Plasma parameters

Plasma parameters define various characteristics of a plasma, an electrically conductive collection of charged particles that responds collectively to electromagnetic forces. Plasma typically takes the form of neutral gas-like clouds or charged ion beams, but may also include dust and grains.^[1] The behaviour of such particle systems can be studied statistically.^[2]

Fundamental plasma parameters

All quantities are in Gaussian (cgs) units except energy and temperature expressed in eV and ion mass expressed in units of the proton mass $\mu =m_{i}/m_{p}$ ; $Z$ is charge state; $k$ is Boltzmann's constant; $K$ is wavenumber; $\ln \Lambda$ is the Coulomb logarithm.

Frequencies

electron gyrofrequency, the angular frequency of the circular motion of an electron in the plane perpendicular to the magnetic field:

\omega _{ce}=eB/m_{e}=1.76\times 10^{11}B\ {\mbox{rad/s}}\,

ion gyrofrequency, the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field:

\omega _{ci}=ZeB/m_{i}c=9.58\times 10^{3}Z\mu ^{-1}B\ {\mbox{rad/s}}\,

electron plasma frequency, the frequency with which electrons oscillate (plasma oscillation):

\omega _{pe}=(4\pi n_{e}e^{2}/m_{e})^{1/2}=5.64\times 10^{4}n_{e}^{1/2}{\mbox{rad/s}}

ion plasma frequency:

\omega _{pi}=(4\pi n_{i}Z^{2}e^{2}/m_{i})^{1/2}=1.32\times 10^{3}Z\mu ^{-1/2}n_{i}^{1/2}{\mbox{rad/s}}

electron trapping rate:

\nu _{Te}=(eKE/m_{e})^{1/2}=7.26\times 10^{8}K^{1/2}E^{1/2}{\mbox{s}}^{-1}\,

ion trapping rate:

\nu _{Ti}=(ZeKE/m_{i})^{1/2}=1.69\times 10^{7}Z^{1/2}K^{1/2}E^{1/2}\mu ^{-1/2}{\mbox{s}}^{-1}\,

electron collision rate in completely ionized plasmas:

\nu _{e}=2.91\times 10^{-6}n_{e}\,\ln \Lambda \,T_{e}^{-3/2}{\mbox{s}}^{-1}

ion collision rate in completely ionized plasmas:

\nu _{i}=4.80\times 10^{-8}Z^{4}\mu ^{-1/2}n_{i}\,\ln \Lambda \,T_{i}^{-3/2}{\mbox{s}}^{-1}

electron (ion) collision rate in slightly ionized plasmas:

\nu _{e,i}=N{\overline {\sigma _{e,i}v}}=N\int \limits _{0}^{\infty }\sigma (v)_{e,i}f(v)vdv

where $\sigma (v)_{e,i}$ is a collision crossection of the electron (ion) on the operating gas atoms (molecules), $f(v)$ is the electron (ion)

distribution function in plasma, and $N$ is an operating gas concentration.

Lengths

Electron thermal de Broglie wavelength, approximate average de Broglie wavelength of electrons in a plasma:

\Lambda _{e}={\sqrt {\frac {h^{2}}{2\pi m_{e}kT_{e}}}}=6.919\times 10^{-8}\,T_{e}^{-1/2}\,{\mbox{cm}}

classical distance of closest approach, the closest that two particles with the elementary charge come to each other if they approach head-on and

each have a velocity typical of the temperature, ignoring quantum-mechanical effects:

e^{2}/kT=1.44\times 10^{-7}\,T^{-1}\,{\mbox{cm}}

electron gyroradius, the radius of the circular motion of an electron in the plane perpendicular to the magnetic field:

r_{e}=v_{Te}/\omega _{ce}=2.38\,T_{e}^{1/2}B^{-1}\,{\mbox{cm}}

ion gyroradius, the radius of the circular motion of an ion in the plane perpendicular to the magnetic field:

r_{i}=v_{Ti}/\omega _{ci}=1.02\times 10^{2}\,\mu ^{1/2}Z^{-1}T_{i}^{1/2}B^{-1}\,{\mbox{cm}}

plasma skin depth, the depth in a plasma to which electromagnetic radiation can penetrate:

c/\omega _{pe}=5.31\times 10^{5}\,n_{e}^{-1/2}\,{\mbox{cm}}

Debye length, the scale over which electric fields are screened out by a redistribution of the electrons:

\lambda _{D}=(kT/4\pi ne^{2})^{1/2}=7.43\times 10^{2}\,T^{1/2}n^{-1/2}\,{\mbox{cm}}

Ion inertial length, the scale at which ions decouple from electrons and the magnetic field becomes frozen into the electron fluid rather than the bulk plasma: