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. [Peratt, Anthony, "Physics of the Plasma Universe" (1992); ] The behaviour of such particle systems can be studied statistically. [Parks, George K., Physics of Space Plasmas (2004, 2nd Ed.)]

Fundamental plasma parameters

All quantities are in Gaussian cgs units except 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 wavelength; γ is the adiabatic index; ln Λ 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: :$omega\_\{ce\}\; =\; eB/m\_ec\; =\; 1.76\; imes\; 10^7\; B\; mbox\{rad/s\}\; ,$
*ion gyrofrequency, the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field: :$omega\_\{ci\}\; =\; eB/m\_ic\; =\; 9.58\; imes\; 10^3\; Z\; mu^\{-1\}\; B\; mbox\{rad/s\}\; ,$
*electron plasma frequency, the frequency with which electrons oscillate when their charge density is not equal to the ion charge density (plasma oscillation): :$omega\_\{pe\}\; =\; (4pi\; n\_ee^2/m\_e)^\{1/2\}\; =\; 5.64\; imes\; 10^4\; n\_e^\{1/2\}\; mbox\{rad/s\}$
*ion plasma frequency: :$omega\_\{pi\}\; =\; (4pi\; n\_iZ^2e^2/m\_i)^\{1/2\}\; =\; 1.32\; imes\; 10^3\; Z\; mu^\{-1/2\}\; n\_i^\{1/2\}\; mbox\{rad/s\}$
*electron trapping rate:$u\_\{Te\}\; =\; (eKE/m\_e)^\{1/2\}\; =\; 7.26\; imes\; 10^8\; K^\{1/2\}\; E^\{1/2\}\; mbox\{s\}^\{-1\}\; ,$
*ion trapping rate:$u\_\{Ti\}\; =\; (ZeKE/m\_i)^\{1/2\}\; =\; 1.69\; imes\; 10^7\; Z^\{1/2\}\; K^\{1/2\}\; E^\{1/2\}\; mu^\{-1/2\}\; mbox\{s\}^\{-1\}\; ,$
*electron collision rate:$u\_e\; =\; 2.91\; imes\; 10^\{-6\}\; n\_e,lnLambda,T\_e^\{-3/2\}\; mbox\{s\}^\{-1\}$
*ion collision rate:$u\_i\; =\; 4.80\; imes\; 10^\{-8\}\; Z^4\; mu^\{-1/2\}\; n\_i,lnLambda,T\_i^\{-3/2\}\; mbox\{s\}^\{-1\}$

Lengths

*Electron thermal de Broglie wavelength, approximate average de Broglie wavelength of electrons in a plasma::$Lambda\_e=\; sqrt\{frac\{h^2\}\{2pi\; m\_ekT\_e=\; 6.919\; imes\; 10^\{-8\},T\_e^\{-1/2\},mbox\{cm\}$
*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::$e^2/kT=1.44\; imes10^\{-7\},T^\{-1\},mbox\{cm\}$
*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::$r\_i\; =\; v\_\{Ti\}/omega\_\{ci\}\; =\; 1.02\; imes10^2,mu^\{1/2\}Z^\{-1\}T\_i^\{1/2\}B^\{-1\},mbox\{cm\}$
*plasma skin depth, the depth in a plasma to which electromagnetic radiation can penetrate::$c/omega\_\{pe\}\; =\; 5.31\; imes10^5,n\_e^\{-1/2\},mbox\{cm\}$
*Debye length, the scale over which electric fields are screened out by a redistribution of the electrons::$lambda\_D\; =\; (kT/4pi\; ne^2)^\{1/2\}\; =\; 7.43\; imes10^2,T^\{1/2\}n^\{-1/2\},mbox\{cm\}$

Velocities

*electron thermal velocity, typical velocity of an electron in a Maxwell-Boltzmann distribution::$v\_\{Te\}\; =\; (kT\_e/m\_e)^\{1/2\}\; =\; 4.19\; imes10^7,T\_e^\{1/2\},mbox\{cm/s\}$
*ion thermal velocity, typical velocity of an ion in a Maxwell-Boltzmann distribution::$v\_\{Ti\}\; =\; (kT\_i/m\_i)^\{1/2\}\; =\; 9.79\; imes10^5,mu^\{-1/2\}T\_i^\{1/2\},mbox\{cm/s\}$
*ion sound velocity, the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons::$c\_s\; =\; (gamma\; ZkT\_e/m\_i)^\{1/2\}\; =\; 9.79\; imes10^5,(gamma\; ZT\_e/mu)^\{1/2\},mbox\{cm/s\}$
*Alfven velocity, the speed of the waves resulting from the mass of the ions and the restoring force of the magnetic field::$v\_A\; =\; B/(4pi\; n\_im\_i)^\{1/2\}\; =\; 2.18\; imes10^\{11\},mu^\{-1/2\}n\_i^\{-1/2\}B,mbox\{cm/s\}$

Dimensionless

*square root of electron/proton mass ratio:$(m\_e/m\_p)^\{1/2\}\; =\; 2.33\; imes10^\{-2\}\; =\; 1/42.9\; ,$
* number of particles in a Debye sphere:$(4pi/3)nlambda\_D^3\; =\; 1.72\; imes10^9,T^\{3/2\}n^\{-1/2\}$
* Alven velocity/speed of light:$v\_A/c\; =\; 7.28,mu^\{-1/2\}n\_i^\{-1/2\}B$
* electron plasma/gyrofrequency ratio:$omega\_\{pe\}/omega\_\{ce\}\; =\; 3.21\; imes10^\{-3\},n\_e^\{1/2\}B^\{-1\}$
* ion plasma/gyrofrequency ratio:$omega\_\{pi\}/omega\_\{ci\}\; =\; 0.137,mu^\{1/2\}n\_i^\{1/2\}B^\{-1\}$
* thermal/magnetic pressure ratio ("beta"):
* magnetic/ion rest energy ratio:$B^2/8pi\; n\_im\_ic^2\; =\; 26.5,mu^\{-1\}n\_i^\{-1\}B^2$

References

* [http://www.ipp.mpg.de/~dpc/nrl/ NRL Plasma Formulary] (esp. [http://www.ipp.mpg.de/~dpc/nrl/28.html p. 28] and [http://www.ipp.mpg.de/~dpc/nrl/29.html p. 29] ), J.D. Huba, Naval Research Laboratory (2007)

Footnotes