Jun He· Yan-Feng Sui · Yan-Hua Lu · Di Yin· Zhe Duan ·Sai-Ke Tian· De-Chong Zhu· Ying Zhao· Jun-Hui Yue ·Jian-She Cao

Abstract To establish a nuclear resonant scattering beamline at the High Energy Photon Source (HEPS), it is essential to develop tools for detection and cleaning of parasitic bunches, for meeting the stringent demands on bunch purity. To this end, a novel time-correlated singlephoton counting system was implemented at the electron storage ring of the Beijing Electron-Positron Collider II(BEPCII). The purity deterioration process over a weeklong operation was recorded by the system. In this study,the mechanism of impurity growth was analyzed by numerical methods and validated on measurements. The agreement between the experimental results and the calculation was fairly good. Two main sources of parasitic bunches,pre-accelerators and the Touschek scattering were confirmed. A bunch-cleaning technique, based on a sinusoidal signal mixed with a pseudo-square wave, was also developed and implemented, and its capability to improve the bunch purity to the level of 10-7 was experimentally demonstrated. We present the experimental setup, principle,and measurement results of a system for detection and cleaning of parasitic bunches.

Keywords Parasitic bunches · Impurity growth · High energy photon source (HEPS)

1 Introduction

In synchrotron radiation light sources, bunch purity,defined as‘‘the ratio of the number of electrons in parasitic bunches to that in the main bunches’’, must be kept sufficiently low in some time-resolved experiments [1]. Bunch purity is 10-4for most third-generation light sources without a bunch-cleaning system [2-6]; however, nuclear resonant scattering spectroscopy experiments, unique in high-energy synchrotron radiation light sources, demand much higher bunch purities, reaching those of a singleelectron-level, because the ratio of the non-resonant signal to the delayed resonant signal is above 106, even for highresolution monochromators [7-10]. Achieving singleelectron-level purity is challenging; for that, the dynamic range of the detection system should be extended to 1010.At the same time,a system for cleaning parasitic bunches is compulsory, because purity is likely to worsen gradually.Impurities proliferate owing to the injector chain and the Touschek scattering in the storage ring [9-11].

The 6-GeV-energy High Energy Photon Source(HEPS)with a circumference of 1360.4 m and a designed natural emittance of 34 pm·rad has been under construction in Beijing [12]. As shown in Fig. 1, there are two filling patterns with bunch numbers of 680 and 63, respectively.The single-bunch charges are 1.33 nC and 14 nC,while the total current is 200 mA. The bunch spacings are 6 ns and 72 ns. The lifetime of the nuclear resonance transition(14.4 keV) of the iron-57 isotope is approximately 141 ns.The bunch spacing of 72 ns in the high-charge mode at the HEPS is slightly longer than a half of the lifetime. There are two beamline installations that demand high bunch purity in 14 beamlines in Phase I of the HEPS project.The Structural Dynamics Beamline (SDB) is intended toperform laser pump X-ray probe experiments with the required purity of 10-6. The Hard X-ray High Energy Resolution Spectroscopy Beamline explores nuclear resonant scattering spectroscopy experiments[13]and requires bunch purities of 10-9in the pattern of 63 bunches.Related beam diagnostic methods should be applied prior to the start-up of the new photon source HEPS. For this purpose,systems for bunch purity measurement and cleaning were installed in the storage ring of the Beijing Electron Positron Collider (BEPCII), which also serves as a synchrotron radiation light source parasitically during high-energy physics runs (the HEP mode), as well as in the dedicated synchrotron radiation mode (the SR mode). For bunch purity studies, all of the results were acquired in the SR mode. Table 1 lists the main parameters of BEPCII in theSR mode. The RF frequency was 499.8 MHz and the minimal bucket spacing was approximately 2 ns. The bunch spacing during a typical operation varied across 4,6,and 8 ns.Normally,only 1/4 of all the buckets were filled.

