maintained through hundreds of reflections, and the spatial pattern of the
Cherenkov ring can be recognized for PID purposes. An excellent $\pi/K$
separation can be achieved up to $p=4~{}{\mathrm{\ Ge\kern-1.00006ptV}/c}$. It
is worth noting that with BaBar DIRC, the time resolution of a single photon
is approximately $1$ ns, which is mainly used to suppress uncorrelated
background through the setting of a proper time window.

With improved timing resolution, better PID capability is expected for new
generation DIRC detectors, such as those proposed in the future PANDA
experiment [420] at FAIR or EID at EIC [421]. The 3-D measurements of
$(x,y,t)$ are achieved by a multianode PMT with high-precision timing
performance, namely, a microchannel plate photomultiplier tube (MCP-PMT). The
volume of such a detector is rather compact, with typical thickness $\leq 5$
cm (excluding the optical focusing part). The radiation resistance and
mechanical robustness are good, as well as the rate capacity, all of which
make it a suitable detector in high luminosity experiments. The excellent
timing capabilities of the new DIRC detectors has also led to the direct
application of the DIRC technology to high time resolution and high rate TOF
measurement. For example, assuming that the time resolution of a single
photoelectron is $\sim 100$ ps, then for $N_{PE}=10$, the total timing
resolution is $\sim 30$ ps, where $N_{PE}$ is the number of photoelectrons.
Such a DIRC-like TOF detector was first proposed for the superB project [141]
and recently adopted for the LHCb upgrade, namely, the Time Of internally
Reflected CHerenkov light (TORCH) detector [422]. For TORCH, a single photon
timing error of $\leq 70$ ps and a light yield of $N_{PE}\sim 25$ are
predicted, which is expected to achieve a high precision with a time
resolution of $\leq 15$ ps.

According to the above discussion, a DIRC-like time-of-flight (DTOF) detector
is supposed to meet the PID requirement for the endcap region of the STCF
owing to the extended distance between the interaction point and the endcap
PID detectors. From physics requirements, a $\pi/K$ misidentification rate
less than 2% with corresponding identification efficiency larger than 97% at
$p=2$ GeV/c is needed. This is equivalent to a $4\sigma$ deviation of two
probability distributions. As a consequence, with a flight length of 1.5 m for
the hadrons, a total time resolution of 35 ps is needed for the TOF
measurements. However, the time measurement with DTOF benefits from both the
time of flight of a hadron and the time of propagation (TOP) of a photon,
which has the potential to provide a 40 ps time resolution, for the DTOF at
the STCF. In the following, the conceptual design of the DTOF detector at the
STCF and its geometry optimization are presented.

####  3.7.2 DTOF Conceptual Design

The proposed DTOF detector consists of two identical endcap discs positioned
at $\sim\pm 1400$ mm away from the collision point along the beam direction.
Each disc is made up of several quadrantal sectors, as shown in Fig. 3.52,
with an inner radius of $\sim 560$ mm and an outer radius of $\sim 1050$ mm,
covering in polar angles of $\sim 22^{\circ}-36^{\circ}$. The sensitive
regions of the the DTOF and RICH detectors overlap, leaving no dead areas
between the barrel and the endcap. In each sector, a synthetic fused silica
plate is used as a radiator to generate Cherenkov photons. The supporting
structure between sectors occupies $\sim 15~{}mm$ of space, approximately
$1.25\%$ of the total sensitive area. Considering the effect of the magnetic
field on the photon sensors, an array of multianode MCP-PMTs are optically
coupled to the radiator along the outer side. Fig. 3.52 also shows an example
of the light path from a photon directly hitting the MCP-PMT. Note that there
are also alternative paths for photons reflecting off the lateral-side mirror.

Figure 3.52: An example of the radiator sector for the DTOF detector and the
light path of the radiator.

##### DTOF Time Resolution

Time resolution is a key indicator of the performance of a DTOF detector. It
is necessary to analyze the factors that affect the timing uncertainty, and
the relative importance of the various factors must be investigated to
optimize the time performance. The main sources contributing to the timing
uncertainty of the DTOF detector can be expressed by

$\sigma^{2}_{\rm tot}\approx\sigma^{2}_{\rm trk}+\sigma^{2}_{\rm
T_{0}}+(\frac{\sigma_{\rm elec}}{\sqrt{N_{PE}}})^{2}+(\frac{\sigma_{\rm
TTS}}{\sqrt{N_{PE}}})^{2}+(\frac{\sigma_{\rm det}}{\sqrt{N_{PE}}})^{2}$ (3.10)

where $\sigma_{\rm trk}$ is the uncertainty caused by track reconstruction,
which is $\sim 10$ ps; $\sigma_{\rm T_{0}}$ is the event reference time (i.e.
the time of $e^{+}e^{-}$ collision, T0) uncertainty, which is $\sim 40$ ps (it
is closely related to the bunch length, which is $\sim 12mm$ in the current
design, as depicted in the STCF accelerator conceptual design report);
$\sigma_{\rm elec}$ is the electronic timing accuracy; $\sigma_{\rm TTS}$ is
the single-photon transit time spread (TTS) of the MCP-PMT; and $\sigma_{\rm
det}$ is the time reconstruction uncertainty of the DTOF detector.

The contribution from $\sigma_{\rm elec}$, $\sigma_{\rm TTS}$ and $\sigma_{\rm
det}$ decreases with increasing $N_{PE}$, and the timing uncertainty of these
three effects can be estimated from the single photoelectron (SPE) time
resolution of the photon sensor and the electronics, called $\sigma_{SPE}$.
The calculation results for the SPE parameter are shown in Fig. 3.53 as a
function of the photon transmission distance $D$. The timing jitter of the
photon sensor plays a major role when $D$ is relatively short ($<1$ m),
whereas the dispersion effect gradually becomes the dominant factor when the
distance from the incident point to the photon sensor $D$ is large ($>1.5$ m).
A proper optical design can be used; then, the dispersion effect can be
corrected by position information if a very precise timing is maintained. For
the DTOF detector, a typical $D$ value is approximately $0.5-1$ m; hence, the
timing uncertainty due to the dispersion effect is smaller than the timing
jitter of the photon sensor. This means that a compact design for the DTOF
with no focusing component is desirable. In addition, the spatial resolution,
including the thickness of fused silica and the pixel size of the photon
sensor, has little effect on the time uncertainty of the DTOF. Therefore, a
photon sensor with a large pixel size can be used to reduce the number of
electronic readout channels. Notably, $N_{PE}$ may also increase with the
thickness of the radiator. However, this can cause an increase in the material
budget, although it has little influence on the SPE time resolution.

From the simulation, the average number of photons detected by the MCP-PMT
arrays is $N_{PE}\approx 17$. By applying a TOP-position calibration, where
the average track length collected by each sensor pixel and the average
velocity of photons are used to calculate the TOP (no dispersion effects are
accounted for), a timing resolution of $\sim 20$ ps or better for the latter
three effects expressed in Eq. 3.10 can be obtained. To further study the time
resolution of the DTOF detector, a reconstruction algorithm is required, which
is presented in Sec. 3.7.3.

Figure 3.53: Main DTOF timing error factors and their dependences on the
distance from the incident point of the particle (kaon at $p=1$ GeV/c) to the
photon detector

##### DTOF Detector Layout

Based on the results from both the simulation study and the experimental test,
we developed the conceptual design of the DTOF at the STCF, as shown in Fig.
3.54. The detailed structure inside a sector is also depicted in Fig. 3.54.
The planar synthetic fused silica radiator is fan shaped and can be viewed as
a composite structure of 3 trapezoidal units, each $\sim 295$ mm (inner side)
$/$ $\sim 533$ mm (outer side) wide, $\sim 470$ mm high and $15$ mm thick. An
array of $3\times\sim 14-16$ multi-anode MCP-PMTs are directly coupled to the
radiator along the outer side. The whole sector is enclosed in a light-tight
black box made of $5$ mm thick carbon fiber, occupying $\sim 200$ mm space
along the beam (Z) direction.

Figure 3.54: The conceptual design of the DTOF detector.

####  3.7.3 DTOF Performance Simulation

##### Reconstruction Algorithm

Geant4 simulations are performed to predict the performance of the DTOF
detector. A $20$ mm thick aluminum plate is added at a distance of $100$ mm in
front of the DTOF detector to simulate the material budget of the MDC endcap.
When tracking photon propagation, the inner and outer sides of the DTOF
radiator are set to be absorptive, while the two lateral sides are set to be
reflective (reflection factor $\sim 92\%$, typical for reflective coatings).
The surface roughness of the radiator is simulated by randomizing the normal
direction of the facet by $\sigma=0.1^{\circ}$ (corresponding to a
conservative average reflection factor of $\sim 97\%$). The wavelength
dependence of the refractive index, absorption length for the radiator, and
quantum efficiency of MCP-PMTs are carefully taken into account. Pion and kaon
particles are emitted from the IP at different momenta and directions.
Different polar angles, azimuth angles and particle momenta are tested. A
typical Cherenkov photon hit pattern of pions at $p=1$ GeV/c,
$\theta=23.66^{\circ}$ and $\phi=15^{\circ}$ is displayed in Fig. 3.55. A
clear correlation between the time of propagation (TOP) and the hit position
is demonstrated by the simulation. There are two bands in the figure: the
lower left band represents direct photons without reflection, and the upper
right band represents indirect photons with one reflection off the lateral
side. Obviously, good separation between the two bands is obtained, except
from a few sensors close to the edge.

Figure 3.55: The simulated TOP vs. hit position pattern of the DTOF detector.

The DTOF reconstruction is performed in the coordinates shown in Fig. 3.56 for
one DTOF quadrant. According to the Cherenkov angle relation

$\cos(\bar{\theta_{c}})=\frac{1}{n_{p}\beta}=\frac{{\vec{v_{t}}}\cdot{\vec{v_{p}}}}{|\vec{v_{t}}|\cdot|\vec{v_{p}}|},$
(3.11)

where $\vec{v_{t}}=(a,b,c)$ is the incident particle velocity vector when the
particle hits the radiator, $\vec{v_{p}}$ is the velocity vector of the
emitted Cherenkov photons, $n_{p}$ is the refractive index of the radiator,
and $\beta$ is the reduced speed of the particle. The directional components
of $\vec{v_{p}}$ can be expressed as $(\Delta{X},\Delta{Y},\Delta{Z})$,
representing the 3D spatial difference between the photon sensor pixel and the
incident position of the particle on the radiator surface, as depicted in Fig.
3.56 (right). Although the 2D (X and Y) difference can be readily obtained,
$\Delta{Z}$ must be deduced with a certain particle species hypothesis. If
$V=\cos(\bar{\theta_{c}})$ is known, the equation for $\Delta{Z}$ can be
expressed as

$(c^{2}-V^{2})\Delta{Z}^{2}+2c(a\Delta{X}+b\Delta{Y})\Delta{Z}+(a\Delta{X}+b\Delta{Y})^{2}-V^{2}(\Delta{X}^{2}+\Delta{Y}^{2})=0.$
(3.12)

By solving this equation, we find
$\Delta{Z}=\frac{-B\pm\sqrt{B^{2}-4AC}}{2A}$, with $A=c^{2}-V^{2}$,
$B=2c(a\Delta{X}+b\Delta{Y})$ and
$C=(a\Delta{X}+b\Delta{Y})^{2}-V^{2}(\Delta{X}^{2}+\Delta{Y}^{2})$. To obtain
a real solution, $\Delta=B^{2}-4AC\geq 0$ is required. Furthermore, after the
physical cuts $V>0$ (Cherenkov photons are forwardly emitted) and
$\frac{\Delta{X}^{2}+\Delta{Y}^{2}}{\Delta{X}^{2}+\Delta{Y}^{2}+\Delta{Z}^{2}}\geq\frac{1}{n_{p}^{2}}$
(internal total reflection is ensured) are applied, the minimal solution of
Eq. 3.12, ($\Delta{Z}=\min{|\Delta{Z}_{1}|,|\Delta{Z}_{2}|}$) is taken as the
optimum.

