Paper  Title  Page 

WEP048  Coherent Undulator Radiation From a Kicked Electron Beam  1 


The properties of offaxis 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 farfield, and compare with simulation. We also present a mechanism for microbunches to tilt toward a new direction of propagation.  
WEP049 
Stimulated Emission/Absorption of Radiation by a Single Electron Quantum Wavepacket  


Funding: Partial support by DeutscheIsraelische Projektkooperation (DIP) and USIsrael 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 radiativeinteraction schemes, and is exemplified for SmithPurcell 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 dimensiondependent 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 multiphoton 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' shotnoise model. 

WEP068 
ThreeDimensional, TimeDependent Simulation of FreeElectron Lasers with Planar, Helical, and Elliptical Undulators  


Freeelectron lasers have been built ranging from longwavelength oscillators through ultraviolet to hard xray 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, timedependent 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 freespace 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 seededtapered amplifier experiment at Brookhaven National Laboratory, and (4) the 10kW 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). 

WEP069 
Simulation of a Terawatt XRay FreeElectron Laser  


The possibility of constructing terawatt xray freeelectron 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.** Steadystate 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). 

WEP070 
Distortion of the Spatial Properties of the Radiation from Seeded and SASE FEL Caused by Energy Chirp in the Electron Beam and Undulator Tapering  


Knowledge of the spatial properties of the radiation properties is a key issue for the users of xray 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 


Funding: U.S. Department of Energy under Contract No. DEAC0205CH11231 Undulator averaging and nonaveraging 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 nonaveraging methods through Lie map formalism. 

WEP074  Simulations of the Dependence of Harmonic Radiation on Undulator Parameters  1 


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. DEAC0205CH11231. 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 highenergy XFELs with parameters relevant to the MaRIE FEL design. Both SASE and seeded FELs are considered. 

Poster WEP074 [0.410 MB]  
WEP078  PeriodAveraged Symplectic Maps for the FEL Hamiltonian  1 


Funding: This work was carried out with support for the United State Department of Energy, Office of Scientific Research, under SBIR contract number DESC0017161. Conventional treatments of synchrotron radiation in electron beams treat the radiation as a nonHamiltonian aspect to the beam dynamics. However, the radiation can be modeled with an electromagnetic Hamiltonian. We present a periodaveraged treatment of the FEL problem which includes the Hamiltonian aspects of the coupled electronradiation dynamics. This approach is then applied to two problems: a 3D splitoperator symplectic integrator, and a 1D singlemode FEL treated using Hamiltonian perturbation theory. 

WEP079 
HighEfficiency, Tapered FELs with a PreBunched Electron Beam  


We study the 1D physics of high gain, high efficiency tapered FELs in the postsaturation 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 1D simulations for a seeded FEL starting from a large seed with a small energy spread electron beam (fresh bunch) with/without prebunching. We show that the efficiency improves substantially when the electron beam is suitably prebunched compared to the unbunched case. Finally, we study the sideband instability growth via 1D timedependent 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 gainmodulation of the FEL using a modulated taper profile.***
* N. M. Kroll, P. L. Morton, and M. Rosenbluth. Quantum Electronics 17(8): 14361468, August 1981. ** R. Iaconescu, at this conference. *** Marinelli et al., PRL 111: 134801 (2015). 

FRB01  TimeDomain Analysis of Attosecond Pulse Generation in an XRay FreeElectron Laser  1 


The method of enhanced selfamplified spontaneous emission (eSASE) is one of the strongest candidates for the generation of subfemtosecond Xray pulses in a freeelectron laser. The optimization of an eSASE experiment involves many independent parameters, which makes the exploration of the parameter space with 3D simulations computationally intensive. Therefore, a robust theoretical analysis of this problem is extremely desirable. We provide a selfconsistent, analytical treatment of such a configuration using a onedimensional, timedependent FEL model that includes the key effects of linear ebeam 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.  
FRB02 
Theory and Simulation of FELs with Planar, Helical, and Elliptical Undulators  


Freeelectron 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 JJfactor for an elliptic undulator as well as both one and threedimensional, timedependent formulations that are capable of simulating elliptic undulators using the PUFFIN and MINERVA simulation codes.*,** We present an analytic model of an APPLEII 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 EBeam and its Spontaneous Emission SelfInteraction  1 


Funding: Partial support by USIsrael Binational Science Foundation (BSF) and by DeutscheIsraelische 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 StimulatedSuperradiance (STSR) is the further enhanced emission of the bunched beam in the presence of a phasematched radiation wave.* These processes are analyzed for undulator radiation in the framework of radiation field modeexcitation theory. In the nonlinear saturation regime the synchronicity of the bunched beam and an injected radiation wave may be sustained by wiggler tapering: TaperingEnhanced Superradiance (TES) and TaperingEnhanced 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 selfinteraction (no input radiation). * A. Gover, Phys. Rev. STAB 8, 030701 (2005). ** J. Duris et al., New J.Phys. 17 063036 (2015). *** E. A. Schneidmiller et al., PRSTAB 18, 03070 (2015). **** C. Emma et al., this conference. 

Slides FRB03 [2.656 MB]  
FRB04  Canonical Formulation of 1D FEL Theory Revisited, Quantized and Applied to Electron Evolution  1 


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 noncanonical 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 BambiniRenieri 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 399404. *** Bonifacio R, Piovella N, Robb G R M and Schiavi A 2006 PRSTAB 9 090701. 

FRB05  Wide Bandwidth, Frequency Modulated Free Electron Laser  1 


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 FMFEL 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.  