Nonlinear gyrokinetic theory for finite-beta plasmas

Hahm, T. S.; Lee, W. W.; Brizard, Alain J.

doi:10.1063/1.866641

Cited by 269 publications

(283 citation statements)

References 26 publications

(2 reference statements)

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“…Linear (Rutherford & Frieman 1968;Taylor & Hastie 1968;Catto 1978;Antonsen & Lane 1980;Catto et al 1981) and nonlinear gyrokinetic theory (Frieman & Chen 1982;Dubin et al 1983;Lee 1983Lee , 1987Hahm et al 1988;Brizard 1992) has proven to be a valuable tool in the study of laboratory plasmas. It has been extensively employed to study the development of turbulence driven by microinstabilities, e.g., the ion and electron temperaturegradient instabilities (e.g., Dimits et al 1996;Dorland et al 2000;Jenko et al 2000Rogers et al 2000;Candy et al 2004;Parker et al 2004).…”

Section: Introductionmentioning

confidence: 99%

Astrophysical Gyrokinetics: Basic Equations and Linear Theory

Howes

Cowley

Dorland

et al. 2006

ApJ

304

669

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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.

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Section: Introductionmentioning

confidence: 99%

Astrophysical Gyrokinetics: Basic Equations and Linear Theory

Howes

Cowley

Dorland

et al. 2006

ApJ

304

669

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“…The transformation approach to gyrokinetic theory: 2 : see Gardner [2], [12]; 3 : see Hahm et al [18] and present theory; 4 : first obtained by Alfven [1]; 5 : see Littlejohn [4]. method has been adopted in gyrokinetic theory only using preliminar non-canonical variables, i.e., representing the Hamiltonian function in terms of suitable, non-canonical variables (similar to those adopted by Littlejohn).…”

Section: Figurementioning

confidence: 99%

“…We notice that ρ ′ coincides with g (1) r ′ the first order Lie generator of the transformation (18). Therefore, P ′ φ results:…”

mentioning

confidence: 99%

Canonical Lie-transform method in Hamiltonian gyrokinetics: a new approach

Nicolini¹,

Tessarotto²

2005

AIP Conference Proceedings

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Abstract. The well-known gyrokinetic problem regards the perturbative expansion related to the dynamics of a charged particle subject to fast gyration motion due to the presence of a strong magnetic field. Although a variety of approaches have been formulated in the past to this well known problem, surprisingly a purely canonical approach based on Lie transform methods is still missing. This paper aims to fill in this gap and provide at the same time new insight in Lie-transform approaches.

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“…The nonlinear gyrokinetic equations in the p -formulation derived from the gyrokinetic Vlasov equation [8] are used to calculate the time evolution of the gyro-center distribution function f s (R, p ,μ) of species s = i, e (ions and electrons) df s dt = ∂f s ∂t + dR dt · ∇f s + dp dt…”

Section: Introductionmentioning

confidence: 99%

“…It uses the so-called pformulation [8] of the gyrokinetic Vlasov-Maxwell system (an alternative v -formulation suffers from the numerical instability associated with the free streaming of the particles, see Ref. [9] for details).…”

Section: Introductionmentioning

confidence: 99%