Ponderomotive force
In physics, a ponderomotive force is a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field.
The ponderomotive force Fp is expressed by
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 E is the amplitude of the electric field. At low enough amplitudes the magnetic field exerts very little force.
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 Fp toward the weak field direction. This is a rare case where the sign of the charge on the particle does not change the direction of the force ((-e)2=(+e)2).
The mechanism of the ponderomotive force can be understood by considering the motion of a charge in an oscillating electric field. In the case of a homogeneous field, the charge returns to its initial position after one cycle of oscillation. In the case of an inhomogeneous field, the force exerted on the charge during the half-cycle it spends in the area with higher field amplitude points in the direction where the field is weaker. It is larger than the force exerted during the half-cycle spent in the area with a lower field amplitude, which points towards the strong field area. Thus, averaged over a full cycle there is a net force that drives the charge toward the weak field area.
The derivation of the ponderomotive force expression proceeds as follows.
Consider a particle under the action of a non-uniform electric field oscillating at frequency in the x-direction. The equation of motion is given by:
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