Preliminary study on detection and cleaning of parasitic bunches

Preliminary study on detection and cleaning of parasitic bunches 1 corresp first-author hejun@ihep.ac.cn (J. He) hejun@ihep.ac.cn (J. He) hejun@ihep.ac.cn https://orcid.org/0000-0002-3631-8657 1 1 1 https://orcid.org/0000-0003-4432-7091 1 1 https://orcid.org/0000-0001-7928-5114 1 https://orcid.org/0000-0001-6697-2310 1 https://orcid.org/0000-0002-6803-1554 1 1 https://orcid.org/0000-0001-6507-2636 Key Laboratory of Particle Acceleration Physics and Technology, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Key Laboratory of Particle Acceleration Physics and Technology, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China 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 single-photon counting system was implemented at the electron storage ring of the Beijing Electron-Positron Collider II (BEPCII). The purity deterioration process over a week-long 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. Parasitic bunches Impurity growth High Energy Photon Source (HEPS) 1　Introduction 1 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 1 ]. Bunch purity is 10 -4 for most third-generation light sources without a bunch-cleaning system [ 2 2 - 6 6 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 single-electron-level, because the ratio of the non-resonant signal to the delayed resonant signal is above 10 6 , even for high-resolution monochromators [ 7 7 - 10 10 7-10 ]. Achieving single-electron-level purity is challenging; for that, the dynamic range of the detection system should be extended to 10 10 . 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 9 - 11 11 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 12 ]. As shown in Fig. 1 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 to perform 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 13 ] and requires bunch purities of 10 -9 in 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 Table 1 lists the main parameters of BEPCII in the SR 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. 1 1  Parameter 1 1 SR mode 1 1 Energy, E 0 (GeV) 1 1 2.5 1 1 Circumference, C (m) 1 1 241.13 1 1 Current, I b (mA) 1 1 250 1 1 Natural bunch length, σ z0 (ps) 1 1 42 1 1 Momentum compaction, α 1 1 0.0182 1 1 Synchrotron radiation energy loss per turn, U 0 (keV) 1 1 384 1 1 Harmonic number, h 1 1 402 1 1 Synchrotron tune, v s 1 1 0.0372 1 1 RF frequency, f RF (MHz) 1 1 499.800 1 1 Revolution frequency, f 0 (MHz) 1 1 1.243 1 1 RF voltage, V RF (MV) 1 1 2.60 1 1 Bucket height, η RF 1 1 ±0.97% Detection of parasitic bunches utilized the time-correlated single-photon counting (TCSPC) [ 14 14 ] technique while the cleaning system used the RF Knock Out (RFKO) [ 15 15 - 16 16 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 re quired 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 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 1 2.1　Theory of the bunch purity deterioration 2 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 9 - 11 11 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. LINAC 3 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 N 0 drops to (1- f ) N 0 , the linac fills the main bunch to N 0 during the top-up mode. The refilling time d t and lifetime τ satisfy the following equation [ 10 10 ]: <math display="block" id="M1"><mrow><mrow><mo>(</mo><mrow><mtext>1-f</mtext></mrow><mo>)</mo></mrow><msub><mtext>N</mtext><mtext>0</mtext></msub><msub><mrow><mtext>=N</mtext></mrow><mtext>0</mtext></msub><mo>×</mo><msup><mtext>e</mtext><mrow><mtext>-dt/τ</mtext></mrow></msup><mtext>.