A METHOD FOR DERIVING THE HAMILTONIANS OF INSERTION DEVICES

Abstract

Effects of wigglers and superconducting wigglers on the electrons in the storage ring are discussed based on the Hamiltonian formalism. In the local coordinates, it is useful to expand the wiggler field in the increasing order of the horizontal coordinate x, in which each coefficient of x(n) is itself an infinite polynomial of the vertical coordinate y. Combined with dimensional analysis, this expansion provides a simple and systematic approximation for normal wigglers of sinusoidal magnetic field. In the case of a non-analytic wiggler field as in superconducting wigglers, this method is still applicable with a little more care. In both cases, approximate Hamiltonians are derived.