[en] To increase charged particle beam intensity the longitudinal dipole instability of bunched beam in a proton synchrotron is considered. A general expression for instability increment is obtained and the conditions, which must be satisfied by the resonance accelerator elements, are found. The numerical investigation of instability damping at the account of bunch to bunch synchrotron frequency spread is carried out. The obtained results are applied for the cases of the IHEP synchrotron and ring injector (booster) at high intensity