Paper  Title  Page 

MOPPH001  Quantum Electrodynamics Theory of a Multimode Undulator Oscillator  


We have studied the operation of a free electron oscillator (FEO) in a multimode regime. Our device includes a long undulator, two mirrors and a spaceuniform ebeam of a Gaussian energy spread. Using the Heisenberg picture and neglecting both the contributions of the electron intrinsic magnetic moment and the positron fields we have derived a set of temporal equations for the operators of the electron and electromagnetic fields. The set correctly describes both the evolution of the modes’ fields from a spontaneous noise and the process of amplification. We have neglected the nonlinear losses and studied a non steadystate lasing regime. Namely, applying a perturbation theory for the electron operators and a technique of slowly varying functions for the electromagnetic field operators we have calculated the operators of the electric fields. Using this result we have estimated the oscillator energy flux in the forward direction. It is shown that within the framework of the chosen model the total flux is a sum of fluxes of unlocked modes. We have estimated the oscillator line width, the number of activated modes and, as a result, the power of the FEO that operates in the exponential regime with unlocked modes.  
MOPPH002  Generation of Short Pulses by an Undulator Oscillator with an Electron Absorber Placed into Cavity  


We have considered the operation of an e electron oscillator, which contains a long undulator, two mirrors, a spaceuniform ebeam and an absorber which allows tuning the lifetime of the electrons within the cavity. Our study is based on the quantum electrodynamics approach. Using a Heisenberg picture we have derived two temporal deferential equations for the electromagnetic field operators. The equations describe the electron absorption by the absorber as well as a wideband spontaneous noise produced by the electron, and the process of the amplification of the activated modes by the electron beam. To maintain a constant value of the system gain we have adopted that there is a pumping mechanism, which compensates the process of the electron absorption and supports the same density of the active medium. We have estimated the oscillator energy flux in the forward direction at a fixed point. It is shown that the device produces a chain of pulses. Since the contribution of losses is omitted the pulse amplitudes exponentially increase in time. The duration of the pulses may be short due to the large number of the locked modes.  
MOPPH003  VOLC: Volume Free Electron Laser Simulation Code  14 


First lasing of Volume Free Electron Laser (VFEL) in mm wavelength range was obtained recently*. Мultiwave volume distributed feedback where electromagnetic waves and electron beam spread angularly one to other in a spatiallyperiodic target is the VFEL distinctive feature**. Mathematical model and numerical methods for VFEL nonlinear stage simulation were proposed*** and implemented in computer code VOLC that means "VOLume Code". It was developed on the basis of multiple Fortran codes created in 19912006 years. VOLC allows to simulate different geometries of two and threewave VFEL in amplifier and oscillator regimes. Electron beam is modelled by averaging over initial phases of electrons. Dimensionality is 2D (one spatial coordinate and one phase space coordinate) plus time. All numerical results obtained using VOLC are in good agreement with analytical predictions of VFEL theory. Different roots to chaos in VFEL were investigated using VOLC. Some successful simulations of VFEL experimental setup at INP were carried out. A description of VOLC possibilities and representative numerical results are presented.
* V. G. Baryshevsky et al., NIMA483 (2002) 21. ** V. G. Baryshevsky, NIMA445 (2000) 281. *** K. Batrakov, S. Sytova, Computational Mathematics and Mathematical Physics 45 (2005) 666. 

