Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g-2 Experiment Storage Ring
AbstractWe consider semi-infinite 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 semi-infinite 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 g-2 Experiment (FNAL-E-0989). 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 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,
in: Proceedings of 13th International Computational Accelerator Physics Conference 2018, (2019) 307-313.
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