LC Circuit

It depends on whether the LC circuit is self-resonant (like in a Colpitts oscillator), or whether it is being driven by an external input at an off-resonant frequency. Suppose the plate circuit (of a vacuum tube) is set to 10.0123 MHz, and the grid is being driven at 10.0000 MHz. The EM waves would be at 10.0000 MHz. Furthermore, because the LC resonant circuit is lossy (has a resistive component), this will also detune the LC resonant frequency of the circuit.

 

I am not quite sure what your question is, but the geometry of the magnetron cavity (slot dimensions, etc,) is equivalent to the physical L and C in a plate circuit (of a vacuum tube). The driving frequency in a magnetron is set by the magnitude of the magnetic field, e.g., 875 Gauss for 2.45 GHz (microwave oven). In both the vacuum tube and the magnetron, the driving force (grid signal or magnetic field) and not the physical parameters (L & C or magnetron geometry) determines the outout frequency

 

You are right. The electrons in the magnetron are a current, and bunches of electrons circulating (at the electron cyclotron frequency) past the vanes in the magnetron produce an EM oscillation in the cavities. An old friend of mine designed the rising sun magnetron for his PH.D. thesis during WW II.