MOPPH004  Measurement and Analysis of CSR effects at FLASH  18 


The vacuumultraviolet Free Electron Laser in Hamburg (FLASH) is a linac driven SASEFEL. High peak currents are produced using magnetic bunch compression chicanes. In these magnetic chicanes, the energy distribution along an electron bunch is changed by effects of Coherent Synchrotron Radiation (CSR). Energy changes in dispersive bunch compressor chicanes lead to transverse displacements along the bunch. These CSR induced displacements are studied using a transverse deflecting rfstructure. Recent experiments and simulations concerning the charge dependence of such transverse displacements are presented and analyzed. In these experiments an overcompression scheme is used which reduces the peak current downstream the bunch compressor chicanes. Therefore other self interactions like space charge forces which might complicate the measurements are suppressed.  
MOPPH005  Improvements of the Tracking Code Astra for the Simulation of Dark Current Losses in the FLASH Linac  22 


At the Free Electron Laser in Hamburg FLASH, the activation of components due to dark current emitted by the gun has become a serious problem. To improve the understanding of dark current transport in the linac, simulations with the Astra tracking code have been conducted. These studies require a big amount of computing time due to the high number of simulated macroparticles. Therefore, the parallelized version of Astra had to be enhanced by features like dynamic load balancing and an improved aperture model. The paper will provide an overview of the new features and discuss possible remedies of the dark current problem based on the simulation results.  
MOPPH006  Longitudinal Wake Field for an Electron Beam Accelerated through a UltraHigh Field Gradient  26 


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 


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)  
MOPPH008  Unaveraged ThreeDimensional Modelling of the FEL  


A new threedimensional model of the FEL is presented. A system of scaled, coupled LorentzMaxwell equations are derived in the paraxial limit. A minimal number of limiting assumptions are made and the equations are not averaged in the longitudinal direction of common radiation/electron beam propagation, allowing the effects of coherent spontaneous emission and nonlocalised electron propagation to be modelled. The equations are solved numerically using a parallel Fourier splitstep method.  
MOPPH009  Undulator Radiation in a Waveguide  34 


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)  
MOPPH010  ThreeDimensional Analysis of the Surface Mode Supported by a Reflection Grating  38 


In a SmithPurcell FreeElectron Laser (SPFEL), the electron beam interacts with the surface mode supported by a metallic reflection grating to produce coherent radiation. All the previous analyses of SPFEL had considered the localization of the surface mode only in the direction perpendicular to the grating surface and assumed translational invariance along the direction of grooves of the grating. In this paper, we include the localization of the surface mode along the direction of grooves and study the threedimensional structure of the surface mode in order to include diffraction effects in the analysis of SPFELs. Full threedimensional MaxwellLorentz equations are derived for the selfconsistent nonlinear analysis of SPFELs.  
MOPPH011  Comparison Between Kinetic and Fluid Description of PlasmaLoladed FreeElectron Laser  42 


In the kinetic treatment of the plasmaloaded FEL in Ref.* single particle equation of motion, for both beam and plasma electrons in the radiation fields, are used. Therefore, interaction terms between the wiggler and the spacecharge wave, in the transverse velocity of electrons, which are important elements in the fluid model, are neglected. A dispersion relation of a plasmaloaded FEL with kinetic theory is found in Ref.* that takes into account the velocity spread of both beam and plasma electrons. In the present analysis, a dispersion relation is obtained, by the fluid theory, with the interaction terms between the wiggler and the spacecharge wave in the transverse velocity of electrons taken into account. Since these interaction terms are inherently missing in the kinetic theory the two dispersion relation are compared to find out about the importance of these terms. It was found that although the absence of these terms has considerable effects on the growth rate, the general kinetic dispersion relation may be used to study the temperature effects of a warm beam/plasma on the instability of a freeelectron laser with a plasma background.
* S. Babaei and B. Maraghechi, "Kinetic description of plasmaloaded freeelectron laser", Phys. Plasmas, to be published. 

