The CompactLight project supported by European H₂020 is to design a hard X-ray FEL facility beyond today’s state of the art. The project integrates photo injector, X-band acceleration and innovative compact short-period undulators together to make the machine more compact. RF undulator has an extraordinary advantage of working at very short undulator period. A conceptual design for a RF undulator at 36 GHz using a corrugated cylindrical waveguide operating in the HE11 mode is presented in this paper. Based on beam dynamics simulation and photon beam radiation simulations, the possibility of RF undulator to be used in CompactLight project is evaluated

Cross, A.

Tan, Y. R. E.

Zhang, L.

Zhu, D.

English

University of Strathclyde Institutional Repository

THE CONCEPTUAL DESIGN OF A 36 GHz RF UNDULATOR ∗D. Zhu†, Y. R. E. Tan, Australian Synchrotron, Clayton, AustraliaL. Zhang, A. Cross, Department of Physics, University of Strathclyde, Glasgow, UKAbstractThe CompactLight project supported by European H2020is to design a hard X-ray FEL facility beyond today’s stateof the art. The project integrates photo injector, X-band ac-celeration and innovative compact short-period undulatorstogether to make the machine more compact. RF undulatorhas an extraordinary advantage working at very short un-dulator period. A conceptual design for a RF undulator at36GHz using a corrugated cylindrical waveguide operatingin the HE11 mode is presented in this paper. Based on beamdynamics simulation and photon beam radiation simulations,the advantage of RF undulator to be used in CompactLightis presented.INTRODUCTIONDuring the past decades Synchrotron Radiation facilitieshave seen a fundamental tool for the study of materials in awide spectrum of sciences, technologies, and applications.The latest generation of light sources, the Free ElectronLasers, capable of delivering high-intensity photon beamsof unprecedented brilliance and quality, provide a substan-tially novel way to probe matter and have very high, largelyunexplored, potential for science and innovation [1–3]. Cur-rently, most of the worldwide existing FELs use conventionalnormal conducting 3GHz S-band or 6GHz C-band linactechnology. The machine can reach to kilometres long. TheCompactLight intends to design a hard X-ray FEL facilitybeyond today’s state of the art, using the latest concepts forbright electron photo injectors, very high-gradient X-bandstructures at 12 GHz, and innovative compact short-periodundulators.RF undulators, suggested long time ago, has the advan-tage of very short undulator period, fast dynamic control ofpolarization, undulator strength and wavelength, large aper-ture, and cheap in comparison with the permanent magnetundulators [4–6]. Conventional permanent magnet undula-tor has undulator periods on the order of a few centimetres,but RF undulator can easily reach to micrometer periods andproduce X-ray energies with lower energy electron beam.With the development of higher power RF sources in highfrequency band, Rf undulator is becoming short-period alter-natives to traditional undulators. It is a potential candidateto be used in CompactLight.In this paper, we present a prototype of a RF undulatorfor CompactLight. A one metre long corrugated cavity setsup electromagnetic fields by pumping in 50MW RF powerwith frequency 36GHz to be used as a RF undulator. Firstly,a brief review of the parameters of RF cavity structure is∗ Work supported by European Horizon 2020 CompactLight project.† dajunz@ansto.gov.aupresented. Then, a further investigation of the electron beamdynamics inside the cavity is given. Later, the RF undulatorradiation spectrum as it is installed in our storage ring isevaluated.THE 36 GHz RF CAVITY STRUCTUREIt’s critical for a RF undulator cavity to build up highertransverse electromagnetic fields along the centre axis towiggler electrons in transverse direction. The high Q cavitywith desired operating mode is needed to maintain a highfield in the cavity centre area. A corrugated waveguide struc-ture with a low loss HE11 mode in a cavity is studied [5,6]. In which the microwave power is mostly concentrated inthe central region of the cavity and the electric field at thecavity wall is much smaller. It operated in X-band achieveda quality factor of 91000. When driven by a 50 MW klystronat 12GHz, an equivalent Bu of 0.65 T and a equivalent un-dulator period of 13.9mm were achieved in the experiment.Based on this, a 36GHz corrugated waveguide structure