Hamiltonian description of low-temperature relativistic plasmas

Variable-moment fluid closures with Hamiltonian structure

Based on ideas due to Scovel-Weinstein, I present a general framework for constructing fluid moment closures of the Vlasov-Poisson system that exactly preserve that system's Hamiltonian structure. Notably, the technique applies in any space dimension and produces closures involving arbitrarily-large finite collections of moments. After selecting a desired collection of moments, the Poisson bracket for the closure is uniquely determined. Therefore data-driven fluid closures can be constructed by adjusting the closure Hamiltonian for compatibility with kinetic simulations.

Time-dependent closure relations for relativistic collisionless fluid equations

Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space (ω,k), where ω and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter ω/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc²/T , where m is the particle rest mass and T, the plasma temperature in energy units.

Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves

A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.

Unphysical kinetic effects in particle-in-cell modeling of laser wakefield accelerators

Unphysical heating and macroparticle trapping that arise in the numerical modeling of laser wakefield accelerators using particle-in-cell codes are investigated. A dark current free laser wakefield accelerator stage, in which no trapping of background plasma electrons into the plasma wave should occur, and a highly nonlinear cavitated wake with self-trapping, are modeled. Numerical errors can lead to errors in the macroparticle orbits in both phase and momentum. These errors grow as a function of distance behind the drive laser and can be large enough to result in unphysical trapping in the plasma wake. The resulting numerical heating in intense short-pulse laser-plasma interactions grows much faster and to a higher level than the known numerical grid heating of an initially warm plasma in an undriven system. The amount of heating, at least in the region immediately behind the laser pulse, can, in general, be decreased by decreasing the grid size, increasing the number of particles per cell, or using smoother interpolation methods. The effect of numerical heating on macroparticle trapping is less severe in a highly nonlinear cavitated wake, since trapping occurs in the first plasma wave period immediately behind the laser pulse.

Warm wave breaking of nonlinear plasma waves with arbitrary phase velocities

A warm, relativistic fluid theory of a nonequilibrium, collisionless plasma is developed to analyze nonlinear plasma waves excited by intense drive beams. The maximum amplitude and wavelength are calculated for nonrelativistic plasma temperatures and arbitrary plasma wave phase velocities. The maximum amplitude is shown to increase in the presence of a laser field. These results set a limit to the achievable gradient in plasma-based accelerators.