U.S. Particle Accelerator School

Classical Mechanics and Electromagnetism in Accelerator Physics

Sponsoring University:

Michigan State University

Course Name:

Classical Mechanics and Electromagnetism in Accelerator Physics


Jeffrey Eldred and Jayakar "Charles" Thangaraj, Fermilab; Stephen Webb, RadiaSoft LLC

Purpose and Audience
The course focuses on several topics of classical mechanics and electrodynamics of particular importance for accelerator physics.

Physics: Upper level undergraduate Classical Mechanics and Electromagnetism.
Mathematics: Multivariate calculus.
Recommended: USPAS course "Fundamentals of Accelerator Physics and Technology with Simulations and Measurements Lab" class or equivalent.

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

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). There will be a final exam at the conclusion of the course.

Course Website

Course Content
Second-order differential equation 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, FELS, and synchrotron light sources. Wake fields, impedances and the Panofsky-Wenzel theorem.

Reading Requirements
(to be provided by the USPAS) "Classical Mechanics" by Herbert Goldstein, Charles P. Poole Jr. and John Safko (3rd edition) 2001.

Credit Requirements
Students will be evaluated based on the following performances: Homework Assignments (70%), Final Exam (20%), First Week Exam (10%).

Michigan State University course number: PHY 963 - 302 - Classical Mechanics and Electromagnetism
Indiana University course number: Physics 570, Introduction to Accelerator Physics
MIT course number: 8.790, Accelerator Physics