Energy Loss of a High Charge Bunched Electron Beam in Plasma:. Analysis

There has been much recent experimental and theoretical interest in the blowout regime of plasma wakefield acceleration, which features ultrahigh accelerating fields, linear transverse focusing forces, and nonlinear plasma motion. A quantitative understanding of the blowout regime including all these effects has, to this point, been available only through detailed simulations. This paper represents an initial step towards an analytical theory of this regime, in which the mechanism of energy loss in the drive beam is investigated. We find, first from examination of electromagnetic particle-in-cell simulations, and then through analytical investigations, that under short pulse, high-charge conditions, the plasma electrons receive a strong initial push along the direction of beam motion. This nonlinear effect is unanticipated by linear theory, where the return current motion is in the opposite direction. In the limit of short pulses (the $\ensuremath{\delta}$-function limit), the beam energy loss is shown to be linear in charge even with a nonlinear plasma response dominated by relativistic, electromagnetic effects, despite the fact that the initial plasma electron response changes qualitatively from the familiar electrostatic, nonrelativistic limit.