Plasma (physics)

:This article is about plasma in the sense of an ionized gas. For other uses of the term, such as blood plasma, see plasma (disambiguation).

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; ? is the adiabatic index; ln ? is the Coulomb logarithm.

Related Topics:
Cgs - Temperature - Proton - Boltzmann's constant - Adiabatic index - 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_{pe} = (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{rac{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 energy ratio

: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

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Miscellaneous

• Bohm diffusion coefficient

:D_B = (ckT/16eB) = 6.25 imes10^6,TB^{-1},mbox{cm}^2/mbox{s}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• transverse Spitzer resistivity

:eta_perp = 1.15 imes10^{-14},Z,lnLambda,T^{-3/2},mbox{s} = 1.03 imes10^{-2},Z,lnLambda,T^{-3/2},Omega,mbox{cm}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~