Improvement of the crossed undulator design for effective circular polarization control in X-ray FELs
aa r X i v : . [ phy s i c s . acc - ph ] J a n DEUTSCHES ELEKTRONEN-SYNCHROTRON
Ein Forschungszentrum der Helmholtz-Gemeinschaft
DESY 11-009January 2011
Improvement of the crossed undulator design fore ff ective circular polarization control in X-rayFELs Gianluca Geloni,
European XFEL GmbH, Hamburg
Vitali Kocharyan and Evgeni Saldin
DeutschesElektronen-Synchrotron DESY, HamburgISSN 0418-9833
NOTKESTRASSE 85 - 22607 HAMBURG mprovement of the crossed undulator design fore ff ective circular polarization control in X-rayFELs Gianluca Geloni, a , Vitali Kocharyan b and Evgeni Saldin b a European XFEL GmbH, Hamburg, Germany b Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
The production of X-ray radiation with a high degree of circular polarization con-stitutes an important goal at XFEL facilities. A simple scheme to obtain circularpolarization control with crossed undulators has been proposed so far. In its sim-plest configuration the crossed undulators consist of pair of short planar undulatorsin crossed position separated by an electromagnetic phase shifter. An advantageof this configuration is a fast helicity switching. A drawback is that a high de-gree of circular polarization (over 90 %) can only be achieved for lengths of theinsertion devices significantly shorter than the gain length, i.e. at output powersignificantly lower than the saturation power level. The obvious and technicallypossible extension considered in this paper, is to use a setup with two or morecrossed undulators separated by phase shifters. This cascade crossed undulatorscheme is distinguished, in performance, by a fast helicity switching, a high degreeof circular polarization (over 95 %) and a high output power level, comparable withthe saturation power level in the baseline undulator at fundamental wavelength.We present feasibility study and exemplifications for the LCLS baseline in the softX-ray regime.
The LCLS baseline includes a planar undulator system, which produceshorizontally polarized X-ray pulses [1]. However, there is an always in-creasing demand by the LCLS users for circularly polarized X-ray pulseswith fast switching of helicity. An APPLE-type undulator [2] can provide variable polarization, but it is di ffi cult to quickly change the polarity due tothe magnet motion mechanism and, thus, to achieve fast helicity switching.One possible solution is to use crossed undulators. The concept of crossedundulators was devised by Kim in order to produce various polarizationstates with planar undulators [3]. The configuration is based on a pair ofplanar undulators in a crossed position, Fig. 1. A phase shifter betweenthe undulators controls the radiation phase between horizontal and verti-cal components by providing a bump orbit to the electron beam with its3 ig. 3. Schematic of the crossed undulator proposed for polarization control at theLCLSFig. 4. Schematic of the cascade crossed undulator proposed for e ff ective polariza-tion control at synchrotron radiation sources magnetic field. This allows for the generation of various polarization statessuch as circular ones. A fast switching of the polarization direction (upto the kHz level) can be achieved by using electromagnetic phase shifters.When this concept is applied to synchrotron radiation sources, the radiationpulses generated in horizontal and vertical undulators by each electron donot overlap in time. Thus, a monochromator after the crossed undulator isrequired to temporally stretch both pulses and to achieve interference, Fig.4. The crossed undulator setup has been installed at BESSY and the degreeof circular polarization was found to be in the range of 40 −
45% [4]. Thedegree of polarization is limited, in practice, by the finite beam emittance,energy spread and resolution of the monochromator. In particular, the angu-lar divergence of the electron beam is responsible for a blurring of the phasebetween the radiation field components, which is a cause of depolarization.A remarkable feature of an XFEL device is a narrow bandwidth in the orderof 0 .
