ICAP 2002 Abstracts and Posters

On the map method for electron optics

Abstract

In electron optics the general trajectory equation of a moving electron is usually expressed in a fixed coordinate frame and the transfer map can be obtained by tracking it from the object plane to the image plane by using a DA integrator. Then, aberration coefficients are extracted from the transfer map elements through arbitrary order. If the aberration coefficients computed in this way are compared with those evaluated in terms of analytical aberration integrals, we will find that they are completely different from each other except for electrostatic lenses. The reason for this is that in electron optics aberrations are always expanded in rotating coordinates instead of fixed ones and only for the electrostatic lenses become they the same. In addition, we have to distinguish two cases [1]: the object is immersed in the lens magnetic field or not. As a result, there exist three types of the DA descriptions in electron optics. They are the DA descriptions in fixed, rotating, and hybrid coordinates, respectively.

In this paper on the basis of the transfer map in fixed coordinates other two transfer maps have been derived through third order and third order geometric aberration coefficients of several electron lenses have been cross-checked by means of aberration integrals. The conclusion is that map methods not only make computation of electron optical aberrations concise and efficient, but possess very high precision and that COSY INFINITY [2,3] provides an excellent programming environment for map methods to be applied to electron optical aberration analysis.

The author is very grateful for Professor M. Berz to provide COSY INFINITY 8.1 for this work.

[1] J. Ximen, Z. Liu, Optik {111} (2000) 355.

[2] M. Berz, Nucl. Instr. Meth. {A298} (1990) 473.

[3] K. Makino, M. Berz, Nucl. Instr. Meth. { A427} (1999) 338.

Zhixiong Liu

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