Measuring and Modelling the Magnetic Field of the MICE Spectrometer Solenoids

Muon accelerators offer precise measurements of the Higgs boson’s properties and the PMNS
matrix parameters. To make muon accelerators possible, tertiary beams of muons must first
be cooled to allow them to be accepted into the accelerator and have a useful luminosity.
The Muon Ionisation Cooling Experiment aims to demonstrate the ionisation cooling
technique. This method involves passing muons through an absorber material. MICE will
demonstrate the method by measuring the emittance of a muon beam before and after it
passes through an absorber material. The two spectrometer solenoids are critical to the
experiment as they produce the magnetic fields which cause the muons to undergo helical
trajectories, thus allowing the two scintillating fibre trackers to measure the emittance.
The field produced by the spectrometer solenoids needs to be known and software models
are required for the tracking algorithm and simulation packages. A custom made field
mapping machine was produced for the task of measuring the field produced by the solenoids.
Using the data from this machine, models of the field are produced using least squares fitting.
The full model uses a two-step procedure. The first step calculates two fields with differing
lengths and thicknesses about the as-built dimensions of the coil being modelled. Then these
fields are mixed until the square residuals with the data are minimised. The residual field
is calculated between the model and data. The next stage of the model solves Laplace’s
equation to yield Fourier-Bessel expansions. The coefficients and phases of each term of
the expansions are found by fitting to different parts of the residual field. The full model is
then a sum of the mixed field and the Fourier-Bessel terms. The results of these models are
compared with data and show decent agreement.