Magnetoplasmadynamic electrical power generation with nonequilibrium ionization

Abstract

An ionized gas is said to be in the non-equilibrium state when the approximately Maxwellian electrons are maintained at a higher temperature than the Maxwellian ions and neutrals. When such a state exists, as for example, in a seeded noble gas, the ions could be primarily generated by ionizing collisions of the hot plasma electrons with the seed atoms and the bulk gas temperature could be maintained at a value compatible with a nuclear reactor heat source. In this paper formulas are presented for the calculation of the electron density, η e , the electrical conductivity, σ, and the corresponding internal electric field, ε e (all as functions of the electron temperature, E e ) in a seeded partially-ionized noble gas in the non-equilibrium state. The electron or ion density, n e , is derived from an ion balance equation which equates the rate of generation of ions (primarily by the hot electrons) to the rate of loss of ions by recombination. The electric field, ε e , is derived from an energy balance equation which equates the rate of energy lost by the electrons in elastic and inelastic collisions with the gas species to the rate of energy fed to the electrons through the electric field. For the case of the motion-magnetically induced electric field formulas are presented for the calculation of the magnetic field, B, required to induce the electric field, E e , which, in turn, is required to maintain the ionized gas in the non-equilibrium state for a given gas velocity, u, and a given ratio of load voltage to open circuit voltage, e L . These formulas are given both for the case of segmented electrodes Faraday and the case of segmented electrode Hall generators. In an example of calculations the equations presented have been applied to show how to calculate the electron density, n e (see Fig. 1), the electrical conductivity, σ, and the corresponding electric field, ε e (see Figs. 2 and 3) as well as the electrical conductivity, σ, the corresponding electric field, E e , and electron temperature, E e , versus the magnetic field required, for a typical gas velocity, u (or Mach number), to induce these quantities (see Fig. 4). Since these calculations are based on values of electron densities which are computed using the ion balance equation rather than those which would be obtained from using the electron temperature, E e , in Saha's equation for thermal ionization it is of interest to compare the two resulting plots of the electron densities versus the electron temperature, E e (see Fig. 1). It is seen that the curve using the electron density derived from Saha's equation with E e inserted gives higher values of electron densities (sometimes by more than an order of magnitude) than the curve using the electron density from the ion balance equation.