Calculation of the ideal isochronous field for the SC200 cyclotron using the Nelder-Mead simplex algorithm

Figures & data

Table 1. Main parameters of the SC200 cyclotron

Parameters	Value
Average magnetic field (central/extraction)	2.95/3.64 T
Minimun/Maximun field	2.8/4.6 T
Number of sectors	4
Pole diameter	1.24 m
Extraction energy	200 MeV
Extraction radius	0.604 m
Maximum spiral angle	65°
Harmonic number	2
RF frequency	91.5 MHz

Figure 1. Overview of the flutter field of the SC200 cyclotron

Figure 2. Flow chart for the Nelder-Mead simplex method

Figure 3. Flow chart for calculating the objective function

Figure 4. Comparison of the isochronous field obtained from Gordon’s method, the gyration frequency-based method, and the 12^th-order simplex method

Figure 5. Difference between the isochronous field obtained from Gordon’s method, the gyration frequency-based method, and the 12^th-order simplex method

Figure 6. Relative error in the orbital frequency of Gordon’s method, the gyration frequency-based method, and the 12^th-order simplex method

Figure 7. Comparison of the integrated phase slip during acceleration from 150 MeV to 200 MeV

Figure 8. Time cost for different-order simplex methods (left), and the value of the objective function for different-order simplex methods during the iterations (right)

Figure 9. Overview of the pole structure for SC200 (left), starting and optimized pole geometry (middle), and the angular width of the poles before and after shimming (right)