KEKB Beam Collision Stability at the Picosecond Timing and Micron Position Resolution as observed with the Belle Detector
H.Kichimi, K.Trabelsi, S.Uehara, M.Nakao, K.Akai, T.Ieiri, M.Tobiyama, M.D.Jones, M.W.Peters, G.S.Varner, T.E.Browder
aa r X i v : . [ phy s i c s . i n s - d e t ] M a r Belle Preprint 2009-1KEK Preprint 2008-47arXiv:1001.1194JINST 006p 0110
KEKB Beam Collision Stability at the PicosecondTiming and Micron Position Resolution as observedwith the Belle Detector
H. Kichimi , K. Trabelsi , S. Uehara , M. Nakao , K. Akai ,T. Ieiri , M. Tobiyama , M. D. Jones , M. W. Peters ,G. S. Varner and T. E. Browder High Energy Accelerator Research Organization (KEK), Tsukuba, 305-0801 Japan Department of Physics and Astronomy, University of Hawaii, Honolulu, 96822 USAE-mail: [email protected]
Abstract.
Using the Belle detector we study the characteristics of beam collisionsat the KEKB 3.5 GeV e + on 8 GeV e − asymmetric energy collider. We investigate thecollision timing t IP and its z -coordinate along the beam axis z IP as a function of theposition of the colliding bunch in a beam train. The various t IP and z IP behaviorsobserved by Belle are attributed to beam loading effects in the radio frequency cavitiesthat accelerate the beams with a beam abort gap. We report these results in detailand discuss the prospects for the SuperKEKB collider.PACS numbers: 41.85.Ct, 12.15.Hh EKB Beam Collision Stability observed with the Belle Detector
1. Introduction
The B-factories, Belle [1] at KEKB [2] and BaBar [3] at PEPII [4], have carried outprecision measurements of various decay modes of B mesons to verify the Kobayashi-Maskawa mechanism [5] that explains CP-violation in the Standard Model. Belle is asophisticated 4 π detector, which provides precision measurements of the B -meson decayvertex, excellent momentum resolution and particle identification capability. KEKB isan asymmetric collider with beams of 3.5 GeV e + in the low energy ring (LER) and8 GeV e − in the high energy ring (HER). The BaBar detector at the PEPII collider iscomparable to the Belle detector at the KEKB collider. The total integrated luminosityof the two B-factories is 1.5 ab − after ten years of data taking.KEK plans to upgrade the detector and collider to study CP-violation in B -decayswith extremely high precision to search for new physics beyond the Standard Model,with an integrated luminosity of at least 50 ab − [6]. The upgrade plan is to developan asymmetric e + e − collider with a super high luminosity of 8 × cm − s − , and todevelop a detector with improved performance under higher beam backgrounds (due tobeam currents that are a few times larger). There are significant challenges to developingsuch a SuperKEKB factory [7].We report a study of the behaviors of the beam collision timing t IP and its position z IP along the beam axis as measured by Belle. These behaviors are finally attributed tothe beam phases of the colliding bunches in KEKB. To date, there has been no reporton these behaviors, as it requires a collaboration between experts from the detector andthe collider. Moreover, the accelerator parameters relevant in this study were measuredonly during certain periods of machine study, while the Belle measurement is availablethroughout physics data taking. In this study, we use the time-of-flight detector (TOF),which has a time resolution of 110 ps, for the study of the collision timing t IP and thesilicon vertex detector (SVD) and the central drift chamber (CDC) for the study ofthe collision z -coordinate z IP , which is measured with a resolution of about 100 µ m [8].These Belle measurements of t IP and z IP can be understood in terms of KEKB designparameters and operating conditions.Our goal is to understand the sources of systematic uncertainties in the timingmeasurements with Belle at KEKB, and to estimate prospects for the Super KEKB-factory, in particular for particle identification detectors such as the time-of-propagation(TOP) [6, 9] and Cherenkov timing detectors [6, 10], which require precision timingmeasurements with systematic uncertainty better than 20 ps. A comprehensive description of the Belle detector is given elsewhere [1]. Figure 1shows the Belle detector configuration. Charged tracks are reconstructed from hitinformation in a central drift chamber (CDC) located in a uniform 1.5 T solenoidalmagnetic field. The z axis of the detector and the solenoid