Nonequilibrium ionization due to electron heating - i - theory

A two-tempeiature conduction law is proposed which accounts for the variation of the electrical conductivity of a plasma due to joule heating of the electrons The conduction law represents the behavior of the plasma over a wide range of conditions likely to be encountered in MHD generators and accelerators It differs from the usual Ohm's law in that the current density is proportional to about the fifth power of the electrical field for a slightly ionized gas with electron temperature more than 10% greater than the gas temperature The process of relaxation from an initial condition of thermal equilibrium to the final nonequilibrium condition is treated for a channel flow that represents conditions in an MHD generator For a mixture of argon and potassium at 1 atm pressure and 2000 °K, the relaxation length is about 1 m at a Mach number of unity if the electric field is held constant The stability of the two-temperature plasma to wavelike disturbances of electron energy and concentration is treated by the classical pertuibation technique It is concluded that such disturbances will amplify at large Hall parameters The exponentiating time may be less than 10~ sec, so that the disturbances could grow vei y large in a time of the order of the fluid residence time in an MHD channel