The Berlin Energy Recovery Linac Project  bERLinPro  is  designed to develop and demonstrateCWLINAC technology  for 100 mA class ERLs. High current operation requires an  effective damping of higher order modes  HOMs  of the 1.3  GHz main linac cavities. We have studied elliptical 7 cell  cavities based on a modified Cornell ERL design combined  with JLab s waveguide HOM damping approach. This paper  will summarize the final optimization of the end cell tuning  for minimum external Q of the HOMs, coupler kick calculations  of the single TTF fundamental power coupler  FPC   as well as multipole expansion analysis of the given modes  and a discussion on operational aspects

Brackebusch, K.

Flisgen, T.

Galek, T.

Knobloch, J.

Neumann, A.

Riemann, B.

van Rienen, U.

HZB Repository

FINAL DESIGN FOR THE bERLinPro MAIN LINAC CAVITY ∗A. Neumann†, J. KnoblochHelmholtz-Zentrum Berlin, 12489 Berlin, GermanyB. Riemann, T. WeisTU Dortmund University, Dortmund, GermanyK. Brackebusch, T. Flisgen, T. Galek, U. van RienenRostock University, Rostock, GermanyAbstractThe Berlin Energy Recovery Linac Project (bERLinPro) isdesigned to develop and demonstrate CWLINAC technologyfor 100-mA-class ERLs. High-current operation requires aneffective damping of higher-order modes (HOMs) of the 1.3GHz main-linac cavities. We have studied elliptical 7-cellcavities based on a modified Cornell ERL design combinedwith JLab’s waveguide HOM damping approach. This paperwill summarize the final optimization of the end-cell tuningfor minimum external Q of the HOMs, coupler kick calcula-tions of the single TTF fundamental power coupler (FPC)as well as multipole expansion analysis of the given modesand a discussion on operational aspects.INTRODUCTIONFor the bERLinPro ERL [1] a 100mA beam has to be ac-celerated and decelerated in the main linac of the recirculatorfrom 6.5MeV to 50MeV and vice versa while preserving alow normalized emittance of smaller than 1 mm mrad. Ef-fectively the linac cavities therefore experience the passageof two with respect to the TM010-pi mode 180 deg. phaseshifted high current beams. Thus strong HOM damping is re-quired in order to avoid beam break-up instability (BBU) [2]by the interaction with dipole-like mode patterns excited bythe beam during previous passages. By that the cavity de-sign has to be optimized for low transverse shunt impedanceR/Q⊥ and low external quality factors Qext regarding theHOMs, while the fundamental has to feature low peak fieldratios and a high shunt impedance. This challenge was ad-dressed by combining Cornell’s mid-cell shape [3] featuringlow Epeak/Eacc, thus avoiding field emission, with JLabs con-cept of waveguide damped cavity structures [4]. The latterhas a natural cutoff frequency by the waveguide dimensionsand the danger of dust propagating from ferrite-based beamtube absorbers is avoided.Figure 1 shows a sketch of the bERLinPro demonstratorERL and the main linac cavity design. By two Y-shapedwaveguide (WG) end groups rotated by 60 deg. any HOM’spolarization is covered. To even improve the propagation ofthe HOMs, the beam tube is enlarged from the 72 mm iristo 105 mm via a spline based nose cone transition. Table 1∗Work supported by German Bundesministerium für Bildung undForschung, Land Berlin, by grants of Helmholtz Association and byFederal Ministry for Research and Education BMBF under contract05K10HRC and 05K10PEA† Axel.Neumann@helmholtz-berlin.desummarizes the calculated RF performance of the cavity.The structure was developed and optimized within a col-laboration of the universities Dortmund and Rostock withHZB. The methods applied and developed for this projectare published in [5–9].Table 1: Calculated RF parameters and operating conditionsof the main