∎

e1e-mail<EMAIL_ADDRESS>e2e-mail<EMAIL_ADDRESS>n1now at Purdue
University, West Lafayette, IN, 47907, U.S.A. n2now at Thomas Jefferson
National Accelerator Facility, Newport News, VA, 23606, U.S.A. n3now at The
Hague University of Applied Sciences, The Netherlands. n4now at University of
Bonn, 53115 Bonn, Germany n5now at Google LLC., Santa Barbara, CA, 93101,
U.S.A.

11institutetext: Max-Planck-Institut für Physik, 80805 München, Germany
22institutetext: High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan 33institutetext: University of Hawaii, Honolulu, Hawaii 96822,
U.S.A. 44institutetext: INFN Laboratori Nazionali di Frascati, I-00044
Frascati, Italy

# A time resolved study of injection backgrounds during the first
commissioning phase of SuperKEKB

Miroslav Gabrieladdr1,e1  Frank Simonaddr1,e2  Hendrik Windeladdr1  Yoshihiro
Funakoshiaddr2  Michael Hedgesaddr3, n1  Naoko Iidaaddr2  Igal Jaegleaddr3, n2
Christian Kieslingaddr1  Naomi van der Kolkaddr1,n3  Peter Lewisaddr3,n4
Hiroyuki Nakayamaaddr2  Yukiyoshi Ohnishiaddr2  Riccardo de Sangroaddr4
Yusuke Suetsuguaddr2  Marco Szalayaddr1,n5  Sven Vahsenaddr3

(October 13, 2021)

###### Abstract

We report on measurements of beam backgrounds during the first commissioning
phase of the SuperKEKB collider in 2016, performed with the plastic
scintillator and silicon photomultiplier-based CLAWS detector system. The sub-
nanosecond time resolution and single particle detection capability of the
sensors allow bunch-by-bunch measurements, enable CLAWS to perform a novel
time resolved analysis of beam backgrounds, and make the system uniquely
suited for the study of injection backgrounds. We present measurements of
various aspects of regular beam background and injection backgrounds which
include time structure and decay behavior of injection backgrounds, hit-energy
spectra and overall background rates. These measurements show that the
elevated background rates following an injection generally last for several
milliseconds, with the majority of the background particles typically observed
within the first $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The injection
backgrounds exhibit pronounced patterns in time, connected to betatron and
synchrotron oscillations in the accelerator rings. The frequencies of these
patterns are determined from detector data.

††journal: Eur. Phys. J. C

##  1 Introduction

The SuperKEKB accelerator Akai:2018mbz  is a next generation flavor factory
currently operating in Tsukuba, Japan. It is an asymmetric-energy electron-
positron collider which runs predominantly at a center-of-mass energy
corresponding to the mass of the $\Upsilon(4S)$ resonance of
$10.58\text{\,}\mathrm{GeV}$. The beam energies are $7\text{\,}\mathrm{GeV}$
for electrons in the high energy ring (HER) and $4\text{\,}\mathrm{GeV}$ for
positrons in the low energy ring (LER). Compared to its predecessor KEKB,
SuperKEKB has a 40 times higher design luminosity of
$8\text{\times}{10}^{35}\text{\,}\mathrm{c}\mathrm{m}^{-2}\mathrm{s}^{-1}$.
This gain in luminosity is mainly achieved by changes in two operational
parameters: doubling of the beam currents to $3.2\text{\,}\mathrm{A}$ (HER)
and $2.6\text{\,}\mathrm{A}$ (LER), and extreme focusing of the beams at the
interaction point (IP) to vertical beam sizes of $50\text{\,}\mathrm{nm}$
using the so-called nano-beam scheme Bona:2007qt . Despite the short beam
lifetimes on the order of minutes, high integrated luminosities are achieved
by continuously injecting new particles at a rate of up to
$25\text{\,}\mathrm{H}\mathrm{z}$ per beam. Both rings have a circumference of
$3016.3\text{\,}\mathrm{m}$ which results in a revolution time, $T_{rev}$, of
$10\,061.4\text{\,}\mathrm{ns}$.

The ambitious luminosity goals are expected to cause challenging levels of
beam backgrounds in various subsystems of the corresponding Belle II
experiment Abe:2010gxa ; Lewis:2018ayu . In particular the backgrounds related
to the continuous top-up injections of new beam particles, or injection
backgrounds, may lead to background levels which require an interruption of
data recording in the detector during the transit of injection bunches. Thus,
a detailed understanding of the backgrounds is of high importance in order to
limit their impact on the Belle II physics program.

To prime SuperKEKB and Belle II for physics operation and full luminosities, a
three-phase commissioning campaign has been performed. Phase 1 focused on the
basic operation of the accelerator and thus the final focusing system and the
detector had not yet been installed at the IP and no intended collisions took
place. The primary objectives were improving vacuum conditions by scrubbing
and performing basic machine studies such as tuning of the feedback system or
low emittance optimization of the beam optics. Focused beams and collisions
always cause luminosity dependent backgrounds which make up a significant part
of the overall backgrounds. Measurements performed during Phase 1, by
contrast, represented the unique opportunity to study beam-induced backgrounds
and injection backgrounds independently in a collision-free environment. For
this purpose, a set of dedicated beam background detectors was installed
around the IP, collectively referred to as BEAST II. Details on this system,
and results of a first comprehensive analysis of the beam backgrounds at the
IP have already been reported in Ref. Lewis:2018ayu .

One of the subsystems of BEAST II is the CLAWS (sCintillating Light And
Waveform Sensors) detector system Gabriel2019 . It consists of eight plastic
scintillators with directly coupled silicon photomultipliers (SiPM) read out
by commercial electronics and a custom-made DAQ capable of continuously
recording data over periods up to several milliseconds. Its primary goal is a
novel time resolved analysis of backgrounds, focussing on injection
backgrounds in particular. The CLAWS system is uniquely capable of a
continuous monitoring of the background conditions following top-up injections
via the detection of charged particles, complementing the capabilities of
other detector systems in BEAST II. On February 10, 2016 and on February 26,
2016, CLAWS observed the very first beam bunches which were successfully
circulated in the LER and the HER of SuperKEKB, respectively firstbeams . It
should be noted that the beam conditions during Phase 1 differ substantially
from those during later physics operations. The absence of the final focusing
elements results in vertical beam sizes approximately three orders of
magnitude larger than the final design values, and the maximum beam currents
were a factor three below the design values in both rings. The positrons are
created from the primary electron beam in a production target and thus have a
significantly higher emittance at the source. The damping ring which reduces
this emittance prior to injection was not yet operational during Phase 1. This
resulted in increased background levels in the LER, as discussed throughout
this paper. Due to these differences between Phase 1 and later phases, only
limited quantitative information for the conditions at Belle II can be
extracted. Nevertheless, the studies during Phase 1 contribute significantly
to the overall understanding of the behaviour of backgrounds in SuperKEKB.

In this publication we report on measurements performed by CLAWS during Phase
1 of the SuperKEKB commissioning campaign. The present analysis updates and
extends the CLAWS results included in Lewis:2018ayu . Section 2 briefly
introduces relevant sources of beam backgrounds at SuperKEKB. In Section 3, we
give an overview of the experimental setup of CLAWS and its data processing
and event selection. Section 4 begins the discussion of the results by
presenting the time structure of beam backgrounds recorded during periods with
continuous top-up injections. Here, we also describe a number of different
timing patterns encountered in the data and discuss their connection to
betatron and synchrotron oscillations performed by the beam particles.
Subsequently, Section 5 studies the composition of backgrounds by examining
the distributions of hit energies and Section 6 demonstrates a method for
quantifying deposited energies and decay behavior of injection backgrounds
with respect to accelerator conditions. Building on this, Section 7 presents a
detailed analysis of the observed timing patterns. Finally, we briefly
summarize the key findings in Section 8.

##  2 Background sources

The term backgrounds generally refers to undesirable particles and can be
divided into three types of processes: backgrounds caused by the circulating
beams, or beam-induced backgrounds; backgrounds as a byproduct of collisions,
also referred to as luminosity-dependent backgrounds; and backgrounds due to
the injection of new beam particles, or injection backgrounds. These
background particles can be the beam particles themselves or secondary
particles generated by beam particles which are colliding with accelerator
elements.

Due to the lack of collisions, only beam-induced and injection backgrounds are
relevant for the study of Phase 1 data. In the following, we provide an
overview of the four main processes for these backgrounds.

#### Synchrotron radiation

The first source of backgrounds is synchrotron radiation (SR), i.e. photons
which are emitted by the beam particles while undergoing centripetal
acceleration in the bending and focusing magnets. For Phase 1, simulations
predict a moderate soft x-ray photon rate with an upper limit of
$500\text{\,}\mathrm{Hz}$. SR photons are therefore assumed to have no
relevance Lewis:2018ayu .

#### Touschek scattering

The term Touschek effect, or Touschek scattering, refers to an intra-bunch
scattering process in which a single Coulomb scattering between two particles
of the same bunch changes their energy significantly Piwinski:1998qs . This
causes beam particles to depart from their nominal orbits, leading to
significantly increased betatron oscillations and consequently a larger
emittance. When these particles exceed the acceptance of the accelerator, they
collide with the beampipe or other parts of the accelerator infrastructure and
cause secondary particle showers. The higher beam currents and the
dramatically reduced beam sizes due to the nano-beam scheme significantly
increases the particle loss rates by Touschek scattering compared to the
situation at KEKB.

#### Beam-gas scattering

The third source of beam backgrounds is beam-gas scattering, which denotes
scattering of beam particles with residual gas molecules in the beam pipe.
Such an interaction can take place through two different processes: elastic
Coulomb scattering and inelastic Bremsstrahlung, resulting in scattering of
beam particles and photon production, which in turn can lead to secondary
particles.

