Theory of ion acceleration by drifting intense relativistic electron beams. I. Theory

Abstract

A theory that describes the collective acceleration of ions by an intense relativistic electron beam injected into a metallic guide tube filled with neutral gas at low pressure is presented. The acceleration mechanism is shown to be of electrostatic origin (although it is different from those employed in previous electrostatic theories), and its many parametric dependences are identified and discussed. In the theory, ion acceleration occurs in the electrostatic fields of a two-dimensional, time-dependent, potential well, which is described by the self-consistent coupling of the beam dynamics with the ionization processes of the neutral gas. The theory divides into the cases (i) I0 ≳ Il, and (ii) I0 ≪ Il, where I0 is the peak injected beam current and Il is the space-charge limiting current. For case (i), the beam initially stops at the anode and creates a deep potential well. At roughly the charge neutralization time, a nonadiabatic transition occurs, the beam begins to propagate, and an ion bunch is accelerated. At low pressures, the ion energy per ion charge may be up to three times the injected electron energy. At higher pressures, the ion energy per ion charge may exceed three times the injected electron energy. At still higher pressures, ion acceleration ceases due either to beam front runaway, ion slip-out, or charge-exchange effects. For case (ii), the beam never stops at the anode, a deep well is never created, and no accelerated ions should occur. All existing ion acceleration data is in the regime I0 ≳ Il, although this was not previously recognized. The effects of ion impact ionization, ion avalanching, and charge exchange (neglected in all previous theories) are shown to play important, and sometimes dominant, roles in the acceleration process.