Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP01

FIREBALL HYPOTHESIS FOR THE TRIGGER OF SUDDEN BEAM
LOSSES AT SuperKEKB
Tetsuo Abe∗High Energy Accelerator Research Organization (KEK),
Tsukuba, Ibaraki 305-0801, Japan∗ tetsuo.abe@kek.jp

Horizontal
Position [mm]SuperKEKB is an asymmetric-energy electron (𝑒− ) andpositron (𝑒+ ) ring collider with a higher-energy (7 GeV) 𝑒−
beam and a lower-energy (4 GeV) 𝑒+ beam stored in the low
emittance double ring (main ring) with a circumference of
3 km and an rf frequency of 509 MHz. The design beam
currents to be stored in the main ring are 2.6 A and 3.6 A for
HER and LER, respectively.
We performed the phase 1 beam operation of SuperKEKB
from February to June in 2016. In this phase, we had no
Belle II detector component nor final focus magnets in theinteraction region with no 𝑒+ 𝑒− beam collision. The main
purposes of this phase are vacuum scrubbing, low-emittancebeam tuning, and beam background study for the Belle IIdetector to be installed before the next phase. We installed
and used two horizontal beam collimators in the main ringtentatively during the phase 1 with a large physical apertureat the heads. Before starting the phase 2 beam operationin March, 2018, the Belle II detector components with apart of the beam-sensitive vertex detectors were installedat the interaction point. We installed the super-conducting
final focus magnet system in the interaction region, and four
more horizontal beam collimators and two vertical onesin the main ring. The major purpose and achievement in
the phase 2 is that we have successfully demonstrated thenano-beam collision scheme [1] at SuperKEKB. The cruxof the scheme is that the beta function at the interaction
point (𝛽∗𝑦 ), whose inverse is roughly proportional to theluminosity, can be squeezed down to values smaller thanthe bunch length for higher luminosities with suppressing
the hourglass effect. So far, the smallest 𝛽∗𝑦 and beam size
have been achieved at SuperKEKB in the world among thecolliders. After the phase 2 ended in July, 2018, we started
the phase 3 beam operation in March, 2019, with seven(four) horizontal (vertical) beam collimators for LER andeleven (nine) horizontal (vertical) ones for HER, where theminimum physical aperture at the beam-collimator head wasaround ±1 mm depending on the beam operation status to(a) Bunch Oscillation Recorder (horizontal)

VerticalPosition [mm]INTRODUCTION(b) Bunch Oscillation Recorder (vertical)

Bunch
Current [mA]

Although we need to increase stored beam currents toimprove the luminosity, we have faced a serious obstacle ofsudden beam losses (SBLs) in the main ring of SuperKEKB.
This study examines whether SBL occurs by the same mechanism as observed in vacuum breakdown of accelerating
cavities, that is triggered by a hot microparticle “fireball”.

suppress beam backgrounds at the Belle II detector. Thosesmall physical apertures are inevitable in the nano-beamcollision scheme because the smallest physical aperture at abeam-collimator head is roughly proportional to 𝛽∗𝑦 in thescheme. The phase 3 is dedicated to taking physics data by
the Belle II detector, where increasing the beam currents
is another solid direction in the luminosity improvement.
However, we have faced a serious obstacle in increasing thebeam currents: sudden beam losses (SBLs), to be describedin the next section. We observed no SBL in the phase 1 ofSuperKEKB nor in the KEKB era.
In this paper, a hypothesis is proposed that SBL canoccur by the same mechanism as observed in Ultra-HighFrequency (UHF) Continuous-Wave (CW) accelerating cavities, that is triggered by a hot microparticle (named “fireball”
by the author). This hypothesis (fireball hypothesis) could
give new directions and perspectives on overcoming the SBL
obstacle, and on future high-intensity lepton accelerators.

