Paper  Title  Page 

MOC01  Circular Polarization Control by Reverse Undulator Tapering  297 


In order to produce circularly polarized light at Xray FEL facilities one can consider an installation of a short helical (or crossplanar) afterburner, but then one should have an efficient method to suppress powerful linearly polarized background from the main undulator. We propose a new method for such a suppression: an application of the reverse taper in the main undulator. We discover that in a certain range of the taper strength, the density modulation (bunching) at saturation is practically the same as in the case of nontapered undulator while the power of linearly polarized radiation is suppressed by orders of magnitude. Then strongly modulated electron beam radiates at full power in the afterburner. Considering SASE3 undulator of the European XFEL as a practical example, we demonstrate that soft Xray radiation pulses with peak power in excess of 100 GW and an ultimately high degree of circular polarization can be produced. The method can be used at different Xray FEL facilities, in particular at LCLS after installation of the helical afterburner in the near future.  
Slides MOC01 [1.545 MB]  
MOC02 
Correlated Energy Spread Removal with Space Charge for High Gain Harmonic Generation  


We study the effect of longitudinal space charge on the correlated energy spread of a relativistic beam that has been microbunched for the emission of coherent, high harmonic radiation. We show that, in the case of microbunching induced by a laser modulator followed by a dispersive chicane, longitudinal space charge forces can act to significantly reduce the induced energy spread of the beam without a reduction in the harmonic bunching content. This effect may be optimized to significantly increase the harmonic number achievable in seeded HGHG free electrons lasers, which are otherwise limited by the induced energy spread from the laser.
The work presented here has been published in Reference [1]. [1] E. Hemsing et al., to appear in Phys. Rev. Lett. (2014) 

Slides MOC02 [4.092 MB]  
MOC03  Radiation Properties of Tapered Hard Xray Free Electron Lasers  300 


We perform an analysis of the transverse coherence of the radiation from a TW level tapered hard Xray Free Electron Laser (FEL). The radiation properties of the FEL are studied for a Gaussian, parabolic and uniform transverse electron beam density profile in a 200m undulator at a resonant wavelength of 1.5 Angstrom. Simulations performed using the 3D FEL particle code GENESIS show that diffraction of the radiation occurs due to a reduction in optical guiding in the tapered section of the undulator. This results in an increasing transverse coherence for all three transverse electron beam profiles. We determine that for each case considered the radiation coherence area is much larger than the electron beam spot size, making Xray diffraction experiments possible for TW Xray FELs.  
Slides MOC03 [3.797 MB]  
MOC04  Chirped and Modulated Electron Pulse Free Electron Laser Techniques  303 


Funding: We acknowledge STFC MoA 4132361; ARCHIEWeSt HPC, EPSRC grant EP/K000586/1; John von Neumann Institute for Computing (NIC) on JUROPA at Jlich Supercomputing Centre (JSC), under project HHH20 A potential method to improve the free electron laser's output when the electron pulse has a large energy spread is investigate and results presented. A simplified model is the first given, in which there are a number of linearly chirped beamlets equally separated in energy and time. By using chicanes, radiation from one chirped beamlet is passed to the next, helping to negate the effect of the beamlet chirps and maintaining resonant interactions. Hence the addition of chicane allow the electrons to interact with a smaller range of frequencies (Δ ω <2 ρ γ_{r}), sustaining the FEL interaction. One method to generate such a beamlet structure is presented and is shown to increase FEL performance by two orders of magnitude. 

