RECENT BEAM-BEAM EXPERIMENTS AT HERA-II AFTER

THE LUMINOSITY UPGRADE

M. Minty

DESY, Hamburg, Germany

This report describes recent observations of the interactions between proton and positron beams in collision with the newly upgraded [1,2] HERA accelerators. While thorough experiments were performed prior to the upgrade under special conditions created to simulate the expected conditions of the interactions [3-5], unambiguous confirmation of certain features of the beam-beam interaction (BBI) could take place only following the upgrade of the accelerator optics and interaction regions. In the experiments presented here, we investigate observed processes which may result in a smaller than expected luminosity and on ways to avoid them in the future.

INTRODUCTION During the design stages of the HERA-I accelerator [6],

the stability of the colliding beams was of great concern given the absence of supporting experimental data for extremely high-energy proton-lepton collisions. In fact, during initial commissioning, the lifetime of the proton beam was seen to depend critically on the presence of collisions with the lepton beam [7]. To maximize the proton lifetime, the betatron tunes were carefully controlled and the beam sizes at the interaction points were carefully centered and made equal in size resulting in proton beam lifetimes of several hundred hours [7]. The HERA-II collider design [1,2] includes new low β-insertions at the interaction points (IPs) and calls for higher beam intensities. To confirm the feasibility of the HERA upgrade proposal, various studies were undertaken [3-5] prior to the upgrade. Experiments in 1999 [3] with high intensity electron bunches (and the normal 60 degree HERA-E optic), demonstrated the absence of proton beam emittance growth with single-bunch electron currents almost a factor of 3 times nominal (or, equivalently, with positron beam-beam tune shifts a factor of 3 times nominal). Furthermore, the specific luminosity was measured to be independent of the electron current. These results strongly suggested that the cores of both beams remained unperturbed by the BBI. In year 2000, experiments with a 72 degree HERA-E optic, as called for in the luminosity upgrade, were performed with the interaction point (IP) optics so modified to produce positron beam-beam tune shifts >4 times nominal [4,5]. During these studies, as shown in Fig. 1, the vertical positron emittance evidenced an 8-fold increase. The measured specific luminosity during these experiments was seen to reduce in accordance with the increased beam

size from Lsp=7.8×1029 cm-2mA-2s-1 at the nominal value of β*e,y of 0.7 m to Lsp<2×1029 cm-2mA-2s-1 with β*e,y= 4 m. The source of this significant decrease in luminosity was attributed to the large tune shift caused by the beam-beam force, which has since been confirmed by simulation [8]. It is worth noting that under the conditions of this experiment, the β* which would mimic the tune shifts of the HERAII upgrade was β*e,y~ 1 m.

Figure 1. Vertical (top, red) and horizontal (bottom, green) beam emittances normalized to their computed value as a function of positron β-function at the IP as measured prior to the luminosity upgrade. Following the installation of the HERAII upgrade in the years 2000-2001, the beam sizes of both beams at both interaction regions are now significantly smaller and the beam-beam tune shifts are somewhat larger. Shown in Table I is a comparison of beam parameters before and after the upgrade [9]. To verify these parameters, experiments have been performed to study the BBI with the HERAII upgrade. The results from early commissioning in year 2002 were presented already in Ref. [10]. There it was reported that following many optics corrections made during early commissioning (see [11]), the measured beam sizes at the IPs were in agreement with design at low beam currents (protons: Isb,p ~200 µA/ bunch, positrons: Isb,e ~45 µA/ bunch). The measured and expected specific luminosity was also found to be in reasonable agreement. At single-bunch proton currents Isb,p > 200 µA/ bunch, however, the measured specific luminosity was consistently lower than

DESY HERA 03-21

expectation. The study of this observation is the motivation for the experiments summarized in this report.

Table 1. Comparison of beam parameters before and after the HERA luminosity upgrade, from Ref. [9].

