Multidimensional short-pulse space-charge-limited flow

The two-dimensional models of the space-charge-limited (SCL) current density at the short pulse limit for which the electron pulse length is comparable or smaller than the electron transit time across the gap (i.e., $XCL⩽1$⁠) have been developed. In particular, the scaling laws for short-pulse SCL electron emission in a planar diode with a circular emitting strip and a cylindrical diode with a finite length have been obtained and verified with particle-in-cell simulation. It is found that the enhancement (in terms of the long-pulse SCL current density) is proportional to $XCL−1$ for small $XCL$ for both planar and cylindrical cases. The enhancement of the cylindrical short-pulse SCL current density is also found to be larger for the convergent flow (cathode outside) than divergent flow (cathode inside). Multidimensional effects are important only for small emitting strips with size comparable to the effective penetration distance (into the gap) of the short-pulse electron beam. Smooth transition between the short-pulse regime and the long pulse (steady-state) regime is demonstrated.