Figure 3.56: The coordinate system used in DTOF reconstruction (left) and the
direction of Cherenkov photons (deep blue line).

The timing error of such an approach is estimated by adding up the possible
factors, such as the dispersion effect, the finite photon sensor size and the
propagation length of photons inside the radiator. The expected timing
uncertainty for a pion of $p\sim 1-2$ GeV/c crossing the radiator
perpendicularly, with $H=0.5$ m (in the coordinate system defined in Fig.
3.56), is shown in Fig. 3.57 for sensors at different positions. The pitch of
the photon sensor is $5.5$ mm. No multiple Coulomb scattering (MCS) effects
are accounted for. It is obvious that the intrinsic detector timing
uncertainty is no more than $40$ ps with this DTOF structure. Furthermore, we
find that the reconstructed length of propagation (LOP) of light inside the
radiator agrees with the MC truth to a precision of $\sim 3.3$ mm, as also
shown in Fig. 3.57. The reconstruction algorithm works well for most photon
sensors independent of the incident position of the particles, except for a
few sensors near the lateral side.

Figure 3.57: The expected timing error and propagation length uncertainty of
Cherenkov photons in a DTOF quadrant.

By applying the formula below

$TOF=T-TOP-
T_{0}=T-\frac{LOP}{v_{g}}-T_{0}==T-\frac{LOP\times\bar{n_{g}}}{c}-T_{0},$
(3.13)

where $v_{g}$ is the group velocity of Cherenkov light in the radiator, the
TOF information is obtained. Figure 3.58 shows the time resolution of the DTOF
detector for a SPE and the average of all photons without taking into account
the timing jitter of the MCP-PMTs and electronics. For an SPE, the intrinsic
time resolution of the DTOF is $\sim 41$ ps. Averaging the timing information
over $\sim$ 18 detected photons, the timing jitter shrinks to $\sim$ 10 ps. It
is also noted that in the TOF distribution plot, a low (but visible) long tail
appears on both sides of the main peak. The tail is mainly caused by secondary
particles along the primary pion, mostly $\delta$-electrons.

Figure 3.58: The TOF resolution of the DTOF detector for a single
photoelectron and the average of all photons.

The TOF information is deduced and compared to the expectation of each
particle hypothesis. Figure 3.59 shows the reconstructed intrinsic TOF
distributions of both pions and kaons at $2~{}$GeV/c. We can easily find if
the particle hypothesis is correct the reconstructed TOF peak is at the
correct position, with a resolution of $\sim$ 10 ps. However, if the
hypothesis is not correct, the reconstructed TOF peak is shifted with respect
to the expectation. The shift makes the separation between the pion and kaon
TOF peaks even larger, which may benefit the PID power. When convoluting all
contributing factors, the overall reconstructed TOF time resolution is $45\sim
50$ ps, as shown in Fig. 3.59. Directly comparing the TOF information shows
that a $3.0\sigma$ separation power for $\pi/K$ at $2$ GeV/c is achieved.
Furthermore, the separation power becomes stronger if we compare the
reconstructed TOFs of various hypotheses for the same set of particles, mainly
due to the beneficial time shift under the incorrect hypothesis (as in Fig.
3.59).

Figure 3.59: The TOF PID capabilities of the DTOF detector for $\pi/K$
separation at $2$ GeV/c, without (left) and with (right) contributions from
other timing uncertainties.

##### Expected Performance

To evaluate the PID capabilities of the DTOF detector, we apply a likelihood
method. The likelihood function is constructed by

$\mathcal{L}_{h}=\Pi^{i}_{i=1}f_{h}(TOF^{h}_{i}),~{}~{}~{}~{}~{}\Delta\mathcal{L}=\mathcal{L}_{\pi}-\mathcal{L}_{K},$
(3.14)

where $h$ denotes hadron species (in our case, $\pi$ and $K$) and $i$ accounts
for each detected photon. The probability density function $f_{h}$ is taken as
a Gaussian fit to the expected TOF distribution (as in Fig. 3.59 (right)),
plus a constant background of 0.05. Fig. 3.60 (left) shows an example of the
reconstructed $\Delta\mathcal{L}$ for $2$ GeV/c $\pi$ and $K$, where a $\pi/K$
separation power better than $4\sigma$ is demonstrated. Fig. 3.60 (right)
shows the corresponding identification efficiency under this condition. When a
kaon misidentification efficiency of $<2\%$ is required, a pion identification
efficiency of $>98\%$ can be achieved, fulfilling the STCF PID requirement.
Furthermore, with improved PID algorithm that includes also the spatial hit
pattern information, the PID performance of DTOF can extend to even higher
momentum range. Fig. 3.61 shows the likelihood PID capabilities of the DTOF
detector for $\pi/K$ separation in different directions and different momenta.
Despite the very different particle directions and momenta, a separation power
of $\sim 4\sigma$ or better over the full DTOF sensitive area is achieved.

Figure 3.60: The likelihood PID capabilities of the DTOF detector for $\pi/K$
separation at $2$ GeV/c emitted at different angles. Figure 3.61: The
likelihood PID capabilities of the DTOF detector for $\pi/K$ separation in
different directions and at different momenta.

#####  $T_{0}$ Determination

The DTOF detector’s excellent timing performance can help determine the
$e^{+}e^{-}$ collision time ($T_{0}$). According to Eq. 3.13, the TOF of
incident particles and the TOP of Cherenkov photons can be obtained from
simulations or calculations with different particles and different $T_{0}$
hypotheses, provided that the track information is known. To evaluate
different hypotheses, we define a likelihood function,

$\mathcal{L}_{h_{1},h_{2}}=\Pi^{i}_{i=0}f_{h_{1},h_{2}}(ch_{i},T_{i}),$ (3.15)

where $h_{1}$ denotes hadron species (in our case, $\pi$ and $K$) and $h_{2}$
denotes different $T_{0}$ (the bunches collide every $4ns$, i.e., $T_{0}=0$,
$\pm 4ns$, $\pm 8ns$,…). The probability density function
$f_{h_{1},h_{2}}(ch_{i},T_{i})$ is the photon arrival-time distribution of
different channels. The ${L}_{h_{1},h_{2}}$ with different particle and
$T_{0}$ hypotheses is compared, and the $T_{0}$ candidate with the maximum
likelihood is determined. Fig. 3.62 shows the $T_{0}$ determination efficiency
using the DTOF detector for $\pi$ samples in different directions and at
different momenta. Despite the very different particle directions or momenta,
$T_{0}$ can be determined correctly with an efficiency $>99\%$. Note that if
the particle velocity is below the Cherenkov threshold, the corresponding
$T_{0}$ cannot be correctly pinpointed. With decreasing momentum, the time
resolution of the DTOF detector worsens, resulting in a decrease in the
$T_{0}$ determination efficiency.

Figure 3.62: The rate at which $T_{0}$ is determined correctly using the DTOF
detector for $\pi$ samples in different directions and at different momenta.

####  3.7.4 DTOF Structure Optimization

Different geometric parameters of the DTOF detector are tested to study their
effects on PID. The $\pi$/K separation powers of different geometry
configurations are compared with the reconstruction algorithm and likelihood
method described above. The geometry configurations studied are listed in
Table 3.15. We study the effects of three main factors: radiator shape/size,
radiator thickness and the setting of mirrors.

Table 3.15: Description of the different DTOF geometry configurations, where A stands for absorber and R for reflective mirror. Configuration/Geometry ID |  0 |  1 |  2 |  3 |  4 |  5 |  6
---|---|---|---|---|---|---|---
Radiator shapes (sector number) | 4 | 12 | 24 | 4 | 4 | 4 | 4
Radiator thickness (mm) | 15 | 15 | 15 | 10 | 20 | 15 | 15
Outer side surface | A | A | A | A | A | R |  $45^{\circ}$ R
Inner side surface | A | A | A | A | A | A | A
Lateral side surface | R | R | R | R | R | R | R

In Table 3.15, three different radiator shapes (and sizes) correspond to
Geometries 0, 1 and 2, where the DTOF disc of Geometry 0 is made up of 4
quadrant sectors, as in Sec. 3.7.2, and for Geometries 1 and 2, the DTOF disc
is made up of 12 and 24 trapezoidal sectors, respectively. Each sector
includes readouts from 18 and 8 MCP-PMTs for Geometries 1 and 2, respectively.
The effect of the radiator thickness is studied by comparing Geometries 0, 3
and 4. The radiator thicknesses are 15 mm, 10 mm and 20 mm, respectively. For
all the geometric configurations listed in Table 3.15, the inner/lateral side
surfaces of the radiator are covered by an absorber/reflective mirror, labeled
A/R, respectively. For the outer side surface, a mirror can extend the
acceptance of Cherenkov light, which increases the number of detected photons.
As shown in Fig. 3.63, in Geometry 5, a mirror is attached to the outer side
surface of the radiator, which is equivalent to putting mirror MCP-PMTs
parallel to the real tubes, and in Geometry 6, a mirror is placed on the
$45^{\circ}$ chamfer, which is equivalent to putting mirror MCP-PMTs
perpendicular to the real tubes.

Figure 3.63: Three different configurations on the outer surface of the
radiator. An absorber (left) or mirror (middle) on the outer surface and a
mirror on the $45^{\circ}$ chamber of the outer side surface (right).

The key results regarding the DTOF performance for different geometry
configurations are listed in Table 3.16 for $\pi/K$ mesons at $p=2$ GeV/c,
$\theta=24^{\circ}$ and $\phi=45^{\circ}$.

Table 3.16: Performance of different geometries at $p=2$ GeV/c, $\theta=24^{\circ}$ and $\phi=45^{\circ}$. Configuration/Geometry ID |  0 |  1 |  2 |  3 |  4 |  5 |  6
---|---|---|---|---|---|---|---
$N_{pe}$ for pions | 21.8 | 21.9 | 17.0 | 15.5 | 25.7 | 33.2 | 38.7
Accumulated charge density on | 10.8 | 10.5 | 9.6 | 8.8 | 11.8 | 17.0 | 25.6
MCP-PMT anode ($C/{\rm cm}^{2}$) |  |  |  |  |  |  |
$\pi$/K separation power | $4.17\sigma$ | $4.08\sigma$ | $3.66\sigma$ | $3.99\sigma$ | $4.27\sigma$ | $4.26\sigma$ | $4.19\sigma$

The effect of radiator shape/size is studied by comparing the DTOF performance
with Geometries 0, 1 and 2. As the radiator becomes smaller, the reflection
time of Cherenkov light off the lateral-side mirror increases, which causes
more photon losses and, more importantly, “confusion” in LOP reconstruction.
Geometry 0 has the best $\pi/K$ separation power, $4.17\sigma$, while Geometry
2 has the worst, $3.66\sigma$, indicating that a larger radiator is preferred.

