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

Classical Mechanics and Electromagnetism in Accelerator Physics

Sponsoring University:


Course Name:

Classical Mechanics and Electromagnetism in Accelerator Physics


Jeffrey Eldred, Fermilab and Xiaobiao Huang, Argonne National Accelerator Lab

Purpose and Audience
The course focuses on topics of classical mechanics and electrodynamics of importance for accelerator physics. The course is appropriate for graduate students in physics and engineering who wish to supplement or physicists or engineers working in accelerator-related fields who wish to replace or supplement university courses with topical emphasis on accelerators.  The course is also appropriate for professional scientists and engineers seeking a review of underlying formulations of classical mechanics and electromagnetic theory as applied in accelerator science. 

Physics: Upper level undergraduate Classical Mechanics and Electromagnetism.

Mathematics: Undergraduate Multivariate Calculus, and Differential Equations.

Accelerators:  Familiarity with accelerator science and technology at the level of USPAS Fundamentals of Accelerator Physics and Technology is strongly recommended.

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

On completion of this course, students are expected to have a broad understanding of the dynamics of particles in electromagnetic fields as well as the physical principles that underpin particle accelerator technology. Along with the graduate-level Accelerator Physics and Technology course, this course is intended to prepare students for specialized USPAS courses and advanced study of cutting-edge accelerator topics.

Instructional Method
The two-week course includes lectures in the morning (3 hrs. per class day), and afternoon review and exercise sessions (minimum of 3 hrs. per class day). Daily problem sets will be assigned to complete outside of class and turned in the next day. Instructors will be available during evening homework sessions. There will be a final exam at the conclusion of the course and a midterm exam at the end of the first week.

Course Website

Course Content
Second-order differential equations and harmonic oscillator (damped, driven). Hamiltonian mechanics, phase-space, invariants of motion, canonical transformations, generating functions, Liouville’s theorem, and action-angle variables. Hamiltonian for a circular accelerator, Hill’s equation, nonlinear accelerator resonances, space-charge and Landau damping. Magnetostatics, Poisson equation, magnetic multipole decomposition, and magnet design. Boundary value problems, cavity modes, and waveguide modes. Special relativity, Lorentz transformations and Maxwell equations. Field of a relativistic beam, retarded time, Lienard-Wiechert potentials, and radiation fields. Synchrotron radiation, transition radiation, coherent radiation. Wake fields, impedances and the Panofsky-Wenzel theorem.

Reading Requirements
(to be provided by the USPAS) Gennady Stupakov and Greg Penn, Classical Mechanics and Electromagnetism in Accelerator Physics, 1st edition, (Springer, 2018). Credit Requirements
Students will be evaluated based on the following performances: Homework assignments (70% grade), Final Exam (20% grade), First Week Exam (10% grade).

TBD course number:
Indiana University course number: Physics 570, Introduction to Accelerator Physics
MIT course number: 8.790, Accelerator Physics