What is Plasma; the free-electron model? — Physics

Definition 14.1 University Physics — Year 2 · Chapter 14 — Electromagnetic Waves in Plasmas, Conductors and Dielectrics

A plasma is a globally neutral gas of free electrons (density $n$ , mass $m$ , charge $-e$ ) and positive ions, which, being thousands of times heavier, are taken as fixed. The upper atmosphere (ionosphere, $n \sim 10^{11}$ – $10^{12}$ m $^{-3}$ ), a discharge tube, the solar corona, and — at optical frequencies — the conduction electrons of a metal are plasmas. Collisions are neglected (the wave’s period is short compared with the time between collisions). Its characteristic frequency is the plasma frequency

\omega_p = \sqrt{\frac{ne^2}{\varepsilon_0m}} , \qquad f_p = \frac{\omega_p}{2\pi} \approx 9\,\text{Hz}\times\sqrt{n\,[\text{m}^{-3}]} :

$3\,\mathrm{MHz}$ to $9\,\mathrm{MHz}$ for the ionosphere, $2 \times 10^{15}\,\mathrm{Hz}$ (ultraviolet) for a metal.

Left: the dispersion relation of a plasma — no propagation below _p, a hyperbola approaching the light line above. Right: shortwaves below the plasma frequency are reflected by the ionosphere and hop around the Earth; higher frequencies escape to space. — Left: the dispersion relation of a plasma — no propagation below $\omega_p$ , a hyperbola approaching the light line above. Right: shortwaves below the plasma frequency are reflected by the ionosphere and hop around the Earth; higher frequencies escape to space.

Examples

Example 14.4 (The ionosphere and radio)

With $n = 1 \times 10^{12}\,\mathrm{m}^{-3}$ in the F layer, $f_p = 9\,\mathrm{MHz}$ : shortwave broadcasts below that are reflected (and can hop around the Earth between the ionosphere and the ground), FM ( $100\,\mathrm{MHz}$ ), television and satellite links pass through. A wave at $3\,\mathrm{MHz}$ penetrates only $1/\kappa = c/\sqrt{\omega_p^2 - \omega^2} = 6\,\mathrm{m}$ into the layer before turning back. A spacecraft re-entering the atmosphere is sheathed in a plasma of $n \sim 10^{18}$ m $^{-3}$ , $f_p \sim 10\,\mathrm{GHz}$ : radio contact is lost for minutes.

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