Geometric analysis of phase bunching in the central region of cyclotron

An optimum condition for realizing phase bunching in the central region of a cyclotron was quantitatively clarified by a simplified geometric trajectory analysis of charged particles from the first to the second acceleration gap. The phase bunching performance was evaluated for a general case of a cyclotron. The phase difference of incident particles at the second acceleration gap depends on the combination of four parameters: the acceleration harmonic number h, the span angle θD of the dee electrode, the span angle θF from the first to the second acceleration gap, the ratio RV of the peak acceleration voltage between the cyclotron and ion source. Optimum values of θF for phase bunching were limited by the relationship between h and θD, which is 90°/h+θD/2≤θF≤180°/h+θD/2, and sinθF>0. The phase difference with respect to the reference particle at the second acceleration gap is minimized for voltage-ratios between two and four for an initial phase difference within 40 RF degrees. Although the slope of the first acceleration gap contributes to the RF phase at which the particles reach the second acceleration gap, phase bunching was not affected. An orbit simulation of the AVF cyclotron at the Japan Atomic Energy Agency verifies the evaluation based on geometric analysis.