U.S. Particle Accelerator School

Fundamentals of Wakefields and Impedance course

Sponsoring University:

Cornell University

Course:

Fundamentals of Wakefields and Impedance: From Physical-Mathematical Analysis to Practical Applications

Instructor:

Roger M. Jones, SLAC


Purpose and Audience
The purpose of the course is to enable students to become well-versed in the beam dynamics of wakefield-beam interaction in high energy accelerators. It is suitable for advanced undergraduates, graduate students and, active researchers in the field.

Prerequisites
A course on Electromagnetism and a minimum of at least a mathematical background of first-year undergraduate calculus.

Objectives
This course will address the fundamentals of wakefields and their relation to the beam impedance. The features of both long-range and short-range wakefields will be discussed. Circuit models of relativistic electron beams coupled to multiple accelerator cavities will be developed to calculate the coupled modal frequencies and wakefields. In addition to the general theoretical formalism of wakefields, practical methods to damp and measure the wakefields will be described with techniques taken from ongoing research on high-energy linacs (L-band and X-band linacs in particular). Throughout the course, basic physical principles such as superposition, energy conservation and causality will be emphasized.

Instructional Method
There will be four mornings spent on lectures. Afternoon sessions will be used for both additional lectures and computer laboratory sessions. There will be homework, a computer project and, a final examination.

Course Content
The progress of multiple bunches of electrons through a linear or circular accelerator gives rise to a trailing electromagnetic field. This wakefield can have catastrophic consequences if its progress is left unchecked as the beam can become unstable and develop a BBU (Beam Break Up) instability. This course discusses the beam dynamics issues associated with wakefields and means of damping the fields to acceptable levels. Examples are taken from the recent international next generation linear colliders damping schemes. Wakefield issues in storage rings will also be discussed.

Background Reading
“RF Linear Accelerators”, Wiley & Sons Publishers (1998), by Thomas Wangler.
“RF Superconductivity for Accelerators”, Wiley Publishers (1998), by Hasan Padamsee, Jens Knobloch and Tom Hays.
"Physics of Collective Beam Instabilities in High Energy Accelerators" (free pdf download) , Wiley & Sons Publishers (1993) by Alexander Chao.
"The Physics of Particle Accelerators: An Introduction", Oxford University Press (2000) by Klaus Wille.
"Fundamentals of Beam Physics" Oxford University Press (2003) by James Rosenzweig.
“Particle Accelerator Physics I & II”, (study edition) Springer-Verlag (2003) by Helmut Wiedemann.

(to be provided by the USPAS) “Impedances and Wakes in High Energy Particle Accelerators”, World Scientific Publishers (1998), by Bruno W Zotter and Semyon Kheifets

Credit Requirements
Students will be evaluated as follows: final exam (50 % of final grade), homework assignments (30 % of final grade) final project based on computer sessions (20 % of final grade).