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Neutron star emission originates typically from its magnetosphere due toradiating electrons. Trajectories of relativistic charged particles underuniform electromagnetic fields can be calculated analytically. However, undermore complex and realistic fields, numerical solutions are required. Two commonschemes are the Boris method, which solves the full equations of motion, andthe guiding center approximation (GCA), which only evolves the orbital center.We compare both methods in a series of tests, discuss their characteristics andquantify their accuracy. We apply the methods to dipolar, quadrupolar, andquadrudipolar magnetic fields, as applicable for magnetospheres. It isessential to consider such realistic neutron star magnetic field geometries tomodel the emission from magnetars and pulsars. Our work can assist the NeutronStar Interior Composition ExploreR (NICER) to understand emission from thesurface and magnetosphere of neutron stars and to study their composition.

Charged Particle Motion in Neutron Star Magnetic Fields: A Comparison Between the Boris Algorithm and the Guiding Center Approximation