Nonlinear gyrofluid description of turbulent magnetized plasmas

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≪Ω_i, ‖k_∥‖/k_⊥≪1, and ε_⊥≡(k_⊥ρ_i)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).