Space-charge driven transverse beam instabilities in synchrotrons

• Main Author: Yuan, Yaoshuo
• Format: Others
• Language: en
• Published: 2018
• Online Access: https://tuprints.ulb.tu-darmstadt.de/8215/1/2018-11-06_Yuan_Yaoshuo.pdf; Yuan, Yaoshuo <http://tuprints.ulb.tu-darmstadt.de/view/person/Yuan=3AYaoshuo=3A=3A.html> (2018): Space-charge driven transverse beam instabilities in synchrotrons.Darmstadt, Technische Universität, [Ph.D. Thesis]

Intense proton or ion beams in charged-particle accelerators are of fundamental importance for many research areas, which relay on such beams, such as those requiring spallation neutrons or radioactive beams. The main subject of this thesis is the detailed investigation of the intense beam motion and instability in synchrotrons, based on two approaches: particle-in-cell (PIC) simulations and the numerical methods for calculating the beam's envelope motion. In the former approach, the accelerator simulation code pyORBIT is employed. In the latter, the widely-used two dimensional (2-D) beam envelope model is extended with a dispersion equation, to describe the beam's coherent motion under the combined effect of space charge and dispersion in circular accelerators. Full numerical solution of the extended envelope model reveals that a new coherent mode, namely, dispersion mode, exists besides the well-known envelope modes. Based on the perturbation theory, the analysis of the beam stability shows that for a phase advance larger than $120^{\circ}$ and sufficiently high intensity, the dispersion mode becomes unstable, and induces the newly discovered ``$120^{\circ}$ dispersion instability''. These numerical results were validated with PIC simulations, showing good agreement. Bunch compression achieved via a fast bunch rotation in longitudinal phase space is a well-accepted scheme to generate short, intense ion bunches for various applications. In this thesis, the set of transverse envelope equations including dispersion are coupled with the longitudinal envelope equation to describe the three dimensional (3-D) beam motion during bunch compression. Furthermore, based on the 3-D coupled envelope model and PIC simulations, an analysis of the relevant space-charge driven beam instability and the particle resonance phenomena during bunch compression is presented. The agreement between the envelope and PIC results indicates that the stop band of the $120^{\circ}$ dispersion instability should be avoided during bunch compression. This work also investigates the stability of all possible second order coherent modes of beams, with a complete set of second-moment oscillation equations. Results are compared with earlier results on mode frequencies obtained from the linearized Vlasov-Poisson equation. Excellent agreement is found in the case of the ``tilting instability'' in constant focusing, which confirms the equivalence of both models - on the level of second order perturbations. In periodic focusing structures the stop bands of the ``sum envelope instability'' are obtained and found to be in very good agreement with PIC simulations, which completes the picture of second order coherent modes in 2-D high intensity beams.