Theory of Plasma Wave Resonances in a Hot Nonuniform Plasma

This work is concerned with the resonant motion exhibited by a plasma column which is excited by an oscillating electric field transverse to the column. A theory is considered which includes the effects of electron temperature and of nonuniformities in the plasma electron density. In order to have a quantitative theory, the nonuniform electron densities used are calculated numerically using a theory due to Tonks and Langmuir. The theory yields a fourth order differential equation which is integrated numerically to find the predicted resonant frequencies. The predictions are compared with experiment and show excellent agreement. It is concluded that the nonuniform electron density plays a crucial role in determining the resonant frequencies. The effect of an axial magnetic field upon the resonances has been investigated. It is shown that the field causes each resonance to split into a right and left circularly polarized resonance whose frequencies depend on the field strength. These preliminary calculations have been checked with experiment and they give good qualitative agreement. Possible diagnostic uses of these results are considered.