Betatron oscillation frequencies calculation program description (Betatron Oscillation Research Program - BORP)

The Betatron Oscillation Research Program (BORP) written in C++ with the use of Visual C++ is described. The program is intended for the calculation of betatron oscillation frequencies f sub r (r) and f sub z (r), whose values are used for the calculation of Walkinshaw resonance and evaluation of its presence. The program algorithm was developed on the basis of the lecture notes 'Cyclotrons', composed by T.Stammbach (Joint Universities Accelerator School, France, 1997). The results of calculation made by the BORP were checked and confirmed by using the numerical methods of calculation of betatron oscillation frequencies f sub r (r) and f sub z (r). The discrepancies between the BORP results and the numerical methods results are from zero to a few percent. It defines the accuracy of calculations made by BORP for the considered isochronous cyclotrons with the azimuthally varying fields. As is evident from the results of calculations, the program can be used for calculations for both straight-sector and spiral-sector isochronous cyclotrons.