Abstract
A linear pinched discharge in fully ionized hydrogen or deuterium is examined theoretically under an idealized steady-state condition, when there is a pressure and an energy balance and no instabilities. Under this condition, the Joule heating caused by the axial current is balanced by bremsstrahlung radiation losses and by axial heat conduction and diffusion to the electrodes. A partial analytical solution is found assuming that the transport coefficients have the usual power dependencies on temperature throughout the plasma. It is shown that all the energy not radiated is carried to the anode, the cathode even having a negative total heat flux at its surface due to thermal effects of diffusion by the current-carrying electrons. The maximum temperature in the discharge is shown to vary directly with the voltage across the tube and only insensitively to other parameters. Further relations are derived involving the dimensions of the discharge, the current and the maximum temperature. The temperature, the line density and the electric field are plotted showing their variation along the axis. The relative importance of heat conduction and radiation losses is seen to depend only on the total axial current which is flowing. A typical example of a discharge shows that temperatures of 106 to 107 oK are quite feasible in the presence of heat losses to the electrodes.