Self-Consistent Hamiltonian Model of Beam Transport in a Laser-Driven Plasma Accelerator

Starting from the two species (bulk and beam electron) Vlasov--Maxwell system, we develop a self-consistent Hamiltonian model of beam transport in a background plasma where the beam is described by phase-space moments. The formalism used, based on the Hamiltonian structure of the Vlasov--Maxwell system, is a direct extension of that previously used to derive our warm fluid model.\footnote{B. A. Shadwick, G. M. Tarkenton and E. H. Esarey, Phys.\ Rev.\ Lett.\ \textbf{93}, 175002 (2004).} The bulk plasma model is independent of the moment model for the beam; in practice we find that a fluid description of the bulk plasma is appropriate. We present a detailed study of beam propagation in a resonant laser-wakefield accelerator. We discuss optimization of the system with regard to energy gain and beam quality. We comment on the implications for GeV-class accelerator stages.