IMPACT OF LONGITUDINAL SPACE-CHARGE WAKE FROM FEL UNDULATORS ON CURRENT-ENHANCED SASE SCHEMES

We present a description of longitudinal wake fields in XFELs that is of relevance in relation with Enhanced Self-Amplified Spontaneous Emission (ESASE) schemes. We consider wakes in XFELs, in the limit when the electron beam has gone inside the undulator for a distance longer than the overtaking length (the length that electrons travel as a light sig- nal from the tail of the bunch overtakes the head of the bunch). We find that the magnitude of the result- ing energy chirp constitutes a reason of concern for the practical realization of ESASE schemes. Am ore detailed report of our study is given in (1). γ 2 � γ 2 , γ being the Lorentz factor of the beam. Based on ¯ γ 2 � γ 2 , we demonstrate that the presence of the undulator strongly influences the space-charge wake. In contrast to this, in literature, wake calcu- lations for the LCLS case are given in free-space, as if the presence of the undulator were negligible. In this paper we pose particular attention to the LCLS case, for which ESASE schemes have been first pro- posed. We thus restrict our attention to a specific region of parameters. First, the longitudinal size of the beam is much larger than the FEL wavelength, i.e. σz � � r. Second, we assume a long satura- tion length compared with the overtaking length, i.e. Ls � 2¯ γ 2 .T hird, e ffects of metallic surroundings can be neglected, i.e. a � ¯ γz. We present a general theory based on these three assumptions. These are satisfied for the LCLS case, together with an extra- assumption on the transverse electron-beam size σ⊥: σ 2 � λw, being the reduced wavelength. Due to this last condition, major simplifications arise in the general theory. Radiation from the undulator is dras- tically suppressed and calculations of impedance and wake function can be performed considering a non- radiating beam, and thus accounting for space-charge interactions only. Space-charge impedance and wake function is found to reproduce the free-space case. Only, γ must be consistently substituted with ¯ γz .W e apply our theory to the ESASE setup referring to the LCLS facility. We calculate the energy chirp associ- ated with wakes inside the undulator and between dispersive section and undulator. Subsequently, the magnitude of their effect is estimated by calculating the linear energy chirp parameter. We find that the gain of the FEL process is sensibly reduced, and that longitudinal wakefields constitute a reason of concern regarding the practical realization of ESASE schemes.