1% of the output radiation. It follows that the monochromator, whichis needed for the operation of the crossed undulator scheme at synchrotronradiation sources, can be avoided. In addition, due to the high quality of theelectron beam at XFELs, emittance and energy spread e ff ects play no sig-nificant roles in the determination of the degree of polarization for crossedundulators.Three di ff erent approaches have been proposed so far for the productionof circularly polarized radiation with crossed undulators at XFELs facili-ties. A first approach was proposed in [5] and further studied in [6]. In thisscheme, a short planar undulator is placed behind the long planar undula-tor, oriented orthogonally to it, Fig. 2. If the length of the short undulatoris approximately 1.3 times the FEL gain length, the two orthogonal linearcomponents have equal intensities. Therefore, if their phase di ff erence is π/
2, their combination results in circular polarization. According to simu-lations [6], the maximum degree of circular polarization in the regime ofSASE saturation is over 80%. The 3D FEL gain length, however, depends ona number parameters such as wavelength, peak current, emittance, energyspread, beta function. Some of them might fluctuate leading to fluctuationsof the polarization degree as well. In addition, this scheme can only be opti-mized for one wavelength with fixed parameters, while for other parameterchoices the degree of polarization drops. A modified second scheme hasbeen proposed in [7] in order to improve stability, Fig. 3. The planar base-line undulator is only used as a buncher, while a short pair of crossed planarundulators tuned to the second harmonic is placed behind the buncher. Theradiation in the baseline undulator is characterized by a di ff erent frequencythan that produced in the crossed undulator, and therefore has no e ff ecton the polarization properties of the harmonic fields. Moreover, the secondharmonic contents generated through the nonlinear harmonic generationprocess in the baseline undulator are smaller than those generated in thecrossed undulator, and can be ignored. The maximum degree of circularpolarization achievable in this case is over 90% at 0 . − ff erent undulators. As a result, the performance of theoutput radiation is significantly lower than that of the light produced by thebaseline undulator, meaning that the intensity is reduced by more than anorder of magnitude.The cascade crossed undulator scheme proposed in [10], Fig. 4 for syn-chrotron radiation sources is a candidate to overcome this di ffi culty. In thispaper, we study the use of this scheme at XFEL facilities as a mean togenerate circularly polarized radiation at the fundamental frequency. Theundulator is composed of several cascades, each of which forms a crossedundulator. We present exemplifications for the LCLS baseline case. The ra-diation from the proposed device is investigated numerically, and showsthat a high degree (over 95%) of circular polarization and, simultaneously, ahigh output power level (10 GW-level) can be obtained if a su ffi ciently largenumber of cascades (up to four) is considered.The applicability of the cascade crossed undulator scheme is obviously notrestricted to the LCLS baseline. Other facilities, e.g. the LCLS-II and theEuropean XFEL, may benefit from this scheme as well. The subject of this article is the proposal of an undulator configuration forX-ray FELs allowing for high and stable degree of circular polarization,high output power and fast helicity switching. Although it is based on theshort crossed undulator configuration, this configuration can achieve muchhigher output power. With reference to Fig. 5, the undulator is composedof several cascades, each of which forms a crossed undulator. The helicityswitching can be performed very quickly [14]. In fact, a fast switching ofthe polarization direction can be achieved by using electromagnetic phaseshifters, Fig. 6.In this section we describe a particular realization of our proposal, a polar-ization control scheme that may be easily developed at the LCLS. It combinesthe cascade crossed undulator arrangement proposed in [10] with the fil-tering method proposed in [11]. An overall sketch of the setup is shownin Fig. 7. The electron beam first goes through the baseline undulator, pro-ducing SASE radiation. This induces energy and density modulation on6 ig. 5. Schematic of the cascade crossed undulator proposed for e ff ective polariza-tion control at the LCLS baseline.Fig. 6. Phase shifter design for the cascade crossed undulator at LCLS. Each phaseshifter controls the radiation phase between undulator segments by providing abump orbit to the electron beam with its magnetic field in order to generate variouspolarization states. the electron beam. Following [11] we assume that the five second harmonicafterburner (SHAB) modules are rolled away [12] from the beamline, Fig. 8.In this way, we provide a total of 40 m straight section for the electron beam,20 m corresponding to the SHAB modules, and further 20 m correspondingto the straight section after the exit of the main undulator. At the end of the7 ig. 7. The installation of the cascade crossed undulator after the LCLS baselineundulator.Fig. 8. Design of the undulator system for e ff ective polarization control at the LCLSbaseline.
