Acceleration of electrons by moving intensity minima of laser fields with dynamic superposition

The question of how the trapping and moving of electrons in the intensity minima is possible is addressed. It has been asked whether the electrons are not slipping through the standing wave field or the accelerated intensity minima if one would follow up the individual quiver motion of the electrons instead of the time averaged nonlinear forces. In order to demonstrate that the electrons are not slipping through the electromagnetic field according to the time averaged nonlinear force, a detailed numerical calculation is performed. A complicated differential equation problem is then solved. The results agree with the otherwise expected time averaged nonlinear force description, and no slipping through or other unexpected mechanisms occur