Speed up field line tracing #79
Description
After discussion at ISHW with @jonathanschilling we had the idea to speed up field line tracing by using symplectic integration.
Another, possibly even faster and simpler alternative would be to construct an interpolation of the single-turn map between Poincaré cuts and then evaluate the map for the number of turns. Construction requires 1e4-1e6 field lines to be traced over a single toroidal turn with the existing Runge-Kutta scheme and can be done in parallel.
See e.g. Kasilov et al, Phys. Plasmas 9, 3508 (2002); https://doi.org/10.1063/1.1493793 which is already much more complicated as particle orbits are mapped instead of field lines. This is also related to #47 as on can start tracing at arbitrary theta based on such a map.