#### Injection background

The final source of backgrounds considered here are injection backgrounds.
SuperKEKB uses top-up injections to compensate for particle losses due to
background processes and collisions while maintaining constant luminosities.
In such top-up injections, new bunches of electrons and positrons are
continuously injected into already circulating bunches at a rate of
$25\text{\,}\mathrm{H}\mathrm{z}$ per ring. According to Liouville’s theorem,
the injected particles can not be incorporated into the same phase space
volume as the circulating beams. SuperKEKB therefore uses the so-called
betatron injection scheme Mori:2014lda , in which new particles are injected
with deliberately large betatron oscillation amplitudes in the accelerator
plane, which initially separates them from the circulating beams. As a
consequence, the injected particles subsequently perform betatron oscillations
around the closed orbit. Over the course of several hundred turns in the
accelerator, these oscillations are then steadily reduced by synchrotron
radiation damping until the injected particles have fully merged into the
already circulating bunches.

Beam particles for which these betatron oscillation amplitudes exceed the
acceptance of the accelerator collide with the beampipe or other accelerator
elements and lead to beam backgrounds. The cooling phase following after the
injection of new particles can thus result in significantly increased
background levels for the detectors whenever the respective particle bunches
pass by the IP. These bunches are therefore referred to as injection bunches
or noisy bunches. The higher emittance of the positrons compared to the
electrons (see Section 1) is expected to result in increased injection
backgrounds in the LER compared to those in the HER.

A more elaborate description of the different background processes can be
found in Lewis:2018ayu . Since the present paper focusses on injection
backgrounds, the other background sources are usually not further
differentiated in the discussions, and are referred to with the term regular
backgrounds for simplicity.

##  3 Experimental setup, data reconstruction and event selection

A time-resolved analysis of injection backgrounds requires a detector that is
capable of detecting signals as low as single minimum-ionizing particles. In
order to differentiate between energy deposits of individuals bunches, a time
resolution smaller than the time between consecutive bunches
($T_{bunch}=$3.930\text{\,}\mathrm{ns}$$) is needed. Capturing the full time
evolution of injection backgrounds requires to monitor background rates over
hundreds of turns in the accelerator or up to several milliseconds. In this
section, an overview of the setup, the data processing and the event selection
of the CLAWS detector is provided.

###  3.1 Experimental setup

The CLAWS sensors use plastic scintillator tiles read out with silicon
photomultipliers (SiPMs) for the detection of the background particles. Figure
1 shows an assembled sensor, as well as a bare scintillator tile and the
readout unit with photon sensor.

Figure 1: Photograph of an assembled CLAWS sensor module and its main
components: a $30\text{\times}30\text{\times}3\text{\,}\mathrm{mm}$
scintillator tile and the PCB with photon sensor, preamplifier and connectors
for power supply and signal transmission.

The scintillator material has a polystyrene base (Styron 143E) with additional
small admixtures of scintillating fluors (p-terphenyl, 2%) and POPOP (0.05%),
and emits photons in the blue visible range with a peak emission of around
$420\text{\,}\mathrm{nm}$ Hahn:1404985 . The design of the scintillator tiles
is based on the SiPM-on-tile technology developed for highly granular analog
hadronic calorimeter of the CALICE collaboration Sefkow:2018rhp . The tiles
are cuboid-shaped with a size of
$30\text{\times}30\text{\times}3\text{\,}\mathrm{mm}$ and have a spherical
dimple drilled in the center of the bottom face of the tile at the position of
the photon sensor Simon:2010hf ; Liu:2015cpe . The dimple has a depth of
$1.5\text{\,}\mathrm{mm}$ and diameter on surface of $6\text{\,}\mathrm{mm}$.

The scintillation photons are captured by SMD-type Hamamatsu MPPC
S13360-1325PE series SiPMs mppc:2019 , which have 2668 pixels with a size of
$25\text{\times}25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ distributed over an
active area of $1.3\text{\times}1.3\text{\,}\mathrm{mm}$, a thermal dark rate
(at room temperature) as low as $70\text{\,}\mathrm{kHz}$ and a crosstalk
probability of 1%. Together, the scintillating tiles and the SiPMs are mounted
on electronics boards that house a pre-amplifier and provide signal
transmission, power distribution and mechanical support. The design of these
sensor modules is based on the CALICE-T3B experiment Simon:2013zya ;
Adloff:2014rya  which was used for the study of the time structure of hadronic
showers in highly granular calorimeters. The detectors are primarily sensitive
to charged particles, but in principle also show responses to high-energy
photons and to MeV neutrons.

Figure 2: Left: Layout of the CLAWS installation around the SuperKEKB
interaction point. The positrons in the LER travel from top right to bottom
left, the electrons in the HER from bottom left to top right. Right:
Photograph of the CLAWS FWD station, showing the three inner sensors FWD1-3.
The FWD4 sensor is not fully visible, as it is located behind another BEAST II
detector element. The beampipe is visible in the lower right corner of the
image.

To cover the full range of expected rates, eight CLAWS sensor modules were
installed at different distances from the beams, arranged in two stations with
four detectors each, as illustrated in Figure 2. In both stations, the modules
are mounted directly on the BEAST II support structure Lewis:2018ayu  such
that they are positioned in the plane of the accelerator in a line roughly
perpendicular to the beam with a spacing of around $10\text{\,}\mathrm{cm}$
between each detector. The sensors in the forward station (referred to as
_FWD1 - 4_) are located outside of the accelerator ring, next to the HER and
downstream of the IP (with respect to the HER); the region for which
simulations predicted the highest background rates. The detectors of the
backward station (referred to as _BWD1 - 4_) are placed inside of the ring,
again next to the HER but upstream of the IP, the region with the lowest
background predictions. The sensors are numbered such that their distance from
the beam increases with increasing number, with FWD1 / BWD1 closest to, and
FWD4/ BWD4 furthest from the beam, respectively. During the runtime of Phase
1, measurements from all sensors provided data for an online monitor used to
tune accelerator parameters and to commission SuperKEKB. For the presented
analysis only data from the channels FWD1-3 are used, for which the full
analog waveform data was saved throughout Phase 1. Despite the location of the
FWD sensors on the outside of the LER, they are also sensitive to particles
originating from the HER at positions further upstream, allowing studies of
background properties in both rings.

The exposure to ionizing particles throughout beam operations leads to
radiation damage of the SiPMs and of the other detector components. A
significant increase of the dark rate of the photon sensors has been observed,
varying with the distance from the beam and depending on the detector
location. The most exposed sensor was BWD1, followed by FWD1. No detailed dose
measurements for the sensor position exist. Based on dosimeter information in
nearby regions available for parts of the data taking period, and based on the
observed particle rates, the TID received by these sensors was estimated to
several 10 Gy. This resulted in an increase of the dark count rate by more
than two orders of magnitude, beyond several 10 MHz. The BWD1 and FWD1 sensors
were replaced after half of the run time to limit the negative effect of the
increased dark rate on the waveform reconstruction.

The analog signals of the sensors are digitized with two 4-channel USB-
controlled Picotech PicoScope 6404D oscilloscopes which sample each channel
with 8 bit resolution at 1.25 GHz pico6404d:2018 . Each oscilloscope has a
shared internal buffer of $2\times 10^{9}$ samples, which allows the recording
continuous waveforms of up to $400\text{\,}\mathrm{ms}$ in length for all four
channels simultaneously. This enables the uninterrupted monitoring of particle
rates over up to around 40000 consecutive turns in SuperKEKB.

The oscilloscopes, as well as a power supply unit and a data acquisition and
control computer, are located in a dedicated counting room outside of the
radiation area. The analog signals of the sensors are transmitted via coaxial
cables over a distance of 40 meters from the detector location to the counting
room. To ensure sufficient signal quality, an additional analog amplification
stage is included in the signal path at a distance of $3\text{\,}\mathrm{m}$
from the detector location.

The CLAWS system uses two different types of trigger for regular data taking.
For the study of injection backgrounds, the trigger pulse sent by the
SuperKEKB injector linac prior to the injection of particles into the
accelerator rings is used to trigger the system. For the measurement of non-
injection backgrounds a random trigger is used, which is implemented as a pre-
defined waiting time after the completion of a readout cycle. The time
required to read out and process the waveforms captured following a single
trigger signal is several tens of seconds. CLAWS is thus not able to record at
the injection rate of $25\text{\,}\mathrm{H}\mathrm{z}$ and only observed a
very small fraction of the injection events.

###  3.2 Data calibration and processing

Over the course of Phase 1, the CLAWS experiment recorded a total of 5 TB of
raw data. This raw data primarily consists of waveforms capturing the output
of the sensors. We differentiate between two different types of such raw
waveforms: calibration waveforms and physics waveforms. A set of one physics
waveform per channel recorded simultaneously following a common trigger is
referred to as an event. A run consists of multiple events ranging from single
events in special cases up to a few hundred events.

The calibration waveforms capture the pulses of single pixels firing due to
thermal excitation (dark noise), and are used to obtain the average response
to a single photon detected by the SiPMs. This average response incorporates
all temperature effects and the majority of the readout effects. For each
channel, 1000 calibration waveforms are recorded at the end of each run. This
updates the calibration used for the interpretation of the physics waveforms
approximately every 30 minutes, which automatically corrects for variations in
environmental and operational parameters. Due to the stable temperature
conditions in the BEAST enclosure during running, the run-by-run variations of
the average single p.e. amplitude are generally smaller than 1%.

