I fully agree with FvM. I have used normal vacuum tubes at up to about 800MHz but beyond that their performance is poor. Even at 800MHz a single transistor amplifier far out-perfomed the tube version.
The problem is that vacuum tubes have inherently high inductances in their connecting wires, have relatively large capacitance between electrodes and unless used in grounded grid configuration, tend to have too much feedback capacitance which makes them unstable. Usually, feedback compensation is needed to cancel the instability.
This isn't the place to explain how TWT work but the principle is to use special materials to slow the signal so it has chance to 'bunch' (accelerate and decelerate) the main tube current. They typically require several KV operating voltage and high power types have to be water cooled.
Klystrons and Magnetrons are not amplifiers as such, they actualy produce the output signal by oscillating themselves although some Klystron types can be fed from external signals. I have always explained Magnetrons as working ike this:
Imagine blowing across the top of an empty bottle, if you get the flow just right you hear a steady tone. The size of the bottle determines the pitch of the tone. The sound is produced by a resonance of the air pressure waves inside the cavity formed by the bottle. Substitute an electron flow for your breath and make the cavity very much smaller, as the electrons skim the entrance to the cavity (like the mouth of the bottle) it sets up an oscillation. A strong magnet is used to bend the electrons so they pass at the optimum angle. Most Magnetrons use multiple cavities arranged in a circle, the oscillation in each cavity reinforces the next to give it more gain. So a Magnetron is a diode with a twisted electron beam that makes a 'tone' as it passes the cavities. The downside to magnetrons is their frequency is decided by the cavity dimensions so they can't easily be tuned to different frequencies. They also run on high voltages, usually in the 2 - 3KV region and can fraw several amps so they must be force cooled.
Brian.