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In this paper, we extend several time reversible numerical integrators tosolve the Lorentz force equations from second order accuracy to higher orderaccuracy for relativistic charged particle tracking in electromagnetic fields.A fourth order algorithm is given explicitly and tested with numericalexamples. Such high order numerical integrators can significantly save thecomputational cost by using a larger step size in comparison to the secondorder integrators.

High Order Numerical Integrators for Relativistic Charged Particle Tracking