.
Anand, Benoy; Podila, Ramakrishna; Lingam, Kiran; Krishnan, S R; Siva Sankara Sai, S; Philip, Reji; Rao, Apparao M
2013-01-01
Nanostructured carbons are posited to offer an alternative to silicon and lead to further miniaturization of photonic and electronic devices. Here, we report the experimental realization of the first all-carbon solid-state optical diode that is based on axially asymmetric nonlinear absorption in a thin saturable absorber (graphene) and a thin reverse saturable absorber (C60) arranged in tandem. This all-optical diode action is polarization independent and has no phase-matching constraints. The nonreciprocity factor of the device can be tuned by varying the number of graphene layers and the concentration or thickness of the C60 coating. This ultracompact graphene/C60 based optical diode is versatile with an inherently large bandwidth, chemical and thermal stability, and is poised for cost-effective large-scale integration with existing fabrication technologies.
Fang, Xiaohui; Wai, P K A; Lu, Chao; Chen, Jinhua
2014-02-10
A pulse-width-tunable 10 GHz flattop pulse (FTP) train is generated based on the combined action of active mode locking and nonlinear polarization rotation pulse shaping. Although the setup was previously used for other applications, the mechanism of FTP generation based on it is first analyzed and confirmed in the experiment. An FTP with pulse width tunable from 12 to 20 ps by changing polarization controllers is generated within the wavelength tuning range of 20 nm. The generated pulse reveals good stability, with the side mode suppression ratio of 65 dB, timing jitter of 92 fs, and amplitude fluctuation of 0.36%.
Back-action on the flux-qubit from a driven non-linear detector
Energy Technology Data Exchange (ETDEWEB)
Leyton Ortega, Vicente Ancelmo; Peano, Vittorio; Thorwart, Michael [Freiburg Institute for Advanced Studies (FRIAS), Albert-Ludwigs Universitaet Freiburg, 79104 Freiburg (Germany); Reina, John Henrry [Universidad del Valle, Departamento de Fisica, A.A. 25360, Cali (Colombia)
2010-07-01
We consider a superconducting flux qubit inductively coupled to a driven SQUID, acting as a detector, in presence of weak dissipation and close to the optimal working point. We study the nonlinear response of the detector to the drive and the population difference of the qubit state. By varying the external magnetic field piercing the SQUID, we access two different regimes: i) For vanishing external flux, the SQUID acts as a Josephson bifurcation amplifier, however, operated here with few energy quanta rather than in its classical regime. In this regime, we show that the back-action of the detector on the qubit is small, rendering the driven SQUID an ideal detector. ii) When the external flux is close to half a flux quantum, the combined qubit-oscillator system implements the two-photon Jaynes-Cummings model. We study multiphoton (anti-)resonances in the two-photon transition regime.
Small-scale dynamo at low magnetic Prandtl numbers.
Schober, Jennifer; Schleicher, Dominik; Bovino, Stefano; Klessen, Ralf S
2012-12-01
The present-day Universe is highly magnetized, even though the first magnetic seed fields were most probably extremely weak. To explain the growth of the magnetic field strength over many orders of magnitude, fast amplification processes need to operate. The most efficient mechanism known today is the small-scale dynamo, which converts turbulent kinetic energy into magnetic energy leading to an exponential growth of the magnetic field. The efficiency of the dynamo depends on the type of turbulence indicated by the slope of the turbulence spectrum v(ℓ)∝ℓ^{ϑ}, where v(ℓ) is the eddy velocity at a scale ℓ. We explore turbulent spectra ranging from incompressible Kolmogorov turbulence with ϑ=1/3 to highly compressible Burgers turbulence with ϑ=1/2. In this work, we analyze the properties of the small-scale dynamo for low magnetic Prandtl numbers Pm, which denotes the ratio of the magnetic Reynolds number, Rm, to the hydrodynamical one, Re. We solve the Kazantsev equation, which describes the evolution of the small-scale magnetic field, using the WKB approximation. In the limit of low magnetic Prandtl numbers, the growth rate is proportional to Rm^{(1-ϑ)/(1+ϑ)}. We furthermore discuss the critical magnetic Reynolds number Rm_{crit}, which is required for small-scale dynamo action. The value of Rm_{crit} is roughly 100 for Kolmogorov turbulence and 2700 for Burgers. Furthermore, we discuss that Rm_{crit} provides a stronger constraint in the limit of low Pm than it does for large Pm. We conclude that the small-scale dynamo can operate in the regime of low magnetic Prandtl numbers if the magnetic Reynolds number is large enough. Thus, the magnetic field amplification on small scales can take place in a broad range of physical environments and amplify week magnetic seed fields on short time scales.
Small-scale dynamo at low magnetic Prandtl numbers
Schober, Jennifer; Schleicher, Dominik; Bovino, Stefano; Klessen, Ralf S.
2012-12-01
The present-day Universe is highly magnetized, even though the first magnetic seed fields were most probably extremely weak. To explain the growth of the magnetic field strength over many orders of magnitude, fast amplification processes need to operate. The most efficient mechanism known today is the small-scale dynamo, which converts turbulent kinetic energy into magnetic energy leading to an exponential growth of the magnetic field. The efficiency of the dynamo depends on the type of turbulence indicated by the slope of the turbulence spectrum v(ℓ)∝ℓϑ, where v(ℓ) is the eddy velocity at a scale ℓ. We explore turbulent spectra ranging from incompressible Kolmogorov turbulence with ϑ=1/3 to highly compressible Burgers turbulence with ϑ=1/2. In this work, we analyze the properties of the small-scale dynamo for low magnetic Prandtl numbers Pm, which denotes the ratio of the magnetic Reynolds number, Rm, to the hydrodynamical one, Re. We solve the Kazantsev equation, which describes the evolution of the small-scale magnetic field, using the WKB approximation. In the limit of low magnetic Prandtl numbers, the growth rate is proportional to Rm(1-ϑ)/(1+ϑ). We furthermore discuss the critical magnetic Reynolds number Rmcrit, which is required for small-scale dynamo action. The value of Rmcrit is roughly 100 for Kolmogorov turbulence and 2700 for Burgers. Furthermore, we discuss that Rmcrit provides a stronger constraint in the limit of low Pm than it does for large Pm. We conclude that the small-scale dynamo can operate in the regime of low magnetic Prandtl numbers if the magnetic Reynolds number is large enough. Thus, the magnetic field amplification on small scales can take place in a broad range of physical environments and amplify week magnetic seed fields on short time scales.
Turbulent dynamo with advective magnetic helicity flux
Del Sordo, Fabio; Brandenburg, Axel
2012-01-01
Many astrophysical bodies harbor magnetic fields that are thought to be sustained by dynamo processes. However, it has been argued that the production of large-scale magnetic fields by a mean-field dynamo is strongly suppressed at large magnetic Reynolds numbers owing to the conservation of magnetic helicity. This phenomenon is known as catastrophic quenching. Advection of magnetic field toward the outer boundaries and away from the dynamo is expected to alleviate such quenching. Examples are stellar and galactic winds. Such advection might be able to overcome the constraint imposed by the conservation of magnetic helicity, transporting a fraction of it outside the domain in which the dynamo operates. We study how the dynamo process is affected by advection. In particular, we study the relative roles played by advective and diffusive fluxes of magnetic helicity. We do this by performing direct numerical simulations of a turbulent dynamo of alpha^2 type driven by forced turbulence in a Cartesian domain in the ...
NRL Satellite Support for DYNAMO Field Program
2012-09-30
1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. NRL Satellite Support for DYNAMO Field Program Jeffrey...Jeff.Hawkins@nrlmry.navy.mil Document Number: N0001412WX20870 LONG-TERM GOALS To provide the ONR-sponsored DYNAMO field program with a...the Indian Ocean. OBJECTIVES Develop a NRL-MRY near real-time web page that enables DYNAMO field program participants to view the evolving
A Vorticity-Magnetic Field Dynamo Instability
1997-01-01
We generalize the mean field magnetic dynamo to include local evolution of the mean vorticity in addition to the mean magnetic field. The coupled equations exhibit a general mean field dynamo instability that enables the transfer of turbulent energy to the magnetic field and vorticity on larger scales. The growth of the vorticity and magnetic field both require helical turbulence which can be supplied by an underlying global rotation. The dynamo coefficients are derived including the backreac...
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
随着天气越来越热，低帮款战靴也越来越受到球迷的喜爱。尤其是拥有高性能、低价位的战靴．会更加让人期待，而Dynamo Formotion 2 Lo就满足了以上两项要求。
SADE: Starspot and Dynamo Explorer
Martens, P. C. H.
2003-05-01
In soft X-rays the solar coronal radiance varies by a factor of 70 over the solar activity cycle. A similar variation in most stars in the existing X-ray database has not been found (Stern 2001); even stars which exhibit chromospheric activity cycles show only marginal evidence for X-ray cycles. This is rather puzzling as the time span and multiple coverage of the X-ray sky should reveal at least a hint of such a pronounced cyclical variation. By the time of the meeting we will have submitted a SMEX proposal with the above acronym to determine the nature and amplitude of the variation in X-ray emission of nearby solar analogs that have a cyclic chromospheric Ca-K variability similar to that of the Sun. In doing so we aim to expand our knowledge of the parameter space of stellar dynamos, which will lead to a better understanding of the dynamo process in general -- an unresolved fundamental problem in astrophysics -- and the solar dynamo in particular. This is an investigation at the cross-section of the NASA themes ``Structure and Evolution of the Universe", and the ``Sun-Earth Connection". In my presentation I will describe the SADE instrument design, observing strategy, and possible science results. SADE is proposed by a consortium led by MSU, including Swales, CfA, LMSAL, UCL, OAP, and Bangalore.
Optimization of the magnetic dynamo.
Willis, Ashley P
2012-12-21
In stars and planets, magnetic fields are believed to originate from the motion of electrically conducting fluids in their interior, through a process known as the dynamo mechanism. In this Letter, an optimization procedure is used to simultaneously address two fundamental questions of dynamo theory: "Which velocity field leads to the most magnetic energy growth?" and "How large does the velocity need to be relative to magnetic diffusion?" In general, this requires optimization over the full space of continuous solenoidal velocity fields possible within the geometry. Here the case of a periodic box is considered. Measuring the strength of the flow with the root-mean-square amplitude, an optimal velocity field is shown to exist, but without limitation on the strain rate, optimization is prone to divergence. Measuring the flow in terms of its associated dissipation leads to the identification of a single optimal at the critical magnetic Reynolds number necessary for a dynamo. This magnetic Reynolds number is found to be only 15% higher than that necessary for transient growth of the magnetic field.
Inverse problem in Parker's dynamo
Reshetnyak, M Yu
2015-01-01
The inverse solution of the 1D Parker dynamo equations is considered. The method is based on minimization of the cost-function, which characterize deviation of the model solution properties from the desired ones. The output is the latitude distribution of the magnetic field generation sources: the $\\alpha$- and $\\omega$-effects. Minimization is made using the Monte-Carlo method. The details of the method, as well as some applications, which can be interesting for the broad dynamo community, are considered: conditions when the invisible for the observer at the surface of the planet toroidal part of the magnetic field is much larger than the poloidal counterpart. It is shown that at some particular distributions of $\\alpha$ and $\\omega$ the well-known thesis that sign of the dynamo-number defines equatorial symmetry of the magnetic field to the equator plane, is violated. It is also demonstrated in what circumstances magnetic field in the both hemispheres have different properties, and simple physical explanati...
Statistical Mechanics of Turbulent Dynamos
Shebalin, John V.
2014-01-01
Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much
MHD Turbulence and Magnetic Dynamos
Shebalin, John V
2014-01-01
Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much
Evidence for dynamo bistability among very low mass stars
Morin, J; Donati, J -F; Dormy, E; Forveille, T; Jardine, M; Petit, P; Schrinner, M
2012-01-01
Dynamo action in fully convective stars is a debated issue that also questions our understanding of magnetic field generation in partly convective Sun-like stars. During the past few years, spectropolari- metric observations have demonstrated that fully convective objects are able to trigger strong large-scale and long-lived magnetic fields. We present here the first spectropolarimetric study of a sample of active late M dwarfs (M5-M8) carried out with ESPaDOnS@CFHT. It reveals the co-existence of two distinct types of magnetism among stars having similar masses and rotation rates. A possible explanation for this unexpected discovery is the existence of two dynamo branches in this parameter regime, we discuss here the possible identification with the weak vs strong field bistability predicted for the geodynamo.
Dynamo generated field emergence through recurrent plasmoid ejections
Warnecke, Jörn
2010-01-01
Magnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical forcing to produce a large-scale dynamo-generated magnetic field, which rises even without magnetic buoyancy. A two layer system is used as computational domain where the upper part represents the solar atmosphere. Here, the evolution of the magnetic field is solved with the stress--and--relax method. Below this region a magnetic field is produced by a helical forcing function in the momentum equation, which leads to dynamo action. We find twisted magnetic fields emerging frequently to the outer layer, forming arch-like structures. In addition, recurrent plasmoid ejections can be found by looking at space--time diagrams of the magnetic field. Recent simulations in spherical coordinates show similar results.
Turbulent transport coefficients in spherical wedge dynamo simulations of solar-like stars
Warnecke, Jörn; Käpylä, Petri J; Käpylä, Maarit J; Brandenburg, Axel
2016-01-01
We investigate the magnetic field generation in global solar-like convective dynamos in the framework of mean-field theory. We simulate a solar-type star in a wedge-shaped spherical shell, where the interplay between convection and rotation self-consistently drives large-scale dynamo. To analyze the dynamo mechanism we apply the test-field method for azimuthally ($\\phi$) averaged fields to determine the 27 turbulent transport coefficients of the electromotive force, of which 9 are related to the $\\alpha$ effect tensor. This method has previously been used either in simulations in Cartesian coordinates or in the geodynamo context and it is applied here for the first time in simulations of solar-like dynamo action. We find that the $\\phi\\phi$-component of the $\\alpha$ tensor does not follow the profile expected from that of kinetic helicity. Beside the dominant $\\alpha$-$\\Omega$ dynamo, also an $\\alpha^2$ dynamo is locally enhanced. The turbulent pumping velocities significantly alter the effective mean flows a...
Bounds on the growth of the magnetic energy for the Hall kinematic dynamo equation
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico Universidad de Valladolid 47005 Valladolid (Spain)
2005-09-09
While the magnetic induction equation in plasmas, governing kinematic dynamos, is a linear one admitting exponential growth of the magnetic energy for certain velocity fields, the addition of the Hall term turns it into a nonlinear parabolic equation. Local existence of solutions may be proved, but in contrast with the magnetohydrodynamics case, for a number of boundary conditions the magnetic energy grows at most linearly in time for stationary velocity fields, and like the square of the time in the general case. It appears that the Hall effect enhances diffusivity in some way to compensate for the positive contribution of the transport of the magnetic field by the flow occurring in fast dynamos.
Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential
Gizzi, A.; Loppini, A.; Ruiz-Baier, R.; Ippolito, A.; Camassa, A.; La Camera, A.; Emmi, E.; Di Perna, L.; Garofalo, V.; Cherubini, C.; Filippi, S.
2017-09-01
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.
Ge, Hao
2016-01-01
Macroscopic entropy production $\\sigma^{(tot)}$ in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation and a house-keeping heat: $\\sigma^{(tot)}=\\sigma^{(fd)}+\\sigma^{(hk)}$; $\\sigma^{(fd)}=-\\rd A/\\rd t$, where $A$ is a generalized free enegy function. This yields a novel nonequilibrium free energy balance equation $\\rd A/\\rd t=-\\sigma^{(tot)}+\\sigma^{(hk)}$, which is on a par with celebrated entropy balance equation $\\rd S/\\rd t=\\sigma^{(tot)}+\\eta^{(ex)}$ where $\\eta^{(ex)}$ is the rate of entropy exchange with the environment.For kinetic system with complex balance,$\\sigma^{(fd)},\\sigma^{(hk)}\\ge 0$: $\\sigma^{(fd)}$ characterizes the irreversibility of a transient relaxation kinetics; while $\\sigma^{(hk)}$ is positive even in a steady state, representing irreversibility in open,driven chemical systems with a chemostat.For kinetic system withoutcomplex balance, negative $\\sigma^{(fd)}$ is a necessary condition for multistability, w...
Global Solar Dynamo Models: Simulations and Predictions
Indian Academy of Sciences (India)
Mausumi Dikpati; Peter A. Gilman
2008-03-01
Flux-transport type solar dynamos have achieved considerable success in correctly simulating many solar cycle features, and are now being used for prediction of solar cycle timing and amplitude.We first define flux-transport dynamos and demonstrate how they work. The essential added ingredient in this class of models is meridional circulation, which governs the dynamo period and also plays a crucial role in determining the Sun’s memory about its past magnetic fields.We show that flux-transport dynamo models can explain many key features of solar cycles. Then we show that a predictive tool can be built from this class of dynamo that can be used to predict mean solar cycle features by assimilating magnetic field data from previous cycles.
Magnetic Helicity Conservation and Astrophysical Dynamos
Vishniac, E T; Vishniac, Ethan T.; Cho, Jungyeon
2000-01-01
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large scale fields in equipartition with the turbulent energy density. In fact, there seems to be little prospect for driving a fast dynamo in a closed box containing homogeneous turbulence. On the other hand, there is an efficient analog to the $\\alpha-\\Omega$ dynamo. Systems whose turbulence is driven by some anisotropic local instability in shearing flow, like real stars and accretion disks, and some computer simulations, ma...
Dynamo transition in low-dimensional models.
Verma, Mahendra K; Lessinnes, Thomas; Carati, Daniele; Sarris, Ioannis; Kumar, Krishna; Singh, Meenakshi
2008-09-01
Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.
A long-lived lunar core dynamo.
Shea, Erin K; Weiss, Benjamin P; Cassata, William S; Shuster, David L; Tikoo, Sonia M; Gattacceca, Jérôme; Grove, Timothy L; Fuller, Michael D
2012-01-27
Paleomagnetic measurements indicate that a core dynamo probably existed on the Moon 4.2 billion years ago. However, the subsequent history of the lunar core dynamo is unknown. Here we report paleomagnetic, petrologic, and (40)Ar/(39)Ar thermochronometry measurements on the 3.7-billion-year-old mare basalt sample 10020. This sample contains a high-coercivity magnetization acquired in a stable field of at least ~12 microteslas. These data extend the known lifetime of the lunar dynamo by 500 million years. Such a long-lived lunar dynamo probably required a power source other than thermochemical convection from secular cooling of the lunar interior. The inferred strong intensity of the lunar paleofield presents a challenge to current dynamo theory.
On self-exciting coupled Faraday disk homopolar dynamos driving series motors
Moroz, Irene M.; Hide, Raymond; Soward, Andrew M.
1998-06-01
We present the results of a preliminary analytical and numerical study of one of the simpler members of a hierarchy of N (where N ≥ 1) coupled self-exciting Faraday disk homopolar dynamos, incorporating motors as additional electrical elements driven by the dynamo-generated current, as proposed by Hide (1997). The hierarchy is a generalisation of a single disk dynamo ( N = 1) with just one electric motor in the system, and crucially, incorporating effects due to mechanical friction in both the disk and the motor, as investigated by Hide et al. (1996). This is describable by a set of three coupled autonomous nonlinear ordinary differential equations, which, due to the presence of the motor, has solutions corresponding to co-existing periodic states of increasing complexity, as well as to chaotic dynamics. We consider the case of two such homopolar dynamos ( N = 2) with generally dissimilar characteristics but coupled together magnetically, with the aim of determining the extent to which this coupled system differs in its behaviour from the single disk dynamo with a series motor (Hide et al. 1996). In the case when the units are identical, the behaviour of the double dynamo system (after initial transients have decayed away) is identical to that of the single dynamo system, with solutions (including “synchronised chaos”) locked in both amplitude and phase. When there is no motor in the system and the coefficient of mechanical friction in the disks is small, these transients resemble the well-known ‘non-synchronous’, but structurally unstable Rikitake solution.
Current Challenges in Dynamo Modeling
Glatzmaier, G. A.
2001-12-01
Three-dimensional, dynamically self-consistent, numerical simulations have been used for two decades to study the generation of global magnetic fields in the deep fluid interiors of planets and stars. In particular, the number of geodynamo models has increased significantly within the last five years. These simulations of magnetic field generation by laminar convection have provided considerable insight to the dynamo process and have produced large-scale fields similar to those observed. However, no global convective dynamo simulation has yet been able to afford the spatial resolution required to simulate turbulent convection, which surely must exist in these low-viscosity fluids. They have all employed greatly enhanced eddy diffusivities to stabilize the low resolution numerical solutions and crudely account for the transport and mixing by the unresolved turbulence. A grand challenge for the next generation of geodynamo models is to produce a simulation with the thermal and viscous (eddy) diffusivities set no larger than the actual magnetic diffusivity of the Earth's fluid core (2 m2/s), while using the core's dimensions, mass, rotation rate and heat flow. This would correspond to the Ekman and magnetic Ekman numbers both set to 10-9 and the Rayleigh number being many orders of magnitude greater than critical. Dynamo models for stars and planets present an additional complication: the large variation of density with radius. A grand challenge for the next generation of these models is to reach similarly low Ekman numbers and high Rayleigh numbers with a density that decreases by at least three orders of magnitude from the base of the convection zone to the model's outer boundary. The advances in numerical methods and massively parallel computing needed to meet these challenges will be discussed.
Tzeferacos, P.; Rigby, A.; Bott, A.; Bell, A. R.; Bingham, R.; Casner, A.; Cattaneo, F.; Churazov, E. M.; Emig, J.; Flocke, N.; Fiuza, F.; Forest, C. B.; Foster, J.; Graziani, C.; Katz, J.; Koenig, M.; Li, C.-K.; Meinecke, J.; Petrasso, R.; Park, H.-S.; Remington, B. A.; Ross, J. S.; Ryu, D.; Ryutov, D.; Weide, K.; White, T. G.; Reville, B.; Miniati, F.; Schekochihin, A. A.; Froula, D. H.; Gregori, G.; Lamb, D. Q.
2017-04-01
The universe is permeated by magnetic fields, with strengths ranging from a femtogauss in the voids between the filaments of galaxy clusters to several teragauss in black holes and neutron stars. The standard model behind cosmological magnetic fields is the nonlinear amplification of seed fields via turbulent dynamo to the values observed. We have conceived experiments that aim to demonstrate and study the turbulent dynamo mechanism in the laboratory. Here, we describe the design of these experiments through simulation campaigns using FLASH, a highly capable radiation magnetohydrodynamics code that we have developed, and large-scale three-dimensional simulations on the Mira supercomputer at the Argonne National Laboratory. The simulation results indicate that the experimental platform may be capable of reaching a turbulent plasma state and determining the dynamo amplification. We validate and compare our numerical results with a small subset of experimental data using synthetic diagnostics.
Energy Technology Data Exchange (ETDEWEB)
Tzeferacos, P. [Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA; Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom; Rigby, A. [Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom; Bott, A. [Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom; Bell, A. R. [Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom; Bingham, R. [Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, United Kingdom; Department of Physics, University of Strathclyde, Glasgow G4 0NG, United Kingdom; Casner, A. [CEA, DAM, DIF, F-91297 Arpajon, France; Cattaneo, F. [Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA; Churazov, E. M. [Max Planck Institute for Astrophysics, D-85741 Garching, Germany; Space Research Institute (IKI), Moscow 117997, Russia; Emig, J. [Lawrence Livermore National Laboratory, Livermore, California 94550, USA; Flocke, N. [Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA; Fiuza, F. [SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA; Forest, C. B. [Physics Department, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA; Foster, J. [AWE, Aldermaston, Reading, West Berkshire, RG7 4PR, United Kingdom; Graziani, C. [Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA; Katz, J. [Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA; Koenig, M. [Laboratoire pour l' Utilisation de Lasers Intenses, UMR7605, CNRS CEA, Université Paris VI Ecole Polytechnique, France; Li, C. -K. [Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA; Meinecke, J. [Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom; Petrasso, R. [Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA; Park, H. -S. [Lawrence Livermore National Laboratory, Livermore, California 94550, USA; Remington, B. A. [Lawrence Livermore National Laboratory, Livermore, California 94550, USA; Ross, J. S. [Lawrence Livermore National Laboratory, Livermore, California 94550, USA; Ryu, D. [Department of Physics, UNIST, Ulsan 689-798, South Korea; Ryutov, D. [Lawrence Livermore National Laboratory, Livermore, California 94550, USA; Weide, K. [Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA; White, T. G. [Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom; Reville, B. [School of Mathematics and Physics, Queens University Belfast, Belfast BT7 1NN, United Kingdom; Miniati, F. [Department of Physics, ETH Zürich, CH-8093 Zürich, Switzerland; Schekochihin, A. A. [Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom; Froula, D. H. [Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA; Gregori, G. [Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom; Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA; Lamb, D. Q. [Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA
2017-03-22
The universe is permeated by magnetic fields, with strengths ranging from a femtogauss in the voids between the filaments of galaxy clusters to several teragauss in black holes and neutron stars. The standard model behind cosmological magnetic fields is the nonlinear amplification of seed fields via turbulent dynamo to the values observed. We have conceived experiments that aim to demonstrate and study the turbulent dynamo mechanism in the laboratory. Here, we describe the design of these experiments through simulation campaigns using FLASH, a highly capable radiation magnetohydrodynamics code that we have developed, and large-scale three-dimensional simulations on the Mira supercomputer at the Argonne National Laboratory. The simulation results indicate that the experimental platform may be capable of reaching a turbulent plasma state and determining the dynamo amplification. We validate and compare our numerical results with a small subset of experimental data using synthetic diagnostics.
Mechanically-forced dynamos (Invited)
Le Bars, M.
2013-12-01
It is a commonly accepted hypothesis that convection is responsible for planetary dynamos. However, the validity of the convective dynamo model can be questioned in various planets and moons as well as in asteroids, where the constraints from thermal evolution and compositional core models are sometimes difficult to reconcile with available data from paleomagnetism and in situ measurements. Over the last few years, researches have thus been pursued to find alternative mechanisms for sustaining intense three-dimensional motions in liquid cores, a necessary ingredient for planetary dynamo. In particular, mechanical forcings driven by libration, precession, nutation and tides, have received a renewed interest, following the first studies by Malkus in the 60's. A huge reservoir of energy is available in the rotational and orbital motions of all planetary systems. If planetary bodies were completely rigid and rotating at a constant spin rate, their fluid layers in the absence of convection would also behave rigidly and follow the spin of their boundaries. But small periodic perturbations of the shape of the core/mantle boundary (i.e. dynamic tides) and/or small periodic perturbations of the direction of the spin vector (i.e. precession and nutation) and/or small periodic perturbations of the spin rate (i.e. libration) systematically perturb this rigid state. Then, each of these small perturbations is capable of triggering instabilities in fluid layers, conveying energy from the spin and orbital motions to drive intense three-dimensional flows in the liquid cores. With the view to establish a general framework for planetary applications, I will present here the basic physical ingredients of these instabilities, which involve a resonance between the considered mechanical forcing and two inertial waves of the core. I will then review the numerical and experimental validations of this generic principle, and the few magnetohydrodynamic validations of their dynamo capacity
An impact-driven dynamo for the early Moon.
Le Bars, M; Wieczorek, M A; Karatekin, O; Cébron, D; Laneuville, M
2011-11-09
The origin of lunar magnetic anomalies remains unresolved after their discovery more than four decades ago. A commonly invoked hypothesis is that the Moon might once have possessed a thermally driven core dynamo, but this theory is problematical given the small size of the core and the required surface magnetic field strengths. An alternative hypothesis is that impact events might have amplified ambient fields near the antipodes of the largest basins, but many magnetic anomalies exist that are not associated with basin antipodes. Here we propose a new model for magnetic field generation, in which dynamo action comes from impact-induced changes in the Moon's rotation rate. Basin-forming impact events are energetic enough to have unlocked the Moon from synchronous rotation, and we demonstrate that the subsequent large-scale fluid flows in the core, excited by the tidal distortion of the core-mantle boundary, could have powered a lunar dynamo. Predicted surface magnetic field strengths are on the order of several microteslas, consistent with palaeomagnetic measurements, and the duration of these fields is sufficient to explain the central magnetic anomalies associated with several large impact basins.
Magnetic and Kinetic Power Spectra as a Tool to Probe the Turbulent Dynamo
Abramenko, V I; Goode, P R
2011-01-01
Generation and diffusion of the magnetic field on the Sun is a key mechanism responsible for solar activity on all spatial and temporal scales - from the solar cycle down to the evolution of small-scale magnetic elements in the quiet Sun. The solar dynamo operates as a non-linear dynamical process and is thought to be manifest in two types: as a global dynamo responsible for the solar cycle periodicity, and as a small-scale turbulent dynamo responsible for the formation of magnetic carpet in the quiet Sun. Numerous MHD simulations of the solar turbulence did not yet reach a consensus as to the existence of a turbulent dynamo on the Sun. At the same time, high-resolution observations of the quiet Sun from Hinode instruments suggest possibilities for the turbulent dynamo. Analysis of characteristics of turbulence derived from observations would be beneficial in tackling the problem. We analyse magnetic and velocity energy spectra as derived from Hinode/SOT, SOHO/MDI, SDO/HMI and the New Solar Telescope (NST) of...
Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory
Rogachevskii, Igor; Ruchayskiy, Oleg; Boyarsky, Alexey; Fröhlich, Jürg; Kleeorin, Nathan; Brandenburg, Axel; Schober, Jennifer
2017-09-01
The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (chiral magnetic effect). We present a self-consistent treatment of the chiral MHD equations, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfvén wave for incompressible flows, increases the frequencies of the Alfvén wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark–gluon plasma.
de Andrade, Garcia
2009-01-01
Boozer addressed the role of magnetic helicity in dynamos [Phys Fluids \\textbf{B},(1993)]. He pointed out that the magnetic helicity conservation implies that the dynamo action is more easily attainable if the electric potential varies over the surface of the dynamo. This provided us with motivation to investigate dynamos in Riemannian curved surfaces [Phys Plasmas \\textbf{14}, (2007);\\textbf{15} (2008)]. Thiffeault and Boozer [Phys Plasmas (2003)] discussed the onset of dissipation in kinematic dynamos. When curvature is constant and negative, a simple simple laminar dynamo solution is obtained on the flow topology of a Poincare disk, whose Gauss curvature is $K=-1$. By considering a laminar plasma dynamo [Wang et al, Phys Plasmas (2002)] the electric current helicity ${\\lambda}\\approx{2.34m^{-1}}$ for a Reynolds magnetic number of $Rm\\approx{210}$ and a growth rate of magnetic field $|{\\gamma}|\\approx{0.022}$. Negative constant curvature non-compact $\\textbf{H}^{2}$, has also been used in one-component elec...
Solar dynamo and geomagnetic activity
Georgieva, Katya
2010-01-01
The correlation between geomagnetic activity and the sunspot number in the 11-year solar cycle exhibits long-term variations due to the varying time lag between the sunspot-related and non-sunspot related geomagnetic activity, and the varying relative amplitude of the respective geomagnetic activity peaks. As the sunspot-related and non-sunspot related geomagnetic activity are caused by different solar agents, related to the solar toroidal and poloidal fields, respectively, we use their variations to derive the parameters of the solar dynamo transforming the poloidal field into toroidal field and back. We find that in the last 12 cycles the solar surface meridional circulation varied between 5 and 20 m/s (averaged over latitude and over the sunspot cycle), the deep circulation varied between 2.5 and 5.5 m/s, and the diffusivity in the whole of the convection zone was ~10**12 m2/s. In the last 12 cycles solar dynamo has been operating in moderately diffusion dominated regime in the bulk of the convection zone....
The DYNAMO Project: An Introduction
Directory of Open Access Journals (Sweden)
R. C. Ferrier
1998-01-01
Full Text Available European concerns about the consequences of anthropogenic impacts on environmental quality have led to the establishment of various dynamic modelling approaches through which the consequences of impacts over time can be assessed. Similarly, throughout Europe, there has been extensive collection of regional data on 'environmental capital' resulting in the production of wide area mapping of environmental quality (soils, land use etc. The aim of the DYNAMO was to integrate data and models, specifically; (1 to enhance the existing process based models to evaluate the impacts of multiple drivers of environmental change; (2 to evaluate these models at intensively studied (and manipulated catchments and stands; (3 to scale up in time from observations collected over several years to predict the long term impacts over decades, and (4 to scale up in space from the individual site level to regional, National and European scale. The project aims to develop and enhance regional modelling approaches so that European scale impacts of acidic deposition, land use (forestry practices and global change can be determined without compromising process level understanding of ecosystem function. The DYNAMO project contributes to the EU TERI (Terrestrial Ecosystems Research Initiative framework of the Environment and Climate Programme of the European Commission.
Some Recent Developments in Solar Dynamo Theory
Indian Academy of Sciences (India)
Arnab Rai Choudhuri
2006-06-01
We discuss the current status of solar dynamo theory and describe the dynamo model developed by our group. The toroidal magnetic field is generated in the tachocline by the strong differential rotation and rises to the solar surface due to magnetic buoyancy to create active regions. The decay of these active regions at the surface gives rise to the poloidal magnetic field by the Babcock–Leighton mechanism. This poloidal field is advected by the meridional circulation first to high latitudes and then down below to the tachocline. Dynamo models based on these ideas match different aspects of observational data reasonably well.
Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
Blackman, Eric G
2012-01-01
Conversion of gravitational energy into radiation near stars and compact objects in accretion disks the origin of large scale magnetic fields in astrophysical rotators have long been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory have exemplified such distinct pursuits. Both are presently incomplete, but 21st century MFD theory has nonlinear predictive power compared to 20th century MFD. in contrast, alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory ar...