RFundulator is suggested [7].The corrugated waveguide is a cylindrical waveguide withperiodic corrugations as shown in Fig. 1.Figure 1: Schematic drawing of the corrugated waveguide.The hybrid HE11 mode which is a cylindrical waveg-uide TM11 mode (with Hz = 0) near cutoff undergoes atransformation due to the corrugations in the waveguidein to a rf field with both an electric and magnetic field(Ez , 0,Hz , 0) in the axial direction as they move awayfrom the waveguide cutoff. Under conditions known as the“balanced hybrid conditions”, when the axial electric field isequal to the axial magnetic field times free space impedance,the transverse electric field is strongly polarized as shownin Fig. 2.Figure 2: Electric field patterns of the HE11 mode.10th Int. Particle Accelerator Conf. IPAC2019, Melbourne, Australia JACoW PublishingISBN: 978-3-95450-208-0 doi:10.18429/JACoW-IPAC2019-TUPRB002TUPRB0021676ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2019).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIMC2: Photon Sources and Electron AcceleratorsT15 Undulators and WigglersAs can be seen from the figure, the fields and power den-sity is very low near the waveguide walls which lead to verylow attenuation for this mode, but this will decrease the wallloss dramatically. Using this kind of structure and mode, ahigh Q factor cavity can be achieved.Figure 3 and Fig. 4 are the electric field and magnetic fieldprofile on the longitudinal axis. The peak electric field is3.8× 108 V/m, the peak magnetic field is 1.27 T. The cavityQ factor can research to 94344.Figure 3: RF undulator cavity on-axis electric field profile.Figure 4: RF undulator cavity on-axis magnetic field profile.BEAM DYNAMICS IN THE CAVITYWhen an electron beam interacts with a guided co-propagating and a counter-propagating deflecting EM wave,the equivalent undulator period λu is given by the followingequation [8]λu =λ01 ± λ0λg(1)where λ0is the free space wavelength, and λg is the waveg-uide wavelength. The plus sign corresponds to the EMwave counter-propagating with the electrons, and the mi-nus sign corresponds to the EM wave co-propagating withthe electrons. These two cases are referred to as short-period and long-period undulation respectively. In the RFundulator cavity, the standing wave can be decomposedin a co-propagating and a counter-propagating EM waves,hence both short and long-period undulation mechanismsare present. Depending on the RF phase of the cavity fieldswhen the beam is injected, the long-period undulation maycause the beam to drift.The relativistic electrons in an RF cavity will interactwith both the electric field Ex = E0sin(2πz)/λg).sin(ωt)and magnetic field By = B0cos(2πz)/λg).cos(ωt). TheLorentz force on electron can be rewritten in the formFx =eE02( ζZω+1)cos(2πz( 1λ0+1λg)) +eE02( ζZω−1)cos(2πz( 1λ0− 1λg))(2)where e is the charge of electron, E0 and B0 are the peakelectric and magnetic field strength in the RF undulatorcavity, respectively. Zω is the wave impedance in the cavityand ζ is the wave impedance in free space. The secondterm leads to a long wavelength and is undesirable in theundulator of a short wavelength FEL. The second term canbe ignored if the wave impedance is close to the free spaceimpedance, which means the operating frequency is far awayfrom the cut-off frequency of the waveguide. In this case,the equivalent magnetic field Bu of the RF undulator is givenbyBu =E02c( ζZω+ 1) (3)For the designed 36GHz RF undulator with 50MW RFinput power, the cavity Q factor can reach to 94344. In thiscondition, the equivalent magnetic field Bu is 1.27 T, theequivalent undulator period λu is 4.34mm.There is electron beam drift due to the long-period un-dulation. It need to perform beam dynamics simulationsfor different RF phases. The maximum drift is small com-pared to the beam apertures of the undulator and could becorrected by beam optics. [6]RADIATION SPECTRUM IN ASLS RINGTo evaluate the advantage of this RF undulator, we usedSPECTRA to do synchrotron radiation [9]. SPECTRA hasbuilt-in models for permanent magnet undulators, as wellas user defined static magnetic field undulators. To simu-late the RF undulator, we used the user defined undulatormodel with the equivalent undulator magnetic field profile.The validation of the correctness of this approximation isproved by performing single electron beam dynamics simu-lation with SPECTRA and solving the equations of motionin Mathematica using the on-axis RF electric and