Table 1 Main nominal parameters of the BEPCII

Detection of parasitic bunches utilized the time-correlated single-photon counting (TCSPC) [14] technique while the cleaning system used the RF Knock Out(RFKO)[15, 16] technique. For the detection of parasitic bunches,the arrival time of single photons emitted by the electron bunches was measured relative to a clock pulse that was synchronized with the bunch revolution frequency via the storage-ring RF system. The TCSPC system generated a histogram of binned arrival time measurements that statistically represented the relative time distribution of electrons in the storage ring. For the cleaning of parasitic bunches, the conventional approach is to stimulate all of the bunches at the betatron frequency of parasitic bunches.The beam impedance of the vacuum chamber induces a shift in the betatron frequency, which depends on the single-bunch current, which has a significantly different betatron frequency (several kHz) from that of the main bunches. The amplitude of the transverse oscillations of parasitic bunches is much larger because of resonance.Consequently, the parasitic branches are filtered out by a scraper. The conventional approach was capable of achieving the required level of purity, but was difficult to tune and it was very sensitive to betatron tune shifts induced by the thermal drift of the storage ring.In addition,even for a properly tuned system, it induced significant main beam losses and required several minutes to complete a cleaning cycle. By contrast, the RFKO approach only required dozens of milliseconds. The RFKO method only stimulated the parasitic bunches and had little effect on the main bunches. In Sect. 2, we briefly describe the mechanism of the bunch purity deterioration, and the results of purity on BEPCII are analyzed using T. Obina’s method[11].The Touschek impurity growth rate is calculated,and the linac impurity growth rate is derived from the difference between the decay and top-up modes. The top-up injection control refilled the smallest bunch in sequence until an additional current of 1 mA was added when the total current dropped to 249.5 mA. The bunches were not refilled during the 4-h-long decay mode operation. Section 3 presents the hardware and the results for the system that was used to clean the parasitic bunches. The conclusions and future improvement approaches are discussed in Sect. 4.

2 Detection of parasitic bunches

2.1 Theory of the bunch purity deterioration

As mentioned before, parasitic electrons in the storage ring could be inherited from pre-accelerators. The sources could be the electron gun, the dark current from the buncher in the linac, or the Touschek scattering in the booster. Parasitic electrons could also be produced owing to the Touschek scattering in the main bunches of the storage ring [9-11]. The contribution ratios of these are different for different machines. At the BEPCII, a full energy linac is injected directly into the storage ring, and we hope to determine the relative ratios of parasitic electron contributions caused by the linac beam and the Touschek scattering in the storage ring.

2.1.1 LINAC

The limit of refill f of the storage ring is 0.5 mA /250 mA = 0.2%. When the number of electrons in the main bunch N0drops to(1 - f)N0,the linac fills the main bunch to N0during the top-up mode. The refilling time dt and lifetime τ satisfy the following equation [10]:

2.1.1.1 Touschek scattering The trajectories of electrons in the longitudinal phase space are described by the synchrotron oscillation equation [17]. When the momentum deviation is small, an electron undergoes a damping oscillation around the synchronous phase. An electron that gains a positive momentum larger than the height of the RF bucket exits the main bunch. The trajectories of the electrons in the longitudinal phase space are shown in Fig. 2.The electrons with positive momenta larger than the RF bucket height move toward the backward buckets + 1, + 2, + 3 (+ represents backward buckets).Without the synchrotron radiation,the electrons thrown out from the 0thbucket are never captured by the following buckets. However, radiation damping produces a momentum window Δpion the i-th bucket. Electrons with momenta corresponding to this window can be captured by the + 1, + 2, + 3 buckets.The increasing rate of parasitic bunches owing to the Touschek scattering and recaptures in subsequent buckets is given by [10, 11]

Fig. 2 (Color online) Trajectories of electrons that are captured by the following buckets in the longitudinal phase space

