Longitudinal impedance and wake from XFEL undulators. Impact on current-enhanced SASE schemes

Abstract

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. Our conclusion is in contrast with results in literature, where wake calculations for the LCLS case are given in free-space, as if the presence of the undulator were negligible.

44 pages, 2 figures

References in corpus (7)

• SASE FEL with energy-chirped electron beam and its application for generation of attosecond pulses
• Start-to-End Simulations of SASE FEL at the TESLA Test Facility, Phase 1
• Statistical properties of the radiation from VUV FEL at DESY operating at 30 nm wavelength in the femtosecond regime
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• Application of a modified chirp-taper scheme for generation of attosecond pulses in XUV and soft X-ray FELs
• Benchmarking Collective Effects of Electron Interactions in a Wiggler with OPAL-FEL