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    Rights statement: Electronic version of this article published as Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY Eremey Valetov (Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA), Martin Berz (Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA), and Kyoko Makino (Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA) International Journal of Modern Physics A 0 0:0... in International Journal of Modern Physics AVol. 34, No. 36, 1942010 (2019) 10.1142/S0217751X19420107 © copyright World Scientific Publishing Company https://www.worldscientific.com/doi/abs/10.1142/S0217751X19420107

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Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY

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Article number1942010
<mark>Journal publication date</mark>30/12/2019
<mark>Journal</mark>International Journal of Modern Physics A
Issue number36
Volume34
Publication StatusPublished
Early online date2/12/19
<mark>Original language</mark>English
EventTenth International Conference on Charged Particle Optics - Key West, United States
Duration: 17/01/201821/10/2018
Conference number: 10
https://www.bt.pa.msu.edu/CPO-10/

Conference

ConferenceTenth International Conference on Charged Particle Optics
Abbreviated titleCPO-10
CountryUnited States
CityKey West
Period17/01/1821/10/18
Internet address

Abstract

The code COSY INFINITY uses a beamline coordinate system with a Frenet–Serret frame relative to the reference particle, and calculates differential algebra-valued transfer maps by integrating the ODEs of motion in the respective vector space over a differential algebra (DA).

We described and performed computation of the DA transfer map of an electrostatic spherical deflector in a laboratory coordinate system using two conventional methods: (1) by integrating the ODEs of motion using a numerical integrator and (2) by computing analytically and in closed form the properties of the respective elliptical orbits from Kepler theory. We compared the resulting transfer maps with (3) the DA transfer map of COSY INFINITY ’s built-in electrostatic spherical deflector element ESP and (4) the transfer map of the electrostatic spherical deflector computed using the program GIOS, which uses analytic formulas from a paper1 by Hermann Wollnik regarding second-order aberrations.

In addition to the electrostatic spherical deflector, we studied an electrostatic cylindrical deflector, where the Kepler theory is not applicable. We computed the DA transfer map by the ODE integration method (1), and we compared it with the transfer maps by (3) COSY INFINITY ’s built-in electrostatic cylindrical deflector element ECL and (4) GIOS.

The transfer maps of electrostatic spherical and cylindrical deflectors obtained using the direct calculation methods (1) and (2) are in excellent agreement with those computed using (3) COSY INFINITY. On the other hand, we found a significant discrepancy with (4) the program GIOS.

Bibliographic note

Electronic version of this article published as Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY Eremey Valetov (Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA), Martin Berz (Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA), and Kyoko Makino (Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA) International Journal of Modern Physics A 0 0:0... in International Journal of Modern Physics AVol. 34, No. 36, 1942010 (2019) 10.1142/S0217751X19420107 © copyright World Scientific Publishing Company https://www.worldscientific.com/doi/abs/10.1142/S0217751X19420107