U.S. Particle Accelerator School

Response Matrix Analysis course

Sponsoring University:

University of California, Santa Cruz


Response Matrix Analysis: Applications to Accelerator Orbit Control, Optics Diagnostics and Correction


Andrei Terebilo, Stanford Linear Accelerator Center

Purpose and Audience
The purpose of this course is to teach students to solve practical problems in accelerator diagnostics and control using Orbit Response Matrix (ORM) techniques. It is intended for graduate or last year undergraduate students who wish to develop deeper understanding of beam optics beyond introductory courses, and get some exposure to accelerator commissioning and operational issues. This course will also benefit practitioners involved in the development of high-level accelerator control applications.

Graduate or advanced undergraduate course in Linear Algebra, an introductory course in Particle Accelerators and Storage Rings. Some MATLAB exposure is highly desirable.

Learn to formulate orbit and optics correction problems using the general language of linear algebra and systems of linear equations: spaces, eigenvectors, eigenvalues, etc… Achieve a level of proficiency in ORM analysis, adequate to solve a wide range of problems in orbit control. Understand the process of fine-tuning accelerator model, based on response matrix measurements and Linear Optics from Closed Orbit (LOCO) technique. Follow this process to resolve model-measurement discrepancies in a given ‘black box’ data set. Develop familiarity with MATLAB sufficient to build basic but functional control-room applications.

Instructional Method
This course is taught entirely in a computer lab setting. Lecture segments are followed by computer examples and assignments. MATLAB computational environment is used.

Course Content
The course will begin with a refresher lecture on select topics in Linear Algebra: systems of liner equations, and singular value decomposition. A review of MATLAB environment and tools will follow. Then we will introduce the Orbit Response Matrix (ORM) for storage rings and single pass systems. We discuss both measurement and model-based calculation of ORM. We will cover orbit control and correction, both static, and as part of an orbit feedback system. Finally we will explore Linear Optics from Closed Orbit (LOCO) – a technique to detect and correct discrepancies between model and real-world accelerator.

Reading Material
(to be provided by USPAS) “Numerical Computing with MATLAB” by Cleve Moler, SIAM Publishers (2004).

Credit Requirements
Students will be evaluated 100% based on the number and level of completeness of individual assignments. Students are expected to turn in assignments in the form of executable MATLAB code with comments.