are along the positronbeam, with the positrons moving in the negative z direction. The CDC measures the EKB Beam Collision Stability observed with the Belle Detector z axis and in the rφ plane, respectively). Charged particle trajectory coordinates near the collision point areprovided by the SVD. Photon detection and energy measurements are performed witha CsI(Tl) electromagnetic calorimeter (ECL). The ECL is also used for identificationof electrons. Identification of pions, kaons and protons is performed using informationfrom the time-of-flight counters (TOF) and silica-aerogel Cherenkov counters (ACC).The ACC provides good separation between kaons and pions or muons at momenta above1.2 GeV/ c . The TOF system consists of a barrel of 128 plastic scintillation counters andcan distinguish K/π for tracks with momenta below 1.2 GeV/ c . Lower energy kaons arealso identified using specific ionization ( dE/dx ) measurements in the CDC. The magnetreturn yoke is instrumented to form the K L and muon detector (KLM), which detectsmuon tracks and provides trigger signals.In order to study the characteristics of t IP and z IP , we use a large sample of µ -pair events ( e + e − → µ + µ − ), which were recorded using the standard Belle trigger andselected through the standard Belle data processing. The accumulation rate of µ -pairevents is about 9 Hz at a nominal luminosity of 1 . × cm − s − . The purity of theselected µ -pair events is better than 98%. e - NikkoSide
Barrel Yoke
KLM
End YokeSC coilBackwardCsI Pole Tip
SVD
Barrel TOF e+ OhoSide
Return Yoke
0 1 2 3(m)
Return Yoke
Barrel CsI
Barrel ACC
ForwardCsI
Barrel CsIBarrel TOFForwardCsICDC Endcap ACCBackwardCsI
Figure 1.
The Belle detector.
The KEKB collider achieved a peak luminosity of 2 . × cm − s − in June 2009, whichis more than twice the design value of 1 × cm − s − . An integrated luminosity of1018 fb − was accumulated with the Belle detector by December 2009. EKB Beam Collision Stability observed with the Belle Detector ◦ C. The RF reference signals are phase-locked at eachstation and distributed to the RF cavities. Thus, the accuracy of the 508.9 MHz RFreference clock is found to be typically 6 ps in one circulation around the KEKB collider.The Belle detector uses the same RF reference signal distributed at TSUKUBA hall.The LER and HER beams collide bunch-by-bunch at the IP with a finite angle of22 mrad in the horizontal plane. Each beam train consists of 5120 buckets synchronousto the 508.9 MHz RF clock. In usual operation, the buckets are filled with three- orfour-bucket spacing and with a period of 49 RF buckets. A typical beam train contains1584 bunches (buckets filled by beam). The beam train is followed by a beam abort gap(BAG) of 270 empty buckets, which is needed to safely kick out the beam from the ring.Figure 3 shows a typical collision bunch pattern as a function of bucket number, whichis obtained from analysis of µ -pair events accumulated with Belle. Here the number of µ -pair events is shown as a function of the bucket number. We clearly see the bunchtrain followed by the BAG as described above.In December 2006, two superconducting crab cavities [12] were installed in theLER and the HER, one for each, in order to operate KEKB in a crab crossing schemeaiming to increase luminosity. Figure 4 illustrates (a) finite angle collisions and (b) crabcrossing at the IP. In the crab crossing scheme the bunches are kicked in the horizontalplane by transverse RF in the crab cavities (located in the NIKKO straight sections) sothat they rotate and collide head-on at the IP (TSUKUBA) even in finite-angle crossingbeam orbits. We study three data sets that are summarized in Table 1 by the run period, LER andHER beam currents, recorded peak luminosity, CM energy and status of crab cavities.(1) Exp55 is the data set before crab cavity installation (no-crab crossing), in whichKEKB achieved the highest peak luminosity with the highest LER and HER currents.(2) Exp61 is the data after the crab cavity installation (crab crossing), during whichKEKB was operated with head-on collisions. (3) Exp65 is the Spring 2008 run period,in which we recorded data at the center-of-mass (CM) energies of the Υ(4S) and Υ(1S)
EKB Beam Collision Stability observed with the Belle Detector TSUKUBA OHOFUJINIKKO
HER
LER
HER
LER IR Linac
RFRF
RF RFe- e+ e+/e-
HER LER
RF RF
WIGGLERWIGGLER (TRISTAN Accumulation Ring)
B Y P A S S
Figure 2.
