  A portion of the Muon g-2 Storage Ring electric system, which provides
vertical beam focusing, exhibited an unexpected time dependence that produced a
characteristic evolution of the stored beam during Run-1 of the Muon g-2
Experiment at Fermilab (E989). A method to reconstruct the Run-1 electric guide
fields has been developed, which is based on a numerical model of the muon
storage ring and optimization algorithms supported by COSY INFINITY. This
method takes beam profile measurements from the Muon g-2 straw tracking
detectors as input, and it produces a full reconstruction of the time-dependent
fields. The fields can then be used for the reproduction of detailed beam
tracking simulations and the calculation of ring lattice parameters for
acceptance studies and systematic error evaluations.
