Mitigating the electron cloud effect in the SuperKEKB positron ring

SuperKEKB is an electron-positron collider with asymmetric energies located at the High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan. After more than five years of upgrading work on KEKB, phase-1 commissioning commenced in February 2016 and ended in June of the same year. Following a 20-month shutdown for the installation of a particle detector, BELLE II, phase-2 commissioning commenced in March 2018 and ended in July of the same year. This paper describes one major issue faced by SuperKEKB: the electron cloud effect (ECE) in the positron ring, which was observed during phase-1 commissioning. In the high-beam-current region, electron clouds, i.e., the source of the ECE, existed in the beam pipes at drift spaces of the ring, which had antechambers and a titanium nitride (TiN) film coating as countermeasures against the ECE. Permanent magnets and solenoids used to generate magnetic fields in the beam direction were attached to the beam pipes as additional countermeasures before the next commissioning phase commenced. Consequently, during phase-2 commissioning, experiments showed that the threshold of the current linear density for exciting the ECE increased by a factor of at least 2 compared to that during phase-1 commissioning. While the countermeasures were strengthened, the effectiveness of the antechambers and TiN film coating of the real beam pipe was reevaluated. Through various simulations and dedicated experiments during phase-2 commissioning, the antechambers were found to be less effective than anticipated with regard to reducing the number of photoelectrons in the beam channel. In contrast, the TiN film coating had a low secondary electron yield, as expected.


I. INTRODUCTION
SuperKEKB is an electron-positron collider with asymmetric energies located at the High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan, and is a successor to the former KEKB (KEKB B-factory) [1][2][3].The collider consists of an injector, a damping ring for positrons, a main ring (MR), and the Belle II particle detector (Fig. 1).The MR itself consists of two rings, each with a circumference of 3016 m.The high-and low-energy rings (HER/LER) are for 7.0 GeV electrons and 4.0 GeV positrons, respectively.Each ring is composed of four arc sections and four straight sections, with lengths of approximately 550 and 200 m, respectively.The straight sections include a beam injection/abort region, wiggler regions, radio-frequency accelerating cavity regions, and a beam collision region (Tsukuba section including Belle II detector).The design beam currents are 2.6 A (HER) and 3.6 A (LER), with a maximum bunch number of 2500 and bunch spacing of two rf buckets (one rf bucket corresponds to approximately 2 ns in the case of SuperKEKB).The design FIG. 1. Layout of the SuperKEKB main ring (MR).One ring consists of four arc sections and four straight sections.luminosity is 8 × 10 35 cm −2 s −1 , which is approximately 40 times higher than that of KEKB [2].
After approximately five years of upgrading work starting in 2010, the first (phase-1) beam commissioning of SuperKEKB commenced in February 2016 and ended in June of the same year [51].Phase-1 commissioning was dedicated to accelerator tuning.After a 20-month shutdown for the installation of the Belle II detector and the final focusing superconducting electromagnets, the second (phase-2) beam commissioning commenced in March 2018 and ended in July of the same year.Phase-2 commissioning was dedicated to collision tuning and optics tuning for verifying the nanobeam scheme [1,2].Various observations and studies of the ECE were performed during phase-1 and phase-2 commissioning.During phase-1 commissioning, the ECE was caused by the electron cloud in the beam pipes at drift spaces in the high-current-region, although these beam pipes had antechambers and a titanium-nitride (TiN) film coating as countermeasures against ECE.After phase-1 commissioning, magnetic fields in the beam direction (B z [mT]) were applied to the beam pipes as an additional countermeasure.As a result, the ECE was well suppressed and was not observed during phase-2 commissioning.The countermeasures for SuperKEKB have been functioning well up to now.While the countermeasures were strengthened, the effectiveness of the antechambers and TiN film coating of the real beam pipes in the ring was reevaluated through various simulations and dedicated experiments during phase-2 commissioning.
In the remainder of this paper, the results from various studies to mitigate the ECE during phase-1 and phase-2 commissioning are described.Furthermore, the results from the reevaluation of the effectiveness of the antechambers and TiN film coating for suppressing the ECE in the real beam pipe are reported.
Antechambers for suppressing the effect of photoelectrons and a TiN film coating for suppressing the secondary electron yield (SEY) [25,26,[33][34][35][36][37]40,41,[44][45][46]52,53] were used in the majority of the new beam pipes, which were made of aluminum (Al) alloy.A schematic of a typical beam pipe at an arc section is presented in Fig. 2. The diameter of the beam channel is 90 mm, the half aperture including the antechamber part is 110 mm, and the height of the antechamber is 14 mm.The TiN film has a typical thickness of 200 nm and was mainly coated on the beam channel.The beam pipes for bending magnets have longitudinal grooves in the beam TABLE I. Countermeasures used to minimize the ECE in the SuperKEKB LER.The circles indicate the countermeasures applied for each main section in the ring [22,24].Abbreviations: rf cavity section: beam pipes around rf cavities; IR: interaction region; n e (circular): electron density expected for circular beam pipe (copper); n e (expected): electron density expected after applying countermeasures; Antechamber: antechamber scheme; Solenoid: solenoid winding, manifested as a magnetic field in the beam direction (B z ); Groove: beam pipe with grooves; Electrode: beam pipe with clearing electrodes.