Geometries 3 and 4 have different radiator thicknesses than Geometry 0, which
affects the photon yield. Although more detected photons mean better time
resolution and PID performance, we favor the 15 mm thick radiator, as it
offers the best balance between reducing the impact of the material budget on
EMC and providing performance redundancy, e.g., for reducing the influence of
the detector aging effect in long-term operation.

To increase the photon yield, mirrors are attached to the outer side surface
of the radiator in different ways in Geometries 5 and 6. The numbers of p.e.
received in these two geometries are $\sim 33$ and $\sim 39$, which are much
higher than that in Geometry 0. However, the mirror also increases the number
of possible light paths, which causes “confusion” similar to the effect of
multiple reflections off the lateral-side mirror and degrades the time
resolution. Therefore, even with more detected photons, the $\pi/K$ separation
powers of Geometries 5 and 6 are similar to that of Geometry 0. In addition,
the accumulated charge densities of these two geometry configurations are much
higher, which affects the lifetime of the MCP-PMTs. Thus, options with mirrors
attached to the outer-side surface of the radiator are not favorable.

According to the above comparison, the optimum geometry configuration of the
DTOF detector is Geometry 0. It is worth noting that the large radiator of
Geometry 0 may result in inefficiency when two tracks hit the same radiator in
one event. The rate of inefficiency due to such pile-ups is studied in two
kinds of MC samples, $J/\psi\to anything$ and $\psi(3770)\to
D^{0}\bar{D}^{0}\to anything$. By requiring the polar angle of the charged
tracks to be within $(22^{\circ},36^{\circ})$, the multiplicity of these
endcap tracks is examined, where one track is dominant and three tracks are
negligible. For the case of two tracks, if the difference in their azimuth
angles is within $(-45^{\circ},45^{\circ})$, it is treated as a pile-up event
and causes inefficiency. These studies show that the rates of inefficiency for
these two MC samples are 0.36% and 0.63%, respectively. It can be concluded
that the large radiator of the DTOF design does not affect the reconstruction
efficiency for most physics programs and is acceptable at the STCF. Therefore,
Geometry 0 can be chosen as the baseline design.

####  3.7.5 Background Simulation

The distributions of background particles obtained by the dedicated MDI and
background study, as discussed in Sec. 3.2.3, are used as input in a DTOF
Geant4 simulation and then to simulate the effect of background on DTOF
performance. The background particles influencing the DTOF detector are mainly
secondary gammas and electrons. Their hit rates are approximately $7\times
10^{9}$ Hz and $6\times 10^{7}$ Hz, respectively, including two main parts:
the beam-induced background ($75\%$) and the physical background ($25\%$). The
beam-induced background is uniformly distributed in time, while the physical
background is related to collisions during bunch crossing (once per 8 ns),
exhibiting a characteristic time structure. With Monte Carlo sampling of the
physical background time distribution combined with the uniform time
distribution of the beam-induced background, the overall time distribution of
background hits on the DTOF detector can be obtained, as shown in Fig. 3.64.

Figure 3.64: Overall time distribution of background particles hitting the
DTOF detector.

$\pi$ and K particles are generated in the Geant4 simulation along with the
background samples to study the effect of the background. In the Geant4
simulation, the time window of the signal acquisition is 100 ns and is placed
within the interval [-40 ns, 60 ns] so that the real signal is in the middle
of the time window. In this time window, the number of background particles is
given by a Poisson distribution, and the time distribution is sampled
according to Fig 3.64. The background may greatly increase the number of
photoelectrons detected by the DTOF detector for a single event, resulting in
an increased possibility of multiple hits in a single channel. The correction
of multiple hits is applied, which means that in the time window of [-40 ns,
60 ns], only the first arriving photoelectron signal is taken, and all other
hits are dismissed. With the background hits taken into account and assuming
an MCP-PMT gain of $10^{6}$, the average accumulated charge density on the
MCP-PMT anode is 12 C/cm2 over 10 years of STCF operation ($50\%$ run time).
Under such a background level, the radiation effects of the quartz radiator
and the MCP-PMTs should be small according to studies of other DIRC and DIRC-
like detectors.

Fig. 3.65 shows the 2D time-position map of DTOF hits. Hits by the background
particles are uniformly distributed throughout the phase space, while the real
signal hits are concentrated as bands. After the time reconstruction, the TOF
distribution of a single photoelectron signal can be obtained, as shown in
Fig. 3.65. The reconstructed TOF of the real signal is a Gaussian distribution
($\sigma\sim 100$ ps), while the TOFs of background particles are uniformly
distributed. Some single-photon electrons with zero TOF do not meet the
reconstruction conditions and are taken as background. Due to the uniform
distribution of the reconstructed background signal, the influence of the
background can be eliminated by using the maximum likelihood method. The
$\pi$/K resolution is found to be $4.1\sigma$, as shown in Fig. 3.66.

Figure 3.65: 2-D time-position map of DTOF hits (left) and reconstructed TOF
distribution of a single photoelectron signal (right), with multiple-hit
correction. Figure 3.66: $\pi/K$ identification capabilities (at $2$ GeV/c) of
DTOF with multiple-hit correction.

Considering the Poisson fluctuation of the background count, the $\pi/K$
resolution remains at 4.12$\sigma$ even under an extreme condition of three
standard deviations above the average background level, i.e., the background
hit rate is increased to $2.1\times 10^{8}$ Hz per single DTOF disc. Although
the number of photoelectrons from the background increases dramatically, the
final effect on $\pi/K$ separation is fairly small.

####  3.7.6 Readout Electronics

In MCP-PMT-based DTOF detectors, particle identification relies on the
Cherenkov photon arrival time rather than the position information of the MCP-
PMTs. Therefore, high timing resolution is an essential feature of DTOF
detectors. Furthermore, DTOF detectors usually have a large channel number and
require a track timing resolution below 30 ps, which is a great challenge for
front-end electronics.

The preliminary structure of the DTOF readout electronics is shown in Fig.
3.67. The readout electronics consist of the front-end board and the data-
control board. The front-end board utilizes a time over multithreshold scheme
to extract timing information from analog signals. The signals from the MCP-
PMTs are preamplified first. The gains of the amplifiers are set independently
to compensate for the gain variations of the individual MCP-PMT channels. The
amplified signals are fed into high-performance comparators, each of which has
a different threshold. The outputs of these comparators are fed into the FPGA.
The time-to-digital converter (TDC) module is implemented in the FPGA. The TDC
measures the arrival time of both edges of the comparator outputs with high
accuracy. Then, the front-end board passes the resulting binary data stream to
the data-control board. The data-control board not only collects data streams
from front-end boards but also sends out a high-performance clock and control
signal to the front-end boards. According to the structure described above, we
can briefly estimate the amount of data that the readout electronic system
feeds into the subsequent DAQ system. Assuming that the event rate of the DTOF
detector is 80M hits/s, the data rate output to the subsequent DAQ system can
be simply calculated to be 960 MB/s without considering the effects of the
detector background noise and crosstalk.

For high time resolution, it is crucial that the front-end electronics have
high bandwidth and a high SNR. The time resolution of the FPGA-based TDC was
found to be 3.9 ps in a previous work of ours [423]. We therefore implement
the TDC that can measure narrow pulse widths, of which the time resolution
will be better than 5 ps. The TDC performance in the radiation environment
will be evaluated. The results of the evaluation will affect our system
structure design. A stable, low-jitter detector-wide clock distribution
network also needs to be developed. Its long-term stability, short-term
stability, and temperature stability will be carefully evaluated. The jitter
of the clock distribution network, which is better than 15 ps, satisfies the
design requirements. To further improve the measurement resolution of the
leading-edge timing, the multithreshold TOT method may be used.

Figure 3.67: The preliminary structure of the DTOF readout electronic system.

The DTOF readout electronic system consists of many front-end boards that need
to be synchronized, so the jitter of the distribution clock network is a key
parameter of the electronic system. It is necessary to develop a clock
distribution network that meets the requirements of the DTOF detector based on
existing technology. The conventional White Rabbit network can provide
subnanosecond accuracy and tens of picosecond precision for synchronization.
To achieve a high synchronization accuracy, a new optical fiber link and
synchronization scheme based on optical circulators and serial transceivers
embedded in FPGAs is proposed [424]. Through a prototype implementation and
performance evaluation, the distributed clock has shown a synchronization
accuracy better than 15 ps, which can meet the requirements of most current
large-scale physics experiments.

Finally, the readout electronics must sustain the radiation loads during the
operational lifetime of the STCF. Among them, the radiation influence on the
FPGA-based TDC needs to be regarded from two aspects, i.e., the damage to the
FPGA-based TDC from a single event and the long-term changes in the FPGA-based
TDC performance under the radiation environment.

####  3.7.7 Summary and Outlook

A conceptual DTOF detector design for an endcap PID detector providing
effective $\pi/K/p$ identification at the STCF is presented. An optimum
quadrantal radiator with a thickness of 15 mm with an absorber attached to its
outer surface is chosen as the baseline design. The performance of the DTOF is
investigated through MC simulation, and a reconstruction algorithm for the
DTOF is developed. The simulation indicates an overall reconstructed TOF time
resolution of $\sim 50$ ps with an average of $\sim 20$ photons detected by
the MCP-PMT arrays when all the contributing factors are converted. It is
worth noting that the uncertainty of $T_{0}$ dominates the overall timing
error; therefore, an optimal design of the STCF bunch size is crucial. By
applying the likelihood method, a $\pi/K$ separation power of DTOF of $\sim
4\sigma$ or better at a momentum of 2 GeV/c is achieved over the entire DTOF
sensitive area. This fulfills the requirements for the PID detector at the
STCF. Extensive R$\&$D works concerning DTOF are underway to verify the
designs and the key technical aspects.

###  3.8 ElectroMagnetic Calorimeter (EMC)

####  3.8.1 Introduction

The electromagnetic calorimeter (EMC) of the STCF detector is a cylindrical
array of scintillating crystals that provides energy and position measurements
for photons with high resolution and 4$\pi$ coverage. It can also identify
particles including photons, electrons and hadrons. The primary detector
requirements leading to the conceptual design of the EMC are listed as
follows:

  * •

Energy resolution of approximately 2.5% for 1 GeV photons and good energy
linearity from 25 MeV to 3.5 GeV.

  * •

Position resolution of about 5 mm for 1 GeV photons.

  * •

Fast response to cope with the expected high rate environment.

  * •

Time resolution of about 300 ps for 1 GeV energy deposits to suppress
background and identify particles.