MOPPH012  Conservation Laws in Quasilinear Theory of Raman FreeElectron Laser  46 


A quasilinear theory of the freeelectron laser, in Raman regime, is presented to establish that conservation laws on number, energy, and momentum are upheld. A high density electron beam is assumed so that the spacecharge potential is no longer negligible. A sufficiently broad band spectrum of waves is assumed so that saturation will be due to the quasilinear spread of the beam electrons. Otherwise, for the single mode excitation, saturation will be due to the electron trapping in the spacecharge potential. It is shown that the quasilinear slow variation of the background distribution function is in the form of the diffusion equation in momentum space. An expression for the time evolution of the spectral energy density is derived. Conservation laws to the quasilinear order (second order) are derived and are proved to be satisfied. Results of the present investigation may be used to study the quasilinear saturation of freeelectron laser in the presence of the spacecharge wave.  
MOPPH013  Raman Scattering of a Perturbed TM Mode in a Dielectric Loaded Plasma Waveguide  


The stimulated Raman scattering of a perturbed TM mode in a dielectric loaded partially filled plasma waveguide is considered. The radiation is the result of the scattering of the pump electromagnetic wave, which is EH waveguide mode, off of a spacecharge wave. In the analysis, a non linear wave equation for the threewave interaction is used to investigate the coupling of the spacecharge and the waveguide modes. Dispersion relations for electromagnetic modes are solved numerically to study the frequency characteristics of the interaction of the EH waveguide modes with the spacecharge modes. Formulas for the spatial and temporal growth rates of the backscattered wave near the electron cyclotron frequency are derived and the effect of the dielectric liner on the growth rates is investigated. The numerical studies show that the presence of the dielectric liner has an effect on the phase matching condition and leads to a rather larger growth rates close to the electron cyclotron resonance.  
MOPPH014  Velocity Shot Noise, Space Charge Effects and Coherence Enhancement Schemes in SASE FEL  


We employ a formulation of the linear transfer matrix of FEL to explore new operating schemes and limiting effects in the high gain regime of FEL. These include analysis of SASE seed radiation injection, prebunching schemes, study of the role of velocity shot noise and collective (space charge effects). We propose new schemes for enhancement of the temporal coherence of SASE radiation, and study them by employing the transfer matrix formulation. The numerical computations indicate that XRay pulses, spatially and temporally (Fourier transform limited) coherent, are attainable with available high gain FEL parameters. The theoretical model is based presently on single transverse mode excitation (optically guided). Extension to a multi transverse modes excitation model will be outlined.  
MOPPH015  Limit for Harmonic Conversion in a Single Cascade of Coherent Harmonic Generation  50 


Harmonic generation is a reliable method for producing coherent highbrightness photon pulses from relativistic electron bunches. The standard process leading to Coherent Harmonic Generation (CHG) is initiated by a powerful seed laser. As a consequence, reaching short wavelengths generally requires a high order frequency conversion. For that reason some of the projects which are presently under development for coherent VUV and softXray emission are based on a series of two or more consecutive "cascades". In these setups, the radiation produced into one CHG stage is used as a seed in a following CHG cascade. The required number of cascades is related to the maximum harmonic conversion which can be obtained in single stages. In this paper the mechanism underlying the CHG, i.e. the bunching creation into the modulator, is studied in detail and the physical limits for the singlestage CHG are investigated. The identification of the limiting parameters may allow the implementation of new methods for enhancing the conversion efficiency. One of these methods, which relies on a simple modification of the standard CHG scheme, has been recently proposed* and shown to be able to significantly improve the system performance. Results are confirmed by numerical simulations using the codes Ginger and Genesis. Expected impact on some of the existing projects for CHG is also presented.
* E. Allaria, G. De Ninno, Phys. Rev. Lett., to be published. 

MOPPH017  1D Linear Intensity Spiking Evolution in a Single Shot of a SASE FEL  54 


The analysis is based on the 1D MaxwellLorentz equations which are reduced to the usual averaged linear equation in the limit of vanishingly small radiation field A(z,t) and average length lm. It is shown that if this equation is solved with initial shot noise conditions in which the widths of the spikes and the average distance between successive spikes are both uniformly smaller than the cooperation length Lc, it may lead to large amplitude coherent signals. The intensity spiking RMS relative amplitude decreases from the 100% values it has at t=0, down to values of the order or less than 0.1% in time intervals from ten to twenty gain times.  
MOPPH018  Particleincell Simulation of Twostream SmithPurcell Freeelectron Laser  


