Stationary MHD waves modified by Hall current coupling—I. Cold compressible flow

Abstract

The stationary wave system generated by the inductive interaction between a conducting body and a magnetized plasma in relative motion is important in such space plasma systems as the Io-Jupiter interaction and tethered satellite systems in the ionosphere. This paper generalizes previous work by the authors on MHD wave perturbations to include Hall current effects, which couples the three MHD modes in a dispersive as well as an anisotropic wave system. There is no longer purely one-dimensional propagation of any perturbation and consequently the wave modes suffer quasi-spherical and conical attenuation. The special cases of cold compressible (part I) and incompressible plasmas (part II) are discussed in detail. In the cold plasma case two wave modes appear: namely the Alfvén ion-cyclotron mode which propagates quasi-one-dimensionally along the background magnetic field and suffers a resonance at the proton gyro-frequency above which it is evanescent; and the quasi-isotropic fast Alfvén mode which continues to propagate above the proton gyrofrequency. The stationary wavecrest surfaces generated in a perpendicular flow reflect the propagation characteristics of the particular mode to which they correspond. Only the fast Alfvén mode experiences the effect of a critical Mach number (at Alfvén Mach number M = 1) below which the associated stationary wavecrest surface disappears and the mode becomes evanescent. Furthermore as a consequence of the dispersive nature of the system the wavecrests do not represent generalized cones as in the MHD case, and are found downstream of and disconnected from the source. The magnetic pressure and parallel current disturbances exhibit characteristics of both wave modes present, while the electric potential perturbations display in addition the influence of an Alfvén-like potential operator together with an “intrinsic” potential which arises as a result of including Hall current effects in the system. In very sub-Alfvénic flows in a cold plasma the parallel current perturbation is largely of Alfven ion-cyclotron mode character, while the dominant contribution to the magnetic pressure disturbance is from the evanescent fast Alfvén mode. The concomitant electric potential is predominantly determined by the intrinsic term.