A finite radius plasma is proposed to generate wakefields that can focus and accelerate positron beams in a plasma wakefield accelerator. The finite radius plasma reduces the restoring force acting on the plasma electrons forming the plasma wakefield, resulting in an elongation of the on-axis return point of the electrons and, hence, creating a long, high-density electron filament. This results in a region with accelerating and focusing fields for positrons, allowing for the acceleration and quality-preserving transport of high-charge positron beams.
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