A Derivation of the Equations of Collisionless Magnetohydrodynamics.

摘要

Magnetohydrodynamic type equations are derived from the Boltzmann equation in the case where collision mean free paths are large compared to other characteristic lengths, (e.g.,Larmor radii,hydrodynamic lengths,etc.) in the plasma. The Boltzmann distribution function is assumed to be isotropic in the components of the thermal velocity perpendicular to the local magnetic field. On the other hand,the distribution function is assumed to have a very general dependence on the velocity component (longitudinal velocity) parallel to the magnetic field. Accordingly,the longitudinal velocity coordinate is retained as an independent variable in the resulting 'collisionless magnetohydrodynamic equations.'The analysis presented in this report begins with a transformation theory of the Boltzmann equation and the resulting magnetohydrodynamic equations apply in the general case where there is no particular symmetry of the plasma or the electromagnetic field. In this sense,the analysis contained in this report is a generalization of that presented in a previous report which assumed axisymmetry. Examples of problems for which the general formalism may find application are (1) the problem of high altitude nuclear explosions where non-axisymmetric effects are important and (2) fusion device plasmas in which geometries other than axisymmetric geometry are appropriate.