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Charged particles are accelerated through a RF cavity:

-Is the electric field accelerating the particles from the electromagnetic field itself?

-Or, is the electric field accelerating the particles from charges on the surface of the conductive cavity being moved to form a capacitor by interaction with the electromagnetic field?

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In a vacuum diode, triode and its varieties the static field between the cathode and the anode is the cause of most acceleration of the electrons. In distributed microwave sources, such as klystrons and travelling wave tubes (TWT), the injected EM wave directly modulates the electron beam. This controlled interaction can only happen over many RF cycles if the propagating EM wave moves slower than $c=3\times10^8[\textrm{m/sec}]$, in fact if it is designed to move at the speed that is nearly the same as that of the electrons. See, https://en.wikipedia.org/wiki/Klystron and https://en.wikipedia.org/wiki/Traveling-wave_tube so then a very strong interaction happens between the electron beam and the EM wave so that the beam transfer its energy that it has obtained from accelerating through the static cathode - anode field and passing it to the EM wave in the right phase.

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