Classical momentum gap for electron transport in vacuum and consequences for space charge in thermionic converters with a grid electrode

Quantum mechanics tells us that the bound states of a potential well are quantized—a phenomenon that is easily understandable based on wave properties and resonance. Here, the authors demonstrate a classical mechanism for the formation of a momentum gap in the phase space of electrons traveling as particles in a potential well in vacuum. This effect is caused by the reflection of electrons from at least two potential maxima, which may, for instance, exist due to space-charge distribution in a triode configuration. This gap plays a critical role in space-charge-mitigated electron transport in vacuum, such as in a thermionic energy converter with a positively biased grid, where it is shown that the current density can be increased by 1–3 orders of magnitude depending on the severity of space charge in the absence of the grid.