Current
Loss [mA]

Abstract

The last turn(c) Bunch Current Monitor

Abort kicker fired(d) Loss in bunch current compared to the previous turnTime

1 turn~10 μsFigure 1: Example of SBL shown in Fig. 4 of [2]. Bunchby-bunch (a) horizontal and (b) vertical positions, and (c)bunch current were measured in one of the straight sectionsof the SuperKEKB main ring. (d) Difference in the bunch
current from that in the previous turn.

SUDDEN BEAM LOSS (SBL)
Figure 1 shows an example of SBL events. The mostsignificant feature of SBL is a short time between the startof the beam-bunch position change or bunch-current loss
and the beam abort timing, which is typically a few tens of
microseconds, much shorter than those in common beam
instabilities of the order of a millisecond or longer. The
typical time of a few tens of microseconds is mostly thetime from significant beam loss detection around a beamcollimator or the Belle II detector to dumping beam bunches
by the fast abort system. SBL can lead to serious damages on
beam collimators (e.g. see Fig. 27 in [3]) and/or the Belle IIdetector, and can cause quench of the super-conducting finalfocus magnet. At SBL, no significant beam-size change- 250 -

Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP01

was observed with an X-ray monitor and an ultrahigh speed
camera [2]. No change in the beam phase relative to thephase of the rf system was also observed, i.e., no energy
loss observed in SBL. Therefore, the beam bunches weresuddenly kicked in the transverse direction in microseconds.
We have confirmed that no machine component is related
to SBL by careful monitoring of the performance. SBL
occurred at not only LER but also HER, not simultaneously
but exclusively. The occurrence rate seems to depend on thebunch current with a threshold around 0.7 mA/bunch in thecase of LER although that has not yet been confirmed dueto the low statistics of SBL events.
There are several hypotheses to explain the trigger mechanism of SBL, including vacuum arcs at rf contacts, dustbeam interaction, and electron cloud. However, it is difficult
for any hypothesis to explain the fast phenomena with asignificant transverse kick in SBL except for the fireball hypothesis. This hypothesis is based on the vacuum breakdown
mechanism observed in UHF CW accelerating cavities triggered by a fireball with a progression time shorter than amicrosecond, to be explained in the next section.

FIREBALL BREAKDOWN IN UHF
CAVITIES
Vacuum breakdown can be caused by a vacuum arc in an
accelerating cavity, that could limit accelerator performance.
It has been revealed by recent experimental studies that suchvacuum arcs are mostly triggered by a hot microparticle1 in
UHF CW cavities [4, 5]. The physical process is:
1. A microparticle in a vacuum with a high sublimation
point, e.g., carbon and molybdenum which are typical heater materials in high temperature furnaces forbrazing, is heated by a high field of microwave in thecavity, turning into a fireball with a temperature reaching 1000 °C or higher, where the thermal conductivity
between the microparticle and a metal surface of thecavity body is tiny if the fireball is attached on the cavity surface, or the microparticle is flying in a vacuum
inside the cavity;
2. The fireball lands on a cavity surface with a relatively
low sublimation point, e.g., copper;
3. Plasma is generated around the fireball landing point;and
4. The plasma eats the field energy in the cavity, leading
to vacuum breakdown.
At any breakdown explained above (fireball breakdown),
the microwave field level in the cavity drops rapidly in atime shorter than 1 µs, meaning that the generated plasma
at the fireball landing point absorbs the field energy in atime scale of 100 ns. Because the typical stored field energy
in a UHF CW cavity is 1 J, the absorbing power is several
megawatts. Another feature is a current flash; significant
X-ray is detected at the moment of any fireball breakdown
during high-power operation with no beam injection into
the cavity, where the X-ray is caused by impacts of electron
1 also called a dust or a particulate

