Connect d1 and d2 to m, ground k1 and k2, heat the filament. Some electrons will be emitted from the heated k, to reach d and so drive it negative. That will repel future electron migration and so limit the voltage. I was thinking to connect d1, d2, k1, k2 all to negative potential. This way, the electrons won't reach d, they'll accelerate towards the mesh. Any that move towards D, will accelerate away from d. D may have to be slightly higher than k to account for the kinetic energy of the emitted electrons.
How will you use 19V to pump charge onto the capacitance of the outer mesh ?
Remember that the filaments should be operated at a similar voltage to the k voltage.
The filament is indirectly heated by 19 volts at .1 amps. I will start by using -19 volts for k and D as well. I'll make adjustments if this is not enough but I think it's plenty.
The mesh could be charged to -100 volts but the electric field isn't going to effect the electrons inside it.
What makes the vacuum tube better than a tin can ?
What do you mean? A tin can isn't in a highly exhausted glass tube. I can't expect the filament to survive for long in the atmosphere. If this works, I'll see how much a custom tube will run me. With some spherical components and a heavy duty filament, I'd like to see the kinds of voltages achievable with a couple 9 volt batteries.