Why does the current saturate?

The vacuum-diode current is limited by two different mechanisms; at high voltage the temperature-related one dominates.

1 · Low voltage — space charge (Child's law)

The filament emits continuously, but the just-emitted electrons form a negative cloud (space charge) that repels the following ones. Raising V pulls more of them through → the current grows.

2 · High voltage — thermionic saturation (Richardson)

The field becomes strong enough to collect every electron the filament can emit: the current no longer depends on V, only on temperature. Raising V does nothing more → the curve flattens.

In short: I = min( I_Child(V), I_sat(T) ). Below the knee the voltage limits it; above, the temperature. Increase the filament heating: the plateau rises and the «knee» shifts to higher voltages.

In the simulation the two laws are reproduced in simplified form: the slider sets a «heating» in per cent, not a temperature in kelvin, and the saturation current is an increasing function of it, not the Richardson formula written above. The qualitative behaviour — growth, knee, plateau — is the right one; the values are not those of a real tube.