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Study on differential algebraic aberration method for electrostatic electron lenses

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Abstract: Differential algebraic method is a powerful technique in computer numerical analysis. It presents a straightforward method for computing arbitrary order derivatives of functions with extreme high accuracy limited only by the machine error. When applied to nonlinear dynamics systems, the arbitrary high order transfer properties of the system can be derived directly. In this paper, the principle of differential algebraic method is applied to calculate high order aberrations of electrostatic electron lenses. Gaussian properties and third order geometric aberration coefficients of an electrostatic lens with analytical expressions have been calculated. Relative errors of the Gaussian properties and spherical aberration coefficient of the lens compared with the analytic solutions are of the order 10–11 or smaller. It is proved that differential algebraic aberration method is very helpful for high order aberration analysis and computation of electrostatic electron lenses
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Keywords: Differential algebra; aberration analysis; electrostatic electron lenses

Document Type: Original Article

Affiliations: Department of Electronics Science and Technology, School of Electronics and Information Engineering, Xi'an Jiaotong University, Xi'an, 710049, P. R. China

Publication date: 01 June 2001

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