JACoW is a publisher in Geneva, Switzerland that publishes the proceedings of accelerator conferences held around the world by an international collaboration of editors.
TY - CONF AU - Kleeven, W.J.G.M. ED - Zhang, Tianjue ED - Schaa, Volker R.W. ED - An, Shizhong ED - Kiselev, Daniela ED - Liu, Yuntao ED - Li, Pengzhan TI - On the Energy Limit of Compact Isochronous Cyclotrons J2 - Proc. of CYCLOTRONS2022, Beijing, China, 05-09 December 2022 CY - Beijing, China T2 - International Conference on Cyclotrons and their Applications T3 - 23 LA - english AB - Existing analytical models for transverse beam dynamics in isochronous cyclotrons are often not valid or not precise for relativistic energies. The main difficulty in developing such models lies in the fact that cross-terms between derivatives of the average magnetic field and the azimuthally varying components cannot be neglected at higher energies. Taking such cross-terms rigorously into account results in an even larger number of terms that need to be included in the equations. In this paper, a method is developed which is relativistically correct and which provides results that are practical and easy to use. We derive new formulas, graphs, and tables for the radial and vertical tunes in terms of the flutter, its radial derivatives, the spiral angle and the relativistic gamma. Using this method, we study the 2nur=N structural resonance (N is number of sectors) and provide formulas and graphs for its stopband. Combining those equations with the new equation for the vertical tune, we find the stability zone and the energy limit of compact isochronous cyclotrons for any value of N. We confront the new analytical method with closed orbit simulations of the IBA C400 cyclotron for hadron therapy. PB - JACoW Publishing CP - Geneva, Switzerland SP - 255 EP - 259 KW - cyclotron KW - resonance KW - hadrontherapy KW - focusing KW - hadron DA - 2023/10 PY - 2023 SN - 2673-5482 SN - 978-3-95450-212-7 DO - doi:10.18429/JACoW-CYCLOTRONS2022-THAO01 UR - https://jacow.org/cyclotrons2022/papers/thao01.pdf ER -