On the Resonance Acceleration of a Charged Particle in a Modulated Magnetic Field

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Abstract
Resonance acceleration of a charged particle in a high-frequency modulated uniform magnetic field is investigated analytically. An approximate expression for the motion of the particle under acceleration is obtained by transforming the equation of motion into a Mathieu-Hill type differential equation and by performing a perturbation calculation for a parametric resonance of an arbitrary order. In the case when the acceleration is limited by collision of the particle with the wall of the vessel as well as with a gas molecule, the maximum attainable velocity of the particle is realized when the order of the resonance takes a certain optimum value. The result is fairly consistent with the experiments on electron cyclotron resonance in a radiofrequency ion source.

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