Resonance oscillations in a hot nonuniform plasma

A quantitative theory of resonance oscillations, such as observed by Dattner and others, is given. The first two moments of the collisionless Boltzmann equation assuming a scalar pressure are used in conjunction with a physically reasonable radial electron density profile to describe the oscillations of a hot nonuniform plasma cylinder. These equations coupled with Maxwell's equations assuming a scalar potential are solved numerically to yield the frequency spectrum of the plasma wave resonances. It is found that the frequency spectrum depends on the parameter r/w2/<λd^2> where rw is the radius of the plasma column and <λd^2> is the mean square Debye length of the electron plasma. New experimental observations of dipole and quadrupole spectra for two plasma columns of differing radii are reported and the results of these observations are in good agreement with the theory. The physical mechanism of the resonances is described.