(These Pleiades experiments are usually done with an EF183 electron tube. Take all safety precautions including a fuse in series with the heater voltage or any other voltage supply).
The cathode and grid supported by the glass, insulator and metal structure is a capacitor with the 2 plates separated by close vacuum.
If we connect a high impedance voltmeter between cathode and grid of a cold electron tube we may still read a small voltage, presumably due to previous use or electrostatic charge. (Later addition: this potential,difference is due to light, when the electro tube is outdoors the pd exceeds 330mV measured with a 10MΩ voltmeter input impedance. So it seems there is photo emission, see also Pleiades (-1), UCC85, ECC82 etc long tailed pair with floating grids. In fact we should be able to observe a voltage due to the capacitance charged but the tube should be in a relative darkened room. See the euroelectron post in the references).
When the cathode is heated by the heater circuit this voltage substantially increases to many hundred millivolts cathode positive wrt grid or grid negative wrt cathode. This should be easy to measure even with low input impedance voltmeters.
Boiling electrons have left the cathode to the electron cloud and the cathode has become positive.
It looks a bit like having charged a capacitor from the inside rather than from the outside.
But if memory is correct when the heater circuit is disconnected and the cathode cools down this voltage drops again. Apparently the electrons have returned from the cloud to the positive cathode. The cathode gradually returns to no charge condition?
A very small voltage of very few millivolts is still left. And perhaps this is due to electrons migrated to the grid charging it a bit negative. (Possibly not, see later addition).
Is we supply externally the grid cathode capacitor with a few hundred millivolts would the new high voltage stay there until it is discharged slowly by say a 10MΩ Voltmenter connected to them? (Later addition: no reading was obtained, too quick discharge time or time constant even with a 10MΩ input impedance voltmeter?)
What happens from inside the electron tube is a bit different.
When the cathode is hot we measure a few hundred millivolts from cathode to grid.
These 2 electrodes have become a source of voltage or electromotive force, EMF. The output impedance of this voltage source should be rather low, perhaps typically only 4 KΩ and could possibly even move the needle of an analog passive moving coil voltmeter. (If we "short circuit" grid to cathode with a micro ammeter we measure a current. Note a micro ammeter has a non zero impedance).
Where does the energy come from?
It comes form the energy we supply to heat the cathode.
At high school the brilliant physicist and teacher Alekos Soupianos was asked. Why does this school book show a diode with cathode and anode connected to an ampere meter and the needle is drawn deflected even with no battery connected to the anode? He replied there are electrons who have enough kinetic energy to escape from cathode and arrive to the anode.
If there is current there must by a voltage source. So it seems when we heat the cathode the electron tube becomes a source of voltage or EMF.
This is an internaly generated negative bias.
The Pleiades bias is a bias applied in the opposite direction so that the electron tube can satisfactorily operate at a very low anode potential.
See also the Armstrong paper on why when we insert a grid on a vacuum electron tube the current drops.
References:
Operating features of the Audion - E. H. Armstrong
Pleiades V6 schematic
http://euroelectron.blogspot.gr/2018/05/why-are-ther-potential-differences.html
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