An analytical dynamo solution for large-scale magnetic fields of galaxies
Chamandy, Luke
2016-11-01
We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parametrized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the `no-z' approximation and the dynamical α-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted on to galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure data sets. Further, we explore the properties of our numerical solutions, and their dependence on certain parameter values. We illustrate and assess the degree to which numerical solutions based on various levels of approximation, common in the dynamo literature, agree with one another.
Comments on the kinetic dynamo
Energy Technology Data Exchange (ETDEWEB)
Fowler, T.K.
1995-08-24
It is conjectured that transport by parallel mass flow in a braided magnetic field, rather than hyper-resistivity, drives the dynamo effect after stochasticity is established. In this paper the authors do not attempt a rigorous proof of this conjecture, which requires showing that braiding introduces correlations analogous to those giving rise to the neoclassical bootstrap current. The authors do offer plausible arguments for the conjecture and show that it leads to interesting consequences if true. Namely, magnetic fluctuations would then scale with the magnetic Reynolds number S like {tilde B}/B {approximately} S{sup {minus}1/2} and the Rechester-Rosenbluth thermal diffusivity like {chi}e {proportional_to} S{sup {minus}1} . This scaling would explain the highest temperatures obtained in the CTX spheromak. It also suggests that a fully-bootstrapped current drive experiment could be carried out on-the DIII-D tokamak.
Dynamo generated by the centrifugal instability
Marcotte, Florence; Gissinger, Christophe
2016-10-01
We present a scenario for magnetic field amplification where an electrically conducting fluid is confined in a differentially rotating, spherical shell with thin aspect ratio. When the angular momentum sufficiently decreases outwards, a hydrodynamic instability develops in the equatorial region, characterized by pairs of counter-rotating toroidal vortices similar to those observed in cylindrical Couette flow. These spherical Taylor-Couette vortices generate a subcritical dynamo magnetic field dominated by nonaxisymmetric components. We show that the critical magnetic Reynolds number seems to reach a constant value at large Reynolds number and that the global rotation can strongly decrease the dynamo onset. Our numerical results are understood within the framework of a simple dynamical system, and we propose a low-dimensional model for subcritical dynamo bifurcations. Implications for both laboratory dynamos and astrophysical magnetic fields are finally discussed.
Statistical tests of galactic dynamo theory
Chamandy, Luke; Taylor, A Russ
2016-01-01
Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare predictions of mean-field dynamo models to observational data on magnetic pitch angle and the strength of the mean magnetic field. We demonstrate that a standard $\\alpha^2\\Omega$ dynamo model produces pitch angles of the regular magnetic fields of nearby galaxies that are reasonably consistent with available data. The dynamo estimates of the magnetic field strength are generally within a factor of a few of the observational values. Reasonable agreement between theoretical and observed pitch angles generally requires the turbulent correlation time $\\tau$ to be in the range 10-20 Myr, in agreement with standard estimates. Moreover, good agreement also requires that the ratio of the ionized gas scale height to root-mean-square turbulent velocity increases with radius. Our results thus w...
Dynamo generated by the centrifugal instability
Marcotte, Florence
2016-01-01
We present a new scenario for magnetic field amplification where an electrically conducting fluid is confined in a differentially rotating, spherical shell with thin aspect-ratio. When the angular momentum sufficiently decreases outwards, an hydrodynamic instability develops in the equatorial region, characterised by pairs of counter-rotating toroidal vortices similar to those observed in cylindrical Couette flow. These spherical Taylor-Couette vortices generate a subcritical dynamo magnetic field dominated by non-axisymmetric components. We show that the critical magnetic Reynolds number seems to reach a constant value at large Reynolds number and that the global rotation can strongly decrease the dynamo onset. Our numerical results are understood within the framework of a simple dynamical system, and we propose a low-dimensional model for subcritical dynamo bifurcations. Implications for both laboratory dynamos and astrophysical magnetic fields are finally discussed.
Simple Scaling Relationships For Stellar Dynamos
Augustson, Kyle; Mathis, Stéphane; Brun, Allan Sacha
2016-12-01
This paper provides a brief overview of dynamo scaling relationships for the degree of equipartition between magnetic and kinetic energies. Three basic approaches are adopted to explore these scaling relationships, with a first look at two simple models: one assuming magnetostrophy and another that includes the effects of inertia. Next, a third scaling relationship is derived that utilizes the assumptions that the dynamo possesses two integral spatial scales and that it is driven by the balance of buoyancy work and ohmic dissipation as studied in Davidson 2013. The results of which are then compared to a suite of convective dynamo simulations that possess a fully convective domain with a weak density stratification and that captured the behavior of the resulting dynamo for a range of convective Rossby numbers (Augustson et al. 2016).
Saturation of the turbulent dynamo.
Schober, J; Schleicher, D R G; Federrath, C; Bovino, S; Klessen, R S
2015-08-01
The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e., on the hydrodynamical Reynolds number and the compressibility of the gas, and on the magnetic diffusivity. While we know the growth rate of the magnetic energy in the linear regime, the saturation level, i.e., the ratio of magnetic energy to turbulent kinetic energy that can be reached, is not known from analytical calculations. In this paper we present a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density. The magnetic resistivity increases compared to the Spitzer value and the effective scale on which the magnetic energy spectrum is at its maximum moves to larger spatial scales. This process ends when the peak reaches a characteristic wave number k☆ which is determined by the critical magnetic Reynolds number. The saturation level of the dynamo also depends on the type of turbulence and differs for the limits of large and small magnetic Prandtl numbers Pm. With our model we find saturation levels between 43.8% and 1.3% for Pm≫1 and between 2.43% and 0.135% for Pm≪1, where the higher values refer to incompressible turbulence and the lower ones to highly compressible turbulence.
Enhancement of small-scale turbulent dynamo by large-scale shear
Singh, Nishant K; Brandenburg, Axel
2016-01-01
Using direct numerical simulations we show that large-scale shear in non-helically forced turbulence supports small-scale dynamo action with zero mean magnetic field, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the dynamo growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are of the same order, we find scalings for the growth rate $\\gamma$ of the small-scale dynamo and the turbulent velocity $u_{\\rm rms}$ with shear rate $S$ that are independent of the magnetic Prandtl number: $\\gamma \\propto |S|$ and $u_{\\rm rms} \\propto |S|^{2/3}$. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the small-scale dynamo exhibits a universal scaling, $\\widetilde{\\gamma}\\propto |S|^{2/3}$, arising solely from the induction equation for a given velocity field.
Dynamo threshold detection in the von Kármán sodium experiment.
Miralles, Sophie; Bonnefoy, Nicolas; Bourgoin, Mickael; Odier, Philippe; Pinton, Jean-François; Plihon, Nicolas; Verhille, Gautier; Boisson, Jean; Daviaud, François; Dubrulle, Bérengère
2013-07-01
Predicting dynamo self-generation in liquid metal experiments has been an ongoing question for many years. In contrast to simple dynamical systems for which reliable techniques have been developed, the ability to predict the dynamo capacity of a flow and the estimate of the corresponding critical value of the magnetic Reynolds number (the control parameter of the instability) has been elusive, partly due to the high level of turbulent fluctuations of flows in such experiments (with kinetic Reynolds numbers in excess of 10(6)). We address these issues here, using the von Kármán sodium experiment and studying its response to an externally applied magnetic field. We first show that a dynamo threshold can be estimated from analysis related to critical slowing down and susceptibility divergence, in configurations for which dynamo action is indeed observed. These approaches are then applied to flow configurations that have failed to self-generate magnetic fields within operational limits, and we quantify the dynamo capacity of these configurations.
Suppression of a laminar kinematic dynamo by a prescribed large-scale shear
Sood, Aditi; Hollerbach, Rainer; Kim, Eun-jin
2016-10-01
We numerically solve the magnetic induction equation in a spherical shell geometry, with a kinematically prescribed axisymmetric flow that consists of a superposition of a small-scale helical flow and a large-scale shear flow. The small-scale flow is chosen to be a local analog of the classical Roberts cells, consisting of strongly helical vortex rolls. The large-scale flow is a shearing motion in either the radial or the latitudinal directions. In the absence of large-scale shear, the small-scale flow operates very effectively as a dynamo, in agreement with previous results. Adding increasingly large shear flows strongly suppresses the dynamo efficiency, indicating that shear is not always a favorable ingredient in dynamo action.
Impact of impellers on the axisymmetric magnetic mode in the VKS2 dynamo experiment.
Laguerre, R; Nore, C; Ribeiro, A; Léorat, J; Guermond, J-L; Plunian, F
2008-09-05
In the von Kármán Sodium 2 (VKS2) successful dynamo experiment of September 2006, the observed magnetic field showed a strong axisymmetric component, implying that nonaxisymmetric components of the flow field were acting. By modeling the induction effect of the spiraling flow between the blades of the impellers in a kinematic dynamo code, we find that the axisymmetric magnetic mode is excited. The control parameters are the magnetic Reynolds number of the mean flow, the coefficient measuring the induction effect alpha, and the type of boundary conditions. We show that using realistic values of alpha, the observed critical magnetic Reynolds number, Rm;{c} approximately 32, can be reached easily with ferromagnetic boundary conditions. We conjecture that the dynamo action achieved in this experiment may not be related to the turbulence in the bulk of the flow, but rather to the alpha effect induced by the impellers.
Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers
Calkins, Michael A; Nieves, David; Julien, Keith; Tobias, Steven M
2016-01-01
Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dynamo, as determined by an increase in the critical magnetic Reynolds number, is observed as the buoyancy forcing is increased. This decreased efficiency may result from both the loss of correlations associated with the increasingly disordered states of flow that are generated, and boundary layer behavior that enhances magnetic diffusion locally. We find that the spatial characteristics of $\\alpha$, and thus the large-sca...
Colloidal Plasmas : Dynamo transformation of the collisional R-T in a weakly ionized plasma
Indian Academy of Sciences (India)
C B Dwivedi
2000-11-01
Theoretical prediction of a new kind of normal mode behaviour of electro-mechanical nature was ﬁrst time reported by Dwivedi and Das in 1992 in the context of mesospheric modeling of observed neutral induced turbulence. Local dynamo action (due to relative neutral ﬂow) governs the basic physical principle for linear excitation of the neutral induced low frequency instability (NILF) in mesospheric plasma, which comprises of weakly ionized inhomogeneous gas conﬁned by the external gravity and ambient magnetic ﬁeld. The present contribution offers physical explanation in terms of dynamo transformation of neutral drag effect as a source to understand complete suppression of the usual collisional R-T and in turn linear driving of the NILF. It is therefore emphasized, worth calling it as the dynamo instability.
Chaotic flows and fast magnetic dynamos
Finn, John M.; Ott, Edward
1988-01-01
The kinematic dynamo problem is considered in the R(m) approaching infinity limit. It is shown that the magnetic field tends to concentrate on a zero volume fractal set; moreover, it displays arbitrarily fine-scaled oscillations between parallel and antiparallel directions. Consideration is given to the relationship between the dynamo growth rate and quantitative measures of chaos, such as the Liapunov element and topological entropy.
Heat flux modulation in domino dynamo model
Reshetnyak, Maxim
2012-01-01
Using domino dynamo model we show how variations of the heat flux at the core-mantle boundary change frequency of geomagnetic field reversals. In fact, we are able to demonstrate effect known from the modern 3D planetary dynamo models using ensemble of the interacting spins, which obey equations of the Langevin-type with a random force. We also consider applications to the giant- planets and offer explanations of some specific episodes of the geomagnetic field in the past.
Magnetic field reversals and galactic dynamos
2012-01-01
We argue that global magnetic field reversals similar to those observed in the Milky Way occur quite frequently in mean-field galactic dynamo models that have relatively strong, random, seed magnetic fields that are localized in discrete regions. The number of reversals decreases to zero with reduction of the seed strength, efficiency of the galactic dynamo and size of the spots of the seed field. A systematic observational search for magnetic field reversals in a representative sample of spi...
A deep dynamo generating Mercury's magnetic field.
Christensen, Ulrich R
2006-12-21
Mercury has a global magnetic field of internal origin and it is thought that a dynamo operating in the fluid part of Mercury's large iron core is the most probable cause. However, the low intensity of Mercury's magnetic field--about 1% the strength of the Earth's field--cannot be reconciled with an Earth-like dynamo. With the common assumption that Coriolis and Lorentz forces balance in planetary dynamos, a field thirty times stronger is expected. Here I present a numerical model of a dynamo driven by thermo-compositional convection associated with inner core solidification. The thermal gradient at the core-mantle boundary is subadiabatic, and hence the outer region of the liquid core is stably stratified with the dynamo operating only at depth, where a strong field is generated. Because of the planet's slow rotation the resulting magnetic field is dominated by small-scale components that fluctuate rapidly with time. The dynamo field diffuses through the stable conducting region, where rapidly varying parts are strongly attenuated by the skin effect, while the slowly varying dipole and quadrupole components pass to some degree. The model explains the observed structure and strength of Mercury's surface magnetic field and makes predictions that are testable with space missions both presently flying and planned.
Variational data assimilation for the initial-value dynamo problem.
Li, Kuan; Jackson, Andrew; Livermore, Philip W
2011-11-01
The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical
Extreme events induced by self-action of laser beams in dynamic nonlinear liquid crystal cells
Bugaychuk, S.; Iljin, A.; Chunikhina, K.
2017-06-01
Optical extreme events represent a feature of nonlinear systems where there may emerge individual pulses possessing very high (or very low) intensity hardly probable statistically. Such property is being connected with the generation of solitons in the nonlinear systems. We carry out the first experiments for detection of extreme events during two-wave mixing with nonlinear dynamical liquid crystal (LC) cells. We investigate the statistics of the extreme events in dependence on relation between the duration of a laser pulse and the time characteristic of dynamic grating relaxation in LC cell. Our research shows that the self-diffraction of laser beams with a dynamical grating support the generation of envelope solitons in this system.
Realistic modeling of local dynamo processes on the Sun
Kitiashvili, I N; Mansour, N N; Wray, A A
2015-01-01
Magnetic fields are usually observed in the quiet Sun as small-scale elements that cover the entire solar surface (the `salt and pepper' patterns in line-of-sight magnetograms). By using 3D radiative MHD numerical simulations we find that these fields result from a local dynamo action in the top layers of the convection zone, where extremely weak 'seed' magnetic fields (e.g., from a $10^{-6}$ G) can locally grow above the mean equipartition field, to a stronger than 2000~G field localized in magnetic structures. Our results reveal that the magnetic flux is predominantly generated in regions of small-scale helical downflows. We find that the local dynamo action takes place mostly in a shallow, about 500~km deep, subsurface layer, from which the generated field is transported into the deeper layers by convective downdrafts. We demonstrate that the observed dominance of vertical magnetic fields at the photosphere and horizontal fields above the photosphere can be explained by small-scale magnetic loops produced ...
Summer Study Program in Geophysical Fluid Dynamics; Order and Disorder Planetary Dynamos
1988-05-01
PARTICIPANTS Fast Dynamos in Chaotic Flow Bruce Bayly 109 Observational Constraints on Theories of the Geodynamo Jeremy BloxhamIl i I Nonlinear...1986. Phys. Rev. Lett., 57, No. 22, 2800. 4’ %.’ I- 111 , OBSERVATIONAL CONSTRAINTS ON THEORIES OF THE GEODYNAMO Jeremy Bloxham Department of Earth... geodynamo ", 1987 Summer Program in Geophysical Fluid Dynamics, Woods Hole Oceanographic Institu- tion, this volume. Bolton, E.W., 1985. "Problems in
Modeling MHD accretion-ejection: episodic ejections of jets triggered by a mean-field disk dynamo
Energy Technology Data Exchange (ETDEWEB)
Stepanovs, Deniss; Fendt, Christian; Sheikhnezami, Somayeh, E-mail: deniss@stepanovs.org, E-mail: fendt@mpia.de [Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg (Germany)
2014-11-20
We present MHD simulations exploring the launching, acceleration, and collimation of jets and disk winds. The evolution of the disk structure is consistently taken into account. Extending our earlier studies, we now consider the self-generation of the magnetic field by an α{sup 2}Ω mean-field dynamo. The disk magnetization remains on a rather low level, which helps to evolve the simulations for T > 10, 000 dynamical time steps on a domain extending 1500 inner disk radii. We find the magnetic field of the inner disk to be similar to the commonly found open field structure, favoring magneto-centrifugal launching. The outer disk field is highly inclined and predominantly radial. Here, differential rotation induces a strong toroidal component, which plays a key role in outflow launching. These outflows from the outer disk are slower, denser, and less collimated. If the dynamo action is not quenched, magnetic flux is continuously generated, diffuses outward through the disk, and fills the entire disk. We have invented a toy model triggering a time-dependent mean-field dynamo. The duty cycles of this dynamo lead to episodic ejections on similar timescales. When the dynamo is suppressed as the magnetization falls below a critical value, the generation of the outflows and also accretion is inhibited. The general result is that we can steer episodic ejection and large-scale jet knots by a disk-intrinsic dynamo that is time-dependent and regenerates the jet-launching magnetic field.
Optical transistor action by nonlinear coupling of stimulated emission and coherent scattering
Andrews, David L.; Bradshaw, David S.
2010-08-01
In the pursuit of improved platforms for computing, communications and internet connectivity, all-optical systems offer excellent prospects for a speed and fidelity of data transmission that will greatly surpass conventional electronics, alongside the anticipated benefits of reduced energy loss. With a diverse range of sources and fiber optical connections already in production, much current effort is being devoted towards forging optical components for signal switching, such as an all-optical transistor. Achievement of the desired characteristics for any practicable device can be expected to depend crucially on the engagement of a strongly nonlinear optical response. The innovative scheme proposed in the present work is based upon a third-order nonlinearity - its effect enhanced by stimulated emission - operating within a system designed to exploit the highly nonlinear response observed at the threshold for laser emission. Here, stimulated emission is strongly driven by coupling to the coherent scattering of a signal input beam whose optical frequency is purposely off-set from resonance. An electrodynamical analysis of the all-optical coupling process shows that the signal beam can significantly modify the kinetics of emission, and so lead to a dramatically enhanced output of resonant radiation. The underlying nonlinear optical mechanism is analyzed, model calculations are performed for realizable three-level laser systems, and the results exhibited graphically. The advantages of implementing this all-optical transistor scheme, compared to several previously envisaged proposals, are then outlined.
Multicolored Dynamos on Toroidal Meshes
Brunetti, Sara; Quattrociocchi, Walter
2010-01-01
Detecting on a graph the presence of the minimum number of nodes (target set) that will be able to "activate" a prescribed number of vertices in the graph is called the target set selection problem (TSS) proposed by Kempe, Kleinberg, and Tardos. In TSS's settings, nodes have two possible states (active or non-active) and the threshold triggering the activation of a node is given by the number of its active neighbors. Dealing with fault tolerance in a majority based system the two possible states are used to denote faulty or non-faulty nodes, and the threshold is given by the state of the majority of neighbors. Here, the major effort was in determining the distribution of initial faults leading the entire system to a faulty behavior. Such an activation pattern, also known as dynamic monopoly (or shortly dynamo), was introduced by Peleg in 1996. In this paper we extend the TSS problem's settings by representing nodes' states with a "multicolored" set. The extended version of the problem can be described as foll...
Galactic Dynamos and Galactic Winds
Beck, Rainer
2007-01-01
Spiral galaxies host dynamically important magnetic fields which can affect gas flows in the disks and halos. Total magnetic fields in spiral galaxies are strongest (up to 30 \\muG) in the spiral arms where they are mostly turbulent or tangled. Polarized synchrotron emission shows that the resolved regular fields are generally strongest in the interarm regions (up to 15 \\muG). Faraday rotation measures of radio polarization vectors in the disks of several spiral galaxies reveal large-scale patterns which are signatures of coherent fields generated by a mean-field dynamo. -- Magnetic fields are also observed in radio halos around edge-on galaxies at heights of a few kpc above the disk. Cosmic-ray driven galactic winds transport gas and magnetic fields from the disk into the halo. The magnetic energy density is larger than the thermal energy density, but smaller than the kinetic energy density of the outflow. The orientation of field lines allows to estimate the wind speed and direction. There is no observation ...
Sur, Sharanya; Schleicher, Dominik R G; Banerjee, Robi; Klessen, Ralf S
2012-01-01
We study the influence of initial conditions on the magnetic field amplification during the collapse of a magnetised gas cloud. We focus on the dependence of the growth and saturation level of the dynamo generated field on the turbulent properties of the collapsing cloud. In particular, we explore the effect of varying the initial strength and injection scale of turbulence and the initial uniform rotation of the collapsing magnetised cloud. In order to follow the evolution of the magnetic field in both the kinematic and the nonlinear regime, we choose an initial field strength of $\\simeq 1\\,\\mkG$ with the magnetic to kinetic energy ratio, $E_{\\rm m}/E_{\\rm k} \\sim 10^{-4}$. Both gravitational compression and the small-scale dynamo initially amplify the magnetic field. Further into the evolution, the dynamo-generated magnetic field saturates but the total magnetic field continues to grow because of compression. The saturation of the small-scale dynamo is marked by a change in the slope of $B/\\rho^{2/3}$ and by...
Influence of high permeability disks in an axisymmetric model of the Cadarache dynamo experiment
Giesecke, A; Stefani, F; Gerbeth, G; Léorat, J; Herreman, W; Luddens, F; Guermond, J -L
2011-01-01
Numerical simulations of the kinematic induction equation are performed on a model configuration of the Cadarache von-K\\'arm\\'an-Sodium dynamo experiment. The effect of a localized axisymmetric distribution of relative permeability {\\mu} that represents soft iron material within the conducting fluid flow is investigated. The critical magnetic Reynolds number Rm^c for dynamo action of the first non-axisymmetric mode roughly scales like Rm^c({\\mu})-Rm^c({\\mu}->infinity) ~ {\\mu}^(-1/2) i.e. the threshold decreases as {\\mu} increases. This scaling law suggests a skin effect mechanism in the soft iron disks. More important with regard to the Cadarache dynamo experiment, we observe a purely toroidal axisymmetric mode localized in the high permeability disks which becomes dominant for large {\\mu}. In this limit, the toroidal mode is close to the onset of dynamo action with a (negative) growth-rate that is rather independent of the magnetic Reynolds number. We qualitatively explain this effect by paramagnetic pumping...
Statistical Tests of Galactic Dynamo Theory
Chamandy, Luke; Shukurov, Anvar; Taylor, A. Russ
2016-12-01
Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare predictions of mean-field dynamo models to observational data on magnetic pitch angle and the strength of the mean magnetic field. We demonstrate that a standard {α }2{{Ω }} dynamo model produces pitch angles of the regular magnetic fields of nearby galaxies that are reasonably consistent with available data. The dynamo estimates of the magnetic field strength are generally within a factor of a few of the observational values. Reasonable agreement between theoretical and observed pitch angles generally requires the turbulent correlation time τ to be in the range of 10-20 {Myr}, in agreement with standard estimates. Moreover, good agreement also requires that the ratio of the ionized gas scale height to root-mean-square turbulent velocity increases with radius. Our results thus widen the possibilities to constrain interstellar medium parameters using observations of magnetic fields. This work is a step toward systematic statistical tests of galactic dynamo theory. Such studies are becoming more and more feasible as larger data sets are acquired using current and up-and-coming instruments.
Turbulent dynamo in a collisionless plasma.
Rincon, François; Califano, Francesco; Schekochihin, Alexander A; Valentini, Francesco
2016-04-12
Magnetic fields pervade the entire universe and affect the formation and evolution of astrophysical systems from cosmological to planetary scales. The generation and dynamical amplification of extragalactic magnetic fields through cosmic times (up to microgauss levels reported in nearby galaxy clusters, near equipartition with kinetic energy of plasma motions, and on scales of at least tens of kiloparsecs) are major puzzles largely unconstrained by observations. A dynamo effect converting kinetic flow energy into magnetic energy is often invoked in that context; however, extragalactic plasmas are weakly collisional (as opposed to magnetohydrodynamic fluids), and whether magnetic field growth and sustainment through an efficient turbulent dynamo instability are possible in such plasmas is not established. Fully kinetic numerical simulations of the Vlasov equation in a 6D-phase space necessary to answer this question have, until recently, remained beyond computational capabilities. Here, we show by means of such simulations that magnetic field amplification by dynamo instability does occur in a stochastically driven, nonrelativistic subsonic flow of initially unmagnetized collisionless plasma. We also find that the dynamo self-accelerates and becomes entangled with kinetic instabilities as magnetization increases. The results suggest that such a plasma dynamo may be realizable in laboratory experiments, support the idea that intracluster medium turbulence may have significantly contributed to the amplification of cluster magnetic fields up to near-equipartition levels on a timescale shorter than the Hubble time, and emphasize the crucial role of multiscale kinetic physics in high-energy astrophysical plasmas.
Role of soft-iron impellers on the mode selection in the von kármán-sodium dynamo experiment.
Giesecke, André; Stefani, Frank; Gerbeth, Gunter
2010-01-29
A crucial point for the understanding of the von Kármán-sodium (VKS) dynamo experiment is the influence of soft-iron impellers. We present numerical simulations of a VKS-like dynamo with a localized permeability distribution that resembles the shape of the flow driving impellers. It is shown that the presence of soft-iron material essentially determines the dynamo process in the VKS experiment. An axisymmetric magnetic field mode can be explained by the combined action of the soft-iron disk and a rather small alpha effect parametrizing the induction effects of unresolved small scale flow fluctuations.
Numerical simulation of Martian historical dynamo: Impact of the Rayleigh number on the dynamo state
Institute of Scientific and Technical Information of China (English)
WANG TianYuan; KUANG WeiJia; MA ShiZhuang
2009-01-01
The observed Mars remnant magnetism suggests that there was an active dynamo in the Martian core.We use the MoSST core dynamics model to simulate the Martian historical dynamo,focusing on the variation of the dynamo states with the Rayleigh number Ra (a non-dimensional parameter describing the buoyancy force in the core).Our numerical results show that the mean field length scale does not vary monotonically with the Rayleigh number,and the field morphology at the core mantle boundary changes with Rayleigh number.In particular,it drifts westward with a speed decreasing with Rayleigh number.
Numerical simulation of Martian historical dynamo:Impact of the Rayleigh number on the dynamo state
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The observed Mars remnant magnetism suggests that there was an active dynamo in the Martian core. We use the MoSST core dynamics model to simulate the Martian historical dynamo, focusing on the variation of the dynamo states with the Rayleigh number Ra (a non-dimensional parameter describing the buoyancy force in the core). Our numerical results show that the mean field length scale does not vary monotonically with the Rayleigh number, and the field morphology at the core mantle boundary changes with Rayleigh number. In particular, it drifts westward with a speed decreasing with Rayleigh number.
Magnetic Field Amplification via Protostellar Disc Dynamos
Dyda, Sergei; Ustyugova, Galina V; Koldoba, Alexander V; Wasserman, Ira
2015-01-01
We model the generation of a magnetic field in a protostellar disc using an \\alpha-dynamo and perform axisymmetric magnetohydrodynamics (MHD) simulations of a T Tauri star. We find that for small values of the dimensionless dynamo parameter $\\alpha_d$ the poloidal field grows exponentially at a rate ${\\sigma} \\propto {\\Omega}_K \\sqrt{\\alpha_d}$ , before saturating to a value $\\propto \\sqrt{\\alpha_d}$ . The dynamo excites dipole and octupole modes, but quadrupole modes are suppressed, because of the symmetries of the seed field. Initial seed fields too weak to launch MHD outflows are found to grow sufficiently to launch winds with observationally relevant mass fluxes of order $10^{-9} M_{\\odot}/\\rm{yr}$ for T Tauri stars. For large values of $\\alpha_d$ magnetic loops are generated over the entire disc. These quickly come to dominate the disc dynamics and cause the disc to break up due to the magnetic pressure.
Dynamo Models of the Solar Cycle
Directory of Open Access Journals (Sweden)
Charbonneau Paul
2005-06-01
Full Text Available This paper reviews recent advances and current debates in modeling the solar cycle as a hydromagnetic dynamo process. Emphasis is placed on (relatively simple dynamo models that are nonetheless detailed enough to be comparable to solar cycle observations. After a brief overview of the dynamo problem and of key observational constraints, we begin by reviewing the various magnetic field regeneration mechanisms that have been proposed in the solar context. We move on to a presentation and critical discussion of extant solar cycle models based on these mechanisms. We then turn to the origin of fluctuations in these models, including amplitude and parity modulation, chaotic behavior, and intermittency. The paper concludes with a discussion of our current state of ignorance regarding various key questions, the most pressing perhaps being the identification of the physical mechanism(s responsible for the generation of the Sun's poloidal magnetic field component.
Dynamos and MHD theory of turbulence suppression
Energy Technology Data Exchange (ETDEWEB)
Yoshizawa, Akira [Institute of Industrial Science, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Itoh, Sanae-I [Research Institute for Applied Mechanics, Kyushu University, 87, Kasuga 810- 8580 (Japan); Itoh, Kimitaka [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Yokoi, Nobumitsu [Institute of Industrial Science, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505 (Japan)
2004-03-01
Characteristics of electrically conducting media are reviewed from the macroscopic viewpoint based on mean-field magnetohydrodynamics, while being compared using the methodology and knowledge in fluid mechanics. The themes covered in this review range from the mechanism of generating stellar magnetic fields (dynamo) to transport properties in fusion. The primary concern here is to see the characteristics common to these apparently different phenomena, within the framework of the mean-field theory. Owing to the intrinsic limitation of the approach, the present discussions are limited more or less to specific aspects of phenomena. They are supplemented with reference to theoretical, numerical, and observational approaches intrinsic to each theme. In the description of dynamo phenomena, emphasis is laid on the cross helicity dynamo. Features common to stellar magnetic-field generation and the rotational-motion drive in toroidal plasmas are illustrated on this basis. (topical review)
Self-consistent simulations of a von Kármán type dynamo in a spherical domain with metallic walls.
Guervilly, Céline; Brummell, Nicholas H
2012-10-01
We have performed numerical simulations of boundary-driven dynamos using a three-dimensional nonlinear magnetohydrodynamical model in a spherical shell geometry. A conducting fluid of magnetic Prandtl number Pm=0.01 is driven into motion by the counter-rotation of the two hemispheric walls. The resulting flow is of von Kármán type, consisting of a layer of zonal velocity close to the outer wall and a secondary meridional circulation. Above a certain forcing threshold, the mean flow is unstable to non-axisymmetric motions within an equatorial belt. For fixed forcing above this threshold, we have studied the dynamo properties of this flow. The presence of a conducting outer wall is essential to the existence of a dynamo at these parameters. We have therefore studied the effect of changing the material parameters of the wall (magnetic permeability, electrical conductivity, and thickness) on the dynamo. In common with previous studies, we find that dynamos are obtained only when either the conductivity or the permeability is sufficiently large. However, we find that the effect of these two parameters on the dynamo process are different and can even compete to the detriment of the dynamo. Our self-consistent approach allow us to analyze in detail the dynamo feedback loop. The dynamos we obtain are typically dominated by an axisymmetric toroidal magnetic field and an axial dipole component. We show that the ability of the outer shear layer to produce a strong toroidal field depends critically on the presence of a conducting outer wall, which shields the fluid from the vacuum outside. The generation of the axisymmetric poloidal field, on the other hand, occurs in the equatorial belt and does not depend on the wall properties.
Turbulent Dynamo in a Conducting Fluid and a Partially Ionized Gas
Xu, Siyao; Lazarian, A.
2016-12-01
By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of a turbulent dynamo process, and we study the dynamo process for a full range of magnetic Prandtl number P m and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on P m in a conducting fluid and { R } (a function of ionization fraction) in a partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regime of dynamo characterized by a linear-in-time growth of magnetic field strength, and the resulting magnetic energy is much higher than the kinetic energy carried by viscous-scale eddies. Unlike the kinematic stage, the subsequent nonlinear stage is unaffected by microscopic diffusion processes and has a universal linear-in-time growth of magnetic energy with the growth rate as a constant fraction 3/38 of the turbulent energy transfer rate, showing good agreement with earlier numerical results. Applying the analysis to the first stars and galaxies, we find that the kinematic stage is able to generate a field strength only an order of magnitude smaller than the final saturation value. But the generation of large-scale magnetic fields can only be accounted for by the relatively inefficient nonlinear stage and requires longer time than the free-fall time. It suggests that magnetic fields may not have played a dynamically important role during the formation of the first stars.
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Spectral gaps, inertial manifolds and kinematic dynamos
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es
2005-10-17
Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.
Dynamo and anomalous transport in the reversed field pinch
Energy Technology Data Exchange (ETDEWEB)
Prager, S.C.
1998-08-01
The reversed field pinch is an effective tool to study the macroscopic consequences of magnetic fluctuations, such as the dynamo effect and anomalous transport. Several explanations exist for the dynamo (the self-generation of plasma current)--the MHD dynamo, the kinetic dynamo, and the diamagnetic dynamo. There is some experimental evidence for each, particularly from measurements of ion velocity and electron pressure fluctuations. Magnetic fluctuations are known to produce energy and particle flux in the RFP core. Current profile control is able to decrease fluctuation-induced transport by a factor of five. Improved confinement regimes are also obtained at deep reversal and, possibly, with flow shear.
Dynamo transition in a five-mode helical model
Kumar, Rohit; Wahi, Pankaj
2017-09-01
We construct a five-mode helical dynamo model containing three velocity and two magnetic modes and solve it analytically. This model exhibits dynamo transition via supercritical pitchfork bifurcation. We show that the critical magnetic Reynolds number for dynamo transition (Rmc) asymptotes to constant values for very low and very high magnetic Prandtl numbers (Pm). Beyond dynamo transition, secondary bifurcations lead to periodic, quasi-periodic, and chaotic dynamo states as the forcing amplitude is increased and chaos appears through a quasi-periodic route.
