Electromagnetic fields: impedances and wakes in particle accelerators and storage rings

Analytic techniques for calculation of impedances and wake potentials in particle accelerators or storage rings are discussed. Derivation of wave and Helmholtz equations from Maxwell’s equations resulting with complicated electromagnetic fields is shown. Simpler wake potentials (which are integrals over the forces exerted by the fields) evaluated at a fixed distance behind the source charge moving with constant velocity are introduced.