For the physics waveforms, the oscilloscopes continuously sample the sensor
output over $2.4\text{\,}\mathrm{ms}$ during regular operation. Following the
technique developed in Simon:2013zya , the processing of this raw data is
built around the so called waveform decomposition, in which the average
response of a single photon is iteratively subtracted from a raw physics
waveform in order to retrieve the time distribution of the scintillation
photons. The single photon response is obtained from the calibration waveforms
updated once per run. This process provides the arrival times of individual
detected photons in bins of $0.8\text{\,}\mathrm{ns}$, converting the analog
signal to a time distribution of photons.

For each sensor module, the response to a traversing minimum-ionizing particle
was established in additional calibration measurements performed in a climate
controlled laboratory environment after the run time of Phase 1. Several
thousand approximately perpendicularly incident cosmic muons were selected by
a coincidence trigger formed by two additional sensor modules placed above and
below the sensor under study. The most probable number of recorded
scintillation photons is used to normalize the distribution of photons, i.e.
convert it into units of MIPs. For all sensors, the most probable number of
scintillation photons as a result of a traversing cosmic muon is between 13
and 16.5. Since this calibration was performed with the sensors having
collected their full radiation dose, the calibration factors for the most
irradiated sensors FWD1 and BWD1 may be influenced by the increased dark rate,
resulting in an overestimation of the true response to minimum-ionising
particles.

Also after the radiation damage collected during operations in Phase 1, the
rate of having three or more simultaneous photons due to thermal dark rate
does not exceed $1\text{\,}\mathrm{kHz}$ Gabriel2019 , resulting in negligible
background in terms of noise hits wrongly identified as an ionising particle.
Similarly, imperfectly shielded ambient light is excluded as a source of
observed signals since pedestal runs, taken at the end of the runtime, do not
show a significant number of hits. The expected number of p.e. due to dark
noise within the integration window of a MIP signal is expected to be below 3
also at the highest dark count rates encountered in Phase 1, and thus stays
below 20% of the MIP most probable value.

###  3.3 Data set and event selection

For the present analysis, all fully processed runs recorded between May 15 and
June 28, 2016 are considered.111Events containing all information necessary
for a full time resolved analysis have only been taken from May 15, 2016
onwards. For these runs, events are classified based on the beam current in
the HER, $I_{HER}$, the current in the LER, $I_{LER}$, and the type of
injection to generate 15 distinct data sets that reflect a variety of
different accelerator conditions. The data sets are summarized in Table 1. Due
to the long readout time of the system of several tens of seconds (see Section
3.1), the data sets do not contain consecutive injection triggers. The larger
data sets with several 1000 events combine data recorded over several days, up
to the full period of data taking.

Table 1: Summary of data sets examined for the time resolved analysis of backgrounds. Beam currents are stated by the range between the minimum and maximum of currents in all events in the data set. Data Set | $BG$ | $I_{HER}$ | $I_{LER}$ | $N_{evts}$
---|---|---|---|---
|  | [$\mathrm{mA}$] | [$\mathrm{mA}$] | [#]
NI-ALL | - | 29 - 788 | 9 - 852 | 2676
NI-HER | - | 38 - 705 | 0 | 1806
NI-LER | - | 0 | 4 - 974 | 4057
NI-VACS | - | 452 - 706 | 105 - 752 | 792
HER-ALL | HER | 1 - 706 | 0 | 2401
LER-ALL | LER | 0 | 1 - 999 | 7936
LER-VACS | LER | 0 | 1 - 875 | 1238
HER-REF | HER | 3 - 149 | 0 | 62
HER-PS | HER | 286 - 449 | 0 | 190
HER-VS1 | HER | 216 - 300 | 0 | 265
HER-VS2 | HER | 301 - 400 | 0 | 162
LER-REF | LER | 0 | 3 - 398 | 220
LER-PS | LER | 0 | 185 - 486 | 617
LER-VS | LER | 0 | 272 - 350 | 97
LER-SA | LER | 0 | 2 - 185 | 239

The naming of the data sets reflects the key features, with the first part of
the name referring to the type of injection required in the selection, and the
second part indicating a specific property to help to differentiate between
the sets. Although longer waveforms have also been recorded, all data sets
studied here consist of waveforms with a length of $2.4\text{\,}\mathrm{ms}$
($3\text{\times}{10}^{6}\text{\,}\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s}$),
since this is the minimum length of all considered data.

The beam gate of the injector linac, $BG$, as provided by the SuperKEKB beam
and condition monitors, is used as an indicator for the type of injection.
Three different cases are considered: events recorded during injections into
the HER, denoted by “HER"; events recorded during injections into the LER,
denoted by “LER"; and events during periods without injections, denoted by “-"
in the table and a NI (short for non-injection) in the name of the respective
data set. The beam currents, also provided by the beam and condition monitors,
are given as the range of values among events in the data set after selection.
A cut on the beam currents is applied to select events with only one of the
two beams filled, or with both beams combined. A beam current above
$1\text{\,}\mathrm{mA}$ in one ring and below $1\text{\,}\mathrm{mA}$ in the
other is required for single ring data sets, whereas a beam current above
$1\text{\,}\mathrm{mA}$ in both rings is required for joint data sets.
Finally, $N_{evts}$ denotes the total number of events in the respective data
set after the selection.

NI-ALL, NI-HER, NI-LER and NI-VACS are non-injection data sets selected for
the study of the structure of backgrounds of regular bunches . Non-injection
events are recorded using the random internal auto-trigger without any time
correlation to processes in the accelerator (see Section 3.1). NI-ALL includes
all events with beams in both rings, and thus covers a wide range of partly
very different accelerator conditions. The equivalents for events with beams
in a single ring are NI-HER and NI-LER.

The term vacuum scrubbing describes the outgassing of impurities in the vacuum
system of a particle accelerator which is accelerated by the circulating beams
via electron-induced and photon-induced desorption. During vacuum scrubbing
very high beam currents and artificially inflated beam sizes are used to
promote desorption reactions, which also maximizes the backgrounds of ordinary
circulating bunches. NI-VACS includes all events with beams in both rings
taken (only) during periods without injections and vacuum scrubbing in both
rings. As such, it is a subset of NI-ALL.

HER-ALL and LER-ALL are collections of all injection-triggered events (see
Section 3.1) with beams only in the respective ring. LER-VACS is a subset of
LER-ALL consisting of events taken during periods of vacuum scrubbing.

During regular physics operation of SuperKEKB, it is foreseen to
simultaneously inject new particles into two bunches separated by 49 RF
buckets ($96.3\text{\,}\mathrm{ns}$). During Phase 1, double bunch injection
was only employed for the LER, and there only in specific cases. One of these
cases is vacuum scrubbing for which it was the default injection scheme. Thus,
LER-VACS exclusively and LER-ALL partially consist of events with double bunch
injections. All other injection data sets are solely based on events with
single bunch injections. The HER-ALL, LER-ALL and LER-VACS data sets consist
of a large number of events but are taken over a wide range of accelerator
conditions.

During Phase 1, SuperKEKB and BEAST II performed a dedicated injection
background study to measure background levels and time structures under
controlled conditions, and to assess the effect of variations in the injection
parameters. The study was conducted separately for HER and LER injections, and
has resulted in four data sets for each beam. First, a reference run with
nominal injection parameters was taken as a baseline for both rings; the data
sets for the reference injection runs are labeled HER-REF and LER-REF. For
each of the other given data sets, one injection parameter was changed from
nominal settings to the value yielding the minimal injection efficiency
222Injections with the highest particle loss rate still consistent with
radiation limits throughout the accelerator tunnel. in order to study its
effect on the time structure and on the background levels. For HER-PS and LER-
PS, the phase with which particles are injected was changed from
$258\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$305\text{\,}\mathrm{\SIUnitSymbolDegree}$ and from
$1\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$31\text{\,}\mathrm{\SIUnitSymbolDegree}$, respectively. For HER-VS1, HER-VS2
and LER-VS, we changed the vertical incidence angle from
$-0.385\text{\,}\mathrm{mrad}$ to $-0.465\text{\,}\mathrm{mrad}$ and
$-0.435\text{\,}\mathrm{mrad}$, and from $0.123\text{\,}\mathrm{mrad}$ to
$0.043\text{\,}\mathrm{mrad}$, respectively. And for LER-SA, we changed the
septum angle from $5.51\text{\,}\mathrm{mrad}$ to
$5.39\text{\,}\mathrm{mrad}$. All of the data sets from the injection study
consist of relatively few events but are each taken under very specific and
homogeneous accelerator conditions.

##  4 Time structure of injection backgrounds

In this section, the general time structure of injection backgrounds observed
with the CLAWS detector is examined. As discussed in Section 2, bunches which
recently received new particles due to an injection exhibit drastically
elevated particle loss rates. It is thus expected that higher background
levels will be observed during transits of these bunches, which recur with
every turn until the new particles have fully merged into the original bunch.
Since the positron damping ring, which is critical for low-emittance
injections of positrons into the main ring, was not yet operational during
Phase 1 data taking, injection backgrounds in the LER are expected to be
higher than those in the HER. The number of particles detected from non-
injection backgrounds is generally low, on the order of $3\times 10^{4}$
particles per bunch, corresponding to less than 1 particle per turn.

###  4.1 HER time structure

Due to significant event-by-event fluctuations, we study the time structure of
backgrounds by averaging the waveforms of all events in a given data set.

Figure 3 shows such an averaged waveform for the HER-ALL set for all three
channels stacked on top of each other (top) and their cumulatives separately
for each channel (bottom).

Figure 3: Averaged background time distribution for the HER-ALL data set for
all three channels stacked on top of each other (top) and their cumulatives
separately for each channel (bottom).

