Comparison of Integrators for Electromagnetic Particle in Cell Methods: Algorithms and Applications

In this paper, we present different types of integrators for electro-magnetic particle-in-cell (PIC) methods. While the integrator is an important tool of the PIC methods, it is necessary to characterize the different conservation approaches of the integrators, e.g. symplecticity, energy- or charge-conservation. We discuss the different principles, e.g. composition, filtering, explicit and implicit ideas. While, particle in cell methods are well-studied, the combination between the different parts, i.e. pusher, solver and approximations are hardly to analyze. we concentrate on choosing the optimal pusher component, with respect to conservation and convergence behavior. We discuss oscillations of the pusher component, strong external magnetic fields and optimal conservation of energy and momentum. The algorithmic ideas are discussed and numerical experiments compare the exactness of the different schemes. An outlook to overcome the different error components is discussed in the future works.