This work demonstrates that two systematic errors, coherent betatron oscillations (CBO) and muon losses can be reduced through application of radio frequency (RF) electric fields, which ultimately increases the sensitivity of the muon $g-2$ experiments. As the ensemble of polarized muons goes around a weak focusing storage ring, their spin precesses, and when they decay through the weak interaction, $mu^+ rightarrow e^+ u_e bar{ u_mu}$, 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 in a selected energy range at the difference frequency between the spin and cyclotron frequencies, $omega_text{a}$. This frequency is directly proportional to the magnetic anomaly $a_mu =(g-2)/2$, where $g$ is the g-factor of the muon, which is slightly greater than 2. The detector acceptance depends on the radial position of the muon decay, so the CBO of the muon bunch following injection into the storage ring modulate the measured muon signal with the frequency $omega_text{CBO}$. In addition, the muon populations at the edge of the beam hit the walls of the vacuum chamber before decaying, which also affects the signal. Thus, reduction of CBO and unwanted muon loss increases the $a_mu$ measurement sensitivity. Numerical and experimental studies with RF electric fields yield more than a magnitude reduction of the CBO, with muon losses comparable to the conventional method.
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