The electrons in the parasitic bunches can be lost owing to the beam-gas or the Touschek scattering. Therefore, the growth rate of the electrons in a parasitic bunch is given by

2.2 Experimental setup

The purity measurement system is shown schematically in Fig. 3a. The visible light that came from a bending magnet was sent to a photon detector(Microchannel Plate-Photomultiplier Tube MCP-PMT, China Electronics Technology Group Corporation or PMA Hybrid 400,Picoquant [19]) after passing through a full reflection mirror, a focus lens, a variable attenuator, a grating spectrometer, and two adjustable apertures. It shared a photon beam transport system with a beam-profile measurement system [20]. Two slits and neutral density (ND) filters located in front of the photon detector were used for reducing the photon flux down to the level of one photon detection per approximately dozens of revolutions of the beam. A grating spectrometer, for rejecting the stray light,was set on the optical line to the detector. As presented in Fig. 3b, the output signal of the detector was sent to a multichannel picosecond event timer (HydraHarp 400,Picoquant or Constant Fraction Discriminator CFD,ORTEC935, time to amplitude converter TAC, ORTEC 567, and multi-channel analyzer MCA, ORTECTRUMPPCI-2 k) modules [21], where the time difference between the trigger signal and the photon detector signal was measured using a time-to-digital converter (TDC). The detector recorded the distribution of photons that corresponded to the distribution of electrons over time in the revolution period.The reference signal was provided by the event generator / event receiver from the timing system,which provided a revolution period signal of 1.2433 MHz in the SR mode. A digital delay generator (DG645, SRS)was used for adjusting the delay between the detection of photons and the reference signal.

Originally, the detector electronics were composed of a nuclear instrumentation module (NIM), and the reason for the recent upgrade to the HydraHarp module was a short dead time of 80 ns, allowing a maximal count rate of 12.5 × 106s-1. The count rates were 10 counts/s for background noise (without synchrotron light) and 106counts/s for purity measurements.The maximal number of time bins was 216= 65,536, which allowed the minimal time resolution of 16 ps for a revolution time of 800 ns.The count depth per time bin was 32 bits,corresponding to 232= 4,294,967,296 increments,which was very useful for high-purity measurements, compared with the Pico-Harp300 module with the storage capability of 16 bits[19].

2.3 Purity measurements

Figure 3c shows the purity measurement results for the top-up operation at the BEPCII. The filling pattern was designed for pump-probe experiments[22].The reading of the bunch current monitor (BCM) is shown in the inset of Fig. 3c; this provided the filling pattern information for operators. The total beam current of 250 mA was distributed equally across a single isolated bunch that was located at the center of a 200-ns-wide gap and another 99 bunches in the bunch train,with the bunch spacing of 6 ns.

The single-photon responses of the two detectors are shown in Fig. 4a. The rise time (10% to 90%) was 380 psfor the hybrid detector,and the response time of the MCPPMT was at the same level but had a different tail. The single-bunch purity measurement results are shown in Fig. 5,both with a tail of several tens of nanoseconds.The bunch root mean square (RMS) length was approximately 50 ps, as measured by a streak camera. The full width at half maximum (FWHM) values of the bunch responses were 427 ps and 128 ps, respectively. The difference was mainly caused by the NIM’s response being much slower than that of HydraHarp. The width of a single bunch is determined by the instrument response function (IRF) of the system and the time structure of the bunch photons.The parasitic bunch signals are very easily smeared by spurious signals induced by the main bunch,especially for detectors with fast responses and high photon-electron conversion gains. This effect is alleviated for slow detectors, such as avalanche photo diodes(APDs).There are several different names and possible reasons for these spurious signals,such as ghost reflection[2]and after-pulsing[14].The details of the hybrid detector’s measurement results near the main signal are shown in Fig. 4b.There are four spurious peaks,located at 0.93 ns, 1.34 ns, 2.94 ns, and 6.81 ns after the main bunch, compared with the MCP-PMT detector that revealed peaks at 4 ns and 26 ns, respectively (data not shown). Several reasons explain why these spurious peaks do not correspond to real electrons. First, they appear outside stable RF phase regions. Second, their characteristics do not depend on injections,and the ratio of spurious to the main peaks sometimes shifts slightly depending on the photon flux but not by the time after an injection, as shown in Fig. 6a.Third,they are not affected by the RFKO system.Finally,different labs have reported similar results,although different detectors yielded spurious peaks at different positions [2, 11]. Yet, baseline counts increase,hindering the accurate evaluation of parasitic branches.Fortunately, none of the spurious peaks were at the locations of the parasitic bunches for the PMA hybrid detector,as shown in Fig. 4b.

