# Plasma parameters

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: :$omega_\left\{ce\right\} = eB/m_ec = 1.76 imes 10^7 B mbox\left\{rad/s\right\} ,$
*ion gyrofrequency, the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field: :$omega_\left\{ci\right\} = eB/m_ic = 9.58 imes 10^3 Z mu^\left\{-1\right\} B mbox\left\{rad/s\right\} ,$
*electron plasma frequency, the frequency with which electrons oscillate when their charge density is not equal to the ion charge density (plasma oscillation): :$omega_\left\{pe\right\} = \left(4pi n_ee^2/m_e\right)^\left\{1/2\right\} = 5.64 imes 10^4 n_e^\left\{1/2\right\} mbox\left\{rad/s\right\}$
*ion plasma frequency: :$omega_\left\{pi\right\} = \left(4pi n_iZ^2e^2/m_i\right)^\left\{1/2\right\} = 1.32 imes 10^3 Z mu^\left\{-1/2\right\} n_i^\left\{1/2\right\} mbox\left\{rad/s\right\}$
*electron trapping rate:$u_\left\{Te\right\} = \left(eKE/m_e\right)^\left\{1/2\right\} = 7.26 imes 10^8 K^\left\{1/2\right\} E^\left\{1/2\right\} mbox\left\{s\right\}^\left\{-1\right\} ,$
*ion trapping rate:$u_\left\{Ti\right\} = \left(ZeKE/m_i\right)^\left\{1/2\right\} = 1.69 imes 10^7 Z^\left\{1/2\right\} K^\left\{1/2\right\} E^\left\{1/2\right\} mu^\left\{-1/2\right\} mbox\left\{s\right\}^\left\{-1\right\} ,$
*electron collision rate:$u_e = 2.91 imes 10^\left\{-6\right\} n_e,lnLambda,T_e^\left\{-3/2\right\} mbox\left\{s\right\}^\left\{-1\right\}$
*ion collision rate:$u_i = 4.80 imes 10^\left\{-8\right\} Z^4 mu^\left\{-1/2\right\} n_i,lnLambda,T_i^\left\{-3/2\right\} mbox\left\{s\right\}^\left\{-1\right\}$

Lengths

*Electron thermal de Broglie wavelength, approximate average de Broglie wavelength of electrons in a plasma::$Lambda_e= sqrt\left\{frac\left\{h^2\right\}\left\{2pi m_ekT_e= 6.919 imes 10^\left\{-8\right\},T_e^\left\{-1/2\right\},mbox\left\{cm\right\}$
*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::$e^2/kT=1.44 imes10^\left\{-7\right\},T^\left\{-1\right\},mbox\left\{cm\right\}$
*electron gyroradius, the radius of the circular motion of an electron in the plane perpendicular to the magnetic field::$r_e = v_\left\{Te\right\}/omega_\left\{ce\right\} = 2.38,T_e^\left\{1/2\right\}B^\left\{-1\right\},mbox\left\{cm\right\}$
*ion gyroradius, the radius of the circular motion of an ion in the plane perpendicular to the magnetic field::$r_i = v_\left\{Ti\right\}/omega_\left\{ci\right\} = 1.02 imes10^2,mu^\left\{1/2\right\}Z^\left\{-1\right\}T_i^\left\{1/2\right\}B^\left\{-1\right\},mbox\left\{cm\right\}$
*plasma skin depth, the depth in a plasma to which electromagnetic radiation can penetrate::$c/omega_\left\{pe\right\} = 5.31 imes10^5,n_e^\left\{-1/2\right\},mbox\left\{cm\right\}$
*Debye length, the scale over which electric fields are screened out by a redistribution of the electrons::$lambda_D = \left(kT/4pi ne^2\right)^\left\{1/2\right\} = 7.43 imes10^2,T^\left\{1/2\right\}n^\left\{-1/2\right\},mbox\left\{cm\right\}$

Velocities

*electron thermal velocity, typical velocity of an electron in a Maxwell-Boltzmann distribution::$v_\left\{Te\right\} = \left(kT_e/m_e\right)^\left\{1/2\right\} = 4.19 imes10^7,T_e^\left\{1/2\right\},mbox\left\{cm/s\right\}$
*ion thermal velocity, typical velocity of an ion in a Maxwell-Boltzmann distribution::$v_\left\{Ti\right\} = \left(kT_i/m_i\right)^\left\{1/2\right\} = 9.79 imes10^5,mu^\left\{-1/2\right\}T_i^\left\{1/2\right\},mbox\left\{cm/s\right\}$
*ion sound velocity, the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons::$c_s = \left(gamma ZkT_e/m_i\right)^\left\{1/2\right\} = 9.79 imes10^5,\left(gamma ZT_e/mu\right)^\left\{1/2\right\},mbox\left\{cm/s\right\}$
*Alfven velocity, the speed of the waves resulting from the mass of the ions and the restoring force of the magnetic field::$v_A = B/\left(4pi n_im_i\right)^\left\{1/2\right\} = 2.18 imes10^\left\{11\right\},mu^\left\{-1/2\right\}n_i^\left\{-1/2\right\}B,mbox\left\{cm/s\right\}$

Dimensionless

*square root of electron/proton mass ratio:$\left(m_e/m_p\right)^\left\{1/2\right\} = 2.33 imes10^\left\{-2\right\} = 1/42.9 ,$
* number of particles in a Debye sphere:$\left(4pi/3\right)nlambda_D^3 = 1.72 imes10^9,T^\left\{3/2\right\}n^\left\{-1/2\right\}$
* Alven velocity/speed of light:$v_A/c = 7.28,mu^\left\{-1/2\right\}n_i^\left\{-1/2\right\}B$
* electron plasma/gyrofrequency ratio:$omega_\left\{pe\right\}/omega_\left\{ce\right\} = 3.21 imes10^\left\{-3\right\},n_e^\left\{1/2\right\}B^\left\{-1\right\}$
* ion plasma/gyrofrequency ratio:$omega_\left\{pi\right\}/omega_\left\{ci\right\} = 0.137,mu^\left\{1/2\right\}n_i^\left\{1/2\right\}B^\left\{-1\right\}$
* thermal/magnetic pressure ratio ("beta"):
* magnetic/ion rest energy ratio:$B^2/8pi n_im_ic^2 = 26.5,mu^\left\{-1\right\}n_i^\left\{-1\right\}B^2$

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

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