The region between a Maxwellian plasma source and an absorbing surface that emits cool electrons is modeled numerically with dynamic, electrostatic particle simulation and theoretically with a static, kinetic plasma‐sheath model. Steady‐state emission results are applied specifically to secondary electrons that are induced by either incident ions or electrons, but are also valid for thermionic and photoelectrons. The ratio of the emitted electron current to incident electron current is varied up to and beyond the critical emission coefficient (ratio) that causes electric field reversal at the collector. Results from these models agree very well over the range from zero to five times the critical emission coefficient. Increasing the secondary emission coefficient is found to reduce the collector potential and decrease the ion energy deposited, yet increase the total energy flux to the collector. In the simulation, some heating of the secondary electron stream is observed to gradually evolve over many Debye lengths, possibly because of a beam–plasma interaction. This heating increases potential fluctuations but causes only small deviations from the predictions with static theory.