Effects of plasma-density inhomogeneity and collisions and their relation to maintenance of waveguide discharges by Trivelpiece-Gould modes: II. Numerical analysis

The effects of collisions and radial inhomogeneity of the plasma density on the behaviour of the azimuthally-symmetric Trivelpiece-Gould modes (includ ing the waveguide resonance and the wave resonance absorption at the upper hybrid frequency) are treated in this study in terms of their relation to g as-discharge production in an external magnetic field. Numerical solutions for the wave-field patterns and for the propagation properties of the waves are presented and their changes are discussed with a varying averaged plas ma density, for various plasma-density profiles. First modifications due to collisions in homogeneous plasmas are presented for different values of th e external magnetic field. Then, for a given magnetic field, the combined e ffects of collisions and Bessel-type radial profiles of the plasma density are emphasized. After which, for a given profile, the influence is discusse d of varying the magnetic field. It became evident that, for low collision frequencies and a cyclotron frequency less than the wave frequency, the pla sma-density profile shape has a strong impact on the results and that the w ave properties, as the average density is varied for dominantly diffusive c harged particle losses, are badly represented by wave properties in uniform plasmas. The behaviour discussed here should be useful in understanding th e structure of diffusion-controlled discharges maintained in the fields of propagating Trivelpiece-Gould modes.