Fig. 4 (Color online) a Single-photon responses of the two detectors. b Spurious peaks of the PMA hybrid detector

Fig. 5 (Color online) Single-bunch purity measurement results for (a) the MCP-PMT + NIM modules, and (b) Hybrid + HydraHarp

Figure 6a shows the bunch purity measurement results at different times during a week-long top-up operation.The main bunch (No. 0, the first bunch in Fig. 3c) located at 635.2 ns is in the center of a 200-ns-wide gap. Besides the parasitic bunches located at 635.2 + 2 × i ns, there are three spurious peaks located at 636 ns, 638.5 ns, and 642 ns. These spurious peaks could not be cleaned by the bunch purification system. Therefore, they do not correspond to real electrons. One possible explanation for the appearance of these peaks is the inner reflection of the photon detector. We excluded the possibility of reflection photons created in the photon transport process. Further studies need to be done for confirming the origin of these spurious peaks.As shown in Fig. 6a,the counts associated with parasitic bunches increase gradually, but those associated with the spurious peaks do not. The ratios of the numbers of electrons in different parasitic branches to that in the main bunch are shown in Fig. 6b. The experimental results confirmed the Obina and Keil theory [10, 11].Impurity growth was never observed in forward (No. -1)bunches. Impurity growth rates were different for parasitic bunches, and were mainly determined by the different momentum gain probabilities through the Touschek scattering.The whole-bunch purity deterioration could be seen clearly throughout the week-long measurement. Equation (6)suggests that purity approaches equilibrium with a rise time of τg. The typical gas lifetime τgfor the BEPCII was 6.77 h, while the elastic and inelastic scattering gas lifetimes were 14.32 h and 12.84 h, respectively, for the pressure of 1.3 × 10-8Pa.

Fig. 6 (Color online) a The bunch purity measurement results for a week-long operation,showing the details of a 14-ns-wide span around the main bunch, located at the center of a 200-ns-wide gap.b Evolution of the different parasitic bunches’ purities (ratios of the numbers of electrons in different parasitic branches to that in the main bunch) during the week-long operation

To elucidate the contributions of the injection and the Touschek scattering to the ratios,the average purities of the 99 bunches in the bunch train in the top-up and decay modes are shown in Fig. 7a. (Figure 6b depicts the purity of a single isolated bunch.)The average purities in the 4-hlong decay mode were compared with that of the normal top-up operation under the same filling pattern.

The main bunch spacing was 6 ns, and there were two possible parasitic bunches between the two main bunches,each of which could be the contribution of two forward main bunches. The bunch purity (+ 2 ns) corresponded to C1T+ C4T, while the bunch purity (+ 4 ns) corresponded to C2T+ C5T. According to Eq. (6), we obtained Eqs. (7)and (10):

3 Cleaning of parasitic bunches

3.1 The principle and experimental setup

The bunch-cleaning technique developed at SPring-8[15] is shown schematically in Fig. 8. A sinusoidal signal comprising the Nthharmonics of the revolution frequency and the vertical betatron frequency as f = N × frev+ fβyis mixed with a pseudo-square wave that defines the bunch fill pattern. The main bunches, which are represented by blue dots, are located at the middle of the rise or fall edge(also the zero-crossing point) of the pseudo-square signal,and all the other bunches (red dots) at both positive and negative polarities of the square signal are cleaned. The mixed signal is amplified and sent to a kicker to stimulate a beam. If the amplitude of the excited oscillations is sufficiently large, parasitic bunches are lost in a vacuum chamber. The main apparatus of the bunch-cleaning system, including the timing system, the kickers, and the amplifiers, is shared with a transverse bunch-by-bunch feedback system.

