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.
All quantities are in Gaussian (cgs) units except energy and temperature expressed in eV and ion mass expressed in units of the proton mass μ = m i / m p ; Z is charge state; k is Boltzmann's constant; K is wavenumber; ln Λ is the Coulomb logarithm.
electron gyrofrequency, the angular frequency of the circular motion of an electron in the plane perpendicular to the magnetic field: ω c e = e B / m e c = 1.76 × 10 7 B rad/s ion gyrofrequency, the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field: ω c i = Z e B / m i c = 9.58 × 10 3 Z μ − 1 B rad/s electron plasma frequency, the frequency with which electrons oscillate (plasma oscillation): ω p e = ( 4 π n e e 2 / m e ) 1 / 2 = 5.64 × 10 4 n e 1 / 2 rad/s ion plasma frequency: ω p i = ( 4 π n i Z 2 e 2 / m i ) 1 / 2 = 1.32 × 10 3 Z μ − 1 / 2 n i 1 / 2 rad/s electron trapping rate: ν T e = ( e K E / m e ) 1 / 2 = 7.26 × 10 8 K 1 / 2 E 1 / 2 s − 1 ion trapping rate: ν T i = ( Z e K E / m i ) 1 / 2 = 1.69 × 10 7 Z 1 / 2 K 1 / 2 E 1 / 2 μ − 1 / 2 s − 1 electron collision rate in completely ionized plasmas: ν e = 2.91 × 10 − 6 n e ln Λ T e − 3 / 2 s − 1 ion collision rate in completely ionized plasmas: ν i = 4.80 × 10 − 8 Z 4 μ − 1 / 2 n i ln Λ T i − 3 / 2 s − 1 electron (ion) collision rate in slightly ionized plasmas: ν e , i = N σ e , i v ¯ = N ∫ 0 ∞ σ ( v ) e , i f ( v ) v d v where σ ( v ) e , i is a collision crossection of the electron (ion) on the operating gas atoms (molecules), f ( v ) is the electron (ion)
distribution function in plasma, and N is an operating gas concentration.
Electron thermal de Broglie wavelength, approximate average de Broglie wavelength of electrons in a plasma: Λ e = h 2 2 π m e k T e = 6.919 × 10 − 8 T e − 1 / 2 cm classical distance of closest approach, the closest that two particles with the elementary charge come to each other if they approach head-on andeach have a velocity typical of the temperature, ignoring quantum-mechanical effects:
e 2 / k T = 1.44 × 10 − 7 T − 1 cm electron gyroradius, the radius of the circular motion of an electron in the plane perpendicular to the magnetic field: r e = v T e / ω c e = 2.38 T e 1 / 2 B − 1 cm ion gyroradius, the radius of the circular motion of an ion in the plane perpendicular to the magnetic field: r i = v T i / ω c i = 1.02 × 10 2 μ 1 / 2 Z − 1 T i 1 / 2 B − 1 cm plasma skin depth, the depth in a plasma to which electromagnetic radiation can penetrate: c / ω p e = 5.31 × 10 5 n e − 1 / 2 cm Debye length, the scale over which electric fields are screened out by a redistribution of the electrons: λ D = ( k T / 4 π n e 2 ) 1 / 2 = 7.43 × 10 2 T 1 / 2 n − 1 / 2 cm 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: d i = c / ω p i = 2.28 × 10 7 Z − 1 ( μ / n i ) 1 / 2 cm Free path is the average distance between two subsequent collisions of the electron (ion) with plasma components: λ e , i = v e , i ¯ ν e , i where v e , i ¯ is an average velocity of the electron (ion), and ν e , i is the electron or ion collision rate.
electron thermal velocity, typical velocity of an electron in a Maxwell–Boltzmann distribution: v T e = ( k T e / m e ) 1 / 2 = 4.19 × 10 7 T e 1 / 2 cm/s ion thermal velocity, typical velocity of an ion in a Maxwell–Boltzmann distribution: v T i = ( k T i / m i ) 1 / 2 = 9.79 × 10 5 μ − 1 / 2 T i 1 / 2 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 = ( γ Z k T e / m i ) 1 / 2 = 9.79 × 10 5 ( γ Z T e / μ ) 1 / 2 cm/s ,
where γ = 1 + 2 / n is the adiabatic index, and here n is the number of degrees of freedom
Alfvén 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 π n i m i ) 1 / 2 = 2.18 × 10 11 μ − 1 / 2 n i − 1 / 2 B cm/s square root of electron/proton mass ratio ( m e / m p ) 1 / 2 = 2.33 × 10 − 2 = 1 / 42.9 number of particles in a Debye sphere ( 4 π / 3 ) n λ D 3 = 1.72 × 10 9 T 3 / 2 n − 1 / 2 Alfvén velocity/speed of light v A / c = 7.28 μ − 1 / 2 n i − 1 / 2 B electron plasma/gyrofrequency ratio ω p e / ω c e = 3.21 × 10 − 3 n e 1 / 2 B − 1 ion plasma/gyrofrequency ratio ω p i / ω c i = 0.137 μ 1 / 2 n i 1 / 2 B − 1 thermal/magnetic pressure ratio ("beta") β = 8 π n k T / B 2 = 4.03 × 10 − 11 n T B − 2 magnetic/ion rest energy ratio B 2 / 8 π n i m i c 2 = 26.5 μ − 1 n i − 1 B 2 Coulomb logarithm is an average coefficient taking into account far Coulomb interactions of charged particles in plasma.Its value is evaluated in the nonrelativistic case approximately for electrons ln Λ ≃ 13.6 ,
for ions ln Λ ≃ 6.8
