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[[Image:Magnetic rope.svg|thumb|300px|The complex self-constricting magnetic field lines and current paths in a [[Birkeland current]] that may develop in a plasma (''[http://history.nasa.gov/SP-345/ch15.htm#250 Evolution of the Solar System]'', 1976) ]] | |||
'''Plasma parameters''' define various characteristics of a [[Plasma (physics)|plasma]], an electrically conductive collection of [[charged particle]]s that responds ''collectively'' to [[electromagnetic force]]s. Plasma typically takes the form of neutral gas-like clouds or charged [[ion beam]]s, but may also include dust and grains. <ref>Peratt, Anthony, ''Physics of the Plasma Universe'' (1992); </ref> The behaviour of such particle systems can be studied statistically. <ref>Parks, George K., Physics of Space Plasmas (2004, 2nd Ed.)</ref> | |||
== Fundamental plasma parameters == | |||
All quantities are in [[Gaussian units|Gaussian]] ([[Centimetre-gram-second system of units|cgs]]) units except [[temperature]] expressed in eV and ion mass expressed in units of the [[proton]] mass <math>\mu = m_i/m_p</math>; ''Z'' is charge state; ''k'' is [[Boltzmann's constant]]; ''K'' is wavenumber; 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: | |||
:<math>\omega_{ce} = eB/m_ec = 1.76 \times 10^7 B \mbox{rad/s} \,</math> | |||
*'''ion gyrofrequency''', the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field: | |||
:<math>\omega_{ci} = eB/m_ic = 9.58 \times 10^3 Z \mu^{-1} B \mbox{rad/s} \,</math> | |||
*'''electron plasma frequency''', the frequency with which electrons oscillate ([[plasma oscillation]]): | |||
:<math>\omega_{pe} = (4\pi n_ee^2/m_e)^{1/2} = 5.64 \times 10^4 n_e^{1/2} \mbox{rad/s}</math> | |||
*'''ion plasma frequency''': | |||
:<math>\omega_{pi} = (4\pi n_iZ^2e^2/m_i)^{1/2} = 1.32 \times 10^3 Z \mu^{-1/2} n_i^{1/2} \mbox{rad/s}</math> | |||
*'''electron trapping rate''': | |||
:<math>\nu_{Te} = (eKE/m_e)^{1/2} = 7.26 \times 10^8 K^{1/2} E^{1/2} \mbox{s}^{-1} \,</math> | |||
*'''ion trapping rate''': | |||
:<math>\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} \,</math> | |||
*'''electron collision rate''': | |||
:<math>\nu_e = 2.91 \times 10^{-6} n_e\,\ln\Lambda\,T_e^{-3/2} \mbox{s}^{-1}</math> | |||
*'''ion collision rate''': | |||
:<math>\nu_i = 4.80 \times 10^{-8} Z^4 \mu^{-1/2} n_i\,\ln\Lambda\,T_i^{-3/2} \mbox{s}^{-1}</math> | |||
=== Lengths === | |||
*'''[[Thermal de Broglie wavelength|Electron thermal de Broglie wavelength]]''', approximate average [[de Broglie wavelength]] of electrons in a plasma: | |||
:<math>\Lambda_e= \sqrt{\frac{h^2}{2\pi m_ekT_e}}= 6.919\times 10^{-8}\,T_e^{-1/2}\,\mbox{cm}</math> | |||
*'''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: | |||
:<math>e^2/kT=1.44\times10^{-7}\,T^{-1}\,\mbox{cm}</math> | |||
*'''electron gyroradius''', the radius of the circular motion of an electron in the plane perpendicular to the magnetic field: | |||
:<math>r_e = v_{Te}/\omega_{ce} = 2.38\,T_e^{1/2}B^{-1}\,\mbox{cm}</math> | |||
*'''ion gyroradius''', the radius of the circular motion of an ion in the plane perpendicular to the magnetic field: | |||
:<math>r_i = v_{Ti}/\omega_{ci} = 1.02\times10^2\,\mu^{1/2}Z^{-1}T_i^{1/2}B^{-1}\,\mbox{cm}</math> | |||
*'''plasma [[skin depth]]''', the depth in a plasma to which electromagnetic radiation can penetrate: | |||
:<math>c/\omega_{pe} = 5.31\times10^5\,n_e^{-1/2}\,\mbox{cm}</math> | |||
*'''[[Debye length]]''', the scale over which electric fields are screened out by a redistribution of the electrons: | |||
:<math>\lambda_D = (kT/4\pi ne^2)^{1/2} = 7.43\times10^2\,T^{1/2}n^{-1/2}\,\mbox{cm}</math> | |||
*'''[[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: | |||
:<math>d_i = c/\omega_{pi}</math> | |||
=== Velocities === | |||
*'''electron thermal velocity''', typical velocity of an electron in a [[Maxwell-Boltzmann distribution]]: | |||
:<math>v_{Te} = (kT_e/m_e)^{1/2} = 4.19\times10^7\,T_e^{1/2}\,\mbox{cm/s}</math> | |||
*'''ion thermal velocity''', typical velocity of an ion in a [[Maxwell-Boltzmann distribution]]: | |||
:<math>v_{Ti} = (kT_i/m_i)^{1/2} = 9.79\times10^5\,\mu^{-1/2}T_i^{1/2}\,\mbox{cm/s}</math> | |||
