Orbit calculation for muon cyclotron

We studied the beam orbit for an AVF cyclotron to accelerate muon (μ⁺) beams to an energy of 5 MeV. The injected muon beams are generated at the J-PARC MLF muon beam line. The muon beams have an energy of 30 keV and a low emittance of 1 πmmmrad because μ⁺ is generated from muonium. In this study, we designed a magnet and RF cavities by using Opera and CST MWS, and calculated the muon beam orbit. The accuracy of the designed isochronous magnetic field is such that the phase change of the beam during acceleration is within the range of ± 5°. Beam orbit calculations from the injection to the extraction turn were performed assuming a beam having a Gaussian shape in each phase space in two directions parallel and orthogonal to the inflector electrode. As a result, the dispersion of the extracted energy was calculated to be 1.2 × 10^-4 for an injection beam with a phase width of ± 4° (pulse width 0.2 ns) when a flattop cavity was used. The emittance in the extraction turn was calculated to be 0.3 to 0.4 πmmmrad in the radial and axial directions, respectively. (author)