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Plasma-based accelerators (PBAs), having demonstrated the production of GeVelectron beams in only centimetre scales, offer a path towards a new generationof highly compact and cost-effective particle accelerators. However, achievingthe required beam quality, particularly on the energy spread for applicationssuch as free-electron lasers, remains a challenge. Here we investigatefundamental sources of energy spread and bunch length in PBAs which arise fromthe betatron motion of beam electrons. We present an analytical theory,validated against particle-in-cell simulations, which accurately describesthese phenomena. Significant impact on the beam quality is predicted forcertain configurations, explaining previously observed limitations on theachievable bunch length and energy spread. Guidelines for mitigating thesecontributions towards high-quality beams are deduced.

Intrinsic energy spread and bunch length growth in plasma-based accelerators due to betatron motion