The Thermionic Conversion Ceiling: The Richardson Bound, the Space-Charge Limit at Practical Gaps, and the Radiation Floor

The maximum efficiency and power density of a vacuum thermionic converter are derived from the Richardson emission law and the emitter/collector work-function difference, and evaluated for a caesiated tungsten emitter (1.80 eV) and a low-work-function collector (1.20 eV) at 700 K, giving an ideal output voltage of 0.60 V and an ideal efficiency of 29.9% at 1100 K falling to 27.5% at 2200 K. That ideal requires emission currents of 657 A/cm2 at 1600 K and 43,709 A/cm2 at 2200 K, which no vacuum gap transmits: the Child-Langmuir space-charge scale at 0.60 V is 1.085 A/cm2 at a 10 micrometre gap and 0.0434 A/cm2 at 50 micrometres. Charging space-charge suppression, radiation exchange at an effective emissivity of 0.20, and optimised-lead conduction, a 10 micrometre gap peaks at 13.22% efficiency and 0.53 W/cm2 at 1200 K, saturates at 0.65 W/cm2, and declines to 3.17% at 2000 K because radiation grows as the fourth power of temperature against the capped current. A 50 micrometre gap never exceeds 1.65%. Below 1012 K the net current is zero, because the collector's back emission (0.135 A/cm2 at 700 K) exceeds the emitter's forward emission, and near 1100 K the emission current changes by one e-fold per 52 K. The competitive regime is therefore narrow: emitter temperatures of roughly 1100 to 1400 K, gaps at or below about 10 micrometres, and a high-grade heat source. A photon-enhanced check within the same framework shows that lowering the emission barrier raises the transmitted current only where the device is emission-limited and changes it by about 0.15% at 1600 K, where space charge binds. All numbers are produced by the deposited compute.py; the device model is simulated, not measured. AI use is disclosed: this paper was produced by Dave, an AI system, at the direction of the author. The author, William Alexander Aldred, directed the work and is sole author of record.