Slides MOC04 [6.777 MB]  
TUP002  Characterization of Partially Coherent Ultrashort FEL Pulses  346 


Temporal metrology is a major need for freeelectron lasers. However, the lack of longitudinal coherence, that is shottoshot fluctuations, of these sources has prevented so far the full amplitude and phase temporal characterization of FEL pulses. To sort out this issue, we propose a solution inspired from attosecond metrology, where XUV pulse measurement techniques already exist, and from coherent diffraction imaging, where numerical solutions have been developed for processing partially coherent diffraction patterns. The experimental protocole implies the measurement of photoelectron spectra obtained through XUVlaser photoionisation. The spectra are then processed with an algorithm in order to retrieve the partially coherent FEL pulse. When applied to SASE FELs, the technique gives access to the full statistics of the emitted pulses. With seededFELs, the pulse shape becomes stable from shottoshot, but an XUVlaser time jitter remains. In that case, the technique enables the joint measurement of the FEL pulse shape (in amplitude and phase) and of the laser/FEL jitter envelope. The concept has been validated with numerical simulations in the context of the LUNEX5 FEL project.  
TUP003  Quantum FEL II: Manyelectron Theory  348 


We investigate the emergence of the quantum regime of the FEL when many electrons interact simultaneously with the wiggler and the laser field. We find the Quantum FEL as the limit where only two momentum states are populated by the electrons. Moreover, we obtain exponential gainperpass and startup from vacuum.  
TUP004  Quantum FEL I: Multimode Theory  353 


The quantum regime of the FEL in a singlemode, singleparticle approximation is characterized by a twolevel behaviour of the centerofmass motion of the electrons. We extend this model to include all modes of the radiation field and analyze the effect of spontaneous emission. In particular, we investigate this scattering mechanism to derive experimental conditions for realizing an FEL in the quantum regime.  
TUP006  Twocolor Freeelectron Laser via Two Orthogonal Undulators  358 


An amplifier Free electron Laser (FEL) including two orthogonal polarized undulators with different periods and field intensities is able to emit two color radiations with different frequency and polarization while the total length of device does not change respect to usual single color FELs. The wavelengths of two different colors can be changed by choosing different periods, while variation in the magnetic strengths can be used to modify the gain lengths.  
TUP007  Spectral Limits and Frequency Sumrule of Current and Radiation Noise Measurement  362 


Funding: This research was supported by a grant from the United StatesIsrael Binational Science Foundation(BSF), Jerusalem, ISRAEL The current noise spectrum of an electron beam is generally considered white and expressed by the shotnoise formula (eI0). It is possible to control the spectral energy of a random electron beam current by longitudinal space charge microdynamics and dispersive transport. Both noise suppression (relative to eI0)[1,2] and noise enhancement[3] have been demonstrated, exhibiting sub/superPoissonian particle distribution statistics, respectively. We present a general theory for the current noise of an ebeam and its radiation emission in the entire spectrum. The measurable current noise spectrum is not white. It is cutoff at high frequencies, limited by the measurement length and the beam axial momentum spread (fundamentally limited by quantum uncertainty). We show that under certain conditions the current noise spectrum satisfies a frequency sumrule: exhibiting noise enhancement in one part of the spectrum when suppressed at another part and vice versa. The spontaneous emission (radiation noise) into a single radiation mode or single direction in any scheme (OTR, Undulator etc.) is subradiant when the beam current is subPoissonian and vice versa, but the sumrule does not apply. 

TUP008  An Analysis of Optimum Outcoupling Fraction for Maximum Output Power in Oscillator FEL  368 


The effect of the outcoupling fraction on the output power in oscillator FEL is analyzed. The formulas of the optimum outcoupling fraction and the corresponding maximum output power are given. They are dependent on the initial small signal gain and the passive loss rate of the light in the optical cavity. The initial comparison show that the result given by the formula agree well with the results in references.  
TUP009  A Simple Method for Generating a Few Femtosecond Pulses in Seeded FELs  371 


Funding: Work supported by Major State Basic Research Development Program of China (2011CB808301) and the Fundamental Research Funds for the Central Universities of China (WK2310000045) We propose a simple method to generate a few femtosecond pulses in seeded FELs. We use a longitudinal energychirped electron beam passing through a dogleg where transverse dispersion will generate a horizontal energy chirp, then in the modulator, a seed laser with narrow beam radius will only modulate the centre part of electron beam and short pulses in high harmonics will be generated in the radiator. Using a representative realistic set of parameters, we show that 30 nm XUV pulse with duration of 8 femtoseconds (FWHM) and peak power of GW level can be generated from a 180 nm UV seed laser with beam waist of 75 m. 

