Variational formulation of macro-particle plasma simulation algorithms

A variation formulation of macro-particle kinetic plasma models is discussed. In the electrostatic case, the use of symplectic integrators is investigated and found to offer advantages over typical generic methods. For the electromagnetic case, gauge invariance and momentum conservation are considered in detail. It is shown that, while the symmetries responsible for these conservation laws are broken in the presence of a spatial grid, the conservation laws hold in an average sense. The requirements for exact invariance are explored and it is shown that one viable option is to represent the potentials with a truncated Fourier basis.