Are there purely diode, vacuum tubes?

[Baluncore]

You can test your idea with any triode.
Heat the cathode as usual. All things are relative, so tie the cathode to a negative DC bias voltage, say -9V. Ground the grid and use ground as the reference voltage. Now the space charge will be accelerated through the grid and some will accumulate on the electrically floating cylindrical plate electrode.

The plate will take up a negative voltage determined by the accumulation of electrons. Once the voltage on the plate falls to that of the cathode, electrons passing through the grid will turn around before reaching the plate, then fall back through the grid towards the cathode, until they end up on the grid.

In theory the voltage on the floating plate will be limited to somewhere between the cathode and the grid voltage. The effect feeds back on itself to self regulate the negative voltage excursion possible on the plate. It is therefore not really possible to generate a voltage outside the bounds of the DC supply available.

 

[the_emi_guy]

The OP may not be aware that the Van de Graaff belt forces the charges mechanically into the sphere, against electrostatic repulsion. The motor does a lot of work getting the charges up there and in (I have burned out a few Van de Graaff motors). Not sure how you would do this in a sealed electron tube.

 

[Svein]

The DY87 (https://frank.pocnet.net/sheets/010/d/DY86.pdf) was the dominating rectifier for the EHT voltage in glass TVs.