TUP012  Numerical Simulation of a Superradiant THz Source Driven by Femtosecond Electron Bunches  374 


Funding: We would like to acknowledge the financial support from the Swedish FEL center. Pulsed THz FELs are typically driven by rf Linacs which produce intense electron bunches with a duration of a few picoseconds or even shorter. When the bunch duration is less than a picosecond, the wavelength of the THz light is greater than the bunch length and the FEL operates in the superradiant (SR) regime*. In the report, we summarize our studies performed for an SR source operating in the THz frequency range. In particular, we focus on an opentype planar undulator comprising no guiding structure. Using a numerical code that supports 3D modeling of the SR dynamics as well as statistical properties of electron bunches, we analyze influence of electron bunch parameters on generated THz radiation and reveal some surprising results. More specifically, for the considered undulator configuration, we predict degradation in the angular divergence and spectral broadening of the generated radiation as the electron bunch emittance decreases. We also demonstrate how electron bunch broadening associated with the electron energy spread can eventually be suppressed. * R. Chulkov, V. Goryashko, and V. Zhaunerchyk, Report III of the series of reports by the Swedish FEL Center and FREIA Group, http://www.divaportal.org/smash/get/diva2:699684/FULLTEXT01.pdf. 

Poster TUP012 [1.553 MB]  
TUP013  XRay SmithPurcell Radiation from a Beam Skimming a Grating Surface  378 


SmithPurcell radiation as a base of Free Electron Lasers is actively studied experimentally and by simulating. Usually the beam is supposed to move at some distance above the target. In practice the distance is tried to decrease so that the beam passes very close to the target surface. Experimental data contains the information about grating heating. The authors of article* suggested the cause of the heating is that the beam skims the grating surface. Developing the method used in**,*** we give the analytical description of the XRay radiation arising when the beam of charge particles moves parallel above the periodical target, but the part of the beam crosses the target. The radiation arising is the superposition of SmithPurcell radiation and transition radiation from the grating. This radiation determines the process of beam bunching and following gain of radiation.
*H.L.Andrews et al,Phys. Rev. ST AB 12 (2009) 080703 **A.A.Tishchenko, A.P.Potylitsyn, M.N.Strikhanov, Phys. Rev. E 70 (2004) 066501 ***D.Yu.Sergeeva, A.A.Tishchenko, M.N.Strikhanov, NIM B 309 (2013) 189 

TUP014  Forward XRay and Ultraviolet SmithPurcell Radiation for FEL  384 


The scheme of Free Electron Lasers based on SmithPurcell effect is well known to describe the process of interaction between an electron beam and evanescent wave, which bunches this beam. In this work we concentrate on the process of generation of the radiation propagating at small angles. In terms of approach described in detail in*,**, we investigate the SmithPurcell radiation at oblique incidence of a single charged particle for XRay and UV frequency region. This forward radiation propagates through all the region of the beam moving and provides more close interaction between the beam and the radiation, than usual surface waves existing in FELs. Spectral and angular characteristics of the forward radiation are discussed from point of view its role in SmithPurcell based FELs.
*A.P.Potylitsyn, M.I.Ryazanov, M.N.Strikhanov, A.A.Tishchenko, Diffraction Radiation from Relativistic Particles, Springer, 2011 **D.Yu.Sergeeva, A.A.Tishchenko, M.N.Strikhanov, NIM B 309 (2013) 189 

TUP015  Radiation and Interaction of Layers in Quasiplane Electron Bunches Moving in Undulators  388 