As discussed in Section 3.1, data taking during injections is triggered by an
external trigger signal which is sent in advance of the injection. The first
injection backgrounds are hence shifted with respect to the start of the
waveform by a trigger delay, $T_{trg}$. The exact value of $T_{trg}$ depends
on the injection settings used by the accelerator and thus varies slightly in
practice. For the HER, three different values of approximately
$107.44\text{\,}\mathrm{\SIUnitSymbolMicro s}$ are observed for the delay
which differ on the order of $10\text{\,}\mathrm{ns}$. 333We determine the
delay by calculating it from the revolution time, $T_{rev}$, and the time in
turn, $t_{turn}$, associated with the injection bunch (see Section 5):
$T_{trg}=n\times T_{rev}+t_{turn}$, where $n$ is obtained from the averaged
waveform. Uncertainties are given by the uncertainties on $t_{turn}$ since
$T_{rev}$ and $n$ are assumed to be exactly known

After the delay, we find several large peaks of significantly elevated
background rates. These peaks are caused by the repeated transit of a single
bunch which received new particles in a top-up injection. Thus, the distance
between the peaks corresponds to multiples of the beam revolution period
($T_{rev}=$10.0614\text{\,}\mathrm{\SIUnitSymbolMicro s}$$); this is further
highlighted in the inset in the upper right corner. Injection backgrounds are
generally declining over time until they return to the levels of regular beam
backgrounds and are mostly confined to the first
$500\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The most striking aspect of the
observed distribution is that they are not decreasing monotonically with every
turn. Instead, the time structure is largely determined by the propagation of
the newly injected particles along the beam lines. In that way, the decay
behavior is connected to properties of the accelerator and does not have an
obvious analytical form.

The background levels observed during transits of the injection bunch are
significantly higher than the signals caused by Touschek and beam-gas
scattering, which are distributed uniformly over the whole waveform. In the
cumulatives in Figure 3 (bottom), larger energy deposits appear as steps,
whereas regular backgrounds are reflected by steady increases with a moderate
slope. Injections primarily cause large instantaneous backgrounds which are
not necessarily a major contribution to the overall background rates. As
expected, FWD1 shows the largest overall background levels. Distributions for
FWD2 and FWD3, on the other hand, are smaller and almost identical.

Other HER data sets generally show a similar behavior. For data sets with few
events (see HER-REF, HER-PS, HER-VS1 and HER-VS2 in Table 1), we observe that
the time structure is less pronounced and subject to large turn-by-turn
fluctuations. This is because peaks in the time structure are driven by single
events with transits with large backgrounds. Absolute background levels and
the decay behavior will be discussed more quantitatively in Sections 5 and 6.

###  4.2 Time patterns

In general, we find that three distinct timing patterns occur in the sequence
of injection backgrounds: signals occurring every other turn, resulting in a
period of 2 turns ($\sim$$20\text{\,}\mathrm{\SIUnitSymbolMicro s}$), from
here on referred to as betatron pattern; groups of signals recurring with a
period of 9 to 11 turns ($\sim$$100\text{\,}\mathrm{\SIUnitSymbolMicro s}$),
from here on referred to as long betatron pattern; and groups of signals
recurring with a period of 40 (HER) or 50 (LER) turns, from here on referred
to as synchrotron pattern. These timing patterns are observed across all
injection data sets, with an intensity that varies from data set to data set.
The observation of these patterns shows that the time structure of injection
backgrounds is strongly affected by betatron and synchrotron oscillations
performed by the injected particles.

Time patterns of background signals due to betatron oscillations occur since
the trajectories of real beam particles differ from the nominal orbit defined
by the lattice of the accelerator. Deviations transverse to the primary
direction of motion result in stable horizontal and vertical betatron
oscillations around the nominal orbit. In addition, the use of the betatron
injection scheme by SuperKEKB, in which new particles are deliberately
injected with a horizontal offset (see Section 2), increases these
oscillations for newly injected particles. At the maxima of the oscillations,
the particles have an increased probability of colliding with machine
elements. If maxima in the amplitude occur in the proximity of the IP such
that scattered or secondary particles can reach the sensors, the oscillations
result in elevated background rates. Since the CLAWS sensors are mounted in
the horizontal plane, they are particularly sensitive to backgrounds generated
by the oscillations of newly injected particles.

Figure 4: Illustration of the horizontal betatron oscillations of the beam
particles relative to the position of the CLAWS FWD sensors.

Figure 4 illustrates the position of the beam particles which are undergoing
such oscillations with respect to the CLAWS FWD sensors.

A tracking simulation of beam orbits in the HER, which was performed using the
same machine parameters as applied during the reference injections (see HER-
REF in Table 1), predicts horizontal and vertical betatron tunes of 45.53 and
43.57 oscillations per turn, respectively Ohnishi:2016yyh . Depending on the
conditions of the machine, the values of the tunes slightly deviate from the
default values.

Since we observe the injection backgrounds from a fixed point and only once
per turn, the integer part of the tune is of no relevance for the following
discussion and will be disregarded. The fact that the betatron tune is
approximately half-integer, on the other hand, can explain the observed
$20\text{\,}\mathrm{\SIUnitSymbolMicro s}$ betatron pattern. If in the $n$th
turn the maximum is located at a position where the generated backgrounds
reach the sensors it will be shifted strongly away from this position in the
$(n+1)$th transit, and vice versa. A good example of this betatron pattern in
Figure 3 are the signals of the sixth
($\sim$$157\text{\,}\mathrm{\SIUnitSymbolMicro s}$), seventh
($\sim$$167\text{\,}\mathrm{\SIUnitSymbolMicro s}$) and eighth
($\sim$$177\text{\,}\mathrm{\SIUnitSymbolMicro s}$) transit. Here, two large
signals separated by $20\text{\,}\mathrm{\SIUnitSymbolMicro s}$ are observed,
which are interleaved by a transit without significant backgrounds.

On closer inspection, the tune differs slightly from the half-integer value by
$0.03$ oscillations per turn. The long betatron pattern is attributed to this
deviation from an half-integer value, which results in a slower modulation of
the betatron pattern discussed above. In Figure 3, this is visible in the
structure at half a millisecond with maxima at around
$450\text{\,}\mathrm{\SIUnitSymbolMicro s}$ and
$550\text{\,}\mathrm{\SIUnitSymbolMicro s}$ which are
$100\text{\,}\mathrm{\SIUnitSymbolMicro s}$, or ten turns, apart.

In addition to betatron oscillations, beam particles also undergo synchrotron
oscillations caused by deviations in the energy of the beam particles. The
difference in energy leads to an altered beam orbit period due to the
deflection in the dipole magnets. The particles which deviate in energy
therefore also undergo transverse oscillations, which affects the background
rates observed by the sensors.

Compared to betatron oscillations, synchrotron oscillations unfold on somewhat
longer time scales with periods of several tens of turns. For nominal
accelerator parameters, beam orbit simulations for the HER for Phase 1 predict
a period of 40.6 turns ($409\text{\,}\mathrm{\SIUnitSymbolMicro s}$) which in
practice again varies by a few turns depending on concrete parameters
Ohnishi:2016yyh ; Lewis:2018ayu . This is reflected in the time distribution
shown in Figure 3, where significant and extended peaks of backgrounds are
separated by around $400\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The periodic
patterns in the data are further explored in an autocorrelation analysis
discussed in Section 7.

###  4.3 LER time structure

Figure 5: Averaged background time distribution for the LER-ALL data set for
all three channels stacked on top of each other (top) and their cumulatives
separately for each channel (bottom).

Figure 5 shows the averaged waveform for the LER-ALL data set for all three
channels stacked on top of each other (top) and their cumulatives separately
for each channel (bottom). Similar to HER-ALL, several large peaks caused by
the repeated transit of the injection bunch are observed. The distances
between these signals correspond again to multiples of the $T_{rev}$,
particularly evident in the inset in the upper right corner.

The time structure for LER-ALL differs from the one for HER-ALL in a number of
respects. The signals are considerably larger in amplitude, and much more
concentrated in time. Small but clear signals (not well visible in Figure 5
due to the chosen vertical scale and the line width of the plot) show that the
$T_{trg}$ for LER injections is approximately the same as for the HER of
$107.4\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The first significant signals,
however, only appear $\sim$$180\text{\,}\mathrm{\SIUnitSymbolMicro s}$ after
the start of the recording, i.e. seven full turns after the first transit when
taking the time between the injection trigger and the first transit into
account. Instead of the smoother evolution of the background rates observed in
HER-ALL, the main particle losses occur in four distinct, non-adjacent
transits. No significant energy deposits are observed beyond
$500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ after the injection. The most
likely explanation for this behavior is the absence of the damping ring for
positrons, which leads to higher loss rates for the newly injected particles.
This also influences the observable time patterns originating from
oscillations of the beams.

For nominal accelerator parameters (see LER-REF in Table 1), beam orbit
simulations for the LER for Phase 1 predict horizontal and vertical betatron
tunes of 44.53 and 46.57 oscillation per turn, as well as a synchrotron
oscillation period of 52.3 turns ($526\text{\,}\mathrm{\SIUnitSymbolMicro s}$)
Ohnishi:2016yyh ; Lewis:2018ayu . As for the HER, these values vary with the
exact beam parameters. Note that the non-integer part of the betatron tunes is
identical to the prediction for the HER. We observe multiple instances of the
betatron pattern, most clearly seen in the inset where the distances between
signals is mostly $20\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The distance
between the two largest peaks corresponds to
$90\text{\,}\mathrm{\SIUnitSymbolMicro s}$ which is a consequence of the long
betatron pattern, which occurs at a slightly changed frequency compared to the
HER. The same timing features are also observed in other data sets. No
indications for synchrotron oscillations are observed, since the overall
duration of the elevated background levels is not sufficiently long for these
longer oscillations to emerge.

