The Joint Accelerator Conferences Website (JACoW) is an international collaboration that publishes the proceedings of accelerator conferences held around the world.
TY - UNPB AU - Smolyakov, N.V. ED - Kuzin, Maxim ED - Schaa, Volker RW TI - Numerical Analysis of Electron Motion in Undulator Fields J2 - Proc. of RuPAC2016, St. Petersburg, Russia, November 21-25, 2016 C1 - St. Petersburg, Russia T2 - Russian Particle Accelerator Conference T3 - 25 LA - english AB - In this contribution we present an analysis of electron trajectories in the three dimensional magnetic field from a planar undulator. The electron trajectory is influenced by the focusing properties of the undulator field. In the European XFEL case, long segmented undulators (21 segments for the SASE3 beamline to 35 for SASE1 and SASE2) are planned to be installed, with quadrupole lenses between different segments. These focusing properties should be taken into account in simulations of spontaneous radiation, which constitutes the background signal of the FEL. The ideal magnetic field of an undulator can be described, in agreement with Maxwell equations, by a sinusoidal vertical magnetic field on the undulator axis, and by horizontal and longitudinal field components that appear out of axis. Exploiting this description for the ideal case, an experimentally measured magnetic field are accounted for by solving the differential equations of motion solved by means of a perturbation theory approach, and the corresponding expressions for the electrons velocities and trajectories are derived. The electrons trajectories for the experimentally measured magnetic field where also simulated numerically. To that aim, a computer code was written, which relies on the Runge-Kutta algorithm. The analytical and numerical methods could then be compared, showing a good agreement. PB - JACoW CP - Geneva, Switzerland ER -