Length
[m] channel [33,34,42,48,49,54] along with a TiN film coating, in order to further reduce the SEY.Instead of the TiN film coating, clearing electrodes [38,39,47,55] were installed in the beam pipes for wiggler magnets, and these also have antechambers.The beam pipes for wiggler magnets were made of copper to manage the intense synchrotron radiation (SR) power.Approximately 90% of the beam pipes in the ring possessed antechambers and the TiN film coating.B z values of up to several millitesla [14,19,50,[56][57][58] were applied by solenoids to the beam pipes in the drift spaces between electromagnets, such as quadrupole or bending magnets, in the ring.
In Table I, the circles indicate the countermeasures applied in each major section.The electron density (n e [m −3 ]) expected in the case of circular beam pipes (copper) and those with the above countermeasures are presented in the table.For the antechamber scheme, coating, solenoid (i.e., B z ), grooved surface, and clearing electrode, the effectiveness in terms of reducing n e is assumed to be 1=5, 3=5, 1=50, 1=2, and 1=100, respectively, on the basis of previous experimental results [22,24].Note here that these effectiveness factors are assumed to be independent of each other.If there are multiple countermeasures, these factors are simply multiplied.For example, if we use both, the antechamber and TiN film coating, the total effectiveness factor should be 1=5 × 3=5 ¼ 3=25.
With all these countermeasures, an n e value of approximately 2 × 10 10 m −3 was expected at the design beam parameters, i.e., a beam current of 3.6 A at a bunch fill pattern of one train of 2500 bunches with a bunch spacing of two rf buckets (hereafter referred to as 1=2500=2RF).This value of n e is sufficiently lower than the n eth value, 3 × 10 11 m −3 .Note that B z at drift spaces was not prepared before phase-1 commissioning, because the maximum stored beam current was not expected to be so high during this phase, i.e., approximately 1 A at the maximum, and the ECE was not anticipated to occur.
The n e around the beam orbit in an Al-alloy beam pipe with antechambers was measured via electron current monitors, which were also used in the previous KEKB experiments [59].Two electron monitors were set up at the bottom of the beam channel of a test beam pipe.The voltage applied to the electron collector was 100 V, while that applied to the grid (repeller) varied from 0 to −500 V.These two electron monitors were attached to the same beam pipe: one in the region with the TiN film coating (as in the other typical beam pipes in the ring) and one in the region without the TiN film coating (i.e., bare Al-alloy surface).The test beam pipe was placed in an arc section of the ring.The line density of photons of the SR was 1 × 10 15 photons s −1 m −1 mA −1 , i.e., 0.16 photons positron −1 m −1 .This line density was almost the same as the average value in the arc sections.

III. ECE IN PHASE-1 COMMISSIONING A. ECE in the early stages
In spite of the countermeasures described above, the ECE was first observed in phase-1 commissioning under a beam

