Theoretical modeling of an A6 relativistic magnetron

Abstract

The analytical modeling of the initialization stage of a relativistic magnetron of the A6 cylindrical design is presented, where only two dominant modes are used: a direct current (dc) background mode and a radio frequency (rf) pump mode. These two modes interaction nonlinearly, with the dc background being driven by the dc electromagnetic forces and the ponderomotive forces of the rf mode, while the rf mode is the most unstable linear eigenmode on this dc background. In cylindrical geometry, the diocotron resonance is found to occur over a broader region than in planar models. In fact, in certain parameter regimes, the resonance can appear twice, once near the Brillouin edge, and second, just below the anode. In these parameter regimes, the oscillating electrons can be accelerated twice. Numerical results for the initiation stage agree quite well with the known experimental results on the A6. Results for 350 kV are emphasized, and similar results have also been obtained for voltages between 300 and 500 kV. Numerical data are presented that indicate a possible source for a nonlinear instability, which could give rise to pulse shortening, in the later operating stage, where the device should be smoothly delivering power.