The lifetime of a light source with small emittance like the Advanced Light Source (ALS) is usually limited by the momentum acceptance of the ring. Large momentum acceptances are reached by providing enough RF voltage and by avoiding a degradation of the dynamic momentum aperture. At the ALS the size of the momentum acceptance depends strongly on the transverse dynamics. It is very sensitive to machine conditions such as the tunes and chromaticities since depending on those conditions the Touschek scattered particles explore different resonance regions in the phase space. In this paper we show that by using a single-turn ’pinger’ magnet together with turn-byturn beam position monitors (BPM) one can identify the cause of a reduction in momentum acceptance and take steps to improve the acceptance

Decking, W

Laskar, J

Nadolski, L

Robin, D

Steier, C

Wu, Y

Steier, C.

Robin, D.

Wu, Y.

Decking, W.

Laskar, J.

Nadolski, L.

DESY

Understanding the Dynamic Momentum Aperture of the Advanced Light Source

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UNDERSTANDING THE DYNAMIC MOMENTUM APERTURE OF THEADVANCED LIGHT SOURCEC. Steier, D. Robin, Y. Wu, LBNL, Berkeley, CA94720, U.S.A.;W. Decking, DESY, Hamburg, Germany; J. Laskar, L. Nadolski, IMC-CNRS, Paris, FranceAbstractThe lifetime of a light source with small emittance likethe Advanced Light Source (ALS) is usually limited bythe momentum acceptance of the ring. Large momentumacceptances are reached by providing enough RF voltageand by avoiding a degradation of the dynamic momen-tum aperture. At the ALS the size of the momentum ac-ceptance depends strongly on the transverse dynamics. Itis very sensitive to machine conditions such as the tunesand chromaticities since depending on those conditions theTouschek scattered particles explore different resonance re-gions in the phase space. In this paper we show that byusing a single-turn ’pinger’ magnet together with turn-by-turn beam position monitors (BPM) one can identify thecause of a reduction in momentum acceptance and takesteps to improve the acceptance.1 INTRODUCTIONThe ALS is a third generation synchrotron light sourcelocated at Lawrence Berkeley National Laboratory [1].Like all other light sources, the beam lifetime is one of themost crucial performance parameters for the users, since ithas a large impact on the stability of the experiments andon the amount of integrated brightness which is delivered tothe experiments. Similar to all other third generation lightsources the lifetime is dominated by the Touschek effect.The Touschek lifetime depends strongly on the momentumacceptance of the machine.Several effects contribute to the overall momentum ac-ceptance (and therefore the Touschek lifetime): The rf-bucket height, the physical apertures and in many cases thedominating effect: the dynamic aperture [2, 3].To achieve small equilibrium emittances in third genera-tion light sources, strongly focusing quadrupoles are used.This requires strong sextupoles to compensate for the chro-matic aberrations in order to damp head-tail modes. Thesextupole fields generate geometric and nonlinear chro-matic aberrations which can excite resonances. Those reso-nances can cause the particle motion to become unstable orchaotic. In the ALS, low order resonances are suppressedby the 12-fold periodicity of the ring.2 RF AMPLITUDE SCANSScanning the rf-bucket height while measuring the beamlifetime can be used to quantify the effects determining theThis work was supported by the U.S. Department of Energy, underContract No. DE-AC03-76SF00098.momentum acceptance. Because of the energy distributionof Touschek scattered particles one expects the lifetime tobe a quadratic (to cubic) function of the RF-bucket height,as long as there are no dynamic effects limiting the ac-ceptance. The turnover point, at which a deviation fromthe quadratic behaviour occurs, provides information aboutthe nonlinear dynamics effects limiting the dynamic accep-tance. Fig. 1 shows three scans of the RF-voltage for dif-ferent linear chromaticities of the ALS.0 0.005 0.01 0.015 0.02 0.025 0.03 0.035012345678∆ p/pτ (@ 400 mA) [h]ξx=0.5, ξy=1.4, εy/εx=4%ξx=0.4, ξy=4.4, εy/εx=4%ξx=2.4, ξy=4.3, εy/εx=4%Figure 1: Scan of the RF amplitude and therefore the lon-gitudinal bucket height for three different sets of horizontaland vertical chromaticities (1.5 GeV).As one can clearly see, the dynamic momentum accep-tance and therefore the maximum achievable lifetime isvery sensitive to the linear chromaticities. It is best forthe nominal chromaticities of x=0.5 and y=1.4, whichare used at the ALS in multibunch operation (blue ’x’ sym-bols), and significantly worse (red ’o’ symbols) for a ver-tical chromaticity increased by 3 units. Unfortunately, in-stabilities require us to increase