Computer simulation of virtual cathode oscillations

Abstract

The dynamics of relativistic electron beam and the oscillations of the virtual cathode in the vircator (virtual cathode oscillator) have been investigated by electrostatic particle-in-cell computer simulations. A specially developed PIC (particle-in-cell) computer code is employed in this study. In the diode region, cathode to anode, the solid electron beam is modeled by one-dimensional sheets for simplicity. In the drift tube region the potential at the center line is obtained by solving the Poisson’s equation analytically in the radial direction and via PIC simulation in the axial direction. The electron beam in the drift tube region is modeled as a solid and uniform beam of constant radius equal to the cathode radius. The simulation results show that the potential minimum in the drift tube region oscillates at broad-band frequencies. The injected electron beam in the diode region is found to be modulated by the bunched reflex electrons. The oscillation frequency of the potential minimum in the drift tube region is found to have strong dependence on the transit time of the electrons between the real cathode and the virtual cathode, and it scales inversely proportional to the cathode to anode distance. The effect of applied voltage, injected current, cathode-to-anode distance, and beam radius on the oscillation frequency has also been studied. The results are compared with predictions of theoretical and empirical formulas. The potential minimum is found to oscillate at a single constant frequency when the reflected electrons are not allowed to enter the diode region.