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

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 11/7/2018 2 2 2 2

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 11/7/2018 3 3 3 3

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

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

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

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

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

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

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

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 11/7/2018 11 11 11 11

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

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 11/7/2018 13 13 13 13