Limited role of spectra in dynamo theory: coherent versus random dynamos.
Tobias, Steven M; Cattaneo, Fausto
2008-09-19
We discuss the importance of phase information and coherence times in determining the dynamo properties of turbulent flows. We compare the kinematic dynamo properties of three flows with the same energy spectrum. The first flow is dominated by coherent structures with nontrivial phase information and long eddy coherence times, the second has random phases and long-coherence time, the third has nontrivial phase information, but short coherence time. We demonstrate that the first flow is the most efficient kinematic dynamo, owing to the presence of sustained stretching and constructive folding. We argue that these results place limitations on the possible inferences of the dynamo properties of flows from the use of spectra alone, and that the role of coherent structures must always be accounted for.
Configuration Design of Novel Manually Operated Dynamo Flashlights
Yan, Hong-Sen; Wang, Hsin-Te
This paper synthesizes novel configurations of manually operated dynamo flashlights. Topology and motion characteristics of existing gear dynamos are modified and concluded. The structural sketches and corresponding graph representations for gear trains and dynamos with the defined induced magnetic circuits are defined. Through the concepts of generalization and specialization, the atlas of the structural sketches and graphs of the embedded gear dynamos is obtained subject to the defined design requirements and constraints. And, a systematic approach is proposed to synthesize the novel mechanisms of the embedded gear dynamos. As a result, the embedded three-link and four-link gear dynamos have 12 and 24 novel design configurations, respectively. One prototype of the embedded three-link and another of the embedded four-link gear dynamo are built.
Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers
Calkins, Michael A.; Long, Louie; Nieves, David; Julien, Keith; Tobias, Steven M.
2016-12-01
Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dynamo, as determined by an increase in the critical magnetic Reynolds number, is observed as the buoyancy forcing is increased. This decreased efficiency may result from both the loss of correlations associated with the increasingly disordered states of flow that are generated, and boundary layer behavior that enhances magnetic diffusion locally. We find that the spatial characteristics of the large-scale magnetic field is dependent only weakly on changes in flow behavior. In contrast, the behavior of the small-scale magnetic field is directly dependent on, and therefore shows significant variations with, the small-scale convective flow field. However, our results are limited to the linear, kinematic dynamo regime; future simulations that include the Lorentz force are therefore necessary to assess the robustness of these results.
Magnetic reversals from planetary dynamo waves.
Sheyko, Andrey; Finlay, Christopher C; Jackson, Andrew
2016-11-24
A striking feature of many natural dynamos is their ability to undergo polarity reversals. The best documented example is Earth's magnetic field, which has reversed hundreds of times during its history. The origin of geomagnetic polarity reversals lies in a magnetohydrodynamic process that takes place in Earth's core, but the precise mechanism is debated. The majority of numerical geodynamo simulations that exhibit reversals operate in a regime in which the viscosity of the fluid remains important, and in which the dynamo mechanism primarily involves stretching and twisting of field lines by columnar convection. Here we present an example of another class of reversing-geodynamo model, which operates in a regime of comparatively low viscosity and high magnetic diffusivity. This class does not fit into the paradigm of reversal regimes that are dictated by the value of the local Rossby number (the ratio of advection to Coriolis force). Instead, stretching of the magnetic field by a strong shear in the east-west flow near the imaginary cylinder just touching the inner core and parallel to the axis of rotation is crucial to the reversal mechanism in our models, which involves a process akin to kinematic dynamo waves. Because our results are relevant in a regime of low viscosity and high magnetic diffusivity, and with geophysically appropriate boundary conditions, this form of dynamo wave may also be involved in geomagnetic reversals.
Converting DYNAMO simulations to Powersim Studio simulations
Energy Technology Data Exchange (ETDEWEB)
Walker, La Tonya Nicole; Malczynski, Leonard A.
2014-02-01
DYNAMO is a computer program for building and running 'continuous' simulation models. It was developed by the Industrial Dynamics Group at the Massachusetts Institute of Technology for simulating dynamic feedback models of business, economic, and social systems. The history of the system dynamics method since 1957 includes many classic models built in DYANMO. It was not until the late 1980s that software was built to take advantage of the rise of personal computers and graphical user interfaces that DYNAMO was supplanted. There is much learning and insight to be gained from examining the DYANMO models and their accompanying research papers. We believe that it is a worthwhile exercise to convert DYNAMO models to more recent software packages. We have made an attempt to make it easier to turn these models into a more current system dynamics software language, Powersim © Studio produced by Powersim AS^{2} of Bergen, Norway. This guide shows how to convert DYNAMO syntax into Studio syntax.
Magnetic Helicity and the Solar Dynamo
Canfield, Richard C.
1997-01-01
The objective of this investigation is to open a new window into the solar dynamo, convection, and magnetic reconnection through measurement of the helicity density of magnetic fields in the photosphere and tracing of large-scale patterns of magnetic helicity in the corona.
Magnetic Helicity in a Cyclic Convective Dynamo
Miesch, Mark S.; Zhang, Mei; Augustson, Kyle C.
2016-05-01
Magnetic helicity is a fundamental agent for magnetic self-organization in magnetohydrodynamic (MHD) dynamos. As a conserved quantity in ideal MHD, it establishes a strict topological coupling between large and small-scale magnetic fields. The generation of magnetic fields on scales larger than the velocity field is linked to an upscale transfer of magnetic helicity, either locally in spectral space as in the inverse cascade of magnetic helicity in MHD turbulence or non-locally, as in the turbulent alpha-effect of mean-field dynamo theory. Thus, understanding the generation, transport, and dissipation of magnetic helicity is an essential prerequisite to understanding manifestations of magnetic self-organization in the solar dynamo, including sunspots, the prominent dipole and quadrupole moments, and the 22-year magnetic activity cycle. We investigate the role of magnetic helicity in a convective dynamo model that exhibits regular magnetic cycles. The cycle is marked by coherent bands of toroidal field that persist within the convection zone and that are antisymmetric about the equator. When these toriodal bands interact across the equator, it initiates a global restructuring of the magnetic topology that contributes to the reversal of the dipole moment. Thus, the polar field reversals are preceeded by a brief reversal of the subsurface magnetic helicity. There is some evidence that the Sun may exhibit a similar magnetic helicity reversal prior to its polar field reversals.
Extrapolating Solar Dynamo Models Throughout the Heliosphere
Cox, B. T.; Miesch, M. S.; Augustson, K.; Featherstone, N. A.
2014-12-01
There are multiple theories that aim to explain the behavior of the solar dynamo, and their associated models have been fiercely contested. The two prevailing theories investigated in this project are the Convective Dynamo model that arises from the pure solving of the magnetohydrodynamic equations, as well as the Babcock-Leighton model that relies on sunspot dissipation and reconnection. Recently, the supercomputer simulations CASH and BASH have formed models of the behavior of the Convective and Babcock-Leighton models, respectively, in the convective zone of the sun. These models show the behavior of the models within the sun, while much less is known about the effects these models may have further away from the solar surface. The goal of this work is to investigate any fundamental differences between the Convective and Babcock-Leighton models of the solar dynamo outside of the sun and extending into the solar system via the use of potential field source surface extrapolations implemented via python code that operates on data from CASH and BASH. The use of real solar data to visualize supergranular flow data in the BASH model is also used to learn more about the behavior of the Babcock-Leighton Dynamo. From the process of these extrapolations it has been determined that the Babcock-Leighton model, as represented by BASH, maintains complex magnetic fields much further into the heliosphere before reverting into a basic dipole field, providing 3D visualisations of the models distant from the sun.
Solar Cycle #24 and the Solar Dynamo
Schatten, Kenneth; Pesnell, W. Dean
2007-01-01
We focus on two solar aspects related to flight dynamics. These are the solar dynamo and long-term solar activity predictions. The nature of the solar dynamo is central to solar activity predictions, and these predictions are important for orbital planning of satellites in low earth orbit (LEO). The reason is that the solar ultraviolet (UV) and extreme ultraviolet (EUV) spectral irradiances inflate the upper atmospheric layers of the Earth, forming the thermosphere and exosphere through which these satellites orbit. Concerning the dynamo, we discuss some recent novel approaches towards its understanding. For solar predictions we concentrate on a solar precursor method, in which the Sun's polar field plays a major role in forecasting the next cycle s activity based upon the Babcock-Leighton dynamo. With a current low value for the Sun s polar field, this method predicts that solar cycle #24 will be one of the lowest in recent times, with smoothed F10.7 radio flux values peaking near 130 plus or minus 30 (2 sigma), in the 2013 timeframe. One may have to consider solar activity as far back as the early 20th century to find a cycle of comparable magnitude. Concomitant effects of low solar activity upon satellites in LEO will need to be considered, such as enhancements in orbital debris. Support for our prediction of a low solar cycle #24 is borne out by the lack of new cycle sunspots at least through the first half of 2007. Usually at the present epoch in the solar cycle (approx. 7+ years after the last solar maximum), for a normal size following cycle, new cycle sunspots would be seen. The lack of their appearance at this time is only consistent with a low cycle #24. Polar field observations of a weak magnitude are consistent with unusual structures seen in the Sun s corona. Polar coronal holes are the hallmarks of the Sun's open field structures. At present, it appears that the polar coronal holes are relatively weak, and there have been many equatorial coronal holes
Triadic resonances in non-linear simulations of a fluid flow in a precessing cylinder
Giesecke, A; Gundrum, T; Herault, J; Stefani, F
2015-01-01
We present results from three-dimensional non-linear hydrodynamic simulations of a precession driven flow in cylindrical geometry. The simulations are motivated by a dynamo experiment currently under development at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) in which the possibility of generating a magnetohydrodynamic dynamo will be investigated in a cylinder filled with liquid sodium and simultaneously rotating around two axes. In this study, we focus on the emergence of non-axisymmetric time-dependent flow structures in terms of inertial waves which - in cylindrical geometry - form so-called Kelvin modes. For a precession ratio ${\\rm{Po}}=\\Omega_p/\\Omega_c=0.014$ the amplitude of the forced Kelvin mode reaches up to one fourth of the rotation velocity of the cylindrical container confirming that precession provides a rather efficient flow driving mechanism even at moderate values of ${\\rm{Po}}$. More relevant for dynamo action might be free Kelvin modes with higher azimuthal wave number. These free Kelvin m...
Generating buoyant magnetic flux ropes in solar-like convective dynamos
Nelson, Nicholas J
2014-01-01
Our Sun exhibits strong convective dynamo action which results in magnetic flux bundles emerging through the stellar surface as magnetic spots. Global-scale dynamo action is believed to generate large-scale magnetic structures in the deep solar interior through the interplay of convection, rotation, and shear. Portions of these large-scale magnetic structures are then believed to rise through the convective layer, forming magnetic loops which then pierce the photosphere as sunspot pairs. Previous global simulations of 3D MHD convection in rotating spherical shells have demonstrated mechanisms whereby large-scale magnetic wreaths can be generated in the bulk of the convection zone. Our recent simulations have achieved sufficiently high levels of turbulence to permit portions of these wreaths to become magnetically buoyant and rise through the simulated convective layer through a combination of magnetic buoyancy and advection by convective giant cells. These buoyant magnetic loops are created in the bulk of the...
TIDALLY DRIVEN DYNAMOS IN A ROTATING SPHERE
Energy Technology Data Exchange (ETDEWEB)
Cébron, D.; Hollerbach, R., E-mail: david.cebron@ujf-grenoble.fr, E-mail: r.hollerbach@leeds.ac.uk [Institut für Geophysik, Sonneggstrasse 5, ETH Zürich, Zürich CH-8092 (Switzerland)
2014-07-01
Large-scale planetary or stellar magnetic fields generated by a dynamo effect are mostly attributed to flows forced by buoyancy forces in electrically conducting fluid layers. However, these large-scale fields may also be controlled by tides, as previously suggested for the star τ-boo, Mars, or the early Moon. By simulating a small local patch of a rotating fluid, Barker and Lithwick have recently shown that tides can drive small-scale dynamos by exciting a hydrodynamic instability, the so-called elliptical (or tidal) instability. By performing global magnetohydrodynamic simulations of a rotating spherical fluid body, we investigate if this instability can also drive the observed large-scale magnetic fields. We are thus interested in the dynamo threshold and the generated magnetic field in order to test if such a mechanism is relevant for planets and stars. Rather than solving the problem in a geometry deformed by tides, we consider a spherical fluid body and add a body force to mimic the tidal deformation in the bulk of the fluid. This allows us to use an efficient spectral code to solve the magnetohydrodynamic problem. We first compare the hydrodynamic results with theoretical asymptotic results and numerical results obtained in a truly deformed ellipsoid, which confirms the presence of elliptical instability. We then perform magnetohydrodynamic simulations and investigate the dynamo capability of the flow. Kinematic and self-consistent dynamos are finally simulated, showing that the elliptical instability is capable of generating a dipole-dominated large-scale magnetic field in global simulations of a fluid rotating sphere.
Convection-driven spherical shell dynamos at varying Prandtl numbers
Käpylä, P. J.; Käpylä, M. J.; Olspert, N.; Warnecke, J.; Brandenburg, A.
2017-02-01
Context. Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims: We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods: We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25 to 5, respectively). Differential rotation and large-scale magnetic fields are produced self-consistently. Results: We find that for high thermal diffusivity, the rotation profiles show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased, corresponding to an increase of the Prandtl number. This coincides with and results in a change of the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the clearly cyclic solutions disappear at the highest magnetic Reynolds numbers and give way to irregular sign changes or quasi-stationary states. The total (mean and fluctuating) magnetic energy increases as a function of the magnetic Reynolds number in the range studied here (5-151), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases, however, we find that two regimes are possible, where either differential rotation is strong and mean magnetic fields are relatively weak, or vice versa. Conclusions: Our simulations indicate a strong nonlinear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large
Saturation of Zeldovich Stretch-Twist-Fold Map Dynamos
Seta, Amit; Subramanian, Kandaswamy
2014-01-01
Zeldovich's stretch-twist fold (STF) dynamo provided a breakthrough in conceptual understanding of fast dynamos, including fluctuation or small scale dynamos. We study the evolution and saturation behaviour of two types of Baker's map dynamos, which have been used to model Zeldovich's STF dynamo process. Using such maps allows one to analyze dynamos at much higher magnetic Reynolds numbers $R_M$ as compared to direct numerical simulations. In the 2-strip map dynamo there is constant constructive folding while the 4-strip map dynamo also allows the possibility of field reversal. Incorporating a diffusive step parameterised by $R_M$, we find that the magnetic field $B(x)$ is amplified only above a critical $R_M=R_{crit} \\sim 4$ for both types of dynamos. We explore the saturation of these dynamos in 3 ways; by a renormalized decrease of the effective $R_M$ (Case I) or due to a decrease in the efficiency of field amplification by stretching (Case II), or a combination of both effects (Case III). For Case I, we s...
Final Technical Report for DOE DE-FG02-05ER54831 "Laboratory Studies of Dynamos."
Energy Technology Data Exchange (ETDEWEB)
Forest, Cary B. [Univ. of Wisconsin, Madison, WI (United States)
2014-11-06
Laboratory Studies of Dynamos: Executive Summary. The self-generation of magnetic fields by astrophysical bodies like planets, stars, accretion disks, galaxies, and even galaxy clusters arises due to a mechanism referred to as a homogeneous dynamo. It is quite simple to demonstrate the generation of a magnetic fi eld from a rotating copper disk coupled with a coil of wire, a device known as the homopolar dynamo. The device works like a magnetic fi eld ampli er with a feedback circuit: the differential rotation of a metal disk past an infinitesimally small seed magnetic field induces currents in the disk which, when coupled to a coil winding, can amplify the field until it becomes strong enough to slow the rotation of the disk. What is remarkable is that the same type of circuit may be achieved in a flowing conducting fluid such as a liquid metal in the case of planetary dynamos or a plasma in the case of astrophysical dynamos. The complexity of describing planetary and stellar dynamos despite their ubiquity and the plethora of observational data from the Earth and the Sun motivates the demonstration of a laboratory homogenous dynamo. To create a homogenous dynamo, one first needs a su fficiently large, fast flow of a highly conducting fluid that the velocity shear in the fluid can bend magnetic field lines. With a high Rm-flow, the magnetic fi eld can be ampli ed by the stretching action provided by di fferential rotation. The other critical ingredient is a flow geometry that provides feedback so that the ampli ed eld reinforces the initial in nitesimal seed field - a mechanism that recreates the feedback provided by the coil of wire in the homopolar dynamo. In the Madison Dynamo Experiment, this combination of magnetic ampli cation and feedback is feasible in the simple geometry of two counter-rotating helical vortices in a 1 meter-diameter spherical vessel lled with liquid sodium. For an optimal helical pitch of the flow the threshold for exciting a dynamo is
Cyclic Evolution of Coronal Fields from a Coupled Dynamo Potential-Field Source-Surface Model.
Dikpati, Mausumi; Suresh, Akshaya; Burkepile, Joan
The structure of the Sun's corona varies with the solar-cycle phase, from a near spherical symmetry at solar maximum to an axial dipole at solar minimum. It is widely accepted that the large-scale coronal structure is governed by magnetic fields that are most likely generated by dynamo action in the solar interior. In order to understand the variation in coronal structure, we couple a potential-field source-surface model with a cyclic dynamo model. In this coupled model, the magnetic field inside the convection zone is governed by the dynamo equation; these dynamo-generated fields are extended from the photosphere to the corona using a potential-field source-surface model. Assuming axisymmetry, we take linear combinations of associated Legendre polynomials that match the more complex coronal structures. Choosing images of the global corona from the Mauna Loa Solar Observatory at each Carrington rotation over half a cycle (1986 - 1991), we compute the coefficients of the associated Legendre polynomials up to degree eight and compare with observations. We show that at minimum the dipole term dominates, but it fades as the cycle progresses; higher-order multipolar terms begin to dominate. The amplitudes of these terms are not exactly the same for the two limbs, indicating that there is a longitude dependence. While both the 1986 and the 1996 minimum coronas were dipolar, the minimum in 2008 was unusual, since there was a substantial departure from a dipole. We investigate the physical cause of this departure by including a North-South asymmetry in the surface source of the magnetic fields in our flux-transport dynamo model, and find that this asymmetry could be one of the reasons for departure from the dipole in the 2008 minimum.
Magnetic material in mean-field dynamos driven by small scale helical flows
Giesecke, A.; Stefani, F.; Gerbeth, G.
2014-07-01
We perform kinematic simulations of dynamo action driven by a helical small scale flow of a conducting fluid in order to deduce mean-field properties of the combined induction action of small scale eddies. We examine two different flow patterns in the style of the G O Roberts flow but with a mean vertical component and with internal fixtures that are modelled by regions with vanishing flow. These fixtures represent either rods that lie in the center of individual eddies, or internal dividing walls that provide a separation of the eddies from each other. The fixtures can be made of magnetic material with a relative permeability larger than one which can alter the dynamo behavior. The investigations are motivated by the widely unknown induction effects of the forced helical flow that is used in the core of liquid sodium cooled fast reactors, and from the key role of soft iron impellers in the von-Kármán-sodium dynamo. For both examined flow configurations the consideration of magnetic material within the fluid flow causes a reduction of the critical magnetic Reynolds number of up to 25%. The development of the growth-rate in the limit of the largest achievable permeabilities suggests no further significant reduction for even larger values of the permeability. In order to study the dynamo behavior of systems that consist of tens of thousands of helical cells we resort to the mean-field dynamo theory (Krause and Rädler 1980 Mean-field Magnetohydrodynamics and Dynamo Theory (Oxford: Pergamon)) in which the action of the small scale flow is parameterized in terms of an α- and β-effect. We compute the relevant elements of the α- and the β-tensor using the so called testfield method. We find a reasonable agreement between the fully resolved models and the corresponding mean-field models for wall or rod materials in the considered range 1\\leqslant {{\\mu }_{r}}\\leqslant 20. Our results may be used for the development of global large scale models with recirculation
The New Mexico alpha-omega Dynamo Experiment Modeling Astrophysical Dynamos
Colgate, S A; Beckley, H F; Ferrel, R; Romero, V D; Weatherall, J C
2001-01-01
A magnetic dynamo experiment is under construction at the New Mexico Institute of Mining and Technology. The experiment is designed to demonstrate in the laboratory the alpha-omega magnetic dynamo, which is believed to operate in many rotating and conducting astrophysical objects. The experiment uses the Couette flow of liquid sodium between two cylinders rotating with different angular velocities to model the omega-effect. The alpha-effect is created by the rising and expanding jets of liquid sodium driven through a pair of orifices in the end plates of the cylindrical vessel, presumably simulating plumes driven by buoyancy in astrophysical objects. The water analog of the dynamo device has been constructed and the flow necessary for the dynamo has been demonstrated. Results of the numerical simulations of the kinematic dynamo are presented. The toroidal field produced by the omega-effect is predicted to be B_{\\phi} \\simeq (R_m/2\\pi) B_{poloidal}\\simeq 20 \\times B_{poloidal} for the expected magnetic Reynold...
Dynamos and anti-dynamos as thin magnetic flux ropes in Riemannian spaces
de Andrade, L Garcia
2007-01-01
Two examples of magnetic anti-dynamos in magnetohydrodynamics (MHD) are given. The first is a 3D metric conformally related to Arnold cat fast dynamo metric: ${ds_{A}}^{2}=e^{-{\\lambda}z}dp^{2}+e^{{\\lambda}z}dq^{2}+dz^{2}$ is shown to present a behaviour of non-dynamos where the magnetic field exponentially decay in time. The curvature decay as z-coordinates increases without bounds. Some of the Riemann curvature components such as $R_{pzpz}$ also undergoes dissipation while component $R_{qzqz}$ increases without bounds. The remaining curvature component $R_{pqpq}$ is constant on the torus surface. The other anti-dynamo which may be useful in plasma astrophysics is the thin magnetic flux rope or twisted magnetic thin flux tube which also behaves as anti-dynamo since it also decays with time. This model is based on the Riemannian metric of the magnetic twisted flux tube where the axis possesses Frenet curvature and torsion. Since in this last example the Frenet torsion of the axis of the rope is almost zero, o...
Mean-field model of the von Kármán sodium dynamo experiment using soft iron impellers.
Nore, C; Léorat, J; Guermond, J-L; Giesecke, A
2015-01-01
It has been observed that dynamo action occurs in the von-Kármán-Sodium (VKS) experiment only when the rotating disks and the blades are made of soft iron. The purpose of this paper is to numerically investigate the role of soft iron in the VKS dynamo scenario. This is done by using a mean-field model based on an axisymmetric mean flow, a localized permeability distribution, and a localized α effect modeling the action of the small velocity scales between the blades. The action of the rotating blades is modeled by an axisymmetric effective permeability field. Key properties of the flow giving to the numerical magnetic field a geometric structure similar to that observed experimentally are identified. Depending on the permeability of the disks and the effective permeability of the blades, the dynamo that is obtained is either oscillatory or stationary. Our numerical results confirm the leading role played by the ferromagnetic impellers. A scenario for the VKS dynamo is proposed.
History and results of the Riga dynamo experiments
Gailitis, Agris; Gundrum, Thomas; Lielausis, Olgerts; Platacis, Ernests; Stefani, Frank
2008-01-01
On 11 November 1999, a self-exciting magnetic eigenfield was detected for the first time in the Riga liquid sodium dynamo experiment. We report on the long history leading to this event, and on the subsequent experimental campaigns which provided a wealth of data on the kinematic and the saturated regime of this dynamo. The present state of the theoretical understanding of both regimes is delineated, and some comparisons with other laboratory dynamo experiments are made.
Predictability and Coupled Dynamics of MJO During DYNAMO
2015-02-03
3. DATES COVERED (From - To) Jan 2013-Dec 2014 4. TITLE AND SUBTITLE Predictability and Coupled Dynamics of MJO During DYNAMO 5a. CONTRACT...release: distribution is unlimited. Predictability and Coupled Dynamics of MJO During DYNAMO Hyodae Seo Woods Hole Oceanographic Institution Woods...scientific goals of the proposed research are: 1. Examine the process by which the SST variability affects the MJO during the DYNAMO using a SCOAR2 regional
Extracting scaling laws from numerical dynamo models
Stelzer, Z
2013-01-01
Earth's magnetic field is generated by processes in the electrically conducting, liquid outer core, subsumed under the term `geodynamo'. In the last decades, great effort has been put into the numerical simulation of core dynamics following from the magnetohydrodynamic (MHD) equations. However, the numerical simulations are far from Earth's core in terms of several control parameters. Different scaling analyses found simple scaling laws for quantities like heat transport, flow velocity, magnetic field strength and magnetic dissipation time. We use an extensive dataset of 116 numerical dynamo models compiled by Christensen and co-workers to analyse these scalings from a rigorous model selection point of view. Our method of choice is leave-one-out cross-validation which rates models according to their predictive abilities. In contrast to earlier results, we find that diffusive processes are not negligible for the flow velocity and magnetic field strength in the numerical dynamos. Also the scaling of the magneti...
Dynamo theory prediction of solar activity
Schatten, Kenneth H.
1988-01-01
The dynamo theory technique to predict decadal time scale solar activity variations is introduced. The technique was developed following puzzling correlations involved with geomagnetic precursors of solar activity. Based upon this, a dynamo theory method was developed to predict solar activity. The method was used successfully in solar cycle 21 by Schatten, Scherrer, Svalgaard, and Wilcox, after testing with 8 prior solar cycles. Schatten and Sofia used the technique to predict an exceptionally large cycle, peaking early (in 1990) with a sunspot value near 170, likely the second largest on record. Sunspot numbers are increasing, suggesting that: (1) a large cycle is developing, and (2) that the cycle may even surpass the largest cycle (19). A Sporer Butterfly method shows that the cycle can now be expected to peak in the latter half of 1989, consistent with an amplitude comparable to the value predicted near the last solar minimum.
Differential Rotation in Solar Convective Dynamo Simulations
Fan, Yuhong
2015-01-01
We carry out a magneto-hydrodynamic (MHD) simulation of convective dynamo in the rotating solar convective envelope driven by the solar radiative diffusive heat flux. The simulation is similar to that reported in Fan & Fang (2014) but with further reduced viscosity and magnetic diffusion. The resulting convective dynamo produces a large scale mean field that exhibits similar irregular cyclic behavior and polarity reversals, and self-consistently maintains a solar-like differential rotation. The main driver for the solar-like differential rotation (with faster rotating equator) is a net outward transport of angular momentum away from the rotation axis by the Reynolds stress, and we found that this transport is enhanced with reduced viscosity and magnetic diffusion.
SADE: The starspot and dynamo explorer
Martens, P. C. H.; Acton, L. W. A.; Klumpar, D.; Kankelborg, C.; Stern, R. A.; Peres, G.; Culhane, J. L.
2003-09-01
We propose a mission called SADE, the Starspot And Dynamo Explorer, to study dynamo activity in nearby late-type stars. The onboard instruments will be a Ca-K telescope for magnetically dominated chromospheric emission, and an X-ray grazing incidence telescope to study coronal emission. We design the mission for a life-time of 15 years or longer to capture a full activity cycle for most solar-type stars. We aim to firmly establish the spectrum of the relation between chromospheric and corona' emission in late-type stars, and capture one or more stars going into or coming out of a Maunder type minimum. Operation costs will be kept to a minimum by automating mission operations to a maximum, and have the science operations be carried out by students at Montana State University.
An ancient core dynamo in asteroid Vesta.
Fu, Roger R; Weiss, Benjamin P; Shuster, David L; Gattacceca, Jérôme; Grove, Timothy L; Suavet, Clément; Lima, Eduardo A; Li, Luyao; Kuan, Aaron T
2012-10-12
The asteroid Vesta is the smallest known planetary body that has experienced large-scale igneous differentiation. However, it has been previously uncertain whether Vesta and similarly sized planetesimals formed advecting metallic cores and dynamo magnetic fields. Here we show that remanent magnetization in the eucrite meteorite Allan Hills A81001 formed during cooling on Vesta 3.69 billion years ago in a surface magnetic field of at least 2 microteslas. This field most likely originated from crustal remanence produced by an earlier dynamo, suggesting that Vesta formed an advecting liquid metallic core. Furthermore, the inferred present-day crustal fields can account for the lack of solar wind ion-generated space weathering effects on Vesta.
Helioseismic Data Assimilation in Solar Dynamo Models
Muñoz-Jaramillo, Andrés; Martens, Petrus C H
2008-01-01
An essential ingredient in kinematic dynamo models is the velocity field within the solar convection zone. In particular, the differential rotation is now well constrained by helioseismic observations. Helioseismology also gives us information about the depth-dependence of the meridional circulation in the near-surface layers. The typical velocity inputs used in solar dynamo models, however, continue to be an analytic fit to the observed differential rotation and a theoretically constructed meridional flow profile that matches only the peak flow speed at the surface. Here we take the first steps towards realistic helioseismic data assimilation, by presenting methodologies for constructing differential rotation and meridional circulation profiles that more closely conform to the observational constraints currently available. We also present simulations driven by the assimilated rotation and four plausible profiles for the internal meridional circulation -- all of which match the helioseismically inferred near-...
Differential rotation in solar convective dynamo simulations
Fan, Yuhong; Fang, Fang
2016-10-01
We carry out a magneto-hydrodynamic (MHD) simulation of convective dynamo in the rotating solar convective envelope driven by the solar radiative diffusive heat flux. The simulation is similar to that reported in Fan and Fang (2014) but with further reduced viscosity and magnetic diffusion. The resulting convective dynamo produces a large scale mean field that exhibits similar irregular cyclic behavior and polarity reversals, and self-consistently maintains a solar-like differential rotation. The main driver for the solar-like differential rotation (with faster rotating equator) is a net outward transport of angular momentum away from the rotation axis by the Reynolds stress, and we found that this transport is enhanced with reduced viscosity and magnetic diffusion.
Predictive Scaling Laws for Spherical Rotating Dynamos
Oruba, Ludivine
2013-01-01
State of the art numerical models of the Geodynamo are still performed in a parameter regime extremely remote from the values relevant to the physics of the Earth's core. In order to establish a connection between dynamo modeling and the geophysical motivation, scaling laws have been proposed. Such scaling laws establish the dependence of essential quantities (such as the magnetic field strength) on measured or controlled quantities. They allow for a direct confrontation of advanced models with geophysical observations.(...)
Does the butterfly diagram indicate asolar flux-transport dynamo?
Schüssler, M
2004-01-01
We address the question whether the properties of the observed latitude-time diagram of sunspot occurence (the butterfly diagram) provide evidence for the operation of a flux-transport dynamo, which explains the migration of the sunspot zones and the period of the solar cycle in terms of a deep equatorward meridional flow. We show that the properties of the butterfly diagram are equally well reproduced by a conventional dynamo model with migrating dynamo waves, but without transport of magnetic flux by a flow. These properties seem to be generic for an oscillatory and migratory field of dipole parity and thus do not permit an observational distinction between different dynamo approaches.
Resonance in Forced Flux Transport Dynamos
Gilman, Peter A
2011-01-01
We show that simple 2 and 3-layer flux-transport dynamos, when forced at the top by a poloidal source term, can produce a widely varying amplitude of toroidal field at the bottom, depending on how close the meridional flow speed of the bottom layer is to the propagation speed of the forcing applied above the top layer, and how close the amplitude of the $\\alpha$-effect is to two values that give rise to a resonant response. This effect should be present in this class of dynamo model no matter how many layers are included. This result could have implications for the prediction of future solar cycles from the surface magnetic fields of prior cycles. It could be looked for in flux-transport dynamos that are more realistic for the Sun, done in spherical geometry with differential rotation, meridional flow and $\\alpha$-effect that vary with latitude and time as well as radius. Because of these variations, if resonance occurs, it should be more localized in time, latitude and radius.
Kinematic dynamo, supersymmetry breaking, and chaos
Ovchinnikov, Igor V.; Enßlin, Torsten A.
2016-04-01
The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry, and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the nondiffusive cases, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both real and complex ground state eigenvalues. Finally, we comment on the nonexistence of dynamos for scalar quantities.
The Alpha Dynamo Effects in Laboratory Plasmas
Energy Technology Data Exchange (ETDEWEB)
Hantao Ji; Stewart C. Prager
2001-10-16
A concise review of observations of the alpha dynamo effect in laboratory plasmas is given. Unlike many astrophysical systems, the laboratory pinch plasmas are driven magnetically. When the system is overdriven, the resultant instabilities cause magnetic and flow fields to fluctuate, and their correlation induces electromotive forces along the mean magnetic field. This alpha-effect drives mean parallel electric current, which, in turn, modifies the initial background mean magnetic structure towards the stable regime. This drive-and-relax cycle, or the so-called self-organization process, happens in magnetized plasmas in a timescale much shorter than resistive diffusion time, thus it is a fast and unquenched dynamo process. The observed alpha-effect redistributes magnetic helicity (a measure of twistedness and knottedness of magnetic field lines) but conserves its total value. It can be shown that fast and unquenched dynamos are natural consequences of a driven system where fluctuations are statistically either not stationary in time or not homogeneous in space, or both. Implications to astrophysical phenomena will be discussed.
Magnetic material in mean-field dynamos driven by small scale helical flows
Giesecke, Andre; Gerbeth, Gunter
2014-01-01
We perform kinematic simulations of dynamo action driven by a helical small scale flow of a conducting fluid in order to deduce mean-field properties of the combined induction action of small scale eddies. We examine two different flow patterns in the style of the G.O. Roberts flow but with a mean vertical component and with internal fixtures that are modelled by regions with vanishing flow. These fixtures represent either rods that lie in the center of individual eddies, or internal dividing walls that provide a separation of the eddies from each other. The fixtures can be made of magnetic material with a relative permeability larger than one which can alter the dynamo behavior. The investigations are motivated by the widely unknown induction effects of the forced helical flow that is used in the core of liquid sodium cooled fast reactors, and from the key role of soft iron impellers in the von-K\\'arm\\'an-Sodium (VKS) dynamo. For both examined flow configurations the consideration of magnetic material within...
