Plasma Physics: Debye Screening & Plasma Oscillations
Quasi-neutrality, Debye length, and plasma frequency — the basic length and time scales.
A plasma is a quasi-neutral collection of charged particles in which collective electromagnetic effects dominate over single-particle ones. Two basic scales:
Debye length: a test charge in a plasma is screened over
$$\lambda_D = \sqrt{\frac{\varepsilon_0 k_B T}{n e^2}}.$$The potential near a charge $q$ becomes $\phi(r) = (q / 4\pi\varepsilon_0 r) e^{-r/\lambda_D}$ — Yukawa-type screening from mobile electrons.
Plasma frequency: small electron displacements oscillate at
$$\omega_p = \sqrt{\frac{n e^2}{\varepsilon_0 m_e}}.$$EM waves below $\omega_p$ cannot propagate (reflected, as off the ionosphere). The number of particles in a Debye sphere $N_D = (4/3)\pi \lambda_D^3 n$ must be $\gg 1$ for plasma behavior; otherwise it's just a neutral gas with a few ions.