</mtext></mrow></math> Assuming that the ratio between the number of parasitic electrons and the number of main bunch electrons in the linac is k i and remains the same across different refills, the number of parasitic electrons for each injection is k i f N 0 , where i indexes parasitic bunches. The growth rate of the number of parasitic electrons owing to the pre-accelerators is given by Eq. (2): <math display="block" id="M2"><mrow><mfrac><mrow><msub><mrow><mtext>dN</mtext></mrow><mtext>i</mtext></msub></mrow><mrow><mtext>dt</mtext></mrow></mfrac><mtext>=</mtext><mfrac><mrow><mtext>-f</mtext></mrow><mrow><mtext>τ×ln(1-f)</mtext></mrow></mfrac><msub><mtext>k</mtext><mtext>i</mtext></msub><msub><mtext>N</mtext><mtext>0</mtext></msub><msubsup><mrow><mtext>=C</mtext></mrow><mtext>i</mtext><mrow><mtext>inj</mtext></mrow></msubsup><msub><mtext>N</mtext><mtext>0</mtext></msub><mo>.</mo></mrow></math> Touschek scattering 3 The trajectories of electrons in the longitudinal phase space are described by the synchrotron oscillation equation [ 17 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 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 0 th bucket are never captured by the following buckets. However, radiation damping produces a momentum window Δ p i on 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 10 , 11 11 ] <math display="block" id="M3"><mrow><mfrac><mrow><msub><mrow><mtext>dN</mtext></mrow><mtext>i</mtext></msub></mrow><mrow><mtext>dt</mtext></mrow></mfrac><mtext>=</mtext><mfrac><mrow><msub><mtext>N</mtext><mtext>0</mtext></msub></mrow><mtext>2</mtext></mfrac><mtext>(</mtext><mfrac><mtext>1</mtext><mrow><msub><mtext>τ</mtext><mtext>t</mtext></msub><mrow><mo>(</mo><mrow><msubsup><mtext>δ</mtext><mtext>i</mtext><mrow><mtext>min</mtext></mrow></msubsup></mrow><mo>)</mo></mrow></mrow></mfrac><mo>−</mo><mfrac><mtext>1</mtext><mrow><msub><mtext>τ</mtext><mtext>t</mtext></msub><mrow><mo>(</mo><mrow><msubsup><mtext>δ</mtext><mtext>i</mtext><mrow><mtext>max</mtext></mrow></msubsup></mrow><mo>)</mo></mrow></mrow></mfrac><mo stretchy="false">)</mo><mo>=</mo><msubsup><mtext>C</mtext><mtext>i</mtext><mtext>T</mtext></msubsup><msub><mtext>N</mtext><mtext>0</mtext></msub><mtext>,</mtext></mrow></math> where <math id="M4"><mrow><msubsup><mtext>δ</mtext><mtext>i</mtext><mrow><mtext>min</mtext></mrow></msubsup></mrow></math> and <math id="M5"><mrow><msubsup><mtext>δ</mtext><mtext>i</mtext><mrow><mtext>max</mtext></mrow></msubsup></mrow></math> are the minimal and maximal momenta, respectively, of the i- th bucket. The coefficient 1/2 is owing to the fact that one of the two electrons that take part in the collision loses momentum and is never captured by the backward buckets. The bucket height of the BEPCII is 0.97% for a cavity voltage of 2.60 MV; the typical parameters of the BEPCII are listed in Table 1 Table 1 . By solving the synchrotron oscillation equation numerically, the RF acceptances with radiation damping are shown in Fig. 2 Fig. 2 , and the momentum windows ( p i = <math id="M6"><mrow><msubsup><mtext>δ</mtext><mtext>i</mtext><mrow><mtext>min</mtext></mrow></msubsup></mrow></math> and △ p i = <math id="M7"><mrow><msubsup><mtext>δ</mtext><mtext>i</mtext><mrow><mtext>max</mtext></mrow></msubsup><mo>−</mo><msubsup><mtext>δ</mtext><mtext>i</mtext><mrow><mtext>min</mtext></mrow></msubsup></mrow></math> ) corresponding to different parasitic bunches are given in Table 2 Table 2 . Electrons with momenta gains larger than 1.8% are expected to be lost in the vacuum chamber because they are outside the lattice transverse momentum acceptance. The Touschek lifetime τ t ( δ ) was calculated using the Elegant code [ 18 18 ]. The simulated growth rates, <math id="M8"><mrow><msubsup><mtext>C</mtext><mtext>i</mtext><mtext>T</mtext></msubsup></mrow></math> , calculated using Eq. (3), are listed in Table 2 Table 2 . 