Fischer, W.

Roser, T.

Schoefer, V.

Y., Luo

Zimmer, C.

English

null Luo Y.

C. Zimmer

W. Fischer

V. Schoefer

T. Roser

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Local 3Qy betatron resonance correction in the 2012 RHIC 250 GeV run

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C-A/AP/#462 Sept. 2012    Local 3Qy betatron resonance correction in the 2012 RHIC GeV run   Y. Luo, C. Zimmer, W. Fischer, V. Schoefer, T. Roser          Collider-Accelerator Department Brookhaven National Laboratory Upton, NY  11973      Notice: This document has been authorized by employees of Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy.  The United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this document, or allow others to do so, for United States Government purposes.  BNL-98560-2012-IR LOCAL 3Qy BETATRON RESONANCE CORRECTIONIN THE 2012 RHIC 250 GEV RUN∗Y. Luo, C. Zimmer, W. Fischer, V. Schoefer, T. Roser, Brookhaven National Laboratory, Upton, NY USAAbstractIn this article we performed numerical simulations tocorrect the local vertical third order betatron resonance3Qy in the interaction regions in the Yellow ring for the2012 RHIC 250 GeV polarized proton run. Consideringthe main sources of skew sextupoles are located in the in-teraction regions, we used local bump methods to mini-mize their contributions to the global 3Qy resonance driv-ing term. Two kinds of correction orbit bumps are testedand the dynamic apertures with these correction strengthsare calculated and compared.INTRODUCTIONTo further increase the luminosity in the RHIC 250 GeVpolarized proton (p-p) run, we planned to increase the pro-ton bunch intensity. Increased bunch intensity will in-crease the beam-beam tune spread and beam-beam reso-nance driving terms (RDTs). In the 2012 run, the peak pro-ton bunch intensity reached 1.7 × 1011 at the beginning ofstore.Fig. 1 shows the proton tune footprint with beam-beamin the current tune space between 2/3 and 7/10 with theproton bunch intensity 2.0 × 1011 and the transverse rmsemittance 2.5 mm.mrad. There is not enough tune spacebetween 2/3 and 7/10 to hold the beam-beam tune spreadwhen the proton bunch intensity is bigger than 2.0 × 1011.To compensate the beam-beam tune spread and beam-beam resonance RDTs, we planned to install electronlenses in both rings for head-on beam-beam compensa-tion [1]. In the RHIC p-p runs, we normally put the work-ing points of both rings below the diagonal in the tune spaceto achieve a better beam lifetime. In this article, we correctthe 3Qy RDT with available interaction region (IR) skewsextupole correctors to mitigate the tune space limit.RESONANCE DRIVING TERMSThe f rst order geometric RDTs caused by skew sex-tupoles areh0030 = −124N∑i=1(K2sL)iβ3/2y,i ei3µy,i , (1)h0021 = +18N∑i=1(K2sL)iβ3/2y,i eiµy,i , (2)∗This work was supported by Brookhaven Science Associates, LLCunder Contract No. DE-AC02-98CH10886 with the U.S. Department ofEnergy. 0.665 0.67 0.675 0.68 0.685 0.69 0.695 0.7 0.705 0.665  0.67  0.675  0.68  0.685  0.69  0.695  0.7  0.705QyQx0-1 σ1-2 σ2-3 σ3-4 σ4-5 σ5-6 σFigure 1: Tune footprint with bunch intensity 2.0 × 1011.h1110 = −14N∑i=1(K2sL)iβx,iβ1/2y,i eiµy,i , (3)h2001 = −18N∑i=1(K2sL)iβx,iβ1/2y,i ei(2µx,i−µy,i), (4)h2010 = −18N∑i=1(K2sL)iβx,iβ1/2y,i ei(2µx,i+µy,i). (5)Here (K2sL) is the integrated strengths of skew sextupoles.The following betatron resonances will be driven:3Qy, Qy, 2Qx − Qy, 2Qx + Qy. (6)Each driving term is a complex number. To correct the3Qy RDT h0030, we need at least two orthogonal skew sex-tupoles or families. In RHIC, there is one skew sextupolecorrector on either side of each