MAGNETOACOUSTIC AND ALFVEN POTENTIALS FOR STATIONARY WAVES IN A MOVING PLASMA

The inductive interaction between a conducting body and a magnetized p lasma in relative uniform motion generates a system of stationary wave s in the frame of the body. This wave system is composed of both Alfve nic and magnetoacoustic perturbations associated with each of which th ere are corresponding electric potentials and currents. Here we develo p the Green's function for each of the modes. The well-known Alfven '' wings'' are represented by delta functions which propagate the paralle l components of vorticity and current along the Alfven lines. The magn etoacoustic modes are characterized by total pressure (plasma plus mag netic) and dilatation perturbations which are propagated along the env elopes of the fast and slow mode characteristics. The concomitant elec tric potentials are then obtainable from a component of the momentum e quation which can be written in the form of a wave equation for the po tential with an Alfvenic wave operator and the magnetoacoustic pressur e gradient acting as the driving term. The important consequence is th at the potential associated with the compressive modes is hybrid in na ture in that it is singular both on the Alfven lines and on the magnet oacoustic characteristics so that the properties of both modes are int erwoven in a complicated fashion. On the other hand, the slow mode pot ential and current perturbations exhibit singularities on the slow mod e wings and the Alfven lines away from both of which they decay rather gently in a two-dimensional dipolelike fashion. By using the method o f stationary phase we elucidate the detailed fine structure of the slo w mode wave crests which consist of two closed, hollow wings, whose cr oss section reflects the topology of the slow mode group velocity surf ace and which emanate from the conducting body and extend out parallel and antiparallel to the background magnetic field. As an example of h ow Green's functions may be used to construct more general solutions a nd in an attempt to tackle the problem of the self-consistent source c urrent distribution inside the conducting body we formulate an integra l equation which determines the current along a thin wire of finite le ngth. We demonstrate that including the effect of induced fields radia ted in the magnetoacoustic modes enhances the effective wave impedance of the plasma environment relative to the results of conventional tre atments which only take account of the Alfven mode.