The Berlin Energy Recovery Linac Project  BERLinPro   is designed to develop and demonstrate CW LINAC technology  for 100 mA class ERLs. High current operation requires  an effective damping of higher ordermodes  HOMs   of the 1.3 GHz main linac cavities.  We have studied elliptical seven cell cavities damped by  five waveguides at the adjacent beam tubes. Eigenmode  calculations for geometrical figures of merit show that the  present design should allow successful cw linac operation  at the maximum beam current of 100 mA   77pC bunch  charge.  In this paper the progress in HOM calculations to avoid  beam breakup instabilities for the favored cavity structure  is presente

Anders, W.

Brackebusch, K.

Flisgen, T.

Galek, T.

Knobloch, J.

Neumann, A.

Papke, K.

Riemann, B.

van Rienen, U.

Weis, T.

HZB Repository

Abstract submission deadline: 30.4.12 Early registration deadline: 30.7.12Website: www.linac12.org.il Conference SecretariatE-mail: linac12@ortra.comTel: +972-3-6384444 International Organizing CommitteeIsrael Mardor, Soreq NRC, Israel (IOC Chair)Dan Berkovits, Soreq NRC, Israel (SPC Chair)Joseph Luner, Soreq NRC, Israel (LOC Chair)Jim Alessi, BNL, USA John Barnard, LLNL, USA Winfried Barth, GSI, Germany Michael Borland, ANL, USA Swapan Chattopadhyary, Cockcroft, UK Jean Delayen, ODU, USA Michael Fazio, LANL, USA Roland Garoby, CERN, Switzerland Terence Garvey, PSI, Switzerland Kazuo Hasegawa, JAEA, Japan Hitoshi Hayano, KEK, Japan Andrew Hutton, JLAB, USA Yoshihisa Iwashita, Kyoto U., Japan Kevin Jones, SNS, USA Horst Klein, U. Frankfurt, Germany Andre Kolomiets, ITEP, Russia Leonid Kravchuk, INR, Russia L. K. Len, DOE, USA Lia Merminga, TRIUMF, Canada Alban Mosnier, CEA, France Won Namkung, Postech, Korea Guoxi Pei, IHEP, China Paolo Pierini, INFN, Italy Milorad Popovic, FNAL, USA John Seeman, SLAC, USA Alessandro Variola, LAL, France Hans Weise, DESY, Germany Richard York, MSU, USA Yanglai Cho, ANL, USAMarion White, ANL, USAStanley Schriber, Idaho, USA   Main topics of the conference:•  Electron Accelerators and Applications•  Proton and Ion Linear Accelerators and Applications•  Linear Accelerator Technology•  Extreme Beams and SourcesTel Aviv, Israel, September 9-14, 2012XXVI Linear Accelerator ConferenceRESULTS AND PERFORMANCE SIMULATIONS OF THE MAIN LINACDESIGN FOR BERLinPro∗A. Neumann , W. Anders, J. Knobloch, Helmholtz-Zentrum Berlin, Berlin, Germany†B. Riemann, T. Weis, TU Dortmund University, Dortmund, GermanyK. Brackebusch, T. Flisgen,T. Galek, K. Papke,U. van Rienen, Rostock University,Rostock, GermanyAbstractThe Berlin Energy Recovery Linac Project (BERLinPro)is designed to develop and demonstrate CW LINAC tech-nology for 100-mA-class ERLs. High-current operation re-quires an effective damping of higher order modes (HOMs)of the 1.3 GHz main linac cavities.We have studied elliptical seven cell cavities damped byfive waveguides at the adjacent beam tubes. Eigenmodecalculations for geometrical figures of merit show that thepresent design should allow successful cw linac operationat the maximum beam current of 100 mA / 77pC bunchcharge.In this paper the progress in HOM calculations to avoidbeam-breakup instabilities for the favored cavity structureis presented.INTRODUCTIONBERLinPro will be a CW driven ERL machine with amaximum current of 100 mA beam and a maximum en-ergy of 50 MeV, while preserving a normalized emittanceof better than 1 mm mrad at a pulse length of 2 ps [1].The main linac cavity has strong HOM damping require-ments since it is passed by two 100 mA beams that bothresonantly interact with transverse deflecting (e.g. TM110)cavity modes, leading to beam break up (BBU) [2].An ERL cavity design must minimize the HOM’sR/Q⊥and external quality factors Qext [8]. The mid-cell de-sign influences the HOM spectrum, dispersion relation andoperational mode acceleration performance (see [8] forop. mode parameters of the tuned structure). By properend-cell tuning that preserves field flatness for the funda-mental TM010-π mode, mode localization (trapping) can beavoided and the Qext can be recuced to a sufficient extent.In this paper updated HOM calculations of the mainlinac cavity using new methods are presented [8], andan outlook on ongoing activities to decompose the cavitystructure into smaller parts is given [5] [9].STRUCTURE EIGENMODECALCULATIONSThe design under consideration is a seven cell structureusing the Cornell ERL mid-cell design [6] and combining it∗Work supported by Federal Ministry for Research