  * •

Good radiation resistance against the radiation dose anticipated of 10 years
of operation.

  * •

Providing critical input to the trigger system.

  * •

Precise luminosity measurement.

####  3.8.2 EMC Conceptual Design

##### Crystal and Photo-Detector Choices

With the advantage of high light-yield, CsI(Tl) crystal based calorimeters
have been widely used in collider experiments in the $\tau$-charm energy
region, for example, in BESIII [425], Belle [426] and Belle II [410]. However,
the decay time of this crystal is so long that it cannot meet the requirements
of a high luminosity experiment. In the STCF, it is necessary to select a
faster crystal for the EMC. Pure CsI (pCsI) crystals, with a short decay time
and excellent radiation resistance, are promising candidates. The light yield
of pCsI crystal is approximately 2% of that from CsI(Tl) [427] and would
further decrease by 20% when the received irradiation dose reaches 100 krad
(the total irradiation dose of the STCF EMC endcap in 10 years would be
approximately 45 krad (see Table 3.6)).

For the readout electronics of a crystal scintillator, semiconductor
photodetectors are favored to operate in a strong magnetic field of 1 T.
Mature commercial semiconductor photodetectors mainly include photodiodes
(PDs), avalanch Photodiodes (APDs) and silicon photomultiplifiers (SiPMs).
Considering the gain performance, large dynamic response range, linear output
signal amplitude, sensitive area and light collection efficiencyof APDs, the
photodetectors are more suitable as light collection devices of pCsI crystals.

A pCsI crystal scintillator with an APD readout is chosen as a possiable
candidate for satisfying the physics requirements of the STCF EMC.Two of the
most important factors regarding the performance of the EMC are the energy
resolution and position resolution. The relevant considerations for the
conceptual design of the EMC are discussed below.

The energy resolution of a calorimeter is affected by the shower leakage,
which is mainly determined by the total radiation length ($X_{0}$) of the EMC.
Figure 3.68 shows the longitudinal development of the shower of a 3.5 GeV
photon (close to the most energetic photon in the STCF) in a pure CsI crystal.
Approximately 95% of the shower energy is deposited within 15 $X_{0}$ (28 cm).
Then, with increasing total radiation length, the total energy deposition
increases slowly, and the improvement in the energy resolution is very small.
Considering the total crystal cost and performance of the EMC, we choose the
crystal radiation length of 15.

\begin{overpic}[width=216.81pt,height=143.09538pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
TotalRL.pdf} \end{overpic}

Figure 3.68: The shower longitudinal distribution.

The position resolution (angular resolution) is affected by the shower
transverse development and the calorimeter segmentation and is an important
parameter for the reconstruction of $\pi^{0}$ particles. According to the
simulation, the minimum angle between two photons from the decay of a 1.5 GeV
$\pi^{0}$ (about the most energetic $\pi^{0}$ in the STCF experiment) is about
10 degrees. To separate these two photons, the maximum coverage of each
crystal should be $\sim$ 3 degrees. In principle, finer dimensions improve the
angular resolution. However, the packaging and supporting materials of the
crystal increase, and the lateral leakage increases, which worsens the energy
resolution. Optimization of the crystal size is performed using simulation and
is discussed in Sec. 3.8.2.

##### Crystal Size Optimization

Figure 3.69 shows the schematic arrangement of crystals in the $X-Y$ plane of
the barrel EMC. The inner radius R of the calorimeter is 105 cm, and the
length of the crystal is 28 cm. The size of the cyrstal, denoted by the
dimension of the front face where particles enter, is a key design parameter
to be optimized.

\begin{overpic}[width=216.81pt,height=143.09538pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
CellSize.pdf} \end{overpic}

Figure 3.69: The schematic arrangement of crystals.

###### Energy Resolution

The influence of the front face size of the crystal on the energy resolution
of the EMC is also investigated. In principle, the angular resolution of the
EMC can be improved by reducing the crystal front face size, but more
packaging and supporting materials would be introduced, which would degrade
the energy resolution of the EMC. Figure 3.70 shows the energy resolution of 1
GeV gamma ray reconstruction, comparing the energy deposition in two layouts:
a 3 $\times$ 3 crystal array with a 5 cm crystal front face size and a
$5\times 5$ array with a 3 cm crystal front face size. The reconstructed
energies are 0.911 GeV and 0.905 GeV, respectively, where a smaller crystal
gives a lower reconstructed energy, but the difference is not significant. To
obtain the energy resolution, a Crystal Ball function is fit to the
reconstructed energy distribution, and the FWHM divided by 2.35 is used as the
energy resolution. For the two layouts, the energy resolutions are found to be
2.46% and 2.56%, respectively, and the smaller crystal results in a larger
energy uncertainty. The total effective areas of the EMC used in both cases
are the same. However, more packaging materials with a smaller crystal size
are needed. The packaging materials here are 300 $\mu$m Teflon film and 200
$\mu$m carbon fiber as crystal support materials.

(a) (b)

Figure 3.70: The energy resolution of the EMC. The pCsI front face size is 5
cm (a) and 3 cm (b).

###### Position Resolution and $\pi^{0}$ Reconstruction Efficiency

The position resolution of incident photons is directly dependent on the
crystal front face size. The shower position measurement is the key to
reconstrcuting the incident angle, where the barycenter method is commonly
used, with the following formula:

$\begin{array}[]{cll}x_{c}=\sum\limits_{j}^{N}w_{j}(E_{j})x_{j}/\sum\limits_{j}^{N}w_{j}(E_{j}),\end{array}$
(3.16)

where $x_{c}$ is the reconstruction position, $x_{j}$ is the spatial
coordinate of the $j-th$ crystal, and $w_{j}$ ($E_{j}$) is the weight of the
$j-th$ crystal involved in the position reconstruction. The weight is related
to the energy deposition in that crystal. The angle can be determined by
reconstructing the incident point on the crystal front surface and the
collision point. Figure 3.71 compares the position resolution of 1 GeV
$\gamma$ reconstructed by the logarithmic weight of energy in crystals with
two different front face sizes of (a) 5 cm $\times$ 5 cm and (b) 3 cm $\times$
3 cm. The position resolutions are 4.8 mm and 3.8 mm, respectively, clearly
showing that the position or angular resolution can be improved by decreasing
the crystal size.

(a) (b)

Figure 3.71: The EMC position resolution based on the logarithmic energy
weighting method, with (a) 5 cm $\times$ 5 cm and (b) 3 cm $\times$ 3 cm
crystal front face sizes.

With decreasing crystal front face size, the proportion of packaging materials
between crystals increases, which leads to degraded reconstruction efficiency
for $\pi^{0}$. The reconstruction efficiencies of $\pi^{0}$ with different
crystal front face sizes are compared, as shown in Fig. 3.72. Here, it is
required that the two photons generated by $\pi^{0}$ decay are both within the
effective acceptance of EMC, and then to reconstruct the $\pi^{0}$ mass. It is
clear that the reconstruction efficiency of $\pi^{0}$ is higher for larger
crystal front face size. The average opening angle of the crystal with the
front end face size of 5 cm relative to the collision point is about 2
degrees, which can distinguish the two photons generated from $\pi^{0}$
($\pi^{0}$ of 1.5 GeV, where the minimum included angle of photons is about 10
degrees). Moreover, the energy resolution of the 5 cm crystal is better than
that of the small-sized crystal, so the reconstruction efficiency of $\pi^{0}$
in the same mass width range is slightly higher.

###### Fake Photon Discrimination

In contrast with the normal photons from the collision point, most of the
false photons are generated at other positions, and their direction of
incidence on the EMC deviates greatly from the axial direction of the crystal,
which causes the hit number and secondary moment of the shower in the EMC to
be different from that of real photons. Another important difference is that
the time information is different from the real signal. This information can
be used to identify false photons. In addition, whether the direction
reconstruction of photons can be realized by longitudinal sampling of the EMC
is still an interesting topic, but considering the importance of energy
resolution, the scheme of longitudinal sampling needs to be carefully
designed.

In conclusion, considering the energy resolution, position resolution,
reconstruction efficiency and total number of readout channels, based on the
premise of meeting the STCF EMC requirements, the end face size of $\sim$5 cm
is selected as the typical size of the crystal.

\begin{overpic}[width=216.81pt,height=143.09538pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
Pi0Efficiency.pdf} \end{overpic}

Figure 3.72: The efficiency of the EMC for $\pi^{0}$.

##### EMC Layout

The calorimeter is composed of a barrel part and an endcap cover, and the
crystal arrangement diagram is shown in Fig. 3.73. The barrel part covers
polar angles from $33.85^{\circ}$ to $146.15^{\circ}$, with an inner radius of
105 cm and length of 320 cm along the beam direction. The endcap part is
located at 160 cm $\leq\left|z\right|\leq$ 190 cm, with an inner radius of 56
cm and an outer radius of 105 cm. The endcap covers polar angles from 19.18∘
to 33.64∘ and 156.15∘ to 160.82∘. The entire EMC provides a 94.45% solid angle
coverage of 4 $\pi$.

There are 51 circles of crystals in the barrel along the beam (Z) direction,
132 crystals per circle, and 6732 crystals in total. The crystal size and
shape in the same circle are the same, and the crystal shapes in different
circles are similar but different. The crystal is in an irregular trapezoid
platform shape, in which the sizes of the front and back faces are about
$5\times 5$ and $6.5\times 6.5$ cm2 respectively, and the longitudinal length
is 28 cm. The endcap is divided into two identical parts, located to the left
and right side of the barrel part, each with 969 crystals, with a total of
1938 crystals. The crystal in the endcap is also in an irregular trapezoid
platform shape. The sizes of the front and back faces are about $4.5\times
4.5$ cm2 and $5.2\times 5.2$ cm2 respectively, and the longitudinal length is
also 28 cm.

To reduce the probability of secondary particles escaping from the gap between
crystals, a defocus design is added to the geometric structure of the EMC to
improve the detection efficiency. In the direction of $\theta$, except for the
middle circle of crystals in the barrel, each circle of crystals points to
$\pm 2.5$ cm away from the collision point, and each circle of crystals in the
endcap points to $\pm 10$ cm away from the collision point, which can also be
seen in Fig. 3.73. In the azimuth direction ($\phi$), the crystal in each
circle deflects 1.36∘ in the direction of phi. In this way, the crystal points
to the circumference with a radius of 2.5 cm centered on the beam line, as
shown Fig. 3.74.

\begin{overpic}[width=346.89731pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
Layout.pdf} \end{overpic}

Figure 3.73: The EMC layout design.

\begin{overpic}[width=216.81pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
Defocus-phi.pdf} \end{overpic}

Figure 3.74: The EMC defocus design.