*'''ion sound velocity''', the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons: | |||
:<math>c_s = (\gamma ZkT_e/m_i)^{1/2} = 9.79\times10^5\,(\gamma ZT_e/\mu)^{1/2}\,\mbox{cm/s}</math> | |||
*'''[[Hannes Alfvén|Alfvén]] velocity''', the speed of the [[Alfvén wave|waves]] resulting from the mass of the ions and the restoring force of the magnetic field: | |||
:<math>v_A = B/(4\pi n_im_i)^{1/2} = 2.18\times10^{11}\,\mu^{-1/2}n_i^{-1/2}B\,\mbox{cm/s}</math> | |||
=== Dimensionless === | |||
[[Image:fusor_running.jpg|thumb|right|300px|A 'sun in a test tube'. The [[Farnsworth-Hirsch Fusor]] during operation in so called "star mode" characterized by "rays" of glowing plasma which appear to emanate from the gaps in the inner grid.]] | |||
*square root of electron/proton mass ratio | |||
:<math>(m_e/m_p)^{1/2} = 2.33\times10^{-2} = 1/42.9 \,</math> | |||
* number of particles in a Debye sphere | |||
:<math>(4\pi/3)n\lambda_D^3 = 1.72\times10^9\,T^{3/2}n^{-1/2}</math> | |||
* Alfvén velocity/speed of light | |||
:<math>v_A/c = 7.28\,\mu^{-1/2}n_i^{-1/2}B</math> | |||
* electron plasma/gyrofrequency ratio | |||
:<math>\omega_{pe}/\omega_{ce} = 3.21\times10^{-3}\,n_e^{1/2}B^{-1}</math> | |||
* ion plasma/gyrofrequency ratio | |||
:<math>\omega_{pi}/\omega_{ci} = 0.137\,\mu^{1/2}n_i^{1/2}B^{-1}</math> | |||
* thermal/magnetic pressure ratio ("[[Beta (plasma physics)|beta]]") | |||
:<math>\beta = 8\pi nkT/B^2 = 4.03\times10^{-11}\,nTB^{-2}</math> | |||
* magnetic/ion rest energy ratio | |||
:<math>B^2/8\pi n_im_ic^2 = 26.5\,\mu^{-1}n_i^{-1}B^2</math> | |||
==See also== | |||
*[[List of plasma (physics) articles]] | |||
==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, [[United States Naval Research Laboratory|Naval Research Laboratory]] (2007) | |||
==Footnotes== | |||
<div style="font-size: 95%"> | |||
<!--See [[Wikipedia:Footnotes]] for an explanation of how to generate footnotes using the <ref(erences/)> tags--> | |||
<references/> | |||
</div> | |||
<!--Categories--> | |||
[[Category:Plasma physics| ]] | |||
[[Category:Plasma diagnostics]] | |||
[[Category:Astrophysics]] |
Revision as of 09:49, 18 January 2014
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 temperature expressed in eV and ion mass expressed in units of the proton mass ; Z is charge state; k is Boltzmann's constant; K is wavenumber; 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:
- ion gyrofrequency, the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field:
- electron plasma frequency, the frequency with which electrons oscillate (plasma oscillation):
- ion plasma frequency:
- electron trapping rate:
- ion trapping rate:
- electron collision rate:
- ion collision rate:
Lengths
- Electron thermal de Broglie wavelength, approximate average de Broglie wavelength of electrons in a plasma:
- 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:
- electron gyroradius, the radius of the circular motion of an electron in the plane perpendicular to the magnetic field:
- ion gyroradius, the radius of the circular motion of an ion in the plane perpendicular to the magnetic field:
- plasma skin depth, the depth in a plasma to which electromagnetic radiation can penetrate:
- Debye length, the scale over which electric fields are screened out by a redistribution of the electrons:
- 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:
Velocities
- electron thermal velocity, typical velocity of an electron in a Maxwell-Boltzmann distribution:
- ion thermal velocity, typical velocity of an ion in a Maxwell-Boltzmann distribution:
- ion sound velocity, the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons:
- Alfvén velocity, the speed of the waves resulting from the mass of the ions and the restoring force of the magnetic field:
Dimensionless
- square root of electron/proton mass ratio
- number of particles in a Debye sphere
- Alfvén velocity/speed of light
- electron plasma/gyrofrequency ratio
- ion plasma/gyrofrequency ratio
- thermal/magnetic pressure ratio ("beta")
- magnetic/ion rest energy ratio
See also
References
- NRL Plasma Formulary (esp. p. 28 and p. 29), J.D. Huba, Naval Research Laboratory (2007)