current (I [mA]
) of approximately 600 mA at a bunch fill pattern of 1=1576=3.06RF[60,61].The vertical beam size began to blow up from this value of I, as shown in Fig. 3(a) (without PM at bellows).In this figure, ECK (emittance control knob) is a tool used to adjust the beam emittance via two skew-type quadrupole magnets in the ring.The ECK was active in this case, but had little effect on the behavior of the vertical beam size at I values above 600 mA.The pressure behavior in an arc section (P [Pa]) divided by I, P=I [Pa mA −1 ], with respect to I is presented in Fig. 3(b) (without PM at bellows).Note that high P=I at low I is caused by the base pressures.If the gas load comes solely from photodesorption by SR, P=I should be a constant because the number of photons is proportional to I. As shown in Fig. 3(b), however, P=I increased with I because of electron-stimulated gas desorption caused by the multipactoring of electrons [62][63][64].This abnormal blowup of beam size and the increase in pressure are typical ECE phenomena.
The blowup of the vertical beam size for bunch fill patterns of 4=150=2RF, 4=150=3RF, 4=150=4RF, and 4=150=6RF is shown in Fig. 4(a) as a function of the current linear density ) at which the ECE occurs, i.e., the blowup of beam size begins, was approximately 0.1 − 0.12 mA bunch −1 rf bucket −1 .As the B z was not applied to the beam pipes during phase-1 commissioning, as described before, the excitation of the ECE was an undeniable possibility.However, the threshold beam current for exciting ECE was much lower than expected.
It was finally found that this ECE was caused by the electrons in the Al-alloy bellows chambers without TiN film coating.These are 200 mm long and are located, on average, every 3 m around the ring.There are approximately 830 bellows chambers in total, occupying ∼5% of the circumference of the ring.However, the value of n e in the test beam pipe at the region without the TiN film coating was found to be on the order of 10 12 m −3 , which is more than 10 times greater than the n e th value of 3 × 10 11 m −3 .
To counteract the ECE, two units (type-1 units) of permanent magnets (PMs) were placed at the top and bottom of each Al-alloy bellows chamber, as shown in Fig. 5.One type-1 PM unit had eight PMs attached to a Cshaped iron plate (yoke) [60].One PM had a diameter of 30 mm and a magnetic field strength at the surface of approximately 85 mT.A B z value of approximately 10 mT was formed in most regions of the PM units, although the polarity reversed locally close to the PMs [60] (Fig. 7 in Sec.IV).After attaching the PM units to all Al-alloy bellows chambers, the abnormal blowup of beam size and increase in P=I disappeared at I values of 600-700 mA, as shown in Fig. 3(a) (with PM at bellows) and Fig. 3(b) (with PM at bellows).A simulation by CLOUDLAND [55] indicated that the n e value around the beam orbit in the Al-alloy bellows chamber with the PM units should be of the order of 10 10 m −3 , even for the design beam parameters, that is, a beam current of 3.6 A at a bunch fill pattern of 1=2500=2RF; here, the maximum SEY (δ max ) was assumed to be 2.0, which is a typical value for bare Al-alloy surfaces (see Sec. VI C).

B. ECE at high current
As described in the previous section, the ECE caused by the electron cloud in the Al-bellows chambers was suppressed by attaching PM units.However, the ECE began to appear again at I values of approximately 900 mA under a bunch fill pattern of 1=1576=3.06RF.The blowup of the beam size started from I ¼ 900 mA, as shown in Fig. 3(a) (with PM at bellows).Figure 4(b) shows the dependence of the vertical beam size on I d for bunch fill patterns of 4=150=2RF, 4=150=3RF, 4=150=4RF, and 4=150=6RF.The I d th value was 0.2 mA bunch −1 rf bucket −1 for two and three rf-bucket spacings, corresponding to I values of approximately 900 mA for a bunch fill pattern of 1=1576=3.06RF.Furthermore, the modes of the transverse coupled bunch instabilities (TCBI) were measured and analyzed using a bunch-by-bunch beam feedback system [65].Unstable modes excited by the electrons in the drift spaces were clearly detected, with frequencies lower by 400-700 times the revolution harmonics with respect to the rf frequency [65][66][67][68].
The value of n e in the test beam pipe at the region with the TiN film coating was observed to be close to the n e th value, that is, approximately 3 × 10 11 m −3 .The value of n e expected from the tune shift, i.e., 4 × 10 11 m −3 , was in good agreement with that directly measured in the test chamber at the region with the TiN film coating [68].Furthermore, the PM units with iron yokes, similar to those used for Al-alloy bellows chambers (Fig. 5), were partially attached for a test around several beam pipes at drift spaces.As a result, the abnormal increase in pressure was suppressed.
From these observations, the electron cloud was considered to exist in the beam pipes at drift spaces.Note that no abnormal increase in pressures was observed in the straight sections, including the wiggler magnet sections.
At this point, approximately 90% of the beam pipes in the LER had antechambers and the TiN coating.Note that the I d th value of 0.2 mA bunch −1 rf bucket −1 , after suppressing ECE through the Al-alloy bellows chambers, is much higher than that in the early stages of KEKB without any countermeasures, that is, 0.04 mA bunch −1 rf bucket −1 [Fig.4(c)] [20,50].The beam pipes and bellows chambers of KEKB had a simple circular cross section and were made of pure copper or stainless steel without any inner coating.Furthermore, B z was not applied at that time.The I d th in SuperKEKB was approximately 5 times that in KEKB.This indicated that the antechambers and TiN coating in SuperKEKB effectively suppressed the ECE to some extent.At the same time, however, the excitation of the ECE showed that the countermeasures in phase-1 commissioning were still insufficient; therefore, additional countermeasures against the ECE were prepared before the next commissioning phase.Furthermore, it was necessary to reevaluate the effectiveness of the antechambers and TiN film coating in the real beam pipe to check whether they were working as expected.

