2019 - 2020

0321-4117   Advanced Electromagnetism  
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Course description

Advanced Electromagnetism
תיבת טקסט: Weekly division
week	subject
1	Methods of electrostatics
2	Green function and dielectrics
3	Covariant formalism
4	Energy and momentum
5	Polarization. Green function solutions of radiation.
6	Multipole radiation
7	Scattering 1
8	Scattering 2
9	Interactions in matter.
10	Lagrangian formulation of electromagnetic theory in matter.
11	Radiation by relativistic particle
12	Distribution of radiation
13	Bremsstrahlung
(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.

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