A sub-micron resolution, bunch-by-bunch beam trajectory feedback system and its application to reducing wakefield effects in single-pass beamlines
D. R. Bett, P. N. Burrows, C. Perry, R. Ramjiawan, N. Terunuma, K. Kubo, T. Okugi
PPrepared for submission to JINST
A sub-micron resolution, bunch-by-bunch beam trajectoryfeedback system and its application to reducing wakefieldeffects in single-pass beamlines
D. R. Bett 𝑎 P. N. Burrows 𝑎 C. Perry 𝑎 R. Ramjiawan 𝑎 N. Terunuma 𝑏 K. Kubo 𝑏 T. Okugi 𝑏 𝑎 John Adams Institute for Accelerator Science at University of Oxford,Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom 𝑏 High Energy Accelerator Research Organization (KEK),1-1 Oho, Tsukuba, Japan
E-mail: [email protected]
Abstract: A high-precision intra-bunch-train beam orbit feedback correction system has beendeveloped and tested in the ATF2 beamline of the Accelerator Test Facility at the High EnergyAccelerator Research Organization in Japan. The system uses the vertical position of the bunchmeasured at two beam position monitors (BPMs) to calculate a pair of kicks which are appliedto the next bunch using two upstream kickers, thereby correcting both the vertical position andtrajectory angle. Using trains of two electron bunches separated in time by 187.6 ns, the system wasoptimised so as to stabilize the beam offset at the feedback BPMs to better than 350 nm, yielding alocal trajectory angle correction to within 250 nrad. The quality of the correction was verified usingthree downstream witness BPMs and the results were found to be in agreement with the predictionsof a linear lattice model used to propagate the beam trajectory from the feedback region. This samemodel predicts a corrected beam jitter of c. 1 nm at the focal point of the accelerator. Measurementswith a beam size monitor at this location demonstrate that reducing the trajectory jitter of the beamby a factor of 4 also reduces the increase in the measured beam size as a function of beam chargeby a factor of c. 1.6.Keywords: Beam-line instrumentation, hardware and accelerator control systemsArXiv ePrint: 2008.12738 a r X i v : . [ phy s i c s . acc - ph ] N ov ontents The Accelerator Test Facility (ATF) is a research facility located at the High Energy AcceleratorResearch Organization (KEK) in Tsukuba, Japan. The ATF is intended to facilitate the developmentof technologies and techniques required for the realization of a future linear electron-positroncollider, either the International Linear Collider (ILC) [2] or the Compact Linear Collider (CLIC) [3].The ATF is shown schematically in Figure 1; it consists of an RF gun, a 1.3 GeV electron linac,a damping ring, and a beamline known as ATF2 [4, 5]. At the end of the ATF2 beamline, a pairof powerful quadrupole magnets is used to focus the electron beam to the smallest size possibleat a location known as the interaction point (IP). The ATF2 beamline is shown in more detail inFigure 2.The ATF2 Collaboration has two goals. Goal 1 is the production of a 37 nm vertical beam spotsize at the IP. Goal 2 is the stabilization of the vertical beam position at the same location to thenanometer level [6, 7]. The ATF is nominally operated with a beam charge of 1 × electronsper bunch and a pulse repetition rate of 3.12 Hz, where each pulse consists of a single bunch witha length of approximately 7 mm [8].The ATF is also capable of generating multi-bunch trains by accumulating bunches in thedamping ring over the course of several pulses and then extracting them in a single pulse. Thesetrains consist of either two or three bunches with a bunch spacing of around 150 ns. The Feedback– 1 – igure 1 . Schematic of the ATF. The label “IP” refers to the nominal location of the focal point of thebeamline where the beam size is minimized. Figure 2 . Schematic [1] of the ATF2 beamline showing the layout of components in the region of the FONTfeedback system and at the IP. See Table 1 for location of components used.
On Nanosecond Timescales (FONT) [9] group at the University of Oxford developed a low-latency( ∼
150 ns) single-phase beam feedback system [10] as a prototype of the intra-train beam stabilisationsystem required for the interaction point of the ILC. Here, we report the results of a feedback systembased on this technology to stabilize both the beam position and the trajectory angle in the ATF2.The corrections were applied in the vertical plane locally in the early part of the ATF2 beamline soas to deliver a stable beam to the entrance of the final focus system.