The KEKB collider complex.
Figure 3.
The number of µ -pair events as a function of the RF bucket number, whichare reconstructed by the Belle detector for Exp61. See Appendix Appendix A.1 fordetails. resonances. To change the CM energy, both the LER and HER beam energies arechanged proportionally. In Table 1, Υ(1S), Υ(4S) and Υ(5S) indicate the CM energiesof 9.460 GeV, 10.580 GeV, 10.860 GeV, respectively. Here Υ(6S) stands for the energy EKB Beam Collision Stability observed with the Belle Detector Figure 4.
Collision schemes at KEKB: (a) finite angle collisions and (b) crab crossing. region just above the Υ(5S). We use more than 300 k µ -tracks for each data sample. Table 1.
Summary of the three run periods (Exp55, Exp61 and Exp65) used in thisanalysis. The peak luminosity is in units of 10 cm − s − . Run period LER HER Peak lum. CM energy CrabExp55 Sept.-Dec. 2006 1.65 A 1.37 A 1.7 Υ(4S) -Exp61 Oct.-Dec. 2007 1.62 A 0.81 A 1.4 Υ(4S,5S,6S) ONExp65 Apr.-June 2008 1.61 A 0.95 A 1.6 Υ(4S,1S) ON
2. Collision timing and collision position t IP We first discuss the long term behavior of the collision timing t IP . We define t IP =( t obs − t exp ) using µ -pair events. Here, t obs is the measured time-of-flight for one µ candidate and t exp is the prediction from its track trajectory in the CDC (see Appendices Appendix A.1and Appendix A.2). We usually obtain a mean t IP = t obs − t exp = 0 for each run usingthe standard TOF calibration after run-by-run correction. For online data processing,we use a default database obtained by TOF calibration using µ -pair events from theprevious run period. Once the database is installed at the beginning of the new runperiod, it is unchanged during the whole run period, typically for several months. Ifboth the KEKB collider and the Belle detector (TOF and CDC) are stable, the mean t IP value should be unchanged. We conclude that the variation of the online t IP valuemust be due to changes in beam conditions or changes in the RF reference timing fromKEKB to the TOF readout system.Figure 5 shows the mean t IP as a function of run number for Exp65, taken atthe energies of the (a) Υ(4S) and (b) Υ(1S) from April to June 2008. We see a slowdrift within a ±
10 ps range and step-like shifts at runs 610 and 810. The t IP changesare due to various effects in the KEKB collider and the Belle detectors. While theindividual sources are not understood completely, the t IP variation can be correctedeven with significant changes of beam energy and frequent optics corrections duringKEKB operation. In practice, we apply a run-by-run correction for t IP to reduce the EKB Beam Collision Stability observed with the Belle Detector
Figure 5. t IP versus run number for Exp65. (a) Υ(4S) runs and (b) Υ(1S) runs. Therun number is reset to 1001 for Υ(1S) runs after run 810. In the analysis that follows, we use the t IP value averaged over a run period andcorrected for the run-by-run variation. Here, a run typically extends for a few hours toa day and contains about 300 k µ -pair events. We normally assume that the collisiontiming is independent of the bunch position in a beam train. However, we observe afine structure in the collision timing as discussed in the following sections. t IP and z IP vs bucket number by Belle The position of each beam bunch may be displaced from that synchronized with theRF frequency, because of dynamic beam loading effects in the RF cavities and thelongitudinal impedance of other accelerating components. Therefore, it is interesting tostudy t IP and z IP as a function of the bucket number N bucket , the collision bunch positionin a bunch train.Figure 6 shows the Belle measurements of t IP and z IP as a function of N bucket ; (a)and (c) show the results for Exp55 while (b) and (d) are the corresponding results forExp61. The open circles indicate the Belle measurements. We see linear t IP variationboth for Exp55 and Exp61. On the other hand, we observe parabolic z IP