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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.  The behaviour of such particle systems can be studied statistically. 

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

Lengths $\Lambda_e= \sqrt{\frac{h^2}{2\pi m_ekT_e}}= 6.919\times 10^{-8}\,T_e^{-1/2}\,\mbox{cm}$
• 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: $e^2/kT=1.44\times10^{-7}\,T^{-1}\,\mbox{cm}$
• 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: $r_i = v_{Ti}/\omega_{ci} = 1.02\times10^2\,\mu^{1/2}Z^{-1}T_i^{1/2}B^{-1}\,\mbox{cm}$
• plasma skin depth, the depth in a plasma to which electromagnetic radiation can penetrate: $c/\omega_{pe} = 5.31\times10^5\,n_e^{-1/2}\,\mbox{cm}$
• Debye length, the scale over which electric fields are screened out by a redistribution of the electrons: $\lambda_D = (kT/4\pi ne^2)^{1/2} = 7.43\times10^2\,T^{1/2}n^{-1/2}\,\mbox{cm}$

Velocities $v_{Te} = (kT_e/m_e)^{1/2} = 4.19\times10^7\,T_e^{1/2}\,\mbox{cm/s}$ $v_{Ti} = (kT_i/m_i)^{1/2} = 9.79\times10^5\,\mu^{-1/2}T_i^{1/2}\,\mbox{cm/s}$
• ion sound velocity, the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons: $c_s = (\gamma ZkT_e/m_i)^{1/2} = 9.79\times10^5\,(\gamma ZT_e/\mu)^{1/2}\,\mbox{cm/s}$
• Alfven velocity, the speed of the waves resulting from the mass of the ions and the restoring force of the magnetic field: $v_A = B/(4\pi n_im_i)^{1/2} = 2.18\times10^{11}\,\mu^{-1/2}n_i^{-1/2}B\,\mbox{cm/s}$

Dimensionless

• square root of electron/proton mass ratio $(m_e/m_p)^{1/2} = 2.33\times10^{-2} = 1/42.9 \,$
• number of particles in a Debye sphere $(4\pi/3)n\lambda_D^3 = 1.72\times10^9\,T^{3/2}n^{-1/2}$
• Alven velocity/speed of light $v_A/c = 7.28\,\mu^{-1/2}n_i^{-1/2}B$
• electron plasma/gyrofrequency ratio $\omega_{pe}/\omega_{ce} = 3.21\times10^{-3}\,n_e^{1/2}B^{-1}$
• ion plasma/gyrofrequency ratio $\omega_{pi}/\omega_{ci} = 0.137\,\mu^{1/2}n_i^{1/2}B^{-1}$
• thermal/magnetic pressure ratio ("beta") $\beta = 8\pi nkT/B^2 = 4.03\times10^{-11}\,nTB^{-2}$
• magnetic/ion rest energy ratio $B^2/8\pi n_im_ic^2 = 26.5\,\mu^{-1}n_i^{-1}B^2$