U.S. Particle Accelerator School
U.S. Particle Accelerator School
Education in Beam Physics and Accelerator Technology

Collective Effects in Beam Dynamics course

Sponsoring University:

Old Dominion University


Collective Effects in Beam Dynamics


Giovanni Rumolo, Hannes Bartosik and Kevin Li, 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 model the dynamics of particle beams in this regime. High intensity effects are important because they usually pose an upper limit 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. In this course we will cover 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. Each topic will be first introduced theoretically and then illustrated through examples from specific accelerator facilities along with interactive computer exercises.

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., CAS Advanced Level).

It is the responsibility of the student to ensure that they meet the course prerequisites or have equivalent experience.

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 model collective effects and overcome the intensity limits they pose.

Instructional Method
This course will alternate lectures, tutorials and hands-on computer exercise sessions based on simulation tools.
Homework problems will be assigned and graded, with answers provided in the exercise sessions. There will be an open-book and open-note, 3-hour final exam at the conclusion of the course.

Course Content
-   Space charge
-   Wake fields and impedances (e.g., resistive wall and resonator impedances)
-   One- or two-particle models to illustrate basic mechanisms
-   Longitudinal single bunch effects (e.g., potential well distortion, energy loss, bunch lengthening, synchrotron frequency shift, microwave instability)
-   Transverse single bunch effects (e.g., head-tail instability and transverse mode coupling)
-   Multi bunch instabilities
-   Two-stream effects: electron cloud and fast ion instability
-   Mitigation and cures
-   Numerical modeling and simulation tools
-   Applications to past, present and future machines

Computer Requirements
Students should bring a laptop to class. Please contact the USPAS if you are not able to do so. Your computer should have Python 2.7 (with the libraries scipy and numpy) preloaded if possible.

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, 2nd edition (2013).

Credit Requirements
Students will be evaluated based on the following performances: final exam (30%), active participation and homework assignments (70%).

IU/USPAS course number P671