Abstract
Emittance is a beam quality that is vital for many future applications of advanced accelerators, such as compact free-electron lasers and linear colliders. In this paper, we review the challenges of preserving the transverse emittance during acceleration, both inside and outside accelerator stages. Sources of emittance growth range from space charge and instabilities caused by transverse wakefields, which can occur in any advanced accelerator scheme regardless of medium or driver type, to sources more specific to plasma accelerators, such as mismatching, misalignment, ion motion, Coulomb scattering, chromaticity between stages, and more.
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