Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades in Magnetized Weakly Collisional Plasmas
Abstract
This paper presents a theoretical framework for understanding plasma turbulence in astrophysical plasmas. It is motivated by observations of electromagnetic and density fluctuations in the solar wind, interstellar medium and galaxy clusters, as well as by models of particle heating in accretion disks. All of these plasmas and many others have turbulent motions at weakly collisional and collisionless scales. The paper focuses on turbulence in a strong mean magnetic field. The key assumptions are that the turbulent fluctuations are small compared to the mean field, spatially anisotropic with respect to it and that their frequency is low compared to the ion cyclotron frequency. The turbulence is assumed to be forced at some systemspecific outer scale. The energy injected at this scale has to be dissipated into heat, which ultimately cannot be accomplished without collisions. A kinetic cascade develops that brings the energy to collisional scales both in space and velocity. The nature of the kinetic cascade in various scale ranges depends on the physics of plasma fluctuations that exist there. There are four special scales that separate physically distinct regimes: the electron and ion gyroscales, the mean free path and the electron diffusion scale. In each of the scale ranges separated by these scales, the fully kinetic problem is systematically reduced to a more physically transparent and computationally tractable system of equations, which are derived in a rigorous way. In the "inertial range" above the ion gyroscale, the kinetic cascade separates into two parts: a cascade of Alfvénic fluctuations and a passive cascade of density and magneticfieldstrength fluctuations. The former are governed by the reduced magnetohydrodynamic (RMHD) equations at both the collisional and collisionless scales; the latter obey a linear kinetic equation along the (moving) field lines associated with the Alfvénic component (in the collisional limit, these compressive fluctuations become the slow and entropy modes of the conventional MHD). In the "dissipation range" below ion gyroscale, there are again two cascades: the kineticAlfvénwave (KAW) cascade governed by two fluidlike electron reduced magnetohydrodynamic (ERMHD) equations and a passive cascade of ion entropy fluctuations both in space and velocity. The latter cascade brings the energy of the inertialrange fluctuations that was Landaudamped 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. Kolmogorovstyle scaling relations are derived for all of these cascades. The relationship between the theoretical models proposed in this paper and astrophysical applications and observations is discussed in detail.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 May 2009
 DOI:
 10.1088/00670049/182/1/310
 arXiv:
 arXiv:0704.0044
 Bibcode:
 2009ApJS..182..310S
 Keywords:

 magnetic fields;
 methods: analytical;
 MHD;
 plasmas;
 turbulence;
 Astrophysics;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Plasma Physics;
 Physics  Space Physics
 EPrint:
 aastex using emulateapj, 65 pages, 10 figures