BEAM-BEAM EXPERIMENTS

The goals of the beam-beam experiments consisted of (i) validating or disproving the occasionally observed strong nonlinear dependence of the luminosity L on the product of the beam currents and (ii) probing to determine if the limitations on total achievable specific luminosity were driven by increased beam emittances and if so, if this could be avoided. A decrease in luminosity with increasing beam currents may be attributable to poor operating conditions (e.g. arising from close proximity of the betatron tunes to resonances, which affect the beam parameters even without collisions). More fundamentally, the deviation from linearity may be indicative of unavoidable emittance blowup of one or both beams due to resonances driven by the nonlinear beam-beam forces. Such behavior becomes manifest with very small beam sizes at the IPs and with very high single-bunch beam intensities. The study of this measured deviation from expectation at an unexpectedly low current product was the primary goal of the beam-beam studies Since high total beam currents give rise to adverse effects, which may confuse interpretation of the experiment (e.g. related to vacuum conditions), it is convenient to consider the specific luminosity Lsp which, assuming head-on collisions of beams with Gaussian transverse charge distributions, is defined as

,1

)2

1()

1( 2

,, yxrcolesbpsbsp feNII

LL

ΣΣ==

π

where Ncol denotes the number of colliding bunches, Σx,y is the convoluted beam size derived from the individual beam sizes σx,y by addition in quadrature, e=1.6×1019 C, and fr=47.3 kHz is the revolution frequency. The beam sizes at the IP are obtained from the measured emittances and the IP β*-functions, which are assumed to be equal to design unless otherwise noted, via σ2

x,y=εx,yβ*x,y. From Eq. (1) the specific luminosity may be inferred in two different ways: from the measured luminosity and single-bunch beam currents, or as a consistency check, from the measured beam emittances.

Beam-beam studies with high single-bunch proton currents

For these experiments, the total number of bunches was reduced to allow for high single-bunch beam intensities while not aggravating conditions arising from high total beam currents. The proton single-bunch currents Isb,p were varied between (100-500) µA while the single-bunch positron currents Isb,e was roughly constant at 265 µA. The measured beam current distributions used with beams in collisions are shown in Fig. 1.

The specific luminosity measured at H1 is shown as a function of the product of the single-bunch currents Isb,p× Isb,e with collisions at one and two IPs in Fig. 2. In both cases a tendency towards lower specific luminosity was observed as the current product Isb,p× Isb,e was increased. Note that the HERAII design specific luminosity of

Eq. (1)

~1.8×1030 cm-2mA-2s-1 was attained thus exceeding that of HERAI by more than a factor of 3. To determine if this dependence was related to proton emittance growth caused by the beam-beam interaction, is shown in Fig. 3 the ratio of the measured proton beam emittances as a function of single-bunch positron current Isb,e measured before and after colliding the beams. The deviation of the average ratio from unity might be explained by a difference in β-functions at the wire scanner in the separation and luminosity optics [12]. The significant feature is the absence of any beam-beam induced emittance growth of the proton beam. Likewise, the dependence of the proton beam emittance ratio on Isb,p was also observed to be constant. We conclude therefore that there is no significant emittance dilution of the proton beam caused by the act of bringing the beams into collision.

On the other hand, the vertical positron emittance was observed to depend on the proton single-bunch beam current as shown in Fig. 4 for the case of collisions at both the H1 and ZEUS IPs and in Fig. 5 for collisions only at H1 (unfortunately, only the data in the vertical plane were available).

To better understand the observed dependence of the positron emittance on proton current, are plotted in Figs. 6 and 7 the incoherent beam-beam tune shifts ξx,y of the positrons as a function of proton single-bunch beam intensity. The incoherent tune shift is given by

,)(2 ,

,*

,yxyx

yx

e

epyx

rNσσσ

βπγ

ξ+

=

Figure 1 Measured beam current distributions of the protons (top) and positrons (bottom) as a function of position along the accelerators during the high current proton experiments.

Figure 2. Measured specific luminosity versus single-bunch current product with collisions at 1 IP only (blue circles) and with collisions at 2 IPs (red crosses).

Figure 3. Ratio of proton emittances (horizontal: top, vertical: bottom) measured before and after collisions as a function of positron single-bunch current.

Figure 4. Measured vertical positron emittance as a function of single-bunch proton current (with collisions at two IPs).

Eq. (2)

where Np is the single-bunch proton population (=Isb,p/efr), re=2.8179×10-13 cm, βx,y

* is the positron beta function at the IP, γe = E/m is the Lorentz factor for the positrons, and σx,y represent the proton beam sizes at the IP.

Figure 5. Measured vertical positron emittance as a function of single-bunch proton current (with collisions at one IP).

In these figures, the solid line shows the design incoherent tune shifts, the circles represent the incoherent tune shift calculated using Eq. (2) with the measured beam emittances, and the red crosses show the measured difference in betatron tunes (non-colliding minus colliding) measured using the positron tune monitor multiplied by a factor of 2 to obtain the incoherent tune

shifts (assuming matched beam sizes and Gaussian transverse profiles of both beams).

