Linear theory of an MHD oscillator

Abstract

The linear theory of a.c. fluctuations in an MHD channel subject to the Hall instability of Velikhov is explored. It is shown that the system as a whole (plasma, plus boundaries, plus external circuitry) is stable to the Velikhov mode except at certain resonant acoustic frequencies. If these resonant frequencies are excited, channels of sufficient size can be made to oscillatei and produce net a.c. power. However, non-linear effects (discussed elsewhere [5]) limit the a.c. power level severely for this geometry, and adversely affect the d.c. performance of the channel. The analysis shows that resonant fluctuations can be controlled by external circuitry.