40 m-long straight section we place horizontal and vertical slits. The schemeis similar to that presented in [11], with the di ff erence that after the slits weinstall a cascade crossed undulator, instead of an APPLE-type undulator.After the straight section, electron beam and radiation pass through hor-izontal and vertical slits, suppressing the linearly-polarized soft X-ray ra-diation from the LCLS baseline undulator. Since the slits are positioned 408 downstream of the planar undulator, the radiation pulse has a ten timeslarger spot size compared with the electron bunch transverse size, and thebackground radiation power can therefore be diminished of two orders ofmagnitude. As discussed in [11], the slits can be made of Beryllium foils,for a total thickness of 150 µ m. Such foils will block the radiation, but willlet the electrons go through [13]. The advantage of the spoiling scheme isthat radiation is attenuated of 20 dB, while the halo of the electron bunchis allowed to propagate through the setup up to the beam dump withoutelectron losses. Ionization losses can be neglected.As already remarked in [11], one should account for the fact that the straightsection acts as a dispersive element. Therefore, a klystron-like bunchinge ff ect should also be accounted for, which modifies the density modulationfrom that found at the exit of the first undulator. From this viewpoint, thefirst (baseline) LCLS undulator behaves as an energy modulator, and thedrift section, i.e. the straight section, transforms the energy into densitymodulation. Estimations for the klystron-bunching e ff ect and the influenceof betatron motion have already been presented in [11]. Here we only sumup the conclusions reached in that reference, repeating that these e ff ectsare not preventing the scheme from working, but that the planar baselineundulator should be operated in the linear regime.Following the slits, the electron beam enters the crossed-undulator cascade,where the microbunched electron beam produces intense bursts of radiationin any selected polarization state. For simplicity we assume average betatronfunction values β =
10 m at 1 . ff erence in the betatron function along the 20m-long drift section and in the SHAB undulator focusing system. Then,we propose to fill two undulator modules of about 3 . In the previous Section we gave a qualitative description of the scheme forpolarization control. Here we present more detailed FEL simulations withthe help of the FEL code GENESIS 1.3 [15] running on a parallel machine. Wepresent a statistical analysis consisting of 100 runs. Parameters used in thesimulations for the low-charge mode of operation in the crossed undulators9 able 1Parameters for the low-charge mode of operation at LCLS used in this paper.UnitsUndulator period mm 30K parameter (rms) - 3.5Wavelength nm 1.5Energy GeV 4.3Charge nC 0.02Bunch length (rms) µ m 1Normalized emittance mm mrad 0.4Energy spread MeV 1.5 -2 0 20.05.0x10 P [ W ] s[ m] Fig. 9. Power distribution after the first SASE undulator (5 cells). Grey lines referto single shot realizations, the black line refers to the average over a hundredrealizations. are presented in Table 1. The choice of the low-charge mode of operation ismotivated by simplicity.First, the LCLS baseline is simulated. As discussed before, and alreadyconsidered in [11], the baseline LCLS undulator should work in the linearregime. An optimum is found when only the last 5 cells upstream of theSHAB are used. In other words we assume that first 23 baseline undulator10 ig. 10. Spectrum after the first SASE undulator (5 cells). Grey lines refer to singleshot realizations, the black line refers to the average over a hundred realizations. modules are detuned. The power and spectrum after the baseline undulatorare shown in Fig. 9 and Fig. 10.The particle file produced by Genesis at the exit of the baseline undulatoris downloaded and transformed assuming a dispersive element with R ≃ L /γ ≃
560 nm, which models the following 40-m long straight section. Thetransformed particle file is used as an input for further simulations throughthe setup described in the previous Section, Fig. 5. The average betatronfunction is assumed to be β =
10 m. By this we assume that the same focusingsystem in the SHAB section is continued through the following 20 m-longstraight section and into the cascade cross-undulator. Such assumption canobviously be relaxed, and it is considered here for simplicity reasons only.Also, the influence of the betatron motion on the microbunching is onlyestimated in [11], but is not explicitly accounted for in simulations. However,from those estimations we expect that such influence would be even smallerthan the influence due to the finite energy spread of the beam.The particle file is used to simulate the radiation output from the first undu-lator in the cascade. In particular, both a field file and a new particle file areproduced by Genesis. The intersection between the first and the second un-dulator is modeled as a straight section. The correct phase shift is simulatedby properly adjusting the length of this straight section. The horizontallypolarized radiation should be further propagated through the second un-11 P ( I ) [ W ] s[ m] Fig. 11. Power after the first crossed-undulator cascade, composed by the firstcrossed undulator. Grey lines refer to single shot realizations, the