Paper 
Title 
Page 
MOPPH006 
Longitudinal Wake Field for an Electron Beam Accelerated through a UltraHigh Field Gradient

26 

 E. Saldin, E. Schneidmiller, M. V. Yurkov, G. Geloni
DESY, Hamburg



Electron accelerators with higher longitudinal field gradients can produce highenergy beams with compact, cheap setups. Laserplasma acceleration appears to constitute the more promising breakthrough in this direction, delivering field gradients up to TV/m. Here we describe the impact of longitudinal wake fields on the electron beam, based on solution of Maxwell's equations for the longitudinal field. We consider an acceleration distance much smaller than the overtaking length (the length that electrons travel as a light signal from the tail of the bunch overtakes the head of the bunch), that is the case for laserplasma devices. We give expressions for impedance and wake function that may be evaluated numerically. We show that the rate of energy loss in the bunch due to radiative interaction is equal to that of coherently radiated energy in the farzone. A limiting expression is found for a large distance of the electron beam from the accelerator compared with the overtaking length. We derive analytical solutions for a Gaussian transverse and longitudinal bunch shape. We apply our analytical asymptote by studying the feasibility of a TableTop FEL based on laserplasma driver. Numerical estimations indicate that the effects of the timedependent energy change induced by the longitudinal wake pose a serious threat to the operation of this device. (See DESY 06222)


MOPPH007 
Theory of Nonlinear Harmonic Generation in FreeElectron Lasers with Helical Wigglers

30 

 E. Saldin, E. Schneidmiller, M. V. Yurkov, G. Geloni
DESY, Hamburg



Coherent Harmonic Generation (CHG), and in particular Nonlinear Harmonic Generation (NHG), is of importance for both short wavelength FreeElectron Lasers (FELs), in relation with the achievement of shorter wavelengths with a fixed electronbeam energy, and highaverage power FEL resonators, in relation with destructive effects of higher harmonics radiation on mirrors. In this paper we present a treatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study is based on an exact analytical solution of Maxwell's equations, derived with the help of a Green's function method. In particular, we demonstrate that nonlinear harmonic generation (NHG) from helical wigglers vanishes on axis. Our conclusion is in open contrast with results in literature, that include a kinematical mistake in the description of the electron motion. (See DESY 07058)


MOPPH009 
Undulator Radiation in a Waveguide

34 

 E. Saldin, E. Schneidmiller, M. V. Yurkov, G. Geloni
DESY, Hamburg



We propose an analytical approach to characterize undulator radiation near resonance, when the presence of the vacuumpipe considerably affects radiation properties. This is the case of the farinfrared undulator beamline at the Freeelectron LASer (FEL) in Hamburg (FLASH), that is designed to deliver pulses in the TeraHertz (THz) range. This undulator can be used for pumpprobe experiments where THz pulses are naturally synchronized to the VUV pulse from the FEL, as well as the development of novel electronbeam diagnostics techniques. Since the THz radiation diffractionsize exceeds the vacuumchamber dimensions, characterization of infrared radiation must be performed accounting for the presence of a waveguide. We developed a theory of undulator radiation in a waveguide based on paraxial and resonance approximation. We solved the field equation with a tensor Green's function technique, and extracted figure of merits describing in a simple way the influence of the vacuumpipe on the radiation pulse as a function of the problem parameters. Our theory, that makes consistent use of dimensionless analysis, allows treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. (See DESY 07031)


MOCAU04 
Impact of Longitudinal Spacecharge Wake from FEL Undulators on Currentenhanced SASE Schemes

196 

 E. Saldin, E. Schneidmiller, M. V. Yurkov, G. Geloni
DESY, Hamburg



In this article we present a description of longitudinal wake fields in Xray FreeElectron Lasers (XFELs) that is of relevance in relation with Enhanced SelfAmplified 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 signal from the tail of the bunch overtakes the head of the bunch). We find that the magnitude of the resulting energy chirp constitutes a reason of concern for the practical realization of ESASE schemes.



Slides

