Various methods to measure the betatron tune of the synchrotron

Hatakeyama, Shuichiro

Generally in the synchrotron, the frequency of transverse oscillation of the bunched beam for each single turn (usually called betatron tune or just "tune") is one of fundamental controllable knobs to avoid the instability of the accelerator. In this report, it is not mentioned about the effect to the beam instability but it is focused to various methods to measure the betatron tune by using bunch-by-bunch transverse beam position. The following items will be presented, (1) least square fitting to the time-domain beam position at specific location. (2) peak finding of the frequency-domain beam position at specific location. (3) phase space analysis of the beam position at specific location. (4) frequency-domain analysis of the beam position in the normalized coordinate at many locations in the ring orbit. For the application to the real accelerator, data of the J-PARC (Japan Proton Accelerator Research Complex) will be shown.