Finite Gyro-Radius Corrections to the Hydromagnetic Equations for a Vlasov Plasma

Abstract

Velocity moments of the Vlasov equation are expanded systematically in m/e and equations obtained giving the fluid velocity transverse to B through second order. These equations include all ``finite gyro-radius'' effects. No a priori form is imposed on the velocity distribution. The transverse electric field E⊥ is allowed to be large. For straight field lines the equations for purely transverse motion are closed. For weak instabilities (E⊥ small) closed equations are obtained only for low plasma pressure.