Theoretical predictions of ablation-stabilised arcs confined in cylindrical tubes

The properties of ablation-stabilised arcs confined in uniform cylinders, open at both ends, are calculated. It is assumed that the arc temperature is uniform with radius. The axial variations of the arc temperature, pressure, radius and plasma velocity are calculated as functions of current by solving the coupled equations of conservation of mass, momentum and energy. It is assumed that a specified fraction of the arc radiation is absorbed at the ablating cylinder wall and that the remainder is absorbed in the ablated vapour from the wall. Radiation losses from the arc are treated by assuming either (i) that the effective emission coefficients of the arc are proportional to pressure and that the arc radiation losses can be characterised by a net emission coefficient, or (ii) that the arc emits black-body radiation appropriate to the central temperature of the arc. For both approximations, detailed numerical solutions show that the arc temperature and radius are almost uniform with axial position. By assuming that the arc temperature and radius are indeed uniform, simple analytic formulae for arc temperature, pressure and Mach number are obtained. Comparisons between theoretical and experimental voltage-current characteristics show good agreement.