The high-power constricted plasma discharge column I. Theoretical analysis

The equation expressing energy balance between Joule heating and thermal conduction is solved under the assumption that the plasma behaves as a Lorentz gas. This yields two relations for the plasma temperature, one in terms of the electric field E and the column radius R ; the other in terms of the current I , the radius R and the ionic charge Z. Elimination of temperature between these relations gives the electrical characteristic E is proportional to Z fraction two-fifths R −fraction seven-fifths I fraction two-fifths . The analysis is valid over a range of temperature and density limited at one extreme by radiation losses and at the other extreme by effects of self magnetic field on the transport processes. There is excellent agreement between the temperatures given by this theory and those recently measured spectroscopically for capillary discharges.