IP and only the 4 correc-tors in the IR6 and IR8 have their own power supplies. Thecontributions from the 2 correctors in one IR have oppo-site contributions and only can be grouped into one family.And the contributions from IR6 and IR8 skew sextupolecorrectors can’t form two orthogonal families for an effec-tive global h0030 correction with current p-p run lattices.SOURCES OF SKEW SEXTUPOLESConsidering that the β function is much larger in the IRthan in the arc, the main sources of skew sextupoles to ex-cite the 3Qy resonance are located in the IR6 and I8. Basedon the off-line IR nonlinear f eld model [2] and Eq. (1),-0.001 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 3140  3160  3180  3200  3220  3240  3260K2sL-100-50 0 50 100 150 200 250 3140  3160  3180  3200  3220  3240  3260β y1.5  K2sLs  [m] Figure 2: K2sL and β1.5y K2sL in IR8 in Yellow ring. 0 50 100 150 200 250 0  500  1000 1500 2000 2500 3000 3500 4000| h0030 | s  [m] Blue RingYellow RingFigure 3: 3Qy RDTs in the Blue and Yellow rings withoutcorrection.Fig. 2 shows K2sL and β1.5y K2sL in the IR8 in the Yel-low ring. In the off-line model, we split each actual magnetinto 8 slices and insert the measured nonlinear f eld errorsbetween slices and append errors on both ends of magnets.The main contribution to the 3Qy resonance are from theD0 and triplets.Fig. 3 shows the 3Qy RDT in the Blue and Yellow ringswithout any skew sextupole correction. The RDT variesalong the ring. The sudden jumps of the RDT’s absolutevalue hints the locations of skew sextupoles. The IR non-linear f eld model predicts that 3Qy RDT is bigger in theYellow ring than that in the Blue ring. In the following, wewill focus on the local 3Qy correction in the Yellow ring.LOCAL RESONANCE CORRECTIONSSince the main sources of skew sextupoles are located inIR6 and IR8, in the following we use local correction meth-ods to minimize their contribution to 3Qy RDT. In RHIC-8-6-4-2 0 2 4 6 8 10 3100  3150  3200  3250  3300y co [ mm ] s  [ m ] IR BumpSector BumpFigure 4: IR bump and sector bump in IR8 in Yellow ring.we already developed an effectivemethod - IR bump to cor-rect the local nonlinear f eld errors in IRs [3]. IR bump canbe an orbit bump covering the whole IR or one only cov-ering one side of an IR. For simplicity, we name the latteras a sector bump. As an example, Fig. 4 shows the orbitbumps in the Yellow ring IR8.For local skew sextupole correction or local 3Qy correc-tion on line, we generate local vertical orbit bumps. Thetune shifts from the feed-down of the skew sextupoles dueto the orbit bump are proportional to βxβ1/2y in the hori-zontal plane and β3/2y in the vertical plane. For the sec-tor bump, we minimize the linear term of the vertical tuneshift w.r.t. the orbit amplitude with the IR skew sextupolecorrector that the bump covers. By doing this, we actu-ally minimize∑β3/2y K2sL in the sector which is their netcontributions to the global h0030 RDT. For the IR bump,we simultaneously minimize the linear terms of the hori-zontal and vertical tune shifts w.r.t. the vertical orbit am-plitude with the 2 skew sextupole correctors in the IR.By doing so, we actually minimize∑βxβ1/2y K2sL and∑β3/2y K2sL in the IR which are the net contributions tothe global h0210,h2010, and h0030 RDTs.Fig. 5 shows 3Qy resonance driving terms in the Yellowring without and with corrections from the IR bump andsector bump methods. Both the IR bump and sector bumpmethods reduce |h0030| along the ring. From Fig. 5, thesector bump method is more effective than the IR bumpin reducing the global |h0030| and |h0030|s at IP6 and IP8.However, the IR bump method reduces