arXiv subjects

A. A. Schekochihin

Publications and source records attributed to A. A. Schekochihin.

At least 109 records · Page 6Linked to original sources

arXiv2009

Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence

Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.

physics.plasm-ph↗

arXiv2009

Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas

We present a theoretical framework for plasma turbulence in astrophysical plasmas (solar wind, interstellar medium, galaxy clusters, accretion disks). The key assumptions are that the turbulence is anisotropic with respect to the mean magnetic field and frequencies are low compared to the ion cyclotron frequency. The energy injected at the outer scale scale has to be converted into heat, which ultimately cannot be done without collisions. A KINETIC CASCADE develops that brings the energy to collisional scales both in space and velocity. Its nature depends on the physics of plasma fluctuations. In each of the physically distinct scale ranges, the kinetic problem is systematically reduced to a more tractable set of equations. In the "inertial range" above the ion gyroscale, the kinetic cascade splits into a cascade of Alfvenic fluctuations, which are governed by the RMHD equations at both the collisional and collisionless scales, and a passive cascade of compressive fluctuations, which obey a linear kinetic equation along the moving field lines associated with the Alfvenic component. In the "dissipation range" between the ion and electron gyroscales, there are again two cascades: the kinetic-Alfven-wave (KAW) cascade governed by two fluid-like Electron RMHD equations and a passive phase-space cascade of ion entropy fluctuations. The latter cascade brings the energy of the inertial-range fluctuations that was damped by collisionless wave-particle interaction at the ion gyroscale to collisional scales in the phase space and leads to ion heating. The KAW energy is similarly damped at the electron gyroscale and converted into electron heat. Kolmogorov-style scaling relations are derived for these cascades. Astrophysical and space-physical applications are discussed in detail.

astro-ph↗

arXiv2009

Formation of Plasmoid Chains in Magnetic Reconnection

A detailed numerical study of magnetic reconnection in resistive MHD for very large, previously inaccessible, Lundquist numbers ($10^4\le S\le 10^8$) is reported. Large-aspect-ratio Sweet-Parker current sheets are shown to be unstable to super-Alfvénically fast formation of plasmoid (magnetic-island) chains. The plasmoid number scales as $S^{3/8}$ and the instability growth rate in the linear stage as $S^{1/4}$, in agreement with the theory by Loureiro et al. [Phys. Plasmas {\bf 14}, 100703 (2007)]. In the nonlinear regime, plasmoids continue to grow faster than they are ejected and completely disrupt the reconnection layer. These results suggest that high-Lundquist-number reconnection is inherently time-dependent and hence call for a substantial revision of the standard Sweet-Parker quasi-stationary picture for $S>10^4$.

astro-ph.SR↗

arXiv2009

Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory

A new analytically and numerically manageable model collision operator is developed specifically for turbulence simulations. The like-particle collision operator includes both pitch-angle scattering and energy diffusion and satisfies the physical constraints required for collision operators: it conserves particles, momentum and energy, obeys Boltzmann's H-theorem (collisions cannot decrease entropy), vanishes on a Maxwellian, and efficiently dissipates small-scale structure in the velocity space. The process of transforming this collision operator into the gyroaveraged form for use in gyrokinetic simulations is detailed. The gyroaveraged model operator is shown to have more suitable behavior at small scales in phase space than previously suggested models. A model operator for electron-ion collisions is also presented.

physics.plasm-ph↗

arXiv2008

Howes et al. Reply

Howes et al. Reply to Comment on "Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas" arXiv:0711.4355

astro-ph↗

arXiv2008

Gyrokinetic turbulence: a nonlinear route to dissipation through phase space

This paper describes a conceptual framework for understanding kinetic plasma turbulence as a generalized form of energy cascade in phase space. It is emphasized that conversion of turbulent energy into thermodynamic heat is only achievable in the presence of some (however small) degree of collisionality. The smallness of the collision rate is compensated by the emergence of small-scale structure in the velocity space. For gyrokinetic turbulence, a nonlinear perpendicular phase mixing mechanism is identified and described as a turbulent cascade of entropy fluctuations simultaneously occurring at spatial scales smaller than the ion gyroscale and in velocity space. Scaling relations for the resulting fluctuation spectra are derived. An estimate for the collisional cutoff is provided. The importance of adequately modeling and resolving collisions in gyrokinetic simulations is biefly discussed, as well as the relevance of these results to understanding the dissipation-range turbulence in the solar wind and the electrostatic microturbulence in fusion plasmas.