The hardware of the feedback system is depicted schematically in Figure 3 and the locations ofthe key components relative to the start of the ATF2 beamline are given in Table 1. P2 and P3– 2 – igure 3 . Schematic of the coupled-loop feedback system using BPMs P2 and P3 and kickers K1 and K2. are stripline beam position monitors (BPMs). The voltage pulses induced on the top and bottomstriplines by the passage of an electron bunch are processed using custom analogue electronicmodules; the design of these BPMs and electronics has been previously reported [11]. The striplinevoltage-difference signal ( Δ ) depends on both the vertical position of the bunch and its charge 𝑄 ,while the stripline voltage-sum signal ( Σ ) depends only on charge. The position of the bunch isderived from the ratio Δ / Σ . A beam position resolution of 291 ±
10 nm for this system in operationat ATF2 has been reported [11]. In 2016 the system was upgraded [12], resulting in an improvedposition resolution of 157 ± . × electrons/bunch).The upgraded system was used for the results reported here.The processed BPM signals are input to a custom-made digital feedback (‘FONT5’) board [10,11]. The FONT5 board design features a Field-Programmable Gate Array (FPGA) along with nineanalogue-to-digital converters and a pair of digital-to-analogue converters. The feedback algorithmruns on the FPGA and is able to calculate the appropriate kicker drive signals from the digitized BPMsignals. The kicker drive signals are then amplified externally using bespoke ultra-fast amplifiersdeveloped by TMD Technologies [13] and applied to the stripline kickers K1 and K2. Furtherdetails of this system are reported in [14–18]. Table 1 . The longitudinal locations of selected beamline components relative to the start of the ATF2beamline.
Name Distance [m]K1 26.672K2 29.598P2 30.123P3 33.025MFB1FF 58.534IPB 89.212IP 89.299IPC 89.386– 3 – igure 4 . BPM resolution vs. beam bunch charge ( 𝑄 ). The filled and unfilled data points correspond tomeasurements with the upgraded and original systems respectively. In each case the line shows the result ofextrapolating the lowest-charge data point to higher charges with a 1 / 𝑄 dependence. For each train of two bunches extracted from the damping ring, the feedback calculation convertsthe measured position of the first bunch at the feedback BPMs P2 and P3 ( 𝑦 and 𝑦 respectively)into a pair of kicker drive signals to be applied to the second bunch at the kickers K1 and K2 ( 𝑣 and 𝑣 respectively). The derivation of the calculation is straightforward. The corrected positionof the second bunch at P2, Φ , is expressed as: Φ = 𝑌 + 𝐻 𝑣 + 𝐻 𝑣 (2.1)where 𝑌 represents the ‘natural’ position of bunch 2 (i.e. the position that bunch 2 would have inthe absence of a kick). The second and third terms correspond to the change in position caused bythe kicks at K1 and K2 respectively with 𝑣 𝑖 representing the magnitude of the kick at K 𝑖 and 𝐻 𝑖 𝑗 the kicker sensitivity constant that describes how a kick at K 𝑖 is converted into a position offset atP 𝑗 . A similar expression is obtained for the corrected position of the second bunch at P3 and thetwo can be expressed together in a single matrix equation:– 4 – Φ Φ (cid:33) = (cid:32) 𝑌 𝑌 (cid:33) + (cid:34) 𝐻 𝐻 𝐻 𝐻 (cid:35) (cid:32) 𝑣 𝑣 (cid:33) (2.2)The goal of the feedback system is to stabilize the position of the second bunch at both BPMsi.e. Φ = Φ =
0. By imposing this condition, and assuming the upstream trajectory of bunch 2matches that of bunch 1 ( 𝑌 = 𝑦 ), the following expression for the kicks is obtained: (cid:32) 𝑣 𝑣 (cid:33) = − (cid:34) 𝐻 𝐻 𝐻 𝐻 (cid:35) − (cid:32) 𝑦 𝑦 (cid:33) (2.3)The calculation is implemented [19, 20] in the firmware of the FONT5 digital board in theform: (cid:32) 𝑣 𝑣 (cid:33) = (cid:34) 𝐺 𝐺 𝐺 𝐺 (cid:35) (cid:32) 𝑦 𝑦 (cid:33) + (cid:32) 𝛿𝑣 𝛿𝑣 (cid:33) (2.4)where the feedback coefficients 𝐺 𝑗𝑖 represent the extent to which the measured offset at P 𝑗 con-tributes to the kick to be delivered at K 𝑖 . The feedback coefficients are derived from the measuredkicker sensitivity constants 𝐻 𝑖 𝑗 , which are constant for a given set of beam optics. The 𝛿𝑣 𝑖 termsare constant offsets that can be optionally applied to the kicks, allowing the mean position of thecorrected bunch to be shifted without affecting the reduction in position jitter that can be achieved. This section presents the results from two separate studies. The first study examined the beamposition stability that could be achieved with the feedback system, using downstream BPMs towitness the correction. The second study explored the effect of the feedback system on the beamsize at the ATF2 focal point.
