U.S. Particle Accelerator School
U.S. Particle Accelerator School
Education in Beam Physics and Accelerator Technology

Cyclotrons: Beam Dynamics and Design

Sponsoring University:

Stony Brook University (ONLINE)

Course Name:

Cyclotrons: Beam Dynamics and Design


Rick Baartman and Thomas Planche, TRIUMF; Paul Jung, University of Victoria; Philippe Belanger, University of British Columbia

Purpose and Audience
Cyclotrons are circular machines where a fixed magnetic field bend particles through a spiraling path that maintains resonance with RF accelerating fields.  They are attractive for particle acceleration where efficiency of conversion from electric power to beam power is a figure of merit.  Cyclotrons historically drove many advances in high energy and nuclear physics and have seen a recent resurgence for radioisotope production, medical treatment facilities, and industrial applications.  This course provides students with an introduction to the physics of charged particle dynamics in cyclotrons and their design. The level is suitable for graduate students and senior undergraduate students in physics and engineering as well as those associated with cyclotron operation of cyclotron facilities.

Undergraduate level Electromagentism and Classical Mechanics including the Hamiltonian approach is required. Familiarity with undergraduate level Special Relativity is recommended. Experience with beam optics, knowledge of Courant-Snyder parameters, transfer matrix approach at the level of the USPAS course Fundamentals of Accelerator Physics and Technology with Simulations and Measurements Lab is recommended.

It is the responsibility of the student to ensure that they meet the course prerequisites or have equivalent experience.

Students will learn how to calculate cyclotron orbits from a given magnetic field configuration, predict the space charge and brightness limits, and devise mitigation for betatron resonances.

Instructional Method
This course will be comprised of morning lectures and afternoon computer-based design labs. The lectures will cover cyclotron fundamentals. The afternoon labs will begin with a tutorial of the simulation tools to be used in the cyclotron design lab. Daily problem sets will be completed outside of scheduled class sessions. Instructors will be available during evening homework sessions.

Course Content
Similar to synchrotrons, but in contrast to linear accelerators, cyclotrons use a magnetic guide field to repeatedly direct the charged particles through the same electric accelerating field. But unlike synchrotrons, they have fixed magnetic fields to guide the particles and thus can run in continuous wave mode without an overall pulsed machine cycle. This makes them attractive for particle acceleration where efficiency is key. But cyclotrons have their own peculiarities and limitations. This course provides students with an introduction to the physics of cyclotrons and their design. The course first covers the historical development, and then concentrates on theoretical orbit dynamics, in particular how the designs change going from low, few-MeV range up to multi-GeV.

Reading Requirements
(to be provided by USPAS) Cyclotrons by Richard Baartman and Thomas Planche, May 2021 [contact baartman@triumf.ca or tplanche@triumf.ca for a link and password] and Principles of Cyclic Particle Accelerators by John Jacob Livingood (D. Van Nostrand Company Inc, 1961). W Kleeven and S Zaremba, CERN Yellow Report Cyclotrons: Magnetic Design and Beam Dynamics, CERN Accelerator School 2015 available at https://publishing.cern.ch/index.php/CYRSP/article/view/99 Additional notes will be provided by the instructors.

Credit Requirements
Students grade will be evaluated based on performance in daily homework assignments.

Stony Brook University course number: PHY 538 01
Indiana University course number: Physics 671 Special Topics in Physics of Beams
Michigan State University course number: PHY 963  US Particle Accelerator School
MIT course number: 8.790 Accelerator Physics