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

Electron transpiration cooling (ETC) can reduce aerothermal loads on sharp hypersonic leading edges, but its performance is governed by whether thermionically emitted electrons escape the hot surface or return as cathode-directed backflow. Here, a one-dimensional-in-space, three-dimensional-in-velocity electrostatic particle-in-cell/Monte Carlo collision model is developed for a full cathode--anode plasma diode, resolving thermionic emission, collisional plasma transport, emitted-electron backflow, and downstream collection. A helium benchmark is used to examine emitted-electron transport and backflow-limited current flow. With increasing imposed emission, the diode first remains in a weak-backflow regime, where net emitted-electron transport and downstream collection both increase with emission. Further increasing the emission produces a sharp transition to backflow-limited transport between $7.0\times10^{19}$ and $7.5\times10^{19},\mathrm{m^{-2},s^{-1}}$. At $7.25\times10^{19},\mathrm{m^{-2},s^{-1}}$, the backflow ratio reaches $54.03$, while the net transport and downstream collection efficiencies fall to about $46$. Above this transition, added backflow overcompensates the imposed emission increase, reducing useful emitted-electron transport rather than causing saturation. Boundary energy diagnostics show that stronger emission may still increase the nominal cathode-side cooling metric, but after transition this metric no longer indicates improved emitted-electron escape or full-gap transport. These results show that the present PIC-MCC framework captures the key kinetic processes governing ETC-relevant emitted-electron escape and backflow limitation.