Cyclotron resonance interaction †

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Abstract
A new method of approach to the old problem of interaction between an electron beam and an electromagnetic field is presented in this paper. It is shown that great simplification can be achieved by directly setting up a differential equation describing the flow of energy between the beam and the field; this obviates the necessity of an explicit calculation of the electron trajectories. A non-linear treatment of the cyclotron resonance interaction is used as an example of the inherent power and relative simplicity of the method.