Dissipative trapped electron instability in a linear machine

Abstract

A study of the dissipative trapped electron instability is greatly simplified, both experimentally and theoretically, when posed in a cylindrical geometry. A derivation of the linear dispersion relation for a finite cylindrical system with two localized magnetic mirrors shows that a linear machine can support the instability with strong localization between the mirrors. The growth rate can be larger than 10% of the wave frequency which is approximately the drift frequency. A simple physical explanation is provided for the dynamics of the instability. An experiment was performed in a Q-machine converted to an ODE-type device in which the dissipative trapped electron instability was definitively identified through the dependence of the wave amplitude on mirror ratio, axial position, temperature gradient, electron collision frequency, and radial position. The wave, with the azimuthal mode number 1, is nearly monochromatic at approximately 50 kHz which is in the neighbourhood of the drift frequency. The density fluctuation in the wave can be as high as 30%.