The effect of barium transport on the operation of dispenser hollow cathodes was investigated in numerical modeling of a cathode with two different orifice sizes. Despite large differences in cathode emitter temperature, emitted electron current density, internal xenon neutral and plasma densities, and size of the plasma-surface interaction region, the barium transport in the two geometries is qualitatively very similar. Barium is produced in the insert and flows to the surface through the porous structure. A buildup of neutral Ba pressure in the plasma over the emitter surface can suppress the reactions supplying the Ba, restricting the net production rate. Neutral Ba flows into the dense Xe plasma and has a high probability of being ionized at the periphery of this zone. The steady state neutral Ba density distribution is determined by a balance between pressure gradient forces and the drag force associated with collisions between neutral Ba and neutral Xe atoms. A small fraction of the neutral Ba is lost upstream. The majority of the neutral Ba is ionized in the high temperature Xe plasma and is pushed back to the emitter surface by the electric field. The steady state Ba^+ ion density distribution results from a balance between electrostatic and pressure forces, neutral Xe drag and Xe^+ ion drag with the dominant forces dependent on location in the discharge. These results indicate that hollow cathodes are very effective at recycling Ba within the discharge and therefore maintain a high coverage of Ba on the emitter surface, which reduces the work function and sustains high electron emission current densities at moderate temperatures. Barium recycling is more effective in the cathode with the smaller orifice because the Ba is ionized in the dense Xe plasma concentrated just upstream of the orifice and pushed back into the hollow cathode. Despite a lower emitter temperature, the large orifice cathode has a higher Ba loss rate through the orifice because the Xe plasma density peaks further upstream.
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