Calculation of Characteristic Time of Space Charge Limited Effect of SGEMP

When an X-ray beam illuminates a material's surface, the backscattered photo-electrons are emitted from the surface and stimulate the system-generated electromagnetic pulse (SGEMP). With the increase in X-ray flux, the space charge-limited (SCL) effect occurs and a relatively thin layer develops near the emitting surface. The characteristic time is defined as the occurring time of the SCL effect. In this article, an accurate analytical equation is derived by applying the momentum conservation equation for the mono-energetic electrons and verified by the particle-in-cell (PIC) simulation. But for electrons with velocity distribution, the analytic equation using the average velocity approximation, instead of the exponential distribution, is not accurate, as the interaction between the low-energy and high-energy electrons is ignored. PIC simulation results show that the characteristic time of the SCL effect is longer by the PIC simulation than the average energy approximation when the average energy of the electrons is relatively low and vice versa.