Astrophysical Gyrokinetics: Basic Equations and Linear Theory

By Gregory G. Howes, S. Cowley, William Dorland, Gregory W. Hammett, E. Quataert, A. Schekochihin. 2005

327 citations recorded by the source corpus.

Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low-frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained, and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code GS2 in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/86b0f280cddb6b1ec04b013af68123533fa17d39

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Citations in the corpus

SOLAR WIND TURBULENT SPECTRUM AT PLASMA KINETIC SCALES (2012, unknown): “Howes et al. (2011) consider a model (“weakened cascade model”) which includes the nonlinear transfer of energy from large to small scales in Fourier space (see Equation (23) in Howes et al. 2011) and the damping of kinetic Alfvén waves (KAWs).”
ENHANCED MAGNETIC COMPRESSIBILITY AND ISOTROPIC SCALE INVARIANCE AT SUB-ION LARMOR SCALES IN SOLAR WIND TURBULENCE (2010, background): “In the inertial range below kρi ∼ 1 both of these modes are decoupled (Howes et al. 2006; Schekochihin et al. 2009).”
Nature of Kinetic Scale Turbulence in the Earth's Magnetosheath (2016, background): “The dispersion relation for the standard kinetic Alfvén wave (e.g., Howes et al. 2006), derived under the assumption ω ≪ kzvth,e, is ω2 = k2zv 2 Ak 2 ⊥ρ 2 i (1 + Te/Ti) 2 + βi(1 + Te/Ti) ≈ k 2 zv 2 Ak 2 ⊥ρ 2 i 2 + βi , (A1) where Te ≪ Ti has been assumed in the last expression.”
Foundations of Nonlinear Gyrokinetic Theory (2007, background): “While this discussion tends to focus on fusion-related magnetically confined plasmas, these nonlinear gyrokinetic equations are valid for arbitrary magnetic geometry and, will find applications in space plasma physics Lin, Wang, et al., 2005 and astrophysics Howes et al., 2006 .”
Solar Wind Turbulence and the Role of Ion Instabilities (2013, unknown): “…Ghosh et al. 1996; Biskamp et al. 1996, 1999; Leamon et al. 1998; Cho and Lazarian 2004; Bale et al. 2005; Galtier 2006; Sahraoui et al. 2010, 2012; Howes et al. 2006, 2008, 2012b; Schekochihin et al. 2009; Gary and Smith 2009; Chandran et al. 2009; Chen et al. 2010b, 2013a; Salem et al. 2012;…”
A Model of Turbulence in Magnetized Plasmas: Implications for the Dissipation Range in the Solar Wind (2007, methodology): “Similarly, the linear frequency in gyrokinetic theory is given by [Howes et al., 2006] ω = ±ω(k⊥)k‖vA. (5) where ω(k⊥) = α(k⊥) in both asymptotic ranges k⊥ρi ≪ 1 and k⊥ρi ≫ 1 but not in the transition region k⊥ρi ∼ 1.”
ASTROPHYSICAL GYROKINETICS: KINETIC AND FLUID TURBULENT CASCADES IN MAGNETIZED WEAKLY COLLISIONAL PLASMAS (2007, methodology): “17 It can be shown that equilibrium temperatures change on the timescale ∼ (ǫ2ω)−1 (Howes et al. 2006).”
Electron Heating in Hot Accretion Flows (2007, background): “This energy is presumably dissipated through collisionless damping of fluctuations in a turbulent cascade at the ion Larmor radius (Quataert 1998; Howes et al. 2006).”
A prescription for the turbulent heating of astrophysical plasmas (2010, methodology): “Such anisotropic fluctuations are optimally described by a low-frequency expansion of kinetic theory called gyrokinetics (Rutherford & Frieman 1968; Frieman & Chen 1982; Howes et al. 2006; Schekochihin et al. 2009).”