Figure 7. Same as Fig. 6 but with collisions at 1 IP. A possible reason for the discrepancy (see also [13]) between the data denoted by circles and crosses for the case of 2 IPs might be explained taking into account the current-dependence of the β-function at the IP (which was taken to be constant and equal to design in the measurement results designated by circles), which arises from the additional focussing caused by the BBI, the so-called “dynamic beta effect”. The incoherent tune shift is more accurately expressed [3] as

[ ] ,)2||2cos()2cos()2sin(

1

2*2

0

0,

−∆+−×

=

QQQ

N IPyx

πθππ

πξ

ξξ

where NIP denotes the number of interaction regions, Qx,y are the betatron tunes, and ∆θ denotes the phase advance between interactions. From Eq. [3] using the parameters of the experiment (Qx=54.236, Qy=51.322), the incoherent tune shift with 2 interaction regions may deviate from the perfectly compensated case by (-6.3 to +7.7)% horizontally and (-15.4 to +6.1)% vertically. This is insufficient to explain the observed variations, which at 500 µA single-bunch proton current were observed to be on the order of (20-30)%. The measured coherent tunes are shown in Figs. 8 and 9, which show the tune diagram Qy vs Qx. The circles / crosses represent the (fractional) betatron tunes of the noncolliding / colliding bunches. As the positron beam-beam tune shift increases (with increasing current), the positrons experience emittance growth due to the 2Qx+2Qy resonance, in the case of 2 IPs, and due to the 3Qx+Qy resonance with only 1 IP. In the case of a single IP, the positron beam was observed to ‘lock’ onto this fourth order resonance. Locking of the beam onto very

Figure 6. Horizontal (top) and vertical (bottom) incoherent tune shift of the positrons versus single-bunch proton current with collisions at 2 IPs. Solid line: design, blue circles: from Eq. 2 with measured emittances, red crosses: direct measurement .

Eq. (3)

high order (13th and 16th) resonances has been observed at the SPS [14].

Figure 9. Measured betatron tunes of the positron beam and nearby strong resonances with 1 IP. With either one or two collision points, the ratio of the specific luminosities measured by H1 and calculated based on the measured beam emittances is roughly constant indicating that the decrease in specific luminosity with increasing current product is attributable to the increased beam sizes. A case of special interest concerns proton beam emittance blowup due to a coherent beam-beam instability occurring at certain values of betatron tunes of the positron beam. This effect was predicted by J. Shi [8] well in advance of the luminosity upgrade and has been observed experimentally and analysed. During the high luminosity studies [15] with single-bunch beam intensities of Isb,p =390 µA and Isb,e= 275 µA, and with measured coherent tunes of Qx=0.215 and Qy=0.296 for

the colliding bunches, the proton beam emittances were observed to have increased from nominal average values of 22×22 nm-rad (2σ, unnormalized) to 27×28 nm-rad representing a (20-30) % increase. Shown in Fig. 10 is the particle distribution in the tune diagram resulting from a beam-beam simulation made with the above experimental input parameters. The simulation shows that the resonance at 2Qx+2Qy leads to depletion of the lepton beam. Shown in Fig. 11 is the tune diagram near the operating point given by the polarization tunes.

Figure 10. Simulated positron particle distribution after 2000 turns with collisions at one IP with Qx=0.215 and Qy=0.296 for the positrons and Qx=0.294 and Qy=0.298 for the proton beam (courtesy J. Shi, April 2003).

Figure 11. Same as Fig. 10 but with positron tunes of Qx=0.140 and Qy=0.210 (courtesy J. Shi, April 2003). The simulated centroid motion of the proton and positron beams is shown in Fig. 12, which demonstrates that the observed emittance blowup of the proton beam is due to a coherent beam-beam instability. Spontaneously occurring centroid motion has been observed in many colliders. To explain this effect, the influence of one

Qy=1/3

Figure 8. Measured betatron tunes of the positron beam and nearby strong resonances with 2 IPs.

2Qx+2Qy

Qx=1/3

Qy=1/4 2Qx + 2Qy

Qy+3Qx

2Qx + 2Qy

Qy=1/4

beam on the fields and particle distributions of the other beam must be taken into account; that is, it is insufficient to consider the influence of one beam on only a single particle within the other beam. Coherent beam-beam interactions are an ongoing subject of intense studies at many colliders.

