ABSTRACT

This chapter discusses how the equations of Magnetohydrodynamic may be derived from the kinetic equations describing each particle species. The kinetic equations describe the behaviour of the particles in detail; and, for many purposes, the average behaviour of the plasma over appropriate time and length scales is sufficient. The chapter shows how the Boltzmann equation can be used to find equations for the evolution in space and time of the moments of the particle distribution of a particle species and, hence, by summing over species, the evolution of the MHD variables to which they are related. A variety of approximations, suiting different situations, is available to close the moment equations. In general, they depend on the nature of the collision process. At one extreme, binary collisions with neutral particles occur at a frequency much greater than the gyrofrequencies of the particles, so that a particle moves over only a small fraction of its gyro-orbit before encountering another particle.