FEL Theory
Paper Title Page
WEP048 Coherent Undulator Radiation From a Kicked Electron Beam 1
  • J.P. MacArthur, Z. Huang, J. Krzywinski, A.A. Lutman
    SLAC, Menlo Park, California, USA
  The properties of off-axis radiation from an electron beam that has been kicked off axis are relevant to recent Delta undualtor experiments at LCLS. We calculate the coherent emission from a microbunched beam in the far-field, and compare with simulation. We also present a mechanism for microbunches to tilt toward a new direction of propagation.  
Stimulated Emission/Absorption of Radiation by a Single Electron Quantum Wavepacket  
  • A. Gover, Y. Pan
    University of Tel-Aviv, Faculty of Engineering, Tel-Aviv, Israel
  Funding: Partial support by Deutsche-Israelische Projektkooperation (DIP) and US-Israel Binational Science Foundation (BSF).
We analyze the stimulated (emission/absorption) interaction of a single electron quantum wavepacket with coherent radiation, using perturbation theory and numerical solution. The analysis applies to a wide class of free electron radiative-interaction schemes, and is exemplified for Smith-Purcell radiation. Contrary to spontaneous emission, stimulated radiative interaction depends on the wavepacket characteristics in a certain quantum range. If the electron drifts beyond a critical length, then dimension-dependent acceleration of the wavepacket is fundamentally impossible because of the wavepacket spread. Below this range, such acceleration is possible, approaching the limit of classical 'point particle' linear acceleration, at the conditions of small wavepacket dimensions relative to the radiation wavelength and multi-photon exchange. Our analysis emulates the FEL gain in the limit of negligible recoil, and the quantum momentum recoil sidebands characteristics of PINEM - when recoil effect is significant. We use the platform for discussing the fundamental physics question of measurability of the quantum wavepacket size and the limitation of the classical 'white' shot-noise model.
Three-Dimensional, Time-Dependent Simulation of Free-Electron Lasers with Planar, Helical, and Elliptical Undulators  
  • H. Freund
    CSU, Fort Collins, Colorado, USA
  • P. Falgari
    Lime BV, Eindhoven, The Netherlands
  • D.L.A. Grimminck, I. Setya
    ASML, Veldhoven, The Netherlands
  • P.J.M. van der Slot
    Mesa+, Enschede, The Netherlands
  Free-electron lasers have been built ranging from long-wavelength oscillators through ultraviolet to hard x-ray that are either seeded or SASE. In addition, FELs that produce different polarizations ranging from linear through elliptic are currently under study. In this paper, we develop a 3D, time-dependent formulation that is capable of modeling this large variety of FEL configurations including different polarizations.* We employ a modal expansion for the optical field, i.e., a Gaussian expansion with variable polarization for free-space propagation. The formulation uses the Lorentz force equations to track particles. Arbitrary 3D representations for different undulators are implemented, including planar, helical, and elliptical. To model oscillators and allow propagation outside the undulator and interaction with optical elements, we link the FEL simulation with the optical propagation code OPC. We present detailed comparisons with experiments including (1) the LCLS, (2) the SPARC SASE FEL experiment at ENEA Frascati, (3) a seeded-tapered amplifier experiment at Brookhaven National Laboratory, and (4) the 10-kW Upgrade Oscillator experiment at Jefferson Laboratory.
* H.P. Freund, P.J.M. van der Slot, D.L.A.G. Grimminck, I.D. Setya, and P. Falgari, New J. Phys. 19, 023020 (2017).
Simulation of a Terawatt X-Ray Free-Electron Laser  
  • H. Freund
    CSU, Fort Collins, Colorado, USA
  The possibility of constructing terawatt x-ray free-electron lasers (FELs) has been discussed using novel superconducting helical undulators.* In this paper, we consider the conditions necessary for achieving powers in excess of 1 TW in a 1.5 Å FEL using the MINERVA simulation code.** Steady-state simulations have been conducted using a variety of undulator and focusing configurations. In particular, strong focusing using FODO lattices is compared with the natural, weak focusing inherent in helical undulators. It is found that the most important requirement to reach TW powers is extreme transverse compression of the electron beam in a strong FODO lattice.
* C. Emma, K. Fang, J. Wu, and C. Pellegrini, Phys. Rev. Accel. Beams, 19, 020705 (2016).
** H. Freund, P. van der Slot, D. Grimminck, I. Setya, and P. Falgari, New J. Phys. 19, 023020 (2017).
Distortion of the Spatial Properties of the Radiation from Seeded and SASE FEL Caused by Energy Chirp in the Electron Beam and Undulator Tapering  
  • E. Schneidmiller, M.V. Yurkov
    DESY, Hamburg, Germany
  Knowledge of the spatial properties of the radiation properties is a key issue for the users of x-ray FEL facilities. In this report, we present a detailed analysis of the spatial properties of the radiation from an FEL amplifier. Two configurations, seeded FEL amplifier, and SASE FEL, are under consideration. Dependence of the spatial distributions on the electron beam properties is studied, and their evolution along the undulator is traced. It is shown that spatial properties of the radiation may be significantly affected by the effect of energy chirp in the electron beam and undulator tapering.  
