Two-dimensional theoretical analysis of the dominant frequency in the inward-emitting coaxial vircator

Two-dimensional steady-state analysis for the electron flow in an inward-emitting coaxial virtual cathode oscillator is presented. Based on the relativistic-fluid-Maxwell equations, the relativistic plasma frequency characteristics and its dependence on the geometric parameters are derived. The resulting plasma frequency solution scales linearly with the diode current. The exact dominant frequency is solved numerically, which gives the theoretical support for the simulation result that the microwave frequency in a coaxial vircator is similar to that produced by a planar vircator with the same small anode-cathode gap distance. Numerical result shows that higher frequency can be achieved in the coaxial vircator for higher applied voltage and smaller anode-cathode gap distance. The numerical solutions of the dominant frequencies predict the measured and simulated values within 10%