The beam stability study was performed using trains of two bunches extracted from the DampingRing with a bunch spacing of 187.6 ns, a train repetition rate of 1.56 Hz and a bunch population of0 . × electrons. The stripline BPM MFB1FF (Figure 2) is located about 25 m downstream of the feedback system(Table 1) and was instrumented with an analogue processor of the same type as used for P2 and P3.The outputs of this processor were monitored using a second FONT5 board operating purely as adigitizer.The cavity BPMs IPB and IPC [21] (Figure 2) are located either side of the focal point. TheseBPMs were instrumented with a completely distinct set of processing electronics [22], the outputsof which were monitored by a third FONT5 board. The operation of these BPMs for multi-bunchintra-train readout has been previously reported [23–26].– 5 – .1.2 Measurements
Distributions of the vertical beam position recorded at each BPM are shown in Figure 5 for a typicalrun comprising 200 beam pulses. The feedback was toggled on and off for alternate beam pulsesand the distributions are shown separately for the feedback-off and feedback-on sets of pulses.The feedback BPMs themselves are mounted on translatable mover stages and, at the start ofa period of data taking, are normally aligned so as to approximately zero the mean of the readoutposition of bunch 1. It is clear from the feedback-off data that there is a difference of ∼ μ min the orbits of the two bunches, suggesting a non-uniformity of the extraction kicker pulse thatremoved the bunch train from the damping ring. The relative timing of the extraction kicker pulsecan be adjusted to ensure that neither bunch is close to the pulse edges, but the goal of this scanis to maximize the bunch-to-bunch correlation rather than match the mean orbits. The higher thecorrelation between the pulse-by-pulse positions of the two bunches, the more stable the position ofthe corrected bunch is. The kick offset parameters (Eq. 2.4) are available to eliminate the residualoffset of the mean position at each BPM.In this case, the requirement to keep the corrected trajectory of the second bunch withinthe dynamic range of the downstream witness BPMs (including MFB1FF, which has no mover)complicates the issue and the set of measured mean positions represents the end result of an iterativeprocess of tuning the corrected orbit of the second bunch while working within the limits imposed bythe incoming orbit difference of the uncorrected bunches and the range of the cavity BPM movers.The performance of the feedback system in terms of the beam stability is shown in Figure 5.Bunch 1 provides the feedback input and its position is not corrected. Bunch 2 is well corrected bythe feedback as shown by the substantial reduction in the position jitter seen at the two feedbackBPMs. Table 2 summarises the measured beam position jitter at each BPM for bunches 1 and 2with feedback off and on, along with the correction factor, defined as the ratio of the feedback-offjitter to the feedback-on jitter. The correction is limited by the resolution of BPMs P2 and P3, whichwas approximately 200 nm for the bunch charge used (0 . × electrons; see Figure 4). Thecorrection factor at all three witness BPMs is consistent with the in-loop correction of roughly afactor of 4.Also shown in Table 2 are the predictions of a linear beam transport model of the ATF2beamline based on MAD [27]. The measured beam positions at P2 and P3 were extrapolated usingthe model to give predicted positions at MFB1FF, IPB and IPC. The predicted jitter values andrespective correction factors are in good agreement with the direct measurements, implying thatthere are no major sources of additional beam jitter between the feedback kickers and the ATF2final focus.As the system is dual-phase, the effect of the feedback on the angular jitter of the beam is alsoof interest. The angular jitter of the bunch is calculated using the position measured at two BPMsand knowledge of how the beam propagates from one BPM to the other; the MAD model is usedfor the transfer matrix from P2 to P3. In the IP