That is like what I wrote. Nobody would want to carry a 5000 watt tube audio amplifier to an event when they can have the same thing as a 2U rack module weighing 14kg.
Such an amplifier likely contains (or requires an external) sound processor that cleverly limits the amplitude without hard clipping.
For the cost of building the most powerful tube amp ever you could buy a pretty nice used sports car. Or less expense. Less dangerous. Girls will like you better.
Thinking about the output device specifics is bikeshedding at this point in the design anyway. If one were serious one would be starting at the PSU and working forwards. Oh, it's gonna be a complex and glorious PSU for sure, with a pretty sophisticated fail-safing system, overvoltage/overcurrent protection, and probably uP-controlled startup sequencing and bias monitoring.
Or u can just build a house-burning down murder machine I guess.
Starting at the output devices is bikeshedding, anyone who was serious/non-crazy would be thinking (sleepless nights in horror) at what the cost in design time and parts to make a safe reliable PSU for such an amplifier would be to start.
Agreed that the PSU is an issue, if you have only a 50/60 Hz single phase feed, especially due to the lack of high voltage electrolytic capacitors.
However, if you have a three phase feed (230/400 V in Europe or
277/480 V in the US) the power supply is trivial. Just put a 6 pulse rectifier after the anode voltage transformer. If you have two secondaries, put one in wye and the other in delta and you can use 12 pulse rectifier, generating smoother DC and reduce the power factor on the primary side.
Tubes can take a lot of punishment, so a 30-60 s time delay should be enough, before switching on the anode voltage, when the cathode has reached full operational temperature.
The OP's an hammerchewer with his talk of using BFO transformers. I'm not surprised I didn't see the OP since I'm guessing I must have killfiled him some time back.
If his plan is to annoy the neighbours, he could scale his BFO Amp requirements back by a good 16 to 20dB using horn loaded pressure transducers just like the old cinema houses used to do when filling a large auditorium with high level sound using just a 5W rms valve amplifier. If he's ok with a cardioid sound field, he could gain an extra
3dB by loading the pressure transducer diaphragm(s) front and back with a matching pair of horns each.
There's no point in wasting energy and money on superfluous matching transformers when you can use paralleled valves (vacuum tubes) in a DC coupled push-pull bridged output configuration fed from a voltage doubled
240v rms supply with +/-300 volt HT rails. That's a configuration that should drive a 16 ohm speaker load to 5KW rms with some margin to spare. :-)
Of course, he could save himself the bother of floating heater supplies and the sheer quantity of 807 valves or whatever readily available valves he can get his hands on if a 10KW am Tx high level modulator amplifier doesn't float his boat by building a solid state equivalent of the DC coupled valve design using high voltage high slew rate power fets instead.
Varian made 23MW (klystrons, I think) for SLAC, and that two-mile accelerator is still in service, so they're probably rebuilding 'em from time to time.
You could look at the Westinghouse FG-10 design as a ballpark for the size power supply you'd need for two channels at 10kW total. "sturdy transformer"? There are _several_ very sturdy-looking iron transformers in it at the bottom of the cabinet, each one looks to be about the size of a microwave oven.
You're not running this hypothetical amp off a 120V wall socket, sorry to say.
You're certainly going to need some kind of fast-acting overcurrent/bias voltage loss detecting system; self-bias is probably a non-starter and at those power levels loss of a bias supply will probably be a genuine disaster that'll make the local news at least ;-)
After that it was leased to China Radio International (ex. Radio Peking). At least the medium wave transmitter at 963 kHz has been used quite recently.
Power the anode supply contactor (relay) from the bias supply. If the bias is lost, the contactor will release. Since in a 3 phase supply, typically there are no big capacitor on the DC side, the anode voltage will drop quite rapidly. As noted previously, tubes can handle some punishment.
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