Linac cavity with a TTF-III FPC and five HOMdamping rectangular waveguides.Number of cells 7R/Q‖ 788 ΩfTM010 − pi 1.3 GHzEpeak/Eacc 2.08Bpeak/Eacc 4.4 mT/MVm-1Qext TM110 dipole ≤ 8 · 103Beam tube TE01 cutoff 1.596 GHzWaveguide TE10 cutoff 1.576 GHzQL for TM010-pi 1 · 107 − 1 · 108Pforward at QL = 5 · 107(∆ f = 0) 1.4 kWRecently [10] end-cell tuning optimizations using CSTMWS’s [11] swarm particle optimizer with the eigenmodesolver were performed to achieve best HOM damping re-sults while still keeping the cavity field-flat and within givenlimits regarding peak field ratios and R/Q‖ . The best candi-date of this approach was selected for more detailed studies,Figure 1: Scheme of the bERLinPro ERLwith the main linacsection within the recirculating ring. Above the linac cavitystructure is shown including the FPC and five waveguidesfor HOM damping.presented here, in order to achieve a design ready for pro-duction.HOM DAMPING CONCEPT ANDPERFORMANCE1.6 1.8 2 2.2 2.4 2.6102103104105106107108Freq. (GHz)Q ext  berlinpro 7−cell5 WG+coaxial FPCTE111, TM110TE211TE011,TM210TM011Figure 2: External Q for the 7-cell bERLinPro linac cavityfeaturing one coaxial FPC and five waveguide based HOMabsorbers obtained by CST MWS eigenmode computations.As it was demonstrated [12], that CW-driven cavities with-out beam-loading can be driven up to loaded Q of 2·108, oneWG was replaced by a variable CW-modified TTF-III cou-pler for a coupling range given in Table 1. Figure 2 showsthe achieved HOM damping of the final model. The dipolemodes are strongly damped, whereas TM quadrupole modesshow a partly localization within the inner cells leading tohigher Qext. Transverse R/Q⊥ calculations by directly inte-grating the Lorentz forces of the on-axis field components,a multipole decomposition and multi-integration path analy-sis [6, 7] have shown, that high Qext m≥2 modes may havedipole-like on-axis field components.Breaking the Symmetry with the Coaxial FPCA reason for this might be the broken symmetry by inser-tion of the coaxial FPC. To tackle this problem, calculationswere done comparing for different FPC penetration depthwith an all WG system having the full symmetry. The out-come with respect to the BBU parameter R/Q⊥ · Qext isdisplayed in Figure 3. The current threshold is given bya dipole component of a quadrupole mode. This on-axisR/Q⊥ > 0 seems to be also common for the full WG system,but is stronger for the coaxial antenna, such that a compen-sating stub might has to be inserted.Further, a localized mode with a strong dipole kick ap-pears between the cavity iris and the WG structure, as shownin Figure 4. To avoid this, being the second strongest candi-date limiting the threshold current, the whole end-group hasto be reworked by inserting shapes similar to [4].Finally, as all calculations needed to be done within 3Dand computational time and power limits the accessible spec-trum, a limited convergence study was started to overcomenumerical outliers. In Figure 5 the result demonstrates, thatthe first dipole bands reached convergence, but that there are2.25 2.3 2.35 2.4 2.45 2.5105Q ext2.25 2.3 2.35 2.4 2.45 2.5100Q ext ⋅ R/Q⊥ (Ω)2.25 2.3 2.35 2.4 2.45 2.5204060R/Q⊥ (Ω)Frequency (GHz)  FPC norm pos.