ANALYSIS OF ELECTRON TRAJECTORIES IN A GYROTRON RESONATOR

A detailed mathematical analysis of the equation describing the electr on interaction with the high-frequency field in a gyrotron resonator i s presented. Electron trajectories in the phase space are classified. It is proven that in the cold-cavity approximation when the high-frequ ency field is represented by a Gaussian-type function, the solutions o f the gyrotron equation are asymptotically equal to the solutions of t he corresponding unforced equation. This means that chaos, which, in p rinciple, can develop in a resonator for some values of control parame ters, can be only transient, i.e., electrons again follow regular traj ectories once they leave the interaction space. Understanding of the d istribution of electron trajectories is important, both from the theor etical and the practical point of view, As an example, detailed numeri cal computations of electron trajectories are performed for those valu es of control parameters which correspond to the maximum efficiency.