Variational formulation of particle algorithms for kinetic electromagnetic plasma simulations

Abstract

Summary form given only. A rigorous variational methodology was used to derive a selfconsistent set of discrete macro-particle kinetic plasma equations from a discretized Lagrangian. Discretization of the Lagrangian was performed by reduction of the phase-space distribution function to a collection of finite-sized macroparticles of arbitrary shape, and subsequent discretization of the field onto a spatial grid. The equations of motion were then obtained by demanding the action be stationary upon variation of the particles and field quantities. This yields a finite-degree of freedom description of the particle-field system which is inherently self-consistent. This project extends the work of Evstatiev et al.1 from a simplified electrostatic formulation to the full electromagnetic case. The primary advantage of variational approaches relative to the more common Particle-In-Cell (PIC) formulation is that they preserve the symmetry of the Lagrangian, which in our case leads to energy conservation and avoids difficulties with grid heating. Additional benefits originate from the decoupling of particle size from grid spacing and a relaxation of the restrictions on particle shape, which leads to a decrease in numerical noise. The variational approach also guarantees a consistent level of approximation, and is amiable to higherorder approximations in both space and time. For many configurations of interest to laser-driven plasma accelerators, it is computationally efficient to use a coordinate system co-moving with the laser pulse. Since we are using a Lagrangian formulation, we can easily transform to moving window coordinates yielding a particle algorithm explicitly formulated in the moving window. Thus we, for the first time, demonstrate an energy conserving set of discrete equations in moving window coordinates rigorously derived from a discretized electromagnetic Lagrangian. Example simulations conducted with the new equations of motion demonstrate the desired energy conservation.