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

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). In our work, 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. Themore » 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.« less

Authors:
ORCiD logo [1];  [1];  [1]
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  1. Michigan State Univ., East Lansing, MI (United States)
Publication Date:
Research Org.:
Michigan State Univ., East Lansing, MI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1661662
Grant/Contract Number:  
SC0018636; FG02-08ER41546
Resource Type:
Accepted Manuscript
Journal Name:
International Journal of Modern Physics A
Additional Journal Information:
Journal Volume: 34; Journal Issue: 36; Journal ID: ISSN 0217-751X
Publisher:
World Scientific
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; Electrostatic deflectors; transfer maps; aberrations; tracking code; COSY INFINITY; differential algebra

Citation Formats

Valetov, Eremey, Berz, Martin, and Makino, Kyoko. Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY. United States: N. p., 2019. Web. doi:10.1142/S0217751X19420107.
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Valetov, Eremey, Berz, Martin, & Makino, Kyoko. Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY. United States. https://doi.org/10.1142/S0217751X19420107
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Valetov, Eremey, Berz, Martin, and Makino, Kyoko. Mon . "Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY". United States. https://doi.org/10.1142/S0217751X19420107. https://www.osti.gov/servlets/purl/1661662.
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@article{osti_1661662,
title = {Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY},
author = {Valetov, Eremey and Berz, Martin and Makino, Kyoko},
abstractNote = {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). In our work, 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.},
doi = {10.1142/S0217751X19420107},
journal = {International Journal of Modern Physics A},
number = 36,
volume = 34,
place = {United States},
year = {Mon Dec 02 00:00:00 EST 2019},
month = {Mon Dec 02 00:00:00 EST 2019}
}
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https://doi.org/10.1142/S0217751X19420107
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