region the transfer matrix is trivially obtained as thebeam propagates in a ballistic fashion from IPB to IPC.The measured position and angle can then be propagated downstream using additional transfermatrices from the model in order to give the predicted distributions of the beam angle at eachwitness BPM. The angles at P3 and in the IP region are shown in Figure 6 and these results, along– 6 – igure 5 . Distribution of position measured at each BPM (rows) for bunch 1 (left column) and bunch 2 (rightcolumn) with feedback off (outline) and on (filled). Where necessary a reduced bin width is used to displaythe feedback-on data so as to limit the maximum frequency of a single bin for display purposes. with those at MFB1FF, are summarized in Table 3. The results show that the angular jitter of bunch2 is also corrected by the feedback by about a factor of 4, consistent with the position-correctionanalysis. The locally-measured beam angle jitter in the IP region is in good agreement with themodel prediction.The performance of the feedback system can be characterised by the degree to which it reducesthe correlation between the position of bunch 1 and the position of bunch 2, and the correlationbetween the angle of bunch 1 and the angle of bunch 2. The calculated Pearson correlationcoefficients for these two cases are shown in Table 4 and Table 5 respectively. The beam transport– 7 – igure 6 . Distribution of angle at P3 (calculated from the position at P2 and P3) and in the IP region(calculated from the position at IPB and IPC) with feedback off (outline) and feedback on (filled). A reducedbin width is used for the feedback on data where necessary to limit the maximum frequency of a single binfor display purposes. Figure 7 . Predicted vertical position jitter (calculated from the position at P2 and P3) in the region of thefocal point with feedback off (solid) and feedback on (dashed). – 8 – igure 8 . Predicted distribution of position at the focal point (calculated from the position at P2 and P3)with feedback off (outline) and feedback on (filled). A reduced bin width is used for the feedback on datawhere necessary to limit the maximum frequency of a single bin for display purposes. model predictions are in good agreement with the measurements. However, the data imply thatthe feedback is slightly over-correcting as the correlation between bunches with feedback activeis slightly negative rather than consistent with zero. Optimization of the feedback coefficients toremove the residual correlation could be the subject of future studies.The model can also be used to predict the beam position distribution at the focal point wherethe vertical beam position jitter is at a minimum. Figure 7 shows the measured jitter at P2 and P3(Table 2) tracked to the focal-point region; the beam waist at the focal point is clearly visible. Thetracked beam position distribution at the focal point is shown in Figure 8. With feedback off thepredicted jitter is 2 . ± . . ± . a b l e . V e r ti ca l b ea m po s iti on jitt e rf o r bo t hbun c h e s f o rf ee db ac ko ff a nd f ee db ac kon . T h e t op fi v e r o w s a r e t h e v a l u e s m ea s u r e d l o ca ll y . T h e bo tt o m t h r ee r o w s a r e t h e r e s u lt o f t r ac k i ng t h e po s iti ond a t a fr o m t h e f ee db ac k B P M s do w n s t r ea m u s i ng t h e m od e l . E rr o r s a r e s t a ti s ti ca l . B P M B un c h1 jitt e r[ μ m ] B un c h2 jitt e r[ μ m ] C o rr ec ti on f ac t o r F B o ff F B on F B o ff F B on M ea s u r e d l o ca ll y P . ± . . ± . . ± . . ± . . ± . P . ± . . ± . . ± . . ± . . ± . M F B FF . ± . . ± . . ± . . ± . . ± . I P B . ± . . ± . . ± . . ± . . ± . I P C . ± . . ± . . ± . . ± . . ± . T r ac k e d fr o m P & P M F B FF . ± . . ± . . ± . . ± . . ± . I P B . ± . . ± . . ± . . ± . . ± . I P C . ± . . ± . . ± . . ± . . ± . T a b l e . V e r ti ca l b ea m a ng l e jitt e rf o r bo t hbun c h e s f o rf ee db ac ko ff a nd f ee db ac kon . T h e t op f ou rr o w s a r e t h e r e s u lt o f t r ac k i ng t h e po s iti ond a t a fr o m t h e f ee db ac k B P M s do w n s t r