Self-correcting longitudinal phase space in a multistage plasma accelerator

Plasma accelerators driven by intense laser or particle beams provide gigavolt-per-meter accelerating fields, promising to drastically shrink particle accelerators for high-energy physics and photon science. Applications such as linear colliders and free-electron lasers (FELs) require high energy and energy efficiency, but also high stability and beam quality. The latter includes low energy spread, which can be achieved by precise beam loading of the plasma wakefield using longitudinally shaped bunches, resulting in efficient and uniform acceleration. However, the plasma wavelength, which sets the scale for the region of very large accelerating fields to be 100 {\mu}m or smaller, requires bunches to be synchronized and shaped with extreme temporal precision, typically on the femtosecond scale. Here, a self-correction mechanism is introduced, greatly reducing the susceptibility to jitter. Using multiple accelerating stages, each with a small bunch compression between them, almost any initial bunch, regardless of current profile or injection phase, will self-correct into the current profile that flattens the wakefield, damping the relative energy spread and any energy offsets. As a consequence, staging can be used not only to reach high energies, but also to produce the exquisite beam quality and stability required for a variety of applications.