Bartolini R

Ding Y

Dunning D

Geng H

Huang Z

Thompson N

English

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POLARIZATION ANALYSIS FOR SEEDED FELSIN A CROSSED-PLANAR UNDULATORH. Geng∗1,2, R. Bartolini3, Y. Ding2, D. Dunning4, Z. Huang2, N. Thompson41National Synchrotron Radiation Laboratory, USTC, Hefei, Anhui 230029, PRC2SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA3Diamond Light Source Ltd, Oxfordshire, OX11 0DE, UK4STFC Daresbury Laboratory, Warrington, UKAbstractThe crossed-planar undulator is a promising scheme forfull polarization control in x-ray FELs. For SASE FELs,it has been shown a maximum degree of circular polariza-tion of about 80% is achievable at fundamental wavelengthjust before saturation. In this paper, we study the effective-ness of a crossed undulator for a seeded x-ray FEL. The de-gree of circular polarization for both the fundamental andthe harmonic radiation are considered. Simulations withrealistic beam distributions show that a degree of circularpolarization of over 90% and 80% is obtainable at the fun-damental and 2nd harmonic frequencies, respectively.INTRODUCTIONSeeded FELs have the advantages of narrower band-width, better temporal coherence, and more stable cen-tral wavelength over SASE FELs. Several soft x-rayFELs based on various seeding schemes have been pro-posed [1, 2]. In this wavelength range, controlling thepolarization state of the radiation has broad applicationsfor probing ultrafast magnetic phenomena and material sci-ence [3].Although polarization control can be provided by theAPPLE-type undulator, the undulator tolerance may bevery tight for lasing at ∼ 1 nm radiation wavelength, andthe slow mechanical movement of APPLE device preventsany fast-switching of polarization states. An alternativemethod is the so-called “crossed undulator” (or “crossed-planar undulator”), first proposed by K.J. Kim [4]. In thismethod circularly polarized light is obtained by interferingthe radiation fields from two adjacent planar undulators ina crossed configuration (see Fig. 1). The first undulator isnormally polarized in x and the second in y , and a phaseshifter between them is used to delay the electron beam andthus control the final polarization state. The phase shiftercan be designed to control the polarization state with a veryfast rate (> 100 Hz).The effectiveness of this method for controlling polar-ization at the fundamental wavelength in a SASE FEL wasstudied in [5]; it was found that over 80% circular polar-ization could be achieved at the end of the exponential gainregime, just before saturation. A modified crossed undu-lator scheme has also been proposed for the second har-monic radiation when the FEL reaches saturation [6]. The∗Email: genghp@mail.ustc.edu.cn.maximum degree of circular polarization is ∼ 90% and isinsensitive to the length of the first undulator.Figure 1: Schematic of the crossed undulator for polariza-tion control at the fundamental wavelength.In this paper, we study the effectiveness of a crossedundulator for a seeded x-ray FEL. The degree of circu-lar polarization for both the fundamental and the harmonicradiation with the normal and modified crossed undulatorschemes will be considered.DEGREE OF POLARIZATIONThe state of polarization can be described by the co-herency matrix [7]J =[Jxx JxyJyx Jyy]=[ 〈Ex(t)E∗x(t)〉 〈Ex(t)E∗y(t)〉〈Ey(t)E∗x(t)〉 〈Ey(t)E∗y(t)〉],(1)where Ex(t)and Ey(t) are the two components of the light,∗ means complex conjugate, and the angular bracket refersto the ensemble average. Stokes parameters are generallyused to describe the state of partially polarized light. Theyare related to the coherency matrix by [7]:S0 = Jxx + Jyy,S1 = Jxx − Jyy, (2)S2 = Jxy + Jyx = 2〈Ax(t)Ay(t)cos[θ(t)]〉,S3 = i(Jyx − Jxy) = 2〈Ax(t)Ay(t)sin[θ(t)]〉.Here Ax(t) and Ay(t) are the amplitudes of the field com-ponents Ex(t) and Ey(t), and θ(t) is the phase differencebetween Ex(t) and Ey(t) (controllable through the phaseshifter in the crossed undulator scheme). The degree of to-tal polarization can be defined as:P =√S21 + S22 + S33/S0. (3)The degree of circular polarization Pc is defined asPc = |S3|/S0. (4)TUPE068 Proceedings of IPAC’10, Kyoto, Japan229002 Synchrotron Light Sources and FELsA06 Free Electron LasersIn the following analysis, we use the time average to re-place the ensemble average for the far-field radiation inboth x and y directions.START-TO-END SIMULATIONS AT THEFUNDAMENTAL WAVELENGTHThe New Light Source (NLS) project [2] is used for thisstudy. In