Classical Mechanics and Electromagnetism
United States Particle Accelerator School, January 25 - February 5, 2016
Course description and materials
This is a course on selected topics in classical mechanics and electrodynamics applied to important topics in accelerator physics. Electron rings will be the main example for a significant portion of the course, but the topics and methods apply more generally.
If you are wondering what to do to prepare for the class, the best thing would
be to review special relativity, especially Lorentz transformations.
Some of this is covered in the 3rd section of the supplementary notes,
available below. This would be a good thing to look over during the weekend
in the middle of the course as well.
Looking over the slides will also be helpful, they are labelled by the day
when the topics will be covered. Here is a rough outline of what will
- Monday Jan 25: oscillators, Lagrangian and Hamiltonian formalism
introduction, lectures 2 and 3 from 2011 lecture notes
- Tuesday Jan 26: canonical transformations, action-angle coordinates, generating functions
lectures 4 and 5, and supplementary notes section 1
- Wednesday Jan 27: circular accelerators, equations of motion,
Hills equation, beta functions
lectures 6, 7, 8
- Thursday Jan 28: field errors, resonances, standard map
lectures 9 and 10, nonlinear resonances will not be covered
- Friday Jan 29: kinetic equation, Vlasov equation, special relativity
lectures 11 and 13, supplementary notes section 2
Files to be downloaded
Course schedule and homeworks. This is subject to change, but the first 2 days will be fixed.
Main lecture notes, from Gennady Stupakov, 2011 USPAS class
Corrections to 2011 lecture notes
A summary of all homework problems from the 2011 lecture notes
Additional homework problems
Only some of the problems will be assigned as homework, about 6/day
Supplementary notes for lectures, which include the following topics:
- Extended canonical transformations
- Fluid equations
- Relativity and Lorentz transformations
- Gaussian laser beams
- Synchrotron radiation and changes in emittances
Slides that will form the bulk of the lectures (these will continue to be updated)
RF Longitudinal dynamics, from Jeff Eldred's thesis
Jeff Eldred's slides from the afternoon sessions:
Homework solutions, complete
Link to web applet for viewing retarded fields, Davidson College.
Textbook, to be used mostly for reference: "Classical Dynamics: A Contemporary Approach", J.V. José and E.J. Saletan.
Last updated, 3 Feb 2016