Magnetoacoustic and Alfvén potentials for stationary waves in a moving plasma

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The inductive interaction between a conducting body and a magnetized plasma in relative uniform motion generates a system of stationary waves in the frame of the body. This wave system is composed of both Alfvénic and magnetoacoustic perturbations associated with each of which there are corresponding electric potentials and currents. Here we develop the Green's function for each of the modes. The well‐known Alfvén “wings” are represented by delta functions which propagate the parallel components of vorticity and current along the Alfvén lines. The magnetoacoustic modes are characterized by total pressure (plasma plus magnetic) and dilatation perturbations which are propagated along the envelopes of the fast and slow mode characteristics. The concomitant electric potentials are then obtainable from a component of the momentum equation which can be written in the form of a wave equation for the potential with an Alfvénic wave operator and the magnetoacoustic pressure gradient acting as the driving term. The important consequence is that the potential associated with the compressive modes is hybrid in nature in that it is singular both on the Alfvén lines and on the magnetoacoustic characteristics so that the properties of both modes are interwoven in a complicated fashion. On the other hand, the slow mode potential and current perturbations exhibit singularities on the slow mode wings and the Alfvén lines away from both of which they decay rather gently in a two‐dimensional dipolelike fashion. By using the method of stationary phase we elucidate the detailed fine structure of the slow mode wave crests which consist of two closed, hollow wings, whose cross section reflects the topology of the slow mode group velocity surface and which emanate from the conducting body and extend out parallel and antiparallel to the background magnetic field. As an example of how Green's functions may be used to construct more general solutions and in an attempt to tackle the problem of the self‐consistent source current distribution inside the conducting body we formulate an integral equation which determines the current along a thin wire of finite length. We demonstrate that including the effect of induced fields radiated in the magnetoacoustic modes enhances the effective wave impedance of the plasma environment relative to the results of conventional treatments which only take account of the Alfvén mode.