It is shown that the evolution of the saw-tooth instability can be reproduced by two coupled nonlinear differential equations, accounting for the time behavior of the instability growth rate and for the anomalous growth of the energy spread. These model equations, which under appropriate conditions reduce to the ordinary Volterra equations, are shown to describe the characteristic features of the instability.
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics
Dattoli, G., Mezi, L., Migliorati, M., & Palumbo, L. (1999). A simple model for the saw-tooth instability in storage rings. La Rivista del Nuovo Cimento, 112(5), 491 - 497. https://doi.org/10.1007/BF03035862