Principles of Free Electron Lasers by H. P. Freund & T. M. Antonsen Jr

Author:H. P. Freund & T. M. Antonsen, Jr.
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The electron beam envelope as it propagates through the wiggler/quadrupole line is largely dependent upon the quadrupoles and relatively independent upon the polarization and field strength of the wigglers. As such, the matched beam sizes (in the x- and y-directions) are nearly invariant with respect to the wiggler, and β x = 2.08 m and β y = 0.58 m. In order to inject such a matched beam, the simulation initializes the electron beam in the simulation with an rms size in the x-direction of about 132 μm with a Twiss-α x = 0.938 and an rms size in the y-direction of about 75 μm with a Twiss-α y = −0.705. The evolution of the beam envelope through the wiggler/quadrupole lattice that results is shown in Fig. 6.22, where the rms beam size in the x-direction is shown in blue on the left axis and the rms beam size in the y-direction is shown in red on the right axis. Observe that this yields an average beam size of about 113 μm.

Fig. 6.22Simulated propagation of the beam envelope in the wiggler/quadrupole lattice, where x c and y c denote the associated beam centroid [49]

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