currents on a cavity metal surface. The speed of the plasma
evolution immediately after fireball landing can be estimatedfrom the fast drop in microwave level in the cavity. The
evolution time to become a macroscopic vacuum arc is of
the order of 100 ns in the case of UHF cavities, that is much
shorter than the revolution time of the SuperKEKB main
ring (≈ 10 µs).
This phenomenon is not so frequent; the average breakdown rate of the thirty ARES cavities used for SuperKEKB
LER and HER was 0.5/cavity/(four months) during beam operation in 2022 at an average cavity voltage (𝑉𝑐 ) of 0.42 MV,
which is approximately one breakdown of any ARES cavity
per week2 . On the other hand, the breakdown rate of theaccelerating cavities for the SuperKEKB damping ring (DRcavities) is roughly 4.1/cavity/day at 𝑉𝑐 = 0.9 MV estimatedfrom the high-power tests at the test stand after rf conditioning at 𝑉𝑐 > 0.9 MV. Assuming that the breakdown rates are
the same between the ARES and DR cavities (at least, themechanical structures are the same except for the coupling
cavity of the ARES three-cavity system), the breakdown
rate is roughly proportional to the ninth power of the cavity voltage. This strong field dependence can make a quasi
threshold for the occurrence rate of fireball breakdown, thatis reminiscent of the bunch-current dependence of the SBL
occurrence rate.
Importantly, an essential situation for fireball breakdown
is coexistence of different materials with largely different
sublimation points in the same place.

(a)Beam-induced field(Order of milliseconds or longer)(b)

Beam-induced field(c)(Order of a microsecond or shorter)

Figure 2: Physical process proposed in the fireball hypothesis. (a) A microparticle with a higher sublimation pointis heated by a beam-induced electromagnetic field into a
fireball. (b) The fireball landing on a metal surface with alower sublimation point, plasma (shown with blue in thisfigure) is generated around the landing point with high electromagnetic fields applied. Then the plasma eats the fieldenergy for evolution. (c) Large currents from the evolved
plasma interacting with beam particles significantly.

FIREBALL HYPOTHESIS FOR SBL
Beam collimators at SuperKEKB have two different materials with largely different sublimation points: the beamcollimator head made from tantalum, tungsten, or carbon,
and vacuum chamber made from copper. Therefore, fireballbreakdown can occur around the beam collimators in principle. In this section, detailed physical process leading to
2 There has been no significant change in the average breakdown rate since

the KEKB era.

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Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP01

Table 1: Simulated equilibrium temperatures in Celsius of spherical microparticles made from tungsten. The time in second
to reach 1000 °C from 30 °C is also shown in parentheses. 𝜖𝑒 and 𝜙 indicate emissivity and diameter of the microparticle,
respectively. 𝑑 indicates the transverse distance between the beam bunch and the center of the microparticle.
𝜙 [mm]
0.01
0.05
0.10
0.50
1.00

𝜖𝑒 = 0.1
𝑑 = 2 mm 5 mm
1019 (0.4)
5951600 (0.7)
8021542 (1.6)
7671670 (6.6)
819
1704 (12)763

𝜖𝑒 = 0.2
2 mm
5 mm
842
467
1253 (0.7)
5971194 (1.9)
5671293 (7.3)
6071322 (13)558𝜖𝑒 = 0.3
2 mm
5 mm
748
400
1079 (0.9)
4951022 (2.6)
4691107 (8.5)
503
1133 (15)458Table 2: The same as in Table 1 for tantalum.
𝜙 [mm]
0.01
0.05
0.10
0.50
1.00

𝜖𝑒 = 0.1
𝑑 = 2 mm 5 mm
923
534
1687 (0.4)
9041625 (1.0)
8771799 (3.7)
9401830 (7.0)
896𝜖𝑒 = 0.2
2 mm
5 mm
759
421
1347 (0.4)
6951284 (1.1)
6681423 (4.0)
7181449 (7.4)
679

SBL based on the fireball breakdown mechanism shown in
Fig. 2 is investigated, and then the possibility of occurrenceof each step of the process is discussed.

