Lattice Boltzmann method for warm fluid simulations of plasma wakefield acceleration

A comprehensive characterization of lattice Boltzmann (LB) schemes to perform warm fluid numerical simulations of particle wakefield acceleration (PWFA) processes is discussed in this paper. The LB schemes we develop hinge on the moment matching procedure, allowing the fluid description of a warm relativistic plasma wake generated by a driver pulse propagating in a neutral plasma. We focus on fluid models equations resulting from two popular closure assumptions of the relativistic kinetic equations, i.e., the local equilibrium and the warm plasma closure assumptions. The developed LB schemes can, thus, be used to disclose insights on the quantitative differences between the two closure approaches in the dynamics of PWFA processes. Comparisons between the proposed schemes and available analytical results are extensively addressed.