A Method to Obtain Single Turn Extraction for a Large Phase Width in Cyclotrons

The description of an acceleration scheme is given in which relatively large phase width may be extracted in one single turn by off-centering the beam at injection. Estimation formulae indicate that the width of an off--centered beam can be made very small at the entrance of an extractor with at the same time an increased turnseparation. The required condition is that the ¿r-value at the last turn be smaller than the ¿r-value averaged over turn number, indicating extraction in the fringing field. The needed radial amplitude is inversely proportional to the averaged ¿r, favouring therefore cyclotrons with large ¿r-values. Energy spread of the extracted beam corresponds to the energy spread in one turn of a beam with the considered phase width.