High order aberrations calculation of a hexapole corrector using a differential algebra method

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• 作者：Yongfeng Kang^a ; ^{yfkang@mail.xjtu.edu.cn} ; Xing Liu^a ; Jingyi Zhao^b ; ^{jingyi.zhao@foxmail.com} ; Tiantong Tang^a
• 关键词：High order aberration ; Differential algebra ; Hexapole corrector
• 刊名：Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
• 出版年：2017
• 出版时间：21 February 2017
• 年：2017
• 卷：846
• 期：Complete
• 页码：8-12
• 全文大小：293 K
• 卷排序：846

文摘

A differential algebraic (DA) method is proved as an unusual and effective tool in numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of a practical hexapole corrector including round lenses and hexapole lenses. The program has been developed and tested as well. The electro-magnetic fields of arbitrary point are obtained by local analytic expressions, then field potentials are transformed into new forms which can be operated in the DA calculation. In this paper, the geometric and chromatic aberrations up to fifth order of a practical hexapole corrector system are calculated by the developed program.