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Study on differential algebraic chromatic aberration method for Glaser's bell-shaped magnetic lenses

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Differential algebraic method is a powerful technique in computer numerical calculation. It presents a straightforward method for computing arbitrary order derivatives of functions with extreme high accuracy limited only by the machine error. In this paper, the differential algebraic chromatic aberration method for Glaser's bell-shaped magnetic lenses is studied, and the differential algebraic expressions of arbitrary order chromatic aberrations are obtained. As an example, the first order chromatic aberration coefficients of a real Glaser's bell-shaped magnetic lens have been calculated. Relative errors compared with the analytic solutions are on the scale of 10–10 or small. It is proved that differential algebraic chromatic aberration method is an efficient and high accurate approach for the numerical calculation of chromatic aberrations.
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Keywords: Bell-shaped magnetic lenses; Differential algebra; chromatic aberrations

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: 2001-12-01

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