not only the RDTof 3Qy resonance but also that of 2Qx ± Qy resonances.DYNAMIC APERTURE CALCULATIONSIn this section we calculate and compare the particle dy-namic aperture with the above local 3Qy resonance correc-tion methods. In the dynamic aperture calculation [4], wetrack particles up to 106 turns in 10 phase angles in thef rst quadrant of (x,y) plane. The initial relative momentum 0 50 100 150 200 250 0  500  1000 1500 2000 2500 3000 3500 4000| h0030 | s  [ m ]  No Corr. IR Bump Corr. Sector Bump Corr.Figure 5: |h0030| with IR bump and sector bump methods. 0 1 2 3 4 5 6 7 8 9 0.666  0.668  0.67  0.672  0.674DA without BB  Fractionla Qy   No Corr. IR Bump Corr. Sector Bump Corr.Figure 6: Comparison of dynamic aperture w/o skew sex-tupole corrections. Beam-beam effect is excluded. 4 4.5 5 5.5 6 6.5 7 7.5 8 0.676  0.678  0.68  0.682  0.684DA with BB  Fractional Qy  No Corr. IR Bump Corr. Sector Bump Corr.Figure 7: Comparison of dynamic aperture w/o skew sex-tupole corrections. Beam-beam effect is included.deviation of the particles is 0.0005. Fig. 6 shows the dy-namic apertures without beam-beam interaction in a tunescan from (28.685, 29.675) to (28.676, 29.666) with a stepsize of 0.001. The horizontal axis is the fractional verticaltune. The skew sextupole correction strengths from the IRbump gives a bigger dynamic aperture than the sector bumpwhen the vertical tune is above 0.669.Fig. 7 shows the dynamic aperture with beam-beam in-teraction in a tune scan from (28.695, 29.685) to (28.686,29.676). The horizontal axis is the fractional vertical tunebefore beam-beam is turned on. The proton bunch in-tensity is 1.65 × 1011. The transverse rms emittance is15 mm.mrad. The beam-beam parameter is about -0.017.From Fig. 7, the correction strengths from the sector bumpmethod gives a lower dynamic aperture than that withoutcorrection and that with the correction strengths from theIR bump method.EXPERIMENTSDuring the normal RHIC operation, the IR skew sex-tupole corrector strengths were installed based on the IRbump method. In a dedicated machine study during 2012RHIC 250 GeV run we re-visited the sector bump methodto focus on correcting only 3Qy resonance in the Yellowring. Experimentally we were able to minimize the lineardependence of the vertical tune shift with respective to thebump amplitude. However, the skew sextupole strengthsfrom the sector bump method reduced the Yellow beamlifetime. We also noticed that the skew sextupole correc-tion strengths were very different from IR bump and sectorbump methods.SUMMARYIn this article we performed numerical simulations tolocally correct the vertical third order betatron resonance3Qy in the Yellow ring for the 2012 RHIC 250 GeV po-larized proton run. We compared the IR bump and sectorbumpmethods to locally correct the IR skew sextupole f elderrors. Simulation and experiment show that the correctionstrengths from the sector bump method reduces the beamlifetime with beam-beam. It is probably due to the fact thatthe sector bump method only focuses on 3Qy resonancecorrection while the IR bump also corrects 2Qx ± Qy res-onances. 2Qx ± Qy resonances also cross (2/3,2/3) in thetune space.REFERENCES[1] Y. Luo, et al., Phys. Rev. ST Accel. Beams 15, 051004(2012).[2] J. Beebe-Wang, et al., in Proceedings of PAC07, Albu-querque, USA, 2007.[3] F. Pilat, Y. Luo, et al., in Proceedings of PAC05, Knoxville,USA, 2005.[4] Y. Luo, in Proceedings of IPAC’10, Kyoto, Japan, 2010.

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Local 3Qy betatron resonance correction in the 2012 RHIC 250 GeV run

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