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

Neutron star emission originates typically from its magnetosphere due to radiating electrons. Trajectories of relativistic charged particles under uniform electromagnetic fields can be calculated analytically. However, under more complex and realistic fields, numerical solutions are required. Two common schemes are the Boris method, which solves the full equations of motion, and the guiding center approximation (GCA), which only evolves the orbital center. We compare both methods in a series of tests, discuss their characteristics and quantify their accuracy. We apply the methods to dipolar, quadrupolar, and quadrudipolar magnetic fields, as applicable for magnetospheres. It is essential to consider such realistic neutron star magnetic field geometries to model the emission from magnetars and pulsars. Our work can assist the Neutron Star Interior Composition ExploreR (NICER) to understand emission from the surface and magnetosphere of neutron stars and to study their composition.