Equations of Motion for an Ideal Plasma.

Equations are presented for the motion of a completely ionized gas, or plasma, in a magnetic field sufficiently strong so that during a single gyration around a Larmor circle the relative changes in all macroscopic quantities, such as the electrical and magnetic fields, E and B, the particle density, n, and the kinetic temperature, T, are very small. The ratio of the radius of curvature, a, of a Larmor circle to the mean free path, X, is also assumed small. Successive approximations are developed in increasing powers of these small quantities. Since, in the plane perpendicular to B, an electrical current arises primarily from a pressure gradient, while an electrical field produces a uniform velocity of the plasma, the current density and the electrical field have no direct relationship. Hence the electrical resistivity is most conveniently defined in terms of the energy dissipated into heat by an electrical current. So defined, the tiansverse resistivity is 1.96 times the normal resistivity for currents parallel to the magnetic field. While no steady current parallel to E is directly produced by a transverse electrical field, a change in E produces a polarization of the plasma; in interstellar space the transverse dielectric constant is about 1 . The Hall current, perpendicular to both E and B, appears only in the third approximation and is generally negligible. Approximate equations for the transverse viscosity and heat conductivity are given. Both of these effects are very small.