####  3.8.3 Expected Performance of the EMC

##### Energy Response

Based on the conceptual design, the response of the EMC to photons with
different energies is studied via Geant4 simulation using 1 GeV photons. As
shown in Fig. 3.75(a), the intrinsic energy resolution is about 1.52% with
only considering the interaction between photons and the crystal. Here, the
energy reconstruction is in the range of the $5\times 5$ array and each
crystal has a cross-section of $5\times 5$ cm2 at the front face. The energy
deposition fluctuation is mostly caused by backscattering and leakage of the
shower tail. The energy resolution is simulated by taking into account several
main factors. The influence of these factors on the energy resolution is given
in Table 3.17. When the light yield of the crystal is set to 100 pe/MeV
(preliminary measurement shows that the light yield of the pCsI crystal can
reach about 150 pe/MeV, see Sec. 3.8.6), the simulated energy resolution is
1.52%. When a 200 $\mu$m thick carbon fiber material is introduced as the
support unit, the energy resolution becomes 1.96%. The light collection
nonuniformity of large crystals can generally reach a few percent. For
example, in the BESIII experiment, the average nonuniformity is about 3%-4%.
After taking into account a 5% nonuniformity, the simulated energy resolution
increases to 2.06%. Considering that the secondary particles generated in the
shower process hit the APD and produce electron-hole pairs, which are
superimposed on the signals, the energy resolution is 2.11%. When electronic
noise of 1 MeV is added, the final energy resolution is 2.15%, as shown in
Fig. 3.75(b).

(a) (b)

Figure 3.75: The expected energy resolution of the EMC, (a) the intrinsic performance without considering material effects and (b) with several main factors. Table 3.17: The energy resolution considering different effects. Condition | Intri | Carbon Fiber (200 um) | Uni (5%) | APD | Noise (1 MeV)
---|---|---|---|---|---
EneRes @1GeV (%) | 1.52 | 1.96 | 2.06 | 2.11 | 2.15

Figure 3.76(a) shows the photon energy response from 50 MeV to 3.5 GeV. The
results show excellent linearity, with a nonlinearity of about 1%. Figure
3.76(b) shows the energy resolution curve. The results show that from 50 MeV -
2 GeV, the energy resolution gradually improves with increasing energy, but it
begins to deteriorate slightly at 2 GeV because of energy leakage in the EMC
back end. At 1 GeV, the energy resolution is better than 2.5 %, which meets
the requirement of the EMC.

(a) (b)

Figure 3.76: The expected performance of (a) the energy linearity, and (b) the
energy resolution.

##### Position Resolution

Figure 3.77(a) shows the performance of the EMC position resolution. The
results show that the position resolution gradually improves with increasing
energy. At 1 GeV, the expected positon resolution is about 5 mm, which meets
the design requirements. With the position resolution, the angular resolution
can be obtained, as shown in Fig. 3.77(b). The angular resolution is 4 mrad at
1 GeV.

(a) (b)

Figure 3.77: The expected (a) position resolution and (b) angular resolution
for 1 GeV photons.

##### Time Resolution

The full response of the EMC including the optical processes, the response of
APD and readout electronics was simulated with Geant4. The output waveform
from the simulation was processed using the template fitting method (see Sec.
3.8.4) to extract the arrival time of the output signal (corresponding to the
hit time of incident particles up to a certain delay). Assuming that the light
yield is 100 pe/MeV, the distribution of the hit time on the seed crystal in a
shower for 100 MeV photons is shown in Fig. 3.78(a). The width of this
distribution representative of the EMC time resolution is 318.8 ps (no
electronic noise is considered here). Figure 3.78(b) shows the time resolution
for different energy deposits. The time resolution improves as the deposited
energy increases and can reach 200 ps at 1 GeV. Our preliminary study has
demonstrated a light yield beyond 100 pe/MeV for the pCsI unit of the EMC. In
view of the enhanced light yield, the time resolution of the EMC could be even
better. For muons or charged hadrons that penetrate the EMC without shower,
the deposited energy is about 100 MeV, and hence the EMC time resolution for
these particles would be about 300 ps. If either charged or neutral hadrons
produced shower in the EMC, the time resolution for these particles may be
subject to the uncertainty of the shower starting point.

(a) (b)

Figure 3.78: (a) The time resoluiton of 100 MeV gamma rays and (b) time
resolution curve.

##### Impact of Upstream Materials

Before arriving at the EMC, photons have a certain probability of interacting
with the beam pipe or other subdetectors that are in front of the EMC. To
study the influence of the upstream materials on the performance of the EMC,
materials with different thicknesses are added in front of the EMC, and the
resulting EMC performance is compared. Four cases of radiation length for
materials in front of the EMC, 23% $X_{0}$, 27% $X_{0}$, 31% $X_{0}$ and 35%
$X_{0}$ are considered. The equivalent mass of aluminum is placed at the RICH
detector position, about 10 cm in front of the EMC. The simulated energy
resolution is shown in Fig. 3.79, and the energy resolution changes from 2.25%
to 2.36%. The photon detection efficiency curve is shown in Fig. 3.80, and it
can be seen that in the low energy region, below 1 GeV, with additional
material, the detection efficiency decreases significantly, and the impact is
found to be very small in the higher energy region.

(a) (b) (c) (d)

Figure 3.79: The energy resolution of EMC with different thicknesses of
upstream materials. (a) 23% $X_{0}$, (b) 27% $X_{0}$, (c) 31% $X_{0}$ and (d)
35% $X_{0}$.

\begin{overpic}[width=216.81pt,height=143.09538pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/9_3_5.pdf}
\end{overpic}

Figure 3.80: The Reconstruction Efficiency curve of the EMC with upstream
materials.

For the baseline design of the STCF detector system, the radiation length of
each subdetector in front of the EMC is studied via simulation, as shown in
Fig. 3.81. In the barrel, the total radiation length is about $0.3X_{0}$,
while in the endcap, the radiation length can reach $0.8X_{0}$, which is
mainly contributed by the MDC. To evaluate the effect of upstream materials, a
Geant4 simulation study is carried out to preliminarily study the energy
resolution of the EMC under the existing structural design. A full STCF
detector simulation is performed, and the performance of the EMC is compared
to that of an EMC-only simulation. The results are shown in Fig. 3.82. Figure
3.82(a) shows that upstream materials have little effect on the energy
resolution of the EMC when considering only the barrel EMC. Figure 3.82(b)
shows the energy resolution at different polar angles of incident photon with
an energy of 1 GeV. In the endcap region, due to material effects of inner
subdetectors, the expected energy resolution decreases from about 2.5% to
about 3.0%. The significant degradation of the energy resolution around
$\theta=10^{\circ}$ and $\theta=60^{\circ}$ is due to the large energy leakage
at the transition region of the barrel and the endcap.

\begin{overpic}[width=216.81pt,height=143.09538pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/STCF-
Materials.pdf} \end{overpic}

Figure 3.81: The radiation length of the inner subdetectors in front of the
EMC.

(a) (b)

Figure 3.82: (a) Comparison of the energy resolution of the EMC (barrel) as a
function of the energy with full detector simulation and EMC-only simulation.
(b) The energy resolution as a function of the incident polar angle for 1 GeV
photons.

####  3.8.4 Pileup Mitigation

##### Challenges of High Background

In Sec. 3.8.3, when studying the expected performance of the EMC, the
background contribution is normally not considered in the simulation. The
photon reconstruction is based on a simple clustering algorithm used in
BESIII. The reconstruction algorithm searches the related crystals in a
shower, adds their energies together, and calculates the hit position.

Considering the high background at the STCF, the EMC background is studied by
Monte Carlo simulation. The simulated background energy distribution of the
EMC is shown in Fig. 3.83(a). Figure 3.83(b) shows the background counting
rate at each position of the calorimeter (with a threshold value of 1 MeV).
The background counting rate is close to about 1 MHz.

Such a high background counting rate has a great impact on the energy
measurement of the calorimeter. As shown in Fig. 3.84, the energy spectrum of
the 1 GeV gamma-ray is reconstructed without and with considering the
background. The results show that the energy resolution values are 2.15% and
5.05%, respectively. After the background is introduced, the energy resolution
is degraded by more than a factor of two.

(a) (b)

Figure 3.83: The background simulation in the EMC: (a) the deposited energy
distribution and (b) the background counting rate.

##### Waveform Fitting

To correct the uncertainty of the energy measurement caused by a high
intensity background, one feasible scheme is to reconstruct the amplitude and
time information by using a waveform fitting algorithm; this was used in the
electromagnetic calorimeter of the CMS experiment at the LHC [428]. The CMS
template fitting technique, named “multifit”, was motivated by the reduction
of the LHC bunch spacing from 50 to 25 ns and by the higher instantaneous
luminosity of Run II, which led to a substantial increase in both the in-time
and out-of-time pileup, where the latter refers to the overlapping signals
from neighboring bunch crossings. It has been demonstrated by CMS that, with
the multifit method, the contribution of out-of-time pileup to the signal
reconstruction is found to be negligible, both in data and in simulated
samples. The energy resolution and response are improved with respect to those
of the Run I method where the amplitude was reconstructed as a weighted sum of
the ten digitized samples.

For the STCF EMC, considering the design parameters of the readout circuit
(see Sec. 3.8.5), the total width of the signal after shaping is about 500 ns,
and the leading edge is about 50 ns. To sample the leading edge and consider
that the total amount of data is controllable, we use a sampling rate of 40
MHz as the baseline design here. In the multiwaveform fitting algorithm, the
time window of the waveform fitting is set to 1000 ns (-250 ns - 750 ns, and
the signal start time is set to 0 ns). The pulse template, $p_{j}$, for both
the signal and the background is built by convoluting the pCsI fluorescence
signal with the CSA impulse response function. The total template, $P$ is
shown in Eq. 3.17; this template is an overlay of the signal template and the
background template but shifted in time, in which the normalizations are free
parameters ($A_{j}$). The total template is then used to fit the waveform
readout by the electronics. Referring to the CMS multifit method, $N=40$
templates with a repetition period of 12.5 ns (CMS uses 25 ns, half of which
is temporarily taken here) are used to fit our results. Starting at -250 ns,
one template is placed every 12.5 ns, and a total of 40 templates are used for
a multitemplate fitting.

$P=\sum_{j=0}^{N}A_{j}p_{j},$ (3.17)

A set of toy events are generated to test the performance of the multiwaveform
fitting. In Fig. 3.85(a), the dotted green curve is the superposition of the
signal and background spectra of one simulated event. The signal peak is
around 120 ns (the integration time is set as 40 ns), and the rest represent
the backgrounds. The background event rate is assumed to be $\sim$ MHz, and
the energy is obtained by sampling according to Fig. 3.83(a). Because of the
background, the peak value of the spectrum is larger than the real value. With
multiwaveform fitting, the original energy can be reconstructed more
precisely. Additionally as shown in Fig. 3.85(a), the red curve represents the
signal template, and blue represents the fitting results of the background
templates. Figure 3.85(b) shows the energy resolution of 1 GeV gamma-ray
events, obtained by multiwaveform fitting. The result is 2.47%, which is 50%
better than that without waveform fitting. This result is close to the result
without considering the background.

