Ponderomotive force, proportional to , ⟨E4⟩ acting on a charged particle travelling across an inhomogeneous electromagnetic wave

A numerical investigation is reported of the passage of charged particles across a spatially inhomogeneous hf field. It is shown that a particle crossing a linearly polarised inhomogeneous wave experiences an average force proportional to ⟨E⁴⟩ . The force has components along the directions of particle motion and wave propagation. Expressions describing this force are obtained in the approximation of a small nonlinear parameter.