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This paper couples exact collisionless sheath calculations to an isothermal electron model of a thermionic converter. The emitter sheath structure takes into account reflected ions, trapped ions, and surface emission ions. It is shown that lessening the net loss of ions at the emitter in the ignited mode by these phenomena degrades performance. In addition, it is shown that when the emitter returns too many of the ions, the arc is extinguished because there is insufficient resistive heating to maintain the necessary plasma electron temperature for ionization. These results suggest that the ignited mode cannot be improved much. However, nonignited modes in which the electron temperature remains low, such as the pulsed mode, do not suffer from this adverse behavior.