The impact of energy spectrum width in the energy selective electron low-temperature thermionic heat engine at maximum power

A model of thermionic heat engine with the energy selective electron mechanism is studied. Analytical expressions of the power output and efficiency of this device are derived at low temperature, where the chemical potentials of the reservoirs are assumed to be constant. After discussing the impact of the energy spectrum width of the energy selective electron mechanism, we find two bounds (η±) of efficiency at maximum power exist naturally. When the energy spectrum width increases gradually from zero and then to the semi-infinite case with the infinite upper limit, the efficiency at maximum power decreases monotonously from the upper bound η+ to the lower bound η− at a given temperature ratio of the cold and hot reservoirs. The two bound are given by numerical simulation and by an analytical expression respectively. These results may provide some guidance for the application of the practical energy selective electron heat engines.