A symplectic, symmetric algorithm for spatial evolution of particles in a time-dependent field

A symplectic, symmetric, second-order scheme is constructed for particle evolution in a time-dependent field with a fixed spatial step. The scheme is implemented in one space dimension and tested, showing excellent adequacy to experiment analysis. Higher order schemes are deduced by composition.

► New algorithm to calculate accurately particle motions in given wavefields.
► Taylored to describe directly observable properties of the particle motion.
► Avoiding interpolations (used to estimate passage times in fixed timestep methods).
► Intrinsically symplectic.