Figure 12. Simulated coherent vertical motion of the proton (top) and lepton (bottom) beams showing the onset of a coherent beam-beam instability (courtesy J. Shi, April 2003). While oscillations of the positron beam may be eventually surpressed through radiation damping, the proton beam emittance may be diluted due to this effect. Shown in Fig. 13 are the simulated beam emittances versus turn number for the two sets of betatron tunes (those used in the experiment and those nearer the tunes which will be used for high polarization). From the simulation results, the proton beam emittances can increase substantially (pink curves) as a result of a coherent beam-beam instability. Fortunately, for the polarization tunes (green curves), such dangerous resonances can be avoided.

Beam-beam studies with high single-bunch lepton currents In these studies, the total number of bunches was intentionally reduced to around 60. The average single-bunch proton current was Isb,p = 135 µA and the single-bunch positron beam current was varied from Isb,e = (50-300) µA. The betatron tunes of the noncolliding positron bunches were set to nominal and maintained via the tune controller. The goal of the experiment was to quantify the rate of proton beam emittance growth with time. This rate relates directly to the rate of decrease of the specific luminosity with time.

Figure 13. Simulated emittance growth of the proton (top) and positron (bottom) beams for betatron tunes as in Fig. 10 (b, pink) and for tunes closer to those used for high polarization as in Fig. 11 (a, green) (courtesy J. Shi, April 2003). The measured proton and positron single-bunch currents are shown as a function of time and location along the accelerator in Fig. 14. The positron beam lifetimes are in general longer than they were before the upgrade with the beam currents used to date [16,17]. The measured proton beam emittances and the measured single-bunch luminosities are shown in Fig. 15. For these data, assuming a coupling of the positron beam of 10%, the measured specific luminosity and that calculated based on the measured proton beam emittances are in agreement. The proton beam emittances measured immediately after establishing collisions are shown in Fig. 16 as a function of the lepton beam single-bunch beam current Isb,e. For Isb,e < 265 µA, which represents the single-bunch current used in HERAI, the proton beam emittances were constant. With Isb,e > 265 µA however, emittance growth in both planes was observed. The HERAII design single bunch current is Isb,e=310 µA corresponding to a total beam current of 58 mA. For reference, the design emittances for HERAII are 20 nm in both planes. The growth rates were fitted and plotted as a function of the current with which the protons collided and are shown in Fig. 17. While the error bars are somewhat large given insufficient statistics, a dependence on Isb,e is observed. The average emittance of the proton beam for colliding bunches is shown as a function of time in Fig. 18. From the fitted slopes, the emittance growth rates were obtained as shown in Table 2. These emittance growth rates, while substantial and deserving of further study, are not signifi-

Figure 14. Measured current distributions of the protons (top) and positrons (bottom) during the high lepton beam current experiments. cantly different from those observed prior to the upgrade [18]. dεx / dt dεy / dt colliding bunches

1.47 +/- 0.60 1.47 +/- 0.65

noncolliding bunches

0.36 +/- 0.07 0.34 +/- 0.05

Table 2. Proton beam emittance growth rates in units of 10-9 m-rad per hour, where the emittances denote the 2σ, unnormalized emittances. In a separate study, to determine the influence of noise in the positron beam tune feedback on the proton beam emittance, the feedback was turned off and the proton beam emittances again measured as a function of time. Due to uncontrolled beam loss (scraping) of the protons

during the measurement, however, the results were inconclusive.

Figure 15. Measured time dependence of the proton horizontal (top) and vertical (middle) emittances and the measured single-bunch luminosities (bottom).

Figure 16. Measured proton beam emittances versus single-bunch positron beam currents immediately after establishing collisions. The HERAII design emittances are 20 nm-rad in both planes.

Figure 17. Proton beam emittance growth rates sorted and fitted according to beam current with which the protons collided.

Figure 18. Average proton emittance versus time with linear fits to determine growth rates.

SUMMARY From the studies with variable, high intensity single-bunch proton beam currents, there were 5 effects which were determined to potentially lead to a decrease in specific luminosity as a function of total current product: (i) positron beam emittance growth via beam-beam induced resonances: From Figs. 5, 7, and 9 the beam was observed to lock onto a skew resonance. The resonance Qy=-3Qx is not naturally driven by the bare lattice. On the other hand, given the symmetry of the beam-beam potential, the even order resonance 2Qy=-6Qx, which occurs at the same location, is a resonance which can be driven by the beam-beam interaction. It is believed that this led to the dramatic increase in the emittance of the positron beam. (ii) proton beam emittance growth via beam-beam induced resonances: Figures 10-13 demonstrated the onset of a coherent beam-beam instability for certain

