Extreme nonlinear dynamics in vacuum laser acceleration with a crossed beam configuration

A relatively simple model problem where a single electron moves in two relativistically strong obliquely intersecting plane wave-packets is studied using a number of different numerical solvers. It is shown that, in general, even the most advanced solvers are unable to obtain converged solutions for more than about 100 fs in contrast to the single plane wave problem, and that some basic metrics of the orbit show enormous sensitivity to the initial conditions. At a bare minimum, this indicates an unusual degree of nonlinearity, and may well indicate that the dynamics of this system are chaotic.