Plasma generation and expansion at the anode surface in a Virtual Cathode Oscillator

We have performed two- and three-dimensional, relativistic, electromagnetic particle-in-cell simulations of an axially-extracted Virtual Cathode Oscillator (vircator). The simulations include, for the first time, self-consistent dynamics of the anode foil under the influence of the intense electron beam. This yields the variation of microwave output power as a function of time, including the role of anode ablation and anode-cathode gap closure. These simulations have been done using locally-developed Particle-in-Cell (PIC) codes. The codes have been validated using two vircator designs available from the literature. The simulations reported in the present paper take account of foil ablation due to the intense electron flux, the resulting plasma expansion and shorting of the anode-cathode gap. The variation in anode transparency due to plasma formation is automatically taken into account. We find that damage is generally higher near the axis. Also, at all radial positions, there is little damage in the early stages, followed by a period of rapid erosion, followed in turn by low damage rates. A physical explanation has been given for these trends. As a result of gap closure due to plasma formation from the foil, the output microwave power initially increases, reaches a near-''flat-top'' and then decreases steadily, reaching a minimum around 230 ns. This is consistent with a typical plasma expansion velocity of ∼2 cm/us reported in the literature. We also find a significant variation in the dominant output frequency, from 6.3 to 7.6 GHz. This variation is small as long as the plasma density is small, up to ∼40 ns. As the AK gap starts filling with plasma, there is a steady increase in this frequency.