and EducationBMBF under contract 05K10HRC and 05K10PEA† Axel.Neumann@helmholtz-berlin.deFigure 1: Rendering of the cavity design under considera-tion for BERLinPro with a cut through the symmetry (FPC)plane and electric field magnitude of the operational mode.ERL shape Spline shapeCornell U. TU Do, v4 / v5Esurf/Eacc (π mode) 2.07 2.08 / 2.07R‖/Q (π mode) 111Ω 113 Ω / 112 Ωintercell coupling κ 2.1 % 1.7 % / 1,9 %Geometry factor G 272.7Ω - / 269.5ΩTable 1: Cavity mid-cell figures of merit comparison.with JLab 3-fold symmetric waveguide HOM couplers [7](see Figure 1). Flexible input power coupling is enabled byreplacing one waveguide with a TTF-III type coaxial fun-damental power coupler (thus breaking the 3-fold symme-try). The design aims at combing the peak field propertiesof the Cornell design with the advantage of waveguide cou-plers having a natural cutoff above the fundamental, andfurther limiting the possibility of dust intruding from fer-rite beam tube absorbers into the cavity.Base cellsIn parallel to periodic boundary mid-cell calculations,such calculations were also performed using Spline-basedcells [4]. Table 1shows a preliminary comparison between36 mm radius mid-cells for both designs. At the moment,development concentrates on the Cornell ERL mid-cell.Further development and degree elevation of the spline de-sign may lead to a mid-cell shape with higher performance.Transverse shunt impedanceThe final goal will be to minimize the product R/Q⊥ ·Qext for all HOMs. |~V⊥|2 ∝ R⊥/Q can be computed di-0 20 40 60 80 100 120 140 16011.522.53mode frequency [GHz]Figure 2: Frequency of all modes up to 2.85 GHz, about thelower range of the 4th dipole band. All modes were com-puted using the JDM eigenmode solver of CST MWSTM.20 40 60 80 100 120 140 1601001011021031041051061071081091010 external QFigure 3: External Q of all TM/TE modes up to 2.85GHz. While the dipole modes are sufficiently damped,some quadrupole modes exhibit large Qext > 1 · 106.rectly from the fields on the central axis by~V⊥ =1q∫~FL(s) exp (ikβs) ds · exp(−iΨ0) ∈ R2 (1)simultaneously with its polarization and additional infor-mation about optimal phase relations in Ψ0 [3]. The result-ing R/Q⊥ is shown in Figure 4. Again the dipole modesseem sufficiently damped while some quadrupole modesdue to their high Qext and a small, but finite non-zero shuntimpedance on axis show to be the most harming modesconcerning BBU.20 40 60 80 100 120 140 160100101102103104105106107108109R⊥/Q [Ω]R⊥×Qext/Q [Ω]Figure 4: Transverse R/Q⊥ and R/Q⊥ · Qext for all TMand TE modes up to 2.85 GHz (beginning of 4th dipoleband). The arrow marks the coupler kick by the TTF-IIIpower coupler at the fundamental mode.Polar path analysisThe action of seemingly small voltages from mainlyquadrupolar modes, giving rise to large instabilities, leadsto the question if and to which extent quadrupole modedamping should be considered in realistic cavity designs,based on the influence of higher order mode coupler kicksand imperfections in beam path position and constructionissues. Due to the broken rotational symmetry, any eigen-mode may consist of different multipole components. Ascheme named polar path analysis was developed [3] to ex-tract the voltage componentsap, bp of the longitudinal (andequivalently, transverse) voltageV‖(r, φ) ≈∑prp[bp cos(pφ) + ap sin(pφ)] (2)from all available longitudinal and transverse voltages onan arbitrary number of integration paths N (the differentpaths are comprised into vectors of the respective voltages)by constructing and pseudo-inverting a rectangular matrixA in an equation system of the form [3]~V‖ω~Vxω~Vy = A(~a~b). (3)To investigate the possible shift of quadrupole modes acalculation of R⊥/Q along circular distributed integrationpaths at an arbitrary offset of 5mm was performed. Fig. 5shows the results of the eigenmode computation for a modewith a dominating quadrupole component. Fig. 6 is a plotof the reconstructed transverse area with the result coeffi-cients |a0 + ib0| = 3, 5 · 104 V (monopole), |a1 + ib1| =1.28 · 105 V/mm (dipole) |a3 + ib3| = 4.6 · 104 V/mm2(quadrupole) and |a4+ib4| = 5.6 ·102 V/mm3 (sextupole).For quadrupolar modes, we are interested in the shift ofthe transverse forceless path. Fig. 6 also shows the markedforceless point given as a solution of the complex polyno-mial X(z) != 0 [3].