WEP073 Lie Map Formalism for FEL Simulation 1
  • K. Hwang, J. Qiang
    LBNL, Berkeley, California, USA
  Funding: U.S. Department of Energy under Contract No. DE-AC02-05CH11231
Undulator averaging and non-averaging are in compromisation between computational speed and reliability. It is hard to catch the advantages of the both methods simultaneously. In this report, we present a method that compromises the between the averaging and non-averaging methods through Lie map formalism.
WEP074 Simulations of the Dependence of Harmonic Radiation on Undulator Parameters 1
  • G. Penn
    LBNL, Berkeley, California, USA
  Funding: This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
The flux and bandwidth of radiation produced at harmonics of the fundamental are very sensitive to the undulator parameter, and thus the beam energy or undulator period. We look at high-energy XFELs with parameters relevant to the MaRIE FEL design. Both SASE and seeded FELs are considered.
poster icon Poster WEP074 [0.410 MB]  
WEP078 Period-Averaged Symplectic Maps for the FEL Hamiltonian 1
  • S.D. Webb
    RadiaSoft LLC, Boulder, Colorado, USA
  Funding: This work was carried out with support for the United State Department of Energy, Office of Scientific Research, under SBIR contract number DE-SC0017161.
Conventional treatments of synchrotron radiation in electron beams treat the radiation as a non-Hamiltonian aspect to the beam dynamics. However, the radiation can be modeled with an electromagnetic Hamiltonian. We present a period-averaged treatment of the FEL problem which includes the Hamiltonian aspects of the coupled electron-radiation dynamics. This approach is then applied to two problems: a 3D split-operator symplectic integrator, and a 1D single-mode FEL treated using Hamiltonian perturbation theory.
High-Efficiency, Tapered FELs with a Pre-Bunched Electron Beam  
  • C. Emma, P. Musumeci, C. Pellegrini, N.S. Sudar, A. Urbanowicz
    UCLA, Los Angeles, USA
  • C. Pellegrini
    SLAC, Menlo Park, California, USA
  We study the 1-D physics of high gain, high efficiency tapered FELs in the post-saturation regime.*,** We derive a basic scaling formula for the FEL output power as a function of the beam current, the seed power and the trapping fraction assuming a constant resonant phase. We examine this analytic scaling using 1-D simulations for a seeded FEL starting from a large seed with a small energy spread electron beam (fresh bunch) with/without pre-bunching. We show that the efficiency improves substantially when the electron beam is suitably pre-bunched compared to the unbunched case. Finally, we study the sideband instability growth via 1-D time-dependent simulations. We confirm the inverse proportionality of the sideband power to the resonant phase as discussed in KMR. We also propose a method of sideband suppression via gain-modulation of the FEL using a modulated taper profile.***
* N. M. Kroll, P. L. Morton, and M. Rosenbluth. Quantum Electronics 17(8): 1436-1468, August 1981.
** R. Iaconescu, at this conference.
*** Marinelli et al., PRL 111: 134801 (2015).
FRB01 Time-Domain Analysis of Attosecond Pulse Generation in an X-Ray Free-Electron Laser 1
  • P. Baxevanis, Z. Huang, A. Marinelli
    SLAC, Menlo Park, California, USA
  The method of enhanced self-amplified spontaneous emission (eSASE) is one of the strongest candidates for the generation of sub-femtosecond X-ray pulses in a free-electron laser. The optimization of an eSASE experiment involves many independent parameters, which makes the exploration of the parameter space with 3-D simulations computationally intensive. Therefore, a robust theoretical analysis of this problem is extremely desirable. We provide a self-consistent, analytical treatment of such a configuration using a one-dimensional, time-dependent FEL model that includes the key effects of linear e-beam chirp and linear undulator taper. Verified via comparison with numerical simulation, our formalism is also utilized in parameter studies that seek to determine the optimum setup of the FEL.  
Theory and Simulation of FELs with Planar, Helical, and Elliptical Undulators  
  • H. Freund
    CSU, Fort Collins, Colorado, USA
  • L.T. Campbell
    STFC/DL/ASTeC, Daresbury, Warrington, Cheshire, United Kingdom
  • P. Falgari
    Lime BV, Eindhoven, The Netherlands
  • D.L.A. Grimminck, I. Setya
    ASML, Veldhoven, The Netherlands
  • J. Henderson, B.W.J. MᶜNeil
    USTRAT/SUPA, Glasgow, United Kingdom
  • P.J.M. van der Slot
    Mesa+, Enschede, The Netherlands
  Free-electron lasers (FELs) that produce different polarizations of the output radiation ranging from linear through elliptic to circular polarization are currently under study. In particular, elliptic polarizations are undergoing increased interest. In this paper, we develop an analytic model of the resonant wavelength and JJ-factor for an elliptic undulator as well as both one- and three-dimensional, time-dependent formulations that are capable of simulating elliptic undulators using the PUFFIN and MINERVA simulation codes.*,** We present an analytic model of an APPLE-II undulator that is capable of modeling arbitrary elliptic polarizations, and discuss examples of simulation results.
