Analysis of self-force error in relativistic PIC simulations

Summary form only given, as follows. A mathematically and physically rigorous error analysis of Maxwell´s equations coupled with Newton-Lorentz equation of motion for relativistic PIC simulations will be given. The goal of this work is an improved PIC algorithm for simulating relativistic plasmas; for example, accelerators and high power microwave tubes. The an analysis shows the error of the method in term of /spl Delta/t and /spl Delta/x, with computational verification. First, a brief review is presented of the error in the Maxwell and Newton-Lorentz equations analyzed separately. Next, the coupled equations will be analyzed for a single particle. The coupling is accomplished through the use of weighting functions to weight the particle contribution to the source terms of the Maxwell equations, /spl rho/ and J, to the grid. The converse operation, weighting the fields back to the particle location, is also considered. Finally, the Klimontovich equation, together with Maxwell´s equations, which constitutes an exact description of a plasma, is analyzed. The difference between this and the PIC algorithm defines the error. Refinements and extensions to reduce the error of the classical PIC method are described. The accuracy and stability of these new algorithms, as well as their impact on performance, are examined.