One electron in a planar diode driven by pure AC, V(t) = V₀ cos(ωt + φ₀), no DC bias. Change any parameter and every plot updates; drag the dot on the phase map to move through (φ₀, Γ).
Starting values come from the reference RUMDEED inputXE decks: gap 1000 nm, peak field 1 V/nm (V_AC = 1000 V), 800 nm drive, work function 5.1 eV, launch at z = 1 nm.
CrossesSweet spot
Drive parameter Γ
Transit time
Charge reaching anode
of all emitted electrons, every launch phase
Impact energy
Trajectory x(t)What this plot shows
Blue line: the electron at your launch phase φ₀ (slider), from emission until it touches a plate.
Grey lines: the same electron launched at −80°, −60° … +80° in 20° steps, labelled at their ends, for comparison. Turn them off under Display.
Green dot: arrives at the anode. Red dot: falls back to the cathode.
Amber strip: the drive field at the cathode; shaded where it pulls electrons out.
Grey bands: the plates, cathode at x = 0 and anode at x = D.
Dashed blue (optional): the formula continued past the plate. Not physical.
Hover or touch the plot to read time, position and velocity. Horizontal axis: time since emission. Vertical axis: distance from the cathode.
Hover or touch the plot to read position and velocity
The equations, with your numbers
Phase map: who crossesWhat this plot shows
Every point is one electron: launch phase φ₀ across, drive parameter Γ up (log scale).
Blue: reaches the anode. Grey: falls back. Amber: oscillates without crossing.
Ring: your current φ₀ and Γ. Drag it: φ₀ follows the horizontal position, and the frequency changes to give the new Γ.
Dashed lines: the sweet-spot band, Γ = 0.5 to 1.
Computed numerically on a 90 × 56 grid with your gap, field, launch height and excess energy. Gap, field, height or energy changes redraw it after you stop moving the slider.
crosses returns trapped
Emitted charge by launch phaseWhat this plot shows
Curve: how much charge leaves the cathode at each launch phase, scaled so the peak is 1.
Green area: charge that reaches the anode. Grey area: charge that falls back or stays trapped.
Percentage: green area divided by total area.
Dashed line: your φ₀.
Field emission (Keldysh γ < 1) peaks at maximum field, φ₀ = 0. Multiphoton emission (γ > 1) is flat, because it follows the pulse envelope rather than the carrier. Override this under Display.
of emitted charge reaches the anode
Transit timeWhat this plot shows
Blue curve: time to reach the anode for each launch phase, in drive cycles, log scale.
Grey columns: phases that never arrive.
Dot: your φ₀, with its value.
The curve rises steeply near φ₀ = 0 because the drift velocity, proportional to −sin φ₀, goes to zero there.
drive cycles, log scale
Impact energy at anodeWhat this plot shows
Blue curve: kinetic energy on arrival at the anode for each launch phase, in eV.
Grey columns: phases that never arrive.
Dot: your φ₀.
When the flight lasts many cycles (small Γ), the carrier phase at arrival is effectively random, so the curve looks jagged. That is real, not numerical noise.
eV
Model: single electron, continuous-wave drive (no pulse envelope), uniform field E₀ = V₀/D, no image force, no space charge, non-relativistic, absorbed on touching either plate. Γ = eE₀/(mω²D). Any excess energy at emission is taken as pointing straight at the anode, which is an upper bound. RUMDEED adds the envelope, the image charge and space charge, so expect differences once those are on.