Solution of the nonlinear (radiative) thermal conductivity equation for pulsed high-current electric discharges in dense gases

A model of the initial expansion stage of cylindrical pulsed high-current electric discharges in dense gases in the approximation of radiative thermal conductivity is proposed. Based on the uniform distribution of the plasma pressure in the discharge channel and its constancy at this stage, the partial difference equations (continuity, Euler, and nonlinear thermal conductivity equations) of this model are reduced to ordinary differential equations. The space-time dependences of the plasma temperature and density in the channel on initial parameters were determined from the solutions to these equations. These dependences are consistent with experimental data within experimental error.