Hori, C. Aoki, T. Hae, T. Hiramoto, H. Seki, T. JACoW Publishing Geneva, Switzerland 978-3-95450-205-9 10.18429/JACoW-Cyclotrons2019-TUP036 English 242-244 TUP036 extraction septum focusing cyclotron resonance Contribution to a conference proceedings 2020 2020-06 https://doi.org/10.18429/JACoW-Cyclotrons2019-TUP036 http://jacow.org/cyclotrons2019/papers/tup036.pdf A trend in proton beam therapy systems is downsizing their footprints. A larger main magnetic field for the downsizing, however, requires a septum magnet to generate a larger magnetic field for beam extraction. In order to relax the specification of the septum magnet, we consider an azimuthally varying field (AVF) weak-focusing accelerator. The magnetic fields of its hills and valleys can be designed while maintaining the average magnetic fields over the design orbits. Thus, by locating the septum magnet near one of the valleys, the specification is relaxed while keeping the footprint of the accelerator. In this study, we show an optical design of an AVF weak-focusing accelerator with cotangential orbits. The magnetic field in the valleys is smaller than the average magnetic field over the maximum energy orbit by 0.2 T. We evaluate gradient magnetic fields required for beam extraction and find the possibility of variable energy extraction by the static gradient fields.