Theory of electromagnetic fields

Details Theory of electromagnetic fields Theory of electromagnetic fields

2011-11-18

arxiv.org/abs/1111.4354v1

CERN-2011-007, pp. 15-65

Physics

Accelerator Physics

Presented at the CERN Accelerator School CAS 2010: RF for accelerators, Ebeltoft, 8-17 June 2010

Scientific paper

We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space, there are solutions to Maxwell's equations representing the propagation of electromagnetic fields as waves. We introduce electromagnetic potentials, and show how they can be used to simplify the calculation of the fields in the presence of sources. We derive Poynting's theorem, which leads to expressions for the energy density and energy flux in an electromagnetic field. We discuss the properties of electromagnetic waves in cavities, waveguides and transmission lines.

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