The electrical conductivity of an ionized gas in a magnetic field, with applications to the solar atmosphere and the ionosphere

Abstract The methods of Chapman and Enskog are used to discuss conduction of electricity and diffusion currents in an ionized gas with several constituents, in a transverse magnetic field. The free-path formula for the conductivity is compared with that derived by the exact methods. The two formulae are identical in form if a correction is applied to the usual freepath method; this correction robs the method of much of its simplicity. The uncorrected freepath method, however, gives correct results for the electron contribution to the conductivity in all practical cases; and for the ion contribution if a large number of neutral molecules are present— e.g. in the earth’s upper atmosphere, about 5 x 105 times the number of ions (of both signs). Numerical values are given for the conductivity in the sun’s outer layers and in the earth’s upper atmosphere. Mechanical forces due to currents induced in moving material are shown to be very important in the sun, and in the F-layer of the earth’s atmosphere. The solar results are used to discuss the motion of solar prominences and eruptions. In the earth’s atmosphere, the observed collision frequencies of electrons are shown to imply upper limits for ion-densities in the E and F layers. The integral conductivities of the E and F layers are estimated, and it is shown that, on the dynamo theory of the lunar variation of the earth’s magnetic field, tidal oscillations in these layers must be between 100 and 1000 times as great as those at the ground. Diamagnetism and drift currents are shown to make negligible contributions to the lunar and solar variations of the earth’s magnetic field. In an Appendix, the applicability of Boltzmann’s equation to strongly ionized gases is discussed.