Numerical Investigation of Shaped and Transparent Cathodes in the Relativistic Michigan Magnetron

RF field penetration has been proposed as a general mechanism for improving output power, efficiency, mode purity, mode selectivity and start-up times in relativistic magnetrons. RF field penetration is achieved through the use of a transparent cathode i.e. a cathode design consisting of a ring of small cathodes and no center cathode. However, RF field priming is not the only means available for improving magnetron performance. Perturbations in the diode static electric field profile may also yield a performance improvement. The shaped cathode produces such perturbations via protrusions located periodically along its surface. The efficacy of both the transparent and shaped cathode designs was investigated using the three-dimensional electromagnetic particle-in-cell code, ICEPIC. A scan across diode voltages, 300-500 kV and magnetic fields, 0.22 T - 0.34 T was carried out. All cathodes used the Michigan Magnetron configuration. It was found that both designs yielded tremendous performance improvements over the standard cylindrical cathode design. Output power efficiency peaked at ~36% for both the shaped and transparent designs. Moreover the peak was at the same location in parameter space, voltage ~350 kV and magnetic field = 0.34 T. Additionally both designs greatly improved mode selectivity and purity. Points in parameter space that functioned in the 2pi/3 mode with considerable mode competition now, with the help of these novel cathodes, function in the desired pi mode with little to no mode competition. Performance improvements in output power and start-up times were also seen. Given that both designs yielded similar performance benefits, the necessity of RF field penetration may be questioned. Both designs share the similar characteristic of perturbing the DC electric field. It may be that this is the source of the performance improvements in the relativistic magnetron.