behaviorfor Exp61, while z IP is almost flat for Exp55. These Belle observations of t IP and z IP behaviors are discussed quantitatively in the next section. EKB Beam Collision Stability observed with the Belle Detector Figure 6. t IP and z IP vs bucket number; (a) and (c) for Exp55, and (b) and (d) forExp61, respectively. The open circles are Belle measurements, while the filled circlesare predictions from the measured LER and HER beam phases (see text). Figure 7 shows the beam phases as a function of the bucket number (N bucket ) measuredby KEKB in the same periods of (a) Exp55 and (b) Exp61. The beam phase isdefined as the phase with respect to the corresponding RF bucket. Here, the phases aremeasured at every 49-th bucket by the gated beam position monitor (GBPM) [13] (seeAppendix Appendix B.1), and the phase of the first bunch after the beam abort gap(bucket number 0) is set to zero by definition. We observe a beam phase advance withincreasing bucket number in the LER and the HER with a maximum phase change ofapproximately 3.5 degrees. Figure 7 (a) shows a similar pattern of beam phases in theLER and the HER for Exp55, while Fig. 7 (b) shows a systematic difference betweenthem for Exp61.
EKB Beam Collision Stability observed with the Belle Detector Figure 7.
Beam phase as a function of bucket number for (a) Exp55 and (b) Exp61.
The observed beam phase modulation is known as ”transient beam loading” in theRF cavities due to the existence of a beam abort gap (BAG) after a bunch train. Thebeam phase change between the head and tail bunches is approximately proportional tothe total beam current and the length of the BAG. The modulation pattern is sensitive tothe type of RF cavities (ARES or SC) and the total beam current, as well as the patternof bunch currents in the bunch train (see Section 3 and Appendix Appendix B.2). t IP and z IP In this section, we give a quantitative discussion of the t IP and z IP behaviors observed byBelle from beam phases of the collision bunches in the beam train. Assuming head-oncollisions of the LER and HER bunches in the horizontal plane at the interaction point(IP) for a finite-angle collision with crab crossing, we derive the following formulae, t IP = T RF × − ( φ HER + φ LER )2 × z IP = L RF × ( φ HER − φ LER )2 × T RF (approximately 2 ns) is one RF period and L RF (approximately 0.6 m) is onebucket interval given by cT RF where c is the speed of light. The beam phases φ HER and φ LER are in degrees. Here we assume that the change of z IP is much smaller thanthe vertical beta function β ∗ y of 6 mm at the IP. If this is not the case, the change of z IP will be smaller than the value given by Eqn. (2) due to the hourglass effect. Thecollision timing of the tail bunch is advanced by about 20 ps relative to the synchronousRF bucket, so that t IP is delayed by the same amount. It should be noted that the z IP EKB Beam Collision Stability observed with the Belle Detector t IP variation is almost proportional to the beam phase modulation.In finite-angle collisions without crab cavities, the bunches are more separated in thehorizontal plane before and after the collision than in the case of the head-on collisionswith crab cavities, as seen in Fig. 4. We estimate the z IP variation by a naive calculationfrom the geometrical overlap of the colliding LER and HER bunches in three dimensionsas a function of time, and taking into account finite-angle collisions with and withoutcrab cavities and the beam focusing optics at the IP. We find that the z IP variation isslightly smaller, about 70% of that predicted by Eqn. (2).Figure 6 shows the Belle measurements (open circles) of t IP and z IP compared withthe predictions (filled circles) from Eqns. (1) and (2). They are in good agreement exceptfor a small systematic difference in Fig. 6(d). In Exp55, the LER and HER beam phasevariations are similar, so that the z IP behavior is flat and has no distinctive structure.In the case