# Frequency higher then plasma frequency

## Main Question or Discussion Point

Electromagnetic wave with higher frequency then plasma frequency are barely attenuated. I always hear that the reason is the electrons cant oscillate fast enought... how does that actually work? (how can an electron not be able to oscillate at the same speed?)

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Born2bwire
Gold Member
Because the behavior of a plasma is non-linear. Take a look at the "Convective Derivative." A normal force equation, assuming constant mass, is just $$m\frac{\partial \mathbf{v}}{\partial t}$$ but when we talk about plasma, there is an extra term that arises resulting in the force being $$m\left[\frac{\partial \mathbf{u}}{\partial t} + \left(\mathbf{u}\cdot \nabla \right)\mathbf{u} \right]$$. This non-linearity gives rise to the ponderamotive force and other effects that will affect the propagation. In addition, electrons have mass and thus will time-lag the electric feld due to their inertia. If the frequency is low enough, the lag is negligible but at very very high frequencies they cannot keep up with the oscillations. This is a common assumption with the ions but it can apply to the electrons too.