The subject of this paper is the mathematical modeling of a recently proposed class of electron‐beam‐controlled high‐power semiconductor switches that are able to overcome the space‐charge limitation of conventional electron bombarded semiconductor devices by utilizing the secondary ionization effects of cathodoluminiscence and bremsstrahlung. Current densities of several kA/cm2at forward voltages some 10 V can be controlled with an electron beam of 100 keV and 1 A/cm2; holdoff voltages of more than 100 kV/cm and dark currents as small as 10 &mgr;A/cm2are possible. The concept has several possible applications: Its fast and repetitive closing and opening under load makes it suitable for inductive energy storage applications; its linear characteristics suggests a use as a high‐power modulation device.