Hydrodynamic equations for plasmas in strong magnetic fields - I: Collisionless approximation

Abstract

A system of hydrodynamic equations for the description of a collisionless plasma is derived. The equations for motion perpendicular to the magnetic field are an extension of those of CHEW et al. (1956). Hydrodynamic description of motion along the magnetic field is possible if v_||t₀/L_|| is a small parameter (v_|| is the thermal velocity parallel to the magnetic field, t₀ the characteristic time, L_|| the characteristic length scale for variation of macroscopic quantities along the magnetic field). The method of deriving the hydrodynamic equations is an extension of a method used by GRAD (1949). This extension is necessary because in collisionless plasma thermal energy is not equally distributed over all degrees of freedom. Therefore one has to consider two heat-flux vectors for the transport in thermal energy of parallel and perpendicular degrees of freedom separately. These independent heat-flux vectors are caused by gradients of the parallel and perpendicular temperature respectively. Thus one arrives at a system of equations for 16 moments of the distribution function.