Journal
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT
Volume 583, Issue 2-3, Pages 228-247Publisher
ELSEVIER
DOI: 10.1016/j.nima.2007.09.019
Keywords
longitudinal impedance; longitudinal wake-function; X-ray free-electron laser (XFEL); enhanced SASE schemes
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In this article we derive longitudinal impedance and wake function for an undulator setup with arbitrary undulator parameter, taking into account a finite transverse size of the electron bunch. Earlier studies considered a line density-distribution of electrons instead. We focus our attention on the long-wavelength asymptote (compared with resonance wavelength), at large distance of the electron bunch from the undulator entrance compared to the overtaking length, and for large vacuum-chamber size compared to the typical transverse size of the field. These restrictions define a parameter region of interest for practical applications. We calculate a closed expression for impedance and wake function that may be evaluated numerically in the most general case. Such expression allows us to derive an analytical solution for a Gaussian transverse and longitudinal bunch shape. Finally, we study the feasibility of current-enhanced SASE schemes (ESASE) recently proposed for LCLS. that fall well-within our approximations. Numerical estimations presented in this paper indicate that impedance-induced energy spread is sufficient to seriously degrade the FEL performance. (c) 2007 Elsevier B.V. All rights reserved.
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