Paper  Title  Page 

TUPAG22  Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g2 Experiment Storage Ring  313 


Funding: This work was supported by the U.S. Department of Energy under Contract DEFG0208ER41546 and by Fermi Research Alliance for U.S. Department of Energy under Contract DEAC0207CH11359. We consider semiinfinite electrostatic deflectors with plates of different thickness, including plates with rounded edges, and we calculate their electrostatic potential and field using conformal mappings. To validate the calculations, we compare the fringe fields of these electrostatic deflectors with fringe fields of finite electrostatic capacitors, and we extend the study to fringe fields of adjacent electrostatic deflectors with consideration of electrostatic induction, where field falloffs of semiinfinite electrostatic deflectors are slower than exponential and thus behave differently from most magnetic fringe fields. Building on the success with electrostatic deflectors, we develop a highly accurate and fully Maxwellian conformal mappings method for calculation of main fields of electrostatic particle optical elements. A remarkable advantage of this method is the possibility of rapid recalculations with geometric asymmetries and mispowered plates. We use this conformal mappings method to calculate the multipole terms of the high voltage quadrupole used in the storage ring of the Muon g2 Experiment (FNALE0989). Completing the methodological framework, we present a method for extracting multipole strength falloffs of a particle optical element from a set of Fourier mode falloffs. We calculate the quadrupole strength falloff and its effective field boundary (EFB) for the Muon g2 quadrupole, which has explained the experimentally measured tunes, while simple estimates based on a linear model exhibited discrepancies up to 2%. 

Slides TUPAG22 [3.780 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018TUPAG22  
About •  paper received ※ 15 October 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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