the vertical chromaticityin two-bunch operation (up to 35 mA/bunch), to provideenough Landau damping. Therefore it is of interest to un-derstand the effect causing this difference (which at firstis surprisingly large, considering that the strength of sex-tupoles is only different by a few percent). The green ’+’symbols indicate a case where based on the studies de-scribed later a lifetime improvement of about 25% wasachieved for the high chromaticity case.3 LOSS MECHANISMTo study and understand the effects limiting the dynamicmomentum acceptance, some methods of Frequency MapAnalysis [4] were modified to study the evolution of off-energy particle trajectories. Frequency Map Analysis is avery effective tool to visualize the global dynamics for sys-0-7803-7191-7/01/$10.00 ©2001 IEEE.Proceedings of the 2001 Particle Accelerator Conference, Chicago434tems of 3 and more degrees of freedom. Originally it hadbeen used at the ALS to study the dynamics of particleswith nominal energy.By simultaneously recording beam currents and there-fore loss rates, the on-energy studies had shown, that cer-tain resonance intersections can lead to diffusion and sub-sequent particle loss [5]. Due to radiation damping, allparticles launched to amplitudes above such a loss regioneventually have to damp back through the region, yieldingsome probability for particle loss. To verify this model,tracking studies were carried out, confirming that indeedparticles damping through a loss region, might experiencelarge diffusion and get lost (or as in the case of Fig. 2, getclose to or outside of a physical aperture, which in the ALSis about 4 mm vertically).14.22 14.23 14.24 14.25 14.26 14.27 14.288.088.098.18.118.128.138.148.158.168.17νxν y0 2000 4000 6000 8000 10000 12000−10−50510turn #x [mm]0 2000 4000 6000 8000 10000 12000−4−2024turn #y [mm]Figure 2: Single particle tracking with synchrotron radi-ation. Left: frequency space (tune calculated every 200turns), right: configuration space.4 PINGER MEASUREMENTSTo study the momentum acceptance in detail, two single-turn ”pinger” magnets together with turn-by-turn beam po-sition monitors (BPM) were used. To collect one data set,the RF-frequency was set to different values, correspond-ing to different beam energies. For each setting of the RF-frequency, the beam was then kicked with increasing hor-izontal amplitude (and a small vertical amplitude) whilethe beam oscillations and the fraction of beam loss wererecorded, until the beam was completely lost.The data sets for the nominal and high vertical chro-maticity cases are shown in Fig. 3 and 4, respectively. Thehorizontal axis is the relative energy deviation, the verticalaxis the kick amplitude in mm. The thickness of the dotsindicates the relative size of the beam loss. The solid lineshows to which horizontal amplitude a particle is launched,if it receives a given change in energy due to Touschek scat-tering in a region with dispersion at the ALS (i.e. the arcs).The intersection of these lines with the loss regions (areaswith thick dots) corresponds roughly to the dynamic mo-mentum acceptance.The agreement between the estimated dynamic momen-tum acceptance from those measurements and the directmeasurement using the RF-amplitude scans is very good.In addition one clearly sees completely different structures−0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 0.050246810121416∆ p/px [mm]0 0.05 0.1 0.15 0.2 0.25 0.3 0.3500.050.10.150.20.250.3νxν yFigure 3: Measurement data showing the relative beam lossin configuration space (upper plot, x=12 m) and in tunespace (lower plot) for the low chromaticity case. The dotthickness corresponds to the amount of normalized beamloss. The solid green line marks the tune shift with energyfor particles with very small oscillation amplitudes.in the shape of the loss regions in the two cases. Usingthe beam oscillation data, which was recorded at the sametime as additional information, one can identify which res-onances in tune space cause those loss regions. The analy-sis showed (compare Fig. 3 and 4) that the large differencein lifetime is not caused by a large difference in strengthof resonances, but by the fact that different linear chro-maticities cause the particles to sample completely differ-ent regions in phase space. Because of that, they experiencecompletely different sets of resonances.The large loss region at positive energy deviations inFig. 