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Differential algebraic method for computing the high order aberrations of practical electron lenses
Yongfeng Kang 1 * #,Tiantong Tang 1,Yan Ren 2,Xiaoli Guo 2
1.Department of Electronics Science and Technology, School of Electronic and Information Engineering, Xi’an Jiaotong university
2.Department of Electronics Science and Technology-School of Electronic and Information Engineering-Xi’an Jiaotong university
*Correspondence author
#Submitted by
Subject:
Funding: 教育部博士点基金（No.20020698020）
Opened online:16 December 2005
Accepted by: none
Citation: Yongfeng Kang,Tiantong Tang,Yan Ren.Differential algebraic method for computing the high order aberrations of practical electron lenses[OL]. [16 December 2005] http://en.paper.edu.cn/en_releasepaper/content/4431
 
 
Differential algebraic method is of an effective technique in computer numerical analysis. It implements exactly differentiation up to arbitrary high order based on the nonstandard analysis. Some complicated nonlinear dynamics problems including high order aberrations of electron optics systems can be solved by mapping properties of differential algebraic quantities. However, the existed electron optical differential algebraic method can only be applied to those problems where the electric and / or magnetic fields are expressed in analytic forms. In this paper, the principle of differential algebraic method is applied to practical electron lenses whose electric / magnetic fields are in the forms of discrete arrays, for example, the files computed by FEM or FDM method. Thus the developed new differential algebraic method is applicable to engineering design. The programs were written for computing the high order aberrations of practical electron lenses. An example is given to show that the numerical results have good accuracy compared with the results computed by using the electric fields expressed in analytical form; the accuracy is limited only by the accuracy of the numerical computation of the fields and the arithmetic errors, and it is enough for engineering design.
Keywords:Different algebra; electron lens; high order aberration of electron optics systems;
 
 
 

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