BERLinPro is using the new energy recovery linac technology. As, maintaining the low emittance and energy spread is of major importance in an ERL, the deep understanding and control of effects which can degrade the emittance and energy spread such as space charge effects are of interest. The microbunching caused by the longitudinal space charge forces can lead to an increase in emittance and energy spread in the arcs of the loop. In this contribution, the impacts of the microbunching instability on the beam quality and its implication for BERLinPro are discusse

Jankowiak, A.

Meseck, A.

Rädel, S.D.

HZB Repository

INVESTIGATION OF MICROBUNCHING-INSTABILITY IN BERLINPRO∗St. Rädel†, A. Jankowiak, A. MeseckHelmholtz-Zentrum für Materialien und Energie GmbH, Berlin, GermanyAbstractThe Helmholtz Zentrum Berlin (HZB) is building an en-ergy recovery linac (ERL) prototype, bERLinPro, to demon-strate the ERL principle at low emittance and high currents.As, maintaining the low emittance and energy spread iscrucial for generation of high brightness synchrotron radia-tion, the deep understanding and control of effects degradingthe emittance and energy spread are of major interest. Themicrobunching instability caused by the longitudinal spacecharge forces can lead to an increase in emittance and energyspread. In this contribution, the impacts of the microbunch-ing instability on the beam quality and its implication forbERLinPro are discussed.INTRODUCTIONIn all types of accelerators space charge effects are present.They influence beam size, bunch length and working point.In order to describe the space charge effects, one needs totake into account that on the one hand electrons repel eachother, on the other hand relativistically moving electronsrepresent parallel currents, leading to attracting forces. Thesum of attraction and rejection lead to a reduced repellingforce.Usually, one assumes a Gaussian longitudinal particledistribution. Even on average, the “real” current profileis not smooth, it comprehends little humps. Dependenton their position the electrons inside these humps sufferdifferent repelling forces. Electrons in the center experiencea similar amount of forces from different sides. So the nettospace charge force is zero for them. Electrons at the edgesexperience the repelling forces only from one side. Thus,these electrons are pressed out. In their case, the repellingforces lead to an acceleration or a deceleration. This way,the space charge forces lead to an energy modulation on theelectrons at different wavelengths.In accelerators, this energymodulation can be transformedto a density modulation due to the longitudinal dispersion.So the energy modulated electrons can either be replacedon top of their old hump or be replaced in between neigh-boured humps, creating microbunches. Thus, one obtainseither an amplified or a reduced microbunching for a givenwavelength. In the amplified case the microbunch gains ahigher amplitude. This gain process can be discribed by [1]:∗ Work supported by German Bundesministerium für Bildung undForschung, Land Berlin, and grants of Helmholtz Association† stephanie.raedel@helmholtz-berlin.deG ≈I0γb IAk f R56energymodulat ion︷                   ︸︸                   ︷∫ L0ds4pi Z (k0; s)Z0︸                              ︷︷                              ︸microbunchingexp *,−k2fR256σ2δ2+-(1)The exponential term in the gain formula includes thewave number k f , the longitudinal dispersion R56 and the ini-tial relative energy spread σδ . It damps the microbunchingeffect in cases where the product k2fR256σ2δis big. In thecase of a small exponential term we achieve a strongly mi-crobunched electron bunch, when the ratio of the bunch peakcurrent, I0, and the Alfven current, IA is big. Taking intoaccount the small energy spread expected for an ERL, onecan assume that with an appropriate undulator the ERL isideally suited for using microbunching instability to producecoherent synchrotron radiation.In this paper results of simulation studies on the impactof the longitudinal space charge forces on the electron dis-tribution in bERLinPro are presented.BERLINPRObERLinPro’s layout is shown in Fig. 1. It is a single-pass-ERL with a 6.5MeV injection line consisting of a supercon-ducting RF photo-injector and a 3 × 2-cell-cavity boostersection. The produced electron bunches have a very lowemittance and small energy spread. The beam is mergedinto the superconducting main linac via a dog-leg mergerwhere it is accelerated to 50MeV. The corresponding elec-tron beam parameters are given in Table 1. The linac and anoptimized subsequent lattice form a closed circuit, so thatthe beam re-enters the linac with a 180° phase shift. Thusduring the second pass, the linac decelerates the electronsand retrieves their energy. The decelerated beam is dumpedin a 650 kW-beam dump at 6.5MeV [2].Table 1: bERLinPro ParametersParameter Value UnitBeam energy 50 MeVBeam current@ 1.3 GHz 100 mABunch charge 77 pCBunch length < 2 psEnergy spread (rel. proj.) 0.5 %Transverse emittance < 1 mm mradBeam loss < 10−5TUPRI044 Proceedings of IPAC2014, Dresden, GermanyISBN 978-3-95450-132-81662Copyright©2014CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD05 Instabilities - Processes, Impedances, CountermeasuresFigure 1: Scheme of bERLinPro with subdivisions in different sections [3].Simulation code ASTRAThe utilized simulation program is ASTRA [4]. The sim-ulations start at the gun, where electron bunches are createdand they end after a recirculation directly after the secondpass through themain linac. In ASTRA the quadrupole fieldsare limited along the moving axis (s-axis) only. This meansthey have infinite focusing fields perpendicular to the s-axis.Thus, while simulating a ring-accelerator a quadrupole fieldwould appear twice, once at the intended quadrupole posi-tion