Particle tracking on triangles and tetrahedrons is done by integrating the relativistic particle dynamical equation from an entry to an exit point within each element that is traversed by the particle. Critical to this approach is the identification of exact entry and exit points so that the particle may be transferred to the next element, so the particle integration is started/stopped at each element boundary.
The dynamical equations that must be integrated to determine the particle trajectory are its velocity:
where is the particle position, is the normalized momentum, and , are the normalized electric and magnetic fields, respectively. Note that for multipacting computations the effects of space-charge on the particle orbits is not considered. Instead, the calculation is a ray-tracing exercise, where the particles move only under the influence of the external static and RF fields. These equations are integrated using either the backward-difference method or the Runge-Kutta method, depending on your selection.