Figure 3.86(a) shows the EMC energy resolution curve from the Geant4
simulation for photons reconstructed in the barrel only. The expected energy
resolution is compared for three scenarios: the traditional clustering
reconstruction algorithm without the influence of background, that with the
influence of the background, and the multifit method with the background
included. The result shows that the pileup background has a significant impact
on the energy resolution, especially in the low energy region (<100 MeV), and
the energy resolution changes from $\sim$ 4.6% to $\sim$ 22% at the energy of
100 MeV when the background effect is included. With increasing energy, the
impact of the background gradually decreases, which is mainly due to the
relatively low energy of the background. By using the waveform sampling and
fitting method, the energy resolution is greatly improved, from $\sim$ 22% to
$\sim$ 5.2%, which is close to the result without considering the background.
The result for the endcap, which suffers from an even higher pileup background
of about 10 MHz, is shown in Fig. 3.86(b). Even for a 10 MHz background rate,
the multiwaveform fitting method works well and can greatly improve the energy
resolution.

(a) (b)

Figure 3.84: The EMC energy response for 1 GeV photons (a) without background
and (b) with background included in the simulation.

(a) (b)

Figure 3.85: (a) An example output pulse of the EMC with multiwaveform
fitting. The dotted green curve is a simulated waveform, which is a
superposition of the signal and background spectra. The red curve represents
the signal template, and the blue represents the fitting results of the
background, (b) The energy resolution of 1 GeV $\gamma$ rays in the EMC using
the multifit method.

(a) (b)

Figure 3.86: The expected EMC energy resolution with the multifit method for
(a) the barrel region and (b) the endcap region.

####  3.8.5 Readout Electronics

The electronics system of the EMC provides the photon detector signal readout,
analog-to-digital conversion and data acquisition. According to the physics
requirements and detector characteristics, some demands placed to the
electronics system, which are listed below:

  * •

The energy deposition on each crystal ranges from 2.5 MeV to 2500 MeV.
Considering that the light yield of pCsI is about 100 p.e./MeV and the gain of
the photodetector is about 50, the dynamic range of each electronics channel
should range from 2 fC to 2000 fC.

  * •

The high luminosity of the STCF results in a high event rate in the detector.
It is estimated that the event rate in the barrel can reach as high as
hundreds kHz, and it can be even higher in the endcap. Therefore, the deadtime
of the readout system should be shorter than 1 $\mu s$.

  * •

In addition to energy measurement, time measurement is needed and the
precision should be better than 200 ps @ 1 GeV.

According to the requirements discussed above, a charge-sensitive amplifier
(CSA) based design is proposed. The structure of the CSA-based readout
electronics is shown in Fig. 3.87, and it mainly consists of a front-end board
(FEB) and a back-end board (BEB). The FEB is placed at the outer end of a pCsI
crystal with 4 APDs on it to receive the fluorescence light. Multiple APDs are
used to improve the light yield and the system robustness. On the other side
of the FEB, 4 CSAs read out the signals of 4 APDs. Then, the outputs of the
CSAs are added by two adders, providing in a dual-gain (high/low) outputs. One
BEB can connect several FEBs via cables. The BEB provides power and high
voltage to FEBs and obtains high-gain and low-gain signals from FEBs. Signals
pass through the CR-RC2 shaping circuits and are then digitized by ADCs on the
BEB. In addition, there is one comparator corresponding to each channel that
can compare the input signal with the threshold and generate a hit for the
FPGA-TDC for time measurement. All data produced by the ADCs and the FPGA-TDCs
are aggregated, packaged and transmitted by the FPGA. Considering the high
event rate, we use the waveform sampling readout method to suppress the high
background. The waveform sampling can retain the original waveform
information, which is also necessary for the waveform fitting mentioned in the
previous background study.

Due to the relatively large size ($\sim 6.5\times 6.5$ cm) of the crystal end,
it is favorable to couple the APD with a large sensitive area to improve the
light yield. Presently, there are only a few commercial models with large
areas available. The HAMAMATSU company mainly provides two models: S8664-55
(effective area of $5\times 5$ mm) and S8664-1010 (effective area of $10\times
10$ mm).

\begin{overpic}[width=216.81pt,height=143.09538pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
Electronics-1st.pdf} \end{overpic}

Figure 3.87: The structure of CSA-based readout electronics.

####  3.8.6 EMC R&D

##### pCsI Crystal

To understand the properties of the pCsI crystal, relevant tests are carried
out in the laboratory. The crystals, as shown in Fig. 3.88, are produced at
the Shanghai Institute of Ceramics, Chinese Academy of Sciences (SIC CAS). The
wavelength of emission spectrum spreads from $\sim$ 260 nm to $\sim$ 700 nm,
with its main component around 310 nm accounting for $\sim$ 3/4 of the total
light intensity.

\begin{overpic}[width=216.81pt,height=143.09538pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
pCsICrystal.pdf} \end{overpic}

Figure 3.88: The pCsI crystal for the EMC.

##### Reflective Material

The efficiency of light collection is an important factor in achieving a high-
precision energy resolution in crystal calorimeters. Since the fluorescence
emitted by pCsI is mainly in the ultraviolet wavelength range (about 310 nm)
and is very easily to be absorbed. Considering the excellent reflection
coefficient of Teflon, which is basically independent of the wavelength, we
chose Teflon with a thickness of 300 um to package the crystal.

##### Cosmic Ray Test

The performance of the sensitive unit (pCsI + APD) is tested with the cosmic
rays. A typical-sized pCsI crystal is coupled with four APDs. In the test, the
crystal is wrapped with three layers of BC642 material. Two large-area APD
models from HAMAMATSU are used, S8664-55 and S8664-1010, with sensitive areas
of 5 mm $\times$ 5 mm and 10 mm $\times$ 10 mm, respectively. The APD is
coupled with silicone (EJ-550, 310 nm wavelength transmission is greater than
90%) at the back end of the crystal. The deposition energy of Minimum
Ionization Particles (MIPs, $\mu$) passing through the pCsI crystal is about
30 MeV. The results are shown in Fig. 3.89. The light yield of pCsI is
calculated to be 54 p.e./MeV (with S8664-55 APD) and 156 p.e./MeV (with
S8664-1010 APD).

(a) (b)

Figure 3.89: The energy deposition of MIPs. (a) S8664-55 result and (b)
S8664-1010 result.

##### Readout Electronics

A prototype readout out electronics system for the CSA-based method, described
in Sec. 3.8.5, has been implemented, as shown in Fig. 3.90. The dynamic range
and noise performance is studied based on a CSA with a 3-JFET as the input
stage with different APDs: Hamamatsu S8664-0505 and S8664-1010.

\begin{overpic}[width=346.89731pt,height=130.08731pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
Electronics-3rd.pdf} \end{overpic}

Figure 3.90: Prototype electronics of the CSA-based method (FEE on the left
and BEU on the right).

The electronic noise of the readout system with two types of APDs at different
shaping times is measured, with an APD gain of 50. Type S8664-1010, which
creates twice as much noise as S8664-0505, achieves similar performance
considering the size of the area. The detailed experimental results are shown
in Fig. 3.91. The noise of S8664-1010 is lower than 0.4 fC when the shaping
time is 100 ns, which means the noise performance would be better than 0.8 fC
when using 4 APDs and 4 CSAs. The equivalent noise energy is 1 MeV when the
light yield reaches 100 p.e./MeV.
Given that the upper limit of the charge measurement of the high-gain channel
is 120 fC, the dynamic range of the high-gain channel can cover the range of 3
MeV (2.4 fC, 3 times noise) - 150 MeV (120 fC). Considering that the gain
ratio of the high- and low-gain channels is 20 and the low-gain noise is close
to 2 fC, the dynamic range of the low-gain channel is 10 MeV (6 fC, 3 times
noise) - 3000 MeV (2400 fC). The dynamic range that can be realized by this
dual gain design is shown in Table 3.18.

\begin{overpic}[width=216.81pt,height=143.09538pt]{Figures/Figs_04_00_DetectorSubSystems/Figs_04_04_ElectromagneticCalorimeter/ECAL-
Electronics-4th.pdf} \end{overpic}

Figure 3.91: Noise of the readout system at different shaping times. Table 3.18: The Dynamic Range of EMC Channel | Low Limit (MeV) | High Limit (MeV)
---|---|---
High Gain | 3 | 150
Low Gain | 10 | 3000

In summary, the conceptual design of the electronics can meet the requirements
of the STCF calorimeter in terms of noise, dynamic range and time resolution.

####  3.8.7 Summary

The baseline design of the STCF EMC adopts a pCsI crystal scintillator coupled
with large area APDs, and a charge-sensitive readout scheme is chosen for the
readout electronics. The preliminary Monte Carlo simulation and experimental
test results show that the conceptual designs can meet the requirements of the
STCF. Extensive R&D works are underway to verify the designs and the key
technical aspects.

###  3.9 Muon Detector (MUD)

####  3.9.1 Introduction

The muon detector (MUD), as the outermost part of the STCF detector system, is
used to provide muon identification in the presence of a significant pion
background. It can also be used for neutral hadron identification to
complement the EMC identification, for example, of neutrons and $K_{L}$. A MUD
usually has a sandwich-like structure that consists of a hadron absorber and a
detector array. Multiple layers of steel plates are used as both the magnetic
flux return yoke and the hadron absorber. The muon detection array is inserted
into the gap of these hadron absorbers.

##### Performance Requirements

For the STCF MUD, a high detection efficiency of muons and a good suppression
power for muons/pions are the main requirements [429]. The momenta of the
final state $\mu$ and $\pi$ produced at the STCF are mostly below 2.0 GeV/c,
as shown in Sec. 3.1. Because of the EMC and solenoid material preceding the
MUD, muons with momenta less than 0.4 GeV/c cannot be detected by the MUD. In
contrast, muons with low momenta can be identified well by the PID system, as
introduced in Sec. 3.6. According to the physics requirements, in the momentum
range of $p>0.7$ GeV/c, the ideal muon detection efficiency should be higher
than 95%; in the range of $0.5<p<0.7$ GeV/c, the muon detection efficiency
should be higher than 70%, with the muon/hadron suppression power being better
than 30.

Additionally, the identification of neutral hadrons with sufficiently high
detection efficiency is important for STCF physics, especially for particles
with momenta in the range of [0.2, 1.2] GeV/c. The probability of obtaining a
hadronic shower in the EMC or MUD for neutrons or $K_{\mathrm{L}}$’s is quite
high, generating a high multiplicity of photons, neutrons, protons and other
hadrons. Thus, a detector array with good photon and neutron sensitivity is
required.

For the STCF, with a luminosity of $1\times 10^{35}$ cm-2s-1, the MUD receives
a nonnegligible background contribution dominated by neutrons with an energy
of [10, 100] keV [430, 431]. This background may cause more hits in the MUD,
which may affect the track finding and identification efficiency of muons.
Thus, the MUD must tolerate the very high background rate of the STCF [432,
433]. In addition, the low energy photon and neutron background may cause
significant contamination in the identification of neutral hadrons [434]. As
mentioned in Section 3.2, the simulated highest background level is
approximately 3.99 Hz/cm2 and 265 Hz/cm2 for barrel and endcap MUD,
respectively. As a consequence, optimization of the detector layout to high-
rate capabilities and excellent background suppression power is important in
the MUD design.

##### Technology Choices

In particle physics experiments, the resistive plate chamber (RPC) and the
plastic scintillator are among the most widely used detector technologies for
the detection of muon particles.

