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_{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"):eta = 8pi nkT/B^2 = 4.03 imes10^{-11},nTB^{-2}
* 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


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