+10mm into beam tubeonly Waveguidestrapped mode in cavityto WG transitionLimits BBUthreshold current:8.6⋅104Figure 3: Comparison ofQext, R/Q⊥ and the BBUparameterR/Q⊥ · Qext for the TTF FPC at nominal position (greendots), 10 mm more into the beam tube (blue squares) and asymmetric system with six waveguides.Figure 4: Localized mode within the iris to Y-shaped waveg-uide section at 2.4 GHz bearing a strong dipole kick on thebeam.1.4 1.6 1.8 2 2.2 2.4 2.6102103104105106107108109Mode frequency (GHz)Q ext  cells/λ: 4567Figure 5: Convergence study of Qext for the HOM spectrumusing different mesh densities with the hexahedral mesh ofCST 2014 using eight cells per max model box edge.still variations within the second monopole band and firstTE/TM quadrupole band, where the latter directly influencesthe BBU limit as for now. More studies with respect to thattopic are underway.Table 2: Beam and cavity parameters for the coupler kickcalculations.n,y,x 1 mm mradσt 5 ps rmsσy,x ≈0.7mm rmsIavg,beam 100mAEkin,ini 6.5MeVVacc 15MVEacc 18.56MV/mΦacc -20 to 20 deg−25 −20 −15 −10 −5 0 5 10 15 20 2577.588.599.51010.51111.512∆εn,y (%)Φacc (deg.)  5WG+1 Coax FPC6WGFigure 6: Relative emittance growth in the vertical planesversus φacc for the 5WG+coax FPC structure and the 6WGcavity in reference to the bare cavity using the PIC code.Coupler Kick and Emittance Dilution CalculationsIn addition to coupler kick effects on the HOM, it has tobe studied whether the 6.5 MeV beam is subject to couplerkick and emittance increase within the linac cavities by thefundamental mode. Using the bunch parameters given inTable 2 kick calculations with the CST PIC tracking solveras described in [13] were performed at nominal field levelfor a given range of accelerating phases comparing the coax-ial FPC design with the full WG structure (without spacecharge). As displayed in Figure 6 the emittance increase forstanding wave regime, as the cavity is operated at zero netbeam-loading under non-matching conditions, is nearly 10%for the coaxial FPC and 5WG design. The correspondingfields are shown in Figure 7. The evolution of the emittancein both transverse planes is given in Figure 8. As it only hap-pens to take place within the coaxial FPC’s plane, also herethe need for a compensating stub or similar is demonstrated.But still the full WG solution shows a stronger emittancedilution, even in both planes.SUMMARYThe design is closing in to be finalized for production.Main emphasis has to be put now on the end-groups andmore in depth and multipole analysis has to be applied inorder to understand the coupler kick effect on the HOMs.Figure 7: On-axis longitudinal and transverse field compo-nents for an electric wall boundary condition for the standingwave regime.−0.2 0 0.2 0.4 0.6 0.8 111.051.1ε n,y (µrad)z (m)−0.2 0 0.2 0.4 0.6 0.8 111.021.041.06ε n,x (µrad)z (m)  Φacc: −20 deg.0 deg.20 deg.TTF−coupler planeFigure 8: Emittance evolution in both transverse planes forthe bERLinPro design.ACKNOWLEDGMENTSThe authors acknowledge the helpful discussion withRobert Rimmer and Haipeng Wang from JLab as well asFrank Marhauser from muons inc. about cavity and HOMabsorber design issues.REFERENCES[1] J. Knobloch et al., ICFA Beam Dynamics Newsletters,No.58, p. 118, August 2012[2] G.H. Hoffstaetter, I.V. Bazarov, and Ch. Song., Phys.Rev. ST Accel. Beams, 10:044401, Apr 2007.[3] N. Valles et al., IPAC’10, Tsukuba, 2010, WEPEC068,p. 3046 ff.,[4] F.Marhauser et al., EPAC’08, Genoa, 2008, MOPP140,p. 886 ff.,[5] B. Riemann et al., ICAP’12, Warnemünde, 2012WEP14, p. 167 ff.,[6] A. Neumann et al., ICAP’12, Warnemünde, 2012FRAAC03, p. 278 ff.,[7] B. Riemann et al., LINAC’12, Tel Aviv, 2012,MOPB066, p. 330ff,[8] A. Neumann et al., LINAC’12, Tel Aviv, 2012,MOPB067, p. 333ff,[9] T. Galek et al., IPAC’13, Shanghai, 2013, WEPWO010,p. 2331ff,[10] T. Galek et al., IPAC’14, Dresden, 2014, MOPME017,p. 412ff,[11] CST AG, Microwave Studior, Darmstadt, Germany[12] A. Neumann et al., SRF’11, Chicago, 2011,MOPO067, p. 262 ff.,[13] A. Neumann et al., IPAC’14, Dresden, 2014,WEPRI007, p. 2490ff,

Final design for the bERLinPro main LINAC cavity

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Final design for the bERLinPro main LINAC cavity

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