Since the beginning of this year, we have made significant improvements in the machine optics at PEP-II. As a result, the specific luminosity increased nearly 20%. The largest luminosity gain actually came from minimizing nonlinear chromatic effects and running both rings much closer to the half integer resonance in the horizontal plane

Cai, Y.

Colocho, W.

Diecker, F. -J.

Nosochkov, Y.

Raimondi, P.

Seeman, J.

Sonnad, K.

Sullivan, M.

Turner, J.

Weaver, M.

Wienands, U.

Wittmer, W.

Woodley, M.

Yan, Y.

Yock, G.

UNT Digital Library

SLAC-PUB-11912June 2006Luminosity Improvement at PEP-II Based on Optics Model andBeam-Beam Simulation∗Y. Cai, W. Colocho, F-J. Decker, Y. Nosochkov, P. Raimondi J. Seeman,K. Sonnad, M. Sullivan, J. Turner, M. Weaver, U. Wienands,W. Wittmer, M. Woodley, Y. Yan G. YockySLAC, Menlo Park, CA 94025, USAAbstractSince the beginning of this year, we have made signiﬁcant improvements in the machineoptics at PEP-II. As a result, the speciﬁc luminosity increased nearly 20%. The largestluminosity gain actually came from minimizing nonlinear chromatic eﬀects and runningboth rings much closer to the half integer resonance in the horizontal plane.(Presented at the Tenth European Particle Accelerator Conference,June 26-30, 2006, Edinburgh, UK)∗Work supported by the Department of Energy under Contract No. DE-AC02-76SF00515.Luminosity Improvement at PEP-II Based on Optics Model and Beam-BeamSimulation∗Y. Cai† , W. Colocho, F-J. Decker, Y. Nosochkov, P. Raimondi, J. Seeman, K. Sonnad, M. Sullivan,J. Turner, M. Weaver, U. Wienands, W. Wittmer, M. Woodley, Y. Yan, G. YockySLAC, Menlo Park, CA 94025, USAAbstractSince the beginning of this year, we have made sig-nificant improvements in the machine optics at PEP-II.As a result, the specific luminosity increased nearly 20%.The largest luminosity gain actually came from minimizingnonlinear chromatic effects and running both rings muchcloser to the half integer resonance in the horizontal plane.INTRODUCTIONThe model independent analysis (MIA) [1, 2] was suc-cessfully used in the past to understand machine optics andimprove the luminosity at PEP-II. However, the rate of suc-cess was rather limited because the improvement of opticsdoes not necessarily lead to increase of luminosity. To im-prove the situation, we introduced a new strategy, as illus-trated in Fig. 1, for tuning the collider. First, we extendedMIA to include the longitudinal excitation. Now, the MIAmodel matches the measured dispersion as well. Second,MIAPEP-IIB-Factory LEGOBBIFigure 1: A tuning strategy using modelling and simulationcodes for PEP-II.we were able to reconstruct MIA model in a full opticscode LEGO [3] and used it to calculate complete lattice andbeam parameters. Finally, these parameters were fed to thebeam-beam code BBI [4, 5] to understand the luminosityhistories at PEP-II over the past year. More importantly, wemade quantitative predictions of luminosity gain by varythe beam parameters in the simulation. These results wereused to guide the choice of machine developments (MD).As shown in Fig. 2, a tune scan was simulated with theparameters listed in Table 1. The machines were operatedwith 1722 colliding bunches. Since the bunch separationis only 4.2 ns, the two adjacent parasitic collisions were in-cluded in the simulation. The simulation showed a possible∗Work supported by DOE Contract DE-AC02-76SF00515† yunhai@slac.stanford.edu15% gain in luminosity if the tunes in both horizontal andvertical planes were moved closer to half integer.7.888.28.28.48.48.48.68.68.68.68.68.88.88.89999.2  0.52 0.525 0.53 0.5350.550.5550.560.5650.570.5750.580.5857.67.888.28.48.68.899.2Figure 2: A contour plot of luminosity in unit of1033cm−2s−1 in the LER tune plane based on the three-dimensional beam-beam simulation. The blue and redsquares indicate respectively the tunes before and after therecent tune change in the LER.Table 1: PEP-II Operating Parameters, April 12, 2006Parameter LER (e+) HER (e-)beam energy E (Gev) 3.1 9.0bunch population N 6.39× 1010 4.39× 1010x beta at the IP βx (cm) 37.0 42.0y beta at the IP βy (cm) 0.97 1.08x emittance x (nm-rad) 27.0 49.0y emittance y (nm-rad) 2.07 1.25x tune νx 38.5350 24.5143y tune νy 36.5965 23.6208synchrotron tune νs 0.0314 0.0438bunch length σz (cm) 1.25 1.15energy spread σδ 6.5× 10−4 6.1× 10−4x,y