What is the critical electron density in a plasma?

Question

In the article Ion Acceleration and D-D Nuclear Fusion in Laser-Generated Plasma from Advanced Deuterated Polyethylene by Lorenzo Torrisi, the author mentions a critical electron density on page 17057. What is this? Can't laser light propagate through a plasma if the electron density exceeds a certain value?

Laser beam propagates through this plasma because its electron density is lower than the critical one losing both spatial and temporal coherence due to the forward scattering of the laser light on the plasma density perturbations induced by the laser itself. [from page 17057]

Answer 1

The dispersion relation for electromagnetic waves in a plasma well below the cyclotron frequency looks like this:

$$ n^2 = 1 - \frac{\omega_{pe}^2}{\omega^2} $$

$\omega_{pe}$ is the plasma frequency. When the propagating wave frequency $\omega$ equals the plasma frequency, the index of refraction $n$ goes to zero.

$$n_{cutoff} = \frac{\omega^2 m}{4 \pi e^2} $$

Above this density, the electromagnetic wave (light) with frequency $\omega$ is attenuated. You have to have pretty high densities for a plasma to be overdense for visible light, but it can be a concern for longer wavelength/lower frequency waves.

There is a treatment of this in Hutchinson's Principles of Plasma Diagnostics amongst other places.

• Wiki - cut-off frequency