FEL Theory

Paper	Title	Page
MOOC02	Growth Rates and Coherence Properties of FODO-lattice based X-ray Free Electron Lasers	25
	S. Reiche, E. Prat PSI, Villigen PSI, Switzerland
	Most hard X-ray Free Electron Lasers are designed with a super-imposed FODO lattice to focus the electron beam for optimum performance of the FEL. Theory predicts an optimum value of the beta-function, where the induced axial velocity spread starts to counteract the increased rho-parameter due to higher electron density. However in a FODO lattice the electron beam envelope varies significantly and disrupts the coupling of the electron beam to the radiation field. This is particularly relevant for hard X-ray FELs, where the radiation mode is smaller than the electron beam size. In this presentation we study the impact of the FODO cell length and the beta-function variation on the FEL gain length and growth of the coherence properties for SASE FELs.
	Slides MOOC02 [2.776 MB]
MOOC03	On Quantum Effects in Spontaneous Emission by a Relativistic Electron Beam in an Undulator	29
	G. Geloni, V. Kocharyan, E. Saldin DESY, Hamburg, Germany
	Robb and Bonifacio (2011) claimed that a previously neglected quantum effect results in noticeable changes in the evolution of the energy distribution associated with spontaneous emission in long undulators. They revisited theoretical models used to describe the emission of radiation by relativistic electrons, and claimed that in the asymptotic limit for a large number of undulator periods the evolution of the electron energy distribution occurs as discrete energy groups according to Poisson distribution. These novel results are based on a one-dimensional model of spontaneous emission and assume that electrons are sheets of charge. However, electrons are point-like particles and the bandwidth of the angular-integrated spectrum of undulator radiation is independent of the number of undulator periods. The evolution of the energy distribution studied with a three-dimensional theory is consistent with a continuous diffusive process. We also review how quantum diffusion of electron energy in an undulator with small undulator parameter can be analyzed using the Thomson cross-section expression, unlike the conventional treatment based on the expression for the Lienard-Wiechert fields.
	Slides MOOC03 [0.980 MB]
MOOC04	Growing Modes of the Free-Electron Laser and Their Bandwidth	33
	G. Wang, V. Litvinenko BNL, Upton, Long Island, New York, USA S.D. Webb Tech-X, Boulder, Colorado, USA
	Forty years after invention of FELs a number of fundamental questions remain unanswered. For example, it is known that for a beam with a Gaussian energy distribution an infinite number of modes exist. But it is unknown how many of these modes are growing, or what frequency cutoffs might exist for these growing modes? In this talk, for the first time, we present the proof that for typical bell-shape energy distribution in the electron beam there is no more that one growing mode - both without [1] and with space charge effects. We also present an analytical expression, which determines the bandwidth of the free-electron laser. Furthermore, we prove that for an energy distribution with N peaks, there is no more than N FEL growing modes. Finally, present a simple method of determining number of growing modes for the case of beam energy distributions with multiple peaks. [1] On Free-Electron Laser Growing Modes and their Bandwidths, S. Webb, V.N. Litvinenko, G. Wang, Submitted to PR ST-AB
	Slides MOOC04 [2.832 MB]
MOOCI01	Laser Phase Errors in Seeded FELs	17
	D.F. Ratner, A.R. Fry, G.V. Stupakov, W.E. White SLAC, Menlo Park, California, USA
	Harmonic seeding is a promising method for producing transform-limited FEL pulses in the soft x-ray region. While harmonic multiplication schemes extend seeding to shorter wavelengths, they also amplify the spectral phase errors of the initial seed laser, degrading the final pulse quality and decreasing longitudinal coherence. Here we consider the effect of seed laser phase errors on longitudinal coherence for high gain harmonic generation and echo-enabled harmonic generation. We develop simulations to confirm analytical results for the case of linearly chirped seed lasers, and extend the results for arbitrary seed laser envelope and phase.
	Slides MOOCI01 [2.534 MB]
MOPD02	Pulse-front Tilt Caused by the Use of a Grating Monochromator and Self-seeding of Soft X-ray FELs	41
	G. Geloni, V. Kocharyan, E. Saldin DESY, Hamburg, Germany
	Self-seeding is a promising approach to significantly narrow the SASE bandwidth of XFELs to produce nearly transform-limited pulses. The development of such schemes in the soft X-ray wavelength range necessarily involves gratings as dispersive elements. These introduce, in general, a pulse-front tilt, which is directly proportional to the angular dispersion. Pulse-front tilt may easily lead to a seed signal decrease by a factor two or more. Suggestions on how to minimize the pulse-front tilt effect in the self-seeding setup are given.