The model of radiating planes (1D radiating gas) consisting of electrons that oscillate and travel with a relativistic translational velocity allows one to develop a simple general theory describing a number of important effects of radiation in a undulator for dense electron bunches formed in photoinjector accelerators. Having based on this method and taking into account both Coulomb and radiation interactions of the planes with an arbitrary density, particle velocity distribution and energy chirp we have found analytically and numerically efficiency and frequency spectrum for coherent spontaneous radiation, including conditions for generation of minimum narrow and very broadband spectra. The developed theory has been applied for estimation of a powerful terahertz radiation source with a moderate energy of electrons.  
TUP016  Quasioptical Theory of Terahertz Superradiance from an Extended Electron Bunch  391 


Funding: This study was supported by the Russian Foundation for Basic Research (project no. 140801180) and the Dynasty Foundation. We consider superradiance of an extended relativistic electron bunch moving over a periodically corrugated surface for the generation of multimegawatt terahertz pulses*. To study the above process we have developed a threedimensional, selfconsistent, quasioptical theory of Cherenkov stimulated emission which includes a description of the formation of evanescent waves near the corrugated surface and its excitation by RF current induced in the electron bunch. Results obtained in the framework of a quasioptical model were confirmed by direct CST STUDIO PIC simulations. There is a possibility of advancement towards still shorter wavelengths (infrared and optical), which can be achieved by decreasing the period of the diffraction gratings and increasing the density and energy of the particles in the electron bunches. Increase of coupling impedance can be obtained by using inclined incidence of electron bunch on corrugated surface (clinotron configuration). Ginzburg N.S et al. Phys. Rev. Lett. 2013. V.110, Iss.18. 184801. 

TUP017  Using Lorentz Transformations for Simulations of Wiggler Superradiance from the Picosecond Electron Bunches  395 


Funding: This work was supported by Russian Foundation for Basic Research under Grant No 120201152. In this paper we present a theoretical analysis of superradiance (SR) from picosecond electron bunches wiggling in periodical undulator field based both on the method of averaged ponderomotive force and on a direct numerical PIC (particleincell) simulation. Within both approaches the analysis takes place in the reference frame comoving with electrons which allows simplifying the procedure of simulation significantly due to the fact that all the spatial scales including the radiation wavelength, the length of the beam and the length of the pump field pacet into which the undulator field is transformed are of the same order. We show that in the reference frame the SR effect can be interpreted as a formation of the distributed Bragg mirror in the bulk of the electron beam which is effectively reflecting (scattering) the pump wave. A possibility of generation of multimegawatt pulses in terahertz and far infrared wave ranges is demonstrated. 

TUP018  Sensitivity Study of a Tapered FreeElectron Laser  399 


The output power of a freeelectron laser (FEL) can be greatly enhanced by tapering the undulator line. In this work, a sensitivity study of a tapered FEL is presented. The study is conducted using the numerical simulation code GENESIS and a taper optimization method. Starting from a possible case for the future Xray FEL at the MAX IV Laboratory in Lund, Sweden, a number of parameters are varied systematically and the impact on the FEL power is investigated. These parameters include the electron beam's initial energy, current, emittance, energy spread, as well as the seed radiation power.  
TUP019  Update on the FEL Code Genesis 1.3  403 


The widely used timedependent code Genesis 1.3 has been modified to address new needs of users worldwide. The existing limitation of tracking isolated slices of the FEL beam has been overcome by keeping the entire electron beam in memory, which is tracked as a whole through the undulator. This modification allows for additional features such as allowing particles to migrate into other slices or applying selfconsistent wakefield and space charge models.  
TUP020  MINERVA, a New Code to Model FreeElectron Lasers  408 


