The impact of emission nonuniformity on transmitted current in vacuum thermionic energy converters

The transmitted current in vacuum thermionic energy converters (TECs) is often limited by space-charge effects. Existing one-dimensional (1D) models and numerical benchmarks provide valuable insights into this limitation. In practical devices, however, the emitter often has a finite area and may be spatially nonuniform; these features can reshape the self-consistent space-charge structure and electron backflow paths and thus degrade performance. We employ two-dimensional (2D) particle-in-cell simulations to compare electron transport and backflow in vacuum TECs with different emitting areas. We first assume a fixed initial velocity for the emitted electrons. The results show that decreasing the emitting area leads to the formation of backflow channels, causing the transmitted current density to fall systematically below the prediction of 1D space-charge-limited (SCL) theory. Replacing the fixed initial velocity with a velocity distribution, we find that the transmitted current increases only gradually with the emission current and the oscillations vanish; nevertheless, reducing the emitting area still induces backflow and decreases the transmitted current. These findings indicate that finite emitting area and emission nonuniformity can modify 1D predictions via geometry-induced backflow and should be accounted for as a key geometric parameter in vacuum TEC modeling and design assessment. They may also serve as a useful reference for the design and optimization of micro-patterned emitter arrays.