1. Review Lecture Jeffrey Eldred Classical Mechanics and Electromagnetism1 1
Review Lecture
Jeffrey Eldred
Classical Mechanics and Electromagnetism
June 2018 USPAS at MSU 1 1 1 1 1 1

2. First Monday 1B Oscillators Oscillators from Linearized Potential
Nonlinear Damped Oscillator
Oscillators Driven with an arbitrary force
1C Perturbation
Direct Perturbation
Poincare Lindstedt Pertubation
1D Special Relativity
Length Contraction, Time-Dilation, Lorentz Boosts
Relativistic Momentum & Energy
Plane Waves & Doppler Shifts
Causality, Minkowsky Diagrams & Paradoxes 2
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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3. First Monday 1E Lagrangians Nonrelativistic & Relativistic Lagrangian
Equations of Motion
Least Action Principal
Change of coordinates for a Lagrangian
Wave Equation for a String
1E Hamiltonians
Canonical Momentum & Obtaining H from L
Obtaining H from equations of motion
Hamiltonian & Conservation Laws 3
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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4. First Tuesday 2A Phase-Space Fixed Points & Stability of Points
Eigenvalues & Eigenvectors
Equipotential Surfaces
2B Canonical Transformations
Properties of Poisson Brackets
Poisson Brackets to Find Invariants
Canonical Transformations & Generating Functions
Jacobian Matrix & Checking for preservation of PhSp area.
Liouville’s Theorem for Volume, Number, Density
Foiling Liouville’s Theorem
Action-Angle Coordinates, what they mean
Action-Angle Coordinates, 1D system
Frequency as a function of Action 4
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/7/2018 4 4 4 4

5. First Tuesday 2A Phase-Space Fixed Points & Stability of Points
Eigenvalues & Eigenvectors
Equipotential Surfaces
2B Canonical Transformations
Properties of Poisson Brackets
Poisson Brackets to Find Invariants
Canonical Transformations & Generating Functions
Jacobian Matrix & Checking for preservation of PhSp area.
Liouville’s Theorem for Volume, Number, Density
Foiling Liouville’s Theorem
Action-Angle Coordinates, what they mean
Action-Angle Coordinates, 1D system
Frequency as a function of Action 5
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/7/2018 5 5 5 5

6. First Tuesday 2C Accelerator Hamiltonian
Electromagnetic Relativistic Hamiltonians
EM Canonical Momentum
Making Canonical Transformations
Assumptions for an Accelerator Hamiltonian
Action-Angle Variables for an Accelerator
Linear Accelerator Motion
2D Accelerator Physics Overview
Transfer Matrices & Finding TWISS Parameters
Particle Motion in terms of TWISS, Action Phase-Advance
Particle Emittance & Adiabatic Damping
Dispersion & Chromaticity 6
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/7/2018 6 6 6 6

7. First Tuesday – First Wednesday
2E Longitudinal Dynamics
Synchrotron Focusing Equations
Phase-slip Factors & Transition
3A Magnetic Multipoles
Vector Potential & Scalar Potential
Basic Magnetic Multipoles
Taylor Expansion for Multipole Components
3B Magnetostatics
Calculating Magnetic Fields from Sources
Amperian Loops
Concept of Magnetization & Hysteresis 7
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/7/2018 7 7 7 7

8. First Wednesday 3C Nonlinear Accelerator Resonance
Action-Angle Hamiltonian
Integrated Hamiltonian
Identifying Resonances from Multipoles
Calculating & Correcting Resonances
Equations of Motion near Resonance
Tune Diagrams
3D Numerical Methods
Poincare Section
FMA Analysis 8
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/7/2018 8 8 8 8

9. First Thursday 4A Electrostatics
Calculating Electric Fields from Sources
Gaussian Surfaces
Electrostatic Multipoles
4A Transformation of EM Fields
Relativistic Charges & Currents
Lorentz Boosts of EM Fields
4B Space-charge
Electric Field from Beams
KV Distributions & Linear Focusing
Beam Envelope Equation
Space-charge Tune-shift 9
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/7/2018 9 9 9 9

10. First Thursday – First Friday
4C Plane Waves
Orientation & Polarization
Poynting Vector
Retarded Time
Fields from a Point Charge
Larmor Formula / Synchrotron Radiation
5A Symplectic Maps
Symplectic vs Nonsympletic Tracking
Meaning of a Lie Operator
BCH Formula for a Corrected Invariant 10
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/7/2018 10 10 10 10

11. Second Monday 6A Cavities & Waveguides Standing Waves
Boundary Conditions for E & B
Separation of Variables
TM vs TE modes
Rectangular & Cylindrical Geometry
Waveguides & Cutoff Frequency
Phase Velocity & Group Velocity
RF Cavities & Eigenmodes
Reflection of EM Waves 11
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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12. Second Monday – Second Tuesday
6B Transmission Lines & Resonators
Complex Impedance, Capacitors, Inductors
Load-matching & Reflections
Propagation of V & I over z
RLC Resonator Model
Loaded Transmission Lines as Resonators
7A Radiation
Synchrotron Radiated Power
Synchrotron Angular Distribution
Synchrotron Spectrum & Critical Frequency
Velocity vs. Radiative Fields
Formation Length
Coherent Radiation 12
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/7/2018 12 12 12 12

13. Second Tuesday – Second Thursday
7B Space-charge
Debye Length, Collisional vs. Space-charge
Pancaking of E&B-fields
Longitudinal Space-charge
Image Charges
8A Wakefields
Panofsky Wenzel with application
Beam moments & Cylindrical Decomposition
Wake potentials & Wake functions
Impedances as Fourier Transform
Collectivity Instabilities from Wakes
Landau Damping Concepts 13
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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