Advanced Electromagnetism

(Core graduate Course)

Detailed program

Week 1: Methods of electrostatics

• Overview of methods: images, expansion in 3D and 2D.
• Conformal maps. Green identity.
• Special coordinate systems.

  Week 2: Green functions and dielectrics

• Sphere example using images.
• Macroscopic Maxwell equations.
• Dielectric constant, permeability, continuity conditions.

  Week 3: Covariant formalism

• Lorentz gauge, Landau gauge, transverse and longitudinal current.
• Relativity theory.
• Tensors, co- and contra-variant, , Maxwell equations in covariant form.

  Week 4: Energy and momentum

• Poynting theorem, stress tensor.
• Momentum conservation, stress tensor in mechanics and in Maxwell equations.
• Linear momentum conservation–pressure example, covariant stress tensor definition. Application to plane waves.

  Week 5: Polarization; Green functions

• Polarization, Stokes parameters.
• Green function solutions.
• Green function solutions for radiation.

  Week 6: Multipole radiation

• Multipole radiation.
• Dipole radiation; example of charge in circular orbit.
• Electric quadrupole and magnetic dipole radiation.

  Week 7: Scattering 1

• Main concepts, scattering from a sphere.
• Thompson scattering and Compton effect.
• Scattering from bound electron and from collection of scatterers.

  Week 8: Scattering 2

• Perturbation theory in scattering.
• Absorption cross section.
• Optical theorem.

  Week 9: Interactions in matter

• Transmission through a slab, relation between forward scattering amplitude and dielectric constant.
• Dynamics of relativistic particles – Lagrangian formulation.
• Spin in magnetic field, spin-orbit coupling, Thomas precession (semi-qualitative treatment).

  Week 10: Lagrangian formulation of electromagnetic theory in matter

• Formulation in continuous system – general theory.
• Formulation of EM field in presence of currents.
• Solution of wave equation in covariant form, Green function.

  Week 11: Radiation of relativistic particle

• Lienard-Wiechert potentials and fields.
• Non-relativistic limit of Lienard-Wiechert formulas. Larmor formula.
• Total radiation by accelerated particle, relativistic Larmor formula, radiation in linac and cyclotron.

  Week 12: Distribution of radiation

• Angular distribution of radiation of accelerated relativistic particle.
• Frequency distribution of radiation.

  Week 13: Bremsstrahlung

• Bremsstrahlung – relativistic case.
• Application to Rutherford scattering.
• Potentials of fast-moving particle in matter.