VALUES OF THE TRANSPORT COEFFICIENTS IN A PLASMA FOR ANY DEGREE OF IONIZATION BASED ON A MAXWELLIAN DISTRIBUTION

Abstract

Values are presented for the electronic conductivity for any degree of ionization, radio frequency, and d-c. magnetic field strength, and various electron speed power law variations of the electron collision frequency with neutral particles. Also, the other transport coefficients, such as electron current due to electron density gradients and temperature gradients, and energy flow due to an electric field and due to density gradients and temperature gradients, are tabulated.The analysis is based on substitution of the usual series expansion of Laguerre polynomials into the Fokker–Planck equation for Coulomb collisions and into the Boltzmann equation for electron collisions with neutral particles. For Coulomb effects, the expressions are the same as those derived by Landshoff. Collisions of electrons with neutral particles are included in addition to ions, and a-c. electric fields are treated as well as d-c. magnetic fields. In the limit of a completely ionized gas, the results also agree with those of Spitzer and Harm and of Kaufman. For a slightly ionized gas, the results are compared with Allis' treatment and with calculations using the Dingle integrals. It is found that the Laguerre convergence is inadequate for large angular frequencies when the power law is less than −2 and for small angular frequencies when the power law is greater than 1.The final results can be put in a form which yields two factors, multiplying, respectively, the average collision frequency and radian frequency, to give correct results from simple equations. These factors are usually of order one, and are functions of three parameters, proportional to angular frequency, ratio of electron–neutral to ion averaged collision frequency, and ion charge number.