Another form of electronc emission is thermionic emission. Heat up a cathode in vacuum and electrons will "boil" off. This is what was used in most vacuum tubes. Even a small potential (say on the grid electrode of a triode) is enough to push them around. Once they fly past the grid, they now see the large anode potential with accelerates them, adding energy. In this case, the maximum current is limited by the rate thermionic emission as well as the repulsion from other electrons pushing them back towards the cathode. Small changes in the grid potential can generate large changes in current flow at first, but eventually saturate.
The vacuum itself doesn't have resistive losses, although the vacuum is different from metalic conduction. In metals, the charges of electrons are screened from each other and they propagate relatively freely. In vacuum, the electrostatic repulsion can be significant.
In a simple thermionic vacuum diode, if you heat the cathode it will emit electrons that just hang around as a "space charge" cloud (with no voltage applied to the anode).
When you add a positive voltage to the anode, there are two important limiting conditions for the anode current as a function of cathode temperature and anode-cathode voltage:
1. "Saturated emission": with a very high anode-cathode voltage, the electrons are drawn away from the cathode fast enough that no space-charge cloud persists. The current is almost independent of voltage (if high enough), but a very strong function of cathode temperature.
2. "Space-charge limited": normal operation for a vacuum tube. The Child-Langmuir law gives a current proportional to
V3/2, roughly independent of cathode temperature (if high enough). For typical amplifiers, this operation is preferred since it is not so sensitive to cathode temperature and depends mainly on the voltages applied to the device.
Adding the grid to control the current, the E-field at the cathode is a function of both the plate-cathode and grid-cathode voltages. Since the grid is much closer to the cathode than is the anode, it has a stronger control of the cathode field (the relative factor is called "mu") than the anode voltage. The field at the cathode surface
Ek is proportional to (
Vak/(mu) +
Vgk).
In this ideal case, if
Vgk = -
Vak/(mu), then the field at the cathode goes to zero and the tube "cuts off".