Effect of soft-iron impellers on the von Kármán-sodium dynamo.
Xu, Mingtian
2014-01-01
The explanation for the observed axisymmetric magnetic field in the von Kármán-sodium (VKS) dynamo experiment is still an unresolved question. In this paper, the integral equation approach is extended to investigate the VKS dynamo action by taking into account the discontinuity of the magnetic permeability and electrical conductivity in the conducting region. When the relative magnetic permeability of the soft-iron impellers is set to 65, a steady toroidal field that is apparently axisymmetric is excited at the critical magnetic Reynolds number, Rmc≈27.23, which is close to the experimental result, Rmc≈30. Our results show that the critical magnetic Reynolds number declines as the relative magnetic permeability of the impellers increases. Furthermore, when the relative magnetic permeability is not greater than 37, an equatorial magnetic field with an azimuthal wave number m=1 is the dominant mode, otherwise a steady toroidal field with an azimuthal wave number m=0 predominates the magnetic field generated by the VKS dynamo action.
Large-scale dynamo of accretion disks around supermassive nonrotating black holes
Directory of Open Access Journals (Sweden)
Poplavsky A.L.
2006-01-01
Full Text Available In this paper one presents an analytical model of accretion disk magnetosphere dynamics around supermassive nonrotating black holes in the centers of active galactic nuclei. Based on general relativistic equations of magneto hydrodynamics, the nonstationary solutions for time-dependent dynamo action in the accretion disks, spatial and temporal distribution of magnetic field are found. It is shown that there are two distinct stages of dynamo process: the transient and the steady-state regimes, the induction of magnetic field at t > 6:6665 x 1011GM/c3 s becomes stationary, magnetic field is located near the innermost stable circular orbit, and its value rises up to ~ 105 G. Applications of such systems with nonrotating black holes in real active galactic nuclei are discussed.
Geodesic dynamo chaotic flows and non-Anosov maps in twisted magnetic flux tubes
de Andrade, Garcia
2008-01-01
Recently Tang and Boozer [{\\textbf{Phys. Plasmas (2000)}}], have investigated the anisotropies in magnetic field dynamo evolution, from local Lyapunov exponents, giving rise to a metric tensor, in the Alfven twist in magnetic flux tubes (MFTs). Thiffeault and Boozer [\\textbf{Chaos}(2001)] have investigated the how the vanishing of Riemann curvature constrained the Lyapunov exponential stretching of chaotic flows. In this paper, Tang-Boozer-Thiffeault differential geometric framework is used to investigate effects of twisted magnetic flux tube filled with helical chaotic flows on the Riemann curvature tensor. When Frenet torsion is positive, the Riemann curvature is unstable, while the negative torsion induces an stability when time $t\\to{\\infty}$. This enhances the dynamo action inside the MFTs. The Riemann metric, depends on the radial random flows along the poloidal and toroidal directions. The Anosov flows has been applied by Arnold, Zeldovich, Ruzmaikin and Sokoloff [\\textbf{JETP (1982)}] to build a unifo...
Shear dynamo, turbulence, and the magnetorotational instability
Squire, Jonathan
The formation, evolution, and detailed structure of accretion disks remain poorly understood, with wide implications across a variety of astrophysical disciplines. While the most pressing question --- what causes the high angular momentum fluxes that are necessary to explain observations? --- is nicely answered by the idea that the disk is turbulent, a more complete grasp of the fundamental processes is necessary to capture the wide variety of behaviors observed in the night sky. This thesis studies the turbulence in ionized accretion disks from a theoretical standpoint, in particular focusing on the generation of magnetic fields in these processes, known as dynamo. Such fields are expected to be enormously important, both by enabling the magnetorotational instability (which evolves into virulent turbulence), and through large-scale structure formation, which may transport angular momentum in different ways and be fundamental for the formation of jets. The central result of this thesis is the suggestion of a new large-scale dynamo mechanism in shear flows --- the "magnetic shear-current effect" --- which relies on a positive feedback from small-scale magnetic fields. As well as being a very promising candidate for driving field generation in the central regions of accretion disks, this effect is interesting because small-scale magnetic fields have historically been considered to have a negative effect on the large-scale dynamo, damping growth and leading to dire predictions for final saturation amplitudes. Given that small-scale fields are ubiquitous in plasma turbulence above moderate Reynolds numbers, the finding that they could instead have a positive effect in some situations is interesting from a theoretical and practical standpoint. The effect is studied using direct numerical simulation, analytic techniques, and novel statistical simulation methods. In addition to the dynamo, much attention is given to the linear physics of disks and its relevance to
无对流区天体中的发电机效应%DYNAMO EFFECT IN NO CONVECTION REGIONS OF THE CELESTIAL BODIES
Institute of Scientific and Technical Information of China (English)
景海荣; 童彝; 张永安
2000-01-01
Based on plasma turbulent wave dynamo equation (p-ω dynamo equation) and using spherical polar coordinates, a set of scalar dynamo equation is obtained. Considered various rotational situations, different analytical solutions are derived. No matter the rotation angular velocity is uniform or not, the convection is absence or presence, the p-ω dynamo is operative. The existence of differential rotation will enhance the action of p-ω dynamo. This dynamo may explain the observed magnetic field of CP stars.%根据等离子体湍动波发电机方程(p-ω发电机方程),应用球坐标系统,得到了一组标量发电机方程.考虑各种不同的旋转情况,得到了不同的分析解.不论旋转角速度是否均匀,对流是否存在,p-ω发电机总能产生作用.较差自转的存在将增强发电机的作用.运用这种发电机模型能够解释所观测的无对流天体的磁场.
A simple stochastic model for dipole moment fluctuations in numerical dynamo simulations
Meduri, Domenico G.; Wicht, Johannes
2016-04-01
Earth's axial dipole field changes in a complex fashion on many different time scales ranging from less than a year to tens of million years. Documenting, analysing, and replicating this intricate signal is a challenge for data acquisition, theoretical interpretation, and dynamo modelling alike. Here we explore whether axial dipole variations can be described by the superposition of a slow deterministic drift and fast stochastic fluctuations, i.e. by a Langevin-type system. The drift term describes the time averaged behaviour of the axial dipole variations, whereas the stochastic part mimics complex flow interactions over convective time scales. The statistical behaviour of the system is described by a Fokker-Planck equation which allows useful predictions, including the average rates of dipole reversals and excursions. We analyse several numerical dynamo simulations, most of which have been integrated particularly long in time, and also the palaeomagnetic model PADM2M which covers the past 2 Myr. The results show that the Langevin description provides a viable statistical model of the axial dipole variations on time scales longer than about 1 kyr. For example, the axial dipole probability distribution and the average reversal rate are successfully predicted. The exception is PADM2M where the stochastic model reversal rate seems too low. The dependence of the drift on the axial dipole moment reveals the nonlinear interactions that establish the dynamo balance. A separate analysis of inductive and diffusive magnetic effects in three dynamo simulations suggests that the classical quadratic quenching of induction predicted by mean-field theory seems at work.
Polar spots and stellar spindown: Is dynamo saturation needed?
Solanki, S. K.; Motamen, S.; Keppens, R.
1997-01-01
Dynamo saturation is often invoked when calculating the rotational evolution of cool stars. At rapid rotation rates a saturated dynamo reduces the angular momentum carried away by the stellar wind. This, in turn, may explain the high rotation rates present in the distribution of rotation periods in
Polar spots and stellar spindown: is dynamo saturation needed?
Solanki, S. K.; Motamen, S.; Keppens, R.
1997-01-01
Dynamo saturation is often invoked when calculating the rotational evolution of cool stars. At rapid rotation rates a saturated dynamo reduces the angular momentum carried away by the stellar wind. This, in turn, may explain the high rotation rates present in the distribution of rotation periods in
Helioseismic Constraints and Paradigm Shift in Solar Dynamo
Kosovichev, Alexander G; Zhao, Junwei
2014-01-01
Helioseismology provides important constraints for the solar dynamo problem. However, the basic properties and even the depth of the dynamo process, which operates also in other stars, are unknown. Most of the dynamo models suggest that the toroidal magnetic field that emerges on the surface and forms sunspots is generated near the bottom of the convection zone, in the tachocline. However, there is a number of theoretical and observational problems with justifying the deep-seated dynamo models. This leads to the idea that the subsurface angular velocity shear may play an important role in the solar dynamo. Using helioseismology measurements of the internal rotation and meridional circulation, we investigate a mean-field MHD model of dynamo distributed in the bulk of the convection zone but shaped in a near-surface layer. We show that if the boundary conditions at the top of the dynamo region allow the large-scale toroidal magnetic fields to penetrate into the surface, then the dynamo wave propagates along the...
Polar spots and stellar spindown: Is dynamo saturation needed?
Solanki, S. K.; Motamen, S.; Keppens, R.
1997-01-01
Dynamo saturation is often invoked when calculating the rotational evolution of cool stars. At rapid rotation rates a saturated dynamo reduces the angular momentum carried away by the stellar wind. This, in turn, may explain the high rotation rates present in the distribution of rotation periods in
Polar spots and stellar spindown: is dynamo saturation needed?
Solanki, S. K.; Motamen, S.; Keppens, R.
1997-01-01
Dynamo saturation is often invoked when calculating the rotational evolution of cool stars. At rapid rotation rates a saturated dynamo reduces the angular momentum carried away by the stellar wind. This, in turn, may explain the high rotation rates present in the distribution of rotation periods in
Efficiency Measurement Using a Motor-Dynamo Module
Ng, Pun-hon; Wong, Siu-ling; Mak, Se-yuen
2009-01-01
In this article, we describe a simple method which can be used to measure the efficiency of a low power dc motor, a motor-converted dynamo and a coupled motor-dynamo module as a function of the speed of rotation. The result can also be used to verify Faraday's law of electromagnetic induction. (Contains 1 table and 8 figures.)
A two-layer $\\alpha\\omega$ dynamo model, and its implications for 1-D dynamos
Roald, C B
1999-01-01
I will discuss an attempt at representing an interface dynamo in a simplified, essentially 1D framework. The operation of the dynamo is broken up into two 1D layers, one containing the $\\alpha$ effect and the other containing the $\\omega$ effect, and these two layers are allowed to communicate with each other by the simplest possible representation of diffusion, an analogue of Newton's law of cooling. Dynamical back-reaction of the magnetic field on them with diagrams I computed for a comparable purely 1D model. The bifurcation structure shows remarkable similarity, but a couple of subtle changes imply dramatically different physical behaviour for the model. In particular, the solar-like dynamo mode found in the 1-layer model is not stable in the 2-layer version; instead there is an (apparent) homoclinic bifurcation and a sequence of periodic, quasiperiodic, and chaotic modes. I argue that the fragility of these models makes them effectively useless as predictors or interpreters of more complex dynamos.
Indian Academy of Sciences (India)
R K Khanna; R C Chouhan
2003-10-01
A somewhat more general analysis for solving spatial propagation characteristics of intense Gaussian beam is presented and applied to the laser beam propagation in step-index proﬁle as well as parabolic proﬁle dielectric ﬁbers with Kerr non-linearity. Considering self-action due to saturating and non-saturating non-linearity in the refractive index, a general theory has been developed without any kind of power series expansion for the dielectric constant as is usually done in other theories that make use of paraxial approximation. Result of the steady state self-focusing analysis indicates that the Kerr non-linearity acts as a perturbation on the radial inhomogeneity due to ﬁber geometry. Analysis indicates that the paraxial rays and peripheral rays focus at different points, indicating aberration effect. Calculated critical power matches with the experimentally reported result.
Persistence and origin of the lunar core dynamo.
Suavet, Clément; Weiss, Benjamin P; Cassata, William S; Shuster, David L; Gattacceca, Jérôme; Chan, Lindsey; Garrick-Bethell, Ian; Head, James W; Grove, Timothy L; Fuller, Michael D
2013-05-21
The lifetime of the ancient lunar core dynamo has implications for its power source and the mechanism of field generation. Here, we report analyses of two 3.56-Gy-old mare basalts demonstrating that they were magnetized in a stable and surprisingly intense dynamo magnetic field of at least ~13 μT. These data extend the known lifetime of the lunar dynamo by ~160 My and indicate that the field was likely continuously active until well after the final large basin-forming impact. This likely excludes impact-driven changes in rotation rate as the source of the dynamo at this time in lunar history. Rather, our results require a persistent power source like precession of the lunar mantle or a compositional convection dynamo.
Analytic solution of an oscillatory migratory alpha^2 stellar dynamo
Brandenburg, Axel
2016-01-01
Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for uniform helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant alpha. We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant alpha, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two ends. We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory dynamos are possible for dynamos with...
Could Giant Basin-Forming Impacts Have Killed Martian Dynamo?
Kuang, W.; Jiang, W.; Roberts, J.; Frey, H. V.
2014-01-01
The observed strong remanent crustal magnetization at the surface of Mars suggests an active dynamo in the past and ceased to exist around early to middle Noachian era, estimated by examining remagnetization strengths in extant and buried impact basins. We investigate whether the Martian dynamo could have been killed by these large basin-forming impacts, via numerical simulation of subcritical dynamos with impact-induced thermal heterogeneity across the core-mantle boundary. We find that subcritical dynamos are prone to the impacts centered on locations within 30 deg of the equator but can easily survive those at higher latitudes. Our results further suggest that magnetic timing places a strong constraint on postimpact polar reorientation, e.g., a minimum 16 deg polar reorientation is needed if Utopia is the dynamo killer.
On the connections between solar and stellar dynamo models
Jouve, Laurène; Kumar, Rohit
2017-10-01
We here discuss the various dynamo models which have been designed to explain the generation and evolution of large-scale magnetic fields in stars. We focus on the models that have been applied to the Sun and can be tested for other solar-type stars now that modern observational techniques provide us with detailed stellar magnetic field observations. Mean-field flux-transport dynamo models have been developed for decades to explain the solar cycle and applications to more rapidly-rotating stars are discussed. Tremendous recent progress has been made on 3D global convective dynamo models. They do not however for now produce regular flux emergence that could be responsible for surface active regions and questions about the role of these active regions in the dynamo mechanism are still difficult to address with such models. We finally discuss 3D kinematic dynamo models which could constitute a promising combined approach, in which data assimilation could be applied.
Rieder, Michael; Teyssier, Romain
2016-04-01
The origin and evolution of magnetic fields in the Universe is still an open question. Their observations in galaxies suggest strong magnetic fields already at high redshift as well as at present time. However, neither primordial magnetic fields nor battery processes can account for such high field strengths, which implies the presence of a dynamo process with rapid growth rates in high-redshift galaxies and subsequent maintenance against decay. We investigate the particular role played by feedback mechanisms in creating strong fluid turbulence, allowing for a magnetic dynamo to emerge. Performing magnetohydrodynamic simulations of isolated cooling gas haloes, we compare the magnetic field evolution for various initial field topologies and various stellar feedback mechanisms. We find that feedback can indeed drive strong gas turbulence and dynamo action. We see typical properties of Kolmogorov turbulence with a k-5/3 kinetic energy spectrum, as well as a small-scale dynamo, with a k3/2 magnetic energy spectrum predicted by Kazantsev dynamo theory. We also investigate simulations with a final quiescent phase. As turbulence decreases, the galactic fountain settles into a thin, rotationally supported disc. The magnetic field develops a large-scale well-ordered structure with even symmetry, which is in good agreement with magnetic field observations of nearby spirals. Our findings suggest that weak initial seed fields were first amplified by a small-scale dynamo during a violent feedback-dominated early phase in the galaxy formation history, followed by a more quiescent evolution, where the fields have slowly decayed or were maintained via large-scale dynamo action.
Solar Cycle 24 and the Solar Dynamo
Pesnell, W. D.; Schatten, K.
2007-01-01
We will discuss the polar field precursor method for solar activity prediction, which predicts cycle 24 will be significantly lower than recent activity cycles, and some new ideas rejuvenating Babcock's shallow surface dynamo. The polar field precursor method is based on Babcock and Leighton's dynamo models wherein the polar field at solar minimum plays a major role in generating the next cycle's toroidal field and sunspots. Thus, by examining the polar fields of the Sun near solar minimum, a forecast for the next cycle's activity is obtained. With the current low value for the Sun's polar fields, this method predicts solar cycle 24 will be one of the lowest in recent times, with smoothed F10.7 radio flux values peaking near 135 plus or minus 35 (2 sigma), in the 2012-2013 timeframe (equivalent to smoothed Rz near 80 plus or minus 35 [2 sigma]). One may have to consider solar activity as far back as the early 20th century to find a cycle of comparable magnitude. We discuss unusual behavior in the Sun's polar fields that support this prediction. Normally, the solar precursor method is consistent with the geomagnetic precursor method, wherein geomagnetic variations are thought to be a good measure of the Sun's polar field strength. Because of the unusual polar field, the Earth does not appear to be currently bathed in the Sun's extended polar field (the interplanetary field), hence negating the primal cause behind the geomagnetic precursor technique. We also discuss how percolation may support Babcock's original shallow solar dynamo. In this process ephemeral regions from the solar magnetic carpet, guided by shallow surface fields, may collect to form pores and sunspots.
Overview of the Madison Dynamo Experiment
Taylor, Nicholas Z.; Forest, C. B.; Kaplan, E. J.; Kendrick, R. D.; Nornberg, M. D.; Spence, E. J.
2010-05-01
The observation of the dynamo effect in a simply connected turbulent system has yet to be observed in the laboratory without the use of highly ferromagnetic materials. In the Madison Dynamo Experiment, two counter-rotating impellers drive a turbulent flow of liquid sodium in a one meter-diameter sphere. Two main results have been discovered so far: first, no sustained self-excited field was seen, but intermittent bursts of a transverse dipole field similar to the induced field predicted by laminar kinematics were observed. Second, a weak, DC external seed field, sharing the symmetry axis of the mean flow, was applied to the flowing sodium. Data modeling showed that the currents measured in the sodium could not be explained from the mean flow alone. However, the overall trend was consistent with an enhanced resistivity (a beta effect). These experiments have demonstrated the need for a turbulent electromotive force to describe the dynamics of the magnetic field evolution. This poster will present efforts to optimize the flow in order to observe spontaneous magnetic field generation as well as methods to characterize the turbulent EMF. The addition of an equatorial and poloidal baffles to the experiment will help in the reduction of large-scale turbulence and optimization of the helicity of the mean flow. A high current H-bridge signal generator has been constructed to apply 500 Gauss, sinusoidal fields with frequencies up to 10 Hz. The profile of the response will be measured by an internal array of 3D hall probes. This profile should provide an indication of the turbulent enhancement to resistivity. The strengthened externally applied field will also be used to explore a sub-critical dynamo transition that has recently been discovered in numerical simulations.
Magnetic reversals from planetary dynamo waves
DEFF Research Database (Denmark)
Sheyko, Andrey; Finlay, Chris; Jackson, Andrew
2016-01-01
place in Earth's core, but the precise mechanism is debated. The majority of numerical geodynamo simulations that exhibit reversals operate in a regime in which the viscosity of the fluid remains important, and in which the dynamo mechanism primarily involves stretching and twisting of field lines...... by columnar convection. Here we present an example of another class of reversing-geodynamo model, which operates in a regime of comparatively low viscosity and high magnetic diffusivity. This class does not fit into the paradigm of reversal regimes that are dictated by the value of the local Rossby number...
The dynamo bifurcation in rotating spherical shells
Morin, Vincent; 10.1142/S021797920906378X
2010-01-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.
Objective vortex detection in an astrophysical dynamo
Rempel, E. L.; Chian, A. C.-L.; Beron-Vera, F. J.; Szanyi, S.; Haller, G.
2017-03-01
A novel technique for detecting Lagrangian vortices is applied to a helical magnetohydrodynamic dynamo simulation. The vortices are given by tubular level surfaces of the Lagrangian averaged vorticity deviation, the trajectory integral of the normed difference of the vorticity from its spatial mean. This simple method is objective, i.e. invariant under time-dependent rotations and translations of the coordinate frame. We also adapt the technique to use it on magnetic fields and propose the method of integrated averaged current deviation to determine precisely the boundary of magnetic vortices. The relevance of the results for the study of vortices in solar plasmas is discussed.
Cosmic dynamo analogue and decay of magnetic fields in 3D Ricci flows
de Andrade, Garcia
2009-01-01
Magnetic curvature effects, investigated by Barrow and Tsagas (BT) [Phys Rev D \\textbf{77},(2008)],as a mechanism for magnetic field decay in open Friedmann universes (${\\Lambda}<0$), are applied to dynamo geometric Ricci flows in 3D curved substrate in laboratory. By simple derivation, a covariant three-dimensional magnetic self-induced equation, presence of these curvature effects, indicates that de Sitter cosmological constant (${\\Lambda}\\ge{0}$), leads to enhancement in the fast kinematic dynamo action which adds to stretching of plasma flows. From the magnetic growth rate, the strong shear case, anti-de Sitter case (${\\Lambda}<0$) BT magnetic decaying fields are possible while for weak shear, fast dynamos are possible. The self-induced equation in Ricci flows is similar to the equation derived by BT in $(3+1)$-spacetime continuum. Lyapunov-de Sitter metric is obtained from Ricci flow eigenvalue problem. In de Sitter analogue there is a decay rate of ${\\gamma}\\approx{-{\\Lambda}}\\approx{-10^{-35}s^{-...
Grand Minima and Equatorward Propagation in a Cycling Stellar Convective Dynamo
Augustson, Kyle; Miesch, Mark; Toomre, Juri
2014-01-01
The dynamo action achieved in a global-scale stellar convection simulation is assessed for a Sun-like star rotating at three times the solar rate. The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH) code, using slope-limited diffusion, is employed to capture convective and dynamo processes. The simulation is carried out in a spherical shell that encompasses 3.8 density scale heights of the solar convection zone. The dynamo generated magnetic fields possess a high degree of time variation, with many periodic polarity reversals occurring every 6.2~years. These magnetic energy cycles arise from a Lorentz-force feedback on the differential rotation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. Yet helical convection acting on large-scale low-latitude magnetic fields influence the subsequent cycle's polarity. An equatorial migration of longitudinal field is seen, which is linked to the changing differential rota...
The Madison plasma dynamo experiment: A facility for studying laboratory plasma astrophysics
Cooper, C. M.; Wallace, J.; Brookhart, M.; Clark, M.; Collins, C.; Ding, W. X.; Flanagan, K.; Khalzov, I.; Li, Y.; Milhone, J.; Nornberg, M.; Nonn, P.; Weisberg, D.; Whyte, D. G.; Zweibel, E.; Forest, C. B.
2014-01-01
The Madison plasma dynamo experiment (MPDX) is a novel, versatile, basic plasma research device designed to investigate flow driven magnetohydrodynamic instabilities and other high-β phenomena with astrophysically relevant parameters. A 3 m diameter vacuum vessel is lined with 36 rings of alternately oriented 4000 G samarium cobalt magnets, which create an axisymmetric multicusp that contains ˜14 m3 of nearly magnetic field free plasma that is well confined and highly ionized (>50%). At present, 8 lanthanum hexaboride (LaB6) cathodes and 10 molybdenum anodes are inserted into the vessel and biased up to 500 V, drawing 40 A each cathode, ionizing a low pressure Ar or He fill gas and heating it. Up to 100 kW of electron cyclotron heating power is planned for additional electron heating. The LaB6 cathodes are positioned in the magnetized edge to drive toroidal rotation through J × B torques that propagate into the unmagnetized core plasma. Dynamo studies on MPDX require a high magnetic Reynolds number Rm > 1000, and an adjustable fluid Reynolds number 10 1). Initial results from MPDX are presented along with a 0-dimensional power and particle balance model to predict the viscosity and resistivity to achieve dynamo action.
Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo.
Mininni, Pablo; Alexakis, Alexandros; Pouquet, Annick
2005-10-01
We study the transfer of energy between different scales for forced three-dimensional magnetohydrodynamics turbulent flows in the kinematic dynamo regime. Two different forces are examined: a nonhelical Taylor-Green flow with magnetic Prandtl number P(M) = 0.4 and a helical ABC flow with P(M) = 1. This analysis allows us to examine which scales of the velocity flow are responsible for dynamo action and identify which scales of the magnetic field receive energy directly from the velocity field and which scales receive magnetic energy through the cascade of the magnetic field from large to small scales. Our results show that the turbulent velocity fluctuations in the inertial range are responsible for the magnetic field amplification at small scales (small-scale dynamo) while the large-scale field is amplified mostly due to the large-scale flow. A direct cascade of the magnetic field energy from large to small scales is also presented and is a complementary mechanism for the increase of the magnetic field at small scales. The input of energy from the inertial range velocity field into the small magnetic scales dominates over the energy cascade up to the wave number where the magnetic energy spectrum peaks. At even smaller scales, most of the magnetic energy input is from the cascading process.
Dynamo dominated accretion and energy flow: The mechanism of active galactic nuclei
Energy Technology Data Exchange (ETDEWEB)
Colgate, S.A.; Li, H.
1998-12-31
An explanation of the magnetic fields of the universe, the central mass concentration of galaxies, the massive black hole of every galaxy, and the AGN phenomena has been an elusive goal. The authors suggest here the outlines of such a theoretical understanding and point out where the physical understanding is missing. They believe there is an imperative to the sequence of mass flow and hence energy flow in the collapse of a galactic mass starting from the first non-linearity appearing in structure formation following decoupling. This first non-linearity of a two to one density fluctuation, the Lyman-{alpha} clouds, ultimately leads to the emission spectra of the phenomenon of AGN, quasars, blazars, etc. The over-arching physical principle is the various mechanisms for the transport of angular momentum. They believe they have now understood the new physics of two of these mechanisms that have previously been illusive and as a consequence they impose strong constraints on the initial conditions of the mechanisms for the subsequent emission of the gravitational binding energy. The new phenomena described are: (1) the Rossby vortex mechanism of the accretion disk {alpha}-viscosity, and (2) the mechanism of the {alpha}-{Omega} dynamo in the accretion disk. The Rossby vortex mechanism leads to a prediction of the black hole mass and rate of energy release and the {alpha}-{Omega} dynamo leads to the generation of the magnetic flux of the galaxy (and the far greater magnetic flux of clusters) and separately explains the primary flux of energy emission as force-free magnetic energy density. This magnetic flux and magnetic energy density separately are the necessary consequence of the saturation of a dynamo created by the accretion disk with a gain greater than unity.
EFFECTS OF LARGE-SCALE NON-AXISYMMETRIC PERTURBATIONS IN THE MEAN-FIELD SOLAR DYNAMO
Energy Technology Data Exchange (ETDEWEB)
Pipin, V. V. [Institute of Solar-Terrestrial Physics, Russian Academy of Sciences (Russian Federation); Kosovichev, A. G. [W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States)
2015-11-10
We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R{sub ⊙} has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.
Large- and small-scale interactions and quenching in an alpha2-dynamo.
Frick, Peter; Stepanov, Rodion; Sokoloff, Dmitry
2006-12-01
The evolution of the large-scale magnetic field in a turbulent flow of conducting fluid is considered in the framework of a multiscale alpha2-dynamo model, which includes the poloidal and the toroidal components for the large-scale magnetic field and a shell model for the small-scale magnetohydrodynamical turbulence. The conjugation of the mean-field description for the large-scale field and the shell formalism for the small-scale turbulence is based on strict conformity to the conservation laws. The model displays a substantial magnetic contribution to the alpha effect. It was shown that a large-scale magnetic field can be generated by current helicity even solely. The alpha quenching and the role of the magnetic Prandtl number (Pm) are studied. We have determined the dynamic nature of the saturation mechanism of dynamo action. Any simultaneous cross correlation of alpha and large-scale magnetic field energy EB is negligible, whereas coupling between alpha and EB becomes substantial for moderate time lags. An unexpected result is the behavior of the large-scale magnetic energy with variation of the magnetic Prandtl number. Diminishing of Pm does not have an inevitable ill effect on the magnetic field generation. The most efficient large-scale dynamo operates under relatively low Prandtl numbers--then the small-scale dynamo is suppressed and the decrease of Pm can lead even to superequipartition of the large-scale magnetic field (i.e., EB>Eu). In contrast, the growth of Pm does not promote the large-scale magnetic field generation. A growing counteraction of the magnetic alpha effect reduces the level of mean large-scale magnetic energy at the saturated state.
Cosmological magnetic fields as string dynamo seeds and axion fields in torsioned spacetime
Energy Technology Data Exchange (ETDEWEB)
De Andrade, L.C. Garcia, E-mail: garcia@dft.if.uerj.br [Departamento de Física Teórica — IF — Universidade do Estado do Rio de Janeiro-UERJ, Rua São Francisco Xavier, 524, Maracanã, Rio de Janeiro, RJ, Cep 20550-003 (Brazil)
2014-08-01
In this paper two examples of the generation cosmological magnetic fields (CMF) are given. The first is the string dynamo seed cosmological magnetic field estimated as B{sub seed}∼10{sup -24} Gauss from a static spin polarised cylinder in Einstein-Cartan-Maxwell spacetime. The string dynamo seeds from a static spin polarised cylinder is given by B∼σ{sup 2}R{sup 2} where σ is the spin-torsion density while R is the string radius. The B-field value above is able to seed galactic dynamo. In the BBN the magnetic fields around 10{sup 12} Gauss give rise to a string radius as small as 10{sup 17}l{sub P} where l{sub P} is the Planck length. The second is the CMF from axionic torsion field which is given by B{sub seed}∼10{sup -27} Gauss which is stronger than the primordial magnetic field B{sub BICEP2}∼10{sup -30} Gauss from the BICEP2 recent experiment on primordial gravitational waves and cosmological inflation to axionic torsion. The interaction Lagrangean between axionic torsion scalar φ and magnetic fields used in this last example is given by f{sup 2}(φ)F{sub μν}F{sup μν}. A similar lagrangean has been used by K. Bamba et al. [JCAP 10 (2012) 058] so generate magnetic fields without dynamo action. Since axionic torsion can be associated with axionic domain walls both examples discussed here could be consider as topological defects examples of the generation of primordial magnetic fields in universes endowed with spacetime torsion.
Superbubbles, Galactic Dynamos and the Spike Instability
Kulsrud, Russell M
2015-01-01
We draw attention to a problem with the alpha-Omega dynamo when it is applied to the origin of the galactic magnetic field under the assumption of perfect flux freezing. The standard theory involves the expulsion of undesirable flux and, because of flux freezing, the mass anchored on this flux also must be expelled. The strong galactic gravitational field makes this impossible on energetic grounds. It is shown that if only short pieces of the undesirable field lines are expelled, then mass can flow down along these field lines without requiring much energy. This expulsion of only short lines of force can be accomplished by a spike instability associated with gigantic astrophysical superbubbles. The physics of this instability is discussed and the results enable an estimate to be made of the number of spikes in the galaxy. It appears that there are probably enough spikes to cut all the undesirable lines into pieces as short as a couple of kiloparsecs during a dynamo time of a billion years. These cut pieces th...
Optimal Length Scale for a Turbulent Dynamo.
Sadek, Mira; Alexakis, Alexandros; Fauve, Stephan
2016-02-19
We demonstrate that there is an optimal forcing length scale for low Prandtl number dynamo flows that can significantly reduce the required energy injection rate. The investigation is based on simulations of the induction equation in a periodic box of size 2πL. The flows considered are the laminar and turbulent ABC flows forced at different forcing wave numbers k_{f}, where the turbulent case is simulated using a subgrid turbulence model. At the smallest allowed forcing wave number k_{f}=k_{min}=1/L the laminar critical magnetic Reynolds number Rm_{c}^{lam} is more than an order of magnitude smaller than the turbulent critical magnetic Reynolds number Rm_{c}^{turb} due to the hindering effect of turbulent fluctuations. We show that this hindering effect is almost suppressed when the forcing wave number k_{f} is increased above an optimum wave number k_{f}L≃4 for which Rm_{c}^{turb} is minimum. At this optimal wave number, Rm_{c}^{turb} is smaller by more than a factor of 10 than the case forced in k_{f}=1. This leads to a reduction of the energy injection rate by 3 orders of magnitude when compared to the case where the system is forced at the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.
Kinematic Dynamo, Supersymmetry Breaking, and Chaos
Ovchinnikov, Igor V
2015-01-01
The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as t...
On the mean-field theory of the Karlsruhe Dynamo Experiment
Directory of Open Access Journals (Sweden)
K.-H. Rädler
2002-01-01
Full Text Available In the Forschungszentrum Karlsruhe an experiment has been constructed which demonstrates a homogeneous dynamo as is expected to exist in the Earth's interior. This experiment is discussed within the framework of mean-field dynamo theory. The main predictions of this theory are explained and compared with the experimental results. Key words. Dynamo, geodynamo, dynamo experiment, mean-field dynamo theory, a-effect
Stretch fast dynamo mechanism via conformal mapping in Riemannian manifolds
Garcia de Andrade, L. C.
2007-10-01
Two new analytical solutions of the self-induction equation in Riemannian manifolds are presented. The first represents a twisted magnetic flux tube or flux rope in plasma astrophysics, where the rotation of the flow implies that the poloidal field is amplified from toroidal field, in the spirit of dynamo theory. The value of the amplification depends on the Frenet torsion of the magnetic axis of the tube. Actually this result illustrates the Zeldovich stretch, twist, and fold method to generate dynamos from straight and untwisted ropes. Based on the fact that this problem was previously handled, using a Riemannian geometry of twisted magnetic flux ropes [Phys Plasmas 13, 022309 (2006)], investigation of a second dynamo solution, conformally related to the Arnold kinematic fast dynamo, is obtained. In this solution, it is shown that the conformal effect on the fast dynamo metric enhances the Zeldovich stretch, and therefore a new dynamo solution is obtained. When a conformal mapping is performed in an Arnold fast dynamo line element, a uniform stretch is obtained in the original line element.