values of the transverse betatron tunes of the positrons. These simulation results explain qualitatively the occasionally observed blowup of the proton beam emittances during luminosity operations. (iii) dependence of proton beam emittance on proton beam current: There was no evidence of proton emittance growth caused by bringing the beams into collision. However, the proton emittance prior to collisions was observed to fluctuate significantly. Shown in Fig. 19 are the proton emittances and single-bunch beam currents Isb,p measured prior to collisions. The same data are plotted versus Isb,p in Fig. 20. The largest emittances, occurring at the smallest beam currents at the end of the bunch trains, arise presumably to poorly timed injection and/or extraction kickers between accelerators. The hint of a current dependence of the proton emittances may result already in the preaccelerators. The sources of these emittance dilutions warrant further study.

Figure 19. Measured proton beam emittances in x (top) and y (middle) and single-bunch beam currents (bottom) before collisions.

Figure 20 (same data as Fig. 19). Proton emittances plotted versus proton single-bunch beam current (iv) positron beam emittance growth via normal lattice and/or beam-beam induced resonances: From Figs. 4 and 8, the positron emittance was increased by the resonance at 2Qx+2Qy, which occurs naturally in the single-ring lattice and, given its symmetry, may be driven by the beam-beam interaction. The strength of this resonance was estimated [19] to be about 20% larger with the optic HELUMGJ used in these experiments. Since the beam-beam simulation results (Fig. 13) did not confirm this observation, the emittance growth is presumed to be driven by nonlinear fields rather than by the beam-beam interaction. (v) effect of dynamic beta function: The variation in the beta functions as the betatron phase advances between IPs varies from 0 to 2π were estimated for the conditions of these experiments and found not to be of large significance.

The relative impact of the effects listed above on the

specific luminosity was evaluated numerically. The beam-beam induced resonances leading to emittance dilution of the proton and positron beams, items (i) and (ii) above, had the most negative influence. Fortunately, by proper choice of betatron tunes of the positrons, these resonances may in the future be avoided. The next leading order effect was observed to arise from emittance variations in the proton beam (item iii), which were present even before collisions. More systematic monitoring and a study to determine if the emittance growth scales with intensity is advised. Positron beam emittance growth (item iv) due to proximity to nearby resonances should also be avoidable with the polarization tunes. Lastly, luminosity degradation due to dynamic beta effects was estimated and predicted not to be a strong factor at the present choice of betatron tunes. As the tunes are adjusted towards the polarization tunes (i.e. towards integer), dynamic beta effects are expected to become more important. A new optic has been developed

which minimizes distortions to the β-functions in the presence of collisions [20].

The experiments with variable, high intensity single-bunch positron beam currents showed emittance dilution of the proton beam immediately following collisions at single-bunch positron currents exceeding those used during HERAI. This effect is likely to be due to the choice of positron beam betatron tunes. The measured time-dependence of the proton emittances, while substantial with beams in collision, were not significantly different than observed in previous years [18].

Concerning prospects for future operations, we conclude that the causes of the observed decrease of the specific luminosity Lsp with increasing beam currents Ip×Ie are understood. To leading order this was found to be attributable to emittance growth of either the lepton or proton beams due to single-beam resonances or driven by the BBI. By proper choice and optimization of the lepton beam betatron tunes (i.e. set near integer and near the coupling resonance Qx=Qy, as will be necessary for high polarization) these effects may be minimized in the future. Another source of dLsp / d (IpIe) ≠ 0 was found to be emittance variations of the proton beam as measured prior to collisions. This and further study of the positron beam lifetime warrants further study to improve prospects for high total integrated luminosity. Adverse effects related to single-beam synchrobetatron resonances [21] of the lepton beam, which could limit high luminosity operations with polarized beams, requires further study. The possible influence of the beam-beam interaction on the lepton beam polarization also awaits further theoretical and experimental studies.

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[16] M. Hoffmann, “Untersuchungen zur Strahl-lebensdauer in HERA-e”, DESY HERA 03-11 (2003)

[17] M. Seidel, “Vacuum in the HERA Interaction Regions: Recent Experiences and Outlook”, DESY HERA 03-10 (2003)

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[20] E. Gianfelice developed the HELUMSM optics, which optimizes the betatron phase advances between the two interactions points of HERA

[21] F. Willeke, “Synchrobetatron Resonances in HERAe after the Luminosity Upgrade”, DESY HERA 03-16 (2003)