U.S. Particle Accelerator School

Accelerator Physics Using Maple course

Sponsoring University:

University of Texas, Austin


Accelerator Physics Using Maple


Uli Wienands, SLAC and Eduardo Marin Lacoma, CERN

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. The course will also be of benefit to practitioners in the field, be it operators or physicists and engineers working on or near particle accelerators.

The course will be appropriate for students having heard lectures on classical mechanics and on electro-dynamics, and/or the USPAS course in “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.

Course Content and Objective:
We will cover first-order beam optics incl. 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 will 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. We will include a module covering powerful modern methods like TPSA that are used in accelerator simulations and design in order to gain a deeper understanding of and optimize the properties of a particular machine lattice. We will cover aspects of particle tracking and similar numerical approaches and briefly review the major design and analysis codes in use nowadays. A case study of design and analysis of an existing or planned facility will demonstrate how the techniques are applied in real life.

At completion of this course, the student will have a thorough understanding of the basic physics underlying beam optics and particle accelerators incl. synchrotron-light sources and FELs and be able to tackle design problems of such machines. 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.

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. The student will also retain a set of Maple routines applicable to real-world problems.

Instructional Method

In this course we 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. All Maple worksheets used in the course will be available to the students in machine-readable form.

Reading Material
Because of the different (for USPAS) approach in teaching we will be providing a detailed script for the course. A fair amount of the course material is covered in part in Wiedemann, “Particle Accelerator Physics” Springer Verlag, 2007, and in part in Mackay & Conte “Introduction to the Physics of Particle Accelerators”, 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 2015 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 (40%), midterm and final exams (20% each) and on participation (20%).

UT Austin course number & course title on transcript: PHY 396T (69872): ACCELERATOR PHY USING MAPLE
Indiana University course number:
Physics 570, Introduction to Accelerator Physics
Michigan State University course number: PHY 963
MIT course number: 8.790 "Accelerator Physics"