Polarization-dependent ponderomotive gradient force in a standing wave

TL;DR

This paper derives a generalized, polarization-dependent ponderomotive force expression for relativistic particles in standing waves, revealing additional terms beyond the classical gradient force and confirming results with simulations.

Contribution

It introduces a new, more accurate ponderomotive force formula that accounts for polarization effects in three-dimensional standing wave fields.

Findings

The classical ponderomotive gradient force does not apply in this scenario.

The modified force includes polarization-dependent terms due to relativistic quiver motion.

Simulation results confirm the validity of the new analytical expression.

Abstract

The ponderomotive force is derived for a relativistic charged particle entering an electromagnetic standing wave with a general three-dimensional field distribution and a nonrelativistic intensity, using a perturbation expansion method. It is shown that the well-known ponderomotive gradient force expression does not hold for this situation. The modified expression is still of simple gradient form, but contains additional polarization-dependent terms. These terms arise because the relativistic translational velocity induces a quiver motion in the direction of the magnetic force, which is the direction of large field gradients. Oscillation of the Lorentz factor effectively doubles this magnetic contribution. The derived ponderomotive force generalizes the polarization-dependent electron motion in a standing wave obtained earlier [A.E. Kaplan and A.L. Pokrovsky, Phys. Rev. Lett. $\bm{95}$, 053601 (2005)]. Comparison with simulations in the case of a realistic, non-idealized, three-dimensional field configuration confirms the general validity of the analytical results.