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TUPSA056 |
Numerical Analysis of Electron Motion in Undulator Fields | |
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Funding: Work supported by Ministry of Education and Science, agreement No. 14.587.21.0001, unique research identifier RFMEFI58714X0001 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. |
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TUPSA055 |
Computer Code for Simulation of Wiggler Radiation Power Distributions | |
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Funding: Work supported by Ministry of Education and Science, agreement No. 14.587.21.0001, unique research identifier RFMEFI58714X0001 A computer code for simulation of spatial distributions of electromagnetic radiation power, which is generated by a relativistic electron beam in the external arbitrary magnetic field, is written. The calculations can be carried out, taking the real distributions of insertion device magnetic field into account as well as the real geometry of setup. The spatial distributions of power, generated by the electron beam in the superconducting 7.5 Tesla wiggler, which is installed in the Siberia-2 storage ring (Moscow, NRC Kurchatov Institute), are calculated. The electron beam emittance effects were also taken into account. The numerical results were compared with the correspondent distributions, obtained by means of the approximate analytical expressions. |
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