Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades In Magentized 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 system-specific 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 magnetic-fieldstrength 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 kinetic-Alfvén-wave (KAW) cascade governed by two fluid-like 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 inertial-range fluctuations that was Landau-damped 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 all of these cascades. The relationship between the theoretical models proposed in this paper and astrophysical applications and observations is discussed in detail.

Neoclassical physics in full distribution function gyrokinetics

“…2. The inclusion of collisional processes is indispensable to realising a statistical steady-turbulent state whilst satisfying an H-theorem; 21 on more practical grounds, the dissipation of the short-scale structures in velocity space 23,24 is also beneficial for improving numerical stability. 3.…”

Structure of Stationary Strong Imbalanced Turbulence

“…Most notably, turbulence has drastically changed the paradigms of interstellar medium (ISM) and molecular cloud evolution (Stone et al 1998;Ostriker et al 2001;Vázquez-Semadeni et al 2007; see also review by McKee & Ostriker 2007). Small-scale turbulence has been probed by a variety of approaches such as gyrokinetics, Hall MHD, and electron MHD (Howes et al 2006;Schekochihin et al 2007;Galtier et al 2003;Cho & Lazarian 2004). This progress calls for better understanding of the fundamentals of turbulence.…”

Experimental Signatures of Critically Balanced Turbulence in MAST

“…Some of these time scales and, consequently, the corresponding physics may be irrelevant, while others play a crucial role for the saturation of the linearly unstable fluctuations. There has been a growing understanding [5], driven largely by theory [6][7][8][9], observations [10][11][12] and simulations of magnetohydrodynamic [13][14][15] and kinetic [7,16] plasma turbulence in space, that if a medium can …”

“…Some of these time scales and, consequently, the corresponding physics may be irrelevant, while others play a crucial role for the saturation of the linearly unstable fluctuations. There has been a growing understanding [5], driven largely by theory [6][7][8][9], observations [10][11][12] and simulations of magnetohydrodynamic [13][14][15] and kinetic [7,16] plasma turbulence in space, that if a medium can support parallel (to the magnetic field) propagation of waves (and/or particles) and nonlinear interactions in the perpendicular direction, the turbulence in such a medium would normally be "critically balanced," meaning that the characteristic time scales of propagation and nonlinear interaction would be comparable to each other and (therefore) to the correlation time of the fluctuations. This means that the turbulence is not weak and not twodimensional, unless specially constrained to be so [9].…”