Modeling Asymmetric Beams Using Higher-Order Phase-Space Moments

Shadwick et al. developed [Commun. Nonlinear. Sci. Numer. Simulat. 17, 2153-2160 (2012)] a self-consistent model of beam transport using a phase-space moment description (up to 2nd order) based on the Vlasov-Maxwell Hamiltonian structure. Tzoufras et al. have shown [Physics of Plasmas 16, 056705 (2009)] that for a laser-wakefield-accelerated electron beam, the spatial profile that minimizes the energy spread is a trapezoidal distribution. This profile is spatially asymmetric and thus cannot be described by only using moments less than order three, and so the moment method developed by Shadwick et al. was expanded upon to account for asymmetry by taking the profile to be a sum of two gaussian >blobs.> It was found that, as long as the electric field across the beam was close to linear, treating the two blobs as separate species was a good approximation.