IV. ADDITIONAL COUNTERMEASURES
As additional countermeasures against the ECE, PM units and solenoids were attached to most of the beam pipes at drift spaces in LER.The PM units with C-shaped iron yokes (type-1 units, similar to those applied to Al-alloy bellows chambers), which produce a B z value of approximately 6 mT, were placed in sequence one after the other around the beam pipe, as shown in Fig. 6.The axial distributions of the vertical and axial components of the magnetic field (B y and B z ) at the top surface, and B z at the center of the beam channel in the type-1 unit are shown in Fig. 7(a).A simulation by the CLOUDLAND code under a magnetic field configuration similar to that in Fig. 7 For the beam pipes that had been used since the KEKB era, where the solenoids were already wound, the solenoids were revived, as shown in Fig. 9 [50,57,58].
The magnetic fields generated by these type-1 and type-2 units for the beam pipes are not uniform in the beam direction, as indicated in Figs.7(a) and 7(b).Consequently, some electrons will be trapped in the magnetic field near the pipe wall, which should be included in the high electron density region in Fig. 8.The effect of these trapped electrons on the beam dynamics has not been observed so far [69].
The dependence of n e on B z in the type-1-like magnetic field was calculated for several δ max at I ¼ 4 A with two rf bucket spacings, and the results are presented in Fig. 10.The number of photoelectrons was changed according to the value of δ max (see Sec. VI for details).The value of n e was found to be less than 1 × 10 11 m −3 when B z was greater than 1 mT.Before commencing phase-2 commissioning, approximately 86% of the drift spaces (approximately 2 km in total) was covered with B z of strengths greater than 2 mT.

V. ECE IN PHASE-2 COMMISSIONING
During phase-2 commissioning from March-July 2018, the vertical beam sizes, pressures, and unstable modes of TCBI were measured as during phase-1 commissioning.
Figure 11 shows the dependence of the vertical beam size on I d for bunch fill patterns of 4=120=2RF, 4=120=3RF, and 4=120=4RF.As shown in Fig. 11, blowup is not observed until I d reaches 0.4 mA bunch −1 rf bucket −1 .The value of I d th required to excite the ECE increased by a factor of at least 2 relative to the phase-1 commissioning [Fig.4(b)].
Figure 12 shows the behavior of P=I at arc sections against I for bunch fill patterns of two rf bucket spacings during phase-1 and phase-2 commissioning.As shown in Fig. 12, during phase-1 commissioning, P=I increased with I at values greater than 300 mA.However, P=I remained almost constant as I increased during phase-2 commissioning.This signifies relatively little multipactoring of electrons.Note that P itself decreased in phase-2 commissioning compared with phase-1 commissioning because of the vacuum scrubbing [70].
The modes and growth rates of the TCBI were again measured and analyzed [68].The modes excited by the electrons at the drift space were not observed, even at an I d value of 0.2 mA bunch −1 rf bucket −1 .Instead, the modes excited by electrons near the inner wall that were trapped by B z were detected, that is, the modes slightly above those corresponding to the bunch filling harmonics.Furthermore, the growth rates of the unstable modes were much lower than those observed in phase-1 commissioning.
The value of n e in the test beam pipe at the region with the TiN film coating was unchanged from that in phase-1 commissioning, i.e., the beam pipe conditions, such as δ max of the TiN film, were the same as in phase-1 commissioning, except for B z applied to beam pipes at the drift spaces.
From these observations, the additional countermeasures, that is, the application of B z by PM units and solenoids, were found to be working well in terms of suppressing the ECE during phase-2 commissioning.