MOPD03	Harmonic Lasing in X-ray FELs	45
	E. Schneidmiller, M.V. Yurkov DESY, Hamburg, Germany
	Contrary to nonlinear harmonic generation, harmonic lasing in a high-gain FEL can provide much more intense, stable,and narrow-band FEL beam which is easier to handle if the fundamental is suppressed. We propose efficient methods for suppression of the fundamental. We perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present explicit expression for FEL gain length, taking into account all essential effects. We conclude that harmonic lasing is much more robust than usually thought, and can be widely used in the existing or planned X-ray FEL facilities. LCLS after a minor modification can lase at the 3rd harmonic up to the photon energy of 25-30 keV providing multi-gigawatt power level. At the European XFEL the harmonic lasing would allow to extend operating range (ultimately up to 100 keV), to increase brilliance, to enable two-color operation for pump-probe experiments,and to provide more flexible operation at different electron energies. We discover that in a part of the parameter space, corresponding to the operating range of soft X-ray beamlines of X-ray FEL facilities, harmonics can grow faster than the fundamental.
MOPD04	Fitting Formulas for Harmonic Lasing in FEL Amplifiers	49
	E. Schneidmiller, M.V. Yurkov DESY, Hamburg, Germany
	One of the most important subjects of the high-gain FEL engineering is the calculation of the gain length, and fitting formulas are frequently used for this purpose. Here we refer to Ming Xie fitting formulas [1] and fitting formulas for optimized FEL written down in an explicit form in terms of the electron beam and undulator parameters [2]. In this paper we perform generalization of these fitting formulas to the case of harmonic lasing. [1] M. Xie, Nucl. Instrum. and Methods A445(2000)59 [2] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt. Commun. 235(2004)415
MOPD05	Harmonic Lasing of Thin Electron Beam	53
	E. Schneidmiller, M.V. Yurkov DESY, Hamburg, Germany
	For a typical operating range of hard X-ray FELs the condition 2π ε/λ ~ 1 is usually a design goal for the shortest wavelength. In the case of the simultaneous lasing the fundamental mode has shorter gain length than harmonics. If the same electron beam is used to drive an FEL in a soft X-ray beamline, the regime with 2π ε/λ << 1 is realized which corresponds to the case of a small value of diffraction parameter. Here we present a detailed study of this regime. We discover that in a part of the parameter space, corresponding to the operating range of soft X-ray beamlines of X-ray FEL facilities (like SASE3 beamline of the European XFEL), harmonics can grow faster than the fundamental wavelength. This feature can be used in some experiments, but might also be an unwanted phenomenon, and we discuss possible measures to diminish it.
MOPD06	Spatial Properties of the Radiation from SASE FELs at the European XFEL	57
	E. Schneidmiller, M.V. Yurkov DESY, Hamburg, Germany
	Recently DESY and the European XFEL GmbH performed revision of the baseline parameters for the electron beam. Operating range of bunch charges has been extended from 20 pC to 1 nC. Different modes of FEL operation become possible with essentially different properties of the radiation. Radiation from SASE FEL with planar undulator contains visible contribution of higher odd harmonics. Knowledge of spatial properties of harmonics is of great practical interest for planning user experiments. In this report we present results of the studies of spatial properties of the radiation from SASE FELs at the European XFEL. We consider nonlinear mechanism of harmonic generation and trace spatial properties of the odd harmonics up to deep nonlinear regime.
MOPD07	On Disruption of the Fundamental Harmonic in SASE FEL with Phase Shifters	61
	E. Schneidmiller, M.V. Yurkov DESY, Hamburg, Germany
	A method to disrupt the fundamental harmonic with phase shifters installed between undulator modules (while keeping the lasing at the third harmonic undisturbed) was proposed in [*]. If phase shifters are tuned such that the phase delay is 2π/3 (or 4π/3) for the fundamental, then its amplification is disrupted. At the same time the phase shift is equal to 2π for the third harmonic, i.e. it continues to get amplified without being affected by phase shifters. We note that simulations in [*] were done for the case of a monochromatic seed, and the results cannot be applied for a SASE FEL. The reason is that in the latter case the amplified frequencies are defined self-consistently, i.e. there is frequency shift (red or blue) depending on positions and magnitudes of phase kicks. This leads to a significantly weaker suppression effect. In particular, we found out that a consecutive use of phase shifters with the same phase kicks 2π/3 (as proposed in [*] is inefficient, i.e. it does not lead to a sufficiently strong suppression of the fundamental wavelength. In the present report we propose a modification of phase shifters method that can work in the case of a SASE FEL. [*] B.W.J. McNeil et al., Phy. Rev. Lett. 96, 084801 (2006).
