U.S. Particle Accelerator School

Response Matrix Measurements and Application to Storage Rings course

Sponsoring University:

University of California, Berkeley


Response Matrix Measurements and Application to Storage Rings


Jeff Corbett and Andrei Terebilo, SLAC

Purpose and Audience
Maximizing the performance of modern particle accelerators requires beam-based diagnostic as well as analytical tools. In this course, response matrix techniques and their application are introduced. This is a graduate-level course and is of most interest to scientists, engineers and technicians engaged in the actual operation and optimization of accelerator systems.

Basic storage ring physics and linear algebra. Familiarity with Matlab or similar programming environment is recommended.

Upon completion of this course, students are expected to be familiar with response matrix techniques and be able to apply them to practical problems in accelerator operations, such as orbit control, optics correction, coupling control and lattice error detection.

Instructional Method
The course will consist of lectures and computer sessions. Homework assignments will involve analytic calculations, modifying and running programs discussed in class, and data interpretation.

Course Content
Modern particle accelerators depend on direct beam measurements to study system performance and to tune the machine to design specifications. In particular, the orbit response matrix technique is a well-established means of analysis that can be used to detect hardware problems and control beam parameters. In this course, we provide a comprehensive review of response matrix theory, measurement techniques and applications to analysis and control of particle accelerators. The curriculum provides a theoretical background, practical guidelines, hands-on experience and Matlab software tools that can be applied to any operational storage ring or storage ring model. Computer simulations will be used for hands-on experience to "measure" response matrices with real machine data used for analysis. The theory of singular value decomposition is covered with application to local and global orbit control. Correction of the accelerator optics using response matrix is addressed theoretically with hands-on data reduction in a Matlab environment using real measurements taken at an operational storage ring. A variety of instructive examples demonstrating detection and compensation of magnet and/or calibration errors will be used. Related topics such as tune and chromaticity response matrix measurement and application are included.

Reading Requirements:
(to be provided by the USPAS) "Numerical Computing with MATLAB" by Cleave. B. Moler. Topical research papers in course reader.

Credit Requirements
Students will be evaluated based on individual assignments (100% of final grade)