U.S. Particle Accelerator School

Classical Mechanics and Electromagnetism in Accelerator Physics

Sponsoring University:

Northern Illinois 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

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

This course will familiarize students with mechanical and electromagnetic dynamics with a focus on the applications for accelerator science and technology. The subject is too broad for an exhaustive treatment, but the goal of this class will be to provide essential background information that will provide access to many areas of specialized study. In mechanics, the course will start with Hamiltonian dynamics and lead into topics related to accelerator stability and nonlinear dynamics. In electromagnetism, the course will start with Maxwell’s Equations and lead into accelerator component design and relativistic radiating particles. At the end of the course, students will feel solidified in their fundamental understanding of mechanical and electromagnetic dynamics and prepared for advanced materials.

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 Content
Second-order differential equation and harmonic oscillator (damped, driven). Hamiltonian mechanics, phase-space, canonical transformations, generating functions, Liouville’s theorem, and action-angle variables. Hamiltonian for a circular accelerator, Hill’s equation, nonlinear accelerator resonances, and Landau damping. Brief introduction to chaos, integrability, Poincare sections, separable motion, and invariants of motion.

Magnetostatics, Poisson equation, magnetic multipole decomposition, and magnet design. Boundary value problems, eigenmodes, 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, and diagnostics. Wake fields, impedances and the Panofsky-Wenzel theorem. Radiation damping, space charge, coherent synchrotron radiation, bunch compression, beam instabilities,  FELs, and synchrotron light sources

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