of Exp61, we see a parabolic z IP behavior with a range of approximately0.6 mm, due to the significant difference between the LER and HER beam phases. Thisis attributed to the difference in the LER beam phase behaviors between Exp55 andExp61 as shown in Fig. 7. The cause of the difference is discussed in Section 3.Thus, the observed t IP and z IP behaviors are explained well by the beam phasechange as a function of the bunch position in the colliding bunch trains (beam phasemodulation), which is caused by the transient beam loading effect in the RF system dueto the beam abort gap in the beam train. z IP Figures 8 (a) and (b) show the z IP distributions for Exp55 and Exp61, respectively.The widths of these distributions, fitted to a Gaussian function with σ = 3 .
71 mm and3.96 mm, respectively, are affected by the LER and HER bunch sizes along the beamaxis and the collision scheme (no-crab or crab crossing).The natural bunch lengths for (LER, HER) are estimated to be (4.86 mm, 4.84 mm)for Exp55 and (4.86 mm, 5.22 mm) for Exp61 from the known KEKB operationparameters (Table 2). The last two columns give the expected z IP widths and thecorresponding Belle measurements. Here, the z IP width is estimated from the naturalbunch lengths by σ IP = 1 / p /σ + 1 /σ . The widths measured by Belle areabout 10 % larger than these estimates, due to the bunch lengthening effect caused bythe inductive part of the longitudinal impedance of the ring components. The z IP widthsin the crab crossing runs (Exp61) seem to be larger than those in the no-crab crossingruns (Exp55).
3. Discussion on the LER beam phase behaviors
Here, we discuss the cause of the significant difference in the LER beam phasebehaviors in Exp55 and Exp61 due to beam loading in the RF cavities (see
EKB Beam Collision Stability observed with the Belle Detector Figure 8. z IP distributions for (a) Exp55 and (b) Exp61. The Gaussian widths are3.71 mm and 3.96 mm, respectively. Table 2.
Size of collision position z IP and LER and HER bunch sizes natural bunch length z IP width z IP width crabLER HER KEKB est. Belle meas. statusExp55 4.86 mm 4.84 mm 3.43 mm 3.71 mm OFFExp61 4.86 mm 5.22 mm 3.56 mm 3.96 mm ONAppendix Appendix B.2). We first consider the possibility that the striking difference isrelated to the crab cavity installation. However, as crab cavities of the same type wereinstalled in both the LER and HER, we cannot explain why we observed a significantdifference only in the LER beam as shown in Fig. 7.In general, the beam phase change with bunch position is attributed to transientbeam loading in the RF cavities, which is sensitive to the total beam current and thebunch current pattern after the BAG. The transient beam loading effect is characterizedby the ratio T /T f , where T is the beam revolution period and T f is the filling time ofthe RF cavity. In the limit T ≫ T f , the beam phase shift (relative to the RF bucket) isexpected to be largest in the beam head just after the BAG. This results in non-linearbehavior of the beam phase. On the other hand, in the limit T ≪ T f , the beam phaseis expected to be linear with bunch position as the effect is averaged over many beamrevolutions. ARES cavities have a T /T f value of 0.54, which is about twice as large asSC cavities. Therefore, the LER, which consists of ARES cavities only, tends to havestronger non-linear behavior of the beam phase.The above discussion is based on the assumption that the bunch current (currentintensity) is uniform along the beam train. Figure 9 shows the LER and HER bunchcurrent variation versus bunch position for (a) Exp55 and (b) Exp61. We see that theHER bunch currents are constant in both; the HER beam phases vary almost linearlywith bunch position as shown in Fig. 7. Using Eqn. (B.2), we calculate the ratio of thehead to tail phase shifts to be 0.74 for Exp61/Exp55 from an HER current of 0.80 A EKB Beam Collision Stability observed with the Belle Detector Figure 9.
