Influence of ion effects on relativistic field-emission-limited diodes

In a previous work, we investigated a relativistic field-emission-limited diode employing a high-transparency mesh anode via a self-consistent approach (M.C. Lin and D.S. Chuu, IVEC 2002, pp. 111-112, 2002, and Appl. Phys. Lett. vol. 80, pp. 4262-4264, 2002). Ionization effects at the high-transparency mesh anode were ignored. However, the ionization effects at the anode cannot be eliminated in the real world, even for the high-transparency mesh anode. It is well known that the emergence of upstream ion current would enhance the space-charge limiting current. In this work, we consider the anode plasma effects on the relativistic field-emission-limiting current. Thus, the previous theory is extended to the bipolar field-emission-limited flow. The ion current has been included in the relativistic Poisson's equation and has been treated as a tuning parameter.