# Computation of the Main and Fringe Fields for the Electrostatic Quadrupoles of the Muon g-2 Storage Ring

### Abstract

We developed a highly accurate and fully Maxwellian conformal mapping 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 used this conformal mapping method to
calculate the multipole terms of the high voltage quadrupoles in the storage ring of the
Muon *g−2* Experiment (FNAL-E-0989). Next, we demonstrate that an effect where
the observed tunes correspond to a voltage that is about 4% higher compared to the
voltage to which the Muon *g−2* quadrupoles are set is explained by the conceptual
and quantitative differences between the beam optics quadrupole voltage and the
quadrupole voltage at the plates. Completing the methodological framework for field
computations, we present a method for extracting multipole strength falloffs of a
particle optical element from a set of Fourier mode falloffs. We calculated the
quadrupole strength falloff and its effective field boundary (EFB) for the Muon *g−2*
quadrupole, which has explained the experimentally measured tunes, while simple
estimates based on a linear model exhibited discrepancies up to 2%.

E. Valetov, M. Berz, K. Makino,
*Int. Journal of Modern Physics A*, **34, 36** (2019) 1942041.
DOI: 10.1142/S0217751X19420417

Go Back to the reprint server.

Go Back to the home page.

This page is maintained by Kyoko Makino. Please contact her if there are any problems with it.