With the growing demand for the high-intensity hadron beams in various applications in recent years, coherent beam instabilities driven by space charge are of critical concern for those high-intensity hadron accelerator projects, where the plasma dynamics of beams is pronounced and requires careful consideration. In this paper, an analytical model is developed to characterize coherent beam instabilities in circular machines. Based on the proposed model, a coherent mode, namely the vertical coupled mode, is identified. It is demonstrated that the tilting instability is more enhanced in circular machines because of the increased anisotropy from dispersion. Moreover, the well-known envelope instability in linear accelerator can be generalized and classified into “a family of envelope instabilities” for high-intensity circular accelerators. The proposed analytical model has been compared to particle-in-cell simulations and shows good agreement. The chart of the envelope instability family can be adopted for optimization of the working point to achieve higher beam intensity.
Yao-Shuo Yuan (Sun,) studied this question.