Theory of multistage intense ion-beam acceleration

We present an analytic theory for magnetically insulated, multistage acceleration of high-intensity ion beams, where the diamagnetic effect due to electron flow is important. Our theory is an extension of the single-stage diode theory developed by Desjarlais [Phys. Rev. Lett. 59, 2295 (1987)], based on a self-consistent calculation of the virtual cathode position, which has been successful in modeling Applied-B ion diode experiments on several accelerators. The new theory incorporates a finite injection energy qW for the beam ions. We have found a critical voltage V1(W) that corresponds to V* of the single-stage theory. As the voltage approaches V1, unlimited beam-current density can penetrate the gap without the formation of a virtual anode because the dynamic gap goes to zero. At voltages lower than V1, a sufficiently large injection current will cause the formation of a virtual anode in response to the large beam space charge. Furthermore, we have found that unlimited beam current can penetrate an accelerating gap operated above a second critical voltage V2(W). At voltages below V2, there is a maximum steady-state current that can be transmitted through the gap. The critical voltage V2 is smaller than V1 and is unique to the multistage theory. If fluctuations allow electron transport across magnetic field lines so that any virtual anode is neutralized, V2 goes to zero for all beam injection energies. This effect can be used to test the importance of field fluctuations on the electron dynamics in magnetically insulated ion acceleration gaps.