Ionization Rates and Power Loss from θ-Pinches by Impurity Radiation

Calculations are presented for the influence of small impurity concentrations on the energy balance and electron temperature during the magnetic compression of a deuterium plasma. The rate equations which describe the ionization are based on the Corona Plasma Model in much the same way as has been done earlier for a plasma assumed to be homogeneous. Despite the comparatively high electron densities (≳1016 cm−3) in these plasmas, this model should be applicable because of the high ionic charge at temperatures over ∼10 eV. The radial temperature and density distributions were obtained numerically by coupling the Hain-Roberts two-fluid, hydromagnetic equations to the Corona equations. The ionization of up to four different impurities, i.e., C, N, O, Ne, can be taken into account. Radiation losses were included in the electron energy-balance equation, but the influence of impurity ionization on the electron density and electrical conductivity was neglected. Therefore, only small impurity concentrations can be considered. However, only a few percent impurities have a drastic effect on the electron temperature so that the present calculations may be meaningful in the interpretation of certain experiments.