Two-dimensional dynamics of the plasma wakefield accelerator

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Abstract
A general analysis of the electromagnetic wakefields for an axisymmetric charge distribution moving through a cold uniform plasma is presented. Particular attention is given to the electromagnetic and relativistic effects influencing the waves. It is shown that the plasma provides shielding of the transverse wakefields on a scale length of a few electromagnetic skin depths (c/ωp). The implications for plasma wakefield accelerators are that driving beams with radii of a few skin depths will experience severe pinching, whereas larger beams will be subject to filamentation instabilities. These conclusions are supported by self‐consistent particle‐in‐cell simulations. The deleterious effects of transverse wakefields will severely limit the accelerating gradients that can be obtained even if a magnetic field is used to guide the driving beam.