Energy Loss of a High Charge Bunched Electron Beam in Plasma:. Simulations, Scaling, and Accelerating Wake-Fields

The energy loss and gain of a beam in the nonlinear, "blowout" regime of the plasma wakefield accelerator (PWFA), which features ultra-high accelerating fields, linear transverse focusing forces, and nonlinear plasma motion, has been asserted, through previous observations in simulations, to scale linearly with beam charge. In a new analysis that is the companion to this article¹, it has been shown that for an infinitesimally short beam, the energy loss is indeed predicted to scale linearly with beam charge for arbitrarily large beam charge. This scaling holds despite the onset of a relativistic, nonlinear response by the plasma, when the number of beam particles occupying a cubic plasma skin-depth exceeds that of plasma electrons within the same volume. This paper is intended to explore the deviations from linear energy loss using 2D particle-in-cell (PIC) simulations that arise in the case of finite length beams. The peak accelerating field in the plasma wave excited behind the finite-length beam is also examined, with the artifact of wave spiking adding to the apparent persistence of linear scaling of the peak field amplitude well into the nonlinear regime. At large enough normalized charge, the linear scaling of both decelerating and accelerating fields collapses, with serious consequences for plasma wave excitation efficiency. Using the results of parametic PIC studies, the implications of these results for observing the collapse of linear scaling in planned experiments are discussed.