Nonlinear gyrofluid description of turbulent magnetized plasmas

Abstract

Nonlinear gyrofluid equations are obtained from the gyrocenter-fluid moments of the nonlinear gyrokinetic Vlasov equation, which describes an equilibrium magnetized nonuniform plasma perturbed by electromagnetic field fluctuations (δφ,δA∥,δB∥), whose space-time scales satisfy the gyrokinetic ordering: ω≪Ωi, ‖k∥‖/k⊥≪1, and ε⊥≡(k⊥ρi)2≂𝒪(1). These low-frequency (reduced) fluid equations contain terms of arbitrary order in ε⊥ and take into account the nonuniformity in the equilibrium density and temperature of the ion and electron species, as well as the nonuniformity in the equilibrium magnetic field. From the gyrofluid equations, one can systematically derive nonlinear reduced fluid equations with finite-Larmor-radius (FLR) corrections, which contain linear and nonlinear terms of 𝒪(ε⊥), by expressing the gyrocenter-fluid moments appearing in the gyrofluid equations in terms of the particle-fluid moments, and then keeping terms up to 𝒪(ε⊥) in the ε⊥ expansion of the gyrofluid equations. By using gyrocenter-fluid moments, this new gyrofluid approach effectively bypasses the issue of the gyroviscous cancellations, while retaining all the important diamagnetic effects and the gyroviscous corrections. From the present FLR-corrected reduced fluid equations, the reduced Braginskii equations are recoverd for the ion and electron species (without collisional dissipation) and the ideal reduced magnetohydrodynamic (MHD) equations (in the absence of FLR effects).

Energy-conserving finite-β electromagnetic drift-fluid equations

“…[23], where v gc denotes the guiding-center (gc) velocity and higher-order corrections (e.g., electromagnetic fluctuations) are omitted for simplicity. Furthermore, because of the presence of δ 3 (R+ρ−r)…”

A compressible Hamiltonian electromagnetic gyrofluid model

“…2D) equilibrium states is essential for physical applications. In the absence of knowledge of the Hamiltonian structure, however, the existence of such equilibrium states can be difficult to ascertain for physically sophisticated models, such as many of the fluid models that are used to describe the dynamics in fusion plasmas (see, for example, [15][16][17][18][19][20][21]). Even simple models that otherwise appear physically compelling can fail to be Hamiltonian.…”

“…[16][17][18]21] These models, known as gyro-fluid models, rely on nonlocal operators to describe the effect of Larmor gyration on the response of the ions.…”

Astrophysical Gyrokinetics: Basic Equations and Linear Theory

“…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).…”