Simulations of multistage intense ion beam acceleration

An analytic theory for magnetically insulated, multistage acceleration of high intensity ion beams, where the diamagnetic effect due to electron flow is important, has been presented by Slutz and Desjarlais [J. Appi. Phys. 67, 6705 (1990)]. The theory predicts the existence of two limiting voltages called V1(W) and V2(W), which are both functions of the injection energy qW of ions entering the accelerating gap. As the voltage approaches V1(W), unlimited beam-current density can penetrate the gap without the formation of a virtual anode because the dynamic gap goes to zero. Unlimited beam current density can penetrate an accelerating gap above V2(W), although a virtual anode is formed. It was found that the behavior of these limiting voltages is strongly dependent on the electron density profile. We have investigated the behavior of these limiting voltages numerically using the 2-D particle-in-cell (PIC) code MAGIC. Results of these simulations are consistent with the superinsulated analytic results. This is not surprising, since the ignored coordinate eliminates instabilities known to be important from studies of single stage magnetically insulated ion diodes. To investigate the effect of these instabilities we have simulated the problem with the 3-D PIC code QUICKSILVER, which indicates behavior that is consistent with the saturated model.