The Current Status of Kinematic Solar Dynamo Models
Indian Academy of Sciences (India)
Arnab Rai Choudhuri
2000-09-01
This review provides a historical overview of how research in kinematic solar dynamo modeling evolved during the last few decades and assesses the present state of research. The early pioneering papers assumed the dynamo to operate in the convection zone. It was suggested in the 1980s that the dynamo operates in a thin layer at the bottom of the convection zone. Some researchers in recent years are arguing that the poloidal field is produced near the surface—an idea that goes back to Babcock (1961) and Leighton (1969).
Experimental observation of spatially localized dynamo magnetic fields.
Gallet, B; Aumaître, S; Boisson, J; Daviaud, F; Dubrulle, B; Bonnefoy, N; Bourgoin, M; Odier, Ph; Pinton, J-F; Plihon, N; Verhille, G; Fauve, S; Pétrélis, F
2012-04-06
We report the first experimental observation of a spatially localized dynamo magnetic field, a common feature of astrophysical dynamos and convective dynamo simulations. When the two propellers of the von Kármán sodium experiment are driven at frequencies that differ by 15%, the mean magnetic field's energy measured close to the slower disk is nearly 10 times larger than the one close to the faster one. This strong localization of the magnetic field when a symmetry of the forcing is broken is in good agreement with a prediction based on the interaction between a dipolar and a quadrupolar magnetic mode.
Magnetic dipole moment estimates for an ancient lunar dynamo
Anderson, K. A.
1983-01-01
The four measured planetary magnetic moments combined with a recent theoretical prediction for dynamo magnetic fields suggests that no dynamo exists in the moon's interior today. For the moon to have had a magnetic moment in the past of sufficient strength to account for at least some of the lunar rock magnetism, the rotation would have been about twenty times faster than it is today and the radius of the fluid, conducting core must have been about 750 km. The argument depends on the validity of the Busse solution to the validity of the MHD problem of planetary dynamos.
Mean-field theory and self-consistent dynamo modeling
Energy Technology Data Exchange (ETDEWEB)
Yoshizawa, Akira; Yokoi, Nobumitsu [Tokyo Univ. (Japan). Inst. of Industrial Science; Itoh, Sanae-I [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
Zhang, Weiqun; Wang, Peng
2008-01-01
Magnetic field strengths inferred for relativistic outflows including gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively expected by orders of magnitude. We present three-dimensional relativistic magnetohydrodynamics (MHD) simulations demonstrating amplification and saturation of magnetic field by a macroscopic turbulent dynamo triggered by the Kelvin-Helmholtz shear instability. We find rapid growth of electromagnetic energy due to the stretching and folding of field lines in the turbulent velocity field resulting from non-linear development of the instability. Using conditions relevant for GRB internal shocks and late phases of GRB afterglow, we obtain amplification of the electromagnetic energy fraction to $\\epsilon_B \\sim 5 \\times 10^{-3}$. This value decays slowly after the shear is dissipated and appears to be largely independent of the initial field strength. The conditions required for operation of the dynamo are the presence of velocity shear and some seed magnetization b...
A coupled $2\\times2$D Babcock-Leighton solar dynamo model. II. Reference dynamo solutions
Lemerle, Alexandre
2016-01-01
In this paper we complete the presentation of a new hybrid $2\\times2$D flux transport dynamo (FTD) model of the solar cycle based on the Babcock-Leighton mechanism of poloidal magnetic field regeneration via the surface decay of bipolar magnetic regions (BMRs). This hybrid model is constructed by allowing the surface flux transport (SFT) simulation described in Lemerle et al. 2015 to provide the poloidal source term to an axisymmetric FTD simulation defined in a meridional plane, which in turn generates the BMRs required by the SFT. A key aspect of this coupling is the definition of an emergence function describing the probability of BMR emergence as a function of the spatial distribution of the internal axisymmetric magnetic field. We use a genetic algorithm to calibrate this function, together with other model parameters, against observed cycle 21 emergence data. We present a reference dynamo solution reproducing many solar cycle characteristics, including good hemispheric coupling, phase relationship betwe...
Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effect
Kelly, Cónall
2016-09-01
We investigate the asymptotic behaviour of a reduced αΩ-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the α-effect results in a system with state-dependent stochastic perturbations. By computing the upper Lyapunov exponent of the linearised model, we can identify regions of instability and stability in probability for the equilibrium of the nonlinear model; in this case the equilibrium solution corresponds to a magnetic field that has undergone catastrophic quenching. These regions are compared to regions of exponential mean-square stability and regions of sub- and super-criticality in the unperturbed linearised model. Prior analysis in the literature which focuses on these latter regions does not adequately address the corresponding transition in the nonlinear stochastic model. Finally we provide a visual representation of the influence of drift non-normality and perturbation intensity on these regions.
An update of Leighton's solar dynamo model
Cameron, R. H.; Schüssler, M.
2017-02-01
In 1969, Leighton developed a quasi-1D mathematical model of the solar dynamo, building upon the phenomenological scenario of Babcock published in 1961. Here we present a modification and extension of Leighton's model. Using the axisymmetric component (longitudinal average) of the magnetic field, we consider the radial field component at the solar surface and the radially integrated toroidal magnetic flux in the convection zone, both as functions of latitude. No assumptions are made with regard to the radial location of the toroidal flux. The model includes the effects of (i) turbulent diffusion at the surface and in the convection zone; (ii) poleward meridional flow at the surface and an equatorward return flow affecting the toroidal flux; (iii) latitudinal differential rotation and the near-surface layer of radial rotational shear; (iv) downward convective pumping of magnetic flux in the shear layer; and (v) flux emergence in the form of tilted bipolar magnetic regions treated as a source term for the radial surface field. While the parameters relevant for the transport of the surface field are taken from observations, the model condenses the unknown properties of magnetic field and flow in the convection zone into a few free parameters (turbulent diffusivity, effective return flow, amplitude of the source term, and a parameter describing the effective radial shear). Comparison with the results of 2D flux transport dynamo codes shows that the model captures the essential features of these simulations. We make use of the computational efficiency of the model to carry out an extended parameter study. We cover an extended domain of the 4D parameter space and identify the parameter ranges that provide solar-like solutions. Dipole parity is always preferred and solutions with periods around 22 yr and a correct phase difference between flux emergence in low latitudes and the strength of the polar fields are found for a return flow speed around 2 m s-1, turbulent
Solar Dynamo Driven by Periodic Flow Oscillation
Mayr, Hans G.; Hartle, Richard E.; Einaudi, Franco (Technical Monitor)
2001-01-01
We have proposed that the periodicity of the solar magnetic cycle is determined by wave mean flow interactions analogous to those driving the Quasi Biennial Oscillation in the Earth's atmosphere. Upward propagating gravity waves would produce oscillating flows near the top of the radiation zone that in turn would drive a kinematic dynamo to generate the 22-year solar magnetic cycle. The dynamo we propose is built on a given time independent magnetic field B, which allows us to estimate the time dependent, oscillating components of the magnetic field, (Delta)B. The toroidal magnetic field (Delta)B(sub phi) is directly driven by zonal flow and is relatively large in the source region, (Delta)(sub phi)/B(sub Theta) much greater than 1. Consistent with observations, this field peaks at low latitudes and has opposite polarities in both hemispheres. The oscillating poloidal magnetic field component, (Delta)B(sub Theta), is driven by the meridional circulation, which is difficult to assess without a numerical model that properly accounts for the solar atmosphere dynamics. Scale-analysis suggests that (Delta)B(sub Theta) is small compared to B(sub Theta) in the dynamo region. Relative to B(sub Theta), however, the oscillating magnetic field perturbations are expected to be transported more rapidly upwards in the convection zone to the solar surface. As a result, (Delta)B(sub Theta) (and (Delta)B(sub phi)) should grow relative to B(sub Theta), so that the magnetic fields reverse at the surface as observed. Since the meridional and zonai flow oscillations are out of phase, the poloidal magnetic field peaks during times when the toroidal field reverses direction, which is observed. With the proposed wave driven flow oscillation, the magnitude of the oscillating poloidal magnetic field increases with the mean rotation rate of the fluid. This is consistent with the Bode-Blackett empirical scaling law, which reveals that in massive astrophysical bodies the magnetic moment tends
Solar Magnetoconvection and Small-Scale Dynamo. Recent Developments in Observation and Simulation
Borrero, J. M.; Jafarzadeh, S.; Schüssler, M.; Solanki, S. K.
2017-09-01
A number of observational and theoretical aspects of solar magnetoconvection are considered in this review. We discuss recent developments in our understanding of the small-scale structure of the magnetic field on the solar surface and its interaction with convective flows, which is at the centre of current research. Topics range from plage areas in active regions over the magnetic network shaped by supergranulation to the ubiquituous `turbulent' internetwork fields. On the theoretical side, we focus upon magnetic field generation by small-scale dynamo action.
Interplay of CR-driven galactic wind, magnetic field, and galactic dynamo in spiral galaxies
Krause, Marita
2009-01-01
From our radio observations of the magnetic field strength and large-scale pattern of spiral galaxies of different Hubble types and star formation rates (SFR) we conclude that - though a high SFR in the disk increases the total magnetic field strength in the disk and the halo - the SFR does not change the global field configuration nor influence the global scale heights of the radio emission. The similar scale heights indicate that the total magnetic field regulates the galactic wind velocities. The galactic wind itself may be essential for an effective dynamo action.
Dissipation in dynamos at low and high magnetic Prandtl numbers
Brandenburg, A
2010-01-01
Using simulations of helically driven turbulence, it is shown that the ratio of kinetic to magnetic energy dissipation scales with the magnetic Prandtl number in power law fashion with an exponent of approximately 0.6. Over six orders of magnitude in the magnetic Prandtl number the magnetic field is found to be sustained by large-scale dynamo action of alpha-squared type. This work extends a similar finding for small magnetic Prandtl numbers to the regime of large magnetic Prandtl numbers. At large magnetic Prandtl numbers, most of the energy is dissipated viscously, lowering thus the amount of magnetic energy dissipation, which means that simulations can be performed at magnetic Reynolds numbers that are large compared to the usual limits imposed by a given resolution. This is analogous to an earlier finding that at small magnetic Prandtl numbers, most of the energy is dissipated resistively, lowering the amount of kinetic energy dissipation, so simulations can then be performed at much larger fluid Reynolds...
BIPOLAR MAGNETIC SPOTS FROM DYNAMOS IN STRATIFIED SPHERICAL SHELL TURBULENCE
Energy Technology Data Exchange (ETDEWEB)
Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor, E-mail: sarahjab@kth.se [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm (Sweden)
2015-06-01
Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, and nonhelical turbulence in the upper, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75° latitude and an azimuthal extent of 180°. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that eventually fill the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from Parker’s Ω-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10°. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths.
An update of Leighton's solar dynamo model
Cameron, R H
2016-01-01
In 1969 Leighton developed a quasi-1D mathematical model of the solar dynamo, building upon the phenomenological scenario of Babcock(1961). Here we present a modification and extension of Leighton's model. Using the axisymmetric component of the magnetic field, we consider the radial field component at the solar surface and the radially integrated toroidal magnetic flux in the convection zone, both as functions of latitude. No assumptions are made with regard to the radial location of the toroidal flux. The model includes the effects of turbulent diffusion at the surface and in the convection zone, poleward meridional flow at the surface and an equatorward return flow affecting the toroidal flux, latitudinal differential rotation and the near-surface layer of radial rotational shear, downward convective pumping of magnetic flux in the shear layer, and flux emergence in the form of tilted bipolar magnetic regions. While the parameters relevant for the transport of the surface field are taken from observations,...
Introduction to Plasma Dynamo, Reconnection and Shocks
Energy Technology Data Exchange (ETDEWEB)
Intrator, Thomas P. [Los Alamos National Laboratory
2012-08-30
In our plasma universe, most of what we can observe is composed of ionized gas, or plasma. This plasma is a conducting fluid, which advects magnetic fields when it flows. Magnetic structure occurs from the smallest planetary to the largest cosmic scales. We introduce at a basic level some interesting features of non linear magnetohydrodynamics (MHD). For example, in our plasma universe, dynamo creates magnetic fields from gravitationally driven flow energy in an electrically conducting medium, and conversely magnetic reconnection annihilates magnetic field and accelerates particles. Shocks occur when flows move faster than the local velocity (sonic or Alfven speed) for the propagation of information. Both reconnection and shocks can accelerate particles, perhaps to gigantic energies, for example as observed with 10{sup 20} eV cosmic rays.
Dynamo efficiency controlled by hydrodynamic bistability.
Miralles, Sophie; Herault, Johann; Herault, Johann; Fauve, Stephan; Gissinger, Christophe; Pétrélis, François; Daviaud, François; Dubrulle, Bérengère; Boisson, Jean; Bourgoin, Mickaël; Verhille, Gautier; Odier, Philippe; Pinton, Jean-François; Plihon, Nicolas
2014-06-01
Hydrodynamic and magnetic behaviors in a modified experimental setup of the von Kármán sodium flow-where one disk has been replaced by a propeller-are investigated. When the rotation frequencies of the disk and the propeller are different, we show that the fully turbulent hydrodynamic flow undergoes a global bifurcation between two configurations. The bistability of these flow configurations is associated with the dynamics of the central shear layer. The bistable flows are shown to have different dynamo efficiencies; thus for a given rotation rate of the soft-iron disk, two distinct magnetic behaviors are observed depending on the flow configuration. The hydrodynamic transition controls the magnetic field behavior, and bifurcations between high and low magnetic field branches are investigated.
Computer simulation of a magnetohydrodynamic dynamo. II
Kageyama, Akira; Sato, Tetsuya; Complexity Simulation Group
1995-05-01
A computer simulation of a magnetohydrodynamic dynamo in a rapidly rotating spherical shell is performed. Extensive parameter runs are carried out changing electrical resistivity. When resistivity is sufficiently small, total magnetic energy can grow more than ten times larger than total kinetic energy of convection motion which is driven by an unlimited external energy source. When resistivity is relatively large and magnetic energy is comparable or smaller than kinetic energy, the convection motion maintains its well-organized structure. However, when resistivity is small and magnetic energy becomes larger than kinetic energy, the well-organized convection motion is highly irregular. The magnetic field is organized in two ways. One is the concentration of component parallel to the rotation axis and the other is the concentration of perpendicular component. The parallel component tends to be confined inside anticyclonic columnar convection cells, while the perpendicular component is confined outside convection cells.
Solar Magnetic Field Reversals and the Role of Dynamo Families
DeRosa, M L; Hoeksema, J T
2012-01-01
The variable magnetic field of the solar photosphere exhibits periodic reversals as a result of dynamo activity occurring within the solar interior. We decompose the surface field as observed by both the Wilcox Solar Observatory and the Michelson Doppler Imager into its harmonic constituents, and present the time evolution of the mode coefficients for the past three sunspot cycles. The interplay between the various modes is then interpreted from the perspective of general dynamo theory, where the coupling between the primary and secondary families of modes is found to correlate with large-scale polarity reversals for many examples of cyclic dynamos. Mean-field dynamos based on the solar parameter regime are then used to explore how such couplings may result in the various long-term trends in the surface magnetic field observed to occur in the solar case.
A 5-D hyperchaotic Rikitake dynamo system with hidden attractors
Vaidyanathan, S.; Pham, V.-T.; Volos, C. K.
2015-07-01
This paper presents a 5-D hyperchaotic Rikitake dynamo system with three positive Lyapunov exponents which is derived by adding two state feedback controls to the famous 3-D Rikitake two-disk dynamo system. It is noted that the proposed hyperchaotic system has no equilibrium points and hence it exhibits hidden attractors. In addition, the qualitative properties, as well as the adaptive synchronization of the hyperchaotic Rikitake dynamo system with unknown system parameters, are discussed in details. The main results are proved using Lyapunov stability theory and numerical simulations are shown using MATLAB. Moreover, an electronic circuit realization in SPICE has been detailed to confirm the feasibility of the theoretical 5-D hyperchaotic Rikitake dynamo model.
Direct numerical simulation of dynamo transition for nonhelical MHD
Energy Technology Data Exchange (ETDEWEB)
Nath, Dinesh; Verma, Mahendra K [Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016 (India); Lessinnes, Thomas; Carati, Daniele [Physique Statistique et Plasmas, Universite Libre de Bruxellers, B-1050 Bruxelles (Belgium); Sarris, Ioannis [Department of Mechanical and Industrial Engineering, University of Thessaly, Volos (Greece)
2010-02-01
Pseudospectral Direct Numerical Simulation (DNS) has been performed to simulate dynamo transition for nonhelical magnetohydrodynamics turbulence. The numerical results are compared with a recent low-dimensional model [Verma et al. [13
A two-billion-year history for the lunar dynamo.
Tikoo, Sonia M; Weiss, Benjamin P; Shuster, David L; Suavet, Clément; Wang, Huapei; Grove, Timothy L
2017-08-01
Magnetic studies of lunar rocks indicate that the Moon generated a core dynamo with surface field intensities of ~20 to 110 μT between at least 4.25 and 3.56 billion years ago (Ga). The field subsequently declined to history requires an extraordinarily long-lived power source like core crystallization or precession. No single dynamo mechanism proposed thus far can explain the strong fields inferred for the period before 3.56 Ga while also allowing the dynamo to persist in such a weakened state beyond ~2.5 Ga. Therefore, our results suggest that the dynamo was powered by at least two distinct mechanisms operating during early and late lunar history.
Hemispherical Parker waves driven by thermal shear in planetary dynamos
Dietrich, Wieland; Wicht, Johannes
2014-01-01
Planetary and stellar magnetic fields are thought to be sustained by helical motions ($\\alpha$-effect) and, if present, differential rotation ($\\Omega$-effect). In the Sun, the strong differential rotation in the tachocline is responsible for an efficient $\\Omega$-effect creating a strong axisymmetric azimuthal magnetic field. This is a prerequisite for Parker dynamo waves that may be responsible for the solar cycle. In the liquid iron cores of terrestrial planets, the Coriolis force organizes convection into columns with a strong helical flow component. These likely dominate magnetic field generation while the $\\Omega$-effect is of secondary importance. Here we use numerical simulations to show that the planetary dynamo scenario may change when the heat flux through the outer boundary is higher in one hemisphere than in the other. A hemispherical dynamo is promoted that is dominated by fierce thermal wind responsible for a strong $\\Omega$-effect. As a consequence Parker dynamo waves are excited equivalent to...
A Non-axisymmetric Spherical α2-Dynamo
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Using the Chebyshev-tau method, the generation of oscillatory nonaxisymmetric stellar magnetic fields by the α2-dynamo is studied in spherical geometry. Following the boundary conditions given by Schubert & Zhang, the spherical α2-dynamo consists of a fully convective spherical shell with inner radius ri and outer radius ro. A comparison of the critical dynamo numbers of axisymmetric and φ-dependent modes for different thicknesses of the convective shell and different α-profiles leads to the following qualitative results: (I) when the angular factor of α-profile is sinnθ cosθ (n = 1, 2, 4) the solutions of the α2-dynamo are oscillatory and non-axisymmetric, (ii) the thinner the convective shell, the more easily is the nonaxisymmetric mode excited and the higher is the latitudinal wave number, (iii) the thickness of the outer convective shell has an effect on the symmetries of the magnetic fields.
Saturation of Zeldovich stretch-twist-fold map dynamos
Seta, Amit; Bhat, Pallavi; Subramanian, Kandaswamy
2015-10-01
> value is determined by the relative importance of the increased diffusion versus the reduced stretching. These saturation properties are akin to the range of possibilities that have been discussed in the context of fluctuation dynamos.
Energy transfers in dynamos with small magnetic Prandtl numbers
Kumar, Rohit
2015-06-25
We perform numerical simulation of dynamo with magnetic Prandtl number Pm = 0.2 on 10243 grid, and compute the energy fluxes and the shell-to-shell energy transfers. These computations indicate that the magnetic energy growth takes place mainly due to the energy transfers from large-scale velocity field to large-scale magnetic field and that the magnetic energy flux is forward. The steady-state magnetic energy is much smaller than the kinetic energy, rather than equipartition; this is because the magnetic Reynolds number is near the dynamo transition regime. We also contrast our results with those for dynamo with Pm = 20 and decaying dynamo. © 2015 Taylor & Francis.
Sharp magnetic structures from dynamos with density stratification
Jabbari, Sarah; Kleeorin, Nathan; Rogachevskii, Igor
2016-01-01
Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and are driven by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 5 times supercritical.
Dynamo magnetic field modes in thin astrophysical disks - An adiabatic computational approximation
Stepinski, T. F.; Levy, E. H.
1991-01-01
An adiabatic approximation is applied to the calculation of turbulent MHD dynamo magnetic fields in thin disks. The adiabatic method is employed to investigate conditions under which magnetic fields generated by disk dynamos permeate the entire disk or are localized to restricted regions of a disk. Two specific cases of Keplerian disks are considered. In the first, magnetic field diffusion is assumed to be dominated by turbulent mixing leading to a dynamo number independent of distance from the center of the disk. In the second, the dynamo number is allowed to vary with distance from the disk's center. Localization of dynamo magnetic field structures is found to be a general feature of disk dynamos, except in the special case of stationary modes in dynamos with constant dynamo number. The implications for the dynamical behavior of dynamo magnetized accretion disks are discussed and the results of these exploratory calculations are examined in the context of the protosolar nebula and accretion disks around compact objects.
SADE, the Student Astrophysical Dynamo Explorer
Martens, P.; Acton, L.; Klumpar, D.; Stern, R.; Peres, G.; Culhane, L.
In soft x-rays the solar coronal radiance varies by a factor of 10-30 over the solar activity cycle. A similar variation in most stars in the existing x-ray database has not been found (Stern 2001); even stars which exhibit chromospheric activity cycles show only marginal evidence for X-ray cycles. This is rather puzzling as the time span and multiple coverage of the x-ray sky should reveal at least a hint of such a pronounced cyclical variation. We propose a mission called the Student Astrophysical Dynamo Explorer to measure the x-ray brightness of about 75 stars once every 5 days for up to 15 years. Selection of prime stars takes into account location (avoid eclipse), rotation rate, Ca-K observations, and magnetic field strength, to focus on the best candidates for dynamo studies. We baseline a nested 4-5 mirror system with 200 cm^2 geometric area, with a 1.5 to 2 meter focal length, 15 arcsec on-axis resolution, and Au or Ni coatings. The strawman detector is a back-illuminated CCD of 512x512 pixels, with pixels that can be large as a 15 arcseconds. Available exposure time per star per visit is about an hour and a half. We are exploring the option of adding a visible light detector for astroseismology. To minimize operations cost for this long duration mission we envisage tracking and commanding from a simple ground station at Montana State University, operated by students under the auspices of MSU's Space Science and Engineering Lab (SSEL).
Nonlinear Oscillators in Space Physics
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
Searching for the fastest dynamo: laminar ABC flows.
Alexakis, Alexandros
2011-08-01
The growth rate of the dynamo instability as a function of the magnetic Reynolds number R(M) is investigated by means of numerical simulations for the family of the Arnold-Beltrami-Childress (ABC) flows and for two different forcing scales. For the ABC flows that are driven at the largest available length scale, it is found that, as the magnetic Reynolds number is increased: (a) The flow that results first in a dynamo is the 2 1/2-dimensional flow for which A=B and C=0 (and all permutations). (b) The second type of flow that results in a dynamo is the one for which A=B≃2C/5 (and permutations). (c) The most symmetric flow, A=B=C, is the third type of flow that results in a dynamo. (d) As R(M) is increased, the A=B=C flow stops being a dynamo and transitions from a local maximum to a third-order saddle point. (e) At larger R(M), the A=B=C flow reestablishes itself as a dynamo but remains a saddle point. (f) At the largest examined R(M), the growth rate of the 2 1/2-dimensional flows starts to decay, the A=B=C flow comes close to a local maximum again, and the flow A=B≃2C/5 (and permutations) results in the fastest dynamo with growth rate γ≃0.12 at the largest examined R(M). For the ABC flows that are driven at the second largest available length scale, it is found that (a) the 2 1/2-dimensional flows A=B,C=0 (and permutations) are again the first flows that result in a dynamo with a decreased onset. (b) The most symmetric flow, A=B=C, is the second type of flow that results in a dynamo. It is, and it remains, a local maximum. (c) At larger R(M), the flow A=B≃2C/5 (and permutations) appears as the third type of flow that results in a dynamo. As R(M) is increased, it becomes the flow with the largest growth rate. The growth rates appear to have some correlation with the Lyapunov exponents, but constructive refolding of the field lines appears equally important in determining the fastest dynamo flow.
Magnetic Field Saturation in the Riga Dynamo Experiment
Gailitis, A; Platacis, E; Dementev, S; Cifersons, A; Gerbeth, G; Gundrum, T; Stefani, F; Christen, M; Will, G; Gailitis, Agris; Lielausis, Olgerts; Platacis, Ernests; Dement'ev, Sergej; Cifersons, Arnis; Gerbeth, Gunter; Gundrum, Thomas; Stefani, Frank; Christen, Michael; Will, Gotthard
2001-01-01
After the dynamo experiment in November 1999 had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.
What can we say about seed fields for galactic dynamos?
2012-01-01
We demonstrate that a quasi-uniform cosmological seed field is a much less suitable seed for a galactic dynamo than has often been believed. The age of the Universe is insufficient for a conventional galactic dynamo to generate a contemporary galactic magnetic field starting from such a seed, accepting conventional estimates for physical quantities. We discuss modifications to the scenario for the evolution of galactic magnetic fields implied by this result. We also consider briefly the impli...
A simple stochastic model for dipole moment fluctuations in numerical dynamo simulations
Directory of Open Access Journals (Sweden)
Domenico G. eMeduri
2016-04-01
Full Text Available Earth's axial dipole field changes in a complex fashion on many differenttime scales ranging from less than a year to tens of million years.Documenting, analysing, and replicating this intricate signalis a challenge for data acquisition, theoretical interpretation,and dynamo modelling alike. Here we explore whether axial dipole variationscan be described by the superposition of a slow deterministic driftand fast stochastic fluctuations, i.e. by a Langevin-type system.The drift term describes the time averaged behaviour of the axial dipole variations,whereas the stochastic part mimics complex flow interactions over convective time scales.The statistical behaviour of the system is described by a Fokker-Planck equation whichallows useful predictions, including the average rates of dipole reversals and excursions.We analyse several numerical dynamo simulations, most of which havebeen integrated particularly long in time, and also the palaeomagneticmodel PADM2M which covers the past 2 Myr.The results show that the Langevin description provides a viable statistical modelof the axial dipole variations on time scales longer than about 1 kyr.For example, the axial dipole probability distribution and the average reversalrate are successfully predicted.The exception is PADM2M where the stochastic model reversal rate seems too low.The dependence of the drift on the axial dipolemoment reveals the nonlinear interactions that establish thedynamo balance. A separate analysis of inductive and diffusive magnetic effectsin three dynamo simulations suggests that the classical quadraticquenching of induction predicted by mean-field theory seems at work.
Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas
Piovesan, P.; Bonfiglio, D.; Cianciosa, M.; Luce, T. C.; Taylor, N. Z.; Terranova, D.; Turco, F.; Wilcox, R. S.; Wingen, A.; Cappello, S.; Chrystal, C.; Escande, D. F.; Holcomb, C. T.; Marrelli, L.; Paz-Soldan, C.; Piron, L.; Predebon, I.; Zaniol, B.; DIII-D, The; RFX-Mod Teams
2017-07-01
Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. In this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8-1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.
Spectroscopic measurement of the MHD dynamo in the MST reversed field pinch
Energy Technology Data Exchange (ETDEWEB)
Chapman, James Tharp [Univ. of Wisconsin, Madison, WI (United States)
1998-09-01
The author has directly observed the coupling of ion velocity fluctuations and magnetic field fluctuations to produce an MHD dynamo electric field in the interior of the MST reversed field pinch. Chord averaged ion velocity fluctuations were measured with a fast spectroscopic diagnostic which collects line radiation from intrinsic carbon impurities simultaneously along two lines of sight. The chords employed for the measurements resolved long wavelength velocity fluctuations of several km/s at 8-20 kHz as tiny, fast Doppler shifts in the emitted line profile. During discrete dynamo events the velocity fluctuations, like the magnetic fluctuations, increase dramatically. The toroidal and poloidal chords with impact parameters of 0.3 a and 0.6 a respectively, resolved fluctuation wavenumbers with resonance surfaces near or along the lines of sight indicating a radial velocity fluctuation width for each mode which spans only a fraction of the plasma radius. The phase between the measured toroidal velocity fluctuations and the magnetic fluctuations matches the predictions of resistive MHD while the poloidal velocity fluctuations exhibit a phase consistent with the superposition of MHD effects and the advection of a mean flow gradient past the poloidal line of sight. Radial velocity fluctuations resolved by a chord through the center of the plasma were small compared to the poloidal and toroidal fluctuations and exhibited low coherence with the magnetic fluctuations. The ensembled nonlinear product of the ion velocity fluctuations and fluctuations in the magnetic field indicates a substantial dynamo electric field which peaks during the periods of spontaneous flux generation.
Dynamo-driven plasmoid formation from a current-sheet instability
Ebrahimi, F.
2016-12-01
Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry. We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal guide field. As helicity is injected, two types of current sheets are formed from (1) the oppositely directed field lines in the injector region (primary reconnecting current sheet), and (2) the poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetric fluctuations arising from the current-sheet instability isolated near the plasma edge have tearing parity but can nevertheless grow fast (on the poloidal Alfven time scale). These modes saturate by breaking up the current sheet. Second, for the first time, a dynamo poloidal flux amplification is observed at the reconnection site (in the region of the oppositely directed magnetic field). This fluctuation-induced flux amplification increases the local Lundquist number, which then triggers a plasmoid instability and breaks the primary current sheet at the reconnection site. The plasmoids formation driven by large-scale flux amplification, i.e., a large-scale dynamo, observed here has strong implications for astrophysical reconnection as well as fast reconnection events in laboratory plasmas.
ON THE ROLE OF TACHOCLINES IN SOLAR AND STELLAR DYNAMOS
Energy Technology Data Exchange (ETDEWEB)
Guerrero, G. [Physics Department, Universidade Federal de Minas Gerais, Av. Antonio Carlos, 6627, Belo Horizonte, MG, 31270-901 (Brazil); Smolarkiewicz, P. K. [European Centre for Medium-Range Weather Forecasts, Reading RG2 9AX (United Kingdom); De Gouveia Dal Pino, E. M. [Astronomy Department, IAG-USP Rua do mato, 1226, São Paulo, SP, 05508-090 (Brazil); Kosovichev, A. G. [New Jersey Institute of Technology, Newark, NJ 07103 (United States); Mansour, N. N., E-mail: guerrero@fisica.ufmg.br, E-mail: smolar@ecmwf.int, E-mail: dalpino@astro.iag.usp.br, E-mail: sasha@bbso.njit.edu, E-mail: Nagi.N.Mansour@nasa.gov [NASA, Ames Research Center, Moffett Field, Mountain View, CA 94040 (United States)
2016-03-10
Rotational shear layers at the boundary between radiative and convective zones, tachoclines, play a key role in the process of magnetic field generation in solar-like stars. We present two sets of global simulations of rotating turbulent convection and dynamo. The first set considers a stellar convective envelope only; the second one, aiming at the formation of a tachocline, also considers the upper part of the radiative zone. Our results indicate that the resulting properties of the mean flows and dynamo, such as the growth rate, saturation energy, and mode, depend on the Rossby number (Ro). For the first set of models either oscillatory (with ∼2 yr period) or steady dynamo solutions are obtained. The models in the second set naturally develop a tachocline, which in turn leads to the generation of a strong mean magnetic field. Since the field is also deposited in the stable deeper layer, its evolutionary timescale is much longer than in the models without a tachocline. Surprisingly, the magnetic field in the upper turbulent convection zone evolves on the same timescale as the deep field. These models result in either an oscillatory dynamo with a ∼30 yr period or a steady dynamo depending on Ro. In terms of the mean-field dynamo coefficients computed using the first-order smoothing approximation, the field evolution in the oscillatory models without a tachocline seems to be consistent with dynamo waves propagating according to the Parker–Yoshimura sign rule. In the models with tachoclines the dynamics is more complex and involves other transport mechanisms as well as tachocline instabilities.
Dynamos at extreme magnetic Prandtl numbers
Verma, Mahendra K
2015-01-01
We present a MHD shell model suitable for the computation of various energy fluxes of magnetohydrodynamic turbulence for very small and very large magnetic Prandtl numbers $\\mathrm{Pm}$; such computations are inaccessible to direct numerical simulations. For small $\\mathrm{Pm}$, we observe that the both kinetic and magnetic energy spectra scale as $k^{-5/3}$ in the inertial range, but the dissipative magnetic energy scales as $k^{-17/3}$. Here, the kinetic energy at large length scale feeds the large-scale magnetic field that cascades to small-scale magnetic field, which gets dissipated by Joule heating. The large $\\mathrm{Pm}$ dynamo has a similar behaviour except that the dissipative kinetic energy scales as $k^{-13/3}$. For this case, the large-scale velocity field transfers energy to large-scale magnetic field, which gets transferred to small-scale velocity and magnetic fields. The energy of the small-scale magnetic field also gets transferred to the small-scale velocity field. The energy accumulated at s...