physics.plasm-ph↗

arXiv2008

Linearized model Fokker-Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests

A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-Theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical (real-space) diffusion. The numerical implementation in the continuum gyrokinetic code GS2 is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation.

physics.plasm-ph↗

arXiv2008

Numerical experiments on dynamo action in sheared and rotating turbulence

Numerical simulations of forced turbulence in elongated shearing boxes are carried out to demonstrate that a nonhelical turbulence in conjunction with a linear shear can give rise to a mean-field dynamo. Exponential growth of magnetic field at scales larger than the outer (forcing) scale of the turbulence is found. Over a range of values of the shearing rate S spanning approximately two orders of magnitude, the growth rate of the magnetic field is proportional to the imposed shear, gamma ~ S, while the characteristic spatial scale of the field is l_b ~ S^(-1/2). The effect is quite general: earlier results for the nonrotating case by Yousef et al. 2008 (PRL 100, 184501) are extended to shearing boxes with Keplerian rotation; it is also shown that the shear dynamo mechanism operates both below and above the threshold for the fluctuation dynamo. The apparently generic nature of the shear dynamo effect makes it an attractive object of study for the purpose of understanding the generation of magnetic fields in astrophysical systems.

astro-ph↗

arXiv2008

Generation of Magnetic Field by Combined Action of Turbulence and Shear

The feasibility of a mean-field dynamo in nonhelical turbulence with superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of magnetic field at scales much larger than the outer scale of the turbulence is found. The charateristic scale of the field is l_B ~ S^{-1/2} and growth rate is gamma ~ S, where S is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows.

astro-ph↗

arXiv2008

Nonlinear growth of firehose and mirror fluctuations in turbulent galaxy-cluster plasmas

In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, dB/B ~ 1, on a timescale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas.

astro-ph↗

arXiv2007

Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas

This letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic and electric-field energy spectra show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfven waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfven waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind. Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale.

astro-ph↗

arXiv2007

Instability of current sheets and formation of plasmoid chains

Current sheets formed in magnetic reconnection events are found to be unstable to high-wavenumber perturbations. The instability is very fast: its maximum growth rate scales as S^{1/4} v_A/L, where L is the length of the sheet, v_A the Alfven speed and S the Lundquist number. As a result, a chain of plasmoids (secondary islands) is formed, whose number scales as S^{3/8}.

astro-ph↗

arXiv2007

Turbulence and Magnetic Fields in Astrophysical Plasmas

We discuss the current understanding of the most basic properties of astrophysical MHD turbulence and trace the origins of the modern views and theoretical uncertainties to the ideas set forth in 1950s and 1960s by Iroshnikov, Kraichnan, Batchelor, Schlueter and Biermann. Universal aspects of the theory are emphasised. Two main astrophysical applications are touched upon: turbulence in the solar wind and in clusters of galaxies. These are, in a certain (very approximate) sense, two ``pure'' cases of small-scale turbulence, where theoretical models of the two main regimes of MHD turbulence -- with and without a strong mean magnetic field -- can be put to the test. They are also good examples of a complication that is more or less generic in astrophysical plasmas: the MHD description is, in fact, insufficient for astrophysical turbulence and plasma physics must make an entrance.

astro-ph↗

arXiv2007

Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers

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 Pm<<1. The dependence of the critical Rm_c for dynamo on the hydrodynamic Reynolds number Re is obtained for 1 6000 compared to Rm_c~60 for Pm>=1. Is is not as yet possible to determine numerically whether the growth rate of the magnetic energy is ~Rm^{1/2} in the limit Rm->infinity, as it should if the dynamo is driven by the inertial-range motions at the resistive scale.