Simulation codes modelling the interaction of electrons with an optical field inside an undulator are an essential tool for understanding and designing freeelectron lasers (FELs). As there exists a large variety of FELs ranging from longwavelength oscillators using partial wave guiding to soft and hard xray FELs that are either seeded or starting from noise, a simulation code should be capable of modelling this huge variety of FEL configurations. A new code under development, named MINERVA, will be capable of modelling such a large variety of FELs. The code uses a modal expansion for the optical field, e.g., a Gaussian expansion for freespace propagation, and an expansion in waveguide modes for propagation at long wavelengths, or a combination of the two for partial guiding at THz frequencies. MINERVA uses the full NewtonLorentz force equation to track the particles through the optical and magnetic fields. To allow propagation of the optical field outside the undulator and interact with optical elements, MINERVA interfaces with the optical propagation code OPC to model oscillators. Here we describe the main features of MINERVA and give various examples of its capabilities.  
TUP021  Recent Updates to the Optical Propagation Code OPC  412 


Funding: This research is supported in part by Office of Naval Research Global, grant number N629091017151 In order to understand and design freeelectron lasers (FELs), simulation codes modeling the interaction of electrons with a copropagating optical field in the magnetic field of an undulator are essential. However, propagation of the optical field outside the undulator is equally important for evaluation of the optical field at the location of the application or to model FEL oscillators. The optical propagation code OPC provides such capabilities and can interface with FEL gain codes like GENESIS 1.3, MEDUSA and MINERVA. Here we present recent additions and modifications to the code that (i) improves the speed of the code and (ii) extends the modeling capabilities. These include amongst other, inline diagnostics that results in considerable faster runtimes, the ability to convert from freespace modes to guided modes (currently only cylindrical waveguides), and the possibility to determine the spectrum at each transverse location. The latter opens the possibility to include dispersion in the optical propagation. Finally, work is underway to support HDF5 to remain compatible with the upcoming new release of GENESIS 1.3. 

TUP022  The Implementation of 3D Undulator Fields in the Unaveraged FEL Simulation Code Puffin  416 


Funding: We acknowledge STFC MoA 4132361; ARCHIEWeSt HPC, EPSRC grant EP/K000586/1; John von Neumann Institute for Computing (NIC) on JUROPA at Jlich Supercomputing Centre (JSC), under project HHH20 The FEL simulation code Puffin is modified to include 3D magnetic undulator fields. Puffin, having previously used a 1D undulator field, is modified to accommodate general 3D magnetic fields. Both plane and curved pole undulators have been implemented. The electron motion for both agrees with analytic predictions. 

TUP023  Modeling CSR in a Vacuum Chamber by Partial Fourier Analysis and the Discontinuous Galerkin Method  419 


Funding: Work supported by DOE contracts DEFG99ER41104 and DEAC0376SF00515. We continue our study of CSR* from a bunch on an arbitrary curved orbit in a plane, which used a Fourier transform in sct. The vacuum chamber has rectangular cross section with possibly varying horizontal width. We use the slowly varying amplitude approximation, and invoke a Fourier expansion in the vertical coordinate y, which meets the boundary conditions on the top and bottom plates and makes contact with the Bessel equation of the frequency domain treatment. The fields are defined by a PDE in s and x, first order in s, which is discretized in x by finite differences (FD) or the discontinuous Galerkin method (DG). We compare results of FD and DG, and also compare to our earlier calculations in 3D (paraxial) which did not use the Fourier series in y*,**. This approach provides more transparency in the physical description, and when only a few ymodes are needed, provides a large reduction in computation time. * See FEL13 Proceedings MOPSO06: http://accelconf.web.cern.ch/AccelConf/FEL2013/papers/mopso06.pdf ** See PRSTAB 7 054403 (2004) and Jpn. J. Appl. Phys. 51 016401 (2012). 

TUP024 
Simple Quantum Mechanical Derivation of FEL Gain  


Funding: This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences under contract No. DEAC0206CH11357 A quantum mechanical derivation of FEL gain in low gain regime is presented. Although nothing new and probably well known to experts, the derivation given here uses two basic principles of physics: (1) energy conservation and (2) the fact that the matrix elements of the photon creation a+ or annihilation operator a between two states of photon number n1 and n2 is proportional to the square root of n1, which is the greater of n1 and n2. The simplicity of this derivation may have some pedagogical value. 