ECH on the Madison Plasma Dynamo Experiment
Milhone, Jason; Clark, Mike; Collins, Cami; Cooper, Chris; Katz, Noam; Nonn, Paul; Wallace, John; Forest, Cary
2012-10-01
The Madison Plasma Dynamo Experiment (MPDX) is a 3 meter diameter sphere consisting of 36 axisymmetric rings of samarium cobalt magnets in a ring-cusp configuration. Electrostatic electrodes on the edge will be used to spin the plasma. The purpose of MPDX is to study flow-driven magnetohydrodynamic instabilities. Electron cyclotron heating will be used for the ionization and heating of the plasma. A benefit of the ECH is the plasma will have hot electrons leading to good electrical conduction and high magnetic Reynolds number. In addition, direct heating of the electrons helps to obtain a large ionization fraction and a low neutral density. The ECH system on MPDX will consist of 5 separate lines distributed at various positions around the vacuum vessel. Each line will have a 20 kW magnetron operating in continuous wave mode at 2.45 GHz outputting in WR-340 waveguide. The power will be transferred to the vacuum vessel through WR-284 waveguide. Each line will contain a directional coupler for measuring reflected power. A manual 3-stub tuner will be used for impedance matching. The purpose of these elements is to optimize the efficiency of energy transfer to the plasma.
Metric-torsion preheating: cosmic dynamo mechanism?
de Andrade, L C Garcia
2014-01-01
Earlier Bassett et al [Phys Rev D 63 (2001) 023506] investigated the amplification of large scale magnetic fields during preheating and inflation in several different models. They argued that in the presence of conductivity resonance effect is weakened. From a dynamo equation in spacetimes endowed with torsion recently derived by Garcia de Andrade [Phys Lett B 711: 143 (2012)] it is shown that a in a universe with pure torsion in Minkowski spacetime the cosmological magnetic field is enhanced by ohmic or non-conductivity effect, which shows that the metric-torsion effects is worth while of being studied. In this paper we investigated the metric-torsion preheating perturbation, which leads to the seed cosmological magnetic field in the universe with torsion is of the order of $B_{seed}\\sim{10^{-37}Gauss}$ which is several orders of magnitude weaker than the decoupling value obtained from pure metric preheating of $10^{-15}Gauss$. Despite of the weakness of the magnetic field this seed field may seed the galact...
The fate of alpha dynamos at large $Rm$
Cameron, Alexandre
2016-01-01
At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha-dynamos as the magnetic Reynolds number $Rm$ is increased. Using Floquet theory, we are able to precisely quantify mean field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large scale separations with minimal computational cost. We apply this framework to helical and non-helical flows as well as to random flows with short correlation time. Our results determine that the alpha-description is valid for $Rm$ smaller than a critical value $Rm_c$ at which small scale dynamo instability starts. When $Rm$ is above $Rm_c$ the dynamo ceases to follow the mean field description and the growth rate of the large scale modes becomes independent of the scale separation while the energy in the large scale modes ...
Modelling the dynamo in fully convective M-stars
Yadav, Rakesh Kumar; Christensen, Ulrich; Morin, Julien; Wolk, Scott; Poppenhaeger, Katja; Reiners, Ansgar; gastine, Thomas
2017-05-01
M-stars are among the most active and numerous stars in our galaxy. Their activity plays a fundamentally important role in shaping the exoplanetary biosphere since the habitable zones are very close to these stars. Therefore, modeling M-star activity has become a focal point in habitability studies. The fully convective members of the M-star population demand more immediate attention due to the discovery of Earth-like exoplanets around our stellar neighbors Proxima Centauri and TRAPPIST-1 which are both fully convective. The activity of these stars is driven by their convective dynamo, which may be fundamentally different from the solar dynamo due the absence of radiative cores. We model this dynamo mechanism using high-resolution 3D anelastic MHD simulations. To understand the evolution of the dynamo mechanism we simulate two cases, one with a fast enough rotation period to model a star in the `saturated' regime of the rotation-activity realtionship and the other with a slower period to represent cases in the `unsaturated' regime. We find the rotation period fundamentally controls the behavior of the dynamo solution: faster rotation promotes strong magnetic fields (of order kG) on both small and large length scales and the dipolar component of the magnetic field is dominant and stable, however, slower rotation leads to weaker magnetic fields which exhibit cyclic behavior. In this talk, I will present the simulation results and discuss how we can use them to interpret several observed features of the M-star activity.
Spatial Nonlocality of the Small-Scale Solar Dynamo
Lamb, Derek A; DeForest, Craig E
2014-01-01
We explore the nature of the small-scale solar dynamo by tracking magnetic features. We investigate two previously-explored categories of the small-scale solar dynamo: shallow and deep. Recent modeling work on the shallow dynamo has produced a number of scenarios for how a strong network concentration can influence the formation and polarity of nearby small-scale magnetic features. These scenarios have measurable signatures, which we test for here using magnetograms from the Narrowband Filter Imager (NFI) on Hinode. We find no statistical tendency for newly-formed magnetic features to cluster around or away from network concentrations, nor do we find any statistical relationship between their polarities. We conclude that there is no shallow or "surface" dynamo on the spatial scales observable by Hinode/NFI. In light of these results, we offer a scenario in which the sub-surface field in a deep solar dynamo is stretched and distorted via turbulence, allowing the field to emerge at random locations on the photo...
Fluctuation Dynamo and Turbulent Induction at Small Prandtl Number
Eyink, Gregory L
2010-01-01
We study the Lagrangian mechanism of the fluctuation dynamo at zero Prandtl number and infinite magnetic Reynolds number, in the Kazantsev-Kraichnan model of white-noise advection. With a rough velocity field corresponding to a turbulent inertial-range, flux-freezing holds only in a stochastic sense. We show that field-lines arriving to the same point which were initially separated by many resistive lengths are important to the dynamo. Magnetic vectors of the seed field that point parallel to the initial separation vector arrive anti-correlated and produce an "anti-dynamo" effect. We also study the problem of "magnetic induction" of a spatially uniform seed field. We find no essential distinction between this process and fluctuation dynamo, both producing the same growth-rates and small-scale magnetic correlations. In the regime of very rough velocity fields where fluctuation dynamo fails, we obtain the induced magnetic energy spectra. We use these results to evaluate theories proposed for magnetic spectra in...
Measurement of the dynamo effect in a plasma
Energy Technology Data Exchange (ETDEWEB)
Ji, H. [Princeton Univ., NJ (United States). Plasma Physics Lab.; Prager, S.C.; Almagri, A.F.; Sarff, J.S. [Univ. of Wisconsin, Madison, WI (United States). Dept. of Physics; Hirano, Y. [Electrotechnical Lab., Tsukuba, Ibaraki (Japan). Plasma Section; Toyama, H. [Univ. of Tokyo (Japan). Dept. of Physics
1995-11-01
A series of the detailed experiments has been conducted in three laboratory plasma devices to measure the dynamo electric field along the equilibrium field line (the {alpha} effect) arising from the correlation between the fluctuating flow velocity and magnetic field. The fluctuating flow velocity is obtained from probe measurement of the fluctuating E x B drift and electron diamagnetic drift. The three major findings are (1) the {alpha} effect accounts for the dynamo current generation, even in the time dependence through a ``sawtooth`` cycle; (2) at low collisionality the dynamo is explained primarily by the widely studied pressureless Magnetohydrodynamic (MHD) model, i.e., the fluctuating velocity is dominated by the E x B drift; (3) at high collisionality, a new ``electron diamagnetic dynamo`` is observed, in which the fluctuating velocity is dominated by the diamagnetic drift. In addition, direct measurements of the helicity flux indicate that the dynamo activity transports magnetic helicity from one part of the plasma to another, but the total helicity is roughly conserved, verifying J.B. Taylor`s conjecture.
Dynamo-driven plasmoid formation from a current-sheet instability
Ebrahimi, F
2016-01-01
Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry. We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal guide field. As helicity is injected, two types of current sheets are formed from 1) the oppositely directed field lines in the injector region (primary reconnecting current sheet), and 2) the poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetic fluctuations arising from the current-sheet instability isolated near the plasma edge have tearing parity but can nevertheless grow fast (on the poloidal Alfven time scale). These modes saturate by breaking up the current sheet. Second, for the first time a dynamo poloidal flux amplification is observed at the reconnetion site (in the region of the oppositely directed magnetic field). This fluctuation-induced flux amplificatio...
The alpha effect with imposed and dynamo-generated magnetic fields
Hubbard, A; Käpylä, P J; Brandenburg, A
2009-01-01
Estimates for the nonlinear alpha effect in helical turbulence are presented using two different approaches where a uniform magnetic field is applied either to the actual field, or where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where with an imposed magnetic field the alpha effect is either drastically overestimated, or drastically underestimated compared with the kinematic value. It is demonstrated that the kinematic value can be estimated correctly by resetting the magnetic field in regular time intervals.
Wang, Cheng-Yu; Chen, Chun-Wei; Jau, Hung-Chang; Li, Cheng-Chang; Cheng, Chiao-Yu; Wang, Chun-Ta; Leng, Shi-Ee; Khoo, Iam-Choon; Lin, Tsung-Hsien
2016-08-05
In this paper, we show that anisotropic photosensitive nematic liquid crystals (PNLC) made by incorporating anisotropic absorbing dyes are promising candidates for constructing all-optical elements by virtue of the extraordinarily large optical nonlinearity of the nematic host. In particular, we have demonstrated several room-temperature 'prototype' PNLC-based all-optical devices such as optical diode, optical transistor and all primary logic gate operations (OR, AND, NOT) based on such optical transistor. Owing to the anisotropic absorption property and the optical activity of the twist alignment nematic cell, spatially non-reciprocal transmission response can be obtained within a sizeable optical isolation region of ~210 mW. Exploiting the same mechanisms, a tri-terminal configuration as an all-optical analogue of a bipolar junction transistor is fabricated. Its ability to be switched by an optical field enables us to realize an all-optical transistor and demonstrate cascadability, signal fan-out, logic restoration, and various logical gate operations such as OR, AND and NOT. Due to the possibility of synthesizing anisotropic dyes and wide ranging choice of liquid crystals nonlinear optical mechanisms, these all-optical operations can be optimized to have much lower thresholds and faster response speeds. The demonstrated capabilities of these devices have shown great potential in all-optical control system and photonic integrated circuits.
The solar dynamo: inferences from observations and modeling
Kitchatinov, L L
2014-01-01
It can be shown on observational grounds that two basic effects of dynamo theory for solar activity - production of the toroidal field from the poloidal one by differential rotation and reverse conversion of the toroidal field to the poloidal configuration by helical motions - are operating in the Sun. These two effects, however, do not suffice for constructing a realistic model for the solar dynamo. Only when a non-local version of the alpha-effect is applied, is downward diamagnetic pumping included and field advection by the equatorward meridional flow near the base of the convection zone allowed for, can the observed activity cycles be closely reproduced. Fluctuations in the alpha-effect can be estimated from sunspot data. Dynamo models with fluctuating parameters reproduce irregularities of solar cycles including the grand activity minima. The physics of parametric excitation of irregularities remains, however, to be understood.
Predicting cycle 24 using various dynamo-based tools
Directory of Open Access Journals (Sweden)
M. Dikpati
2008-02-01
Full Text Available Various dynamo-based techniques have been used to predict the mean solar cycle features, namely the amplitude and the timings of onset and peak. All methods use information from previous cycles, including particularly polar fields, drift-speed of the sunspot zone to the equator, and remnant magnetic flux from the decay of active regions. Polar fields predict a low cycle 24, while spot zone migration and remnant flux both lead to predictions of a high cycle 24. These methods both predict delayed onset for cycle 24. We will describe how each of these methods relates to dynamo processes. We will present the latest results from our flux-transport dynamo, including some sensitivity tests and how our model relates to polar fields and spot zone drift methods.
An Instability-driven Dynamo for $\\gamma$ Ray Bursts
Araya-Gochez, R A
2000-01-01
We show that an MHD-instability driven dynamo (IDD) operating in a hot accretion disk is capable of generating energetically adequate magnetic flux deposition rates above and below a mildly advective accretion disk structure. The dynamo is driven by the magnetorotational instability (MRI) of a toroidal field in a shear flow and is limited by the buoyancy of `horizontal' flux and by reconnection in the turbulent medium. The efficiency of magnetic energy deposition is estimated to be comparable to the neutrino losses although an MHD collimation mechanism may deem this process a more viable alternative to neutrino-burst-driven models of gamma ray bursts.
Cause of equatorward migration in global convective dynamo simulations
Warnecke, Jörn; Käpylä, Maarit J; Brandenburg, Axel
2014-01-01
We present results from four convectively-driven stellar dynamo simulations in spherical wedge geometry. All of these simulations produce cyclic and migrating mean magnetic fields. Through detailed comparisons we show that the migration direction can be explained by an $\\alpha\\Omega$ dynamo wave following the Parker--Yoshimura rule. We conclude that the equatorward migration in this and previous work is due to a positive (negative) $\\alpha$ effect in the northern (southern) hemisphere and a negative radial gradient of $\\Omega$ outside the inner tangent cylinder of these models. This idea is supported by a strong correlation between negative radial shear and toroidal field strength in the region of equatorward propagation.
Magnetohydrodynamic dynamo: global flow generation in plasma turbulence
Energy Technology Data Exchange (ETDEWEB)
Yokoi, Nobumitsu; Yoshizawa, Akira [Tokyo Univ. (Japan). Inst. of Industrial Science; Itoh, Kimitaka; Itoh, Sanae-I.
1999-07-01
Generation mechanism of the spontaneous plasma rotation observed in an improved confinement mode in tokamak's is examined from the viewpoint of the turbulent magnetohydrodynamic (MHD) dynamo. A dynamo model, where the concept of cross helicity (velocity/magnetic-field correlation) plays a key role, is applied to the reversed shear (RS) modes. The concave electric-current profile occurred in the RS modes is shown to be a cause of the global plasma rotation through a numerical simulation of the cross-helicity turbulence model. (author)
Abrosimov, N. A.; Elesin, A. V.
2016-07-01
On the basis of the applied theory of shells, a resolving system of equations is formulated and a method for the numerical solution of problems of nonlinear nonaxisymmetric deformation and fracture of composite cylindrical shells at explosive loadings of different intensity is developed. A model of progressive destruction of a composite shell based on the degradation of stiffness characteristics of individual layers in a multilayer package is elaborated, which depends on the fracture mode of the binder and fiber. The reliability of the technique considered is proved by comparing calculation results with known experimental data. Results of an analysis of the effect of nonaxisymmetric arrangement of an explosive charge on the fracture behavior of composite cylindrical shells with different reinforcement structures are presented.
Influence of a coronal envelope as a free boundary to global convective dynamo simulations
Warnecke, J.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A.
2016-12-01
Aims: We explore the effects of an outer stably stratified coronal envelope on rotating turbulent convection, differential rotation, and large-scale dynamo action in spherical wedge models of the Sun. Methods: We solve the compressible magnetohydrodynamic equations in a two-layer model with unstable stratification below the surface, representing the convection zone, and a stably stratified coronal envelope above. The interface represents a free surface. We compare our model to models that have no coronal envelope. Results: The presence of a coronal envelope is found to modify the Reynolds stress and the Λ effect resulting in a weaker and non-cylindrical differential rotation. This is related to the reduced latitudinal temperature variations that are caused by and dependent on the angular velocity. Some simulations develop a near-surface shear layer that we can relate to a sign change in the meridional Reynolds stress term in the thermal wind balance equation. Furthermore, the presence of a free surface changes the magnetic field evolution since the toroidal field is concentrated closer to the surface. In all simulations, however, the migration direction of the mean magnetic field can be explained by the Parker-Yoshimura rule, which is consistent with earlier findings. Conclusions: A realistic treatment of the upper boundary in spherical dynamo simulations is crucial for the dynamics of the flow and magnetic field evolution.
Transport coefficients for the shear dynamo problem at small Reynolds numbers.
Singh, Nishant K; Sridhar, S
2011-05-01
We build on the formulation developed in S. Sridhar and N. K. Singh [J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients α(il) and η(il) are derived. We prove that when the velocity field is nonhelical, the transport coefficient α(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X(3) and time τ; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Rädler, M. Rheinhardt, and P. J. Käpylä [Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor η(il)(τ). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.
Moffatt drift driven large scale dynamo due to $\\alpha$ fluctuations with nonzero correlation times
Singh, Nishant K
2015-01-01
We present a theory of large-scale dynamo action in a turbulent flow that has stochastic, zero-mean fluctuations of the $\\alpha$ parameter. We extend the Kraichnan-Moffatt model to explore effects of finite memory of $\\alpha$ fluctuations, in a spirit similar to that of Sridhar & Singh (2014), hereafter SS14. Using the first-order smoothing approximation, we derive a linear integro-differential equation governing the dynamics of the large-scale magnetic field, which is non-perturbative in the $\\alpha$-correlation time $\\tau_{\\alpha}$. We recover earlier results in the exactly solvable white-noise (WN) limit where the Moffatt drift does not contribute to the dynamo growth/decay. To study finite memory effects, we reduce the integro-differential equation to a partial differential equation by assuming that the $\\tau_{\\alpha}$ be small but nonzero and the large-scale magnetic field is slowly varying. We derive the dispersion relation and provide explicit expression for the growth rate as a function of four in...
A Critical Assessment of the Flux Transport Dynamo
Indian Academy of Sciences (India)
Arnab Rai Choudhuri
2015-03-01
We first discuss how the flux transport dynamo with reasonably high diffusion can explain both the regular and the irregular features of the solar cycle quite well. Then, we critically examine the inadequacies of the model and the challenge posed by some recent observational data about meridional circulation, arriving at a conclusion that this model can still work within the bounds of observational data.
Helicity of Solar Active Regions from a Dynamo Model
Indian Academy of Sciences (India)
Piyali Chatterjee
2006-06-01
We calculate helicities of solar active regions based on the idea that poloidal flux lines get wrapped around a toroidal flux tube rising through the convection zone, thereby giving rise to the helicity. We use our solar dynamo model based on the Babcock–Leighton -effect to study how helicity varies with latitude and time.
Gravitational dynamos and the low-frequency geomagnetic secular variation
Olson, P.
2007-01-01
Self-sustaining numerical dynamos are used to infer the sources of low-frequency secular variation of the geomagnetic field. Gravitational dynamo models powered by compositional convection in an electrically conducting, rotating fluid shell exhibit several regimes of magnetic field behavior with an increasing Rayleigh number of the convection, including nearly steady dipoles, chaotic nonreversing dipoles, and chaotic reversing dipoles. The time average dipole strength and dipolarity of the magnetic field decrease, whereas the dipole variability, average dipole tilt angle, and frequency of polarity reversals increase with Rayleigh number. Chaotic gravitational dynamos have large-amplitude dipole secular variation with maximum power at frequencies corresponding to a few cycles per million years on Earth. Their external magnetic field structure, dipole statistics, low-frequency power spectra, and polarity reversal frequency are comparable to the geomagnetic field. The magnetic variability is driven by the Lorentz force and is characterized by an inverse correlation between dynamo magnetic and kinetic energy fluctuations. A constant energy dissipation theory accounts for this inverse energy correlation, which is shown to produce conditions favorable for dipole drift, polarity reversals, and excursions. PMID:18048345
A 3D Babcock-Leighton Solar Dynamo Model
Miesch, Mark S
2014-01-01
We present a 3D kinematic solar dynamo model in which poloidal field is generated by the emergence and dispersal of tilted sunspot pairs (more generally Bipolar Magnetic Regions, or BMRs). The axisymmetric component of this model functions similarly to previous 2D Babcock-Leighton (BL) dynamo models that employ a double-ring prescription for poloidal field generation but we generalize this prescription into a 3D flux emergence algorithm that places BMRs on the surface in response to the dynamo-generated toroidal field. In this way, the model can be regarded as a unification of BL dynamo models (2D in radius/latitude) and surface flux transport models (2D in latitude/longitude) into a more self-consistent framework that captures the full 3D structure of the evolving magnetic field. The model reproduces some basic features of the solar cycle including an 11-yr periodicity, equatorward migration of toroidal flux in the deep convection zone, and poleward propagation of poloidal flux at the surface. The poleward-p...
Fluctuation dynamo and turbulent induction at small Prandtl number.
Eyink, Gregory L
2010-10-01
We study the Lagrangian mechanism of the fluctuation dynamo at zero Prandtl number and infinite magnetic Reynolds number, in the Kazantsev-Kraichnan model of white-noise advection. With a rough velocity field corresponding to a turbulent inertial range, flux freezing holds only in a stochastic sense. We show that field lines arriving to the same point which were initially separated by many resistive lengths are important to the dynamo. Magnetic vectors of the seed field that point parallel to the initial separation vector arrive anticorrelated and produce an "antidynamo" effect. We also study the problem of "magnetic induction" of a spatially uniform seed field. We find no essential distinction between this process and fluctuation dynamo, both producing the same growth rates and small-scale magnetic correlations. In the regime of very rough velocity fields where fluctuation dynamo fails, we obtain the induced magnetic energy spectra. We use these results to evaluate theories proposed for magnetic spectra in laboratory experiments of turbulent induction.
Analytic solution of an oscillatory migratory α2 stellar dynamo
Brandenburg, A.
2017-02-01
Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α. Aims: We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant α, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. Methods: We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. Results: The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of α. Conclusions: The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant α.
Magnetohydrodynamic dynamo in disc-like astrophysical bodies
Energy Technology Data Exchange (ETDEWEB)
Stepinski, T.F.
1986-01-01
Magnetohydrodynamic dynamos in disc-like astrophysical bodies have been considered for some time. Important astrophysical objects like accretion discs, protostellar and protoplanetary nebulae, and galaxies are thought to regenerate a magnetic field through a dynamo mechanism. Although there is a well-developed theory for describing the regeneration of magnetic fields in these objects, there are not any specific methods to calculate such magnetic fields in the general case. In this work, after a description of the dynamo theory, the specific method for solving the nonspherical dynamo is introduced. The unique feature of this method is accommodation of variable magnetic diffusivity in order to model the shape of a disc-like body. The detailed construction of the method is presented, as well as description of mathematical and numerical methods used for obtaining the solution. The method of checking the model with respect to sell-established spherical models is also presented. Finally, some examples are calculated and discussion is given on the behavior of calculated magnetic fields and possible astrophysical implications.
On the role of tachoclines in solar and stellar dynamos
Guerrero, G; Pino, E M de Gouveia Dal; Kosovichev, A G; Mansour, N N
2015-01-01
Rotational shear layers at the boundary between radiative and convective zones, tachoclines, play a key role in the dynamo process of magnetic field generation in the Sun and solar-like stars. We present two sets of global simulations of rotating turbulent convection and dynamo. The first set considers a stellar convective envelope only; the second one, aiming at the formation of a tachocline, considers also the upper part of the radiative zone. Our results indicate that dynamo properties like the growth rate, the saturation energy and mode depend on the Rossby (Ro) number. The models with slow rotation in the first set of simulations reproduce remarkably well the solar differential rotation in the convection zone. Depending on the value of Ro either oscillatory (with ~2 yr period) or steady dynamo solutions are obtained. The models in the second set naturally develop a tachocline which, in turn, leads to the generation of strong mean magnetic field (~1 Tesla). Since the field is also deposited into the stabl...
Fluctuation dynamo at finite correlation times using renewing flows
Bhat, Pallavi
2014-01-01
Fluctuation dynamos are generic to turbulent astrophysical systems. The only analytical model of the fluctuation dynamo, due to Kazantsev, assumes the velocity to be delta-correlated in time. This assumption breaks down for any realistic turbulent flow. We generalize the analytic model of fluctuation dynamo to include the effects of a finite correlation time, $\\tau$, using renewing flows. The generalized evolution equation for the longitudinal correlation function $M_L$ leads to the standard Kazantsev equation in the $\\tau \\to 0$ limit, and extends it to the next order in $\\tau$. We find that this evolution equation involves also third and fourth spatial derivatives of $M_L$, indicating that the evolution for finite $\\tau$ will be non-local in general. In the perturbative case of small-$\\tau$ (or small Strouhl number), it can be recast using the Landau-Lifschitz approach, to one with at most second derivatives of $M_L$. Using both a scaling solution and the WKBJ approximation, we show that the dynamo growth r...
Robustness of oscillatory α2 dynamos in spherical wedges
Cole, E.; Brandenburg, A.; Käpylä, P. J.; Käpylä, M. J.
2016-10-01
Context. Large-scale dynamo simulations are sometimes confined to spherical wedge geometries by imposing artificial boundary conditions at high latitudes. This may lead to spatio-temporal behaviours that are not representative of those in full spherical shells. Aims: We study the connection between spherical wedge and full spherical shell geometries using simple mean-field dynamos. Methods: We solve the equations for one-dimensional time-dependent α2 and α2Ω mean-field dynamos with only latitudinal extent to examine the effects of varying the polar angle θ0 between the latitudinal boundaries and the poles in spherical coordinates. Results: In the case of constant α and ηt profiles, we find oscillatory solutions only with the commonly used perfect conductor boundary condition in a wedge geometry, while for full spheres all boundary conditions produce stationary solutions, indicating that perfect conductor conditions lead to unphysical solutions in such a wedge setup. To search for configurations in which this problem can be alleviated we choose a profile of the turbulent magnetic diffusivity that decreases toward the poles, corresponding to high conductivity there. Oscillatory solutions are now achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By changing both the turbulent magnetic diffusivity and α profiles so that both effects are more concentrated toward the equator, we see oscillatory dynamos with equatorward drift, shorter cycles, and magnetic fields distributed over a wider range of latitudes. Those profiles thus remove the sensitive and unphysical dependence on θ0. When introducing radial shear, we again see oscillatory dynamos, and the direction of drift follows the Parker-Yoshimura rule. Conclusions: A reduced α effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and
Portacio, Alfonso A.; Rodríguez, Boris A.; Villamil, Pablo
2017-04-01
The linear and nonlinear optical response in a cylindrical quantum dot (CQD) of GaAs / Ga0.6Al0.4 As with a donor impurity in a uniform magnetic field applied in the axial direction of the cylinder is studied theoretically. The calculations were carried out in approximations of effective mass and two-level quantum systems. Using the variational method, the binding energies and the wave functions of the 1s-like y 2pz-like states for different positions of the impurity inside the CQD were found. It was found that the binding energy is greatest in the center of the CQD and diminishes as the impurity moves radially and/or axially. The optical rectification, the change in the refractive index, and the optical absorption were studied as functions of the energy of a photon incident on the CQD and different intensities of the magnetic field, with an impurity located at various positions. It was found that in a CDQ with an impurity inside, the effect of the variation of the intensity of the magnetic field on the optical response is much less than the effect produced by the variation of the position of the impurity. The physical reason for this behavior is that in nanostructures with impurities the Coulomb confinement is stronger than the magnetic confinement. It was also found that when the impurity is in the center of the quantum dot, the optical rectification coefficient is zero, due to the symmetry that the wave function of the impurity exhibits at this geometric point. When the impurity moves in the axial direction, the symmetry is broken and the optical rectification coefficient is different from zero, and its value increases as the impurity moves away from the center of the CQD.
Solar Activity Predictions Based on Solar Dynamo Theories
Schatten, Kenneth H.
2009-05-01
We review solar activity prediction methods, statistical, precursor, and recently the Dikpati and the Choudhury groups’ use of numerical flux-dynamo methods. Outlining various methods, we compare precursor techniques with weather forecasting. Precursors involve events prior to a solar cycle. First started by the Russian geomagnetician Ohl, and then Brown and Williams; the Earth's field variations near solar minimum was used to predict the next solar cycle, with a correlation of 0.95. From the standpoint of causality, as well as energetically, these relationships were somewhat bizarre. One index used was the "number of anomalous quiet days,” an antiquated, subjective index. Scientific progress cannot be made without some suspension of disbelief; otherwise old paradigms become tautologies. So, with youthful naïveté, Svalgaard, Scherrer, Wilcox and I viewed the results through rose-colored glasses and pressed ahead searching for understanding. We eventually fumbled our way to explaining how the Sun could broadcast the state of its internal dynamo to Earth. We noted one key aspect of the Babcock-Leighton Flux Dynamo theory: the polar field at the end of a cycle serves as a seed for the next cycle's growth. Near solar minimum this field usually bathes the Earth, and thereby affects geomagnetic indices then. We found support by examining 8 previous solar cycles. Using our solar precursor technique we successfully predicted cycles 21, 22 and 23 using WSO and MWSO data. Pesnell and I improved the method using a SODA (SOlar Dynamo Amplitude) Index. In 2005, nearing cycle 23's minimum, Svalgaard and I noted an unusually weak polar field, and forecasted a small cycle 24. We discuss future advances: the flux-dynamo methods. As far as future solar activity, I shall let the Sun decide; it will do so anyhow.
Effects of a radially varying electrical conductivity on 3D numerical dynamos
Gomez-Perez, Natalia; Wicht, Johannes; 10.1016/j.pepi.2010.03.006
2010-01-01
The transition from liquid metal to silicate rock in the cores of the terrestrial planets is likely to be accompanied by a gradient in the composition of the outer core liquid. The electrical conductivity of a volatile enriched liquid alloy can be substantially lower than a light-element-depleted fluid found close to the inner core boundary. In this paper, we investigate the effect of radially variable electrical conductivity on planetary dynamo action using an electrical conductivity that decreases exponentially as a function of radius. We find that numerical solutions with continuous, radially outward decreasing electrical conductivity profiles result in strongly modified flow and magnetic field dynamics, compared to solutions with homogeneous electrical conductivity. The force balances at the top of the simulated fluid determine the overall character of the flow. The relationship between Coriolis and Lorentz forces near the outer boundary controls the flow and magnetic field intensity and morphology of the...
Influence of a coronal envelope as a free boundary to global convective dynamo simulations
Warnecke, Jörn; Käpylä, Maarit J; Brandenburg, Axel
2015-01-01
We explore the effects of an outer stably stratified coronal envelope on rotating turbulent convection, differential rotation, and large-scale dynamo action in spherical wedge models of the Sun. We solve the compressible magnetohydrodynamic equations in a two-layer model with unstable stratification below the surface, representing the convection zone, and a stably stratified outer layer, the coronal envelope. The interface emulates essentially a free surface. We compare with models that have no coronal envelope. The presence of a coronal envelope is found to modify the Reynolds stress and the $\\Lambda$-effect resulting in a weaker and non-cylindrical differential rotation. This is related to the reduced latitudinal temperature variations, which are caused by and dependent on the Coriolis force. Some simulations develop a rudimentary near-surface shear layer, which we can relate to a sign change of the meridional Reynolds stress term in the thermal wind balance equation. Furthermore, the presence of a free sur...
Evidence for a dynamo in the main group pallasite parent body.
Tarduno, John A; Cottrell, Rory D; Nimmo, Francis; Hopkins, Julianna; Voronov, Julia; Erickson, Austen; Blackman, Eric; Scott, Edward R D; McKinley, Robert
2012-11-16
Understanding the origin of pallasites, stony-iron meteorites made mainly of olivine crystals and FeNi metal, has been a vexing problem since their discovery. Here, we show that pallasite olivines host minute magnetic inclusions that have favorable magnetic recording properties. Our paleointensity measurements indicate strong paleomagnetic fields, suggesting dynamo action in the pallasite parent body. We use these data and thermal modeling to suggest that some pallasites formed when liquid FeNi from the core of an impactor was injected as dikes into the shallow mantle of a ~200-kilometer-radius protoplanet. The protoplanet remained intact for at least several tens of millions of years after the olivine-metal mixing event.
Energy Technology Data Exchange (ETDEWEB)
Raphaldini, Breno; Raupp, Carlos F. M., E-mail: brenorfs@gmail.com, E-mail: carlos.raupp@iag.usp.br [Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Departamento de Geofísica, Rua do Matão, 1226-Cidade Universitária São Paulo-SP 05508-090 (Brazil)
2015-01-20
The solar dynamo is known to be associated with several periodicities, with the nearly 11/22 yr cycle being the most pronounced one. Even though these quasiperiodic variations of solar activity have been attributed to the underlying dynamo action in the Sun's interior, a fundamental theoretical description of these cycles is still elusive. Here, we present a new possible direction in understanding the Sun's cycles based on resonant nonlinear interactions among magnetohydrodynamic (MHD) Rossby waves. The WKB theory for dispersive waves is applied to magnetohydrodynamic shallow-water equations describing the dynamics of the solar tachocline, and the reduced dynamics of a resonant triad composed of MHD Rossby waves embedded in constant toroidal magnetic field is analyzed. In the conservative case, the wave amplitudes evolve periodically in time, with periods on the order of the dominant solar activity timescale (∼11 yr). In addition, the presence of linear forcings representative of either convection or instabilities of meridionally varying background states appears to be crucial in balancing dissipation and thus sustaining the periodic oscillations of wave amplitudes associated with resonant triad interactions. Examination of the linear theory of MHD Rossby waves embedded in a latitudinally varying mean flow demonstrates that MHD Rossby waves propagate toward the equator in a waveguide from –35° to 35° in latitude, showing a remarkable resemblance to the structure of the butterfly diagram of the solar activity. Therefore, we argue that resonant nonlinear magnetohydrodynamic Rossby wave interactions might significantly contribute to the observed cycles of magnetic solar activity.
Recent Progress in Understanding the Sun's Magnetic Dynamo
Hathaway, David. H.
