(Core graduate Course)
Week 1: Methods of electrostatics
- 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.