* J. Henderson, L. Campbell, H. Freund, and B. McNeil, New J. Phys. 18, 062003 (2016).
** H. Freund, P. van der Slot, D. Grimminck, I. Setya, and P. Falgari, New J. Phys. 19, 023020 (2017).
FRB03 Dynamics of Superradiant Emission by a Prebunched E-Beam and its Spontaneous Emission Self-Interaction 1
  • R. Ianconescu, A. Gover
    University of Tel-Aviv, Faculty of Engineering, Tel-Aviv, Israel
  • C. Emma, P. Musumeci
    UCLA, Los Angeles, USA
  • A. Friedman
    Ariel University, Ariel, Israel
  Funding: Partial support by US-Israel Binational Science Foundation (BSF) and by Deutsche-Israelische Projektkooperation (DIP).
In the context of radiation emission from an electron beam, Dicke's superradiance (SR) is the enhanced coherent spontaneous radiation emission from a prebunched beam, and Stimulated-Superradiance (ST-SR) is the further enhanced emission of the bunched beam in the presence of a phase-matched radiation wave.* These processes are analyzed for undulator radiation in the framework of radiation field mode-excitation theory. In the nonlinear saturation regime the synchronicity of the bunched beam and an injected radiation wave may be sustained by wiggler tapering: Tapering-Enhanced Superradiance (TES) and Tapering-Enhanced Stimulated Superradiance Amplification (TESSA).** Identifying these processes is useful for understanding the enhancement of radiative emission in the tapered wiggler section of seeded FELs.***,**** The nonlinear formulation of the energy transfer dynamics between the radiation wave and the bunched beam fully conserves energy. This includes conservation of energy without radiation reaction terms in the interesting case of spontaneous self-interaction (no input radiation).
* A. Gover, Phys. Rev. ST-AB 8, 030701 (2005).
** J. Duris et al., New J.Phys. 17 063036 (2015).
*** E. A. Schneidmiller et al., PRST-AB 18, 03070 (2015).
**** C. Emma et al., this conference.
slides icon Slides FRB03 [2.656 MB]  
FRB04 Canonical Formulation of 1D FEL Theory Revisited, Quantized and Applied to Electron Evolution 1
  • P.M. Anisimov
    LANL, Los Alamos, New Mexico, USA
  An original FEL theory relied on quantum analysis of photon generation by relativistic electrons in alternating magnetic field.* In most cases, however, the system of pendulum equations for non-canonical variables and the theory of classical electromagnetism proved to be adequate. As XFELs advance to higher energy photons, quantum effects of electron recoil and shot noise has to be considered. This work presents quantization procedure based on the Hamiltonian formulation of an XFEL interaction in 1D case. The procedure relates the conventional variables to canonical coordinates and momenta and does not require the transformation to the Bambini-Renieri frame.** The relation of a field operator to a photon annihilation operator reveals the meaning of the quantum FEL parameter, introduced by Bonifacio, as a number of photons emitted by a single electron before the saturation takes place.*** The quantum description is then applied to study how quantum nature of electrons affects the startup of XFEL and how quantum electrons become indistinguishable from a classical ensemble of electrons due to their interaction with a ponderomotive potential of an XFEL.
* Madey JMJ 1971 J. Appl. Phys. 42 1906 13.
** Bambini A and Renieri A 1978 Lett. Nuovo Cimento 21 399-404.
*** Bonifacio R, Piovella N, Robb G R M and Schiavi A 2006 PRSTAB 9 090701.
FRB05 Wide Bandwidth, Frequency Modulated Free Electron Laser 1
  • L.T. Campbell, B.W.J. MᶜNeil
    USTRAT/SUPA, Glasgow, United Kingdom
  The resonant frequency of a free electron laser may be modulated via the undulator or electron beam parameters. This modulation may generate sidebands which can subsequently undergo amplification, analogous to frequency modulation in a conventional cavity laser. However, due to the relative slippage of the light through the relativistic electron beam, the FM-FEL system has a more complex behavior than its conventional laser counterpart. The system may be described in the linear regime by a summation over exponential gain modes, allowing the amplification of multiple light frequencies simultaneously. It is found that, with only small, few percent variations of the FEL parameters, one may generate and amplify multiple modes within a frequency bandwidth which greatly exceeds that of normal FEL operation.