A Langmuir probe discharge has electron density and electron temperature

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Plasma Physics, Ch Waves that need pressure or tension: Langmuir, ion-acoustic, Alfven and magnetosonic

Problem

A Langmuir probe discharge has electron density

n_e = 5.0\times10^{18}\,\mathrm{m^{-3}}

and electron temperature

T_e = 3.0\,\mathrm{eV}

. A Bohm-Gross wave propagates with

k\lambda_{De} = 0.20

, where

\lambda_{De}

is the electron Debye length. ((a)) Find the electron plasma frequency

\omega_{pe}

and the electron thermal speed

v_{te} = (T_e/m_e)^{1/2}

. ((b)) Find

\lambda_{De}

and hence the wavenumber

k

. ((c)) Find the wave frequency

\omega

from the Bohm-Gross relation

\omega^2 = \omega_{pe}^2 + 3k^2v_{te}^2

, and the group velocity

v_g = 3kv_{te}^2/\omega