A RPC is a traditional option for large-area muon detection with centimeter-
level spatial resolution [435], and have been used in many experiments as the
MUD, such as ATLAS [436], BaBar [437], Belle [438], STAR [439], BESIII [440]
and Daya Bay [441]. RPCs are robust and low cost for large detection areas and
have simple manufacturing and maintenance processes. In addition, their
centimeter-level spatial resolution can satisfy the demand of particle
detection with an area of hundreds of square meters. A Bakelite-RPC, which
operates in the avalanche mode, has count rate capabilities over 1 kHz/cm2,
and it also offers the advantage of low background sensitivity. Thus,
Bakelite-RPC is chosen as a candidate for the STCF MUD.

A plastic scintillator with a silicon photo-multiplier (SiPM) is also a choice
for the MUD. In the Belle II experiment, a combination of polystyrene
scintillator strips, wavelength shifting fibers and SiPM was selected as the
upgrade of the $K_{L}$ and muon detector to replace the low-count rate RPCs
[442]. Compared with the Bakelite-RPC, the plastic scintillator detector has a
much higher count rate and is more sensitive to photons and neutrons,
resulting in powerful neutral/hadron separation. However, the plastic
scintillator detector suffers from higher background counts, leading to worse
track-finding and particle identification. As a result, the design of the MUD
should be optimized to achieve a balance between the rate capabilities and the
identification of low-momentum muons. Consequently, a hybrid muon detector
design that combines a Bakelite-RPC with a plastic scintillator is proposed
for the STCF. Details regarding the design, optimization, and particle
identification performance are presented in the following.

####  3.9.2 MUD Conceptual Design

##### Detector Layout

The baseline design of the MUD is a combination of a Bakelite-RPC and plastic
scintillator detector: 3 layers of Bakelite-RPC are placed in the innermost
part, and 7 layers of the plastic scintillator detector form the outer layers.

Considering that the dominant background sources are photons and neutrons, the
usage of the Bakelite-RPC in inner layers can decrease the background level in
the MUD and help to separate the charged particle tracks and neutral particle
shower signals. The plastic scintillator detector is more sensitive to photon
and neutron particles, which are the main background contributors to neutral
hadron detection and identification. The Geant4 [443] simulation results
indicate that with the expected STCF background level described in Sec. 3.2,
the muon detection efficiency in the momentum range of [0.4, 0.6] GeV/c
decreases by 10-20% if the MUD detectors are all plastic scintillators
compared with that of the STCF MUD baseline design.

Fig. 3.92 shows a schematic of the baseline design of the MUD. The barrel MUD
covers the solid angle of 79.2%$\times$4$\pi$ (37.63∘$<$$\theta$$<$142.37∘),
and the endcap MUD covers the solid angle of 14.8%$\times$4$\pi$
(20∘$<$$\theta$$<$37.63∘ and 142.37∘$<$$\theta$$<$160∘). Both the barrel and
endcap MUD contain 10 layers of detectors, and the iron yoke layout can be
seen at Sec. 3.11.

In MUD, the width of the RPC $X/Y$ readout strips and the width of the plastic
scintillator are both 4 cm. The maximum length of the Bakelite-RPC module is
approximately 1.1 m, and the maximum length of the plastic scintillator strip
is 2.4 m [442]. As shown in Fig. 3.93, each layer of barrel MUD consists of 8
rectangle detector module. For Bakelite-RPC, the module is divided into 5 sub-
modules along Z direction, and 2 sub-modules along R$\phi$ direction to
control the maximum length of readout strips around 1.1 m. In each sub-module,
the 2-D readout strips are perpendicularly arranged. For plastic scintillator,
the axis of the scintillator strip is perpendicular to the Z direction. Each
layer of the endcap MUD consists of 8 trapezoidal modules. For both Bakelite-
RPC and plastic scintillator, the module has 60 strips in R$\phi$ direction,
and 49 to 43 strips in R direction, due to the increase of the inner radius.

Figure 3.92: Schematic of the MUD design. (a) Half-section view of the MUD,
and partial enlarged view of the sandwich placement of the Bakelite-RPC,
plastic scintillator, and iron yoke. (b) Cutaway view of the MUD and the
setting of the main structural parameters. Figure 3.93: Module layout of the
MUD design. (a) Bakelite-RPC in barrel MUD. (b) Scintillator in barrel MUD.
(c) Bakelite-RPC and scintillator in endcap MUD

##### Neutron Shield and Cylindrical Yoke Component

Previous studies by Belle II indicated that the detector system was affected
by the neutron background generated by the GeV level electrons and positrons
that escape from the beam background [433]. To suppress the effect of the
neutron background, the outer face of the endcap MUD is covered by a 15 cm
neutron shielding layer, as shown in Fig. 3.92. The outer layer of the neutron
shielding is 5 cm lead, and the inner layer is 10 cm boron-doped polyethylene
(10%wt of nat-boron). Lead can moderate fast neutrons to an energy of
approximately 1 MeV, and boron-doped polyethylene can moderate neutrons to the
thermal neutron level. Neutrons with energies less than 1 eV have a large
probability of being absorbed by the boron atoms. A Geant4 simulation
demonstrated that the 15 cm-thick composite neutron shielding could decrease
the MUD hits by approximately 90% for neutrons with a kinetic energy less than
1 MeV.

A cylindrical yoke component is arranged between the beamline and endcap MUD
detector array, which is designed to make the magnet field uniform in the STCF
detector system. The thickness of this cylindrical yoke is approximately
$40\sim 45$ cm. Geant4 simulations indicate that the yoke provides background
suppression capabilities similar to those of composite shielding.

##### MUD Optimization

The thickness of the iron yoke and the number of detector layers are optimized
via a simulation study, and the detailed parameters are summarized in Table
3.19. Fig. 3.94 illustrates the muon detection efficiency curves for different
detector layer settings and a yoke with a thickness of 51 cm. In the
simulation, 9 to 11 layers are applied and evaluated. The result indicates
that 10 or 11 detector layers can produce a higher and smoother muon detection
efficiency. Considering the detector complexity and manufacturing costs, the
MUD baseline design incorporates 10 detector layers. It should be noted that
in the muon detection efficiency curves, $\mu/\pi$ suppression powers of both
33 and 100 are applied, while the former is sufficient for most physics
processes containing muons at the STCF.

Table 3.19: The structure parameters of the conceptual baseline design of the MUD. Rin and Rout are the inner and outer radius of the barrel MUD, respectively, including the 15 cm-thick iron plate shielding outside the detector system. Re is the inner radius of the endcap MUD. LBarrel and TEndcap are the length of the barrel and endcap MUD in the z-direction, respectively. The size of neutron shielding layer is not included. Parameter |  Baseline design
---|---
Rin [cm] | 185
Rout [cm] | 291
Re [cm] | 85
LBarrel [cm] | 480
TEndcap [cm] | 107
Segmentation in $\phi$ | 8
Number of detector layers | 10
Iron yoke thickness [cm] | 4/4/4.5/4.5/6/6/6/8/8 cm
($\lambda$=16.77 cm) |  Total: 51 cm, 3.04$\lambda$
Solid angle |  79.2%$\times$4$\pi$ in barrel
|  14.8%$\times$4$\pi$ in endcap
|  94%$\times$4$\pi$ in total
Total area [m2] |  Barrel $\sim$717
|  Endcap $\sim$520
|  Total $\sim$1237
Figure 3.94: The muon detection efficiency curve from the Geant4 simulation.
Efficiencies are compared with different detector layer settings. The results
for two scenarios of muon/pion suppression power, 33 and 100, are shown.

The arrangement of the Bakelite-RPC and plastic scintillator in the ten layers
affects the performance of the MUD. On one hand, the plastic scintillator has
higher robustness and higher detection efficiency for high-momentum muon.
However, the Geant4 simulation indicates that the Bakelite-RPC exhibits better
performance in detecting low-momentum muons in the high-background region of
the MUD. Fig. 3.95 shows the Geant4-simulated muon detection efficiency as a
function of momentum for different MUD layouts at the full STCF luminosity.
The MUD designs with two-, three-, or four-layer Bakelite-RPCs exhibit similar
$\mu/\pi$ separation power under the current luminosity and background level.
For the design with the two-layer Bakelite-RPC, a high count rate and
significant interference may occur. in the 3rd (plastic scintillator) layer
due to the potential fluctuations in the background level or the future
upgrades of the STCF. As a result, the hybrid MUD design with the three-layer
Bakelite-RPC and a seven-layer plastic scintillator is considered the optimal
choice.

Figure 3.95: The muon detection efficiency curves with different combinations
of Bakelite-RPC and plastic scintillator in the MUD design along the direction
of $\theta=90^{\circ}$ and $\phi=90^{\circ}$ ($\theta$: polar angle, $\phi$:
azimuth angle) including the background.

The granularity is determined by the readout strip pitch of the Bakelite-RPC
and the size of the plastic scintillator strips. Physical simulations of the
measurement precision for reconstructed muons indicate that a spatial
resolution of 1–2 cm is required in the MUD, equivalent to a detector
granularity of 3.5 - 7 cm. Fig. 3.96 presents simulated muon detection
efficiency curves with different granularities, indicating similar particle
detection performances. As a smaller granularity implies additional electronic
channels, both the readout strip pitch of the Bakelite-RPC and the width of
the plastic scintillator strips are chosen to be 4 cm.

Figure 3.96: Geant4-simulated muon detection efficiency with different
granularities along the zenith direction.

####  3.9.3 Expected Performance

To evaluate the expected performance of the MUD, Geant4-based full simulations
are studied. The identification efficiency of muons and neutral hadrons is
obtained using boosted decision tree (BDT) algorithms. The details of BDT
algorithms can be found in Ref. [444]. In the MUD, both the Bakelite-RPC and
the plastic scintillator have very high sensitivity to charged muons and
pions, and the required spatial resolution is within 2 cm, which can be
ensured by the 4 cm detector granularity.

##### Muon Identification Efficiency

Fig. 3.97 shows the probability of a muon arriving at the MUD as a function of
the muon momentum. In the simulation, the bin width is 50 MeV/c. The result
indicates that a muon with momentum between 400 and 450 MeV/c only has a
probability of 0.68% of arriving at the MUD. When the muon momentum reaches
550 MeV/c, almost all of muons can generate signals in the MUD.

Figure 3.97: The probability that a muon arrives at the MUD as a function of
the muon momentum in the zenith direction.

Fig. 3.98 shows the simulated muon detection efficiency with a polar angle of
90 deg and with $\mu/\pi$ suppression power of 33 and 100. A significant
increase in the muon detection efficiency can be observed in the momentum
range of [0.65, 1.5] GeV/c owing to a thicker yoke and an optimized detector
setting. This result indicates that the muon detection efficiency curve of the
baseline design is smoother than that of the BESIII-like MUD geometry. In the
low momentum range [0.4-0.6] GeV/c, the STCF MUD design exhibits a performance
similar to that of the BESIII geometry, ensuring an acceptable muon detection
efficiency. Fig. 3.99 shows the muon identification efficiency of the baseline
design, with the particle momentum in [0, 2.5] GeV/c and polar angle in [20∘,
160∘] considering a pion rejection rate of 97% and background influence.

