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We describe a method for symplectic tracking of charged particles throughstatic electric and magnetic fields. The method can be applied to cases wherethe fields have a dependence on longitudinal as well as transverse position,and where the reference trajectory may have non-zero curvature. Application ofthe method requires analytical expressions for the scalar and vectorpotentials: we show how suitable expressions, in the form of series analogousto multipole expansions, can be constructed from numerical field data, allowingthe method to be used in cases where only numerical field data are available.

Explicit symplectic integrator for particle tracking in s-dependent static electric and magnetic fields with curved reference trajectory