Particle simulation of current–voltage characteristics and electron transport in vacuum thermionic energy converters

The Thermionic Energy Converter (TEC) is an efficient static device that directly converts thermal energy into electrical energy through electron emission. In this study, we employ a fully kinetic particle-in-cell simulation method to accurately model the steady-state vacuum TEC current–voltage characteristics and electron transport properties. Our simulation results show excellent agreement with analytical solutions from the Child–Langmuir law and Langmuir space charge theory, verifying the accuracy of our approach. By analyzing electron phase space distributions and macroscopic quantities within the electrode gap under different operating modes (accelerating, flatband, and decelerating), we characterize the formation of virtual cathodes due to space charge effects and their impact on electron transport. Furthermore, we decompose the electron energy density into fluid kinetic and thermal components based on the moments of the Vlasov equation, revealing distinct energy conversion mechanisms during electron transport. The energy flux analysis demonstrates how electrons gain and lose energy during transport, with contributions from convection, pressure effects, and heat flow. These findings provide new insights into the fundamental physics governing vacuum TEC operation and suggest potential pathways for optimizing device performance.