Physics
Vacuum tube
A thermionic diode as a live 1D plasma: the kenotron.
What happens
A kenotron simulated honestly: the heater feeds Richardson emission, electrons fly the gap under the field of their own space charge (Poisson every step), and the Child-Langmuir three-halves law EMERGES from the virtual cathode instead of being typed in. Bias the anode negative and the tube cuts off - rectification you can watch. Press the sweep and the module measures its own I-V curve against the analytic law.
Equations used in the module
Equations d²φ/dx² = −ρ / ε₀, ρ = J / v, ½ m v² = e φ J = (4ε₀/9) √(2e/m) V^(3/2) / d² (Child–Langmuir) current saturates at the emission limit