Fig. 7 (Color online) a Purity results for the top-up and decay modes, with the fill pattern being the same as in Fig. 1c. b Fit results for Pu2nsTop-up, using Eq. (6)

Fig. 8 (Color online) Schematic of the bunch-cleaning system

The bunch-cleaning system in the BEPCII consists of an arbitrary waveform generator (UHFAWG, 1.8 GSa/s, 14 bit,600 MHz,Zurich Instruments;the minimal time step of programming is 555 ps), a function/arbitrary waveform generator (33250A, Agilent), a digital delay generator(DG645), a solid-state amplifier (Amplifier Research 10 kHz-250 MHz 75 W),and a 60 cm strip-line transverse feedback kicker.

3.2 Bunch-cleaning experiments

Fig. 9 (Color online) a-b Typical signals generated by the bunchcleaning system. c BPM (upper trace) and the strip-line kicker downstream port (lower trace) signals of the cleaning system.d Detailed view of the rise edge of the excitation signal. The arrow shows the safe point where the main bunch is located. The results in Fig. 9a and Fig. 9b were obtained in the single-shot mode, while the results in Fig. 9c and Fig. 9d were obtained in the infinite persistence mode

Figures 9a and 9b shows the typical signals generated by the bunch-cleaning system. Curve 1 in red shows the output of the UHFAWG arbitrary waveform generator,while Curve 2 in blue is a sinusoidal wave with a frequency of frev+ fβy, produced by the Agilent arbitrary waveform generator. Curve 3 in green shows the waveform after mixing.(The colors of the curves in Fig. 9 are the same as in Fig. 8). Curve 4 is not a real signal but the result of a mathematical operation(multiplication)on Curves 1 and 2.The maximal output Vpp of the UHFAWG was 750 mV,so there is a factor of 3 in Curve 4.To show this more clearly,the curves were translated along the vertical axis.Figure 9b shows the result of the scope in the single-shot mode, and Figs. 9c and 9d shows the infinite persistence modes. The time scales were 100 ns and 4 ns per division,respectively.Figure 9c shows the BPM (upper trace) and the strip-line kicker (lower trace) signals of the cleaning system. The BPM signal was used for monitoring the effect of cleaning,and the signal originating from the downstream port of the strip-line kicker was used for observing the temporal relations between the excitation signal and the bunches.First,we set the frequency of the sinusoidal wave far away from the resonance frequency,so the bunches located at the flat part of the kicker signal would not be cleaned, as shown in Fig. 9c. Several bunches were located at the flat of the square wave, and we then changed the delay to ensure that the main bunch was located at the lowest point,as indicated by the arrow in Fig. 9d. After finding the proper timing set, we changed the frequency of the sinusoidal wave to the right resonance frequency, which was cleaned in less than 100 ms.The lost electrons in the main bunch were ignored, and the perturbation was very small,demonstrating the possibility of using the system transparently during user operation.