Bunch current at each 49-th bucket for (a) Exp55 and (b) Exp61. (1.26 A) and an RF voltage of 13 MV (15 MV). We also measure an HER beam phaseshift of 2.8 (Exp61) and 3.7 (Exp55) degrees, and find the ratio of 0.76, which is in goodagreement with the above estimate.On the other hand, the LER bunch current in Exp55 shows a slow increase of about20% in the head part (up to bucket number 1000), while it is almost uniform in Exp61.We conclude that the non-linear behavior of the beam phase (Exp61) can be attributedto the transient response of the ARES cavities to the uniform bunch currents along thebunch train. In the case of Exp55, the pattern of non-uniform bunch currents weakensthe steep increase of the beam phase in the head part and increases the phase changein the tail part, and thus gives almost linear phase behavior.The SuperKEKB [7] collider was initially designed to store currents of 9.4 A in theLER and 4.1 A in the HER (High Current scheme), which are four times larger thanthose of KEKB. To reduce the beam-loading effect due to the beam abort gap, which isproportional to the beam currents, we have designed a gap length of 2% (5% at KEKB)that will require development of new beam abort kickers. Recently an alternative designcalled the Nano-Beam scheme has been proposed and is the baseline option. This schemeobtains high luminosity via small beam sizes, which are achieved by reducing emittancesand β -functions. The required beam currents of 3.3 A (LER) and 1.9 A (HER) aresmaller than in the initial SuperKEKB proposal and hence the beam loading effects aresomewhat reduced.
4. Summary
Using the Belle detector, we study the characteristics of colliding beams at the KEKBasymmetric energy collider. The behaviors of the collision timing ( t IP ) and its z - EKB Beam Collision Stability observed with the Belle Detector z IP ) observed by Belle are well explained by the beamphase variations along the LER and HER beam trains (beam phase modulation). Here,we calibrate for the long term variations of t IP (see subsection 2.1) whose causes arenot well understood. The studied beam phase variations are caused by transient beamloading in the RF systems due to the beam abort gap in the beam train. The z IP behavior is very sensitive to the beam phase difference between LER and HER beamtrains. The beam phase variation is sensitive to the bunch current pattern along thebeam train as well. In collisions of LER 1.6 A and HER 1.2 A beams with a 5 % beamabort gap at KEKB, we find an z IP variation of about 0.6 mm, and an t IP variation ofabout 20 ps. To reduce the beam loading effect, we have designed a gap length of 2%to allow the SuperKEKB collider to store currents of 9.4 A (LER) and 4.1 A (HER) forthe High Beam current scheme. The beam loading effect is much reduced with the samegap design for the Nano Beam scheme.We are able to reduce the systematic errors in collision timing and position due tothe beam loading in the RF system to insignificant levels by correcting the data for thefine structure as a function of the bucket number, as discussed in this report. A crucialissue for the SuperKEKB factory detector, which must realize a systematic error of lessthan 20 ps, will be to reduce time jitter in the readout system synchronized with theRF clock and in the calculation of the time-of-flight value from tracking information. Acknowledgments
We are grateful to the Belle collaboration and the KEKB members who made this studypossible and fruitful.