The absence of the damping ring for positrons leads to larger injection
backgrounds in the LER than in the HER, with observed instantaneous background
levels as much as five times higher. The radial dependence, in contrast, is
comparable to the one observed for HER injections: the signals in FWD1 are
larger than in FWD2 which are larger than in FWD3. The background from regular
circulating bunches is similar to the one observed in HER injection and non-
injection events; it is uniformly distributed and the overall height is
negligible compared to the signals from the injected bunch. The overall
background levels in the cumulatives are dominated by injection backgrounds,
which appear as steps of large energy deposits. The total number of observed
particles is an order of magnitude larger than in the HER and driven almost
entirely by injection backgrounds.

The averaged waveforms for the other LER injection data sets generally show a
background time structure with similar features and overall background levels.
For sets with a small number of events (LER-REF, LER-PS, LER-VS and LER-SA in
Table 1), large fluctuations in the structure are observed. LER-VACS was
recorded during vacuum scrubbing and using double bunch injections. Here, we
find that the majority of backgrounds comes from Touschek and Beam-gas
interactions of regular bunches and that there is no noticeable difference
between the behavior of the two injection bunches. For double bunch injections
into the LER, the separation of the two injection bunches has been measured by
CLAWS to be $96.8\text{\,}\mathrm{n}\mathrm{s}$ Lewis:2018ayu , with a trigger
delay relative to the first bunch measured at
$107.38\text{\,}\mathrm{\SIUnitSymbolMicro s}$.

##  5 Hit energy spectra

As a next step, the hit energies in the detectors are studied. First the
analysis methodology is introduced and then the hit energy distributions for
backgrounds recorded during injection and non-injection periods are discussed.

###  5.1 Methodology

Instead of averaging the waveforms as done for the study of the time structure
discussed in the previous section, here an event-by-event analysis of each
individual waveform of a data set is performed to identify signals from the
interaction of a single particle, or from the simultaneous interaction of
multiple particles that originate from the same particle bunch in the
accelerator. Such a signal is referred to as a hit. Since the emission and
detection of the scintillation photons is not instantaneous, the capturing of
the full energy to be associated to a hit requires to reconstruct clusters of
detected photons in time. Clusters are formed by identifying photon deposits
within an integration window of 76.8 ns from the first observed photon. The
amplitude of the hit is given by the integral over the full duration of the
cluster with additional corrections for noise and pedestal uncertainties,
while the time is determined from a constant fraction of 0.1 of the total
integral. The parameters were obtained from an optimisation taking stability,
precision and probability for the identification of fake hits into account
Gabriel2019  In the following, the distribution of the reconstructed energies
of hits is referred to as hit energy distribution.

To cleanly separate background contributions of the injection bunch from the
contributions of other processes, an additional time-based variable referred
to as the time in turn, $t_{turn}$, is introduced. It represents the time
within one turn of the accelerator, relative to an arbitrary starting time
given by the external trigger,

$t_{turn}=t\bmod T_{rev},$ (1)

where $t$ is the absolute time after the start of the waveform and $T_{rev}$
is the revolution time of the accelerator. Over multiple turns, all transits
of a particular particle bunch thus correspond to the same $t_{turn}$.

To enable quantitative comparisons, the distributions discussed in the
following are typically normalized to the number of events, to the length of
the waveforms in time and to the area of the sensors. Since the detectors are
orthogonal to the beam direction, the integral of the distributions represents
the particle flux through the respective CLAWS sensor.

###  5.2 Time in turn and time resolved hit energy spectra

Figure 6: The distribution of the time in turn versus the hit energy for the
HER-ALL data set for channel FWD1. The distribution is normalized to the
number of events, the length of the waveforms and the area of the sensors.

Figure 6 shows the distribution of hit energies for the time in turn versus
the hit energy for the HER-ALL data set. The $t_{turn}$ of the injection bunch
clearly stands out in this distribution as a narrow peak extending to high hit
energies. The rate of hits with small reconstructed energies below
$2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$ is significantly elevated compared
to the surrounding area which shows regular beam backgrounds. Hit energies
above $2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$ occur almost exclusively with
a $t_{turn}$ corresponding to the injection bunch. This shows that hits caused
by multiple simultaneous particles in the CLAWS sensors are essentially
confined to the injection bunch, while signals for the other bunches are
characterized by the sporadic detection of single charged particles and other
low-amplitude signals.

Figure 7: Particle rate mapped onto the time in turn for the HER-REF dataset.
The left panel shows the rate over the full turn, while the right panel shows
a $60\text{\,}\mathrm{n}\mathrm{s}$ window around the location of the
injection bunch. The time window used to assign energy deposits to the
injection bunch, given by $\pm 5\sigma$ around the maximum of the fitted
Gaussian, is also indicated.

For a more detailed study of the energy distribution of injection backgrounds
the averaged particle rate as a function of the $t_{turn}$ is used instead of
the distribution shown in Figure 6. For each data set, the $t_{turn}$
corresponding to the injection bunch is determined by fitting a Gaussian
distribution to the peak caused by the elevated particle rates due to the
injection background. This is illustrated in Figure 7, which shows the
detected particle rate mapped onto $t_{turn}$ for the HER-REF dataset. The
right panel shows the region around the injection bunch, with the Gaussian fit
used to extract the position and width. In the subsequent analyses, all hits
which lie within 5 $\sigma$ of the fitted mean are classified as injection
backgrounds. In this concrete case, the fitted $\sigma$ of
$2\text{\,}\mathrm{n}\mathrm{s}$ results in a time window of
$\pm$10\text{\,}\mathrm{n}\mathrm{s}$$ that is used to assign particles to the
injection bunch. For data sets that combine runs from the full time period
studied here, such as HER-ALL, two small changes of the injection trigger
offset occurred due to changes made by the machine group. This results in
three different times for the $t_{turn}$ of the injection bunch, with
variations of approximately $\pm$10\text{\,}\mathrm{n}\mathrm{s}$$. For these
data sets, each of the three peaks is fitted separately, and the combined time
window for all three is used to identify the injection bunch. In these cases,
the time window increases from a width of $20\text{\,}\mathrm{n}\mathrm{s}$ to
approximately $40\text{\,}\mathrm{n}\mathrm{s}$. This does not have a
noticeable influence of the results.

###  5.3 Hit energy spectra comparison

Figure 8: Distributions of hit energies for the given data sets for channel
FWD1. The distributions are normalized to the length of the waveforms, the
area of the sensors and the number of events. For the distributions HER-ALLib
and LER-ALLib a $t_{turn}$-based timing cut is applied to select only hits
caused by the injection bunch.

Figure 8 compares the hit energy spectra for the NI-ALL, HER-ALL and LER-ALL
data sets. It also shows the corresponding distributions of hits caused only
by the injection bunches selected by a cut on the $t_{turn}$, as described in
the previous section. We refer to these subsets as HER-ALLib and LER-ALLib.

The probability of observing Touschek and beam-gas backgrounds during the
transit of a regular bunch is estimated by calculating the number of hits per
bunch for the non-injection data set NI-ALL.444The number of hits per bunch is
calculated by multiplying the particle flux, i.e. the integral of the
distribution, by the area of the sensors and the time difference between two
consecutive bunches ($3\times T_{bucket}=$5.895\text{\,}\mathrm{ns}$$
Lewis:2018ayu .) Here it is found that on average only around one in ten
thousand bunches generates an observable signal, which leads to the conclusion
that non-injection backgrounds are caused almost exclusively by single
particles. The distribution hence reflects the functional form expected for a
single charged particle, which is also observed in calibration measurements
using cosmic muons. The characteristic peak of this distribution can therefore
be described by a convolution of a Landau and a Gaussian distribution.

For hit energies up to $2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$, all
distributions show a similar shape. Since the NI-ALL, HER-ALL and LER-ALL data
sets have been taken under vastly different accelerator conditions, the total
number of hits between these sets cannot be compared. The difference in the
number of hits between HER-ALL and HER-ALLib or LER-ALL and LER-ALLib, on the
other hand, shows that the majority of the hits in this energy range stem from
Touschek and Beam-gas interactions. Nevertheless, the injection bunch is only
one (or two in the case of double bunch injection events) of 1576 bunches, but
contributes around 10% of the hits.

The similarity in the shape of the distributions suggests that injection
backgrounds in this range are also caused by single charged particles and can
be described by convolutions of a Landau and a Gaussian distribution. Since
the sensors have been calibrated 555Performed after the run time of Phase 1.
using cosmic muons, the most probable value (MPV) of such a fit should
correspond to an energy of $1\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$. For a
given channel, the values of the MPVs are consistent across all data sets
shown in Figure 8 with mean values and corresponding sample standard
deviations of $0.75\pm 0.03\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$ (FWD1),
$0.93\pm 0.03\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$ (FWD2) and $1.10\pm
0.02\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$. The relatively larger deviation
from the calibration value for FWD1 is attributed to the fact that the sensor
for this channel was most exposed to radiation, and thus has increased
uncertainties in the calibration with cosmic muons after the Phase 1
measurements as discussed in Section 3.1. In addition, the reconstructed hit
energy for small signals in the MIP range is affected by uncertainties in the
pedestal determination as part of the photon signal reconstruction due to the
high dark count rate, which increases the probability to miss true photon
signals in the tails of the time distribution when the signal merges back into
the baseline. The FWD1 sensor was replaced during the Phase 1 run time, which
is an additional source of systematic uncertainties on the average detector
response.

