Nonlocal properties of the ponderomotive force in high intensity laser fields-An approach based on the noncanonical Lie perturbation theory

In order to study the nonlocal particle dynamics in tightly focused laser fields in the order of wave length, we present a theoretical framework of relativistic ponderomotive force by using the noncanonical Lie perturbation theory based on the phase space Lagrangian formalism that keeps the Hamiltonian structure rigorously. Introducing a smallness parameter e, the ratio of the particle excursion length to the scale length of the gradient of the laser field amplitude, we perform the perturbation analysis up to the second order e2, which contain the effect of the field curvature, and obtain the oscillation center equation of motion averaged over the fast laser period. A betatron-like oscillation which corresponds to a confinement state of the particle in the laser field without suffering ejection due to the field curvature is analytically found.