## Classical Mechanics and Electromagnetism for Accelerators

Notes for 2016 USPAS Course

Gregory Penn

Jeff Eldred, TA

Kilean Hwang, grader

### 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 be covered the first week (the second week focuses on electromagnetic radiation):

- 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

Textbook, to be used mostly for reference: "Classical Dynamics: A Contemporary Approach", J.V. JosÃ© and E.J. Saletan.

### Files for download:

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

Note: Only some of the problems will be assigned as homework, about 6/daySupplementary 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)

Jeff Eldred's slides from the afternoon sessions:

- Monday, week 1
- Tuesday, week 1
- Wednesday, week 1
- Thursday, week 1
- Monday, week 2
- Tuesday, week 2
- Wednesday, week 2
- Thursday, week 2

Selected papers:

- RF Longitudinal dynamics, from Jeff Eldred's thesis
- Frequency maps, Laskar
- Frequency maps, Laskar et al
- note on damped oscillators by K. McDonald
- Panofsky-Wenzel theorem paper
- Panofsky-Wenzel theorem short note
- Terahertz radiation

Link to web applet for viewing retarded fields, Davidson College.