VI. REEVALUATION OF THE EFFECTS OF ANTECHAMBERS AND TIN COATING
First, as a measure of the effectiveness of a beam pipe with an antechamber with regards to the suppression of photoelectrons, the rate of reduction in the number of photoelectrons in the beam channel, relative to a simple circular beam pipe, is defined as where p b and p a are the numbers of photoelectrons generated in the beam channel and antechamber, respectively.The total number of photoelectrons at the location is, therefore, p b þ p a .β is the probability that the electrons in the antechamber pass into the beam channel.A small value of α would indicate that the antechambers are highly effective.The maximum SEY, δ max , was used here to measure the effectiveness of the TiN film coating with regard to the suppression of secondary electrons.Note, however, that while δ max is the most important parameter, it is not the only one that determines n e .For example, the electron reflectivity at very small energies is also a sensitive parameter [71].

A. Calculation of β
First, β in Eq. ( 1) was estimated from a simulation code PEI [4] to calculate the motion of electrons.The electric field due to an electron cloud in the beam channel was calculated by a band-matrix solver.The force from a positron beam was calculated using the Bassetti-Erskine equation or the beam potential equation for electrons inside or outside a diameter of 10 σ x , respectively, where σ x is the transverse beam size.Photoelectrons were assumed to be generated only at the innermost wall of the antechamber.Furthermore, because the wall is a technical surface and is also roughened by glass bead blasting (GBB) [24,44], the emission angle of photoelectrons was assumed to obey the cosine law [72][73][74].
In cases where the space charge effect and the reflection of electrons were neglected, i.e., low n e , the value of β was approximately 0.07.In contrast, when the space charge was taken into account assuming I bunch ¼ 1 mA bunch −1 , a bunch spacing of three rf buckets, δ max ¼ 1.2, and a reflection rate of electrons of 0.7, i.e., high n e , the value of β was 0.03-0.04.In the following discussions, a β value of 0.05 is assumed as a typical value.

B. Relationship between α and δ max under a constant n e
Figure 13 shows n e as a function of δ max for α values of 0.01, 0.03, 0.06, and 0.09 at a bunch fill pattern of 1=150=2RF, calculated by the simulation code PyECLOUD [75], using a circular beam pipe.The line density of photons was 1 × 10 15 photons s −1 m −1 mA −1 , i.e., 0.16 photons positron −1 m −1 .The value of I bunch was 0.8 mA bunch −1 .For δ max values of less than 1.2, n e was of the order of 10 10 -10 11 m −3 , where the space charge effect is small, and is almost proportional to α for a constant δ max .In contrast, for δ max values greater than 1.5, n e was of the order of 10 12 -10 13 m −3 , where the space charge limits n e , which is independent of both α and δ max .As described above, the value of n e th for our case is approximately 3 × 10 11 m −3 .Therefore, n e values of the order of n e th values were not only determined by the SEY (i.e., δ max ), but also by the number of photoelectrons in the beam channel (i.e., α), and n e was almost proportional to α for a fixed δ max .
From the observations made during phase-1 commissioning, the ECE was observed, i.e., the beam size blowup started, at an I value of approximately 900 mA for a bunch fill pattern of 1=1576=3.06RF.This means that n e should be approximately 3 × 10 11 m −3 for these beam parameters.
Actually, the measured n e at the region with the TiN film coating in the test beam pipe was almost the same under the same beam parameters [60,61].Under this condition, δ max was calculated as a function of the number of photoelectrons in the beam channel using the simulation code CLOUDLAND, where a circular beam pipe was again used as a model.The results are presented in Fig. 14.The value of α corresponding to the number of photoelectrons in the beam channel is also plotted in Fig. 14.Here, the bunch fill pattern was 1=150/3RF, the number of positrons in a FIG. 13.Dependence of calculated electron density (n e ) on the maximum SEY (δ max ) for several α, that is, the number of photoelectrons in a beam channel, at a bunch fill pattern of 1=150=2RF.The dotted line denotes the combination of α and δ max that gives a constant n e .FIG. 14. Calculated results for combinations of δ max and number of photoelectrons in a beam channel that give the same electron density (n e ) of 3 × 10 11 m −3 at 900 mA for a bunch fill pattern of 1=1576=3.06RF.The values of α corresponding to the number of photoelectrons are also given.bunch was 3.1 × 10 10 bunch −1 (corresponding to 0.5 mA bunch −1 ), and the line density of photons from SR was 0.16 photons positron −1 m −1 .This line density is equal to the average value in the arc sections, as mentioned above.The quantum efficiency was assumed to be a constant 0.1.Furthermore, the photoelectrons were emitted uniformly inside the beam channel.
It is interesting that the combinations of α and δ max similar to the line in Fig. 14 can be plotted along the dotted line in Fig. 13, although the beam parameters are different.This tendency is a characteristic of n e at this order of magnitude.
If α was estimated from simulations or measurements, δ max at the surface could be deduced using Fig. 14.For example, the α value was estimated to be 0.01 from an experiment during KEKB commissioning using a test beam pipe with an antechamber made of pure copper [44].In this case, δ max was estimated to be approximately 1.4 from Fig. 14.This value of δ max is higher than the 1.0-1.2obtained for the TiN film coating after sufficient electron bombardment in a laboratory [46].Various hypotheses explaining this discrepancy, such as the imperfect TiN film coating, insufficient electron bombardment (i.e., aging), or high pressures in the beam pipe, have been considered, but they do not provide definitive explanations.For example, n e in the test beam pipe at the region with the TiN film coating did not change during phase-2 commissioning, as described in Sec.V.The pressures in the arc sections during phase-2 commissioning were a similar order of magnitude as those in the laboratory experiments.Therefore, to evaluate the actual δ max , it is necessary to estimate α in a real beam pipe.

