Model for the operation of an emissive cathode in a large magnetized-plasma

A model for the steady-state operation of an emissive cathode is presented. The cathode, biased negative with respect to a cold anode, emits electrons thermionically and is embedded within a large magnetized-plasma column. The model provides formulas for the spatial shape of the global current system, the partition of potential across the plasma-sheath system, and the effective plasma resistance. The formation of a virtual cathode is explored, and an analytical expression for the critical operating conditions is derived. The model is further developed to include the self-consistent increase in plasma temperature which results from thermionic injection. In a companion paper [S. Jin et al., Phys. Plasmas 26, 022105 (2019)], results from transport experiments in the Large Plasma Device at the University of California Los Angeles are compared with this model, and excellent quantitative agreement is achieved. Published under license by AIP Publishing.