Full-gap kinetic limitation of thermionic-electron transport for electron transpiration cooling

Electron transpiration cooling (ETC) requires thermionic electrons to escape from a hot surface and transport energy through the surrounding plasma. However, increasing emission does not necessarily improve ETC performance because electron backflow can reduce useful transport. A model with one spatial dimension and three velocity dimensions combines the electrostatic particle in cell method with Monte Carlo collisions to investigate thermionic electron transport in a cathode to anode helium plasma diode. For the fixed cross section benchmark, useful transport first increases in a low backflow regime. A narrow transition then occurs between emission fluxes of 7.0 × 10¹⁹ and 7.5×10¹⁹m⁻²s⁻¹. At an emission flux of 7.25×10¹⁹m⁻²s⁻¹, the backflow ratio reaches approximately 57% and the net transport efficiency decreases to approximately 43%. At higher emission, backflow increases faster than the imposed emission, causing both net electron transport and downstream collection to decrease. This overcompensated backflow branch is accompanied by potential restructuring across the full gap and kinetic redistribution of electrons, demonstrating a global transport limitation rather than a local sheath effect. Energy dependent helium cross sections alter the transition behavior, showing that the transition location depends on the collision model. Boundary energy diagnostics further show that stronger emission does not necessarily improve ETC performance. These results show that evaluating ETC performance requires accounting for electron escape, backflow, and downstream collection rather than emission intensity alone.