Modeling of required operation modes and analysis of their stability for multipurpose isochronous cyclotrons

The mathematical and computer modeling of operation modes of multipurpose isochronous cyclotrons is based on the calculation of currents in trim coils of correction of the basic magnetic field (Ii, i=1,2,..., n) at a certain level of current in the main coil (Imc). The calculation is made for a given kinetic energy (Ek) at a certain radius or for orbital frequency of particles (F0). The results of the calculation allow the required magnetic field to be formed with a certain accuracy in the range from the ion source to the extraction system of particles. A series of numerical and physical experiments on calculation of the basic operation mode of the multipurpose isochronous cyclotron AIC144, INP PAS, Krakow (p, Ek=60 MeV, F0=26.25 MHz), confirmed both the necessity of including the evaluation of solution stability into the calculation, and the possibility of producing the beams of protons in the range of acceleration radii without essential phase losses in the range of isochronization radii of the required magnetic field