Appendix A. Event timing determination with the TOF detector
Appendix A.1. Bucket number determination
A detailed description of the TOF readout system and analysis procedure is foundin Ref. [14]. Here, we explain the TOF timing measurement scheme with the TimeStretcher [15] (TS) and TDC (TS-TDC), as it is essential to determining the bucketnumber of a colliding bunch for each event.The TOF readout system records a set of charges Q i and timings T i from the risingedges of discriminator outputs for each PMT signal from the TOF detector. Figure A1shows the block diagram of the TS-TDC scheme. The TS circuit finds the first risingedge T of the TS reference (reduced RF) clocks following the rising edge T of theTOF signal, and expands the time interval T = T − T by a factor of approximately f = 20 to obtain T ( T − T = T × f + a ). These times are then read out with theBelle standard TDC with a 0.5 ns least significant bit (LSB), providing a 25 ps LSBresolution. We reconstruct the TOF timing T TS − TWC from timings, T , T and T , using EKB Beam Collision Stability observed with the Belle Detector f and a calibrated for each TS channel. We further apply a Time WalkCorrection (TWC) to correct for timing variation proportional to 1 / √ Q [14]. Collision time Ref T
BCO 2.2 (cid:80) s - 30 (cid:80) s : given by GDL
Common stopt RF signal 508.9 MHzReduced RF signal
BC/O reference time128 MHz
TOF signal t
TOF
Time Stretcher output to TDC1877S : LSB = 0.5 ns 30 ns W8 ns2 ns (cid:39) t (cid:55) (cid:20) (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:55) (cid:21) (cid:55) (cid:22) (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:55) (cid:23) T stop f x (cid:39) t Figure A1.
Time Stretcher TDC scheme for TOF. The TS reference clock ofapproximately 8 ns period is generated from the KEKB RF signal of 508.9 MHz.
The TS reference clock of approximately 8 ns (127.2 MHz) is generated from theRF clock of 508.9 MHz. As the RF clock is used for the entire KEKB timing controlof the LER and HER beams, the TS clock is necessarily synchronized with the beamcollision timing.Each event is triggered with a DAQ clock of approximately 16 ns periodsynchronized with every 8-th RF bucket. An RF bucket number n DAQ (a multipleinteger of 8) corresponding to the trigger is then recorded. In the standard TOF offlineanalysis, we determine a precise time relative to the DAQ clock. In particular, wedetermine an integer n TOF (a fine bucket number relative to n DAQ ), by taking intoaccount track momenta and their path lengths to the TOF counter (times-of-flight with e, µ, π , kaon and proton mass hypotheses). We obtain n TOF with a candidate set ofthe mass assignments for each track, by optimizing a sum of squared time differences P ij ( δT ij ) for all tracks in the event, where δT ij = ( T TS − TWC ij − n TOF × T RF ) − t exp ij is the time difference using the j -th mass hypothesis for the i -th track. Here, T RF isthe RF period of approximately 2 ns. Thus, we find n TOF , and obtain the measuredTOF timing t obs i = ( T TS − TWC i − n TOF × T RF ) for the track and the bucket number N bucket = n DAQ + n TOF of the collision bunch in the train. Figure 3 shows the numberof µ -pair events as a function of the reconstructed bucket number. Appendix A.2. Time resolution of the TOF detector
Here, we discuss the sources of the time resolution for the TOF detector. Figure A2 (a)shows the distribution of time difference ( t A − t B ) between two measurements withindependent channels t A and t B for the same input signal, in order to study the time EKB Beam Collision Stability observed with the Belle Detector σ ( t A − t B ) / √ t = ( t obs − t exp ) (= t IP ) for µ -pair events. Here, t obs is the measuredtime with TWC calibration after TS reconstruction, while t exp is the predicted timecalculated from the track trajectory in the CDC and its extrapolation to the TOF.Whenever both KEKB operation and the Belle detector (TOF and CDC) are stable,the mean of ∆ t should be zero. However, ∆ t varies run-by-run and in the long term.In practice, we correct for the run-by-run variation to set the mean ∆ t to zero for eachrun, so that we have no bias in physics analysis.The present time resolution