ea m u s i ng t h e m od e l . T h e fi n a l r o w i s ob t a i n e du s i ng t h e I P B a nd I P C po s iti ond a t a . E rr o r s a r e s t a ti s ti ca l . B P M B un c h1 jitt e r[ μ r a d ] B un c h2 jitt e r[ μ r a d ] C o rr ec ti on f ac t o r F B o ff F B on F B o ff F B on T r ac k e d fr o m P & P P . ± . . ± . . ± . . ± . . ± . P . ± . . ± . . ± . . ± . . ± . M F B FF . ± . . ± . . ± . . ± . . ± . I P . ± . . ± . . ± . . ± . . ± . M ea s u r e d l o ca ll y I P . ± . . ± . . ± . . ± . . ± . – 10 – able 4 . Bunch-to-bunch position correlation coefficient for feedback off and feedback on. The top five rowsare the values measured locally. The bottom three rows are the result of tracking the position data from thefeedback BPMs downstream using the model. Errors are statistical. BPM FB off FB onMeasured locally P2 0.95 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 5 . Bunch-to-bunch angle correlation coefficient for feedback off and feedback on. The top four rowsare the result of tracking the position data from the feedback BPMs downstream using the model. The finalrow is obtained using the IPB and IPC position data. Errors are statistical.
BPM FB off FB onTracked fromP2 & P3 P2 0.98 ± ± ± ± ± ± ± ± ± ± In addition to its application as a direct means of achieving the beam stability goal at ATF2, theFONT beam orbit feedback system has also been observed to cause a reduction in the apparent beamsize at the IP [28]. This is thought to be a result of a better-controlled beam experiencing smallerwakefield-induced distortions of the bunch shape within particular structures along the beamline.We report the results of a study to investigate the effect of beam orbit control on the measured beamsize as a function of the bunch charge.
A nanometer-resolution IP beam size monitor (IPBSM) is installed at the ATF2 IP [29]. The deviceworks by splitting a laser beam in two and then crossing the two halves at the IP to form a fringepattern in the beam focal plane. The size of the fringes is given by 𝑑 = 𝜆 / ( 𝜃 / ) , where 𝜆 isthe laser wavelength and 𝜃 is the crossing angle of the two laser paths. Laser photons are inverseCompton scattered by the electron beam and measured downstream of the IP. The position of thefringes relative to the beam is scanned by phase shifting one of the laser beams and the degree ofvariation of the scattered photon signal is quantified as a modulation depth ( 𝑀 ). The vertical beamsize ( 𝜎 ) can then be estimated from: – 11 – = 𝑘 √︄
12 ln (cid:18) 𝐶 | cos 𝜃 | 𝑀 (cid:19) (3.1)where 𝑘 = 𝜋 / 𝑑 and 𝐶 expresses the contrast reduction of the laser fringe pattern due to factors suchas deteriorated spatial coherency of the laser. The interaction of the electromagnetic field surrounding a bunch of charged particles with geomet-rical discontinuities in the beamline results in wakefields. Each particle in the bunch receives atransverse deflection from the wakefield induced in the beam pipe by the passage of the precedingparticles, leading to both a change in the measured orbit of the bunch as a whole as the center ofmass shifts and a change in the orbit of the tail of the bunch relative to the head. As the IPBSMeffectively measures the size of the distribution of particles at the IP integrated over many bunches,any increase in the beam position jitter or distortion of the transverse profile of the bunch is perceivedas an increase in beam size.ATF2 is known [30] to be particularly sensitive to wakefields due to the long bunch lengthand the relatively low beam energy. The primary sources of wakefields in the ATF2 beamline areC-band cavity BPMs, bellows and vacuum flanges [31]. The orbit change caused by wakefields atATF2 has been reported [32] and several of the cavity BPMs were removed in order to reduce it.As the magnitude of the wakefield kick is proportional to the position offset between bunch andwakefield source (for small offsets), a position feedback that reduced the offset between bunch andwakefield source would be expected to mitigate the increase in beam size due to wakefields. Thisis described in the next section.
