Energy Loss of a High Charge Bunched Electron Beam in Plasma: Nonlinear Plasma Response and Linear Scaling

There has been much experimental and theoretical interest in blowout regime of plasma wakefield acceleration (PWFA), which features ultra-high accelerating fields, linear transverse focusing forces, and nonlinear plasma motion. Using an exact analysis, we examine here a fundamental limit of nonlinear PWFA excitation, by an infinitesimally short, relativistic electron beam. The beam energy loss in this case is shown to be linear in charge even for nonlinear plasma response, where a normalized, unitless charge exceeds unity, and relativistic plasma effects become important or dominant. The physical bases for this persistence of linear response are pointed out. As a byproduct of our analysis, we re-examine the issue of field divergence as the point-charge limit is approached, suggesting an important modification of commonly held views of evading unphysical energy loss. Deviations from linear behavior are investigated using simulations with finite length beams. The peak accelerating field in the plasma wave excited behind a 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. On the other hand, at large enough normalized charge, linear scaling of fields collapses, with serious consequences for plasma wave excitation efficiency. The dramatic implications of these results for observing the collapse of linear scaling in planned experiments are discussed.