ABSTRACT
In aerodynamics, most practical problems can be very accurately treated by means of the ordinary equations of momentum, thermodynamic state, heat conduction, and so on, the only common exception being the very difficult question of the structure of shock waves. For plasmas there is a rather richer variety of phenomena which involve velocity space, for example Landau damping, cyclotron resonances, and many of the microinstabilities. It ought to be possible to obtain the equations of magnetohydrodynamics (MHD) from the Boltzmann equation by means of suitable approximations. The physical content of the required approximation is that there should be sufficient "localization" of the particles in physical space. The only distant influence which can be included in the hydrodynamic scheme is a self-consistent field, which appears as a body force. In ordinary gases this localization is provided by collisions.