and a second time as an extended field on the oppositeside of the ring. Therefore, a ring-shaped transport line hasto be cut in several sections, each being simulated in itsown simulation run. For bERLinPro the first section endsafter the dog-leg merger. The electron distribution has to berotated about 18° before entering the recirculator. Due tothe transversally infinite quadrupole fields in the simulationcode, the ’simulation transport-lines’ end each after a dipole.There the electron distribution is rotated about 45° beforebeing send through the next section.The simulations presented in this paper use the 3D spacecharge calculation routine in ASTRA. The algorithm is basedon a fast Fourier transform. It uses a Cartesian grid in eachplain. The number of grid lines is equal to 2n [5]; where n isthe number of the grid lines. For a good resolution in the sim-ulations, the number of the longitudinal grid lines is around256. For the simulations, electron bunches with 200,000particles and a total charge of 77 pC are used. To ensure thatthe numerical noise issues do not lead to missleading effects,the simulations are repeated 20 times.RESULTSTo present the results of the simulation studies, bERLin-Pro has been divided in three parts. Each part has beenmarked with a different background colour shown in Fig. 1.Please note, that each part is simulated as sequence of con-sequent simulation runs according to the discussion above.The injector has a magenta-coloured background, while thebackground of “Arc 1” section, which starts from the exit ofthe injector and ends at the exit of the first arc, is blue. “Arc2” section includes a long drift and the second arc. It has agreen background.InjectorThe injector section is about 10.71m long. It consistsof the photo injector, booster and the dog-leg merger. Fig-ure 2 shows the longitudinal particle distribution, as well ascurrent profile and the bunch form factor (Fourier transforma-tion of the current profile, which shows the microbunchingas a function of the wavelength) at the exit of the injector.Along the injector no higher amplitude of microbunchingcan be observed, as clearly indicated by the low amplitudeof the Fourier transformation.Figure 2: current profile (up left), bunch form factor (upright) and longitudinal phase space (bottom left), longitudi-nal phase space statistics (bottom right) at the end of injector.Arc 1The Arc 1 sections starts at the “merger” exit and endsafter the fourth dipol of the arc. The main linac is alsopart of the Arc 1. Figure 3 shows the longitudinal particledistribution, as well as current profile and the bunch formfactor at the exit of Arc 1. The exit shows a hint of a higherProceedings of IPAC2014, Dresden, Germany TUPRI04405 Beam Dynamics and Electromagnetic FieldsD05 Instabilities - Processes, Impedances, CountermeasuresISBN 978-3-95450-132-81663 Copyright©2014CC-BY-3.0andbytherespectiveauthorsamplitude of the microbunching. This fact is also confirmedby analytical calculations using eq. 1.Figure 3: current profile (up left), bunch form factor (upright) and longitudinal phase space (bottom left), longitudi-nal phase space statistics (bottom right) at the end of Arc 1.Arc 2The Arc 2 section starts at the end of Arc 1, contains along drift, the return arc and ends befor the dump. Figure4 shows the longitudinal particle distribution, the currentprofile and the bunch form factor in the middle of Arc 2.The point of this subsection shows a smooth current profile.A look to the longitudinal phase space gives a clear reason.The electron bunch is located vertical in the middle of Arc 2(Fig. 4). Along Arc 2 no higher amplitude of microbunchingcan be observed, as clearly indicated by the low amplitudeof the Fourier transformation.Figure 4: current profile (up left), bunch form factor (upright) and longitudinal phase space (bottom left), longitu-dinal phase space statistics (bottom right) in the middle ofArc 2.CONCLUSIONThe simulations of the ERL demonstrator bERLinProshows an accelerator without microbunching instablity prob-lems. It can be observed, that the electron bunch will smearout at the beginning of the arcs befor microbunching candevelop. In addition there seems to be a hint of microbunch-ing at the end of the first arc. This fact could be used todesign a transparent microbunching amplifying optics in thefollowing long drift, which can lead to coherent emission inthe first dipole of the return arc.ACKNOWLEDGMENTI’m grateful to Aleksandr Matveenko for the rotation-matlab-skript and to Jens Völker for motivating discussionsand his help. I’m also thankful to Bettina Kuske and ViktoriaLaux for providing the initial particle distribution and forhelping me with the bERLinPro database.REFERENCES[1] Z. Huang et al., “Microbunching Instability due to BunchCompression”, ICFA Beam Dynamics Newsletter, De-cember 2005, http://www.slac.stanford.edu/pubs/slacpubs/11000/slac-pub-11597.html[2] M. Abo-Bakr et al., “Status of the HZB ERL Project bERLin-Pro”, IPAC 2014, Dresden, Germany, June 2014, MOPRO106,These Proceedings.[3] A. Jankowiak, FLS 2012, Newport News, Virginia, USA,http://www.jlab.org/conferences/FLS2012/talks/Mon/FLS2012-BERLinPro_Status-AndreasJankowiak.pptx[4] DESY.de website: http://www.desy.de/~mpyflo/, AS-TRA for Windows, Version 3.0[5] DESY.de website: http://www.desy.de/~mpyflo/Astra_dokumentation/, "Astra-Manual_V3.1.pdf", last lala ll modified 14 April 2014.TUPRI044 Proceedings of IPAC2014, Dresden, GermanyISBN 978-3-95450-132-81664Copyright©2014CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD05 Instabilities - Processes, Impedances, Countermeasures

Investigation of Microbunching instability in BERLinPro

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Investigation of Microbunching instability in BERLinPro

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