Interpolation of turbulent magnetic fields and its consequences on diffusive cosmic ray propagation

Abstract: Numerical simulations of the propagation of charged particles through magnetic fields solving the equation of motion often leads to the usage of an interpolation in case of discretely defined magnetic fields, typically given on a homogeneous grid structure. However, the interpolation method influences the magnetic field properties on the scales of the grid spacing and the choice of interpolation routine can therefore change the result. At the same time, it provides an impact, i.e.\ error, on the spatial particle distribution. We compare three different interpolation routines -- trilinear, tricubic and nearest neighbor interpolation -- in the case of turbulent magnetic fields and show that there is no benefit in using trilinear interpolation. We show that in comparison, the nearest neighbor interpolation provides the best performance, i.e.\ requires least CPU time and results in the smallest error. In addition, we optimize the performance of an algorithm that generates a continuous grid-less turbulent magnetic field by more than an order of magnitude. This continuous method becomes practicable for the simulation of large particle numbers and its accuracy is only limited by the used number of wave-modes. We show that by using more than 100 wave-modes the diffusive behavior of the spatial particle distribution in form of the diffusion coefficient is determined with an error less than a few percentage.