Computation Of The Main And Fringe Fields For The Electrostatic Quadrupoles Of The Muon G-2 Storage Ring

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 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%.