The analytical solution of the equation of motion of a charged particle in the field of the T-wave and homogeneous magnetic field is obtained in the case of exact autoresonance and in the nonresonant case. Using this solution, the band and critical factor of the conditions of autoresonance is investigated in different situations and for different relativistic levels β_0=v_0/c.A singularity of resonance curves at the point of resonance is established. It is shown that, when the length of the domain of interaction or β_0 increase, the resonance band sharply narrows and the critical factor of resonance conditions becomes more pronounced.
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