An approach to enhancement of terahertz (THz) SmithPurcell (SP) radiation from an open rectangular grating driven by two electron beams is presented in this paper. The two electron beams with a velocity separation propagate over the grating. With the help of a twodimensional particleincell (PIC) simulation, some nonlinear processes from spontaneous emission to superradiant radiation are demonstrated. The optimum voltage ratio is obtained where the SP radiation power achieves the maximum. The simulation results show that the enhancements of radiation power, the shortened saturation time, and the decrease of critical current for spontaneous SPR to superradiant at a proper voltage ratio. The simulation results can correspond to the linear analyses.  
MOPPH019  Optimized Designs for CAEP IR Freeelectron Laser  58 


The characteristics of CAEP IR freeelectron laser are estimated and the optimized designs of the resonator parameters such as radius of output hole, the size of mirror, the resonator length is carried out using our 3D FEL oscillator code. Based on the appropriate parameters, the saturated power, output power, gain and construction of optical modes are calculated.  
MOPPH020  FEL with Orotron Type Feedback  61 


In microwave electronics orotron is widely used as a source of RF radiation in millimeter and submillimeter wavebands. In this device an electron beam is coupled to a mode of quasioptical resonator by means of the periodical grating one of the resonator mirror. In our paper we discuss a relativistic modification of such a device. A novel FEL scheme is suggested in which the slow wave structure of orotron is replaced by shallow Bragg corrugation which provides the coupling of the transverse (with respect to direction of beam propagation) mode of a twomirror cavity with longitudinally propagating wave. The latter can be excited by the electron beam wiggling in undulator field. Described scheme allows to combine selective properties of an orotron with relativistic frequency conversion of a free electron laser. The transverse mode provides the feedback in the system thus leading to selfexcitation, while the propagating wave is responsible for energy extraction in the steadystate regime of operation. The discussed system was investigated both analytically and numerically using direct codes and averaged equations approach.  
MOPPH021  Karat PicCod Simulation of SmithPurcell Radiation from Gratings with Different Profiles  


Particleincell simulation of SmithPurcell radiation from gratings with lamellar, triangle, "volume" and "flat" profile using PICcode KARAT is carried out. The paper present some calculation results compared with experimental data obtained on the 6Mev microtron. It is shown that the maximal SPR yield for different gratings are in agreement with experiment.  
MOPPH022  A Description of Guided FEL Radiation Using Dielectric Waveguide Eigenmodes  65 


An analysis of the radiation field of an FEL in terms of eigenmodes of a linear dielectric waveguide is presented.  
MOPPH023  Enhancing FEL Power with Phase Shifters  69 


Undulator taper is a wellknown technique to increase the FEL efficiency past saturation by maintaining the resonant condition. In this paper, we demonstrate that shifting the electron bunch phase relative to the radiation is equivalent to tapering the undulator parameter. Using discrete phase changes derived from optimized undulator tapers for the LCLS xray FEL, we show that placing appropriate phase shifters between undulator sections can reproduce the power enhancement of these undulator tapers. The phase shifters are relatively easy to implement and operate, and hence can be used to aid or replace the undulator taper for optimizing the FEL performance.  
MOPPH025  Threedimensional Theory of the Cerenkov FreeElectron Laser  73 


We present an analytical theory for the operation of a Cerenkov freeelectron laser which includes diffraction of the optical mode in the direction transverse to the electron beam. Because the width of the optical mode depends on the gain, the usual cubic dispersion relation is replaced by a 5/2power dispersion relation, however, only two of these roots are allowed. These two roots both have positive real parts, indicating that they are slow waves. For a narrow electron beam, the optical mode is much wider than the beam, thus reducing the gain by an order of magnitude from that predicted by the two dimensional theory. In the limit of a wide electron beam, the two dimensional theory is recovered.  
MOPPH026  ThreeDimensional Theory of the SmithPurcell FreeElectron Laser  77 


