U.S. Particle Accelerator School

Accelerator Physics Using Maple course

Sponsoring University:

University of New Mexico


Accelerator Physics Using Maple


Uli Wienands and Eduardo Marin Lacoma, SLAC National Accelerator Laboratory

Purpose and Audience

This course will give a comprehensive introduction to the physics of particle accelerators large and small, protons (hadrons) and electrons, linear and circular. Topics to be covered include particle motion in electro-magnetic fields, beam-guidance systems, linear accelerators, and circular accelerators. The course is directed towards graduate students in physics with a desire to learn more about particle accelerators—for a possible career, to gain an understanding of the machines that deliver the beams they may be using as experimenters, or simply to better understand these instruments that affect the lives of many of us.

Knowledge of classical mechanics and electro-dynamics, and/or the USPAS course “Fundamentals of Accelerator Physics and Technology.” Experience with computer-algebra systems is of benefit but not required.

Students should bring their own laptop computer to the school. Please contact the USPAS if you are not able to do so.

It is the responsibility of the student to ensure that he or she meets the course prerequisites or has equivalent experience.

At completion of this course, the student will have a thorough understanding of the basic physics underlying beam optics and particle accelerators including synchrotron-light sources. The student will also have had a glimpse into the rich physics associated with intensity-dependent effects which in many cases can dominate the performance of particle accelerators. In addition the student will have gained experience with the use of computer algebra systems (CAS) and an appreciation of their power but also of their limitations.

Instructional Method

In this course I will make full use of the computer algebra system Maple in analysis and visualization of the physics discussed. The aim is to make the physics tangible to the student and, where possible, allow exploration by the students of the dynamics of the systems we are discussing. While the course is focused on accelerator physics, the student will also finish the course with an understanding of the potential as well as the limits of CAS. The course will use Maple, but many concepts are easily applied to other CAS. It is planned to make a Maple license available to each student. All Maple worksheets used in the course will be available to the students in machine-readable form.

Course Content

We will cover first-order beam optics including fundamentals of accelerator magnet-lattice design. Rf acceleration and transition. Higher-order beam dynamics and resonance effects in circular accelerators as well as a number of beam-intensity related effects wil be analysed using concepts like phase space and Hamiltonian mechanics. Synchrotron-radiation and radiation damping in circular machines. Basics of free-electron lasers (FEL). The emphasis will be on understanding the physics and the quantitative description of the phenomena being discussed, as opposed to pure and abstract theory.

Reading Requirements

Written course materials will be provided by the instructor. In general, most of the material is covered in part in “Particle Accelerator Physics” (third ediction) by Helmut Wiedemann, Springer Verlag 2007 and in part in “An Introduction to the Physics of Particle Accelerators” by Mario Conte and William M. MacKay, World Scientific 2008.

Computer Requirements
Students should bring their own laptop computer to the school. Please contact the USPAS if you are not able to do so. The USPAS will make a Maple Student License available to each student. Here are the system requirements.

Credit Requirements

Upon successful completion the student will earn 3 course credits. The students’ progress will be evaluated on homework (30%), midterm and final exams (25% each) and on participation (20%).

IU/USPAS course: Physics 570