TUP025  TW Xray Free Electron Laser Optimisation by Transverse Pulse Shaping  425 


We study the dependence of the peak power of a 1.5 Angstrom TW, tapered Xray freeelectron laser on the transverse electron density distribution. Multidimensional optimization schemes for TW hard XRay free electron lasers are applied to the cases of transversely uniform and parabolic electron beam distributions and compared to a Gaussian distribution. The optimizations are performed for a 200 m undulator and a resonant wavelength of 1.5 Angstrom using the fully 3dimensional FEL particle code GENESIS. The study shows that the flatter transverse electron distributions enhance optical guiding in the tapered section of the undulator and increase the maximum radiation power from a maximum of 1.56 TW for a transversely Gaussian beam to 2.26 TW for the parabolic case and 2.63 TW for the uniform case. Spectral data also shows a 3070 % reduction in energy deposited in the sidebands for the uniform and parabolic beams compared with a Gaussian.  
TUP026  Transverse Coherence Properties of a TGUbased FEL  429 


The use of a transverse gradient undulator (TGU) is considered an attractive option for FELs driven by electron beams with a relatively large energy spread. In this scheme, a dispersion is introduced in the beam while the undulator poles are inclined so that the undulator field acquires a linear dependence upon the transverse position in the direction of dispersion. By suitably selecting the dispersion and the field gradient, the energy spread effect can be significantly mitigated, thus avoiding a drastic reduction in the FEL gain. However, adding the dispersion typically leads to electron beams with large aspect ratios. As a result, the presence of higherorder modes in the output FEL radiation can become significant. To investigate this effect, we study the properties of the higherorder eigenmodes of a TGUbased, highgain FEL, using both a simplified, analyticallysolvable model and a variational technique. This formalism is then used to provide an estimate of the degree of transverse coherence for a representative soft Xray, TGU FEL example.  
TUP027  Initial Value Problem for an FEL Driven by an Asymmetric Electron Beam  433 


FEL configurations in which the driving electron beam is not axially symmetric (round) are important in the study of novel concepts (such as TGUbased FELs) but also become relevant when one wishes to explore the degree to which the deviation from symmetryinevitable in practical casesaffects the performance of more conventional FEL schemes. In this paper, we present a technique for solving the initial value problem of such an asymmetric FEL. Extending an earlier treatment of ours, we start from a selfconsistent, fully 3D, evolution equation for the complex amplitude of the electric field of the FEL radiation, which is then solved by expanding the radiation amplitude in terms of a set of orthogonal transverse modes. The numerical results from such an analysis are in good agreement with simulation and provide a full description of the radiation in the linear regime. Moreover, when the electron beam sizes are constant, this approach can be used to verify the predictions of the standard eigenmode formalism.  
TUP028  Mode Contents Analysis of a Tapered Free Electron Laser  437 


For the ultimate use for the scientific experiments, the free electron laser (FEL) will propagate for long distance, much longer than the Rayleigh range, after exiting the undu lator. To characterize the FEL for this purpose, we study the electromagnetic field mode components of the FEL photon beam. With the mode decomposition, the transverse coher ence can be analyzed all along. The FEL here in this paper is a highly tapered one evolving through the exponential growth and then the postsaturation taper. Modes contents are analyzed for electron bunch with three different types of transverse distribution: flattop, Gaussian, and parabolic. The tapered FEL simulation is performed with Genesis code. The FEL photon beam transverse electric field is decom posed with GaussianLaguerre polynomials. The evolutions of spot size, source location, and the portion of the power in the fundamental mode are discussed here. The approach can be applicable to various kind scheme of FEL.  
TUP029  iSASE Study  442 


