• beam dynamics
• muon
• g-2
• particle physics

In the E989 experiment, positive 3.1 GeV/c muons are injected into a 14 m diameter storage ring (SR), where both muon's spin and momentum vectors precede. The difference between the spin frequency and the cyclotron frequency is called "anomalous precession frequency", related to a_μ through ω_a = a_μ B q/m, where B is the dipole magnetic field inside the SR. Therefore, a_μ can be extracted by accurately measuring ω_a and B.
This thesis describes how ω_a is measured. In particular, I will show the analysis I have carried out on two specific systematic effects due to beam dynamics, that can alter the ω_a value if not properly taken into account.
A kicker system produces a ~250 G magnetic field parallel to the ring dipole field that steers the muon beam onto the designed orbit. The large high voltage field of ~ 120 kV in the kickers' plates induces eddy currents that produce a magnetic field that lasts few tens of microseconds, well into the ω_a analysis region. This spurious field modifies the main dipole field at the ppm level, thus modifying the measured ω_a, if not corrected. I will describe how this field can be measured by a Faraday Magnetometer which I have contributed to build and characterize in the laboratories of the Istituto Nazionale di Ottica (INO) in Pisa, and that will be installed inside the g-2 SR during summer 2021.
The second effect that I will discuss is related to muons which disappear because of their interaction with the material near the storage region, and in particular with the beam collimators. Muon losses are due to the beam betatron oscillations and they are present mostly in the microseconds after the injection. This effect distorts the spectrum of the muons decay and, if not properly corrected, can result in a systematic modification of the muon precession frequency. A study both on data and on Monte Carlo simulations has been performed to better understand this loss mechanism and to include it into the final ω_a measurement.
Finally, this thesis will report the measured a_μ value specifying the contribution that the above-mentioned effects have on the total systematic error.