Kinetic Continuum Simulations of Special Relativistic Plasmas
Grant Johnson, Princeton University
We have extended the existing Maxwell solver in the code Gkeyll in order to simulate relativistic plasmas. The extensions include routines for calculating the special relativistic moments in our Discontinuous-Galerkin scheme, as well as initializing the plasma to a relativistic Maxwell-Jüttner (MJ) distribution. Inaccuracies in the projected distribution arise from the finite velocity bounds of the domain, which may not capture the entire distribution function, and from projecting the function onto the discrete grid. Additional complications occur when calculating nonlinear quantities (e.g., the Lorentz factor) for the moments on the grid. By computing the moments of the projected distribution function, using Gauss-Legendre quadrature for nonlinear quantities, and iteratively perturbing moments calculated by this procedure until they converge to machine precision, we can correct for these errors introduced by the discrete projection. The resulting routine was shown to maintain the moments with a BGK operator while reshaping the distribution, a critical property for not introducing charge perturbations. As well, we verified the accuracy of the integrated Vlasov-Maxwell system by close agreement between the linear growth rates of relativistic, warm Weibel and two-stream instabilities and analytic theory.
Abstract Author(s): Grant Johnson, Jimmy Juno, Ammar Hakim