C. Reevaluation of α and δ max
The values of α and δ max in the real beam pipe of the ring were reevaluated using four methods, including simulations and dedicated experiments, during phase-2 commissioning.

From the photon distribution
Using the cross section and surface roughness of a real beam pipe with antechambers, the number of photons inside the beam pipe was calculated by the simulation code Synrad3D [76].The innermost wall of the antechamber in the real beam pipe, where the SR is directly irradiated, was roughened by GBB [24,44].The measured roughness in rms (σ [μm]) was 11.59 μm and the correlation length of the roughness (T [μm]) was 47.59 μm, giving a ratio T=σ of 4.11.The inner wall of the beam channel, which is a surface of an extruded Al-alloy pipe, had a σ value of 0.647 μm and a T value of 9.52 μm, giving T=σ ¼ 14.12.The distribution of photons absorbed to the inner wall of the beam pipe was calculated under the real layout of electromagnets at the location where n e was measured.The scattered photons from upstream of the location were taken into account in the calculation under the assumption that a TiN film with a thickness of 200 nm was coated on the Al-alloy surface [46].
Figure 15(a) shows the calculated distribution of absorbed photons along the periphery of the cross section, and Fig. 15(b) shows the angular distribution, where θ ¼ 0 corresponds to the innermost part of the antechamber.The line density of total photons absorbed at this location was 0.16 photons positron −1 m −1 .The line density of photons absorbed in the beam channel was 0.00956 photons positron −1 m −1 .The number of photoelectrons can be obtained by multiplying the quantum efficiency with the number of absorbed photons.Assuming a constant value for the quantum efficiency as a function of the photon energy, we have Using β ¼ 0.05, a value of α ¼ 0.11 was calculated from Eqs. ( 1) and ( 2).The value of δ max was then evaluated as 0.5-0.6 from the extrapolated line in Fig. 14.This value of δ max is quite low comparing the obtained thus far [46]; this will be discussed again in Sec.VI D.

From the measured n e
For values of the order of 10 11 m −3 , n e is almost proportional to the number of photoelectrons in the beam channel for a constant δ max , as indicated in Fig. 13.The ratio of n e when the number of electrons from the antechambers is negligible, n e0 , to that under usual conditions, n e , can be computed as follows: Therefore, if n e0 is measured, α can be deduced using Eqs.( 1) and ( 3).
During phase-2 commissioning, n e0 was measured by attaching weak PMs along the ends of the antechambers of the test beam pipe, as shown in Fig. 16.These magnets generate weak vertical magnetic fields (B y [mT]) along the antechamber, trapping the emitted photoelectrons inside.The value of B y near the PMs was approximately 10 mT, but that in the beam channel was less than 0.05 mT, which is the same order as terrestrial magnetism.In the simulation, B y of this order of magnitude had no effect on n e in the beam channel.Furthermore, B y of this order of magnitude was experimentally found to have little effect on the measurement of n e by the present electron monitors.
The measured n e0 and n e at a bunch fill pattern of 1=1576=3.06RFduring phase-2 commissioning are presented in Fig. 17.Note that the high n e values at low I bunch are not reliable, as the volume used in the calculation of n e is so small that the estimation method is no longer valid in principle [59].The value of n e0 =n e was 1.5=3.3 at an I bunch value of 0.45 mA bunch −1 .From Eq. ( 3), the value of p b =p a was calculated to be 0.04 for a β value of 0.05.The value of α was then calculated to be 0.08 using Eq.(1).
Consequently, using the relation in Fig. 14, δ max was estimated to be approximately 0.7-0.8.

