Relativistic Eulerian Plasma Kinetic Simulation Through Galerkin‐Ritz‐Like Base Functions

Vlasov equation is a partial differential equation of Hamiltonian‐Jacobi type. It combines with Maxwell equations and some special requirements to form a very fundamental model in plasma and beam physics. Even though these special requirements, such as macroscopic and microscopic non‐negativity, microscopic relativistic boundary conditions, are favorable to obtain strict solutions of the model, they are rarely utilized in many related theoretical and computational investigations. The idea of utilizing these special requirements is analogous to that of the Galerkin‐Ritz method, which refers to using a class of functions respecting special requirements to express test functions used in variational optimization of the “energy” functional associated with a partial differential equation. This work outlines a detailed procedure for achieving this method in Eulerian plasma kinetic simulation.