A time-of-flight system for determining the absolute energy of ion beams has been developed for the azimuthally-varying-field (AVF) cyclotron at Japan Atomic Energy Agency (JAEA). Ion detectors, a microchannel-plate detector and a plastic scintillation detector, were applied to the system in order to achieve high time resolution measurement of the flight time and to cover a wide range of beam intensity in combination with a beam attenuator. The change of the flight length, performed by moving the plastic scintillation detector with flexible bellows, allows determining the mean beam energy only from the relative measurement of the flight time and the flight length without knowing their absolute values. The maximum movable distance of 2 m yields the difference in the time-of-flight from 16 to 94 ns for the energy range of ion beams accelerated by the JAEA AVF cyclotron. The time-of-flight system even with the 2 m change in the flight length achieves accurate energy determination, since the relative measurement has an advantage of elimination of the uncertainties in determination of the time-zero and the length-zero. The time-of-flight measurement with the relative measurement also allows estimation of the beam energy spread without conventional expensive systems such as a magnetic spectrometer. By comparing the widths of the time-of-flight spectra of ions accumulated at different flight lengths, we have estimated the energy spread. In order to reduce a labor process of the coincidence detection of ions in the time-of-flight measurement, we have also accomplished a simple estimation method for mean beam energy determination with a beam bunch, naturally modulated with the acceleration RF of the cyclotron. The mean beam energy has been obtained from the shift of the beam bunch centroids at different flight lengths in the time-of-flight spectrum.
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