From the beha vior of n e with respect to I
Both α and δ max were estimated from the behavior of the measured n e against I d and compared with the values obtained by simulations.The behavior depends on α, δ max , and also the bunch fill pattern [75].Figures 18(a

From the dependence of n e on the train length
This method is suitable for deducing δ max .As n e generally increases (builds up) with bunches from the beginning of a bunch train [6,9], its value should depend on the length of the train.The solid lines in Figs.19(a  simulation code PyECLOUD.Here α was set to as a typical value from methods (i)-(iii) above.Actually, the value of α has little effect on the qualitative behavior of n e against I bunch .For small δ max (δ max < 1.2), the multiplication of electrons is small and n e soon becomes saturated at the limit determined by the balance between the generation and loss of electrons.Therefore, the dependence of n e on the train length is weak when the train length is longer than several tens of bunches.For larger δ max (1.2 < δ max < 1.6), n e continues to increase with the number of bunches by multipactoring until the limit determined by the space charge effect.As it takes some time to reach this limit, n e depends on the train length.For larger δ max (δ max > 2.0), n e soon reaches the limit determined by the space charge effect owing to the strong multipactoring, and then the dependence on the train length again becomes weak.These tendencies are indicated in Fig. 19.Note that the vertical scale in each plot is adjusted to focus on the specific behavior.
The dependence of n e on the train length in the test beam pipe at the region with the TiN film coating was measured during phase-2 commissioning.The results for bunch fill patterns of 4=60=2RF and 1=150=2RF are plotted in Fig. 19(b).Comparing the measured results with the calculated ones in the same figure, the behavior of the measured n e gives the best fit when δ max ¼ 0.8-1.0.
For reference, the behavior of the measured n e with respect to I bunch at the region without the TiN coating (i.e., bare Al alloy) for these two bunch fill patterns is shown in Fig. 19(f).The behavior of the measured n e fits well for δ max ∼ 2.0.
Note that the evaluation by method (i) used the number of photoelectrons calculated from the number of photons assuming a constant quantum efficiency for both the antechamber (rough surfaces and no TiN film coating) and the beam channel (smooth surface and TiN film coating).This is different from methods (ii) and (iii), where the number of photoelectrons is directly included.The difference may explain the relatively high value of α given by method (i).If the quantum efficiency of the TiN film coating is less than that of the Al surface, for example [45], α should be smaller than the obtained value.
Although the results are relatively scattered, all values of α are greater than that obtained in the KEKB experiments, i.e., 0.01 [44].This difference can be explained by the following: (a) the location of the experimental setup, i.e., just downstream (KEKB) and 7 m downstream (SuperKEKB) of a bending magnet, (b) the height of the antechamber, i.e., 18 mm (KEKB) and 14 mm (SuperKEKB), (c) the beam pipe material, i.e., copper (KEKB) and Al-alloy (SuperKEKB), (d) the treatment of the innermost surface of the antechamber where the SR is directly irradiated, and so on.Among these, reasons (a) and (b) seem the most plausible.Some photons from upstream should hit the beam channel far downstream of the bending magnets because of the vertical spread and scattering of SR in the real machine.Further investigations are required to clarify the precise reason.
As for δ max of the TiN film, the values are close to or somewhat lower than those obtained in the laboratory [46].The TiN film coating seems to be working as well as expected with regard to reducing the emission of secondary electrons.

