Title: High Order Numerical Integrators for Relativistic Charged Particle Tracking,
Abstract: In this paper, we extend several time reversible numerical integrators to
solve the Lorentz force equations from second order accuracy to higher order
accuracy for relativistic charged particle tracking in electromagnetic fields.
A fourth order algorithm is given explicitly and tested with numerical
examples. Such high order numerical integrators can significantly save the
computational cost by using a larger step size in comparison to the second
order integrators.