**June 2018 United States Particle Accelerator School Course**

**Classical Mechanics & Electromagnetism**

Jeffrey Eldred, Kiersten Ruisard, Jayakar “Charles” Thangaraj, Stephen Webb

Course Textbook: *“Classical Mechanics”* 3rd. Ed. by Goldstein, Poole, & Safko

Gennady Stupakov Text and Errata

- Other Books:
*Classical Electrodynamics*3rd. Ed. by Jackson*Mathematical Method in Physical Sciences*3rd. Ed. by Boas*Lectures on Nonlinear Orbit Dynamics*Dragt.*Classical Dynamics*1st. Ed. by Jose and Saletan*Theory and Design of Charged Particle Beams*by Martin Reisner

**Class Lectures:**

**First Monday**

Lecture 1A Introduction

Lecture 1B Oscillators

Lecture 1C Perturbation Methods

Lecture 1D Relativity

Lecture 1E Hamiltonian Mechanics

**First Tuesday**

Lecture 2A Phase-Space

Lecture 2B Canonical Transformations

Lecture 2C Accelerator Hamiltonian

Lecture 2D Accelerator Physics Overview

Lecture 2E Longitudinal Dynamics

**First Wednesday**

Lecture 3A Magnetic Multipoles

Lecture 3B Magnetostatics & Magnet Design

Lecture 3C Nonlinear Resonances

Lecture 3D Numerical Methods in Dynamics

HW 2.2 Phase-space Diagram

**First Thursday**

Lecture 4A Electrostatics & EM Transformation

Lecture 4B Space-charge

Lecture 4C Lienard-Wierchert Potentials

**First Friday**

S. Webb Lecture Symplectic Maps

S. Webb Lecture Symplectic Tracking

Dragt *Lectures on Nonlinear Orbit Dynamics* (Primary Reference)

Forest *Dispersive Lattice Functions in a 6D Psuedeo-Harmonic Oscillator*

Ruth *A Canonical Integration Technique*

Neri *Lie Algebras and Canonical Integration*

Forest *Geometric Integration for Particle Accelerators*

Forest-Ruth *Fourth-Order Symplectic Integration*

Wu-Forest-Robin *Explicit Symplectic Integrator for s-dependent Static Magnetic Field*

**Second Monday**

Lecture 6A Cavities & Waveguides

Lecture 6B Transmission Lines & Resonators

**Second Tuesday**

Synchrotron Radiation 1

Synchrotron Radiation 2

Space-charge Lecture

**Second Wednesday**

Lecture 8A Wakefields

Animations of Beam Breakup

**Second Thursday**

Review Lecture

**Homework Assignments:**

HW 1 Assignment

HW 2 Assignment

HW 3 Assignment

HW 4 Assignment

HW 5 Assignment

HW 6 Assignment

HW 7 Assignment

**Jan 2016 USPAS Course in Classical Mechanics & Electromagnetism**

The 2016 version of this course was taught by Greg Penn of LBL and I served as a associate instructor. I’ve uploaded the lectures as a resource.

**USPAS2016 lectures:**

Lecture 1 Syllabus

Lecture 2 Linear and Nonlinear Oscillators

Lecture 3 Lagrangian and Hamiltonian

Lecture 4 Canonical Transformations

Lecture 5 Liouville’s Theorem

Lecture 6 Hamiltonian of a Circular Accelerator

Lecture 7 Equations of Motion in an Accelerator

Lecture 8 Action-Angle Variables in an Accelerator

Lecture 9 Closed Orbit Distortion

Lecture 10 Resonance Overlap and Dynamic Aperture

Lecture 11 Vlasov Equation and Decoherence

Lecture 13 Special Relativity and Electromagnetic Equations

Lecture 14 Electrostatics

Lecture 15 Self-field Relativistic Beam

Lecture 16 Aperture Effects on a Beam

Lecture 17 Plane Waves & Gaussian Beams

Lecture 18 Radiation and Retarded Potentials

Lecture 20 Synchrotron Radiation

Lecture 22 Transition and Diffraction Radiation

Lecture 23 Formation Length and Coherent Radiation

Lecture 24 Coherent Synchrotron Radiation Wake

Lecture 25 RF Cavity and Waveguide Modes

Original Supplemental Lectures:

Mon Week 1 Longitudinal Accelerator Dynamics

Tues Week 1 Generating Functions and Action-Angle

Wed Week 1 Betatron Motion

Thur Week 1 Nonlinear Sextupole Resonance

Mon Week 2 Retarded Potentials

Tues Week 2 Wakefield Impedance

Wed Week 2 Electron Cloud

Thur Week 2 Review