PHYS 571: Electromagnetism II
Last update: Sept. 3rd, 2005
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Announcement: Homework assignment posted (see end of page) |
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Instructor: Philippe Piot Classes: Tuesdays and Thursdays 4:00 pm-5:15 pm,
Faraday West 227 |
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Text: J.D. Jackson, Classical Electrodynamics, John Wiley & Sons, Inc, 3rd edition .
Grading: The final course grades in PHYS 571 will be determined as follows:
Homework 20%,
Midterm Exam 30%,
Final Exam 50%.
I Electromagnetic
resonance in cylindrical cavities and waveguides
Lesson 1 - setting up and categorizing the Problem
o Review of Maxwell-s equations
o General formulation and algorithm
o Wave equations
o Categorizing of resonant modes
Lesson 2 - Solving for the resonant electromagnetic fields (reading assign. JDJ, 8.1-8.5)
o Resonant frequencies
o TM-mode fields
o TE-mode fields
Lesson 3 - Practical aspects of cavity design (reading assign. JDJ, 8.6-8.7)
o Stored energy in cavity
o Power dissipated in cavity
Lesson 4 - Practical aspects of cavity design (reading assign. JDJ, 8.8)
o Quality factor for resonant modes
o Perturbation of cavity wall
o Tuning,
o Removal of degeneracies,
o Bead pull for measuring field profiles
II Theory of
special relativity
Lesson 5 - Electromagnetic field of point charge moving at constant velocity (reading assign. JDJ, 11.1-11.2)
o Maxwell-s equations - formulation and solution
o Space-charge force in Lorentz frame
Lesson 6 - Fundamental Theoretical Constructs (reading assign. JDJ, 11.3-11.5)
o Proper time and its invariance
o Minkowski metric and Lorentz transformation
Lesson 7 - Conservation Laws and Dynamics (reading assign. JDJ, 11.6-11.7)
o Particle dynamics in special relativity
o Photon emission and absorption
Lesson 8 - Covariance and Electrodynamics (reading assign. JDJ, 11.9-11.10, and 11.12)
o SI vs Gaussian (vs Heaviside-Lorentz) units
o Field-strength tensor
o Transformation of electromagnetic field
III Particle
Dynamics in Electromagnetic Fields
Lesson 9 - Lagrangian and Hamiltonian Formulations (reading assign. JDJ, 12.1A, 12.2)
o Principle of least action and Euler-Lagrange equation of motion
o Lorentz invariance, Lagrangian and Hamiltonian
Lesson 10 - Charged-particle motion in constant, uniform fields (reading assign. JDJ, 12.3-12.4)
o Electric field only
o Magnetic field only
Lesson 11 - charged-particle motion in constant, uniform Electric and Magnetic fields (reading assign. JDJ, 12.5)
o Formulation of covariant equation of motion
o Solution for general field configuration, i.e., nonzero E and B
o Example: ExB drift
o Non-uniform B and adiabatic invariance
IV Mid-term
-deliberations-
Lesson 12 - Review of chapter 9, 11, and 12
Lesson 13 - Mid-term Exam
V Radiation from
accelerating charges
Lesson 14 - Causality and Lienard-Wiechert potentials (reading assign. JDJ, 14.1)
o Retarded times
o Retarded 4-potential and electromagnetic fields
Lesson 15 - Causality and Lienard-Wiechert potentials (reading assign. JDJ, 14.2)
o Electromagnetic fields of an accelerating charge
o Charged particle moving at a constant velocity - revisited
o Velocity fields vs. radiation fields
Lesson 16 - Total power radiated by an accelerating charge (reading assign. JDJ, 14.3-14.4)
o As viewed in a frame commoving with the particle
o As viewed in a far-field laboratory frame
o Instantaneous rate of radiation
Lesson 17 - Energy loss from accelerated charged-particle beams
o Example: radiative energy loss in a linear accelerator
o Example: radiative energy loss in a circular accelerator
Lesson 18 - Energy loss from accelerating charged particle beam (reading assign. JDJ, 14.5)
o Angular distribution of radiation
o For linear motion,
o For circular motion
Lesson 19 - radiation spectrum of an accelerating charge (reading assign. JDJ, 14.6)
o Definition and general motion
o For instantaneous circular motion
Lesson 20 - Radiated energy from an accelerating charge
o Angular distribution of radiated energy
o Total radiated energy
Lesson 21 - Radiation spectrum of an accelerating charge (reading assign. JDJ, 14.8)
o Angular distribution of radiated energy
o Total radiated energy
Lesson 22 - Thomson Scattering of radiation
o Cross-section for free charge
o Cross-section for bound charge
o
Low-frequency limit and Rayleigh scattering
VI Collisions,
Energy Loss, and Scattering of Charged Particles
Lesson 23 - Energy transfer per impulse approximation (reading assign. JDJ, 13.1-13.2)
o Content of impulse approximation and regimes of validity
o Results - classical and quantum-mechanical
Lesson 24 - Influence of dielectric screening (reading assign. JDJ, 13.3)
o Formal result for energy loss in dielectric
o A simple model of frequency dependence in dielectrics
o Closed-form expression for energy loss including dielectric screening
Lesson 25 - Cerenkov radiation (reading assign. JDJ, 13.4-13.5)
o Energy loss in bulk medium
o Electromagnetic shock formation and structure
o 4-potential in the Cerenkov regime
Lesson 26 - Momentum transfer (Scattering) per the impulse approximation (reading assign. JDJ, 13.6)
o Rutherford scattering
o Average deflection angle
o Many small-angle scatterings
o Few large-angle scatterings
o Comparison of angular distributions
Lesson 27 (time permitting) - Transition radiation
o Radiation spectrum for single particle
o Angular dependence
o Frequency dependence
o Radiation spectrum for charged-particle bunch
o Bunch form factor
o Coherence vs. incoherence
VII Final
-deliberations-
Lesson 28 - Course review (preparatory to final exam)
Lesson 29 - Final exam
Homework Assignments:
Homework 1, Due date September 13th ,
2005 pdf
Homework 2, Due date September --, 2005 ---