A Vacuum Diode for Make: Magazine

It should be noted that, as seen at your link, at high forward voltages the characteristic curves of a vacuum diode do not look like those of a semiconductor diode, because the current saturates, which does not happen in semiconductor diodes, which at very high forward currents behave like a small resistance in series with a voltage source with a value typically between a half of volt and two volts, depending on the semiconductor material.

The value at which the current saturates in a vacuum diode depends on the temperature of the filament and of the area of the filament, because at a given temperature the filament emits a fixed current per unit of filament area. If the forward voltage is high enough, all the emitted electrons are attracted by the anode and reach it, so the current saturates at that maximum value.

Thus the forward characteristics of a vacuum diode look more like the characteristics of a depletion-mode JFET, with the different filament voltages corresponding to different gate biases of the JFET.

When a vacuum diode is used as a rectifier, the circuits must be designed such that the forward voltage remains always smaller than the voltage at which the diode current saturates, otherwise it no longer behaves like a rectifier.

The same is true for the amplifier tubes, like triodes or pentodes, which also must be used only in conditions when the anode current is smaller than the saturation current determined by the filament, otherwise they no longer behave as amplifiers controlled by the grid input voltage, because the saturation current depends only on the filament voltage.

Due to this saturation of the current emitted by a hot filament, vacuum tubes are usable only at small currents, typically much less than one ampere, even if handling great voltages, even up to one hundred kilovolt, is not a problem for vacuum tubes.

Before WWII, great currents were handled with gas tubes, not with vacuum tubes, e.g. with thyratrons and mercury-arc rectifiers, where the ionization of the gas by the electrons emitted by the filament can generate enough mobile charge carriers to sustain even huge currents.

You'll find a similar thing in vacuum fluorescent displays as well [0].

[0]: https://ibb.co/XZHWLD3x