What operating range is the ponderomotive approximation valid? Recalling the equation on the ponderomotive force experienced by a particle in a non-uniform oscillating electric field:
$$
F = \frac{q^{2}}{4 \ m \ \omega^{2}} \nabla E^{2}
$$
Could anyone shed light on what frequency range  the approximation applies?
 A: You generally assume the force is varying temporally fast, but spatially slow such that you can define a particle's position as a function of time as:
$$
x(t) = x_{o}(t) + \delta x(t)
$$ 
where the $x_{o}$ term is slowly varying term and the $\delta x$ term is for the quickly varying temporal term.  From this we also assume that $\lvert \delta x \rvert$ $\ll$ $\lvert x_{o} \rvert$ and $\lvert \delta \ddot{x} \rvert$ $\gg$ $\lvert \ddot{x}_{o} \rvert$ (where $\ddot{x}$ = $\tfrac{d^{2} x}{dt^{2}}$), i.e., the $\delta x$ changes are small spatially but the acceleration is large.  Another way to say this is that the following should be satisfied:
$$
k \lvert \delta x \rvert \ll 1
$$
which is basically saying the wavelength should be large compared to the spatial oscillation scale length.
As for the frequency, the ponderomotive effect is often invoked for Langmuir waves, which have rest frame frequencies, $\omega_{o}$, near the local electron plasma frequency, $\omega_{pe}$.  That is, the effect is valid for $\omega_{o}$ ~ $\omega_{pe}$.  If the rest frame frequency were down near the proton cyclotron frequency, $\Omega_{cp}$, however, and one wanted to examine ponderomotive effects on electrons the effect would not matter.  This is because the time varying fields are slower than the transit time of the electrons, which would violate the fast time variation assumption discussed above.
You can think of it in terms of potentials, where the ponderomotive potential goes as $\phi$ $\propto$ $\langle \delta v^{2} \rangle$, where $\delta v$ is the fluctuation velocity of the particles in the potential and $\langle \rangle$ is a spatial ensemble average.
Note that the lower frequency bound is not some set value but rather a relative term.  The proton plasma frequency ($\omega_{pp}$), for instance, is still fast enough for ponderomotive effects to matter on electrons.  In the case of three-wave decay of Langmuir waves, one of the daughter waves is an electrostatic ion acoustic wave which oscillates nearly at $\omega_{pp}$.  Note that $\omega_{pe}$ ~ 43 $\omega_{pp}$, but even so the ponderomotive force still matters.
