Traveling Wave Interaction and Wave Growth in a Dense Plasma

Abstract

Traveling wave interaction for one‐dimensional flow is analyzed using small‐perturbation theory. This permits a separate treatment of the two major fluctuations, i.e., the harmonic response due to the imposed magnetic wave and the transient response to natural disturbances in the presence of the magnetic wave. No interaction takes place when both wave and plasma velocity are equal. The interaction increases as the relative velocity increases, and there are definite resonance peaks for the harmonic fluctuations at the relative sound speeds. The resonance is normally damped; however, the perturbation of the electrical parameters such as the electrical conductivity can have a destabilizing effect. Transient disturbances which travel at the relative magneto acoustic speed are normally damped when moving along the wave. However, as the relative speed is raised, these disturbance waves can be made to grow. Stability criteria are established, defining regions of instability for the relative speed. It is shown that the electrical conductivity and the Hall factor are primarily responsible for instability due to their critical dependence on the fluctuating thermodynamic quantities in magnetohydrodynamic converters.