Gas Law and Conductivity of a Collision-Free Plasma

Abstract

The moment method is used to derive a form of two‐component magneto‐gas dynamics for a collision‐free plasma. Closure of the moment equations is achieved by ignoring variations of fourth moments of the peculiar velocities for each component. This provides a ``fully adiabatic gas law'' which represents a generalization of the single or double adiabatic laws in that it predicts the gyrations of the pressure tensor, as well as the principal pressures. The currents which small perturbing electric fields cause to flow in each species in accordance with its own adiabatic gas dynamics are calculated. A complex conductivity tensor thus is deduced. This tensor is compared with that resulting from rigorous kinetic theory (without closure), for the case of a uniform plasma. It is found to be identical with the ``warm plasma approximation'' which takes into account temperature to first order. Hence a two‐component fully adiabatic theory describes supersonic phenomena adequately but misses (altogether) the phenomenon of Landau damping. It could serve to provide pessimistic stability tests for nonuniform (confined) plasmas.