On the nonlocal properties of relativistic ponderomotive force

Abstract

A theory of relativistic ponderomotive force of transversely localized laser fields is presented by taking into account the nonlocal effects that correspond to higher order terms of the expansion parameter ϵ≡l/L, i.e., the ratio between particle excursion length and scale length of the field amplitude gradient, while the existing local theory is the first order of ϵ. As a method for preserving the Hamiltonian structure up to higher orders, we employ the variational principle in noncanonical phase space coordinates incorporated with the Lie transformation. By finding noncanonical coordinates and gauges, we obtain a new formula for the ponderomotive force that involves new terms in the third order represented by the second and third spatial derivatives. The force then depends not only on the local field gradient but also on the curvature and its variation which represent the effects of higher-order nonlocal particle motion. The higher-order terms are found to be subject to the symmetry of the field structure. The obtained formula is accessible to the regime in which the higher derivatives of the field amplitude regulate the interaction. We have applied the formula to laser fields exhibiting flat-top super Gaussian and concave hollow transverse structures which are effective in maintaining the long time scale interaction. The associated nonlocal effects are found to play a key role in determining the interactions. Comparison with the direct integration of the particle orbit demonstrates the validity of the derived formula.