magneticfields can get the same orbit.The ASLS storage ring electron beam parameters is usedin the radiation simulation. If the RF undulator is installedin our storage ring, what’s kind of photon beam can beproduced. The ASLS is a medium-energy third generationsynchrotron facility running in Melbourne since 2007. Thestorage ring specifications are shown in Table 1.Fig. 5 shows the radiation flux density for the first (blue),the third (red) and the fifth (green) harmonics on the photonenergy map. The plot was obtained from SPECTRA far fieldcalculation assuming an ideal permanent magnet undulator10th Int. Particle Accelerator Conf. IPAC2019, Melbourne, Australia JACoW PublishingISBN: 978-3-95450-208-0 doi:10.18429/JACoW-IPAC2019-TUPRB002MC2: Photon Sources and Electron AcceleratorsT15 Undulators and WigglersTUPRB0021677ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2019).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOITable 1: ASLS Beam Parameters at the Straight SectionEnergy 3 GeVCircumference 216 mAverage Current 200 mAHorizontal Emittance 10.4 nm radCoupling Constant 0.012Energy Spread 0.001βx 8.92 mβy 2.42 mσx 0.32 mmσy 17.5 umσz 9.0 mmof 230 periods, 10 m from the undulator centre. The otherparameters for the photon beam is listed in Table 2.Figure 5: Radiation flux from the 1m long RF undulatorTable 2: Photon Radiation Parameters with RF Undulator.Bu 1.27 Tλu 4.34 mmTotal Length 1.0 mNumber of Periods 230K Value 0.52First Harmonic Energy 17.8 keVFirst Harmonic Flux 7.24 × 1014First Harmonic Flux Density 3.2 × 1017Total Power 1.87 kWIn Table 2, the unit for flux isphoton/s/0.1percent.B.W ., The unit for flux densityis photon/s/mr2/0.1percent.B.W ..The simulation results show that a very narrow band highenergy and intense density photon beam emits from the RFundulator. The first harmonic energy is 17 keV with fluxdensity 3.2 × 1017photon/s/mr2/0.1percent.B.W . . Com-paring with our conventional 2m long in-vacuum undulator,the flux density increases 20 times at 17 keV. This advantagemakes it possible to use low energy electron to produce highenergy photon beam. It is possible to use RF undulator asinsertion device in synchrotron beamlines.CONCLUSIONWe presented a new type of RF undulator which workingat 36GHz HE11 mode with corrugated waveguide structure.In this structure, a high equivalent magnetic field Bu anda short equivalent undulator period λu are achieved. Weinvestigated the beam dynamics inside the RF undulator. Weget the radiation spectrum using ASLS storage ring electronbeam parameters. The results show that we can producehigh energy and high brilliance photon beam from the RFundulator.ACKNOWLEDGEMENTSThe authors would like to thank the European Horizon2020 CompactLight project for supporting this work.REFERENCES[1] Linac Coherent Light Source (LCLS) Project homepage:http://www-ssrl.slac.stanford.edu/lcls/[2] M. Altarelli et al., Ed., “The European X-Ray Free-ElectronLaser – Technical Design Report”, DESY, Hamburg, Germany,Rep. DESY 2006-097, July 2007.[3] T. Shintake et al., “SPring-8 Compact SASE Source (SCSS)”,SPIE, Optics for Fourth-Generation X-Ray Sources, Belling-ham, Aug. 2001, p. 12 (2001).[4] T. Shintake et al., “Development of microwave undulator”, Jpn.J. Appl. Phys, vol. 22, no. 5, pp. 844–851, May 1983.[5] S. Tantawi et al., “Experimental demonstration of a tunablemicrowave undulator”, Phys. Rev. Lett., vol. 112, no. 16, pp.164802, Apr. 2014.[6] M. Shumail, Ph.D. thesis, Stanford University, USA 2014.[7] L. Zhang et al., “Microwave undulator using a helically corru-gated waveguide”, IEEE Trans. on Electron Devices, vol. 65,no. 12, pp. 5499, Dec. 2018.[8] T. Shintake, “Experimental results of microwave undulator”,International Conference on Insertion Devices for SynchrotronSources, 0582, pp. 336-343, May 1986.[9] T. Tanaka and H. Kitamura, “SPECTRA: a synchrotron radia-tion calculation code”, Journal of Synchrotron Radiation, 8,pp.1221-1228, Nov. 2001.10th Int. Particle Accelerator Conf. IPAC2019, Melbourne, Australia JACoW PublishingISBN: 978-3-95450-208-0 doi:10.18429/JACoW-IPAC2019-TUPRB002TUPRB0021678ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2019).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIMC2: Photon Sources and Electron AcceleratorsT15 Undulators and Wigglers

The conceptual design of a 36 GHz RF undulator

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The conceptual design of a 36 GHz RF undulator

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