FEL-3, a HHG seed at λHHG = 12.4 nm anda two stage up-conversion are used to generate final radi-ation at λs = 1.24 nm . The schematic layout of FEL-3 is shown in Fig. 2. FEL-3 consists of two modula-tors, two dispersion sections and one radiator. The firstmodulator(modulator-1) has a period of λu1 = 4.4 cm andit is resonant at λHHG . The second modulator (modulator-2) has a period of λu2 = λu1 = 4.4 cm and is resonant atthe second harmonic of the seed laser, e.g. λHHG/2 . Theradiator has a period of λu = 3.22 cm and is resonant atλHHG/10 = 1.24 nm. In the latest optimization study forFEL-3, the scheme with the second modulator length twicethat of the first modulator yields the best performance [8].Thus, this latest optimal FEL-3 configuration will be usedfor our start-to-end simulations.Figure 2: Schematic layout of the NLS FEL-3 at 1.24 nmFEL wavelength.The simulated S2E beam parameters for the NLSprojects are E0 = 2.25 GeV , Ipk = 1200 A , σγ =0.7 × 10−4 and n = 0.3 mm-mrad. The undulator isseparated into 2.5 m sections, and a distance of 1 m isreserved between adjacent sections for the installation ofphase shifters, focusing quads, and diagnostic components.FODO lattice is chosen for focusing the beam in the undu-lator with the average β = 8 m [9].For polarization control at the fundamental wavelength,the radiator in FEL-3 will be used as the first main undu-lator (undulator-1). The crossed undulator can be formedby adding a phase shifter and a vertical-polarized undulator(undulator-2) as in Fig. 1. Undulator-2 has the same periodand strength as the radiator.We use the 3D time dependent FEL simulation codeGENESIS [10] to calculate the radiation fields. The S2Ebeam with realistic distributions are read into GENESISat the beginning of modulator-1. The numbers of macro-particles npart = 147 k and particle bins in particle load-ing nbins = 24 are chosen to effectively suppress numer-ical noise in the frequency up-conversion[11]. The seedlaser is assumed to be a gaussian beam with a peak powerof 400 kW and a fwhm pulse duration of 20 fs. Afterundulator-1, the electron beam file is dumped and is im-ported in undulator-2 to generate Ey , while the radiationfield Ex from undulator-1 is allowed to propagate freely tothe end of undulator-2. The polarization analysis is per-formed with the on-axis far field intensity and phase of the−4 −2 0 2 40.511.52s  (μ m)Power   (GW)  PxPy0 0.5 1 1.5 2 2.5 3020406080100phase shift (rad)Degree of polarization (%)  totalcircularFigure 3: Power profiles from horizontal and vertical un-dulators (upper plot), and degree of polarization vs. phaseshift (lower plot) at the fundamental wavelength.two radiation components.After optimization studies, we choose L1 = 14 m forundulator-1 (4 sections), and L2 = 2.5 m for undulator-2(1 section). The average FEL power is about 3 m beforesaturation. Power profiles of the two radiation componentsare shown in the top plot of Fig. 3, while both the totaland the circular degree of polarization at the fundamentalwavelength as a function of the phase shift are shown in thelower plot. We see that the power of the horizontal compo-nent (Px) is higher than that of the vertical component (Py)at the center part of the pulse, while the duration of Py iswider than that of Px. This tendency in the pulse shape de-velopment can be explained by the gaussian shape of theseed laser. The electrons at the bunch center interacts withthe maximum laser intensity and hence reaches saturationfaster than the head/tail part of the bunch. For a longer un-dulator length, the FEL microbunching at the bunch centerstarts to decrease after saturation, but the microbunching ofthe head/tail part of the bunch still increases. This nonuni-form bunching profile leads to a more flat radiation pro-file for the vertical component in undulator-2. In the lowerplot we see that the optimal degree of circular polarizationis ∼ 93% with a radiation phase close to π for the phaseshifter. Note that there is an intrinsic phase shift betweenEx and Ey . Therefore, the optimal phase for the circulardegree of polarization is nowhere near π/2.In passing we note that the proposed cross undulatorconfiguration can be easily realized with APPLE undu-lators. Suppose that the radiator consists of several 2.5-m APPLE undulators. The first four sections can betuned to the horizontal polarization for undulator-1, andthe fifth section can be tuned to the vertical polarizationProceedings of IPAC’10, Kyoto, Japan TUPE06802 