Relativistic ponderomotive force, uphill acceleration, and transition to chaos

Starting from a covariant cycle-averaged Lagrangian the relativistic oscillation center equation of motion of a point charge is deduced and analytical formulae for the ponderomotive force in a travelling wave of arbitrary strength are presented. It is further shown that the ponderomotive forces for transverse and longitudinal waves are different; in the latter, uphill acceleration can occur. In a standing wave there exists a threshold intensity above which, owing to transition to chaos, the secular motion can no longer be described by a regular ponderomotive force. PACS number(s): 52.20.Dq,05.45.+b,52.35.Mw,52.60.+h