Exact solution of multi-bunch instabilities for ultra-relativistic constant energy bunches in particle accelerators. (15th April 2019)

• Record Type: Journal Article
• Authors: Shumail, Muhammad; Dolgashev, Valery A
• Is Part Of: Physica scripta. Volume 94:Number 6(2019)
• Publication Date: 2019-04-15
• Subjects: accelerator physics -- multi-bunch instabilities -- beam breakup -- uni-directional many body problem; Physics -- Periodicals; 530.05
• DOI: 10.1088/1402-4896/ab07e3
• Languages: English
• ISSNs: 0031-8949

Abstract

Abstract: In particle accelerators the multi-bunch beams of charged particles excite electromagnetic wakefields in the accelerating cavities and other beam-line components. These wakefields may cause instability in the longitudinal and transverse motion of these bunches leading to the beam loss. Thus, the analysis of such multi-bunch effects is critical in any accelerator design. Here, we present a new analytical method to exactly describe the multi-bunch transverse instabilities for ultra-relativistic electron bunches coasting at a constant energy through a uniform beam-focusing system. We discuss two cases: same bunch energy for all bunches and different energy from bunch to bunch. For the first case the solution is based on a special class of polynomials, while for the second case the solution is a finite sum of sinusoidal functions. We demonstrate the use of this approach with examples and compare the results of a numerical differential equation solver against our rigorous results. Our method could also be applied to the analysis of beam breakup within a single bunch. This approach can be extended beyond accelerator physics to study other many-body systems where an n th body is affected by only the preceding n − 1 bodies.