Robinson instability is a common beam instability that is caused by the wakefield excited in the resonant cavity. It will cause the energy spread to increase and deteriorate the beam quality, so it is essential to understand its mechanism and suppress it. Based on the bunch longitudinal motion equation, this paper analyzes two bunches with different particle numbers and synchrotron oscillation frequencies and extends the existing single-bunch Robinson instability theory to the double-bunch system. The particle motion is simulated by software MATLAB, and the simulation results are consistent with the theoretical formulas. This research puts forward specific parameter requirements for the design of the storage ring resonator cavity in the fourth-generation synchrotron radiation light source and gives a strategy to suppress beam instability, which provides a reference for subsequent engineering construction.

Robinson instability; longitudinal wakefield; resonant cavity