1 1 i 1 1 p i (×10 -2 ) 1 1 △ p i (×10 -5 ) 1 1 <math id="M9"><mrow><msub><mi>τ</mi><mtext>t</mtext></msub><mo stretchy="false">(</mo><msubsup><mi>δ</mi><mi>i</mi><mrow><mi>min</mi></mrow></msubsup><mo stretchy="false">)</mo></mrow></math> h 1 1 <math id="M10"><mrow><msub><mi>τ</mi><mtext>t</mtext></msub><mo stretchy="false">(</mo><msubsup><mi>δ</mi><mi>i</mi><mrow><mi>max</mi></mrow></msubsup><mo stretchy="false">)</mo></mrow></math> h 1 1 C T i (×10 -5 h -1 ) 1 1 1 1 1 1.19508 1 1 4.23 1 1 143.367 1 1 144.460 1 1 2.6384 1 1 2 1 1 1.38351 1 1 3.68 1 1 197.103 1 1 198.257 1 1  1.4776  1 1 3 1 1 1.54988 1 1 3.30 1 1 252.858 1 1 254.045 1 1 0.9239 1 1 4 1 1 1.70056 1 1 3.02 1 1 310.390 1 1 311.605 1 1 0.6281 1 1 5 1 1 1.83937 1 1 2.79 1 1 369.541 1 1 370.796 1 1 0.4581 1 1 6 1 1 1.96876 1 1 2.62 1 1 430.202 1 1 431.477 1 1 0.3433 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 <math display="block" id="M11"><mrow><mfrac><mrow><msub><mrow><mtext>dN</mtext></mrow><mtext>i</mtext></msub></mrow><mrow><mtext>dt</mtext></mrow></mfrac><mtext>=</mtext><mrow><mo>(</mo><mrow><msubsup><mtext>C</mtext><mtext>i</mtext><mtext>T</mtext></msubsup><msubsup><mrow><mtext>+C</mtext></mrow><mtext>i</mtext><mrow><mtext>inj</mtext></mrow></msubsup></mrow><mo>)</mo></mrow><msub><mtext>N</mtext><mtext>0</mtext></msub><mtext>-</mtext><mfrac><mrow><msub><mtext>N</mtext><mtext>i</mtext></msub></mrow><mrow><msub><mtext>τ</mtext><mtext>t</mtext></msub><msub><mrow><mtext>(N</mtext></mrow><mtext>i</mtext></msub><mtext>)</mtext></mrow></mfrac><mtext>-</mtext><mfrac><mrow><msub><mtext>N</mtext><mtext>i</mtext></msub></mrow><mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub></mrow></mfrac><mtext>,</mtext></mrow></math> where τ g and τ t are the lifetimes associated with the beam-gas scattering and the Touschek scattering, respectively. The time τ g is independent of the number of electrons in a parasitic bunch, while τ t is not. The Touschek lifetime of a parasitic bunch is very long owing to the low bunch current compared with that owing to the beam-gas scattering, and can therefore be neglected. The impurity growth rate d Pu i / d t = d( N i /N 0 ) / d t can be described as <math display="block" id="M12"><mrow><mfrac><mrow><msub><mrow><mtext>dPu</mtext></mrow><mtext>i</mtext></msub><mtext>(t)</mtext></mrow><mrow><mtext>dt</mtext></mrow></mfrac><mo>=</mo><mrow><mo>(</mo><mrow><msubsup><mtext>C</mtext><mtext>i</mtext><mtext>T</mtext></msubsup><mo>+</mo><msubsup><mtext>C</mtext><mtext>i</mtext><mrow><mtext>inj</mtext></mrow></msubsup></mrow><mo>)</mo></mrow><mo>−</mo><mfrac><mrow><msub><mrow><mtext>Pu</mtext></mrow><mtext>i</mtext></msub><mtext>(t)</mtext></mrow><mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub></mrow></mfrac></mrow></math> with the solution of <math display="block" id="M13"><mrow><msub><mrow><mtext>Pu</mtext></mrow><mtext>i</mtext></msub><mtext>(t)</mtext><mo>=</mo><mrow><mo>(</mo><mrow><msubsup><mtext>C</mtext><mtext>i</mtext><mtext>T</mtext></msubsup><mo>+</mo><msubsup><mtext>C</mtext><mtext>i</mtext><mrow><mtext>inj</mtext></mrow></msubsup></mrow><mo>)</mo></mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub><msup><mrow><mtext>(1-e</mtext></mrow><mrow><mtext>-</mtext><mfrac><mrow><msub><mrow><mtext>t-t</mtext></mrow><mtext>0</mtext></msub></mrow><mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub></mrow></mfrac></mrow></msup><mtext>)</mtext><mtext>.