Potential and current distribution in MPD arcs.

Abstract

Based on calculations of two basically similar devices, in which the anode and cathode geometries were the same but the distance between the cathode tip and exit plane of the anode L were different, it is shown that the electrode geometry has a pronounced effect on the cur- rent and potential distribution in MPD arcs. The plume contribution to the thrust increases with a decrease in L; however, for the configurations considered, the acceleration is generally restricted to a region of about 1-anode diam downstream of the cathode tip. The cal- culations also show that the Hall current densities are, in general, higher than radial current densities throughout the engine and exhaust plume, and are comparable to the axial current densities within the electrode region. N spite of the efforts of a number of investigators , the acceleration resulting from the interaction of an externally applied magnetic field with the plasma in MPD arcs is not well understood. Early works14 attributed the acceleration in these devices to two mechanisms; the first results from the interaction of the Hall current with the radial component of the magnetic field jeBr, and the second follows from changing rotational energy, resulting from jzBT and jrBz, into directed kinetic energy. However, recent diagnostic studies in ex- haust plumes of these devices showed that the Hall currents5'6 and rotational velocities5 were very small. The result re- garding Hall currents is in apparent disagreement with the measurements of Ref. 4. Although probing the plume can give some indication of the possible acceleration mechanisms, complete understand- ing of the problem requires rather detailed diagnostics within the engine itself. This is especially true in those cases where the fraction of the total current in the exhaust plume is small. Since detailed probing of the engine has not been possible yet, the desirability of calculating the potential and current distributions in MPD arcs is evident. This is the subject of the present investigation. Two axially symmetric geometries have been used in this investig? aon. The first is that of the device of Refs. 4 and 7, and the second employs the same anode and cathode geometries, but the cathode tip is moved to the right. The magnetic field distribution employed is that given in Ref. 4. Because of the complexity of the problem, a simple plasma model that assumes the electrical conductivity along the magnetic field lines to be constant is employed. In addi- tion, when utilizing the generalized Ohm's law, the pressure gradient terms are assumed negligible and the various collision frequencies are assumed constant. The results show that for a given magnetic field strength, mass flow rate, and power input the electrode configuration has a pronounced effect on current and potential distribu- tions. The Hall current densities are, in general, higher than the radial current densities, and comparable with the axial current densities in the annulus and exhaust plume. It is also shown that, for the geometries under consideration, the