Influence of ion effects on a space charge limited field emission flow: From non-relativistic to ultra-relativistic regimes

Influence of ion effects on a space charge limited field emission flow has been studied systematically, by employing both analytical and numerical approaches. The analytic calculations are carried out self-consistently to yield the steady states of the bipolar flow. It is found that the field emission currents in the presence of saturated ion currents can be enhanced to be nearly 1.8, 1.5, and 1.4 times of the cases with no upstream ion current in non-relativistic, intermediate, and ultra-relativistic regimes, respectively. The solutions have also been verified using 1D PIC simulations, as implemented in the OOPD1 code developed by PTSG of UC Berkeley.