DESIGN STUDY FOR AN ADJUSTABLE PHASE UNDULATOR

This is a presentation of the results of a design study for an adjustable phase undulator. Earlier work described the basic theory of these undulators, whose magnetic fields are adjusted by moving the rows of magnets longitudinally with respect to each other, while keeping the gap fixed. This paper explores further details of a proposed permanent magnet, phase adjustable, soft x-ray undulator that will be used to test theoretical and calculated performance predictions. We present the Hamiltonian mechanics of the electron-beam and numerical calculations of magnetic fields and trajectories of electrons, including end effects. We also discuss the trajectories of off-axis electrons, the vertical focusing effect, the effects of magnetic errors, and finite emittance effects on the x-ray spectrum.