# How does a plasma react to a non-uniform, oscillating magnetic field?

The ponderomotive force tells me that if I apply some non-uniform oscillating acceleration field $$\ddot{x} = g(x) cos (\omega t)$$ where $$g(x)$$ is the strength of the field as a function of location and $$cos(\omega t)$$ describes high frequency oscillations, it will result in some motion towards decreasing $$g(x)$$:

$$\ddot{x}_0 = - \frac{1}{4 \omega^2}\frac{d}{dx}[g(x)^2]$$

This makes sense intuitively and the wiki page explains the phenomenon of the ponderomotive force well.

But supposing now that I have some plasma with known properties that is subject to a non-uniform oscillating magnetic field (as is the case in the Electrodeless Plasma Thruster), what is the function that describes the net force exerted on the plasma?

What's confusing me is that I cannot simply ask "what's the motion of the plasma under a magnetic field" and then derive the ponderomotive effect myself, because a plasma is electrically neutral so presumably that wouldn't get me very far.

• Have you tried looking at Faraday's law? Jun 1, 2020 at 13:31
• No I haven't, but thanks for the tip - I'll have a look. Jun 2, 2020 at 9:48