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Derivation of Analytic Formulas for Electrostatic Deflector Aberrations, and Comparison with the Code COSY INFINITY

Abstract

Analytic formulas for aberrations of an electrostatic deflector can be obtained using an iterative order-by-order perturbation method. We will derive the first and second order analytic formulas in the horizontal transverse plane x-a for an electrostatic deflector specified by the reference orbit radius, the central angle spanning the deflector, and its inhomogeneity coefficients. The derivation will be performed in a Frenet-Serret beamline coordinate system.

For the test cases of an electrostatic spherical deflector and an electrostatic cylindrical deflector, we will perform a comparison between aberrations obtained using (1) the derived analytic formulas and (2) differential-algebraic (DA) numerical integration of the equations of motion in COSY INFINITY. A comparison will be also made with the results of our earlier report [1], where we computed the DA transfer maps of electrostatic spherical and cylindrical deflectors in polar laboratory coordinates. The appendices include a C program titled edabrt for calculation of the first and second order aberrations of an electrostatic deflector, as well as the COSY INFINITY codes used for the test cases comparison.

Codes discussed in this report are

DEFLECTOR-ABERRATIONS-COSY.fox : Apendices C and D. COSY INFINITY Code for Calculation of Aberrations of an Electrostatic Spherical Deflector and of a Cylindrical Deflector

edabrt.c : Apendix E. C Program edabrt for Calculation of Aberrations of an Electrostatic Deflector

E. Valetov, M. Berz, MSUHEP-180212, Michigan State University (2018)

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