black line refersto the average over a hundred realizations. dulator and through the second phase shifter. To this purpose we still usedGenesis after switching o ff the interaction with the electron bunch . Then,the particle file at the entrance of the second undulator is used as an inputfor Genesis to calculate the vertically polarized field from the second undu-lator. The total output power from the first cascade, composed by the firstcrossed undulator is shown in Fig. 11.In order to calculate the average degree of polarization we used the simpli-fied approach presented in [6]. Instead of averaging over a three-dimensionalfield distribution we reduce the averaging procedure to a one-dimensionalcalculation by, first, taking the Fourier transform of the horizontal and ver-tical radiation field at this position down the setup. This yields the far-zoneradiation field. The on-axis far-zone field is then used to calculate the Stokesparameters and yields the circular polarization degree as a function of timefor a given pulse, P c ( t ). We subsequently weight P c ( t ) over the on-axispower density of the pulse, I ( t ), and we make an ensemble average overmany pulses according to This is done by decreasing the electron bunch current to 1A. P c () a ft e r t he f i r s t c a sc ade [rad]0.96 Fig. 12. Circular degree of polarization as a function of the phase shift, after the firstcrossed-undulator cascade. Grey lines refer to single shot realizations, the blackline refers to the average over a hundred realizations. An average 96% degree ofpolarization can be obtained when the right phase is chosen. P c = N p N p X n = R ∞−∞ I ( t ) P c ( t ) dt R ∞−∞ I ( t ) dt , (1) N p =
100 being the number of pulses in our statistical run. The degree of po-larization is obviously a function of the phase between the two polarizationcomponents. A plot of the circular degree of polarization as a function ofthe phase shift, after the first crossed-undulator cascade is shown in Fig. 12.Grey lines refer to single shot realizations, the black line refers to the averageover a hundred realizations. An average 96% degree of polarization can beobtained when the right phase is chosen.The particle file resulting from the propagation at nominal current and thefield file for the horizontally and vertically polarized radiation are used asinput files for the following cascade, and the process is repeated up to thelast cascade. The total output power is shown in Fig. 13, while the degree ofpolarization as a function of the phase is shown in Fig. 14. An average 95%degree of polarization can be obtained when the right phase is chosen, andhigh-power pulses can be produced in the 10 GW-level.13 P ( I V ) [ W ] s[ m] Fig. 13. Power after the fourth crossed-undulator cascade. Grey lines refer to singleshot realizations, the black line refers to the average over a hundred realizations.
In this paper we exploit the cross-undulator cascade scheme developedin [10] in order to achieve ultimate performance in polarization control,yielding high-power pulses of X-ray radiation with arbitrary state of polar-ization, very high degree of polarization, and fast switching of helicity. Theproposed setup can be composed of an unlimited number of cascades, upto the full scale of the baseline undulator, the degree of polarization beingindependent of the length of the setup. This hints to possible future designsfor baseline XFEL undulators where, for example, one half of the total lengthcan be taken by a long cross-undulator cascade. In this case one may achievecircular polarization for soft and hard X-rays using the same scheme, andwithout problems of linearly polarized radiation background from the firstpart of the undulator.We presented an illustration of the scheme for the LCLS, although otherfacilities like the LCLS-II and the European XFEL may also benefit fromit, limiting ourselves to the soft x-ray range. We combined this methodwith the filtering concept considered in [11]. The main advantage achievedconsists in obtaining fast helicity-switching up the the KHz level and, si-multaneously, in retaining the 10-GW power level typical of APPLE-typeundulators. In fact, by increasing the number of cascades from one to four14 P c () a ft e r t he f ou r t h c a sc ade [rad]0.95 Fig. 14. Circular degree of polarization as a function of the phase shift, after thefourth crossed-undulator cascade. Grey lines refer to single shot realizations, theblack line refers to the average over a hundred realizations. An average 95% degreeof polarization can be obtained when the right phase is chosen. we increase the output power by ten times from half GW to 5 GW at thesame high (95%) degree of polarization. Moreover, the use of planar devicesis much less expensive compared to the APPLE-type. The exploitation of thefiltering concept, which was first presented in the case of an APPLE-typeradiator [11], solves the issue of separating planar from circular polariza-tion radiation components. The setup can be installed at the LCLS in a littletime. It constitutes a cost-e ff ective, risk-free alternative to currently availablemethods for polarization control. We are grateful to Massimo Altarelli, Reinhard Brinkmann, Serguei Molodtsovand Edgar Weckert for their support and their interest during the compila-tion of this work. 15 eferences [1] P. Emma et al., Nature photonics doi:10.1038 //