Virtual cathode formation due to electromagnetic transients

The process of virtual cathode formation in a gap is critically examined via particle simulations. It is found that the limiting current obtained from the electrostatic approximation is valid only in the deeply nonrelativistic regime. For injection energy as low as 30 keV, the transients in the injected current may produce an inductive voltage that can significantly lower the limiting current from the classical, electrostatic value. Although the source of the virtual cathode is transient in nature, the virtual cathode formed due to this inductive voltage persists long after the injected current has reached a steady-state value. The self-magnetic field is unimportant, however, at this low energy. This result has implications for scaling devices with rapid current rise times to weakly nonrelativistic energies as well as for Particle-In-Cell (PIC) codes which use field emission models with electric field thresholds.