Physical process
The process is divided into three elementary steps:
1. A microparticle with a higher sublimation point isheated by a beam-induced electromagnetic field into a
fireball (step 1) shown in Fig. 2(a);2. The fireball lands on a metal surface with a lower sublimation point, leading to plasma generation and evolution (step 2) shown in Fig. 2(b); and3. There is a significant interaction between currents fromthe evolved plasma and beam particles circulating in
the SuperKEKB main ring (step 3) shown in Fig. 2(c).
Step 1: Heating of a microparticle into a fireball This
step is examined based on a first-principles simulation using CST Particle Studio to calculate temperatures of
microparticles located and fixed near a beam bunch. The
equilibration temperature is determined by the heat value
and thermal radiation power, where the microparticle is located inside a vacuum duct with no contact with any solid.
The results for microparticles made of tungsten or tantalum (materials of the SuperKEKB beam-collimator heads)
are shown in Table 1 and Table 2, respectively, for a bunch
length of 6 mm, total current of 900 mA, and 1272 bunches
per ring, which is a typical set of operational parameters for
SBL at LER. The results show that fireballs can be generated
realistically if a submillimeter or smaller microparticle getsto a few millimeters from a beam bunch for a second with alow emissivity of the fireball material. It is also revealed that
fireballs can be generated more probably around tantalum
than tungsten.

𝜖𝑒 = 0.3
2 mm
5 mm
673
362
1175 (0.5)
5891113 (1.3)
564
1235 (4.3)
607
1258 (7.9)
570

In the fireball hypothesis, a microparticle is assumed tocome from a surface of or close to a beam-collimator head,
where the microparticle should be charged up, negatively
in LER or positively in HER to get close to a beam bunch
for a certain time. Some experiments and theories indicatethat microparticles can be charged up by irradiation negatively or positively depending on the situation [6]. The headsof the SuperKEKB beam collimators are subject to strong
synchrotron radiations during beam operation, so that microparticles around beam-collimator heads have a chance tobe charged up positively or negatively. Similar phenomena
were observed in the photon-factory ring accelerator PF-AR
at KEK [7].
Step 2: Fireball landing and plasma generation Even
though we do not know the details in this step, we can parameterize the physics with two parameters: the current ofelectrons and metal ions from and the initial temperature of
the plasma because only the two quantities are related to theinteraction with beam particles to be described in the next
step.
During this step, the fireball material is assumed to break
up into infinitesimally small pieces, and will not be taken
into account in the next step; only the currents from theevolved plasma will interact with beam particles.
Step 3: Significant interaction with beam The interaction between the currents from the evolved plasma andbeam particles is calculated using first-principles ParticleIn-Cell (PIC) simulation of CST Particle Studio (CSTPIC solver) for a vertical beam collimator of SuperKEKB
LER with a ±2 mm physical aperture at the head. A fireballis assumed to land 17 mm away from the center of the headin the beam direction (𝑧 = −17 mm at 𝑦 < 0), indicated by the- 252 -

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vertical red cone in Fig.3. Equinumerous 𝑒− and copper ions
(Cu+ ) are generated at the fireball landing point, emitted
in the normal direction to the copper surface plane with anangular spread of ±45°. The emission time is modeled as agaussian function with one-sigma width of 1 µs, where thissimulation covers the time period of five-sigma, i.e., the simulated time (𝑡) reaches 𝑡 = 10 µs with a peak emission current(𝑒𝑚𝑖)(𝐼peak) at 𝑡 = 5 µs. The initial velocities of emitted particles
at the fireball landing point are determined by the initial(𝑒𝑚𝑖)
temperature (𝑇ini) according to the Maxwell distribution.
(𝑒𝑚𝑖)
(𝑒𝑚𝑖)
The two parameters of 𝐼peak
and 𝑇ini
determine the parameterization of this simulation model. Positron buncheswith a bunch length of 6 mm and a bunch charge of 7 nC
come with a two-bucket spacing, i.e., approximately at a 4 ns
interval, which is a typical parameter set for SBL at LER. In
this condition, the peak electric and magnetic field strengths
at the fireball landing point due to the beam bunch are approximately 2.8 MV/m and 7.4 kA/m, respectively, which
are roughly the same as those on the inner surface of UHF
cavities during high-power operation (e.g. see [5]). In theearly stage of this simulation, emitted 𝑒− moves from theside of the fireball landing point (𝑦 < 0) to the other side (𝑦 >0) at every passage of beam bunches in a time scale of 10 ns.
On the other hand, Cu+ can not significantly move in thistime scale due to the heavy mass; they significantly move ina time scale of 1 µs. In any case, no current can be emitted
from the fireball landing point if the charge density reachthe space charge limit at the kinematic energy of emitted
particles.