</mtext></mrow></math> 2.2　Experimental setup 2 The purity measurement system is shown schematically in Fig. 3a 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 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 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 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, ORTECTRUMP-PCI-2k) modules [ 21 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 × 10 6 s -1 . The count rates were 10 counts/s for background noise (without synchrotron light) and 10 6 counts/s for purity measurements. The maximal number of time bins was 2 16 = 65536, 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 2 32 = 4,294,967,296 increments, which was very useful for high-purity measurements, compared with the PicoHarp300 module with the storage capability of 16 bits [ 19 19 ]. 2.3　Purity measurements 2 Figure 3c 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 22 ]. The reading of the bunch current monitor (BCM) is shown in the inset of Fig. 3c 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 Fig. 4a . The rise time (10% to 90%) was 380 ps for the hybrid detector, and the response time of the MCP-PMT was at the same level but had a different tail. The single-bunch purity measurement results are shown in Fig. 5 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 2 ] and after-pulsing [ 14 14 ]. The details of the hybrid detector’s measurement results near the main signal are shown in Fig. 4b 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 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 2 , 11 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. 4b . Figure 6a 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 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 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 Fig. 6b . The experimental results confirmed the Obina and Keil theory [ 10 10 , 11 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 τ g . The typical gas lifetime τ g for 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 -8 Pa. 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 Fig. 7a . ( Fig. 6b Fig. 6b depicts the purity of a single isolated bunch.) The average purities in the 4-h-long 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 C 1 T + C 4 T , while the bunch purity (+4 ns) corresponded to C 2 T + C 5 T . According to Eq. (6), we obtained Eqs. (7) and (10): <math display="block" id="M14"><mrow><msubsup><mrow><mtext>Pu</mtext></mrow><mrow><mtext>2ns</mtext></mrow><mrow><mtext>Decay</mtext></mrow></msubsup><mtext>(t)</mtext><mo>=</mo><mrow><mo>(</mo><mrow><msubsup><mtext>C</mtext><mtext>1</mtext><mtext>T</mtext></msubsup><mo>+</mo><msubsup><mtext>C</mtext><mtext>4</mtext><mtext>T</mtext></msubsup></mrow><mo>)</mo></mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub><msup><mrow><mtext>(1-e</mtext></mrow><mrow><mtext>-</mtext><mfrac><mrow><msub><mrow><mtext>t-t</mtext></mrow><mtext>0</mtext></msub></mrow><mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub></mrow></mfrac></mrow></msup><mtext>)</mtext><mo>,</mo></mrow></math> <math display="block" id="M15"><mrow><msubsup><mrow><mtext>Pu</mtext></mrow><mrow><mtext>2ns</mtext></mrow><mrow><mtext>Top-up</mtext></mrow></msubsup><mtext>(t)</mtext><mo>=</mo><mrow><mo>(</mo><mrow><msubsup><mtext>C</mtext><mtext>1</mtext><mtext>T</mtext></msubsup><mo>+</mo><msubsup><mtext>C</mtext><mtext>4</mtext><mtext>T</mtext></msubsup><mo>+</mo><msubsup><mtext>C</mtext><mtext>1</mtext><mrow><mtext>inj</mtext></mrow></msubsup></mrow><mo>)</mo></mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub><msup><mrow><mtext>(1-e</mtext></mrow><mrow><mtext>-</mtext><mfrac><mrow><msub><mrow><mtext>t-t</mtext></mrow><mtext>0</mtext></msub></mrow><mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub></mrow></mfrac></mrow></msup><mtext>)</mtext><mo>,</mo></mrow></math> <math