damping τt (turns) 9800 5030z damping τz (turns) 4800 2573NONLINEAR MODELIn the MD that implemented the suggested tune change,we found the beam-beam lifetime of the several bunches inthe head of the bunch train was extremely low. The poorlifetime indicated that the tune space near the half integerwas rather small and not enough to accommodate the tunespread along the train. As a result, the tune change in themachine was backed out.To understand the poor lifetime problem near the half in-teger, we used the beam-based MIA/LEGO model outlinedin the previous section and actual setting of the sextupolesto calculate the tune shifts as a function of Δp/p as shownin Fig. 3. The calculated values were in a good agreementwith the measurements. One can see from the figure thatthere was a large quadratic term in the vertical plane anda cubic term in the horizontal plane. We set the negativechromaticity (between -1 to -2) in the horizontal plane inthe LER to compensate the cubic term, and in the verticalplane we raised the strength of the four local sextupoles 7%to reduce the quadratic term. Both changes nearly doubledthe beam-beam lifetime (30 minutes) when they were im-plemented during the delivery of luminosity. Since the gainin the lifetime is not required because of the trickle chargeinjection, it was quickly traded to a gain in luminosity bylowering the tunes respectively as shown in Fig. 2. 0.5 0.52 0.54 0.56 0.58 0.6 0.62-0.006 -0.004 -0.002  0  0.002  0.004  0.006LER MIA tune vs. dp/p.’tune’ u 1:2’tune’ u 1:3'p/pQyQx2Qx-2Qs2Qx-QsFigure 3: Tunes as a function of Δp/p in the LER.Dynamic aperture was also scanned in the tune plane asshown in Fig. 4. To determine a dynamic aperture, the par-ticles were tracked using LEGO up to 1024 turns with 5σpsynchrotron oscillation. It is worth noting that the best tunein the scan coincides with the working point used over ayear in the LER before the recent tune change. It also pre-dicted that the off-energy particles will become unstablewhen νx < 0.516. That was the reason why the beam-beam tune scan shown in Fig. 2 was limited to νx > 0.516.The final jump of the tune toward νx = 0.508 wasachieved during the delivery of luminosity by operators af-ter the RF voltage was lowered from 4.5 MV to 4.0 MV tolengthen the bunches and reduce the heating in the ring. Itis not yet clear to us if the change of the synchrotron tunewas the sole reason that allowed the machine to operate so0.52 0.525 0.53 0.535 0.540.560.5650.570.5750.580.585Min. dyn. aperture. LER MIA, v. 30−Apr−2006, 4.0 MV, dp=5sigma.QxQy0246810121416'p/p = 5V = .00355best aperture 2Qx-2QsQx+Qy-3QsQx+Qy-4QsFigure 4: Scan of dynamic aperture in the tune plane usinga beam-based model of the LER.close to the half integer.Since our model predicted an unstable machine at νx =0.508, ironically, one may note that we have made so muchprogress in the modelling of the accelerators that we suc-ceeded in pushing the accelerators beyond the expectationof the models. This indicates that machine near the half in-teger is much more sensitive and a better model is requiredto make any meaningful prediction.LUMINOSITYMore than 10% specific luminosity was gained after thetune change in the LER. Since then, additional 6% gainwas coming from the minimization of the W-functions (theenergy dependence of the beta-functions) in the horizon-tal plane in both rings by tweaking the sextupoles near theinteraction point during the collision.0 1 2 3 4 5 6x 106024681012x 1033I+xI−(mA2)Luminosity(cm−2 s−1 )May 29, 2006October 10, 2005Figure 5: Measured luminosity as a function of productof beam currents for PEP-II. The blue pluses represent thebest results achieved in October 2005 and the red circlesare data in May 2006.To show the recent increase of the luminosity, we plottedtwo sets of data in Fig. 5, each covered twenty consecutivedays and included the peak luminosity in that run respec-tively. Compared to the last run, we were able to reachhigher luminosity with less beam currents because of thereduction of beam sizes at the collision. The peak luminos-ity 1.0877× 1034cm−2s−1 was achieved in May 25, 2006,with 1722 bunches at the beam currents, 1775mA in theHER and 2700mA in the LER.OTHER IMPROVEMENTSIn this paper, we made emphasis on the most recentevents largely because they have made direct impacts onachieving the peak luminosity. Actually, many small butsteady advances made on machine optics paved the wayto the final success. Here is a list of major improvementssince the beginning of this year:• Reduced the beta beating in the HER from 250%to 10% and allowed its horizontal tune operated ex-tremely close to the half integer.