Space charge modeling of dense electron beams with large energy spreads

Theoretical and numerical studies of the transport in vacuum of multi-nC, multi-MeV electron beams are performed using several methods, including envelope models, a novel semianalytic approach using ellipsoidal shell decomposition, a modified electrostatic particle-in-cell method, and a point-to-point interaction model. The effects of space-charge forces on the longitudinal and transverse bunch properties are evaluated for various bunch lengths, energies, energy spreads, and charges. An evaluation of the various methods for studying space-charge effects in large energy spread, high charge beams is summarized. Examples are given for beam distributions typical of those generated by plasma-based accelerators. It is found that, for the highly correlated beams produced in the self-modulated regime, the high energy portion of the beam can gain significant energy while propagating in vacuum due to space-charge effects.