Numerical simulations for field formation in cyclotrons


Completed orders:

Efremov Inst. (St.-Petersburg, Russia) – cyclotron CC18/9
Efremov Inst. (St.-Petersburg, Russia) – cyclotron CC12


3D magnetic field simulation was applied to optimise geometry of the sectors and shims and location of the active coil. A precision finite-element model allows consideration of non-linear effects and the actual geometry specifics. The simulated radial distribution of an average field complies with the given isochronous curve.

The numerical procedure of the CC12 field formation included 4 main stages.

1. At the first stage basic parameters of the magnet system were determined from the magnetooptic calculations performed at Efremov Institute.

2. The second stage involved the development of a realistic 3D model for the DC60 magnet system. The model used detailed descriptions of the magnet geometry, media interfaces, and non-linear properties of steel. For initial calculations a standard near-realistic B-H curve was used as reference. Then steel properties were corrected using the results of magnetic measurements on samples of steel used in the fabrication of the magnet. The curves В(Н), m(Н), m(В), m / H ) obtained for the real magnet were used to simulate the expected field distribution and to choose the shimming method. Figures 1,2 present a part of the finite-element model of CC12 magnet system (magnetic circuit and coils only). The model covers a 1/16 of the magnet system and includes boundary conditions with respect to the magnet symmetry. The external boundary for the calculated region was taken so that to avoid the influence of the boundary conditions on the field behaviour inside the working zone and type of field decay with distance from the magnet. The finite-element mesh has about 230000 nodes.

3. The finite-element model was applied to preliminary analyse a spatial field distribution. From the magnetooptic analysis a required isochronous curve was found. The next step was to vary geometrical parameters in order to calculate the influence functions [2] for different magnet components and select the shimming method. From the results of the calculation, the azimuthal shimming by shaping the sector sides was chosen to form a desired field distribution.

4. The influence functions obtained were used to form an isochronous field with the accuracy required. Figures 3,4 show calculated field distributions over typical cross sections for the optimised magnet configuration.



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