Convergence, stability and accuracy of a new high order relativistic particle push method

Abstract

Within the environment of the 3D/PIC code PicLas development for simulating the plasma flow in IMPD thruster we present a new algorithm for the particle treatment which supports any arbitrary order of approximation of the Maxwell field solver. The new approach is not limited to special kind of field solver, it can be linked with all classical methods as well as finite volume and discontinuous Galerkin schemes. To achieve a high order Maxwell-Vlasov module, we propose a particle treatment based on Taylor series expansion in time up to the desired (high) order of the field solver, where the occurring derivatives in the expansion can be computed in a recursive manner. The high order time derivatives of the electromagnetic fields needed for particle treatment are directly given from the Maxwell solver, where a Cauchy-Kovalevskaya procedure is applied. The evidence of the effective order of convergence for this method is demonstrated with 3D examples and listed in charts. Furthermore we investigated the properties of this new method and compare them to the well known classic Boris leap frog scheme. With a comparison in numerical effort and accuracy we like to point out the decisive advantage of our new approach.