PHYS 571: Electromagnetism II

Northern Illinois University, Fall 2005
Last update: Sept. 3rd, 2005

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Announcement: Homework assignment posted (see end of page) 



Instructor: Philippe Piot
Phone: 630 840 6389 (FNAL) 815 753 6468 (NIU)
Office: Faraday Hall, room 220

Classes: Tuesdays and Thursdays 4:00 pm-5:15 pm, Faraday West 227
Office Hours: Thursdays 5:30-6:30 pm and Fridays 1:00-3:00 by appointment







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 ---