↑
Head

±2 mm

Figure 3: PIC simulation for the SuperKEKB beam collimator. The red cones indicate particle sources. The horizontal cone in the left-hand side is for 𝑒+ beam buncheswith 7 nC/bunch, 6 mm bunch length, and 4 ns bunch spacing. The vertical cone is for plasma particles consisting ofelectrons and copper ions emitted at the same point.
What to calculate is a transverse kick angle (𝑘𝑦 ) during thebeam bunch passage. Setting up zero transverse momentum
in the initial state, the transverse kick angle is calculated as:𝑘𝑦=

𝑃𝑦 /𝑃𝑧(1)where 𝑃𝑦 (𝑃𝑧 ) indicates the 𝑦-directional transverse (𝑧directional longitudinal) momentum of the beam bunch after
it passed. The momentum and its standard deviation of thebeam bunch is calculated as:
𝑁mp

𝑃𝑦

=

Δ𝑃𝑦

=

1
∑ 𝑝(𝑖) 𝑞(𝑖)𝑄𝑏 𝑖=1 𝑦√√ 1 𝑁mp (𝑖)2√∑ (𝑝𝑦 − 𝑃𝑦 ) 𝑞(𝑖)⎷ 𝑄𝑏 𝑖=1

(2)
(3)

(a)

(b)

(c)

(d)

(e)

(f)

Figure 4: Kick angles of 𝑒+ beam bunches simulated with
the CST PIC solver up to 𝑡 = 10 µs of one revolution time of
the SuperKEKB main ring. (a) No particle emission from(𝑒𝑚𝑖)
the fireball landing points. (b) to (e) for 𝐼peak= 70 A and

(𝑒𝑚𝑖)
𝑇ini
= 1000, 10 000, 300 000, 1 000 000 °C, respectively.
(f) in the same conditions as in (d) except that no Cu+ isemitted, i.e., only 𝑒− emitted.

(𝑖)and the same for 𝑃𝑥 and 𝑃𝑍 , where 𝑝(𝑖)𝑦 (𝑞 ) indicates the𝑦-directional transverse momentum of particles (electriccharge) of the 𝑖-th macroparticle in the PIC simulation for the
beam bunch, 𝑄𝑏 is the bunch charge (7 nC), and 𝑁mp is thenumber of macroparticles in the beam bunch (= 266). The
kick angle should be non-zero if there are particle emissions
from the fireball landing point, leading to interactions between the 𝑒+ beam bunches and emitted particles of 𝑒− andCu+ . However, the kick angle can be non-zero even with no(𝑒𝑚𝑖)particle emission at the fireball landing point, i.e., 𝐼peak= 0,
due to some numerical noise. Figure 4(a) shows kick anglesof the 2500 𝑒+ beam bunches (up to 𝑡 = 10 µs) with no emission at the fireball landing point. There are non-zero kickangles of the order of 100 nrad, but they are negligibly small
because significant kick angles for SBL should be around
1 µrad or larger. On the other hand, Fig. 4(b) shows kick angles with particle emissions at the fireball landing point with
(𝑒𝑚𝑖)
(𝑒𝑚𝑖)
𝐼peak
= 70 A and 𝑇ini
= 1000 °C, where 70 A is the sameas the peak current of the 𝑒+ beam bunch in this simulation,and 1000 °C is the typical temperature of fireballs. There is- 253 -

Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP01(𝑒𝑚𝑖)
no significant kick even in Fig. 4(c) for 𝑇ini
= 10 000 °C.
(𝑒𝑚𝑖)
Significant kicks appear for 𝑇ini > 100 000 °C as shownin Fig. 4(d) where the 𝑒+ beam bunches are attracted by theemitted 𝑒− at the fireball landing point at 𝑦 < 0. However,
too high temperature does not lead to large kick angles as(𝑒𝑚𝑖)shown in Fig. 4(e). For 𝐼peak= 70 A, several hundreds ofthousands degrees Celsius leads to significant kick angles
around 2 µrad for the beam bunch center of charge.

