Jaffe Current Density Confirmed as True Bifurcation Point in Vacuum Diode Hysteresis

The arXiv preprint challenges prior claims that J_hys equals the bifurcation solution J_LD by showing J_LD produces unphysical charge densities exceeding the true space-charge limit given by J_Jaffe. Using PIC runs with nonzero initial electron velocity, the authors map reflection onset and virtual-cathode oscillation thresholds, establishing J_Jaffe itself as the mathematical bifurcation point where steady-state solutions cease. This corrects an inconsistency that had persisted in diode theory since early extensions of the Child-Langmuir law.

Past studies reported hysteresis loops closing near J_LD, but the new simulations reveal J_hys lies between J_Jaffe and J_CL and scales with their ratio through a compact empirical fit. The discrepancy arises because J_LD was treated as a valid steady state despite violating Poisson-equation boundary conditions at the virtual cathode. The result implies that oscillation quenching in high-power vacuum devices is governed by Jaffe kinetics rather than the zero-velocity assumption.

Context from related diode literature shows this finding aligns with measured current-voltage curves in thermionic converters and high-power microwave sources, where observed hysteresis margins exceed J_LD predictions. The work highlights how analytic approximations can embed hidden inconsistencies when initial velocity is nonzero.

Next steps include targeted experiments measuring oscillation spectra versus injected current density to test the semi-empirical fit at higher voltages and varied cathode temperatures.