Mathematical Aspects of Modeling of Required Operation Modes of Multi Purpose Isochronous Cyclotrons

A mathematical and computer modelings of required operation modes for multipurpose isochronous cyclotrons is presented. The considered procedure is based on a calculation of current values in trim coils correcting the basic magnetic field (Ij, j = 1,2,…,n) for a certain current level in the main coil (Imc ). A series of numerical and physical experiments on modelings and testing the main operation mode for the multipurpose isochronous cyclotron AIC-144 (proton, Eout ∼ 60.3∕60.7 MeV, Frf = 26.155∕26.25 MHz), proved both the necessity of taking into account the estimate of the stability of the sought solution, and the possibility of accelerating proton beams in the all range of working radii from the ion source to the ion-beam extraction system for small phase losses of protons in the range of isochronization of required magnetic field.

isochronous cyclotron, mathematical model, least squares method, Gauss method, conditionality number, proton beam current