High Frequency

A comprehensive analysis of high frequency (100-200 GHz) and high power (> 100 kW) gyrotrons has been conducted. It is shown that high frequencies will be required in order for electron cyclotron radiation to propagate to the center of a compact tokamak power reactor. High power levels will be needed in order to ignite the plasma with a reasonable number of gyrotron units. In the first part of this research, a set of analytic expressions, valid for all TE cavity modes and all harmonics, is derived for the starting current and frequency detuning using the Vlasov-Maxwell equations in the weakly relativistic limit. These results are applicable for any longitudinal distrubution of the RF field. It is shown that the starting current can be expressed in a simple form which contains the Fourier transform of this distribution. This formalism is used to investigate the effect of RF field profiling, and it is found that a weak RF field at the input end of the cavity prebunches the electrons and reduces the starting current. This theory is also used to study mode competition and starting characteristics in the high frequency regime. In the second part of this thesis, the use of an optical cavity is investigated. It is found that such a resonator has good mode selectivity characteristics, and may be capable of supporting much higher power levels than a closed cavity. A general linear theory is derived that includes both the electric and magnetic interaction mechanisms that is valid for any angle between the wave vector k and the beam direction. Two configurations are studied in detail: k perpendicular to and parallel to the beam. The former case is of interest only when E is perpendicular to the beam, and gives a pure ECM interaction with no magnetic contribution analogous to the mechanism analyzed in the first part of this thesis. In the latter case, both electric and magnetic terms are present but tend to offset one another yielding rather high, but feasible, starting currents. A 140 GHz gyrotron operating in the TEM0 0-18 mode is designed which exhibits good mode separation properties but requires a perpendicular velocity dispersion of less than 1%. This thesis concludes with the design of an ECR heating system for a commercial fusion reactor. This consists of a parametric