2004-01-01
100 years ago we thought that the Sun and stars shone as a result of slow gravitational contraction over a few tens of millions of years - putting astronomers at odds with geologists who claimed that the Earth was much, much older. That mystery was solved in the 1920s and 30s with the discovery of nuclear energy (proving that the geologists had it right all along). Other scientific mysteries concerning the Sun have come and gone but three major mysteries remain: 1) How does the Sun produce sunspots with an 11-year cycle? 2) What produces the huge explosions that result in solar flares, prominence eruptions, and coronal mass ejections? and 3) Why is the Sun's outer atmosphere, the corona, so darned hot? Recent progress in solar astronomy reveals a single key to understanding all three of these mysteries.The 11-year time scale for the sunspot cycle indicates the presence of a magnetic dynamo within the Sun. For decades this dynamo was though to operate within the Sun's convection zone - the outmost 30% of the Sun where convective currents transport heat and advect magnetic lines of force. The two leading theories for the dynamo had very different models for the dynamics of the convection zone. Actual measurements of the dynamics using the techniques of helioseismology showed that both of these models had to be wrong some 20 years ago. A thin layer of strongly sheared flow at the base of the convection zone (now called the tachocline) was then taken to be the seat of the dynamo. Over the last 10 years it has become apparent that a weak meridional circulation within the convection zone also plays a key role in the dynamo. This meridional circulation has plasma rising up from the tachocline in the equatorial regions, spreading out toward the poles at a top speed of about 10-20 m/s at the surface, sinking back down to the tachocline in the polar regions, and then flowing back toward the equator at a top speed of about 1-2 m/s in the tachocline itself. Recent dynamo
Recent Progress in Understanding the Sun's Magnetic Dynamo
Hathaway, David. H.
2004-01-01
100 years ago we thought that the Sun and stars shone as a result of slow gravitational contraction over a few tens of millions of years - putting astronomers at odds with geologists who claimed that the Earth was much, much older. That mystery was solved in the 1920s and 30s with the discovery of nuclear energy (proving that the geologists had it right all along). Other scientific mysteries concerning the Sun have come and gone but three major mysteries remain: 1) How does the Sun produce sunspots with an 11-year cycle? 2) What produces the huge explosions that result in solar flares, prominence eruptions, and coronal mass ejections? and 3) Why is the Sun's outer atmosphere, the corona, so darned hot? Recent progress in solar astronomy reveals a single key to understanding all three of these mysteries.The 11-year time scale for the sunspot cycle indicates the presence of a magnetic dynamo within the Sun. For decades this dynamo was though to operate within the Sun's convection zone - the outmost 30% of the Sun where convective currents transport heat and advect magnetic lines of force. The two leading theories for the dynamo had very different models for the dynamics of the convection zone. Actual measurements of the dynamics using the techniques of helioseismology showed that both of these models had to be wrong some 20 years ago. A thin layer of strongly sheared flow at the base of the convection zone (now called the tachocline) was then taken to be the seat of the dynamo. Over the last 10 years it has become apparent that a weak meridional circulation within the convection zone also plays a key role in the dynamo. This meridional circulation has plasma rising up from the tachocline in the equatorial regions, spreading out toward the poles at a top speed of about 10-20 m/s at the surface, sinking back down to the tachocline in the polar regions, and then flowing back toward the equator at a top speed of about 1-2 m/s in the tachocline itself. Recent dynamo
Convection-driven spherical shell dynamos at varying Prandtl numbers
Käpylä, P J; Olspert, N; Warnecke, J; Brandenburg, A
2016-01-01
(abidged) Context: Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims: We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods: We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers. Results: We find that the rotation profiles for high thermal diffusivity show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased. This coincides with a change in the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the cyclic solutions disappear at the highest magnetic Reynolds numbers. The total magnetic energy ...
Magnetic helicity in stellar dynamos new numerical experiments
Brandenburg, A; Subramanian, K
2002-01-01
The theory of large scale dynamos is reviewed with particular emphasis on the problem of magnetic helicity conservation in the presence of closed and open boundaries. It is concluded that in solar and stellar large scale dynamos the production and destruction of magnetic helicity during one cycle may still be accomplished by ordinary Spitzer resistivity. This is mainly because of geometric effects causing significant magnetic helicity cancellation on each hemisphere, but also partly because the generation of toroidal field by shear does not involve the production of magnetic helicity. A number of alternatives are discussed and dismissed. These include open boundaries which lead to preferential loss of large scale magnetic helicity together with large scale magnetic fields. It is also shown that artificially induced losses of small scale field do not accelerate the production of large scale (poloidal) field. In fact, resistively limited evolution towards saturation is also found at intermediate scales before t...
Emission of Gravitational Waves from a Magnetohydrodynamic Dynamo
Winterberg, Friedwardt
2015-01-01
The failure of the laser-interferometer gravitational wave antennas to measure the tiny changes of lengths many orders of magnitude smaller than the diameter of a proton raises the question of whether the reason for this failure is a large gravitational wave background noise, and if so, where this background noise is coming from. It is conjectured that it comes from gravitational waves emitted from a magnetohydrodynamic dynamo in the center of the sun, with the large magnetic field from this dynamo shielded by thermomagnetic currents in the tachocline. Using the moon as a large Weber bar, these gravitational waves could possibly be detected by the Poisson diffraction into the center of the lunar shadow during a total solar eclipse.
The small-scale turbulent dynamo in smoothed particle magnetohydrodynamics
Tricco, Terrence S; Federrath, Christoph
2016-01-01
Supersonic turbulence is believed to be at the heart of star formation. We have performed smoothed particle magnetohydrodynamics (SPMHD) simulations of the small-scale dynamo amplification of magnetic fields in supersonic turbulence. The calculations use isothermal gas driven at rms velocity of Mach 10 so that conditions are representative of star-forming molecular clouds in the Milky Way. The growth of magnetic energy is followed for 10 orders in magnitude until it reaches saturation, a few percent of the kinetic energy. The results of our dynamo calculations are compared with results from grid-based methods, finding excellent agreement on their statistics and their qualitative behaviour. The simulations utilise the latest algorithmic developments we have developed, in particular, a new divergence cleaning approach to maintain the solenoidal constraint on the magnetic field and a method to reduce the numerical dissipation of the magnetic shock capturing scheme. We demonstrate that our divergence cleaning met...
Stellar dynamo models with prominent surface toroidal fields
Bonanno, Alfio
2016-01-01
Recent spectro-polarimetric observations of solar-type stars have shown the presence of photospheric magnetic fields with a predominant toroidal component. If the external field is assumed to be current-free it is impossible to explain these observations within the framework of standard mean-field dynamo theory. In this work it will be shown that if the coronal field of these stars is assumed to be harmonic, the underlying stellar dynamo mechanism can support photospheric magnetic fields with a prominent toroidal component even in the presence of axisymmetric magnetic topologies. In particular it is argued that the observed increase in the toroidal energy in low mass fast rotating stars can be naturally explained with an underlying $\\alpha\\Omega$ mechanism.
Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers.
Iskakov, A B; Schekochihin, A A; Cowley, S C; McWilliams, J C; Proctor, M R E
2007-05-18
Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>1 and small magnetic Prandtl number Pmdynamo on the hydrodynamic Reynolds number Re is obtained for 1 less than or similar Re less than or similar 6700. In the limit Pmdynamo at large and moderate Prandtl numbers: Rmc less than or similar 200 for Re greater than or similar 6000 compared to Rmc approximately 60 for Pm>or=1. It is not yet possible to determine numerically whether the growth rate of the magnetic energy is proportional, Rm1/2 in the limit Rm-->infinity, as it should be if the dynamo is driven by the inertial-range motions at the resistive scale.
Stellar Dynamo Models with Prominent Surface Toroidal Fields
Bonanno, Alfio
2016-12-01
Recent spectro-polarimetric observations of solar-type stars have shown the presence of photospheric magnetic fields with a predominant toroidal component. If the external field is assumed to be current-free it is impossible to explain these observations within the framework of standard mean-field dynamo theory. In this work, it will be shown that if the coronal field of these stars is assumed to be harmonic, the underlying stellar dynamo mechanism can support photospheric magnetic fields with a prominent toroidal component even in the presence of axisymmetric magnetic topologies. In particular, it is argued that the observed increase in the toroidal energy in low-mass fast-rotating stars can be naturally explained with an underlying αΩ mechanism.
Smoothed Particle Magnetohydrodynamics Simulations of Protostellar Jets and Turbulent Dynamos
Tricco, Terrence S; Federrath, Christoph; Bate, Matthew R
2013-01-01
We presents results from Smoothed Particle Magnetohydrodynamics simulations of collapsing molecular cloud cores, and dynamo amplification of the magnetic field in the presence of Mach 10 magnetised turbulence. Our star formation simulations have produced, for the first time ever, highly collimated magnetised protostellar jets from the first hydrostatic core phase. Up to 40% of the initial core mass may be ejected through this outflow. The primary difficulty in performing these simulations is maintaining the divergence free constraint of the magnetic field, and to address this issue, we have developed a new divergence cleaning method which has allowed us to stably follow the evolution of these protostellar jets for long periods. The simulations performed of supersonic MHD turbulence are able to exponentially amplify magnetic energy by up to 10 orders of magnitude via turbulent dynamo. To reduce numerical dissipation, a new shock detection algorithm is utilised which is able to track magnetic shocks throughout ...
Dynamo magnetic-field generation in turbulent accretion disks
Stepinski, T. F.
1991-01-01
Magnetic fields can play important roles in the dynamics and evolution of accretion disks. The presence of strong differential rotation and vertical density gradients in turbulent disks allows the alpha-omega dynamo mechanism to offset the turbulent dissipation and maintain strong magnetic fields. It is found that MHD dynamo magnetic-field normal modes in an accretion disk are highly localized to restricted regions of a disk. Implications for the character of real, dynamically constrained magnetic fields in accretion disks are discussed. The magnetic stress due to the mean magnetic field is found to be of the order of a viscous stress. The dominant stress, however, is likely to come from small-scale fluctuating magnetic fields. These fields may also give rise to energetic flares above the disk surface, providing a possible explanation for the highly variable hard X-ray emission from objects like Cyg X-l.
BigTable, Dynamo & Cassandra – A Review
Directory of Open Access Journals (Sweden)
Kala Karun A,
2013-01-01
Full Text Available The main aspect of NoSQL data stores is “shared nothing” horizontal scaling, which enables them to support a large number of simple read/write operations per second. Most of the NoSQL data stores generally do not provide strict ACID properties. The idea is that by giving up strict ACID constraints high performance and scalability can be achieved. The objective of this paper is to study and compare the features of the most popular NoSQL data stores like Bigtable (used in Google, Dynamo (used in Amazon and Cassandra (used in Facebook. The significance of these data stores is that most of the NoSQL data stores available today are developed using the concepts put forwarded by Bigtable and Dynamo. They can be considered as the foundation stones of today’s NoSQL data stores.
Maximizing Science Return: A Representative Trajectory for Dynamo
Lyons, Daniel T.
1999-01-01
This presentation discusses a possible Dynamo Orbit for a future Mars global surveyor. The goal of the proposed orbit is to allow for the greatest amount of mapping of the Martian surface during the mission. The presentation discusses the dynamic pressure, periapsis altitude, the Apoapsis Altitude, the aerodynamic heating rate,and the change in velocity during the aerobraking phase of the orbit and the orbital insertion.
Constraining Substellar Magnetic Dynamos using Auroral Radio Emission
Kao, Melodie; Hallinan, Gregg; Pineda, J. Sebastian; Escala, Ivanna; Burgasser, Adam J.; Stevenson, David J.
2017-01-01
An important outstanding problem in dynamo theory is understanding how magnetic fields are generated and sustained in fully convective stellar objects. A number of models for possible dynamo mechanisms in this regime have been proposed but constraining data on magnetic field strengths and topologies across a wide range of mass, age, rotation rate, and temperature are sorely lacking, particularly in the brown dwarf regime. Detections of highly circularly polarized pulsed radio emission provide our only window into magnetic field measurements for objects in the ultracool brown dwarf regime. However, these detections are very rare; previous radio surveys encompassing ˜60 L6 or later targets have yielded only one detection. We have developed a selection strategy for biasing survey targets based on possible optical and infrared tracers of auroral activity. Using our selection strategy, we previously observed six late L and T dwarfs with the Jansky Very Large Array (VLA) and detected the presence of highly circularly polarized radio emission for five targets. Our initial detections at 4-8 GHz provided the most robust constraints on dynamo theory in this regime, confirming magnetic fields >2.5 kG. To further develop our understanding of magnetic fields in the ultracool brown dwarf mass regime bridging planets and stars, we present constraints on surface magnetic field strengths for two Y-dwarfs as well as higher frequency observations of the previously detected L/T dwarfs corresponding ~3.6 kG fields. By carefully comparing magnetic field measurements derived from auroral radio emission to measurements derived from Zeeman broadening and Zeeman Doppler imaging, we provide tentative evidence that the dynamo operating in this mass regime may be inconsistent with predicted values from currently in vogue models. This suggests that parameters beyond convective flux may influence magnetic field generation in brown dwarfs.
Acceleration of Plasma Flows Due to Inverse Dynamo Mechanism
Mahajan, S M; Mikeladze, S V; Sigua, K I; Mahajan, Swadesh M.; Shatashvili, Nana L.; Mikeladze, Solomon V.; Sigua, Ketevan I.
2005-01-01
The "inverse-dynamo" mechanism - the amplification/generation of fast plasma flows by short scale (turbulent) magnetic fields via magneto-fluid coupling is recognized and explored. It is shown that large-scale magnetic fields and flows are generated simultaneously and proportionately from short scale fields and flows. The stronger the short-scale driver, the stronger are the large-scale products. Stellar and astrophysical applications are suggested.
On chaos synchronization of a complex two coupled dynamos system
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Gamal M. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)]. E-mail: gmahmoud@aun.edu.eg; Aly, Shaban A. [Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511 (Egypt)]. E-mail: shhalyl2@yahoo.com; Farghaly, Ahmed A. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)]. E-mail: ahmed_l_66@yahoo.com
2007-07-15
The main objective of this work is to investigate the chaotic behavior and chaos synchronization of a complex two coupled dynamos system subject to different initial conditions. This system exhibits a chaotic attractor which is found numerically. The global synchronization and active control techniques are used in this investigation. The feedback gain matrix and Lyapunov function are calculated and used to show that the linear error dynamical system is asymptotically stable. The analytical results are tested numerically and excellent agreement is found.
Simple Model of the (alpha)(omega) Dynamo: Self-Excited Spheromaks
Energy Technology Data Exchange (ETDEWEB)
Fowler, T K
2010-01-26
The astrophysical {alpha}{omega} dynamo converting angular momentum to magnetic energy can be interpreted as a self-excited Faraday dynamo together with magnetic relaxation coupling the dynamo poloidal field to the toroidal field produced by dynamo currents. Since both toroidal and poloidal fields are involved, the system can be modeled as helicity creation and transport, in a spheromak plasma configuration in quasi-equilibrium on the time scale of changes in magnetic energy. Neutral beams or plasma gun injection across field lines could create self-excited spheromaks in the laboratory.
Rotating convection-driven dynamos at low Ekman number.
Rotvig, Jon; Jones, Chris A
2002-11-01
We present a fully 3D self-consistent convection-driven dynamo model with reference to the geodynamo. A relatively low Ekman number regime is reached, with the aim of investigating the dynamical behavior at low viscosity. This regime is computationally very demanding, which has prompted us to adopt a plane layer model with an inclined rotation vector, and to make use of efficiently parallelized code. No hyperdiffusion is used, all diffusive operators are in the classical form. Our model has infinite Prandtl number, a Rayleigh number that scales as E(-1/3) (E being the Ekman number), and a constant Roberts number. The optimized model allows us to study dynamos with Ekman numbers in the range [10(-5),10(-4)]. In this regime we find strong-field dynamos where the induced magnetic fields satisfy Taylor's constraint to good accuracy. The solutions are characterized by (i) a MAC balance within the bulk, i.e., Coriolis, pressure, Lorentz, and buoyancy forces are of comparable magnitude, while viscous forces are only significant in thin boundary layers, (ii) the Elsasser number is O(10), (iii) the strong magnetic fields cannot prevent small-scale structures from becoming dominant over the large-scale components, (iv) the Taylor-Proudman effect is detectable, (v) the Taylorization decreases as the Ekman number is lowered, and (vi) the ageostrophic velocity component makes up 80% of the flow.
Large-scale-vortex dynamos in planar rotating convection
Guervilly, Céline; Jones, Chris A
2016-01-01
Several recent studies have demonstrated how large-scale vortices may arise spontaneously in rotating planar convection. Here we examine the dynamo properties of such flows in rotating Boussinesq convection. For moderate values of the magnetic Reynolds number ($100 \\lesssim Rm \\lesssim 550$, with $Rm$ based on the box depth and the convective velocity), a large-scale (i.e. system-size) magnetic field is generated. The amplitude of the magnetic energy oscillates in time, out of phase with the oscillating amplitude of the large-scale vortex. The dynamo mechanism relies on those components of the flow that have length scales lying between that of the large-scale vortex and the typical convective cell size; smaller-scale flows are not required. The large-scale vortex plays a crucial role in the magnetic induction despite being essentially two-dimensional. For larger magnetic Reynolds numbers, the dynamo is small scale, with a magnetic energy spectrum that peaks at the scale of the convective cells. In this case, ...
DYNAMO: A Dynamic Architectural Memory On-line
Directory of Open Access Journals (Sweden)
Ann Heylighen
2000-01-01
Full Text Available This paper describes the current status of DYNAMO, a web-based design assistant for students and professional designers in the field of architecture. The tool can be considered a Case-Based Design (CBD system in so far that it was inspired by the view of cognition underlying CBD. The paper points out how DYNAMO incorporates this view, and at the same time extrapolates it beyond the individual. In this way, the tool attempts to embrace and profit from several kinds of interaction that are crucial for the development and renewal of design knowledge. This should result in a design tool that both feels cognitively comfortable to (student- designers, and offers them a platform for exchanging knowledge and insights with colleagues in different contexts and at different levels of experience. In addition, the paper describes the implementation of these theoretical ideas as a working prototype, which has recently been tested by 4th year design students. Finally, DYNAMO is situated in the context of other comparable tools that have been or are being developed in the field of architectural design.
The Small-Scale Dynamo at Low Magnetic Prandtl Numbers
Schober, Jennifer; Bovino, Stefano; Klessen, Ralf S
2012-01-01
The present-day Universe is highly magnetized, even though the first magnetic seed fields were most probably extremely weak. To explain the growth of the magnetic field strength over many orders of magnitude fast amplification processes need to operate. The most efficient mechanism known today is the small-scale dynamo, which converts turbulent kinetic energy into magnetic energy leading to an exponential growth of the magnetic field. The efficiency of the dynamo depends on the type of turbulence indicated by the slope of the turbulence spectrum v(l) \\propto l^{theta}, where v(l) is the eddy velocity at a scale l. We explore turbulent spectra ranging from incompressible Kolmogorov turbulence with theta = 1/3 to highly compressible Burgers turbulence with theta = 1/2. In this work we analyze the properties of the small-scale dynamo for low magnetic Prandtl numbers Pm, which denotes the ratio of the magnetic Reynolds number, Rm, to the hydrodynamical one, Re. We solve the Kazantsev equation, which describes the...
Some consequences of shear on galactic dynamos with helicity fluxes
Zhou, Hongzhe; Blackman, Eric G.
2017-08-01
Galactic dynamo models sustained by supernova (SN) driven turbulence and differential rotation have revealed that the sustenance of large-scale fields requires a flux of small-scale magnetic helicity to be viable. Here we generalize a minimalist analytic version of such galactic dynamos to explore some heretofore unincluded contributions from shear on the total turbulent energy and turbulent correlation time, with the helicity fluxes maintained by either winds, diffusion or magnetic buoyancy. We construct an analytic framework for modelling the turbulent energy and correlation time as a function of SN rate and shear. We compare our prescription with previous approaches that include only rotation. The solutions depend separately on the rotation period and the eddy turnover time and not just on their ratio (the Rossby number). We consider models in which these two time-scales are allowed to be independent and also a case in which they are mutually dependent on radius when a radial-dependent SN rate model is invoked. For the case of a fixed rotation period (or a fixed radius), we show that the influence of shear is dramatic for low Rossby numbers, reducing the correlation time of the turbulence, which, in turn, strongly reduces the saturation value of the dynamo compared to the case when the shear is ignored. We also show that even in the absence of winds or diffusive fluxes, magnetic buoyancy may be able to sustain sufficient helicity fluxes to avoid quenching.
Performance benchmarks for a next generation numerical dynamo model
Matsui, Hiroaki; Heien, Eric; Aubert, Julien; Aurnou, Jonathan M.; Avery, Margaret; Brown, Ben; Buffett, Bruce A.; Busse, Friedrich; Christensen, Ulrich R.; Davies, Christopher J.; Featherstone, Nicholas; Gastine, Thomas; Glatzmaier, Gary A.; Gubbins, David; Guermond, Jean-Luc; Hayashi, Yoshi-Yuki; Hollerbach, Rainer; Hwang, Lorraine J.; Jackson, Andrew; Jones, Chris A.; Jiang, Weiyuan; Kellogg, Louise H.; Kuang, Weijia; Landeau, Maylis; Marti, Philippe; Olson, Peter; Ribeiro, Adolfo; Sasaki, Youhei; Schaeffer, Nathanaël.; Simitev, Radostin D.; Sheyko, Andrey; Silva, Luis; Stanley, Sabine; Takahashi, Futoshi; Takehiro, Shin-ichi; Wicht, Johannes; Willis, Ashley P.
2016-05-01
Numerical simulations of the geodynamo have successfully represented many observable characteristics of the geomagnetic field, yielding insight into the fundamental processes that generate magnetic fields in the Earth's core. Because of limited spatial resolution, however, the diffusivities in numerical dynamo models are much larger than those in the Earth's core, and consequently, questions remain about how realistic these models are. The typical strategy used to address this issue has been to continue to increase the resolution of these quasi-laminar models with increasing computational resources, thus pushing them toward more realistic parameter regimes. We assess which methods are most promising for the next generation of supercomputers, which will offer access to O(106) processor cores for large problems. Here we report performance and accuracy benchmarks from 15 dynamo codes that employ a range of numerical and parallelization methods. Computational performance is assessed on the basis of weak and strong scaling behavior up to 16,384 processor cores. Extrapolations of our weak-scaling results indicate that dynamo codes that employ two-dimensional or three-dimensional domain decompositions can perform efficiently on up to ˜106 processor cores, paving the way for more realistic simulations in the next model generation.
Institute of Scientific and Technical Information of China (English)
王志仁; 吴德星; 陈大可; 吴辉碇; 宋学家; 张占海
2002-01-01
研究了气候海洋与大气的临界时间跨度及其非线性作用的大致结构.与预报的空间分辩率及系统的非线性强度相联系,气候大气和海洋的临界时间跨度可反映系统可预报的相对时间尺度.对于具有同样空间特征尺度的大气和海洋,海洋的最小临界时间跨度约是大气的9倍(可达数日至数十日).一般(外源变化缓慢的)气候海洋与大气的一阶非线性越强,其临界时间跨度越小.气候海洋与大气非线性作用的大致结构是:通常与科里奥利力对流体运动的规范作用(如地转运动)有关,非线性作用随纬度增加而减弱.距平流场的切变结构及其沿经向与纬向上强度的比较直接改变气候大气和海洋的非线性作用(比如,向东的距平环流强度与经向环流强度相当时,非线性作用最强),较强的外部驱动(风应力和压强梯度力)使非线性作用加大等等.%This paper studies the critical time span and the approximate nonlinear action structure of climatic atmosphere and ocean. The critical time span of the climatic atmosphere and ocean, which is related to the spatial resolution required, the strength of nonlinear action, and the calculation exactness, may represent the relative temporal scale of predictability. As far as the same characteristic spatial scale is concerned, the minimum critical time span of the ocean is about 9 times of that of atmosphere, several days or more. Usually,the stronger the nonlinear action, the shorter the critical time span with smooth changes of external forces.The approximate structure of nonlinear action of climatic atmosphere and ocean is: the nonlinear action decreases usually with increasing latitude, which is related to the role of the Coriolis force in fluid motion (forming geostrophic current); the nonlinear action changes with the anomalous cyclonic or anticyclonic circulation shear, for instance, when the strength of anomalous eastward zonal circulation
Fast magnetic and electric dynamos in flat Klein bottle plasma flows
de Andrade, L C Garcia
2009-01-01
Recently Shukurov et al [Phys Rev \\textbf{E} (2008)] presented a numerical solution of a Moebius strip dynamo flow, to investigate its use in modelling dynamo flows in Perm torus of liquid sodium dynamo experiments. Here, by analogy one presents an electric dynamo on a twisted torus or Klein bottle topology. An exact solution in the form of flat Klein bottle dynamo flow is obtained. It is shown that even in the absence of magnetic dynamos initial electric fields can be amplified in distinct points of the Klein bottle. In this case diffusion is taken as ${\\eta}\\approx{5.0{\\times}10^{-3}{\\Omega}-m}$ the electric potential is obtained. The difference of electric fields at the beginning of plasma flow profile is ${\\Delta}E_{Dyn}\\approx{468\\frac{V}{m}}$, which is stronger than the electric dynamo field obtained in the magnetic axis of spheromaks, which is of the order of $E_{Dyn}\\approx{200\\frac{V}{m}}$. The potential of the dynamo at the surface of the Earth computed by Boozer [Phys Fluids \\textbf{B} (1993)] of $...
Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment
Kenjereš, S.; Hanjalić, K.; Renaudier, S.; Stefani, F.; Gerbeth, G.; Gailitis, A.
2006-01-01
Magnetic fields of planets, stars, and galaxies result from self-excitation in moving electroconducting fluids, also known as the dynamo effect. This phenomenon was recently experimentally confirmed in the Riga dynamo experiment [ A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000) ; A. Gailitis et
Observations of non-solar-type dynamo processes in stars with shallow convective zones
Jeffers, S.V.; Donati, J.F.; Alecian, E.; Marsden, S.C.
2010-01-01
The magnetic field topology and differential rotation are fundamental signatures of the dynamo processes that generate the magnetic activity observed in the Sun and solar-type stars. To investigate how these dynamo processes evolve in stars with shallow convective zones, we present high-resolution s
Reuter, K.; Jenko, F.; Forest, C. B.; Bayliss, R. A.
2008-08-01
A parallel implementation of a nonlinear pseudo-spectral MHD code for the simulation of turbulent dynamos in spherical geometry is reported. It employs a dual domain decomposition technique in both real and spectral space. It is shown that this method shows nearly ideal scaling going up to 128 CPUs on Beowulf-type clusters with fast interconnect. Furthermore, the potential of exploiting single precision arithmetic on standard x86 processors is examined. It is pointed out that the MHD code thereby achieves a maximum speedup of 1.7, whereas the validity of the computations is still granted. The combination of both measures will allow for the direct numerical simulation of highly turbulent cases ( 1500
Role of large-scale velocity fluctuations in a two-vortex kinematic dynamo.
Kaplan, E J; Brown, B P; Rahbarnia, K; Forest, C B
2012-06-01
This paper presents an analysis of the Dudley-James two-vortex flow, which inspired several laboratory-scale liquid-metal experiments, in order to better demonstrate its relation to astrophysical dynamos. A coordinate transformation splits the flow into components that are axisymmetric and nonaxisymmetric relative to the induced magnetic dipole moment. The reformulation gives the flow the same dynamo ingredients as are present in more complicated convection-driven dynamo simulations. These ingredients are currents driven by the mean flow and currents driven by correlations between fluctuations in the flow and fluctuations in the magnetic field. The simple model allows us to isolate the dynamics of the growing eigenvector and trace them back to individual three-wave couplings between the magnetic field and the flow. This simple model demonstrates the necessity of poloidal advection in sustaining the dynamo and points to the effect of large-scale flow fluctuations in exciting a dynamo magnetic field.
Magnetic energy cascade in spherical geometry: I. The stellar convective dynamo case
Strugarek, A; Mathis, S; Sarazin, Y
2013-01-01
We present a method to characterize the spectral transfers of magnetic energy between scales in simulations of stellar convective dynamos. The full triadic transfer functions are computed thanks to analytical coupling relations of spherical harmonics based on the Clebsch-Gordan coefficients. The method is applied to mean field $\\alpha\\Omega$ dynamo models as benchmark tests. From the physical standpoint, the decomposition of the dynamo field into primary and secondary dynamo families proves very instructive in the $\\alpha\\Omega$ case. The same method is then applied to a fully turbulent dynamo in a solar convection zone, modeled with the 3D MHD ASH code. The initial growth of the magnetic energy spectrum is shown to be non-local. It mainly reproduces the kinetic energy spectrum of convection at intermediate scales. During the saturation phase, two kinds of direct magnetic energy cascades are observed in regions encompassing the smallest scales involved in the simulation. The first cascade is obtained through ...
The metastable dynamo model of stellar rotational evolution
Energy Technology Data Exchange (ETDEWEB)
Brown, Timothy M., E-mail: tbrown@lcogt.net [Las Cumbres Observatory Global Telescope Network, 6740 Cortona Drive, Suite 102, Goleta, CA 93117 (United States)
2014-07-10
This paper introduces a new empirical model for the rotational evolution of Sun-like stars—those with surface convection zones and non-convective interior regions. Previous models do not match the morphology of observed (rotation period)-color diagrams, notably the existence of a relatively long-lived 'C-sequence' of fast rotators first identified by Barnes. This failure motivates the Metastable Dynamo Model (MDM) described here. The MDM posits that stars are born with their magnetic dynamos operating in a mode that couples very weakly to the stellar wind, so their (initially very short) rotation periods at first change little with time. At some point, this mode spontaneously and randomly changes to a strongly coupled mode, the transition occurring with a mass-dependent lifetime that is of the order of 100 Myr. I show that with this assumption, one can obtain good fits to observations of young clusters, particularly for ages of 150-200 Myr. Previous models and the MDM both give qualitative agreement with the morphology of the slower-rotating 'I-sequence' stars, but none of them have been shown to accurately reproduce the stellar-mass-dependent evolution of the I-sequence stars, especially for clusters older than a few hundred million years. I discuss observational experiments that can test aspects of the MDM, and speculate that the physics underlying the MDM may be related to other situations described in the literature, in which stellar dynamos may have a multi-modal character.
New approach to scaling rules for stellar and planetary dynamos
Barrois, Bertrand
2016-01-01
Glorified dimensional analysis is used to derive scaling rules for internal and external magnetic field strengths and various time scales. Naive dimensional analysis is inconclusive because of multiple time scales, but physical arguments serve to weed out irrelevant parameters. Time scales can be derived from linearized instability analysis instead of ill-founded assumptions of Magnetic-Archimedean-Coriolis (MAC) balance. Further relationships can be derived from high-level models of coupled main field components and differential rotation. The ratios of the external dipole field to internal magnetic fields and of differential to overall rotation depend on details of the dynamo mechanism.
Using Jupiter's gravitational field to probe the Jovian convective dynamo.
Kong, Dali; Zhang, Keke; Schubert, Gerald
2016-03-23
Convective motion in the deep metallic hydrogen region of Jupiter is believed to generate its magnetic field, the strongest in the solar system. The amplitude, structure and depth of the convective motion are unknown. A promising way of probing the Jovian convective dynamo is to measure its effect on the external gravitational field, a task to be soon undertaken by the Juno spacecraft. We calculate the gravitational signature of non-axisymmetric convective motion in the Jovian metallic hydrogen region and show that with sufficiently accurate measurements it can reveal the nature of the deep convection.
The magnetic universe geophysical and astrophysical dynamo theory
Rüdiger, Günther
2004-01-01
Magnetism is one of the most pervasive features of the Universe, with planets, stars and entire galaxies all having associated magnetic fields. All of these fields are generated by the motion of electrically conducting fluids, the so-called dynamo effect. The precise details of what drives the motion, and indeed what the fluid consists of, differ widely though. In this work the authors draw upon their expertise in geophysical and astrophysical MHD to explore some of these phenomena, and describe the similarities and differences between different magnetized objects. They also explain why magn
Finite correlation time effects in kinematic dynamo problem
Energy Technology Data Exchange (ETDEWEB)
Schekochihin, A.A.; Kulsrud, R.M.
2000-02-11
One-point statistics of the magnetic fluctuations in kinematic regime with large Prandtl number and non delta-correlated in time advecting velocity field are studied. A perturbation expansion in the ratio of the velocity correlation time to the dynamo growth time is constructed in the spirit of the Kliatskin-Tatarskii functional method and carried out to first order. The convergence properties are improved compared to the commonly used van Kampen-Terwiel method. The zeroth-order growth rate of the magnetic energy is estimated to be reduced (in three dimensions) by approximately 40%. This reduction is quite close to existing numerical results.
MHD Dynamo phenomenon in our lab (Petrus Peregrinus Medal Lecture)
Gailitis, Agris
2016-04-01
Celestial objects generate magnetic field very like technical dynamo do. Field induces current in a moving electroconductor. The induced current amplifies magnetic field. At large enough product conductivity time's velocity time's size amplification exceeds losses and situation without magnetic field is impossible. Such scenario is obvious for technical dynamo made from insolated wire but not so for uniform conductor as in celestial bodies. Development of the idea took literally the entire 20th century. Discovery of sunspot magnetic fields at the century rise and laboratory verification at the very fall. At thirties Cowling noticed that geometrically simple shaped (axially symmetrical) field can't sustain itself. Process must be more complex, somehow spatially fragmented. At the middle of century Parker and Steenbeck saw such fragmentation in a turbulent structure of hydrodynamic flow. Shortly after his α-effect approach was made ready Steenbeck invited us to think on molten Na experiments for theory verification. The first idea was to push the Na flow through the hand-blown pipe maze. Similar industrial scale experiment after years and regardless of us was realized in Karlsruhe. Seeking for something cheaper we stopped at Ponomarenko idea - axially symmetric helical flow can't generate axi-simmetric field but it can generate azimuthally structured one. The mathematical model was modified to experimental conditions and numerically optimized. The Dynamo stand was built and it works. Even after optimization Dynamo stand exceeds usual size of hydraulic experiments. 2m3 of molten Na circulate there by means of propeller powered from 200kW motor. When circulation exceeds 0.6 m3/s (at 120°C) seemingly from nowhere appears magnetic field. Twisted field pattern slowly (about 1.5Hz) rotates round flow axis. Up to 0.1T field stay as long as stay circulation and temperature. When sodium is heated up or slowed down the field is slowly dying out. Phenomenon is much richer
Dynamo-generated magnetic fields in fast rotating single giants
Konstantinova-Antova, Renada; Schröder, Klaus-Peter; Petit, Pascal
2009-01-01
Red giants offer a good opportunity to study the interplay of magnetic fields and stellar evolution. Using the spectro-polarimeter NARVAL of the Telescope Bernard Lyot (TBL), Pic du Midi, France and the LSD technique, we began a survey of magnetic fields in single G-K-M giants. Early results include 6 MF-detections with fast rotating giants, and for the first time a magnetic field was detected directly in an evolved M-giant: EK Boo. Our results could be explained in the terms of $\\alpha$--$\\omega$ dynamo operating in these giants.