We present an analytic theory for the operation of a SmithPurcell freeelectron laser (SPFEL) that includes transverse diffraction of the optical beam. For the case of an infinitely wide electron beam, this theory agrees with previous twodimensional analyses. When the electron beam is narrow compared to the mode, the gain (amplifier regime) is substantially reduced by diffraction, while its dependence on the beam current is increased due to gain guiding. A 5/2power dispersion relation replaces the conventional cubic dispersion relation. Additionally, the constituent waves of the laser mode are found to have different transverse decay rates. An estimate of the start current (oscillator regime) of the device is obtained by satisfying the appropriate boundary conditions on the beam axis.  
MOCAU01  Short Wavelength Regenerative Amplifier FELs  182 


In this paper we discuss the possibility of extending the operating wavelength range of tunable Regenerative Amplifier FELs to shorter wavelengths than current design proposals, notably into the XUV regions of the spectrum and beyond where the reflectivity of broadband optics is very low. Simulation studies are presented which demonstrate the development of good temporal coherence in generic systems with a broadband radiation feedback of less than one part in ten thousand.  
Slides  
MOCAU02  Numerical Solution of the FEL Correlation Function Equation  188 


The equation for twoparticle correlation function in FEL was derived recently to provide a new way of noise calculations in FELs*. In this paper this equation is solved numerically for the simplest case of narrow electron beam. Time independent solution with saturation is obtained. It is compared with the results of quasilinear theory and results of previous SASE linewidth estimates.
* O. A. Shevchenko, N. A. Vinokurov, NIM A507 (2003) 8488 

Slides  
MOCAU03  Numerical Propagation Simulations and Coherence Analysis of SASE Wavefronts  192 


Examples of wavefront propagation simulation and coherence analysis of SASE, seeded and startedup from noise, are presented. The calculations are performed using SRW – the waveoptics computer code optimized for synchrotron radiation, and the 3D FEL simulation code GENESIS 1.3. To ensure easy interoperation and data exchange between the two codes, GENESIS has been integrated into the "emission" part of the SRW, which is dedicated for calculation of initial wavefronts in the form ready for subsequent propagation simulations. In the examples described, after each run of GENESIS in timedependent mode, the electric field is transformed from time to frequency domain, and the wavefront obtained this way is numerically propagated, using Fourieroptics methods implemented in the SRW, from the exit of the FEL undulator to image plane of a simple interferometertype optical scheme. Intensityaveraged patterns, obtained after multiple cycles of the SASE (in presence of shot noise and/or a timing jitter) and the wavefront propagation calculations, allow for straightforward characterization of spatial coherence by visibility of interference fringes. SRW code can also be used for complete optimization of optical beamlines for 4th generation synchrotron radiation sources, which require accurate treatment of waveoptical phenomena in the frequency and time domains.  
Slides  
MOCAU04  Impact of Longitudinal Spacecharge Wake from FEL Undulators on Currentenhanced SASE Schemes  196 


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  
MOCAU05  Space Charge Effect in an Accelerated Beam  200 


It is usually assumed that the space charge effects in relativistic beams scale with the energy of the beam as the inverse relativistic factor gamma factor squared. We show that for a beam accelerated in the longitudinal direction there is an additional space charge effect in free space that scales as the ratio of the accelerating field to the gamma factor. This space charge field has the same origin as the "electromagnetic mass of the electron" discussed in textbooks on electrodynamics. It keeps the balance between the kinetic energy of the beam and the energy of the electromagnetic field of the beam. We then consider the effect of this field on a beam generated in an RF gun and calculate the energy spread produced by this field in the beam.  
Slides  
WEPPH058  Modeling a RF Linac Based Short Pulse Waveguide FEL  487 


We discuss modeling a highly slippage dominated short pulse, long wavelength rf linac based THz FEL in a waveguide cavity. 