General power relations of cyclotron waves

The power exchange between synchronous or cyclotron space charge waves and a potential field is investigated in a general way without considering particular coupler designs. It is shown that the transverse velocity of the helical beam and not the electron velocity is decisive for the power exchange. The power carried by the synchronous wave and the cyclotron wave is calculated and it is shown that the first of the two is exchanged with the axial component of the field, while the latter is exchanged with the rotational part of the transverse field component and the remaining part of the axial field component. The results agree with earlier calculations performed by Siegman for the Cuccia coupler. [J. Appl. Phys. (USA), Vol. 31, No. 2A, 17 (1960)].