基于台阶垫补的磁场优化算法研究

Research on Magnetic Field Optimization Algorithm Based on Step Shimming

  • 摘要: 在回旋加速器磁铁设计过程中,磁场优化是非常重要的一个环节。由于加速器磁铁的磁场响应随着磁极台阶高度变化呈现非线性的特点,使得在优化复杂的磁场时,计算过程复杂、时间成本高且需要手动迭代。以1台圆形轴对称磁铁垫补为例,发展了磁场优化算法。利用三维电磁场仿真软件CST和数据分析软件MATLAB,研究了单个台阶垫补块对中心平面上不同半径处磁场幅值的影响,实现了一种自动优化磁场的算法,并以磁场降落指数为0.2的磁场为优化模拟实例,最终求得了对应的磁极台阶高度,证明了本算法的可行性和便捷性。

     

    Abstract: Magnetic field optimization is a very important part in the design of cyclotron magnets. Many disadvantages are revealed when traditional magnetic field optimization methods were used, and complex magnet models calculated: 1) complicated calculation process; 2) high time cost; 3) manual iterative calculations, the reason is that the magnitude of the magnetic field response changes nonlinearly with the main magnet pole steps height changing, and it is time to use more efficient optimization methods. The main magnet of the circular cyclotron was chosen as the research model to study the optimization method of the magnetic field, and the optimization calculation was based on the MATLAB codes which controlled the three-dimensional electromagnetic field simulation software CST. The axial component of the magnetic field at different positions along the radial direction on the center plane of the dipole magnet could be changed by adjusting the height of the annular magnetic pole steps on the magnetic pole face, and the magnetic field changes were called the contribution of a single step block shimmied to the magnetic field. The new calculated average field of the magnetic field can be obtained after correcting the heights of all magnetic pole steps, ideally, it was the same as the object average field. But the calculated value usually deviates from the object value because of the numerical calculations and approximate operations during optimization. The steps height correction coefficient can be obtained by combining with the deviation amplitude of the average field and the contribution, and the new steps height value of each step can be solved with the functional relationship between the correction factor and the step height, then the new calculated average field and deviation were also available. If the deviation meets the accuracy conditions, the optimization calculation is completed, and the height value of the steps is also satisfied now, otherwise, the next generation calculation is needed to go. The correction calculation is very critical in the every iteration as the correction contributions can make theoretical shimming changes closer to the simulated changes to improve the accuracy of magnetic field shimming. The ratio between the average field deviation obtained in the previous steps and the correction coefficient is called the contribution correction changes. The updated contribution can be obtained by subtracting the ratio from the contribution in the previous steps, and it also is the basis of the next generation calculations. Then keeping going to the loop iterative optimization calculation until a solution is obtained which meet the conditions or used up the set maximum number of iterations, and the best result is available. Based on the method above, a magnetic field optimization algorithm for automatic shimming steps height was available. Finally, an example of the algorithm was to be simulated under the condition of that the magnetic field drop index is 0.2, and the parameters of the steps height can be obtained. The result not only shows the feasibility and convenience of the optimization algorithm, but also provides a reference theoretically on the optimization method of the magnetic field in the magnet design.

     

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