astro-ph↗

arXiv2007

Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers

This paper is a detailed report on a programme of simulations used to settle a long-standing issue in the dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rm_c vs. the hydrodynamic Reynolds number Re is obtained for 1 1. The stability curve Rm_c(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate is ~Rm^{1/2} in the limit Re>>Rm>>1, as should be the case if the dynamo is driven by the inertial-range motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm>1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At 1<Rm<Rm_c, the magnetic fluctuations induced via the tangling by turbulence of a weak mean field are investigated and the possibility of a k^{-1} spectrum above the resistive scale is examined. At low Rm<1, the induced fluctuations are well described by the quasistatic approximation; the k^{-11/3} spectrum is confirmed for the first time in direct numerical simulations.

physics.flu-dyn↗

arXiv2006

Turbulence, magnetic fields and plasma physics in clusters of galaxies

Observations of galaxy clusters show that the intracluster medium (ICM) is likely to be turbulent and is certainly magnetized. The properties of this magnetized turbulence are determined both by fundamental nonlinear magnetohydrodynamic interactions and by the plasma physics of the ICM, which has very low collisionality. Cluster plasma threaded by weak magnetic fields is subject to firehose and mirror instabilities. These saturate and produce fluctuations at the ion gyroscale, which can scatter particles, increasing the effective collision rate and, therefore, the effective Reynolds number of the ICM. A simple way to model this effect is proposed. The model yields a self-accelerating fluctuation dynamo whereby the field grows explosively fast, reaching the observed, dynamically important, field strength in a fraction of the cluster lifetime independent of the exact strength of the seed field. It is suggested that the saturated state of the cluster turbulence is a combination of the conventional isotropic magnetohydrodynamic turbulence, characterized by folded, direction-reversing magnetic fields and an Alfvén-wave cascade at collisionless scales. An argument is proposed to constrain the reversal scale of the folded field. The picture that emerges appears to be in qualitative agreement with observations of magnetic fields in clusters.

astro-ph↗

arXiv2006

Interplanetary and interstellar plasma turbulence

Theoretical approaches to low-frequency magnetized turbulence in collisionless and weakly collisional astrophysical plasmas are reviewed. The proper starting point for an analytical description of these plasmas is kinetic theory, not fluid equations. The anisotropy of the turbulence is used to systematically derive a series of reduced analytical models. Above the ion gyroscale, it is shown rigourously that the Alfven waves decouple from the electron-density and magnetic-field-strength fluctuations and satisfy the Reduced MHD equations. The density and field-strength fluctuations (slow waves and the entropy mode in the fluid limit), determined kinetically, are passively mixed by the Alfven waves. The resulting hybrid fluid-kinetic description of the low-frequency turbulence is valid independently of collisionality. Below the ion gyroscale, the turbulent cascade is partially converted into a cascade of kinetic Alfven waves, damped at the electron gyroscale. This cascade is described by a pair of fluid-like equations, which are a reduced version of the Electron MHD. The development of these theoretical models is motivated by observations of the turbulence in the solar wind and interstellar medium. In the latter case, the turbulence is spatially inhomogeneous and the anisotropic Alfvenic turbulence in the presence of a strong mean field may coexist with isotropic MHD turbulence that has no mean field.

astro-ph↗

arXiv2005

Fast growth of magnetic fields in galaxy clusters: a self-accelerating dynamo

We propose a model of magnetic-field growth in galaxy clusters whereby the field is amplified by a factor of about 10^8 over a cosmologically short time of ~10^8 yr. Our model is based on the idea that the viscosity of the intracluster medium during the field-amplification epoch is determined not by particle collisions but by plasma microinstabilities: these give rise to small-scale fluctuations, which scatter particles, increasing their effective collision rate and, therefore, the effective Reynolds number. This gives rise to a bootstrap effect as the growth of the field triggers the instabilities which increase the Reynolds number which, in turn, accelerates the growth of the field. The growth is explosive and the result is that the observed field strength is reached over a fraction of the cluster lifetime independent of the exact strength of the seed field (which only needs to be above ~10^{-15} G to trigger the explosive growth).

astro-ph↗