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Analysis and Fringe Field Scaling of a Legacy Set of Electrostatic Deflector Aberration Formulas

Abstract

We performed an analysis of the derivation of first and second order analytic aberration formulas by Wollnik (1965)* for the case of electrostatic deflectors in the horizontal plane. We found that these aberration formulas are valid for the main field of the deflector; however, they do not account for any fringe field effects. To address this issue, we modified the aberration formulas from Wollnik (1965) for a hard edge fringe field by scaling the particle inclinations at the entrance and exit edges of the deflector. These modified aberration formulas fully agree with electrostatic aberration formulas derived by Valetov and Berz (2020)**, as well as with differential-algebraic (DA) calculations of electrostatic deflector aberrations using the code COSY INFINITY.

* H. Wollnik, Second Order Approximation of the Three-Dimensional Trajectories of Charged Particles in Deflecting Electrostatic and Magnetic Fields, Nucl. Instrum. Methods 34, 213 (1965).

** E. Valetov, M. Berz, Derivation, Cross-Validation, and Comparison of Analytic Formulas for Electrostatic Deflector Aberrations, Advances in Imaging and Electron Physics 213, 145 (2020).

E. Valetov, Advances in Imaging and Electron Physics, 213 (2020) 205-224. DOI: 10.1016/bs.aiep.2019.11.008

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