Magnetohydrodynamic equations for plasmas with finite-Larmor-radius effects

Abstract

It is shown that the truncation of the infinite hierarchy of fluid equations obtained as moments of the Vlasov kinetic equation leads to a system of nonlinear equations that describe finite-Larmor-radius effects with good accuracy. Inertial terms in the momentum balance, viscosity and heat-flux evolution equations are crucial for a uniform description of the plasma response with an arbitrary Larmor radius. In the low-frequency ordering, the obtained equations are simplified by an expansion in the parameter 1/B, where B is the equilibrium magnetic field. The results of the second-order [Oscr ](1/B2) and the fourth-order [Oscr ](1/B4) closures are compared. It is shown that the accuracy of the description improves for higher-order closures.