Improved Self Amplified Spontaneous Emission (iSASE) is a scheme that reduces FEL bandwidth by increasing phase slippage between the electron bunch and radiation field. This is achieved by repeatedly delaying electrons using phase shifters between undulator sections. Genesis code is modified to facilitate this simulation. With this simulation code, the iSASE bandwidth reduction mechanism is studied in detail. A Temporal correlation function is introduced to describe the similarity between the new grown field from bunching factor and the amplified shifted field. This correlation function indicates the efficiency of iSASE process.  
TUP030  Mode Component Evolution and Coherence Analysis in Terawatt Tapered FEL  446 


A fast and robust algorithm is developed to decompose FEL radiation field transverse distribution into a set of orthonormal basis. Laguerre Gaussian and Hermite Gaussian can be used in the analysis. The information of mode components strength and Gaussian beam parameters allows users in downstream better utilize FEL. With this method, physics of mode components evolution from starting stage, to linear regime and post saturation are studied with detail. With these decomposed modes, correlation function can be computed with less complexity. Eigenmodes of the FEL system can be solved using this method.  
TUP031  FEL Code Comparison for the Production of Harmonics via Harmonic Lasing  451 


Harmonic lasing offers an attractive option to significantly extend the photon energy range of FEL beamlines. Here, the fundamental FEL radiation is suppressed by various combinations of phase shifters, attenuators, and detuned undulators while the radiation at a desired harmonic is allowed to grow linearly. The support of numerical simulations is extensively used in evaluating the performance of this scheme. This paper compares the results of harmonic growth in the harmonic lasing scheme using three FEL codes: FAST, GENESIS, and GINGER.  
TUP032  FEL Simulation and Performance Studies for LCLSII  456 


The design and performance of the LCLSII freeelectron laser beamlines are presented using starttoend numerical particle simulations. The particular beamline geometries were chosen to cover a large photon energy tuning range with xray pulse length and bandwidth flexibility. Results for selfamplified spontaneous emission and selfseeded operational modes are described in detail for both hard and soft xray beamlines in the baseline design.  
TUP034 
A New 4D Model of Shortpulse FEL Oscillators  


Funding: This work has been supported by the Office of Naval Research and the High Energy Laser Joint Technology Office. At the Naval Postgraduate School, we have recently developed a new 4D (x,y,z,t) model for FEL oscillators where the pulse length is comparable to the slippage distance. The model follows multiple transverse and longitudinal optical modes over many passes through a resonator, including the effects of diffraction, pulse slippage and desynchronism. The code is parallelized to run on a cluster computer, and the resonator optics are selfcontained, so no external optics program is necessary. The mirrors and the electron beam can be shifted or tilted offaxis to study misalignment effects. This new model is useful for studying the combined effects of longitudinal and transverse modes, the trapped particle instability, and the development of sidebands. The model is currently being validated by comparison to analytic formulas and other FEL codes, as well as existing and proposed FEL experiments. Results of these studies and examples of various effects that this new model can be used to understand will be presented. 

TUP035  Investigation of Reverse Taper to Optimize the Degree of Polarization for the Delta Undulator at the LCLS  465 


Funding: U.S. Department of Energy under contract No. DEAC0276SF00515 A 3.2 m adjustable phase Delta undulator* will soon be installed on the last girder of the LCLS undulator line. The Delta undulator will act as an afterburner terminating the 33 undulator line, providing arbitrary polarization control to users. Two important figures of merit for users will be the degree of polarization and the xray yield. In anticipation of this installation, machine development time at the LCLS was devoted to maximizing the final undulator xray contrast and yield with a standard canted pole undulator acting as a stand in for the Delta undulator. Following the recent suggestion** that a reverse taper (dK/dz > 0) in the main undulator line could suppress linearly polarized light generated before an afterburner while still producing the requisite microbunching, we report on a reverse taper study at the LCLS wherein a yield contrast of 15 was measured along the afterburner. We also present 1D simulations comparing the reverse taper technique to other schemes. * Nuhn, H.D., Anderson, S., Bowden, G., Ding, Y., Gassner, G., et al., (2013). ** Schneidmiller, E. A. and Yurkov, M. V., Phys. Rev. ST Accel. Beams 16, 110702 (2013). 
