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Relativistic particle motion in a non-uniform linearly polarized high intensity laser field is analyzed by using the noncanonical Lie perturbation method, which is based on the perturbation theory of the phase space Lagrangian. By introducing the smallness parameter e as the ratio between the excursion length l and the scale length of the laser field amplitude L, the relativistic ponderomotive force and particle motion are derived up to the second order with respect to e, which correspond to the nonlocal extension of the conventional ponderomotive force. Specifically, the particle is found to exhibit a betatron-like oscillation with long period characterized by the curvature of the laser field amplitude. c

plasma and fusion research

Analysis of the Relativistic Ponderomotive Force and Higher-Order Particle Motion in a Non-Uniform Laser Field Using the Noncanonical Lie Perturbation Method