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Using the Bogolyubov method, the solution of equations of electron motion in a combined mirror-type magnetic trap is obtained in cases when the electron approaches the cyclotron resonance region and when it passes through it. It is assumed that the synchronism between particle and the resonator standing wave is maintained by means of slow time variation of the guiding magnetic field. The problem is solved within the framework of the simplified model using the weakly relativistic approximation.

Theory of electron motion in combined magnetic trap under conditions of gyromagnetic autoresonance