EM Wave in Plasma: Reflection, Attenuation & Radiated Power

[Euclid]

Can a monochromatic plane EM wave exists in a plasma when $$\omega$$ is less than $$\omega_p$$ (the plasma frequency)? If so, is it attenuated?
I read in a text that a wave incident on a plasma with $$\omega < \omega_p$$ is completely reflected, but does this mean such a wave can't exist in a plasma?
If $$\omega > \omega_p$$, is the (time averaged) power radiated just the same as a plane wave in vacuum ?

I get $$\mathbb{S} = \frac{cE^2}{8\pi \omega}\sqrt{\omega^2 - \omega_p^2}\textbf{z}$$ for omega > omega_p.

 

[Tide]

Your answer to power flux question (Poynting vector) should convince you that a wave whose frequency is less than the plasma frequency cannot propagate.

 

[Euclid]

It does not convince me because my solution is not valid in that domain. For when omega < omega_p the wave vector k becomes complex, so the wave has spatial dependence ~e^(-alpha z) for some real alpha. In a wave guide, this implied attenuation, but here it seems to imply that the wave cannot propogate.

 

[Tide]

It does not convince me because my solution is not valid in that domain. For when omega < omega_p the wave vector k becomes complex, so the wave has spatial dependence ~e^(-alpha z) for some real alpha. In a wave guide, this implied attenuation, but here it seems to imply that the wave cannot propogate.

That's precisely because it does not propagate and is what "attenuation" or evanescence means.