display="block" id="M16"><mrow><msubsup><mrow><mtext>Pu</mtext></mrow><mrow><mtext>4ns</mtext></mrow><mrow><mtext>Decay</mtext></mrow></msubsup><mtext>(t)</mtext><mo>=</mo><mrow><mo>(</mo><mrow><msubsup><mtext>C</mtext><mtext>2</mtext><mtext>T</mtext></msubsup><mo>+</mo><msubsup><mtext>C</mtext><mtext>5</mtext><mtext>T</mtext></msubsup></mrow><mo>)</mo></mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub><msup><mrow><mtext>(1-e</mtext></mrow><mrow><mtext>-</mtext><mfrac><mrow><msub><mrow><mtext>t-t</mtext></mrow><mtext>0</mtext></msub></mrow><mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub></mrow></mfrac></mrow></msup><mtext>)</mtext><mo>,</mo></mrow></math> <math display="block" id="M17"><mrow><msubsup><mrow><mtext>Pu</mtext></mrow><mrow><mtext>4ns</mtext></mrow><mrow><mtext>Top-up</mtext></mrow></msubsup><mtext>(t)</mtext><mo>=</mo><mrow><mo>(</mo><mrow><msubsup><mtext>C</mtext><mtext>2</mtext><mtext>T</mtext></msubsup><mo>+</mo><msubsup><mtext>C</mtext><mtext>5</mtext><mtext>T</mtext></msubsup><mo>+</mo><msubsup><mtext>C</mtext><mtext>2</mtext><mrow><mtext>inj</mtext></mrow></msubsup></mrow><mo>)</mo></mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub><msup><mrow><mtext>(1-e</mtext></mrow><mrow><mtext>-</mtext><mfrac><mrow><msub><mrow><mtext>t-t</mtext></mrow><mtext>0</mtext></msub></mrow><mrow><msub><mtext>τ</mtext><mtext>g</mtext></msub></mrow></mfrac></mrow></msup><mtext>)</mtext><mo>.</mo></mrow></math> As shown in Fig. 7a Fig. 7a , the difference between Pu 4ns Top-up and Pu 4ns Decay was very small, indicating a small C 2 inj compared with C 2 T . C 1 inj could be determined using Eq. (8) over Eq. (7). Thus, C 1 inj was (9.123 ± 0.204) × 10 -6 h -1 . The result of Pu 2ns Decay over Pu 4ns Decay was 1.32 ± 0.075, very close to the momentum window calculation result of 1.69, as shown in Table 2 Table 2 . The fit result for Pu 2ns Top-up is shown in Fig. 7b Fig. 7b , indicating that C 1 inj was (1.38 ± 0.0504) × 10 -5 h -1 . Then, k = 2.22 × 10 -6 was determined from Eq. (2) with f = 0.2 % and τ g = 6.77 h. The horizontal error bars in Fig. 7b Fig. 7b represent the time spent on the purity measurement. The vertical error bars were calculated as follows: To calculate the average value of the background counts, including all the time bins (outside of the RF stable region), there were no electrons, and to calculate the average value of the peak counts for the main bunches, the uncertainty was determined by the ratio of the two counts. The final calculation results yielded the purity uncertainty in the 5 × 10 -6 – 7 × 10 -6 range, depending on the discrimination threshold setting of the electronic and filling patterns. The purity uncertainty evaluated by this method was almost the same as that shown in Fig. 6 Fig. 6 , and was larger than the special mode in Sect. 3, where there were only several bunches in the ring. There was no significant difference between Pu 4ns Top-up and Pu 4ns Decay after 2 h, and then the range C 2 inj ≤ 1.25× 10 -6 h -1 – 1.75 × 10 -6 h -1 was determined from the uncertainty. 