Phase Velocity and Particle Injection in a Self-Modulated Proton-Driven Plasma Wakefield Accelerator

Abstract

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.

Particle beam self-modulation instability in tapered and inhomogeneous plasma

“…9,12 This result indicates that the energy gain of a PWFA driven by a self-modulated beam in a uniform plasma will be severely limited by dephasing, and that, in the long-beam regime, dephasing is reached in less than four e foldings, independent of beam-plasma parameters. 9 For a PWFA in the linear regime, a witness bunch that propagates more than a dephasing length will not only move from an accelerating to a decelerating region, losing energy, but also from a focusing to a defocusing region, scattering the beam transversely.…”

“…Equation (4) indicates the inhomogeneity will not affect the growth if |(k 2 p − 1)r| ≪ |∂ζr|, which yields the condition In this work we have shown that tapering can be an effective method to compensate for the reduced phase velocity of the self-modulated beam-driven plasma wave. 9,12 For sufficiently fast taper, decoherence effects suppress the instability. A general condition for suppression of the growth via an initial plasma density inhomogeneity was derived, Eq.…”

Physics of beam self-modulation in plasma wakefield accelerators

“…There are two of them available. One model is the wave growth in the linearly responding uniform plasma [21]. It is characterized by the amplitude growth (4) and the phase shift…”

“…[11,21]. Since the plasma response is linear and axisymmetric, we simulate the SMI with the axisymmetric quasi-static 2d3v hybrid code LCODE [40,41], in which the beam is modeled with macro-particles, and plasma is treated as the electron fluid.…”

Coherent seeding of self-modulated plasma wakefield accelerators

“…It was also shown that the phase velocity of the plasma wave excited by a beam undergoing selfmodulation is significantly less than the velocity of the drive beam, limiting the energy gain. 14,15 Tapered plasmas may be considered to control the phase velocity of the selfmodulated beam-driven plasma wave, although sufficiently large background plasma density variations will suppress the self-modulation. 16 To avoid a witness bunch interacting with the slow-phase-velocity plasma wave driven by the self-modulating beam, one may consider injection of a witness bunch after saturation of the instability, when the drive beam is no 2 longer strongly evolving and the phase velocity approaches the drive beam velocity.…”