Implementation of high order spline interpolations for tracking test particles in discretized fields

A systematic approach for constructing high order spline interpolation methods is proposed for fields known on regular, rectangular grids. These interpolation methods are tested in tracking trajectories of particles submitted to a force that derives from a potential known on a grid. The interplay between the time advancement scheme and the spatial interpolation is studied in detail and it is shown how the order of the trajectory solver is directly affected by the order of the spline interpolation. It is also shown how an interpolation method that preserves topological properties of physical fields can be better exploited with these higher order spline approximations.