Same 1000 nm gap, same 10 V/nm peak field, no DC bias. Only the drive frequency changes, and with it Γ. Every dot is one electron from the AC1 RUMDEED runs, launched when and where RUMDEED emitted it.
What decides it. A launch before the peak drifts towards the anode and always gets there. A launch after the peak drifts back, so it crosses only if its first forward swing reaches the anode. The swing is at most 2ΓD long, so a slow drive (large Γ) carries even late launches over, and a fast drive (small Γ) sends them home. Watch the histograms: the grey starts exactly where the dashed line says it should.
The sweet spot is Γ between about 0.5 and 1: the fastest drive at which an electron born at peak field still crosses in one swing. Faster than that (Γ = 0.2), only the rising-edge half crawls over, cycle by cycle. Slower (Γ = 4), everything crosses, but in a tenth of a period, so the field barely changes on the way and it behaves almost like DC.
Emission time, emitter position and fate of each electron come from the RUMDEED output (gold, 5.1 eV, 30 × 30 nm emitter, space charge off). In flight, each one follows the exact single-electron path, which reproduces RUMDEED electron by electron: same fate for all 14 460 electrons, transit times within 3 parts in 10⁴. Counts at the end of each run are RUMDEED's own.