Synchrotron Light Sources and FELsA06 Free Electron Lasers 2291for undulator-2. Thus, the phase shifter between the fourthand the fifth sections can be used for polarization control.START-TO-END SIMULATIONS AT THESECOND HARMONIC WAVELENGTHFor polarization control at the second harmonic wave-length we use the modified crossed undulator scheme asproposed in [6]. It consists of three undulators: a first(main) undulator of length L1 that reaches saturation andgenerates microbunching at the fundamental and harmonicfrequencies; two short undulators of equal length L2 = L3with the crossed configuration as shown in Fig.4. The res-onant wavelength of the two short undulators is chosen tobe the second harmonic of the first undulator (λ2 = λ3 =λ1/2). The radiator in FEL-3 will again be used as the firstundulator. An important feature of this method is its capa-bility to generate a high level of circular polarization whenthe first undulator operates in saturation. To demonstratethis feature, we choose the length of undulator-1 to be atsaturation, e.g., L1 = 17 m.Figure 4: Schematic of the crossed undulator for polariza-tion control at the 2nd harmonic wavelength.Similar to the previous section, the S2E beam with re-alistic distributions are read into Genesis at the beginningof modulator-1. The same seed laser is used in the simu-lations. The beam file is dumped at the exit of undulator-1and then used for the generation of Ex and Ey in undulator-2 and 3. The radiation field Ex from undulator-2 is allowedto propagate freely to the end of undulator-3. The polariza-tion analysis will be performed with the on-axis far fieldintensity and phase of the two field components.When we choose L2 = L3 = 1 m with an undulatorperiod λu/2 = 1.61 cm, the simulation results are shownin Fig. 5. The upper plot shows the radiation power pro-files Px and Py at 0.62 nm, and the lower plot shows thetotal and the circular degree of polarization at this wave-length as a function of the phase shift. We see that Px andPy both have spikes at the head/tail part of the pulse dueto the intrinsic evolution of the FEL microbunching aftersaturation. The maximum degree of circular polarization isshown to be 86% with a proper phase shift, again close toπ.DISCUSSIONIn this paper we have studied the generation of circularlypolarized radiation in a seeded soft x-ray FEL using thecrossed undulator scheme. We have shown that arbitrarilypolarized radiation can be achieved at both the fundamental−4 −2 0 2 4010203040s  (μ m)Power   (MW)  PxPy0 0.5 1 1.5 2 2.5 3020406080100phase shift (rad)Degree of polarization (%)  totalcircularFigure 5: Power profiles from horizontal and vertical un-dulators (upper plot), and degree of polarization vs. phaseshift (lower plot) at the fundamental wavelength (1.24 nm).and the 2nd harmonic wavelengths. For the fundamentalradiation, a maximum degree of ∼ 93% is obtainable justbefore FEL saturation. For the second harmonic radiation,the modified scheme can work well in the saturation regimewith over 80% of circular polarization.Compared to the SASE FEL, the synchrotron oscilla-tion for the FEL microbunching is more pronounced fora seeded FEL. Thus, the microbunching decreases quicklyonce the part of the bunch reaches saturation. This effectlimits the vertical radiation power and also the uniformityof the radiation profile, especially for polarization controlat the fundamental wavelength. Therefore, the lengths ofthe undulators should be designed properly in order to usethe crossed undulator scheme.REFERENCES[1] Fermi@Elettra conceptual design report ,http://www.elettra.trieste.it/FERMI, Elettra (2007).[2] J. Maraangos et. al., NLS Project: Science Case & OutlineFacility Design, www.newlightsource.org, 2009[3] U. Bergmann et al., Science and Technology of Future LightSources: A White Paper, SLAC-R-917 (2009).[4] K.-J. Kim, Nucl. Instrum. Methods A 445, 329 (2000).[5] Y. Ding, Z. Huang, Phys. Rev. ST-AB 11, 030702 (2008).[6] H. Geng, Y. Ding, Z. Huang, Proceedings of PAC09, 2009.[7] M. Born, E. Wolf, Principles of Optics (1999).[8] D. Dunning et. al., these proceedings.[9] N.R. Thompson et. al., Proceedings of FEL09, 2009.[10] S. Reiche, Nucl. Instr. and Meth. A 429 (1999) 243.[11] J. Rowland et. al., these proceedings.TUPE068 Proceedings of IPAC’10, Kyoto, Japan229202 Synchrotron Light Sources and FELsA06 Free Electron Lasers

Polarization analysis for seeded FELs in a crossed-planar undulator

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