of the TOF system is found to be 110 ps for µ -pairtracks. This resolution includes a systematic error of 40 ps consisting of the followingcomponents; a time jitter of 10 ps between the RF and TS clocks, 35 ps in the TOFreadout system (front-end and TS-TDC circuits), 10 ps uncertainty in the time-of-flightcalculation from µ -track information, and 13 ps due to the collision position spread of4.0 mm because of bunch length. The 10 ps uncertainty in the time-of-flight calculationis estimated for µ -pair events (by Monte Carlo), while it is larger than 10 ps for hadrontracks due to effects from hadronic interactions. The resolution of 110 ps is degradedfrom the initial resolution of 96 ps obtained in 1999 [14]. Taking into account theuncertainties discussed above, we extract intrinsic time resolutions of the Belle TOFdetector of 102 ps and 87 ps for June of 2008 and 1999, respectively. The degradation ismainly due to ageing, a reduction of the attenuation length and light yield in the TOFscintillation counters over a ten year period. Figure A2. (a) Distribution of ( t A − t B ) for times measured by two independentreadout channels A and B for the same input signal. (b) Distribution of ∆ t TOF = t obs − t exp for µ -pair events for Exp 65, which gives a TOF time resolution of σ =110 ps. EKB Beam Collision Stability observed with the Belle Detector Appendix B. Beam bunch phase vs bucket number at KEKB
Appendix B.1. Bunch-by-bunch phase detection
In the KEKB collider about 450 beam position monitors (BPM) are mounted along thebeam pipe for both of the LER and HER, in order to provide the beam position atspecific locations. Each BPM consists of four electro-static electrodes to detect beampassages. One BPM is used to study possible beam phase variation as a function ofbucket number in a beam train. The beam pick-up signal is fed into a gated beam-position monitor system (GBPM) that employs an I/Q (In-phase and Quadrature-phase)demodulator operating at the RF frequency of 508.9MHz to extract two orthogonalsignals, V sin and V cos for each bunch. A gate module in the front end selects a specificbucket in a beam train and enables bunch-by-bunch detection of the beam. The twoorthogonal components and a specific bucket number are sampled by a beam revolutionclock of approximately 10 µ s and stored in memory by GBPM. The beam phase φ beam of a specific bunch, with respect to its bucket phase φ RF synchronous to the 508.9 MHzRF clock, is calculated from the two components V sin and V cos by: φ beam − φ RF = tan − ( − V sin V cos ) . (B.1)When the GBPM data are averaged over 2,000 turns, we estimate a resolution of ± . ± . Appendix B.2. Transient beam loading effect
The amplitude and phase of the RF in the accelerating cavities is modulated by theBAG, since the beam loading is different between the BAG and the beam train occupiedby bunches. As a result, the synchronous position is shifted bunch-to-bunch in a beamtrain. Assuming that the cavity is operated at the optimum tuning and that the fillingtime of the cavity T f is much longer than the revolution period T , i.e. T /T f ≪
1, thebeam-phase difference ∆ φ HT between the head and tail bunches is given approximatelyin ref. [16] as: ∆ φ HT = I t V c R s Q ω RF ∆ t g , (B.2)where I t is the total beam current, R s is the shunt impedance, V c is the cavity voltage, Q is the Q-value of the cavity, ω RF is the angular RF frequency and ∆ t g is a transit timeof one BAG. In KEKB, the LER operates using ARES cavities with T /T f = 0 .
54, whilethe HER operates using two different types of cavities, ARES and SC (about a half ofthe ARES T /T f value). This causes the LER to have stronger non-linear behavior ofthe beam phase.In order to evaluate the modulation due to the BAG, a time domain simulationcode was developed, taking into account beam loading on the accelerating mode ofthe cavities [17]. The simulation result was compared with the LER beam phase EKB Beam Collision Stability observed with the Belle Detector
Figure B1.
Beam phase (in degrees) as a function of bucket number. The solidcircles are the measured values while the dashed line shows the results of simulation.
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