Ponderomotive force

In physics, a ponderomotive force is a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field. It causes the particle to move towards the area of the weaker field strength, rather than oscillating around an initial point as happens in a homogeneous field. This occurs because the particle sees a greater magnitude of force during the half of the oscillation period while it is in the area with the stronger field. The net force during its period in the weaker area in the second half of the oscillation does not offset the net force of the first half, and so over a complete cycle this makes the particle accelerate towards the area of lesser force.

The classical expression for the ponderomotive force F_p is

${\displaystyle \mathbf {F} _{\text{p}}=}$${\displaystyle -{\frac {e^{2}}{4m\omega ^{2}}}}$${\displaystyle \nabla }$${\displaystyle ({\hat {E}}^{2})}$

which has units of newtons (in SI units) and where e is the electrical charge of the particle, m is its mass, ω is the angular frequency of oscillation of the field, and ${\displaystyle {\hat {E}}}$ is the amplitude of the electric field. At non-relativistic particle velocities the magnetic field exerts very little force and can be disregarded.

This equation means that a charged particle in an inhomogeneous oscillating field not only oscillates at the frequency of ω of the field, but is also accelerated by F_p toward the weak field direction. This is a rare case in which the direction of the force does not depend on whether the particle is positively or negatively charged.