4 turned out to be caused by the coupling reso-nance, which is intentionally excited at the ALS to in-crease/control the vertical beam size in order to achieveacceptable lifetimes. In the case with low vertical chro-maticity on the other hand, the tunes do not cross the cou-pling resonance. Based on this it was predicted, that rais-ing the horizontal chromaticity simultaneously should helpto increase the momentum acceptance in the high verticalchromaticity case by shifting the crossing point with thecoupling resonance to larger energy deviations. The mea-surements indeed showed that there was an improvementof about 25% in lifetime which immediately benefits thetwo-bunch operation of the ALS.5 COMPARISON WITH SIMULATIONSSimulations based on tracking with the calibrated modelof the ALS [5] are in very good agreement with the mea-Proceedings of the 2001 Particle Accelerator Conference, Chicago435−0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 0.050246810121416∆ p/px [mm]0 0.05 0.1 0.15 0.2 0.25 0.3 0.3500.050.10.150.20.250.3νxν yFigure 4: Measurement data for the case with higher ver-tical chromaticity. Significantly different areas of the tunespace are sampled compared to the low chromaticity case.surements (see Fig. 5, where the high vertical chromaticitycase is shown). The color code in the plots indicates thediffusion rate (as defined by the change in betatron tune inone turn) on a logarithmic scale. Blue areas indicate lowdiffusion, red areas high diffusion and areas without colorindicate unstable regions.−10−9 −8 −7 −6 −5 −4 −3 −0.05 0 0.050246810121416∆ p/px position [mm] (injection straight)Figure 5: Simulation of a frequency map with the energyoffset and the horizontal oscillation amplitudes as the vari-ables spanning the configuration space. The color code in-dicates the diffusion rate on a logarithmic scale.6 APPLICATION TO THE ALSSUPERBEND UPGRADETo satisfy the demand for more high energy, high bright-ness beamlines at the ALS, a project is underway to re-place three regular bend magnets with three 5.75 T super-conducting magnets (Superbends) [6] in August of 2001.This will impact the symmetry of the lattice functions andtherefore the single particle dynamics. Extensive simula-tion studies have been carried out to ensure that the impacton the machine performance is small. To study the impactexperimentally before the actual installation of the Super-bends, three pairs of additional quadrupoles in the Super-bend sectors were used to simulate the symmetry breakingas closely as possible. Using frequency analysis to analyzethe experimental dynamic momentum acceptance studiesproved very valuable. It allowed to immediately under-stand initial problems and to verify that the impact of theSuperbends indeed will be minimal, as long as the tunesand chromaticities are kept close to their nominal values.7 SUMMARYMeasurements have demonstrated that the dynamic mo-mentum acceptance in the ALS is the dominant effect de-termining the Touschek lifetime. Employing the methodof frequency analysis provides a very powerful model in-dependent diagnostic tool to visualize the global dynamicsof the system, understand limitations and suggest improve-ment strategies. Even with the limitation of only two avail-able sextupole families in the ALS, a significant improve-ment of the lifetime in two bunch operation was realized.For newer light sources with very elaborate sextupole con-figurations, this method can help to systematically optimizethe momentum acceptance.The agreement between measured data and simulationresults which are based on calibrated machine models isgood, providing both confidence in the model and the pos-sibility to accurately predict the performance of upgradesto the ALS or the performance of new machines.To make the method more usable as a tool for onlineoptimization of the accelerator, we plan to reduce the mea-surement time significantly by upgrading the control sys-tem interface of BPMs and the pinger magnets. Moreoverwe plan to study a case nearly identical to Touschek scat-tering by applying transverse and longitudinal kicks simul-taneously.8 REFERENCES[1] 1-2 GeV Synchrotron Radiation Source Conceptual DesignReport, LBNL publication PUB-5172 Rev. (1986)[2] W. Decking and D. Robin, ”Momentum Aperture of the Ad-vanced Light Source”, AIP conf. proc. 468 (1998), p. 119[3] W. Decking and D. Robin, ”Dynamic Aperture Measure-ments at the Advanced Light Source”, Proceedings of PAC1998, New York, USA[4] D. Robin, C. Steier, J. Laskar, L. Nadolski, “Global Dynam-ics of the Advanced Light Source Revealed through Exper-imental Frequency Map Analysis”, Phys. Rev. Lett. 85, 3,(July 2000), pp. 558-561[5] C. Steier et al., “Lattice Model Calibration and FrequencyMap Measurements at the ALS”, Proceedings of EPAC 2000,p. 1077, Vienna, Austria[6] D. Robin et al., “Superbend Project at the Advanced LightSource”, these proceedingsProceedings of the 2001 Particle Accelerator Conference, Chicago436

Understanding the dynamic momentum aperture of the Advanced Light Source

Understanding the dynamic momentum aperture of the Advanced Light Source

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