Analysis of the analytic formulae application area for free oscillation frequency calculation in isochronous cyclotrons

Selection of optimal analytic formulae for calculation of free oscillation frequencies of the particles in isochronous cyclotrons, νr (r) and νz (r), and their application area are described. The selected formulae are used in the program BORP SR - Betatron Oscillation Research Program Second Release - written in C++ with the help of MS Visual C++ .NET. The free oscillation frequencies, calculated by using the program, are used for the evaluation of the modeled regimes of the work of the AIC144 isochronous cyclotron. The analytic formulae were selected by comparing the results of the calculations performed by using formulae adduced by T.Stammbach, Y.Jongen - S.Zaremba, V.V.Kolga with the results of the calculations performed by using the CYCLOPS iterative program, developed by M.M.Gordon. The least difference in the calculation results was obtained for the analytic formulae adduced by V.V.Kolga. The νr (r) calculation difference ranged from -0.5 to 1.5% and the νz (r) calculation difference ranged from -5 to 4% for the working radii of the isochronous cyclotron. As the beam was obtained, the selected analytic formulae can be successfully used in the program BORP SR for free oscillation frequency calculation during the evaluation of the modeled regimes of the work of different isochronous cyclotrons