• Speeded up the MIA fitting process and made it avail-able online in the control system to improve the orbitsteering and bump making.• Minimized the orbit excursion and corrected the betabeating and coupling in the LER to reduce the overheating in the beam position monitors.• Introduced many new correction schemes in LEGO toreduce the beta beating, coupling, and dispersion us-ing orbit bumps at paired sextupole positions.• Made the emittance knobs to better match the beamsduring the collision.−1 0 1 2 3 4 5 6x 10601234567x 1030I+xI−(mA2)Specfic Luminosity(cm−2 s−1 mA−2 )March 18, 2006October 10, 2005Figure 6: Specific luminosity as a function of product ofbeam currents for PEP-II. The blue pluses represent thebest results achieved in October 10, 2005 and the red cir-cles are the data in March 18, 2006.As this progress was made, we saw a steady improve-ment in the specific luminosity, for example as shown inFig. 6, at the low beam currents, which were limited by thevacuum problems at the time.CONCLUSIONThe modern accelerators are controlled and continuallyimproved using linear optics model. In this paper, we pro-vided examples of how to use nonlinear models includingthe beam-beam interaction to improve the machine perfor-mance. These models were not only used to select a betterset of machine parameters but also used to validate sug-gested optical improvements. As a result of using thesenonlinear models, we have significantly increased in therate of success for the MD at PEP-II and therefore savedvaluable machine time for the delivery of luminosity.As one could see in this paper, sometimes a predictionbased on the model could be wrong. There are several com-mon reasons that cause a model makes a wrong prediction:first, due to the inaccuracy of the data used to build model;second, missing nonlinear elements in the model; third,physics that is neglected in the codes; finally, human errorsduring the implementation of the prediction. All these un-certainties make the accurate and reliable prediction verydifficult. Sometime making a prediction seems more likean art than science. Finally, we would like to point out thatdespite so many improvements we have made in the mod-elling efforts, the empirical tweak of skew quadrupoles andsexupole bumps by operators and accelerator physicists arestill necessary and vital to achieve the peak luminosity atPEP-II.It takes many years to develop codes for these sophis-ticated simulations. More importantly, dedicated experi-ments are required to validate the simulation codes beforethey could be used to make any reliable prediction. Here,we would like to stress the importance of supporting thelong-term research activities for accelerator physics.As the machines operated near the half integer, we foundout recently that the beta beating in both rings became quitelarge again. A new round of improvement in optics is nec-essary to gain more luminosity. A challenge and quest foraccurate modelling remain as we approach ever closer tothe half integer.REFERENCES[1] J. Irwin, et al, “Model-independent beam dynamics analysis,”Phys. Rev. Lett. 82 1684-1687, 1999.[2] Y.T. Yan and Y. Cai, “Precision PEP-II optics measurementwith an SVD-enhanced least-square fitting,” Nucl. Instrum.Meth. A558:336-339, 2006.[3] Y. Cai, M. Donald, J. Irwin, and Y. Yan, “LEGO: a modularaccelerator design code,” SLAC-PUB-7642, August 1997.[4] Y. Cai, A.W. Chao, S.I. Tzenov, and T. Tajima, “Simulationof the beam-beam effects in e+e- storage rings with a methodof reducing the region of mesh,” Phys. Rev. ST Accel. Beams.4, 011001 (2001).[5] Y. Cai, “Symplectic treatment of a finite crossing angle inthe beam-beam collision,” SLAC-PUB-10674, August 2004,ICFA Beam Dyn. Newsletter, 34 11-19, 2004.

Luminosity Improvement at PEP-II Based on Optics Model and Beam-Beam Simulation

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Luminosity Improvement at PEP-II Based on Optics Model and Beam-Beam Simulation

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