MOPD08	Coherence Properties of the Odd Harmonics of the Radiation from SASE FEL with Planar Undulator	65
	E. Schneidmiller, M.V. Yurkov DESY, Hamburg, Germany
	We present a comprehensive analysis of coherence properties of odd harmonics radiated from a SASE FEL with planar undulator. Nonlinear mechanism of harmonic generation is under study. Temporal and space correlation functions, coherence time and degree of transverse coherence are calculated by means of numerical simulations with the code FAST. Similarity techniques have been used to derive general coherence properties of the radiation in the saturation regime.
MOPD10	Nonlinear Harmonic Selection in an FEL Undulator System	69
	S. Biedron, L. Giannessi, K. Horovitz, S.V. Milton CSU, Fort Collins, Colorado, USA
	Sandra Biedron1, William Fawley1,2, Luca Giannessi1,2,3, Karen Horovitz1, Stephen Milton1 1Colorado State University, Department of Electrical and Computer Engineering, 1373 Campus Delivery, Fort Collins, Colorado 80523 2 and Sincrotrone Trieste 34149 Basovizza (Trieste) Italy 3and ENEA, C.R. Frascati Via Enrico Fermi, 45 - 00044 Frascati (Roma) Italy The area of harmonic selection in undulator magnets is an important area of free electron laser (FEL) research. Within the undulator section of an FEL system, a wiggling electron beam emits coherent radiation at multiple wavelengths (harmonics), but in some cases the output should only be in the desired region for application purposes. Dispersion sections and unique undulators can be tailored in order to select harmonics and control their power levels. GINGER and PERSEO code were used for simulations. This research will lead to a better understanding of the emission process as well as the interaction of beam density distribution, the frequency and phase relationship of emission, and the amplitude of the emission as a function of time. Furthermore, harmonic control has applications within oscillator or amplifier-based FEL systems.
MOPD12	Puffin: A Three Dimensional, Unaveraged Free Electron Laser Simulation Code	73
	L.T. Campbell, B.W.J. MᶜNeil USTRAT/SUPA, Glasgow, United Kingdom
	The broadband, 3D FEL code Puffin is presented. The analytical model is derived in absence of the Slowly Varying Envelope Approximation, and can model undulators of any polarisation. Due to the enhanced resolution, the memory and processing requirements are greater than equivalent unaveraged codes. The numerical code to solve the system of equations is therefore written for a parallel computing environment utilizing MPI. Some example simulations are presented.
MOPD17	Nonlinear effects in FEL theory and their role in coherent electron cooling	77
	A. Elizarov SUNY SB, Stony Brook, New York, USA V. Litvinenko BNL, Upton, Long Island, New York, USA
	The novel cooling technique, the coherent electron cooling [1] relies on the amplification of the interaction between hadrons and electrons by an FEL. The linearity of the amplification process is essential for operation of such cooler. In this paper we propose a theoretical method of taking into account nonlinear effects in computation of evolution of charge perturbation in an FEL. This will allow to explore the limits of the FEL gain with special attention to the smearing of the phase caused by nonlinear and saturation effects. [1] V. N. Litvinenko, Y. S. Derbenev, Phys. Rev. Lett. 102, 114801 (2009).
MOPD22	A General Method for Analyzing 3-D Effects in FEL Amplifiers	81
	P. Baxevanis, Z. Huang, R.D. Ruth SLAC, Menlo Park, California, USA
	FEL configurations in which the parameters of the electron beam vary along the undulator become relevant when considering new aspects of existing FELs or when exploring novel concepts. This paper describes a fully three-dimensional, analytical method suitable for studying such systems. As an example, we consider a seeded FEL driven by a beam with varying transverse sizes. In the context of the Vlasov-Maxwell formalism, a self-consistent equation governing the evolution of the radiation field amplitude is derived. An approximate solution to this equation is then obtained by employing an orthogonal expansion technique. This approach yields accurate estimates for both the amplified power and the radiation beam size. Specific numerical results are presented for two different sets of X-ray FEL parameters.
