A complete algebraic analysis has been obtained for the variation of the steady state ion density n with injected current I in an OGRA-type fusion device (i.e., a device based on trapping of ions, by/breakup of energetic molecular ions on collision with either the background gas or trapped ions). The most general variation of n with I is shown to be an s-curve with at most three roots;of n for a given input I. A physical interpretation of these three roots is given. In addition algebraic expressions are obtained for the two currents at which the bends in the s-curve occur. It will be necessary to attain the larger current in order to build up a high density plasma-when the density is being increased from below. On the other hand, once the high density has been achieved it may be maintained by steady injection of a current larger than the lower value. Parameters corresponding roughly to the specifications of OGRA are used to obtain some numerical results. In the final appendix, the previously published formulas for burnout in DCX are extended to include effects of neutral backstreaming from the input beam and "ion-pumping."
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