Variational Formulation of Macroparticle Models for Electromagnetic Plasma Simulations

A variational method is used to derive a self-consistent macroparticle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work, discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macroparticles of arbitrary shape and discretization of field quantities onto a spatial grid. This approach may be used with lab frame coordinates or moving window coordinates; the latter can greatly improve computational efficiency for studying some types of laser-plasma interactions. The primary advantage of the variational approach is the preservation of Lagrangian symmetries, which in our case leads to energy conservation and thus avoids difficulties with grid heating. In addition, this approach decouples particle size from grid spacing and relaxes restrictions on particle shape, leading to low numerical noise. The variational approach also guarantees consistent approximations in the equations of motion and is amenable to higher order methods in both space and time. We restrict our attention to the 1.5-D case (one coordinate and two momenta). Simulations are performed with the new models and demonstrate energy conservation and low noise.