Figure 9a shows the beam size as a function of the beam charge when the beam was operatedin single bunch mode. The vertical beam size ( 𝜎 ) can be expressed as a function of a chargedependence parameter ( 𝑤 ): 𝜎 = √︃ 𝜎 + 𝑤 𝑄 (3.2)where 𝜎 is the beam size in the absence of wakefields. Fitting Eq. 3.2 to the data yields 𝑤 = . ± . 𝑒 − (Figure 9a). Using measurements from the cavity BPMs in the ATF2 beamline [33],the IP vertical angle jitter was estimated to be 220 μ rad (Figure 9b) for a bunch charge between4 × and 6 × electrons.After the measurement in single bunch mode, the ATF was set up to provide trains consistingof two bunches separated by 302.4 ns. Using the ATF2 cavity BPMs, the uncorrected verticalangle jitter of the second bunch at the IP was estimated to be ∼ μ rad (Figure 10b). With theupstream feedback system active, the jitter is reduced to 51 μ rad. Figure 10a shows the measuredsize of the second bunch as a function of beam charge, both with and without feedback. It can beseen that stabilizing the position and angle of the second bunch with the FONT feedback systemalso reduced the charge dependence of the beam size measured at the IP by a factor of 1 . ± . . ± . 𝑒 − to 16 . ± . 𝑒 − . Table 6 shows a summary of the IP vertical– 12 – able 6 . Summary of charge dependence of beam size. Errors are statistical. IP angle jitter [ μ rad] 𝑤 [nm/10 𝑒 − ]Single bunch operation 220 ±
16 25 . ± . ±
15 27 . ± . ± . ± . Figure 9 . Beam size as a function of beam charge (left) and distribution of the IP vertical angle jitter (right)for single bunch operation. Each point represents a single beam size measurement. The line is a fit of Eq. 3.2.
Figure 10 . Beam size as a function of beam charge (left) and distribution of IP vertical angle jitter (right)for two bunch operation with feedback on (unfilled points, dashed line) and feedback off (filled points, solidline). Each point represents a single beam size measurement. The lines are fits of Eq. 3.2. – 13 –
Conclusions
An intra-train position and angle feedback system has been developed to achieve the ATF2 beamstability goal. Operating on a train of two bunches separated by 187.6 ns, the feedback systemstabilized the position of the second bunch at the feedback BPMs to the 270-340 nm level and theangle to within 250 nrad. The model of the beamline predicts that this level of correction shoulddeliver a factor 4.5 reduction in both position and angle at the downstream witness BPMs, and theactual observed factor is 4 . ± .
6. The model also predicts that the jitter at the focal point shouldbe reduced from 3 . ± . . ± . . ± . electrons in the bunch. Repeating the charge scan using trains of two bunchesseparated by 302.4 ns showed that the feedback system reduced the charge dependence of thequadrature growth in beam size from 27 . ± . 𝑒 − to 16 . ± . 𝑒 − .The position and angle feedback system presented here is based on earlier development of theILC IP collision feedback system prototype that was reported in [10]. The current system wasdeveloped for specific application to beam jitter reduction at the ATF2, and, as we have shownhere, as such it is successful in yielding a significant reduction in the impact of wakefields on thebeam-size growth. Such a system would also be directly applicable to deployment in the ILC linacsand/or beam-delivery system for removal of correlated position/angle jitter among the c. 1300bunches per train of each beam pulse. We thank KEK for their support of ATF/ATF2 operations, and KEK staff for their outstandinglogistical support. In addition, we thank our colleagues from the ATF2 Collaboration for their helpand support. In particular, we thank the IFIC group from the University of Valencia for providingthe mover system for the feedback BPMs, the LAL group from the Paris-Saclay University forproviding the mover system for the cavity BPMs at the IP, and the team from Kyungpook NationalUniversity for providing the interaction point cavity BPMs.We acknowledge financial support for this research from the United Kingdom Science andTechnology Facilities Council via the John Adams Institute, University of Oxford, and CERN,CLIC-UK Collaboration, Contract No. KE1869/DG/CLIC. The research leading to these resultshas received funding from the European Commission under the Horizon 2020/Marie Skłodowska-Curie Research and Innovation Staff Exchange (RISE) project E-JADE, Grant Agreement No.645479. – 14 – eferences [1] P. Burrows et al. , in
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