A Method to Reduce the Coherent Betatron Oscillations in a Muon g-2 Storage Ring Experiment using RF Fields
The muon $g-2$ storage-ring experiments store a beam of polarized muons in a weak focusing storage ring. As the ensemble of muons goes around the ring, their spin precesses, and when they decay through the weak interaction: $\mu^+ \rightarrow e^+ \nu_e \bar{\nu_\mu}$ the decay positrons are detected by electromagnetic calorimeters. In addition to the expected exponential decay in the positron time spectrum, the weak decay asymmetry causes a modulation in the number of positrons at the difference frequency between the spin and cyclotron frequencies, $\omega_a$. This frequency is directly proportional to the magnetic anomaly $a =(g-2)/2$, where $g$ is the gyromagnetic ratio of the muon, which is slightly greater than 2. The detector acceptance depends on the radial position of the muon decay, so the coherent betatron oscillations (CBO) of the muon bunch following injection into the storage ring amplitude modulates the measured muon signal with the frequency $\omega_{CBO}$. A new method using radio frequency (RF) electric fields has the potential to significantly decrease the beam CBO, and additionally to scrape the beam to reduce muon losses from the storage ring during the measurement period.