It is demonstrated that the performance of the self-modulated proton driver plasma wakefield accelerator (SM-PDPWA) is strongly affected by the reduced phase velocity of the plasma wave. Using analytical theory and particle-in-cell simulations, we show that the reduction is largest during the linear stage of self-modulation. As the instability nonlinearly saturates, the phase velocity approaches that of the driver. The deleterious effects of the wake's dynamics on the maximum energy gain of accelerated electrons can be avoided using side-injections of electrons, or by controlling the wake's phase velocity by smooth plasma density gradients.
An analytic model of the electric and magnetic fields surrounding the nonlinear plasma “bubble” formed around the high-current electron bunch in a plasma wakefield accelerator is developed. The model, justified by the results of particle-in-cell simulations, accurately captures the thin high-density plasma sheath and extended return current layer surrounding the bubble. The resulting global fields inside and outside the bubble are used to investigate electron self-injection in a plasma with a smooth density gradient. It is shown that accurate description of the current/density sheaths is crucial for quantitative description of self-injection.
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