After confirming the functionality of the bunch-cleaning system,a special fill pattern was designed for testing.Five bunches with a spacing of 100 ns shared a total current of 15 mA equally, and the bunches were not refilled during the entire test. Figure 10a shows the purity results before and after the cleaning system came into effect. Purity before cleaning was measured 10 min after the injection,and the purity measurement process took several minutes.Figure 10b shows the details of the remaining bunch.Only the third main bunch survived. Table 3 shows the purity results after and before the cleaning system was used. All of the parasitic bunch purities after cleaning reached 10-7.The parasitic bunches after No. + 2 were submerged in noise. The purity of the theoretical value given by CiTin Table 2 is shown in the last column of Table 3.The purity results show that the cleaning system works well and the sensitivity of the purity measurement system is 10-7, limited by the photon detector’s characteristics. Detection of visible light suffered from a relatively high background caused by the detector itself or by stray light. Both the spurious peaks and dark counts increased the uncertainty of the purity. Using the method mentioned in Sect. 2.3, the uncertainty was in the 8 × 10-8-9 × 10-8range, much better than that for the normal operation.

The absolute uncertainty (or sensitivity) of the system was difficult to evaluate, but the factors affecting it could be identified, as follows. The impulse response of the photon detector, with spurious peak counts much higher than normal noise counts, is expected to strongly deteriorate the uncertainty. The effective dynamic range of the system, which is determined by the minimum across all components, is smaller for the photonic detector than for the electronic one for the purity system, and count rate above 107is expected to trigger the PMA Hybrid 400 detector self-protection.The overall current for the normal operation was 17 (20 for the bunch amount) times higher than that in Fig. 10, and the uncertainty was 70 times worse. The time spent on purity measurements is typically 4-8 min, and purity increases to the 9.8 × 10-7-19.6 × 10-7range, according to the growth rate C1T-= 2.64 × 10-7in Table 2. The discrimination threshold setting of the electronic system also plays an important role. Quantification using the ratio of average background counts to the main bunch counts only provides a reference,but it is a good approximation.

Fig. 10 (Color online) a Purity results, after and before the cleaning system operation. The purity results before cleaning were obtained in 10 min after the injection. b Details around the remaining bunch

Table 3 Purity results for different bunches, before and after the cleaning procedure

4 Conclusion and outlook

A novel bunch-purity measurement system was implemented at the BEPCII, and we successfully tested the HydraHarp module combined with the PMA hybrid photon detector to evaluate the growth of impurities. HydraHarp 400, with its 32-bit histogram capability, 1 ps resolution,and the acquisition rate of 107counts/s appears to be an excellent instrument adapted for purity measurements.The growth of impurities was recorded by the TCSPC system over a week-long operation. Two sources of parasitic bunch populations have been identified: the linac and the Touschek scattering of the main bunch. The parasitic bunches exhibited different growth rates, which has been confirmed by theoretical calculations and measurements.The difference between the growth rates of the decay and top-up modes indicates that the contributions to the linac were C1inj≈ 10-5/h and C2inj≤10-6/h. The transfer fraction of the linac was k ≈10-6. The measurements showed that the bunch purity gradually worsened after the first injection, approaching equilibrium after a time that was several-fold the gas lifetime τg. A bunch-cleaning system based on the RFKO technique was successfully tested,and the achieved purity was 10-7.Overall,the novel procedure was much easier to use than the previous one,and allowed very fast cleaning of bunches.The purification procedure only took dozens of milliseconds compared with dozens of seconds required by the traditional method. The effect on the main bunches was much smaller.

The sensitivity of the purity measurement system was better than 10-7in the best case, and was limited by the dynamic range and noise counts of the detector. An APD detector that is only sensitive to X-rays and a gated device that could provide a better contrast for main bunches relative to parasitic bunches, are under development. The APD detector will be helpful for improving the sensitivity by decreasing the counts associated with spurious peaks and stray photons. A gated device or a fast light shutter system,such as the one using Pockels cells,will extend the dynamic range of the system, which is considered to be a necessary condition for achieving purities on the order of 10-9. The purity measurement and purification system for the HEPS is currently under construction.

AcknowledgementsThe authors would like to thank Joachim Keil and Jiu-Qing Wang for their helpful discussions.

Author contributionsAll authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Jun He and Yan-Feng Sui. The first draft of the manuscript was written by Jun He and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.