Incoherent tune measurement of an ion storage ring using single ions

The measurement of betatron tunes is important in the studies of beam dynamics in circular accelerators. Here, we report a new method to extract the fractional tune values using revolution times of single ions stored for a few hundred turns in a heavy-ion storage ring utilizing a single time-of-flight detector. The experiment was done at the experimental Cooler Storage Ring (CSRe) in Lanzhou. The unbunched cocktail secondary beam was injected into the ring and allowed to coast without further excitation. Since the average number of simultaneously stored ions inside the 128.8 m-circumference ring was merely $\sim 20$, the obtained tune values are considered to be incoherent. Given that the revolution time of an individual ion is related to its momentum, the chromaticity of the ring could be addressed. Moreover, the data indicate a possible beam mismatch in vertical direction $\widehat{y}$ at the injection into CSRe. The new method is developed for ultralow beam intensities and is thus a sensitive approach to tune measurements. Thanks to its simplicity, the method can straightforwardly be employed at other circular accelerators by applying the same detection approach.