3　Cleaning of parasitic bunches 1 3.1　The principle and experimental setup 2 The bunch-cleaning technique developed at SPring-8 [ 15 15 ] is shown schematically in Fig. 8 Fig. 8 . A sinusoidal signal comprising the N th harmonics of the revolution frequency and the vertical betatron frequency as f = N × f rev + f βy is 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. 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 2 Figures 9a and 9b Figures 9a and 9b show 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 f rev + f βy , produced by the Agilent arbitrary waveform generator. Curve 3 in green shows the waveform after mixing (the colors of the curves in Fig. 9 Fig. 9 are the same as in Fig. 8 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 V pp 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 Figure 9b shows the result of the scope in the single-shot mode, and Figs. 9c and 9d Figs. 9c and 9d show the infinite persistence modes. The time scales were 100 ns and 4 ns per division, respectively. Fig. 9c Fig. 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 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 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. Fig. 10a Fig. 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. Fig. 10b Fig. 10b shows the details of the remaining bunch. Only the third main bunch survived. Table 3 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 C i T in Table 2 Table 2 is shown in the last column of Table 3 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 -8 range, much better than that for the normal operation. 1 1 1 1 Purity before cleaning 1 1 Purity after cleaning 1 1 Purity before cleaning as C i T calculation 1 1 -1 1 1 3.79×10 -7 1 1 4.98×10 -8 1 1 0 1 1 +1 1 1 1.98×10 -5 1 1 7.23×10 -7 1 1 4.397×10 -6 1 1 +2 1 1 7.44×10 -6 1 1 1.74×10 -7 1 1 2.460×10 -6 1 1 +3 1 1 - 1 1 - 1 1 1.539×10 -6 1 1 +4 1 1 - 1 1 - 1 1 1.046×10 -6 1 1 +5 1 1 - 1 1 - 1 1 7.636×10 -7 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 10 7 is 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 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 -7 range, according to the growth rate C 1 T = 2.64 × 10 -7 in Table 2 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. 4　Conclusion and outlook 1 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 10 7 counts/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 C 1 inj ≈ 10 -5 /h and C 2 inj ≤ 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 τ g . 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 -7 in the best case, and was limited by the dynamic range and noise counts of the detector. 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Bunch purity measurement for BEPCII D. R. Sun , J. He , Y. Tao et al. , Implementation of ultrafast X-ray diffraction at the 1W2B wiggler beamline of Beijing Synchrotron Radiation Facility . J. Synchrotron Rad. 23 , 830 – 835 ( 2016 ). doi: 10.1107/S1600577516004252 http://doi.org/10.1107/S1600577516004252 Implementation of ultrafast X-ray diffraction at the 1W2B wiggler beamline of Beijing Synchrotron Radiation Facility All 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. The authors would like to thank Joachim Keil and Jiu-Qing Wang for their helpful discussions. 10.1007/s41365-021-00948-1 This work was supported by the Foundation of Youth Innovation Promotion Association and Key Laboratory of Particle Acceleration Physics &Technology, CAS. 2021-05-18 2021-08-13 2021-08-16 2021-10-11 2021-10-01 2021-11-29 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2021 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-021-00948-1 http://dx.doi.org/10.1007/s41365-021-00948-1 . 2021 Nuclear Science and Techniques 10 32