U.S. Particle Accelerator School

Collective Effects in Beam Dynamics course

Sponsoring University:

University of New Mexico


Collective Effects in Beam Dynamics


Giovanni Rumolo and Elias Métral, CERN

Purpose and Audience
Beam Dynamics is a discipline that describes the motion of a charged particle beam in a specific accelerator environment. Low intensity particle beams can be satisfactorily modeled by using single particle dynamics, in which particles are only tracked through the external electromagnetic fields, with all beam induced electromagnetic interactions neglected. Basic concepts from classical mechanics (linear and nonlinear), electrodynamics and special relativity are the necessary background for this approach. High intensity particle beams require a more complicated description which involves interactions between beam particles. The powerful tools of plasma physics are needed to understand the dynamics of particle beams in this regime. High intensity effects are important because they usually pose an upper limitation to the number of particles that can be injected into an accelerator or storage ring. These phenomena are associated with the collective responses of the particle beams to intensity dependent excitations. Examples that will be surveyed in this course are the beam's own space charge, the electromagnetic interaction of the beam with the surrounding environment (described through impedances), and the interaction of the beam with electron or ion clouds. Typically, a topic first will be discussed abstractly and then illustrated through examples from specific accelerator facilities. This course is designed for graduate students or graduate engineers who want to learn in more detail about advanced concepts of accelerator physics. 

Classical mechanics, electrodynamics, and physical or engineering mathematics, all at entrance graduate level; and the USPAS course "Accelerator Physics" or equivalent (e.g., CERN Accelerator School, Intermediate Level).

On completion of this course, the students are expected to understand the physical principles that govern collective interactions inside particle beams, together with their role in limiting the performance of accelerators. The students are also expected to acquire a basic knowledge of the techniques used to overcome the intensity limits posed by collective effects.

Instructional Method
This course includes a series of lectures and exercise sessions. Homework problems will be assigned which will be graded, with answers provided in the exercise sessions. There will be an open-book and open-notes, 3-hour final exam at the conclusion of the course.

Course Content
- Space charge
- Wakefields and impedances:
- Resistive wall and resonator impedances
- Longitudinal single bunch effects (potential well distortion, energy loss, bunch lengthening, synchrotron frequency shift, microwave instability)
- Transverse single bunch effects (head-tail instability and transverse mode coupling)
- Multi bunch instabilities
- Two-stream effects: electron cloud and fast ion instability
- Mitigation and cures

Reading Requirements
(to be provided by the USPAS) Alexander W. Chao, "Physics of Collective Beam Instabilities in High Energy Accelerators", John Wiley & Sons, Inc. (1993) and "Handbook of Accelerator Physics and Engineering", edited by Alexander W. Chao and Maury Tigner, World Scientific, 3rd print (2006).

Credit Requirements
Students will be evaluated based on the following performances: final exam (50%), homework assignments (50%).