The Cockcroft Institute
Post-graduate
Lecture Courses: Academic Year 2005-6
Specialist
Course
Electromagnetism
and Geometry
Tutors: Dr J Gratus, Prof RW
Tucker, Dr DA Burton
These courses are run every academic year by the Mathematical Physics
Group in the Department of Physics, Lancaster University.
Part I : 7th October to
16th December
Location : TBA
Duration : TBA
Syllabus
1. Geometric methods in Electromagnetism including perturbative
waveguide
and cavity mode analysis.
Elements of vector spaces, elements of
differential geometry, exterior
methods, frames and coframes, metric, connections and covariant
derivatives, Stokes theorem, the Frenet apparatus, Fermi transport, use
of curvilinear coordinates in field systems, the covariant Maxwell
equations, gauge covariance, electromagnetic interactions with charged
particles, boundary conditions and constitutive relations, applications
to RF cavity mode analysis.
2. Theory of Interacting Fields and particles with emphasis on
relativistic effects and radiative phenomena.
Motion of charged particles in regular
electromagnetic external fields,
radiation from charged particles, charged fluids, radiation reaction
and the Lorentz-Dirac equation, multi-pole analysis and electromagnetic
scattering from a conducting and dielectric sphere, Eikonal methods for
high frequency Maxwell fields.
3. Initial and Boundary value Problems, including relativistic moving
media, discontinuous fields and moving boundaries
Elements of distribution theory,
applications to Sagnac effect.
4. Approximation schemes including variational methods
Linearisation techniques, applications
to analysis of (non-planar)
design orbits in cyclic accelerators, machine coordinates based on
design orbits with curvature and torsion, multiple resonance phenomena.
Part II: 13th January to 24th
March
Location : TBA
Duration : TBA
Syllabus
5. Global and Local Stability Analysis.
Hill's equation and Floquet theory,
applications to transverse charged
beam oscillation stability, notions of symplectic methods for beam
dynamics and phase space.
6. Stochastic Methods.
Elements of stochastic methods and
stochastic differential equations,
the Fokker-Planck equations and its uses.
7. Modelling Techniques and Numerical Analysis.
Coding techniques in Maple and use of
numerical algorithms for
integrating non-linear differential systems.
8. Coupled Electromagnetic and Thermo-Mechanics.
Elements of
continuum mechanics,
Maxwell and Cauchy stress tensors, the
stress-energy tensor for coupled relativistic systems, divergence
theorems, Cosserat dynamics, coupled
elasto-thermodynamics for
charged
matter.
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