Help with EM waves travelling through a plasma

[can't.do.phys]

I've been given a practice question for an exam and I can't quite get it started. The question is: Intelligent beings on a distant planet try and communicate with Earth by sending powerful radio waves swept in frequency from 10 to 50MHz per minute. The linearly polarized emissions must pass through a radiation belt plasma in such a way that E and k are perpendicular to B₀. It is found that during solar flares on their sun, frequencies between 24.25 and 28MHz do not get through their radiation belt. From this deduce the plasma frequency and magnetic field there.
I think I have to figure out the group velocity but does it also have to do with the cut off region of a plasma frequency? and how do I connect it all together to find out the plasma density and magnetic field? I'm so confused.

 

[the_wolfman]

First you need to identify what type plasma wave(s) are being used. There are a multitude of different EM waves that propagate in a plasma. Some of them have k parallel to the background B others have k perpendicular to B. The same is true with the perturbed E and background B.

Once you have narrowed down the possible waves, start looking at their properties. Do they have cutoffs? Do they have any resonances? Are there frequencies where these waves are evanescent (they don't propagate)?

How do you relate these cut-offs and such to the plasma density or background B?

I suggest looking at Chen's Introduction to Plasma Physics and Controlled Fusion for a detailed introduction to plasma waves.