(a)

(b)

(𝑖𝑖)

𝑝𝑝𝑦𝑦 /(𝑚𝑚𝑒𝑒 𝑐𝑐0 )Figure 6: Kick angles of 𝑒− beam bunches simulated with
the CST PIC solver up to 𝑡 = 10 µs of one revolution time of
the SuperKEKB main ring for emission parameters of (a)
(𝑒𝑚𝑖)
(𝑒𝑚𝑖)
(𝑒𝑚𝑖)
𝐼peak
= 70 A and 𝑇ini
= 300 000 °C, (b) 𝐼peak= 280 A

Bunch charge distribution(𝑒𝑚𝑖)
and 𝑇ini= 100 000 °C.

Figure 5: Transverse normed momenta (upper) and electriccharges (lower) of the macroparticles of the beam bunch as afunction of the 𝑧 position in the beam direction for Fig. 4(d)at 𝑡 = 5137.09 ns. 𝑚𝑒 and 𝑐0 are the electron mass and speedof light in vacuum, respectively. Normed momentum of 0.01
roughly corresponds to a kick angle of 1 µrad for LER.
The kick angles in Fig. 4(d) reach around 4 µrad at thelargest including the standard deviation, which means thatkick angles of each macroparticle are different inside a beam
bunch. Figure 5 shows an example of transverse momentaof the macroparticles inside a beam bunch after it passes asa function of the 𝑧 position, showing a significant gradient.
The first half of the beam bunch is lightly kicked, on the other
hand, the second half is largely kicked, which is consistent
with the observation that not all but a part of a beam bunch islost in most of the SBL events. According to this simulation,
the first half of a significantly kicked beam bunch can survive
in SBL in this case.
Figure 4(f) shows kick angles in the same conditions as inFig. 4(d) except for copper ions: no Cu+ emitted in Fig. 4(f),i.e., only 𝑒− emitted at the fireball landing point. This meansthat Cu+ ions can push up the space charge limit of emitted
𝑒− . Figure 4(e) indicates that too high initial temperaturedoes not make the average kick angle larger.
Figure 6 shows kick angles for HER with the same beam
bunch parameters as in Fig. 4 except for the sign of charge.
The kick angles in Fig. 6(a) are roughly half of that in(𝑒𝑚𝑖)
Fig. 4(d) even with the same emission parameters of 𝐼peak(𝑒𝑚𝑖)
and 𝑇ini. The kick angles shown in Fig. 6(b) are comparable with those in Fig. 4(d).

SUMMARY AND FUTURE PROSPECTS
The fireball hypothesis for SBL at SuperKEKB has been
proposed based on the vacuum breakdown mechanism observed in UHF accelerating cavities. As results of the first-

principles numerical simulations performed in this study,
fireballs can be generated by the beam-induced electromagnetic field, and not only LER but also HER beam particles
can be kicked by a few to several µrad although the investigated parameter space is still limited. This simulation is tobe performed for other landing points, i.e., not close to thebeam-collimator head. It also should be verified if such kickangles are enough to lead to SBL.
How to demonstrate the fireball hypothesis is to observe:• Acoustic wave generated from the fireball landing point,and• SBL with a single beam (LER or HER only) with thesame beam operation parameters as in physics run.
The final goal is to understand what is essential in thefireball hypothesis, and to find out the way to prevent significant transverse kicks of beam bunches in SBL because
removing all dusts, candidates of fireballs, in an accelerator
is not realistic.

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