At energies of approximately $2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$, the
distributions for the injection data sets and NI-ALL are beginning to diverge.
For amplitudes beyond this point, it is more likely that hits are caused by
injection backgrounds than by beam-gas or Touschek scattering. Above
$5\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$, the distributions for the
injection bunch alone account for more than 90% of the observed signals. The
distribution for NI-ALL shows a power law behavior with a steady decrease to
higher hit energies, reaching negligible rates beyond
$12\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$. The highest hit energies observed
are $33\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$. The distribution for HER-ALL
is following a similar power law, but its decline is less steep in particular
once particles from the injection bunch dominate beyond
$5\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$, and it reaches considerably higher
energies of up to $64\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$. LER-ALL shows a
small ankle at around $10\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$ for which
the decline slows down slightly. The spectrum is cutting off at around
$113\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$, which is due to the limited
dynamic range of the CLAWS system. Here two effects come into play, the limit
of the analog range of the amplifier chain of the system, and the saturation
of the SiPM due to the finite number of pixels of the photon sensor. The
former effect truncates signals that exceed an amplitude corresponding to
approximately 450 p.e. simultaneously. The reconstructed amplitude of such
signals then only grows with the length of the signal in time above the cut-
off, rather than with its full amplitude. The SiPM saturation itself results
in a non-linear behaviour of the detection of the scintillation photons,
reducing the sensor response for large signals. Both effects limit the maximum
hit energy that can be observed, shifting larger signals to lower
reconstructed hit energies. This results in an increased rate observed close
to the highest energy, visible as a bump at the end of the spectrum.

While the saturation effects are clearly noticeable in the hit energy
spectrum, they only affect a very small fraction of the observed hits. The
dynamic range of the CLAWS system approximately matches the largest signal
amplitudes observed, with only few events on a steeply falling spectrum
entering into the range where saturation effects become relevant. Saturation
thus has a negligible impact on more global variables discussed in the next
section. This is also true for LER-PS, the subset of LER-ALL with the largest
overall background levels, where saturation effects are most pronounced. As a
consequence, no saturation corrections are applied in the analysis of Phase 1
data.

The most striking result to emerge from the data is that the distributions of
HER-ALLib and LER-ALLib are merging with HER-ALL and LER-ALL, respectively, at
hit energies above 3 – 4 MIP. This shows that large instantaneous background
levels with multiple particles hitting the CLAWS sensors simultaneously are
caused exclusively by injection bunches.

Qualitatively, similar distributions are also observed for the channels
further away from the beam line, FWD2 and FWD3. The overall number of hits is
generally decreasing with the distance from the beams as expected from the
radial profile of the sensor positions (FWD1 > FWD2 > FWD3). Across all
injection data sets, significantly elevated instantaneous background levels
are observed during transits of the injection bunches. The highest injection
background levels observed during Phase 1 do not exceed the levels of regular
beam backgrounds by more than an order of magnitude. These results, together
with other BEAST II results, have contributed to the assessment that the
injection background is manageable, and the overall radiation levels are safe
for the installation of Belle II for the subsequent commissioning phases.

##  6 Overall injection background levels and decay behavior

Understanding the impact of injection backgrounds on the operation of the
Belle II detector requires detailed knowledge of the overall particle rates
and the duration of the period of elevated backgrounds which follow an
injection. In this section, a method for quantifying these deposited energies
and the decay behavior of injection backgrounds with respect to accelerator
conditions is discussed.

###  6.1 Methodology

Table 2: Key quantities summarizing injection background energy levels and decay behavior for all injection data sets for channel FWD1. Values are stated by the median of all the values in the data set; subscripts denote the difference from the median to the $16\text{\,}\mathrm{\char 37\relax}$ quantile, whereas superscripts indicate the difference from the median to the $84\text{\,}\mathrm{\char 37\relax}$ quantile. Data Set |  |  $E$ [MIP] |  |  $E_{ib}$ [MIP] |  |  $E_{ib}$/$E$ [%] |  $E_{ib}$($t<$$0.5\text{\,}\mathrm{ms}$)/$E_{ib}$ [%] |  $t(E_{ib}<$$2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$) [$\mathrm{\SIUnitSymbolMicro s}$]
---|---|---|---|---|---|---|---|---
HER-ALL |  | $27_{-19}^{+81}$ |  | $10_{-10}^{+94}$ |  | $55_{-53}^{+43}$ | $64_{-64}^{+27}$ | $292_{-292}^{+1469}$
LER-ALL |  | $123_{-82}^{+147}$ |  | $80_{-78}^{+91}$ |  | $86_{-77}^{+11}$ | $99_{-11}^{+1}$ | $359_{-201}^{+241}$
LER-VACS |  | $41_{-32}^{+50}$ |  | $2_{-2}^{+8}$ |  | $6_{-6}^{+70}$ | $100_{-41}^{+0}$ | $0_{-0}^{+369}$
HER-REF |  | $11_{-9}^{+7}$ |  | $9_{-8}^{+7}$ |  | $86_{-25}^{+14}$ | $81_{-33}^{+19}$ | $141_{-141}^{+322}$
HER-PS |  | $48_{-16}^{+18}$ |  | $32_{-16}^{+13}$ |  | $65_{-19}^{+8}$ | $76_{-26}^{+14}$ | $775_{-483}^{+493}$
HER-VS1 |  | $15_{-6}^{+11}$ |  | $3_{-3}^{+11}$ |  | $22_{-22}^{+36}$ | $78_{-58}^{+22}$ | $141_{-141}^{+0}$
HER-VS2 |  | $26_{-10}^{+12}$ |  | $7_{-6}^{+11}$ |  | $30_{-23}^{+24}$ | $78_{-78}^{+19}$ | $141_{-141}^{+0}$
LER-REF |  | $144_{-21}^{+15}$ |  | $138_{-20}^{+12}$ |  | $96_{-4}^{+2}$ | $100_{-1}^{+0}$ | $379_{-20}^{+50}$
LER-PS |  | $262_{-104}^{+23}$ |  | $242_{-92}^{+21}$ |  | $95_{-3}^{+2}$ | $99_{-1}^{+1}$ | $590_{-141}^{+91}$
LER-VS |  | $176_{-15}^{+20}$ |  | $162_{-14}^{+19}$ |  | $94_{-3}^{+2}$ | $99_{-1}^{+1}$ | $409_{-50}^{+201}$
LER-SA |  | $181_{-15}^{+13}$ |  | $176_{-13}^{+14}$ |  | $99_{-1}^{+1}$ | $97_{-2}^{+2}$ | $661_{-302}^{+20}$

As mentioned in the previous two sections, three main features of injection
backgrounds are: the time evolution does not follow a well defined functional
form; the background levels and the time structures fluctuate substantially
between individual events of a data set; and the background levels and the
time structures also fluctuate substantially for different accelerator
conditions represented by the different data sets. For Phase 1 of SuperKEKB
commissioning, injection backgrounds can therefore not be described
analytically.

Instead, the behavior of injection backgrounds is characterized based on the
following quantities which are sensitive to the total and injection background
levels and the time evolution of the injection background:

  * •

the total energy deposited in a single event including regular beam
backgrounds, $E$, given by the sum of all hit energies in the event;

  * •

the energy deposited only by the injection bunch, $E_{ib}$, given by the sum
of the energies of all hits selected by the cut on $t_{turn}$ (see Section
5.2);

  * •

their ratio $E_{ib}$/$E$;

  * •

the fraction of the energy deposited by the injection bunch within
$500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ after the first transit, 666This
range is chosen because the analysis in Section 4 shows that injection
backgrounds are often confined to the first
$500\text{\,}\mathrm{\SIUnitSymbolMicro s}$. $E_{ib}(t<$
$500\text{\,}\mathrm{\SIUnitSymbolMicro s}$)/$E_{ib}$;

  * •

and the time of the last transit in which the $E_{ib}$ per transit is larger
than $2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$, $t(E_{ib}>$ 2 MIP).777For the
analysis of Phase 1 data, $2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$ is chosen
as a limit because it is approximately the energy at which the hit energy
spectra of injection and non-injection backgrounds begin to diverge (see
Section 5.3).

These quantities are determined independently for each event.

No notable differences are observed in the behavior of the first and second
injection bunch for data sets which include events recorded during double
bunch injections (i.e. LER-ALL and LER-VACS, see Section 3.3). Contributions
from the second bunch are selected by a dedicated timing cut and subtracted
from the quantities in order to make all data sets comparable.

For the HER-ALL and LER-ALL data sets, the large number of events allows to
determine meaningful distributions of the quantities. For all other sets, the
quantities are stated by the median; the difference between the median and the
$16\text{\,}\mathrm{\char 37\relax}$ quantile (denoted in subscript); and the
difference between the median and the $84\text{\,}\mathrm{\char 37\relax}$
quantile (denoted in superscript). The values obtained for the quantities for
all injection data sets are summarized in Table 2. The detailed distributions
of the quantities for the HER-ALL and LER-ALL data sets are introduced in the
following, prior to a discussion of the findings for all data sets.

###  6.2 Total and relative deposited energies

As expected, the total deposited energy in LER-All is considerably larger than
for HER-ALL. Comparing $E_{ib}$ with $E$ for both data sets shows that the
majority of the observed backgrounds is caused by the injection bunch. The
fraction of the total observed energy originating from the injection bunch,
$E_{ib}$/$E$, is examined on an event-by-event basis in Figure 9.