MOPD28	Theoretical Study of Smith-Purcell Free-Electron Lasers	85
	D. Li, K. Imasaki ILT, Suita, Osaka, Japan M.R. Asakawa, Y. Tsunawaki Kansai University, Osaka, Japan M. Hangyo ILE Osaka, Suita, Japan S. Miyamoto LASTI, Hyogo, Japan Y. Wei, Z. Yang UESTC, Chengdu, Sichuan, People's Republic of China
	We report here a theory to calculate the growth rate and start current of a Smith-Purcell free-electron lase. The mechanism of the interaction between a sheet electron beam and the surface wave above a lamellar grating is well investigated. After deriving the growth rate from the dispersion equation, the start current is dexterously worked out by considering the energy flow above the grating. The predictions of our theory agree with the results from the particle-in-cell simulations.
MOPD31	Injector Optimization for a High-repetition Rate X-ray FEL	89
	C. F. Papadopoulos, J.N. Corlett, P. Emma, D. Filippetto, G. Penn, J. Qiang, M.W. Reinsch, F. Sannibale, M. Venturini LBNL, Berkeley, California, USA
	Funding: This work was supported by the Director of the Office of Science of the US Department of Energy under Contract no. DEAC02-05CH11231 In linac driven free electron lasers, the final electron beam quality is constrained by the low energy (<100 MeV) beam dynamics at the injector. In this paper, we present studies and the optimized design for a high-repetition (>1 MHz) injector in order to provide a high brightness electron beam. The design effort is also extended to multiple modes of operation, in particular different bunch charges. The effects of space charge and low energy compression on the electron beam brightness are also discussed for the different modes.
MOPD32	Theory of the Quantum FEL in a Nutshell	93
	P. Preiss, R. Sauerbrey HZDR, Dresden, Germany R. Endrich, E.A. Giese, P. Kling, M. Knobl, W.P. Schleich Uni Ulm, Ulm, Germany S.M. Zubairy Texas A&M University, College Station, Texas, USA
	New developments in accelerator and laser physics raise hope for the so-called QFEL, a free-electron laser operating in the quantum mechanical regime. We develop a fully quantized single-particle theory describing the dynamics of the interaction between the electron, the wiggler and the laser field. In the quantum mechanical regime the dynamics are reminiscent of the standard laser theory with a two-level atom. Indeed, we find oscillations between two entangled states - where the entanglement appears between the electron momentum state and the Fock states of the laser and wiggler field. Compared to a two-level system with one internal degree of freedom (e.g. an atom with a ground and one excited state) the state of our system is mainly determined by the momentum of the electron in the co-moving Bambini-Renieri frame. In contrast to the classical regime here the electron propagating through the wiggler field can only emit or absorb a single laser photon. Transitions including the emission or absorption of many photons are substantially much suppressed.
MOPD33	Saturation in Free Electron Laser with Quadrupole Wiggler and Axial Magnetic Field	97
	P. Yahyaee, A.A. Kordbacheh IUST, Narmac, Tehran, Iran
	In this paper, we study the nonlinear evolution of a quadrupole wiggler free electron laser, in the presence of a helical wiggler, which increases adiabatically from zero to a constant level. To focus the electron beam, we apply an axial magnetic field. By using Maxwell equations and Lorentz force equation of motion for electrons, a set of coupled nonlinear equation is derived and solved numerically. The beam is cold and propagates with a relativistic velocity. Results are compared with dipole wiggler FEL.
MOPD35	Detailed Modeling of Seeded Free-electron Lasers	101
	S. Reiche PSI, Villigen PSI, Switzerland M. Carlà UNIFI, Sesto Fiorentino (FI), Italy
	Seeding schemes for Free Electron Lasers have mostly a strong impact on the electron distribution by either a conversion of an energy modulation into a current modulation with high harmonic content (HGHG seeding) or an over-compression of this energy modulation to induce energy bands (EEHG seeding) or smear out any bunching in the electron beam (self-seeding). Most codes follow an approach to use thin electron slices, which are carefully generated to provide the correct shot-noise but which also prevents them from mixing and re-sorting the macro-particle distribution. The FEL code Genesis 1.3 has been modified to allow resolution of each individual electron. Using this approach the correct shot noise at all frequencies is provided and permits "re-binning" of the particles to the 3D radiation grid at any time. The results for self-seeding and HGHG seeding are discussed.