Transverse laser cooling is pursued at an ion storage/cooler ring, S-LSR, Kyoto University. An RF bunched Mg+ beam was cooled transversely through synchro-betatron resonance coupling by a co-propagating laser. We investigated peaks of synchrotron oscillation spectroscopically so that we can observe them stably. Oscillation signals from a parallel-plate pickup were observed by a spectrum analyzer. We also observed the coherent synchrotron modes. As the beam temperature decreases, the ion beam would be in space charge limited region. According to the computer simulation, in the case the beam turns to be space charge limited, the disappearance of peaks of synchrotron oscillation is expected. We would like to propose a capability of detecting space charge limited region by observing such a frozen synchrotron oscillation
