The MERMAID program will be used to isochronise the nominal magnetic field of the VINCY Cyclotron. This program simulates the response, i. e. calculates the magnetic field, of a previously defined model of a magnet. The accuracy of 3D field calculation depends on the density of the grid points in the simulation model grid. The size of the VINCY Cyclotron and the maximum number of grid points in the XY plane limited by MERMAID define the maximumobtainable accuracy of field calculations. Comparisons of the field simulated with maximum obtainable accuracy with the magnetic field measured in the first phase of the VINCY Cyclotron magnetic field measurements campaign has shown that the difference between these two fields is not as small as required. Further decrease of the difference between these fields is obtained by the simulation model calibration, i. e. by adjusting the current through the main coils in the simulation model
In an isochronous relativistic cyclotron, axial defocusing of a beam caused by the radial growth of the isochronous magnetic field is compensated by the azimuthal field gradient introduced by sectors. The focusing capabilities of sectors set the maximum ion energy obtainable from the machine. Usually, the focusing limit of a machine is determined by using the criterion for axial beam instability evolving from the equations of betatron oscillations. The obtained value of the focusing limit is approximate because the equations of betatron oscillations it originates from are approximate as well. The accurate value of the focusing limit is obtained by simulating accelerated beam dynamics in the extraction region. It is shown that the focusing limit of a cyclotron resulting from the two methods could differ for more than 9%. The suggested third method for focusing limit computation relies on the beam dynamics simulation along the critical equilibrium orbit rather than the acceleration orbit and thus it is less time consuming although equally accurate
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