How do temperature-limited and space-charge-limited operation differ in thermionic devices?

In thermionic devices, the difference between temperature-limited and space-charge-limited operation relates to the factors that constrain the flow of electrons from the emitter to the collector.1

• Temperature-limited operation: In this state, the current is determined primarily by the temperature of the emitter. According to the Richardson–Dushman equation, the rate of electron emission increases rapidly as the emitter temperature rises. When a device is temperature-limited, the electric field at the emitter surface is sufficient to pull all emitted electrons toward the collector as soon as they are released.21

• Space-charge-limited operation: This occurs when the density of emitted electrons creates a negative "cloud" in the space between the electrodes. Because these electrons are negatively charged, they repel one another and push low-energy electrons back toward the emitter, thereby restricting the total current. In this regime, the current is governed by the Langmuir-Child law, which depends on the voltage applied to the collector and the distance between the electrodes, rather than just the emitter temperature.21

To maximize efficiency in thermionic power converters, engineers often seek to mitigate the space-charge effect by reducing electrode spacing or introducing positive ions to neutralize the electron cloud.2