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Plasmas available for plasma wakefield accelerator experiments may have longitudinal and transverse density profiles that could affect the outcome of an experiment. This paper investigates the effect of plasmas with finite radius and inhomogeneous transverse density profiles on the wakefield excitation and the self-modulation instability (SMI) development in overdense plasmas. We focus here on the case of an electron bunch. Simulation results show that such plasmas generate larger focusing force for the propagating electron beam and therefore higher growth rate for the SMI. Although the initial accelerating field (Ez) amplitude is lower in such plasmas, the increased focusing force can dominate the development trend of the SMI, i.e., larger saturated Ez amplitude can be reached over similar plasma lengths.

Abstract. The proton bunch-driven plasma wakefield acceleration (PWFA) has been proposed as an approach to accelerate an electron beam to the TeV energy regime in a single plasma section. An experimental program has been recently proposed to demonstrate the capability of proton-driven PWFA by using existing proton beams from the European Organization for Nuclear Research (CERN) accelerator complex. At present, a spare Super Proton Synchrotron (SPS) tunnel, having a length of 600 m, could be used for this purpose. The layout of the experiment is introduced. Particlein-cell simulation results based on realistic SPS beam parameters are presented. Simulations show that working in a self-modulation regime, the wakefield driven by an SPS beam can accelerate an externally injected ∼10 MeV electrons to ∼2 GeV in a 10-m plasma, with a plasma density of 7 × 10 14 cm −3 .

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