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 studies 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 $\backslash mu\; =\; m\_i/m\_p$; 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:

$\backslash omega\_\{ce\}\; =\; eB/m\_ec\; =\; 1.76\; \backslash times\; 10^7\; B\; \backslash mbox\{rad/s\}$

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

$\backslash omega\_\{ci\}\; =\; eB/m\_ic\; =\; 9.58\; \backslash times\; 10^3\; Z\; \backslash mu^\{-1\}\; B\; \backslash mbox\{rad/s\}$

• electron plasma frequency, the frequency with which electrons oscillate when their charge density is not equal to the ion charge density (plasma oscillation):

$\backslash omega\_\{pe\}\; =\; (4\backslash pi\; n\_ee^2/m\_e)^\{1/2\}\; =\; 5.64\; \backslash times\; 10^4\; n\_e^\{1/2\}\; \backslash mbox\{rad/s\}$

• ion plasma frequency:

$\backslash omega\_\{pe\}\; =\; (4\backslash pi\; n\_iZ^2e^2/m\_i)^\{1/2\}\; =\; 1.32\; \backslash times\; 10^3\; Z\; \backslash mu^\{-1/2\}\; n\_i^\{1/2\}\; \backslash mbox\{rad/s\}$

• electron trapping rate

$\backslash nu\_\{Te\}\; =\; (eKE/m\_e)^\{1/2\}\; =\; 7.26\; \backslash times\; 10^8\; K^\{1/2\}\; E^\{1/2\}\; \backslash mbox\{s\}^\{-1\}$

• ion trapping rate

$\backslash nu\_\{Ti\}\; =\; (ZeKE/m\_i)^\{1/2\}\; =\; 1.69\; \backslash times\; 10^7\; Z^\{1/2\}\; K^\{1/2\}\; E^\{1/2\}\; \backslash mu^\{-1/2\}\; \backslash mbox\{s\}^\{-1\}$

• electron collision rate

$\backslash nu\_e\; =\; 2.91\; \backslash times\; 10^\{-6\}\; n\_e\backslash ,\backslash ln\backslash Lambda\backslash ,T\_e^\{-3/2\}\; \backslash mbox\{s\}^\{-1\}$

• ion collision rate

$\backslash nu\_i\; =\; 4.80\; \backslash times\; 10^\{-8\}\; Z^4\; \backslash mu^\{-1/2\}\; n\_i\backslash ,\backslash ln\backslash Lambda\backslash ,T\_i^\{-3/2\}\; \backslash mbox\{s\}^\{-1\}$

Lengths

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

$\backslash Lambda\_e=\; \backslash sqrt\{\backslash frac\{h^2\}\{2\backslash pi\; m\_ekT\_e\}\}=\; 6.919\backslash times\; 10^\{-8\}\backslash ,T\_e^\{-1/2\}\backslash ,\backslash mbox\{cm\}$

• 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:

$e^2/kT=1.44\backslash times10^\{-7\}\backslash ,T^\{-1\}\backslash ,\backslash mbox\{cm\}$

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

$r\_e\; =\; v\_\{Te\}/\backslash omega\_\{ce\}\; =\; 2.38\backslash ,T\_e^\{1/2\}B^\{-1\}\backslash ,\backslash mbox\{cm\}$

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

$r\_i\; =\; v\_\{Ti\}/\backslash omega\_\{ci\}\; =\; 1.02\backslash times10^2\backslash ,\backslash mu^\{1/2\}Z^\{-1\}T\_i^\{1/2\}B^\{-1\}\backslash ,\backslash mbox\{cm\}$

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

$c/\backslash omega\_\{pe\}\; =\; 5.31\backslash times10^5\backslash ,n\_e^\{-1/2\}\backslash ,\backslash mbox\{cm\}$

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

$\backslash lambda\_D\; =\; (kT/4\backslash pi\; ne^2)^\{1/2\}\; =\; 7.43\backslash times10^2\backslash ,T^\{1/2\}n^\{-1/2\}\backslash ,\backslash mbox\{cm\}$

Velocities

• electron thermal velocity, typical velocity of an electron in a Maxwell-Boltzmann distribution:

$v\_\{Te\}\; =\; (kT\_e/m\_e)^\{1/2\}\; =\; 4.19\backslash times10^7\backslash ,T\_e^\{1/2\}\backslash ,\backslash mbox\{cm/s\}$

• ion thermal velocity, typical velocity of an ion in a Maxwell-Boltzmann distribution:

$v\_\{Ti\}\; =\; (kT\_i/m\_i)^\{1/2\}\; =\; 9.79\backslash times10^5\backslash ,\backslash mu^\{-1/2\}T\_i^\{1/2\}\backslash ,\backslash mbox\{cm/s\}$

• ion sound velocity, the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons:

$c\_s\; =\; (\backslash gamma\; ZkT\_e/m\_i)^\{1/2\}\; =\; 9.79\backslash times10^5\backslash ,(\backslash gamma\; ZT\_e/\backslash mu)^\{1/2\}\backslash ,\backslash mbox\{cm/s\}$

• Alfven velocity, the speed of the waves resulting from the mass of the ions and the restoring force of the magnetic field:

$v\_A\; =\; B/(4\backslash pi\; n\_im\_i)^\{1/2\}\; =\; 2.18\backslash times10^\{11\}\backslash ,\backslash mu^\{-1/2\}n\_i^\{-1/2\}B\backslash ,\backslash mbox\{cm/s\}$

Dimensionless

• square root of electron/proton mass ratio

$(m\_e/m\_p)^\{1/2\}\; =\; 2.33\backslash times10^\{-2\}\; =\; 1/42.9$

• number of particles in a Debye sphere

$(4\backslash pi/3)n\backslash lambda\_D^3\; =\; 1.72\backslash times10^9\backslash ,T^\{3/2\}n^\{-1/2\}$

• Alven velocity/speed of light

$v\_A/c\; =\; 7.28\backslash ,\backslash mu^\{-1/2\}n\_i^\{-1/2\}B$

• electron plasma/gyrofrequency ratio

$\backslash omega\_\{pe\}/\backslash omega\_\{ce\}\; =\; 3.21\backslash times10^\{-3\}\backslash ,n\_e^\{1/2\}B^\{-1\}$

• ion plasma/gyrofrequency ratio

$\backslash omega\_\{pi\}/\backslash omega\_\{ci\}\; =\; 0.137\backslash ,\backslash mu^\{1/2\}n\_i^\{1/2\}B^\{-1\}$

• thermal/magnetic energy ratio ("beta")

$\backslash beta\; =\; 8\backslash pi\; nkT/B^2\; =\; 4.03\backslash times10^\{-11\}\backslash ,nTB^\{-2\}$

• magnetic/ion rest energy ratio

$B^2/8\backslash pi\; n\_im\_ic^2\; =\; 26.5\backslash ,\backslash mu^\{-1\}n\_i^\{-1\}B^2$

Footnotes

Plasma physics | Astrophysics