VII. SUMMARY
The ECE was excited in the SuperKEKB LER during phase-1 commissioning.The serious ECE observed in the high-current region was caused by the electron cloud in the beam pipes at drift spaces, which already had the TiN film coating and antechambers.Additional countermeasures, that is, the application of permanent magnet units and solenoids to generate a B z of several tens of mT, worked well during phase-2 commissioning, and the ECE was not observed until a current linear density of 0.4 mA bunch −1 rf bucket −1 .Although the current linear density at the design parameters is 0.7 mA bunch −1 rf bucket −1 , the countermeasures in SuperKEKB have been working almost as expected.
During phase-2 commissioning, the effectiveness of the antechamber (α) and TiN film coating (δ max ) of the real beam pipe in the ring was reevaluated through simulations and dedicated experiments.The value of α in the real beam pipe was found to be larger than expected.The most plausible reason for this large value is the irradiation of photons in the beam channel due to the spread and scattering of SR in the real ring.The value of δ max , however, decreased to the values obtained in the laboratory.These results indicate the importance of photoelectrons for the ECE in the real machine [52,76,77].
Phase-3 commissioning of SuperKEKB will start in early 2019, and the beam current will be increased further.Before commencing phase-3 commissioning, PM units will be added with the aim of covering over 90% of the drift spaces with a B z greater than 2 mT.Careful observations of the ECE will continue during phase-3 commissioning and beyond.
In terms of beam optics, the PMs and solenoids can be a source of error, especially for the extremely low beam emittance required by SuperKEKB.Careful consideration on this point will be required in the future.
This experience of the ECE and its countermeasures in SuperKEKB provide valuable information for designing the vacuum systems of future high-intensity machines [78,79].

FIG. 2 .
FIG. 2. Typical cross section of a beam pipe at arc sections for LER.

FIG. 4 .
FIG. 4. Measured vertical beam sizes as a function of the current line density (I d ) for several bunch fill patterns measured (a) before and (b) after attaching PM units to Al-alloy bellow chambers in phase-1 commissioning, and (c) in the early stage of the KEKB era.
FIG. 5. PM units attached to an Al-alloy bellows chamber.FIG. 6. Type-1 and type-2 units at drift spaces.

FIG. 7 .
FIG. 7. Axial distributions of the measured vertical and axial components of the magnetic field (B y and B z ) at the top surface, and B z at the center of the beam channel in (a) type-1 and (b) type-2 unit.

FIG. 11 .
FIG. 11.Measured vertical beam sizes as a function of the current linear density (I d ) for several bunch fill patterns during phase-2 commissioning.

FIG. 15 .
FIG. 15.(a) Positions of absorbed photons along the peripheral of the beam pipe, and (b) their angular distribution, where 0°c orresponds to the inner most side of the antechamber, calculated by the simulation code Synrad3D.
) and18(b)   show the dependencies of n e measured at the region with the TiN film coating in the test beam pipe (without PM units) on I d for bunch fill patterns of 1=150=2RF and 1=120=3RF, respectively, during phase-2 commissioning, and also show the dependencies of n e calculated using the simulation code PyECLOUD with a circular pipe model and bunch fill patterns of 1=150=2RF and 1=150=3RF, respectively, for ðδ max ; αÞ ¼ ð0.8; 0.09Þ, (1.0, 0.06), (1.2, 0.04), and (1.4,0.01).These combinations of δ max and α give the same n e value of approximately 3 × 10 11 m −3 at an I bunch value of 0.5 mA bunch −1 and a bunch fill pattern of 1=150=3RF, and almost follow the relation indicated by the line in Fig.14.The calculated behavior of n e was very similar to the measured relations for α ¼ 0.03-0.06and δ max ¼ 1.0-1.2.Similar results were obtained for other bunch fill patterns of four rf-bucket spacings.
FIG.16.Weak PMs attached at the antechambers of the test beam pipe with electron monitors to prevent the photoelectrons generated in the antechamber from entering the beam channel.

FIG. 17 .
FIG. 17. Measured electron density (n e ) near the beam orbit for the cases with and without PMs in the antechambers.

FIG. 18 .
FIG. 18. Measured electron density (n e ) near the beam orbit and calculated density for several combinations of (δ max , α) as a function of the current linear density (I d ) for bunch fill patterns of (a) two and (b) three rf-bucket spacings.

FIG. 19 .
FIG. 19.Calculated behaviors of the electron density (n e ) with respect to the bunch current (I bunch ) for bunch fill patterns of 1=60=2RF and 1=150=2RF and δ max from (a) 0.8, (b) 1.0, (c) 1.2, (d) 1.4, (e) 1.6, and (f) 2.0, respectively, where α ¼ 0.06.Vertical scales are adjusted to focus on the specific behavior.Measured behaviors of the electron density (n e ) in the test beam pipe at the region with and without the TiN coating against the bunch current (I bunch ) at bunch fill patterns of 8=60=2RF and 4=150=2RF are also plotted in (b) and (f), respectively.