Figure 9: Distributions of the ratios of the energy deposited only by the
injection bunch, $E_{ib}$, to the total deposited energy, $E$, for channel
FWD1 for HER and LER injection runs. Events without any detected backgrounds
are ignored ($0.8\text{\,}\mathrm{\char 37\relax}$ and
$1.6\text{\,}\mathrm{\char 37\relax}$ for HER-ALL and LER-ALL, respectively).

Events in which no background hits are observed are ignored
($0.8\text{\,}\mathrm{\char 37\relax}$ and $1.6\text{\,}\mathrm{\char
37\relax}$ for HER-ALL and LER-ALL, respectively). In a small fraction of the
events ($15.2\text{\,}\mathrm{\char 37\relax}$ and $6.5\text{\,}\mathrm{\char
37\relax}$ for HER-ALL and LER-ALL, respectively), the injection bunch did not
deposit any energy in the sensors, which leads to large peaks at zero. These
events can be explained by injections with low efficiency leading to severe
instantaneous particle loss before the bunch reaches the IP, or situations
where the particle loss takes place only at locations other than the IP. They
could also represent events which are falsely classified as injection events
in the event selection (see BG in Section 3.3).

There is a relatively uniform distribution of values for ratios between 0.2
and 0.8, with a strong rise and subsequent peaks around 0.95 for the LER, and
1 for the HER. These are caused by events with low regular beam backgrounds
and/or large injection backgrounds.

###  6.3 Injection background decay time

Figure 10: Distributions of the ratios of the energy deposited within the
first $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ after the first transit,
$E_{ib}$($t<$$0.5\text{\,}\mathrm{\SIUnitSymbolMicro s}$), to the full energy
deposited by the injection bunch, $E_{ib}$, for channel FWD1 for HER and LER
injection runs. Events without any injection backgrounds are disregarded
($15.9\text{\,}\mathrm{\char 37\relax}$ and $7.9\text{\,}\mathrm{\char
37\relax}$ for HER-ALL and LER-ALL, respectively).

The time it takes for the background to reach normal levels after an injection
is a critical parameter for the operation of the Belle II detector. The
absence of focusing elements and other accelerator elements that are present
for physics running significantly changes the timing patterns of the injection
background, as discussed in Section 4. Nevertheless, the evolution of the
background levels over many revolutions of the accelerator can provide
important insights. To make this accessible despite the large turn-to-turn
fluctuations in the background level, the fraction of the energy which is
deposited within the first $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ to the
total energy deposited by the injection bunch, $E_{ib}(t<$
$500\text{\,}\mathrm{\SIUnitSymbolMicro s}$), is studied.

Figure 10 shows this variable for the HER-ALL and LER-ALL data sets. Events
without any injection backgrounds ($15.9\text{\,}\mathrm{\char 37\relax}$ and
$7.9\text{\,}\mathrm{\char 37\relax}$ for HER-ALL and LER-ALL, respectively),
are ignored, but events in which the injection bunch did not cause any hit
within the first $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$
($18.6\text{\,}\mathrm{\char 37\relax}$ and $2.2\text{\,}\mathrm{\char
37\relax}$ for HER-ALL and LER-ALL, respectively) are included, which results
in the peak at 0. Neglecting the edges, the distribution for the HER-ALL set
shows a relatively uniform distribution with a skewness to larger ratios. This
clearly shows that injection backgrounds in the HER are only partially
confined to the first $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The
distribution for LER-ALL, on the other hand, is peaking at one and is
declining steeply to smaller ratios. Injection backgrounds in the LER are thus
decaying faster and are mostly confined to the fist 50 turns.

###  6.4 Time of the last hit

Figure 11: The distribution of the time of the last transit in which the
energy per transit was larger than $2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$
and the corresponding cumulative distribution function for channel FWD1 for
the HER-ALL data set. Distribution of the time of the last transit (not
cumulative) does not show events in which the injection bunch did not cause
any hit above the threshold ($42.3\text{\,}\mathrm{\char 37\relax}$).

Another parameter that provides information of the temporal extension of
elevated background levels following particle injection is the time of the
last transit in which the energy deposited by the injection bunch is above a
predefined limit. For the analysis of Phase 1 data,
$2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$ is chosen as a limit since this is
the energy at which the hit energy spectra of injection and non-injection
backgrounds begin to diverge (see Section 5.3). Thus, $t(E_{ib}<$
$2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$) indicates the time after which
injection backgrounds are comparable to regular beam backgrounds. In principle
it is possible that a hit, which is recorded during a transit and exceeds the
limit, is caused by regular beam backgrounds and not by injection backgrounds.
The hit energy spectra for non-injection backgrounds, however, suggest that
such a hit occurs in less than 1.1% of the events.

Figure 11 shows the distribution of the time of the last transit and the
corresponding cumulative distribution function for the HER-ALL data set. The
observations are generally in agreement with the findings from the fractions
of $E_{ib}(t<$ $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$). In
$42.3\text{\,}\mathrm{\char 37\relax}$ of the events, the injection bunch did
not cause any hit above the threshold (disregarded in the distribution, not in
the cumulative). The two largest peaks are located directly at the first and
fourth transit of the injected bunch. Apart from that, the distribution is
stretching across the full $2.4\text{\,}\mathrm{ms}$ with periodically
repeating patterns attributed to synchrotron oscillations of the beam
particles (see Section 4.2). This indicates that the timescale of injection
backgrounds in the HER is fluctuating strongly from injection to injection,
and that in a significant fraction of all injections a full decay requires at
least $2.4\text{\,}\mathrm{ms}$.

For the majority of the events of the LER data sets, the decay is taking place
entirely within $700\text{\,}\mathrm{\SIUnitSymbolMicro s}$ after the first
transit. In a small number of events, however, injection backgrounds are also
long lasting, showing influences of synchrotron oscillations.

###  6.5 Overall results and injection studies

Following the discussion of individual variables for selected high-statistics
data sets, the quantities obtained for all injection data sets are compared
(summarized in Table 2). Particular emphasis is placed on the sets which are
part of the dedicated injection studies. The values determined for the overall
background, $E$, range from $\mathrm{1}\mathrm{1}$ to
$262\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$, with LER data sets showing
significantly higher energies than HER sets. The corresponding spread
indicates large event-to-event fluctuations across all data sets, which can be
more than $100\text{\,}\mathrm{\char 37\relax}$ of the median total energy.
Comparing the $E_{ib}$ with $E$ suggests that in all data sets except LER-
VACS, a major part of the observed backgrounds is caused by the injection
bunch. By contrast, overall backgrounds in LER-VACS are driven by the
exceptionally large regular backgrounds caused by vacuum scrubbing.

For all injection study data sets, the beam currents and thus the regular beam
backgrounds are relatively low. For three of the four HER data sets of the
study, injection and regular beam background levels are similar and small. As
an exception, HER-PS shows significantly elevated levels of injection
backgrounds which surpass all other HER data sets. The ratios of $E_{ib}/E$
for all four HER sets are subject to fluctuations and vary between
$22\text{\,}\mathrm{\char 37\relax}$ and $86\text{\,}\mathrm{\char 37\relax}$
which reflects the different levels of injection backgrounds for the different
injection settings. By contrast, the four LER injection study sets clearly
show overall background levels comparable to the ones for LER-ALL, and are
dominated by injection backgrounds. This can be seen in the ratios of
$E_{ib}/E$, where the sets show values of $95\text{\,}\mathrm{\char 37\relax}$
and above.

Across all injection study data sets, the fraction of $E_{ib}$ which is
deposited within the first $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ is
relatively stable for a respective ring.

Compared to the reference injections, variations in the phase shift in both
rings (given by HER-PS and LER-PS) are found to have the largest impact on the
injection backgrounds. For HER-PS and LER-PS, the $E_{ib}$ are significantly
larger than in the other sets for the respective ring. A larger overall
background level also increases the probability for later hits which are above
the predefined $2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$ limit. As a
consequence, the $t(E_{ib}<$ $2\text{\,}\mathrm{M}\mathrm{I}\mathrm{P}$) for
these two sets with changed phase shift is also longer.

Finally, no significant increase in the energy levels or decay times is
observed for variations in the vertical steering (HER-VS1, HER-VS2 and LER-
VS). A possible explanation for this finding is that, due to their position in
the horizontal plane, the CLAWS sensors are more sensitive to horizontal than
to vertical deviations.

##  7 Time pattern analysis

As discussed in the previous sections, the time structure of injection
backgrounds is largely determined by the propagation of the newly injected
particles in the accelerator lattice, which is affected by several different
recurring time patterns connected to properties of the accelerator. In this
section, a comprehensive study of the periods of the different time patterns
is performed. It is based on an analysis of the autocorrelation of the CLAWS
measurements.

###  7.1 Analysis methodology

The autocorrelation analysis is based on a discrete autocorelation using the
averaged time series of backgrounds, as shown in Figure 3, as input. Here, the
magnitude of the autocorrelation for a given time distance $d_{k}$ is given by

$R_{AA}(d_{k})=\sum_{i}(A_{i}\times A_{i-k}),$ (2)

with the time distance given by the size of one time bin of
$0.8\text{\,}\mathrm{ns}$ multiplied by the shift in the correlation $k$,

$d_{k}=$0.8\text{\,}\mathrm{ns}$\times k,$ (3)

and the sum running over the full length of the waveform.

The result of the autocorrelation is a spectrum of distances in time between
signals with their corresponding magnitudes. In this spectrum, the distances
which are particularly common, or are separating large signals, appear as
peaks. These peaks are connected to regular patterns in the time structure of
background signals, making these patterns easily accessible for further study.
This enables the identification of the underlying accelerator properties that
drive the observed patterns.

