The effect of the external pressure on the internal conditions inside the discharge tube

The model for quasi-steady-state operation of the discharge tube by A. Loeb and Z. Kaplan (see IEEE Trans. Magn., vol.25, p.342-6, Jan. 1989) is extended to include the dependence of the axial pressure, density, and velocity profiles inside the discharge tube on the external conditions. An interesting analogy between the discharge tube and the subsonic converging nozzle is demonstrated. The sensitivity of internal tube parameters to the external pressure is determined. The axial profiles are calculated and plotted, and three qualitatively different regimes are identified. Although the present analysis is semiqualitative and cannot replace a full 1-D time-dependent simulation, its results might be helpful as guidelines in the design of discharge tubes for electrothermal accelerators