One-dimensional flow of an ionized gas through a magnetic field

Abstract

As a primary step towards understanding the flow of a partially ionized gas in a magnetic field, we have studied both theoretically and experimentally the problem in which the gas flow is one-dimensional. This simplification permits a detailed calculation of the flow field and a quantitative comparison of the theory with observations made in a shock tube.

An ionized gas is composed of three species: electrons, ions and neutral particles. To take complete account of all the phenomena occurring when the high-velocity gas interacts with the magnetic field, the motion of all three species must be considered. When this is done, it is found that the electrical conductivity of the gas is a tensor dependent on both the magnitude and geometry of the magnetic field. However, when the collision frequency for the electrons is greater than their cyclotron frequency in a magnetic field, the gas may be treated as a continuum with a scalar conductivity. For such gas states, all of the observed effects for two experimental geometries in which the gas current forms closed loops in the magnetic field can be explained with a simple theory. The interaction produces a flow completely analogous to pipe flow with friction and no heat transfer, where the wall friction force is replaced by the magnetic body force which can choke the flow if the body forces are larger than a certain minimum value.

Using the same experimental geometries, the gas state is then adjusted so that the electrical conductivity is a tensor. Outstanding among the observed effects are ion slip, where the ions and neutrals travel through the field at different velocities, and Hall currents, generated by the drift of the charged particles across magnetic field lines. The observed effects again agree with the predicted values.