###  7.2 Autocorrelation results

Figure 12: Autocorrelation of the averaged background time series for the HER-
ALL data set for channel FWD1. Colored Gaussian fits and corresponding labels
indicate responses of specific timing patterns connected to properties of the
accelerator. For long time differences, even and odd multiples of the
revolution time $T_{rev}$ are indicated separately, since the pronounced
betatron oscillations, which lead to large differences in amplitude between
subsequent revolutions, affect the observable time pattern. See text for
details.

Since the background signals are significantly more extended in time in the
HER than in the LER, the HER data provide better access to extended timing
patterns. The following discussion thus concentrates in this data set,
mentioning LER specific aspects where relevant. Figure 12 shows the result of
the autocorrelation applied to the HER-ALL data set. On a semi-logarithmic
scale in time, the spectrum ranges from time patterns which take place on the
time scale of several nanoseconds up to patterns that extend over
milliseconds. Very short time scales are dominated by large values originating
from neighboring bunches as well as from the temporal extension of individual
reconstructed signals over a few nanoseconds. This results in a broad peak
extending to around $10\text{\,}\mathrm{ns}$, which cannot be resolved for
further analysis and is thus not shown in the figure. The first visible
structure originates from a single turn of the accelerator at approximately
$10\text{\,}\mathrm{\SIUnitSymbolMicro s}$.

For events with double bunch injections in the LER, where two bunches
simultaneously receive new particles, an additional peak emerges for a time
distances of $96.7\pm 0.2\text{\,}\mathrm{ns}$, which is in agreement with the
separation in time for the two injection bunches in that mode of operation of
$96.3\text{\,}\mathrm{ns}$. This structure is not visible in Figure 12 since
it shows HER data where only single bunch injection was used.

In the following, the features of the autocorrelation of the HER-ALL data set
is discussed in more detail, with additional remarks on other datasets where
relevant differences appear. Quantitative results for identified maxima in the
autocorrelation and the corresponding uncertainties are given by the mean of a
fit with a Gaussian distribution.888A two stage maximum likelihood fit in the
range of $\pm 2\text{\,}\sigma$ of the mean is used; uncertainties on the
parameters are adopted from the fit.

#### Revolution time

The first peak in Figure 12 is due to the beam revolution period, $T_{rev}$
($10\,061.4\text{\,}\mathrm{ns}$). Here, we obtain a mean value of $10\,061\pm
3\text{\,}\mathrm{ns}$, which is, again, in good agreement with the prediction
by the machine. Results for all other data sets generally show a similar level
of agreement. The rest of the spectrum is composed of multiples of $T_{rev}$
and, in that way, by the propagation of the injected bunches along the beam
lines. These timing patterns affect the variation of backgrounds between
consecutive transits of the injected bunches.

#### Betatron oscillations

For backgrounds recurring with every transit of the injected bunch, the
distance corresponding to a full turn in the ring should be the most abundant
and therefore the dominant signal in the autocorrelation spectrum. Across all
data sets, however, this is not the case. Instead, the largest peak is located
at a distance of two consecutive turns (i.e. $2\times T_{rev}$). As discussed
in Section 4.2, this is attributed to large amplitude betatron oscillations of
the newly injected particles for which the betatron tune has an approximately
half integer value. Qualitatively, this behavior appears to be more pronounced
for injections into the LER than into the HER, which is consistent with the
observed time structure (see Figures 3 and 5). This behavior gets further
amplified for injections which use a non-optimal phase shift during injections
given by the HER-PS and LER-PS sets.

For several data sets, the peaks corresponding to distances from nine to
eleven turns are clearly surpassing all but the peak for a distances of two
consecutive turns. This suggests that the non-integer part of the vertical
betatron tune (see Section 4.2) is deviating from a strict half-integer value
by around $0.05$ oscillations per turn, roughly in agreement with the
deviation by $0.03$ from the half-integer value predicted by simulations. This
behavior is generally more pronounced in LER injection data sets than in HER
sets, in line with the overall larger betatron oscillation signals in the LER.

#### Synchrotron oscillations

From the timing patterns accessible via the autocorrelation analysis, patterns
related to synchrotron oscillations of the beam particles are the ones
occurring on the longest time scales. In the majority of the events recorded
by CLAWS, the level of injection backgrounds decays to the level of regular
beam backgrounds after $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ (around 50
turns), as discussed in Section 6. As such, only a small fraction of the
events exhibit synchrotron oscillations beyond more than one period. It should
be noted that even if these are only few events, they are the ones which are
ultimately determining the length of the gating windows for the rejection of
injection backgrounds. Due to the long periods compared to typical background
decay times, in the presented analysis synchrotron oscillations can only be
observed for data sets with large statistics (i.e. HER-ALL).

Since the pronounced betatron oscillations affect all higher multiples of the
beam revolution period in the autocorrelation analysis, two separate
distributions are formed for the study of very long oscillation pattern.
Beginning with the 20th multiple of the beam revolution period, the positions
of all peaks are determined by a Gaussian fit as mentioned above. The
resulting positions of the local maxima are then split into even and odd
multiples of $T_{rev}$ as indicated by small blue and red markers in Figure
12. Here, the strong amplification of signals with a period of 2 $T_{rev}$,
which manifests as the maximum of the autocorrelation distribution at
approximately $20\text{\,}\mathrm{\SIUnitSymbolMicro s}$, results in stronger
signals for even multiples than for odd multiples over most of the time range
of the distribution.

The even multiples reveal a structure of several normal-distributed peaks.
These peaks are again fitted with Gaussians for which the determined mean
values are given in the figure.999A maximum likelihood fit with an arbitrary
range us used, the uncertainties on the mean are taken from the fit. The value
of the first mean, $372\pm 1\text{\,}\mathrm{\SIUnitSymbolMicro s}$,
represents a concrete measurement of the period of the synchrotron
oscillations of particles in the HER; the other mean values are multiples of
the synchrotron oscillation period. This result is in approximate agreement
with the simulation prediction of an oscillation period of
$409\text{\,}\mathrm{\SIUnitSymbolMicro s}$ (40.6 turns, see Section 4.2).
This finding, however, must be interpreted with some caution since the studied
data set covers a wide range of accelerator conditions.

Injection backgrounds in the LER show particle loss rates which are
considerably higher early on and are more localized in time, with very little
activity beyond $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ after the
injection. As a result, long lasting effects like synchrotron oscillations are
less pronounced in the data sets. A decisive measurement of the synchrotron
oscillation period with the same methodology as used for the LER-ALL data set
as described above is not possible, since most events show at most one
synchroton-oscillation related signal enhancement of the injection background.
A measurement of this parameter for the LER is thus not reported here.

##  8 Summary and Outlook

The CLAWS detector systems has performed extensive studies of beam backgrounds
during the first phase of the commissioning of SuperKEKB, referred to as Phase
1. The sub-nanosecond time resolution of the sensors and the low threshold and
good energy resolution which enables the detection of single particles allow
time-resolved bunch-by-bunch measurements of beam-induced and injection
backgrounds.

The time structure observed during injections shows clear peaks of
significantly elevated background rates during the recurring transits of
injection bunches, as well as significantly lower, uniformly distributed beam-
induced backgrounds. The comparison of the hit energy distributions of regular
and injection backgrounds demonstrates that the signal of regular backgrounds
originate from the detection of single charged particles, while the large
signals of the injection background are caused by the simultaneous detection
of many particles. Nevertheless, the hit energy distributions also show that
instantaneous background levels observed during injections in Phase 1 did not
exceed regular beam backgrounds by more than one order of magnitude.

Injections into the LER generally result in significantly higher background
levels than those into the HER. This is due to the absence of the positron
damping ring, which was only taken into operation after Phase 1. For both
rings, the majority of the injection backgrounds are normally observed within
the first $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ after the injection. The
individual decay times back to the regular background levels are fluctuating
strongly from injection to injection, and also depend on the exact injection
parameters used, in particular on the phase shift.

The different timing patterns of the injection backgrounds are studied with an
autocorrelation analysis. The results show effects of betatron and synchrotron
oscillations of the particles in the accelerator rings, which influence the
background rates over extended time periods.

Together, the presented studies give insights into the beam backgrounds of
SuperKEKB, in particular the background originating from the continuous top-up
injection required to achieve high luminosities. The time structure and the
measurement of the duration of the elevated background levels provide
important information for the further operation of the Belle II experiment.

The large fluctuations observed in injection background behaviour and the
significant changes in the accelerator and in its operational parameters for
physics operation underline the importance of studies and monitoring of
injection and other backgrounds also in later phases of SuperKEKB. Based on
the successful use of the CLAWS system in Phase 1 reported here, CLAWS was
also used in Phase 2 in a different layout, with two ladders with eight
channels each as part of the modified inner detector of Belle II. This system
performed studies on injection backgrounds during Phase 2 with even longer
continuous monitoring as the one reported here. The results will be reported
in an upcoming publication. For the physics runs in Phase 3, a total of 32
further developed CLAWS sensors are installed on the cryostat of the final
focusing system (QCS). The injection background-induced particle rates in this
location are typically too low for a detailed study. Instead, the CLAWS
sensors are now used to monitor large background spikes due to unstable beam
conditions, and provide a fast beam abort signal in case dangerous background
levels are detected. Further uses for CLAWS sensors as background rate
monitors in collimator locations around the SuperKEKB ring are being
investigated at the time of writing.

###### Acknowledgements.

The authors thank Yong Liu, formerly University Mainz, for the scintillator
material used for the fabrication of the scintillator tiles. The work was
partially supported by the DFG Excellence Cluster “Origin and Structure of the
Universe” of Germany and by the European Union’s Horizon 2020 Research and
Innovation programme under Grant Agreement no. 654168.

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