The Puzzling Dynamos of Stars: Recent Progress With Global Numerical Simulations
Strugarek, Antoine; Beaudoin, Patrice; Charbonneau, Paul; Brun, Allan S.
2017-10-01
The origin of magnetic cycles in the Sun and other cool stars is one of the great theoretical challenge in stellar astrophysics that still resists our understanding. Ab-initio numerical simulations are today required to explore the extreme turbulent regime in which stars operate and sustain their large-scale, cyclic magnetic field. We report in this work on recent progresses made with high performance numerical simulations of global turbulent convective envelopes. We rapidly review previous prominent results from numerical simulations, and present for the first time a series of turbulent, global simulations producing regular magnetic cycles whose period varies systematically with the convective envelope parameters (rotation rate, convective luminosity). We find that the fundamentally non-linear character of the dynamo simulated in this work leads the magnetic cycle period to be inversely proportional to the Rossby number. These results promote an original interpretation of stellar magnetic cycles, and could help reconcile the cyclic behaviour of the Sun and other solar-type stars.
Abdeldayem, Hossin A.; Sheng, Wen; Venkateswarlu, P.; Witherow, William K.; Frazier, Don O.; Chandra Sekhar, P.; George, M. C.; Kispert, Lowell; Wasielewski, Michael R.
1993-01-01
Quantitative measurements of the nonlinear refractive index coefficient n(2) and the third-order nonlinear susceptibility chi(3) for a solution of 7-prime,7-prime-dicyano-7-prime-apo-beta-carotene (DCAC) in hexane have been measured at different concentrations. The measurements have been performed by both the self-trapping and self-phase modulation techniques using a CW Ar(+) laser. The results show that DCAC has a relatively large nonlinearity, attributed to a thermal mechanism, with n(2) of the order of 10 exp 9 times that of CS2.
Can Core Flows inferred from Geomagnetic Field Models explain the Earth's Dynamo?
Schaeffer, Nathanaël; Pais, Maria Alexandra
2015-01-01
We test the ability of velocity fields inferred from geomagnetic secular variation data to produce the global magnetic field of the Earth. Our kinematic dynamo calculations use quasi-geostrophic (QG) flows inverted from geomagnetic field models which, as such, incorporate flow structures that are Earth-like and may be important for the geodynamo. Furthermore, the QG hypothesis allows straightforward prolongation of the flow from the core surface to the bulk. As expected from previous studies, we check that a simple quasi-geostrophic flow is not able to sustain the magnetic field against ohmic decay. Additional complexity is then introduced in the flow, inspired by the action of the Lorentz force. Indeed, on centenial timescales, the Lorentz force can balance the Coriolis force and strict quasi-geostrophy may not be the best ansatz. When the columnar flow is modified to account for the action of the Lorentz force, magnetic field is generated for Elsasser numbers larger than 0.25 and magnetic Reynolds numbers l...
Structure and variability of dynamo driven accretion discs
Energy Technology Data Exchange (ETDEWEB)
Pudritz, R.E. (Cambridge Univ. (UK). Inst. of Astronomy); Fahlman, G.G. (British Columbia Univ., Vancouver (Canada). Dept. of Geophysics and Astronomy)
1982-02-01
A turbulent dynamo operating in an accretion disc around a black hole can produce fields strong enough so that the Maxwell stress due to the fluctuations dominates. In this dynamo driven limit, enormous localized fluctuations can be expected because the Kepler flow energy density is efficiently tapped. The detailed radial structure of this model is calculated, which for Cyg X-1, predicts a cool (Tsub(max) approximately < 10/sup 8/ K), dense, thin (z/sub 0//r approximately < 10/sup -2/), and optically thick disc. A mean field B approximately < 10/sup 8/ G can be generated. Fluctuations of order b approximately 10/sup 12/ G at the inner accretion disc radius (rsub(*) approximately 1), falling to b approximately 10/sup 10/ G at rsub(*) approximately 30, provide an explanation for the Cyg X-1 millisecond bursts and shot noise in terms of flares on the disc surface. This is established by means of model independent, scaled reconnection experiments. The optical variability of 3C 273 could be explained as arising from flares on an accretion disc around a 10/sup 9/ solar masses black hole, with flare fields of b approximately 10/sup 7/ G at rsub(*) approximately 1.
Dynamos, Super-pulsars and Gamma-ray bursts
Rosswog, S; Rosswog, Stephan; Ramirez-Ruiz, Enrico
2003-01-01
The remnant of a neutron star binary coalescence is expected to be temporarily stabilised against gravitational collapse by its differential rotation. We explore the possibility of dynamo activity in this remnant and assess the potential for powering a short-duration gamma-ray burst (GRB). We analyse our three-dimensional hydrodynamic simulations of neutron star mergers with respect to the flow pattern inside the remnant. If the central, newly formed super-massive neutron star remains stable for a good fraction of a second an efficient low-Rossby number $\\alpha-\\Omega$-dynamo will amplify the initial seed magnetic fields exponentially. We expect that values close to equipartition field strength will be reached within several tens of milliseconds. Such a super-pulsar could power a GRB via a relativistic wind, with an associated spin-down time scale close to the typical duration of a short GRB. Similar mechanisms are expected to be operational in the surrounding torus formed from neutron star debris.
Dynamo tests for stratification below the core-mantle boundary
Olson, Peter; Landeau, Maylis; Reynolds, Evan
2017-10-01
Evidence from seismology, mineral physics, and core dynamics suggests a layer with an overall stable stratification in the Earth's outer core, possibly thermal in origin, extending below the core-mantle boundary (CMB) for several hundred kilometers. Yet vigorous deep mantle convection with locally elevated heat flux implies locally unstable thermal stratification below the CMB, consistent with interpretations of non-dipole geomagnetic field behavior that favor upwelling flows in places below the CMB. To resolve this apparent inconsistency, we investigate the structure of convection and magnetic fields in the core using numerical dynamos with laterally heterogeneous boundary heat flux. Strongly heterogeneous boundary heat flux generates localized convection beneath the CMB that coexists with an overall stable stratification there. Our partially stratified dynamos are distinguished by their time average magnetic field structures. Without stratification or with stratification confined to a thin layer, the octupole component is small and the CMB magnetic field structure includes polar intensity minima. With more extensive stratification, the octupole component is large and the magnetic field structure includes intense patches or high intensity lobes in the polar regions. Comparisons with the time-averaged geomagnetic field are generally favorable for partial stratification in a thin (<400 km) layer but unfavorable for stratification in a thick (∼1000 km) layer beneath the CMB.
A long-lived lunar dynamo driven by continuous mechanical stirring.
Dwyer, C A; Stevenson, D J; Nimmo, F
2011-11-09
Lunar rocks contain a record of an ancient magnetic field that seems to have persisted for more than 400 million years and which has been attributed to a lunar dynamo. Models of conventional dynamos driven by thermal or compositional convection have had difficulty reproducing the existence and apparently long duration of the lunar dynamo. Here we investigate an alternative mechanism of dynamo generation: continuous mechanical stirring arising from the differential motion, due to Earth-driven precession of the lunar spin axis, between the solid silicate mantle and the liquid core beneath. We show that the fluid motions and the power required to drive a dynamo operating continuously for more than one billion years and generating a magnetic field that had an intensity of more than one microtesla 4.2 billion years ago are readily obtained by mechanical stirring. The magnetic field is predicted to decrease with time and to shut off naturally when the Moon recedes far enough from Earth that the dissipated power is insufficient to drive a dynamo; in our nominal model, this occurred at about 48 Earth radii (2.7 billion years ago). Thus, lunar palaeomagnetic measurements may be able to constrain the poorly known early orbital evolution of the Moon. This mechanism may also be applicable to dynamos in other bodies, such as large asteroids.
IS THE SMALL-SCALE MAGNETIC FIELD CORRELATED WITH THE DYNAMO CYCLE?
Energy Technology Data Exchange (ETDEWEB)
Karak, Bidya Binay; Brandenburg, Axel, E-mail: bbkarak@nordita.org [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm (Sweden)
2016-01-01
The small-scale magnetic field is ubiquitous at the solar surface—even at high latitudes. From observations we know that this field is uncorrelated (or perhaps even weakly anticorrelated) with the global sunspot cycle. Our aim is to explore the origin, and particularly the cycle dependence, of such a phenomenon using three-dimensional dynamo simulations. We adopt a simple model of a turbulent dynamo in a shearing box driven by helically forced turbulence. Depending on the dynamo parameters, large-scale (global) and small-scale (local) dynamos can be excited independently in this model. Based on simulations in different parameter regimes, we find that, when only the large-scale dynamo is operating in the system, the small-scale magnetic field generated through shredding and tangling of the large-scale magnetic field is positively correlated with the global magnetic cycle. However, when both dynamos are operating, the small-scale field is produced from both the small-scale dynamo and the tangling of the large-scale field. In this situation, when the large-scale field is weaker than the equipartition value of the turbulence, the small-scale field is almost uncorrelated with the large-scale magnetic cycle. On the other hand, when the large-scale field is stronger than the equipartition value, we observe an anticorrelation between the small-scale field and the large-scale magnetic cycle. This anticorrelation can be interpreted as a suppression of the small-scale dynamo. Based on our studies we conclude that the observed small-scale magnetic field in the Sun is generated by the combined mechanisms of a small-scale dynamo and tangling of the large-scale field.
Kinematic α tensors and dynamo mechanisms in a von Kármán swirling flow.
Ravelet, F; Dubrulle, B; Daviaud, F; Ratié, P-A
2012-07-13
We provide experimental and numerical evidence of in-blades vortices in the von Kármán swirling flow. We estimate the associated kinematic α-effect tensor and show that it is compatible with recent models of the von Kármán sodium (VKS) dynamo. We further show that depending on the relative frequency of the two impellers, the dominant dynamo mechanism may switch from α2 to α - Ω dynamo. We discuss some implications of these results for VKS experiments.
Generation of a dynamo magnetic field in a protoplanetary accretion disk
Stepinski, T.; Levy, E. H.
1987-01-01
A new computational technique is developed that allows realistic calculations of dynamo magnetic field generation in disk geometries corresponding to protoplanetary and protostellar accretion disks. The approach is of sufficient generality to allow, in the future, a wide class of accretion disk problems to be solved. Here, basic modes of a disk dynamo are calculated. Spatially localized oscillatory states are found to occur in Keplerain disks. A physical interpretation is given that argues that spatially localized fields of the type found in these calculations constitute the basic modes of a Keplerian disk dynamo.
Generation of dynamo magnetic fields in protoplanetary and other astrophysical accretion disks
Stepinski, T. F.; Levy, E. H.
1988-01-01
A computational method for treating the generation of dynamo magnetic fields in astrophysical disks is presented. The numerical difficulty of handling the boundary condition at infinity in the cylindrical disk geometry is overcome by embedding the disk in a spherical computational space and matching the solutions to analytically tractable spherical functions in the surrounding space. The lowest lying dynamo normal modes for a 'thick' astrophysical disk are calculated. The generated modes found are all oscillatory and spatially localized. Tha potential implications of the results for the properties of dynamo magnetic fields in real astrophysical disks are discussed.
Generation of dynamo magnetic fields in protoplanetary and other astrophysical accretion disks
Energy Technology Data Exchange (ETDEWEB)
Stepinski, T.F.; Levy, E.H.
1988-08-01
A computational method for treating the generation of dynamo magnetic fields in astrophysical disks is presented. The numerical difficulty of handling the boundary condition at infinity in the cylindrical disk geometry is overcome by embedding the disk in a spherical computational space and matching the solutions to analytically tractable spherical functions in the surrounding space. The lowest lying dynamo normal modes for a thick astrophysical disk are calculated. The generated modes found are all oscillatory and spatially localized. Tha potential implications of the results for the properties of dynamo magnetic fields in real astrophysical disks are discussed. 30 references.
A large-scale dynamo and magnetoturbulence in rapidly rotating core-collapse supernovae.
Mösta, Philipp; Ott, Christian D; Radice, David; Roberts, Luke F; Schnetter, Erik; Haas, Roland
2015-12-17
Magnetohydrodynamic turbulence is important in many high-energy astrophysical systems, where instabilities can amplify the local magnetic field over very short timescales. Specifically, the magnetorotational instability and dynamo action have been suggested as a mechanism for the growth of magnetar-strength magnetic fields (of 10(15) gauss and above) and for powering the explosion of a rotating massive star. Such stars are candidate progenitors of type Ic-bl hypernovae, which make up all supernovae that are connected to long γ-ray bursts. The magnetorotational instability has been studied with local high-resolution shearing-box simulations in three dimensions, and with global two-dimensional simulations, but it is not known whether turbulence driven by this instability can result in the creation of a large-scale, ordered and dynamically relevant field. Here we report results from global, three-dimensional, general-relativistic magnetohydrodynamic turbulence simulations. We show that hydromagnetic turbulence in rapidly rotating protoneutron stars produces an inverse cascade of energy. We find a large-scale, ordered toroidal field that is consistent with the formation of bipolar magnetorotationally driven outflows. Our results demonstrate that rapidly rotating massive stars are plausible progenitors for both type Ic-bl supernovae and long γ-ray bursts, and provide a viable mechanism for the formation of magnetars. Moreover, our findings suggest that rapidly rotating massive stars might lie behind potentially magnetar-powered superluminous supernovae.
Magneto-Vortex Dynamo Model in Solar convection zone
Ershkov, Sergey V
2011-01-01
Here is presented a new magneto-vortex dynamo model for modeling & predicting of a processes in Solar plasma convection zone. Solar convection zone is located above the level r > 0,6-0,7 R, where R is a Solar radius. A key feature of such a model is that equation of Solar plasma motion as well as equation of magnetic fields evolution - are reduced to Helmholtz's vortex equation, which is up-graded in according with alpha-effect (Coriolis force forms an additional vorticity field or magnetic field due to Sun's differential rotation). Such an additional vorticity or magnetic field are proved to be concentrated at the proper belt in Solar convection zone under the influence of Coriolis force (at the middle latitudes of the Sun in respect to equator). Besides, such an an additional vorticity & magnetic fields are to be the basic sources of well-known phenomena "Maunder's butterfly" diagram.
A new simple dynamo model for stellar activity cycle
Yokoi, Nobumitsu; Pipin, Valery; Hamba, Fujihiro
2016-01-01
A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous mean flow effect on turbulence, it is shown that turbulent cross helicity (velocity--magnetic-field correlation) should enter the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. The inclusion of the cross-helicity effect makes the present model different from the current $\\alpha$--$\\Omega$-type models mainly in two points. First, in addition to the usual $\\alpha$ (helicity effect) and $\\beta$ (turbulent magnetic diffusivity), we consider the $\\gamma$ coefficient (cross-helicity effect). Second, unlike the $\\alpha$ and $\\beta$ coefficients, which are often treated as an adjustable parameter in the current studies, the spatiotemporal evolution of $\\gamma$ coefficient should be solved simultaneously with the mean magnetic-field equations. The basic scenario for the stellar activity cycle in the present model is as follows: In the presence of turbulent cross he...
Spherical convective dynamos in the rapidly rotating asymptotic regime
Aubert, Julien; Fournier, Alexandre
2016-01-01
Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state...
Solar Physics at Evergreen: Solar Dynamo and Chromospheric MHD
Zita, E. J.; Maxwell, J.; Song, N.; Dikpati, M.
2006-12-01
We describe our five year old solar physics research program at The Evergreen State College. Famed for its cloudy skies, the Pacific Northwest is an ideal location for theoretical and remote solar physics research activities. Why does the Sun's magnetic field flip polarity every 11 years or so? How does this contribute to the magnetic storms Earth experiences when the Sun's field reverses? Why is the temperature in the Sun's upper atmosphere millions of degrees higher than the Sun's surface temperature? How do magnetic waves transport energy in the Sun’s chromosphere and the Earth’s atmosphere? How does solar variability affect climate change? Faculty and undergraduates investigate questions such as these in collaboration with the High Altitude Observatory (HAO) at the National Center for Atmospheric Research (NCAR) in Boulder. We will describe successful student research projects, logistics of remote computing, and our current physics investigations into (1) the solar dynamo and (2) chromospheric magnetohydrodynamics.
Magnetorotational Turbulence and Dynamo in a Collisionless Plasma
Kunz, Matthew W; Quataert, Eliot
2016-01-01
We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model of a collisionless accretion disc. The kinetic magnetorotational instability grows from a subthermal magnetic field having zero net flux over the computational domain to generate self-sustained turbulence and outward angular-momentum transport. Significant Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabilities through particle trapping and pitch-angle scattering. The latter endow the plasma with an effective viscosity that is biased with respect to the magnetic-field direction and spatio-temporally variable. Energy spectra suggest an Alfv\\'en-wave cascade at large scales and a kinetic-Alfv\\'en-wave cascade at small scales, with strong small-scale density fluctuations and weak non-axisymmetric density waves. Ions undergo n...
Kinematic solar dynamo models with a deep meridional flow
Guerrero, G. A.; Muñoz, J. D.
2004-05-01
We develop two different solar dynamo models to verify the hypothesis that a deep meridional flow can restrict the appearance of sunspots below 45°, proposed recently by Nandy & Choudhuri. In the first one, a single polytropic approximation for the density profile was taken, for both radiative and convective zones. In the second one, that of Pinzon & Calvo-Mozo, two polytropes were used to distinguish between both zones. The magnetic buoyancy mechanism proposed by Dikpati & Charbonneau was chosen in both models. We have in fact obtained that a deep meridional flow pushes the maxima of toroidal magnetic field towards the solar equator, but, in contrast to Nandy & Choudhuri, a second zone of maximal fields remains at the poles. The second model, although closely resembling the solar standard model of Bahcall et al., gives solar cycles three times longer than observed.
Kinematic solar dynamo models with a deep meridional flow
Guerrero, G A
2004-01-01
We develop two different solar dynamo models to verify the hypothesis that a deep meridional flow can restrict the apperance of sunspots below 45 degrees, proposed by Nandy & Choudhuri (2002). In the first one, a single polytropic approximation for the density profile was taken, for both radiative and convective zones. In the second one, two polytropes were used to distinguish between both zones Pinzon & Calvo-Mozo (2001). The magnetic buoyancy mechanism proposed by Dikpati & Charbonneau (1999) was chosen in both models. We, actually, have obtained that a deep meridional flow pushes the maxima of toroidal magnetic field toward the solar equator, but in contrast to Nandy & Choudhuri (2002) a second zone of maximal fields remains at the poles. The second model, although closely resembling the solar standard model of Bahcall, Pinsonneault & Wasserbug (1995); Bahcall, Pinsonneault & Basu (2001), gives solar cyles three times longer than observed.
Characterizing the mean-field dynamo in turbulent accretion disks
Gressel, Oliver
2015-01-01
The formation and evolution of a wide class of astrophysical objects is governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step towards an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically-stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter as well as the amount of net-vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale depen...
Magnetic Helicity Reversals in a Cyclic Convective Dynamo
Miesch, Mark S; Augustson, Kyle C
2016-01-01
We investigate the role of magnetic helicity in promoting cyclic magnetic activity in a global, 3D, magnetohydrodynamic (MHD) simulation of a convective dynamo. This simulation is characterized by coherent bands of toroidal field that exist within the convection zone, with opposite polarities in the northern and southern hemispheres. Throughout most of the cycle, the magnetic helicity in these bands is negative in the northern hemisphere and positive in the southern hemisphere. However, during the declining phase of each cycle, this hemispheric rule reverses. We attribute this to a global restructuring of the magnetic topology that is induced by the interaction of the bands across the equator. This band interaction appears to be ultimately responsible for, or at least associated with, the decay and subsequent reversal of both the toroidal bands and the polar fields. We briefly discuss the implications of these results within the context of solar observations, which also show some potential evidence for toroid...
Cosmic ray driven dynamo in galactic disks. A parameter study
MichaÅHanasz,; Kowal, Grzegorz; Lesch, Harald
2008-01-01
We present a parameter study of the magnetohydrodynamical dynamo driven by cosmic rays in the interstellar medium (ISM) focusing on the efficiency of magnetic field amplification and the issue of energy equipartition between magnetic, kinetic and cosmic ray (CR) energies. We perform numerical CR-MHD simulations of the ISM using the extended version of ZEUS-3D code in the shearing box approximation and taking into account the presence of Ohmic resistivity, tidal forces and vertical disk gravity. CRs are supplied in randomly distributed supernova (SN) remnants and are described by the diffusion-advection equation, which incorporates an anisotropic diffusion tensor. The azimuthal magnetic flux and total magnetic energy are amplified depending on a particular choice of model parameters. We find that the most favorable conditions for magnetic field amplification correspond to magnetic diffusivity of the order of $3\\times 10^{25} \\cm^2\\s^{-1}$, SN rates close to those observed in the Milky Way, periodic SN activity...
Weak and Strong Field Dynamos: from the Earth to the stars
Morin, J; Schrinner, M; Donati, J -F
2011-01-01
Observations of magnetism in very low mass stars recently made important progress, revealing characteristics that are now to be understood in the framework of dynamo theory. In parallel, there is growing evidence that dynamo processes in these stars share many similarities with planetary dynamos. We investigate the extent to which the weak \\emph{vs} strong field bistability predicted for the geodynamo can apply to recent observations of two groups of very low mass fully-convective stars sharing similar stellar parameters but generating radically different types of magnetic fields. Our analysis is based on previously published spectropolarimetric and spectroscopic data. We argue that these can be interpreted in the framework of weak and strong field dynamos.
A new method for computing the eigenfunctions and their adjoints of the dynamo operator
Schrinner, M; Jiang, J; Hoyng, P
2009-01-01
We present a new method to determine the eigensolutions of the induction and the dynamo equation in a fluid embedded in vacuum. The magnetic field is expanded in a complete set of functions. The new method is based on the biorthogonality of the adjoint electric current and the vector potential with an inner product defined by a volume integral over the fluid domain. The advantage of this method is that the velocity and the dynamo coefficients of the induction and the dynamo equation do not have to be differentiated and thus even numerically determined tabulated values of the coefficients produce reasonable results. We provide test calculations and compare with published results obtained by the classical treatment based on the biorthogonality of the magnetic field and its adjoint. We especially consider dynamos with mean-field coefficients determined from direct numerical simulations of the geodynamo and compare with initial value calculations and the full MHD simulations.
Starspots, stellar cycles and stellar flares: Lessons from solar dynamo models
Choudhuri, Arnab Rai
2017-01-01
In this review, we discuss whether the present solar dynamo models can be extrapolated to explain various aspects of stellar activity. We begin with a summary of the following kinds of data for solar-like stars: (i) data pertaining to stellar cycles from Ca H/K emission over many years; (ii) X-ray data indicating hot coronal activity; (iii) starspot data (especially about giant polar spots); and (iv) data pertaining to stellar superflares. Then we describe the current status of solar dynamo modelling—giving an introduction to the flux transport dynamo model, the currently favoured model for the solar cycle. While an extrapolation of this model to solar-like stars can explain some aspects of observational data, some other aspects of the data still remain to be theoretically explained. It is not clear right now whether we need a different kind of dynamo mechanism for stars having giant starspots or producing very strong superflares.
A solar dynamo surface wave at the interface between convection and nonuniform rotation
Parker, E. N.
1993-01-01
A simple dynamo surface wave is presented to illustrate the basic principles of a dynamo operating in the thin layer of shear and suppressed eddy diffusion beneath the cyclonic convection in the convection zone of the sun. It is shown that the restriction of the shear delta(Omega)/delta(r) to a region below the convective zone provides the basic mode with a greatly reduced turbulent diffusion coefficient in the region of strong azimuthal field. The dynamo takes on the character of a surface wave tied to the lower surface z = 0 of the convective zone. There is a substantial body of evidence suggesting a fibril state for the principal flux bundles beneath the surface of the sun, with fundamental implications for the solar dynamo.
The DYNAMO Simulation Language--An Alternate Approach to Computer Science Education.
Bronson, Richard
1986-01-01
Suggests the use of computer simulation of continuous systems as a problem solving approach to computer languages. Outlines the procedures that the system dynamics approach employs in computer simulations. Explains the advantages of the special purpose language, DYNAMO. (ML)
CONTINUOUS DEPENDENCE ON VELOCITY FOR THE BACKWARD DYNAMO EQUATION ON AN EXTERIOR DOMAIN
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper we study solutions to a forward Dynamo equation depending continuously on the velocity on an exterior domain,using Logarithmic Convexity Methods.We obtain some more weaker conditions by introducing the unbounded domain.
Dynamo saturation in direct simulations of the multi-phase turbulent interstellar medium
Bendre, A; Elstner, D
2015-01-01
The ordered magnetic field observed via polarized synchrotron emission in nearby disc galaxies can be explained by a mean-field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical-flux initial conditions are potentially able to influence this dynamo via the occurrence of the magneto-rotational instability (MRI). We aim to study the influence of various initial field configurations on the saturated state of the mean-field dynamo. This is motivated by the observation that different saturation behavior was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three-dimensional local boxes of the vertically stratified, turbulent interstellar medium, employing shearing-periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth of the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with a...
Consequences of Giant Impacts on the Martian dynamo
Monteux, J.; Amit, H.; Arkani-Hamed, J.; Choblet, G.; Langlais, B.; Tobie, G.; Johnson, C. L.; Jellinek, M.
2015-12-01
The Martian surface exhibits a strong dichotomy in elevation, crustal thickness and magnetization between the southern and northern hemispheres. A giant impact has been proposed to explain the formation of the Northern Lowlands on Mars. Such an impact probably led to strong and deep mantle heating and merging between the two cores. These processes will have implications on the thermal state and on the magnetic evolution of the planet. We model the effects of such an impact on the Martian magnetic field (1) by characterizing the thermochemical consequences of the sinking of the impactor's core as a single diapir, (2) by imposing a heat flux heterogeneity on the Martian core-mantle boundary (CMB). Our results show that large viscosity contrasts between the impactor's core and the surrounding mantle silicates can reduce the duration of the merging down to 1 kyr. Direct impact heating of Martian core favor thermal stratification of the core and core dynamo cessation. The merging of the impactor's core with the Martian core only delays the re-initiation of the dynamo for a very short time. While the core thermal stratification is likely to be evacuated rapidly, the impact induced thermal anomaly within the mantle is likely to remain stable for a longer timescale above the CMB. This thermal anomaly generates a large scale cooling heterogeneity at the CMB and a magnetic field dichotomy. A polar impactor leads to a north-south hemispheric magnetic dichotomy that is stronger than an east-west dichotomy created by an equatorial impactor. The amplitude of the magnetic dichotomy is mostly controlled by the horizontal Rayleigh number that represents the vigor of the convection driven by the lateral variations of the CMB heat flux. Our results imply that an impactor radius of 1000 km could have recorded the magnetic dichotomy observed in the Martian crustal field only if very rapid post-impact magma cooling took place.
Simulation of an Ice Giant-style Dynamo
Soderlund, K. M.; Aurnou, J. M.
2010-12-01
The Ice Giants, Uranus and Neptune, are unique in the solar system. These planets are the only known bodies to have multipolar magnetic fields where the quadrupole and octopole components have strengths comparable to or greater than that of the dipole. Cloud layer observations show that the planets also have zonal (east-west) flows that are fundamentally different from the banded winds of Jupiter and Saturn. The surface winds are characterized by strong retrograde equatorial jets that are flanked on either side by prograde jets at high latitudes. Thermal emission measurements of Neptune show that the surface energy flux pattern peaks in the equatorial and polar regions with minima at mid-latitudes. (The measurements for Uranus cannot adequately resolve the emission pattern.) The winds and magnetic fields are thought to be the result of convection in the planetary interior, which will also affect the heat flux pattern. Typically, it is implicitly assumed that the zonal winds are generated in a shallow layer, separate from the dynamo generation region. However, if the magnetic fields are driven near the surface, a single region can simultaneously generate both the zonal flows and the magnetic fields. Here, we present a novel numerical model of an Ice Giant-style dynamo to investigate this possibility. An order unity convective Rossby number (ratio of buoyancy to Coriolis forces) has been chosen because retrograde equatorial jets tend to occur in spherical shells when the effects of rotation are relatively weak. Our modeling results qualitatively reproduce all of the structural features of the global dynamical observations. Thus, a self-consistent model can generate magnetic field, zonal flow, and thermal emission patterns that agree with those of Uranus and Neptune. This model, then, leads us to hypothesize that the Ice Giants' zonal flows and magnetic fields are generated via dynamically coupled deep convection processes.
The MSE Budget in Hindcast Experiments During DYNAMO
Hannah, W.; Maloney, E. D.
2013-12-01
The Dynamics of the MJO (DYNAMO) field campaign took place in the Indian Ocean during boreal fall and winter of 2011-2012 to collect observations of the initiation of the Madden-Julian Oscillation (MJO). Hindcast experiments are conducted with an atmospheric general circulation model with varying values of a dilute CAPE entrainment rate parameter for the first two MJO events of DYNAMO from 01 October - 15 December 2011. Higher entrainment rates better reproduce the gross features of precipitation and zonal wind, with MJO hindcast skill up to 20 days. Simulations with lower entrainment rapidly diverge from observations such that no coherent MJO convective signal is present after five days, and the model has no MJO skill beyond 12 days. Analysis of the tropical Indian Ocean column moist static energy (MSE) budget reveals that the simulations with superior MJO performance are characterized by strong positive vertical MSE advection, indicating that convection and associated divergent circulations act to moisten the column. This is inconsistent with ERA-I reanalysis in which vertical MSE advection contributes a drying tendency on average. All simulations have weaker MSE tendency due to MSE sources such as radiation and surface fluxes compared to reanalysis. The concept of gross moist stability (GMS) is invoked to interpret these MSE budget results in a normalized framework relevant to moisture mode theory. A larger entrainment rate is found to produce negative effective GMS (which includes vertical advection and all MSE sources), in agreement with observations, indicating a favorable environment for moisture mode amplification. However, the simulations with higher entrainment appear to get the right answer for the wrong reason because unrealistically strong positive vertical MSE advective tendencies per unit convective activity appear to compensate for weak radiation and surface flux feedbacks.
Research in Solar Dynamo Theories%太阳发电机理论研究
Institute of Scientific and Technical Information of China (English)
吴建清; 杨志良
2011-01-01
太阳活动主要是由磁场产生的，因此，对太阳磁场性质和起源的研究具有重要意义．太阳发电机理论主要研究的是太阳上观测到的与太阳活动相关的磁场起源、磁场特征、各种活动现象之间的相关性及其变化规律．其是太阳物理学中有待解决的最基本、最重要的问题．根据太阳黑子及太阳周期的相关观测，介绍了构成发电机的基本要素，具体描述了各种典型发电机模型，并对其分别进行评述，进而探讨了目前存在的问题及发展方向．%Various activities of the Sun, such as flare, coronal mass ejections, solar wind, which will affect the normal work of satellites, radio communication and electric power system. Therefore, researching the activities of the Sun has great significance for human. Moreover, these activities are dominated by the magnetic field. The purpose of study the solar dynamo theories is not only to unpuzzle the correlation and variation among various activities, but also to explain the origin and character of the magnetic fields on the Sun. The paper briefly reviews the relevant observational data pertaining to sunspots and solar cycle first and researches evolution if the solar dynamo theories. Then the three basic elements of the dynamo, the differential rotation, meridional circulation and magnetic diffusivity, with the fundamental equations of magnetic field generation are introduced. Magnetic induced equation is the first basic equation for dynamo theories and the first item of induced equation is from Ohm Law. Moreover, mean field dynamos which contain Babcock-Leighton dynamo, interface dynamo and flux transport dynamo, non-axisymmetric dynamo, MHD simulation and small scale dynamo are described. The advantages and shortcomings of them are presented respectively. Finally, the existing problems and possible development in the future for solar dynamo theories are suggested.
Differential rotation of stretched and twisted thick magnetic flux tube dynamos in Riemannian spaces
de Andrade, Garcia
2007-01-01
The topological mapping between a torus of big radius and a sphere is applied to the Riemannian geometry of a stretched and twisted very thick magnetic flux tube, to obtain spherical dynamos solving the magnetohydrodynamics (MHD) self-induction equation for the magnetic flux tubes undergoing differential (non-uniform) rotation along the tube magnetic axis. Constraints on the shear is also computed. It is shown that when the hypothesis of the convective cyclonic dynamo is used the rotation is ...
DEFF Research Database (Denmark)
Sheyko, A.A.; Finlay, Chris; Marti, P.
We present a set of numerical dynamo models with the convection strength varied by a factor of 30 and the ratio of magnetic to viscous diffusivities by a factor of 20 at rapid rotation rates (E =nu/(2 Omega d^2 ) = 10-6 and 10-7 ) using a heat flux outer BC. This regime has been little explored...... on the structure of the dynamos and how this changes in relation to the selection of control parameters, a comparison with the proposed rotating convection and dynamo scaling laws, energy spectra of steady solutions and inner core rotation rates. Magnetic field on the CMB. E=2.959*10-7, Ra=6591.0, Pm=0.05, Pr=1....