−6 −4 −2 0 2 4 6−6−4−202468x [mm]y [mm]−505−50523456x 104x [mm]y [mm]V || [Ω]Figure 5: Polar plot of transverse (left, arrows) and longitu-dinal (right) voltages determined on circularly arranged in-tegration paths at 5mm offset from beam axis for a mainlyquadrupolar mode.Most modes of these quadrupole bands are shifted morethan the expected vertical beam size in the linac and thusmainly quadrupole modes may exhibit a non-neglectibledipole component. This effect needs to be investigated inmore detail and it has to be understood how much the cou-pler’s position influences this effective dipole componentof the quadrupole modes.x [mm]y [mm]−5 0 5−5−4−3−2−1012345Figure 6: Reconstruction of the transverse (arrows) andlongitudinal (isolines) voltages in the beam area from thedata shown in Fig. 5. The red square marks the transverseforceless point.0 20 40 60 80 100 120 140 16010−210−1100101102103104105106107108Treshold current [A]Figure 7: Approximate (orders of magnitude) calculationsfor the treshold current based on Eq. 4.Treshold currentTo evaluate and optimize the cavity, we use a simpfliedequation for the treshold currentIth ≈2ceE0R⊥/QQextω(4)for one cavity HOM that still depends on the mode’s trans-verse shunt impedance R/Q⊥, its external quality factorQext and frequency ω and the beam’s energy E0, but ne-glects the influence of recirculation time and the recircula-tion arc linear beam optics (“worst phase” assumption).The results of our preliminary treshold current calcula-tion for all modes are shown in Fig. 7. The seeminglysmallest current value is not valid due to being equivalentto a coupler kick of the operational mode which is exter-nally driven and cannot be described by the treshold currentformula.OUTLOOKFull 3d structure eigenmode computations using severalmillion mesh cells for hundreds of modes need too muchcomputational resources to implement them as iterationsteps into an optimizer routine for end-cell tuning (to lowerthe Qext for the dangerous HOMs). Thus, the next stepsin BERLinPro main linac cavity design will either consistof using Coupled S-parameter Calculations [11] of the seg-Figure 8: Cavity separation planned for CSC. The rota-tionally symmetric structure is decomposed along the equa-tor radii, with an additional separation at the outer endcelliris. The resulting structure is concatenated with the 3dFPC/waveguide damping structure and the 2d (cartesian)3-fold symmetric waveguide damping structure.mented structure (see Fig. 8) with 2d eigenmode calcula-tions of the rotationally symmetric cavity, or using a state-space equation system with a similarly separated structure[9] to find a set of end-cells with field-flat op. modes thatare then optimized for maximum overall HOM damping(R⊥/Q · Qext) [5]. The sufficient cavity sets will then beconcatenated to the full three cavity string, as already thelowest order dipole modes propagate along the beam tubeand couple to the neighboring rf structures.REFERENCES[1] M. Abo-Bakr et al., “BERLinPro - A Compact Demon-strator ERL for High Current and Low Emittance Beams”,LINAC’10, Tsukuba, September 2010,.[2] Y. Petenev et al., “Modeling of the Beam Break Up Insta-bility for BERLinPro ”, IPAC’11, San-Sebstian, September2011, MOPS051, p. 718, http://www.JACoW.org[3] B. Riemann et al., “Alternative approaches for HOM-damped cavities,” MOPB066, these proceedings[4] B. Riemann et al., “Design of SRF cavities with profilesbased on Bezier splines”, ICAP’12, Rostock, August 2012,WEP14.[5] T. Galek et al., “Traveling Poles Elimination Scheme andCalculations of External Quality Factors of HOMs in SCCavities”, ICAP’12, Rostock, August 2012, WEP07.[6] N. Valles and M. Liepe, “Seven-cell Cavity Optimizationfor Cornell’s Energy Recovery Linac”, SRF’09, Berlin,September 2009, THPPO008, p. 538.[7] F. Marhauser, “JLab High Current Cryomodule Develop-ment”, ERL’09, Ithaca NY, September 2009, WG307.[8] A. Neumann et al., “Status of the HOM calculations for theBERLinPro main linac cavity”, ICAP’12, Rostock, August2012, FRAAC3.[9] T. Flisgen et al., “Lumped equivalent models of complex RFstructures”, ICAP’12, Rostock, August 2012, THACI1.[10] Computer Simulation Technology AG, Mi-crowave Studior, 64289 Darmstadt, Germanyhttp://www.cst.com[11] K. Rothemund, H.-W. Glock, U. van Rienen, “Eigenmodecalculation of complex rf-structures using S-parameters”,(2000) IEEE Transactions on Magnetics, 36 (4 I), pp. 1501-1503.

Results and Performance Simulations of the Main Linac Design for BERLinPro

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Results and Performance Simulations of the Main Linac Design for BERLinPro

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