Figure 3.98: The muon detection efficiency curve from the Geant4 simulation,
with a polar angle of 90 deg. Results for two scenarios of muon/pion
suppression power, 33 and 100, are also shown.

Figure 3.99: 2D map of the muon identification efficiency as a function of the
momentum and the $\theta$ angle from Geant4 simulation. The $\mu/\pi$
suppression power is assumed to be 33.

##### Neutral Hadron Detection and Identification

At the STCF, the MUD is set as an auxiliary neutral hadron detector to
complement the EMC. In this baseline MUD design, the 3-layer Bakelite-RPC acts
as a filter, preventing too many secondary gamma and neutron hits from being
generated by background interference. The Geant4 simulation illustrates that
approximately 40% of the neutrons and $K_{L}$ deposit a very small amount of
energy, less than 40 MeV, in the EMC. Thus, the MUD is responsible for
detecting them. Table 3.20 shows the Geant4 simulated cluster size of neutral
hadrons in the 7 layers of plastic scintillator detectors, and Fig. 3.100
presents the neutral hadron detection efficiency curves with different fake
rates. When a neutral hadron cannot be detected by EMC directly, the MUD has a
quite high efficiency in terms of detection and identification of the hadron,
demonstrating the excellent identification power of the MUD for neutral
hadrons.

Table 3.20: The Geant4 simulated neutron and $K_{L}$ cluster parameters in plastic scintillator detector layers. |  Neutron Average cluster size in scintillators |  Probability of cluster size $\geq$2 |  $K_{L}$ Average cluster size in scintillators |  Probability of cluster size $\geq$2
---|---|---|---|---
200 MeV/c | 2.42 | 5% | 4.42 | 32%
400 MeV/c | 4.07 | 31% | 6.48 | 50%
600 MeV/c | 5.57 | 49% | 7.88 | 68%
800 MeV/c | 7.23 | 66% | 9.20 | 74%
1000 MeV/c | 8.31 | 74% | 8.96 | 76%
1200 MeV/c | 9.03 | 79% | 11.18 | 84%
Figure 3.100: The detection efficiency curves of various neutral hadrons in
the MUD (notice: all of these neutral hadrons deposit less than 40 MeV energy
in the EMC).

##### Background Simulation

Table 3.21 shows the background count rate in the barrel MUD, calculated based
on the STCF full Geant4 simulations. The background estimation demonstrates
that the rate capabilities of both the barrel and endcap MUD detectors can
meet the requirements. For good neutral hadron detection performance, the
usage of a plastic scintillator in the MUD is necessary. The simulation result
indicates that with the compound detector design of the MUD, the first layer
of the Bakelite-RPC and the first layer of the plastic scintillator have
background count rates with the same order of magnitude, ensuring minimal
background interference over the whole MUD detector volume. In this case, a
higher accuracy of identification for both muons/pions and neutral hadrons can
be obtained. The background level in the endcap MUD is almost 2 to 3 times
that in the barrel MUD, indicating the necessity of a background shield on the
outer surface of the endcap MUD.

Table 3.21: The Geant4 simulated barrel MUD background count rate. Detector type | Bakelite-RPC | Plastic scintillator
---|---|---
Detector layer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
Simulated background | 9.2 | 3.54 | 1.42 | 4.25 | 6.50 | 2.80 | 1.77 | 0.76 | 0.39 | 0.36
count rate in the barrel
(Hz/cm2)

As shown in Tables 3.6 and 3.7, the highest TID and NIEL damage values in the
MUD are 0.37 Gy/y and $2.79\times 10^{12}$ n/y, respectively. Good working
conditions can be maintained in the Bakelite-RPC by flushing the working gas.
Other studies indicate that the plastic scintillator can tolerate more than
1000 Gy [445, 446], indicating that the MUD detector system can work well
under background radiation for decades.

##### Readout Design

In the MUD conceptual design, a 3-layer Bakelite-RPC and 7-layer plastic
scintillator are used. The plastic scintillator strips in the barrel are
double-ended readouts, and those in the endcap are single-ended readouts. The
numbers of readout channels in the MUD are estimated in Table 3.22, with a
total number of readout channels of 16000 for the Bakelite-RPC and 25280 for
the plastic scintillator, considering a 4 cm granularity in the detector.

In the MUD, the signal position information can be obtained by the number of
channels, so it is only necessary to record the time information of signals
whose amplitude exceeds the threshold for particle discrimination. For the
Bakelite-RPC in avalanche mode, the front-end electronics are required to
achieve an effective gain of 10-fold and a pulse time width of 50 ns.
Considering that the count rate of the MUD is not high, an ordinary charge-
sensitive amplifier and integral shaping circuit can satisfy the requirements.
For the plastic scintillator, a SiPM is used as an electron multiplier. With 5
p.e. thresholds, the noise rate can be controlled within 1 kHz, and the
measurement efficiency of MIP could exceed 99%. This can meet our needs.
Additionally, in the barrel-MUD, a double-ended readout is required to
determine the hit position, which requires a time resolution of approximately
0.5 ns. Using the waveform sampling method, a 0.25 ns time resolution can be
achieved, and we are still studying a lower-cost implementation for the
barrel-MUD.

Table 3.22: The estimated readout channel requirement in the MUD conceptual design. |  Detector |  |  Barrel |  MUD |  |  |  Endcap |  MUD |
---|---|---|---|---|---|---|---|---|---
| layer | Half- | Half- | Channel | Channel | Inner | Outer | Channel | Channel
|  | length | length | number | number | radius | radius | number | number
|  | in X | in Z | in X | in Z | (cm) | (cm) | in X | in Z
|  | (cm) | (cm) |  |  |  |  |  |
Bakelite- | 1 | 76.6 | 240 | 1535 | 1920 | 94 | 290 | 960 | 784
RPC | 2 | 79.9 | 240 | 1600 | 1920 | 94 | 290 | 960 | 784
| 3 | 83.3 | 240 | 1670 | 1920 | 98 | 290 | 960 | 768
Plastic | 4 | 86.8 | 240 | 0 | 1920 | 98 | 290 | 960 | 768
scintillator | 5 | 90.3 | 240 | 0 | 1920 | 102 | 290 | 960 | 752
| 6 | 94.4 | 240 | 0 | 1920 | 102 | 290 | 960 | 752
| 7 | 98.6 | 240 | 0 | 1920 | 106 | 290 | 960 | 736
| 8 | 102.7 | 240 | 0 | 1920 | 110 | 290 | 960 | 720
| 9 | 107.7 | 240 | 0 | 1920 | 114 | 290 | 960 | 704
| 10 | 112.7 | 240 | 0 | 1920 | 118 | 290 | 960 | 688

According to the background simulation results, the highest count rate per
channel in the barrel MUD appears in the first layer of the Bakelite-RPC, with
an average count rate of 4 Hz/cm2. The corresponding Bakelite-RPC readout
strip has a size of 1.1 m$~{}\times~{}$ 4 cm, leading to the highest count
rate of 1.76 kHz. The highest count rate per channel in the endcap MUD is in
the first layer of the plastic scintillator close to the MDI, which is
approximately 102 Hz/cm2. With the longest scintillator strip (2.4
m$~{}\times~{}$4 cm), the highest count rate per channel is calculated to be
98 kHz.

In the reconstruction of tracks and clusters in MUDs, the position information
of hits can be reconstructed by the number of readout channels or strips;
thus, only the hit-time information should be transported from the detector to
the data storage system, corresponding to 4 bytes/signal (16 bits for time
information, 12 bits for the channel number, 4 bits for quality). Considering
the background level of the MUD and the 300 ns time window, the data stream
size is approximately 105 MB/s for the MUD system.

####  3.9.4 Conclusion and Outlook

The conceptual baseline design of the MUD is a combination of Bakelite-based
RPC and plastic scintillator detectors. This design can improve the neutral
hadron identification efficiency with the proper $\mu/\pi$ separation
capabilities. Detailed detector technologies and further optimization will be
studied in the future, such as the optimization of the muon/pion
identification algorithm, the detection and identification of neutral hadrons,
and R&D of MUD detectors.

###  3.10 Solenoid

The STCF detector magnet is a superconducting solenoid coil which is
surrounded by iron yoke to provide an axial magnetic field of 1.0 Tesla over
the tracking volume. Particle detectors within this volume will measure the
trajectories of charged tracks emerging from the collisions. Particle momentum
is determined from the measured curvature of these tracks in the field.

The main parameters of the STCF detector superconducting magnet are listed in
Table 3.23. Its room temperature bore diameter is approximately 2.98 m. The
conceptual design of the magnet, including the design of the magnetic field,
solenoid coil, cryogenics, quench protection, power supply and the iron Yoke
are briefly described in this section.

Table 3.23: Main parameters of the STCF detector superconducting magnet. Cryostat |
---|---
Inner radius | 1.450 m
Outer radius | 1.850 m
Length | 4.760 m
Coil |
Mean radius | 1.565 m
Length | 4.000 m
Conductor dimension |  4.67$\times$15.0 mm2
Electrical parameters |
Central field | 1.0 T
Nominal current | 3820 A
Inductance | 1.68 H
Stored energy | 12.3 MJ
Cold mass | 4.6 ton
Radiation thickness |  1.9 X0
Cool down time from room temperature |  $\leq$7 days
Quench recovery time |  $\leq$7 hours

####  3.10.1 Magnetic Field Design

The STCF detector magnet will comprise the design concepts similar to TOPAZ
magnet in Tristan and CMS magnet in LHC [427, 447, 448]. The magnet system
consists of the superconducting coil and the iron yoke with a barrel yoke and
two end-cap yokes. The superconducting coil is designed as a single layer
solenoid wound on the inner surface of an aluminum cylinder. It will run in an
operating current 3820 A which corresponding to 1 T magnetic field at the
interaction point. The geometrical layout of magnet are shown in Fig. 3.101.

Figure 3.101: 2D geometrical layout of the STCF detector magnet, which
consists of a superconducting coil and an iron yoke with a barrel yoke and two
end-cap yokes.

The magnetic field simulation has been calculated in 2D FEA model, with a fine
structure of the barrel Yokes and end-cap Yokes with pole tips at each end
side. The iron yoke act as the absorber plates of the MUD and provide the
magnetic flux return. There are two main field parameters concerned, one is
the uniformity in the tracking volume, and the other is the fringe field along
the beam axis outside the detector.

Fig. 3.102 shows the magnetic field flux of the magnet. The distribution of
the magnetic field along the beam line is shown in Fig. 3.103(a), and the
field uniformity is presented in Fig. 3.103(b). The uniformity in the tracking
volume is approximately 2%. The fringe field remains at 50 Gauss at a distance
of 5.1 m from the IP. It decreases sharply to less than 50 Gauss with the
addition of some iron material to the gap between the barrel yoke and end
yoke.

Figure 3.102: Flux of the magnetic field.

(a)

(b)

Figure 3.103: (a) Bz as a function of Z along the beam axis. (b) The field
uniformity in the tracking area.

####  3.10.2 Solenoid Coil Design

By referring to similar magnets in other HEP laboratories, we decide to adopt
a single layer of coil, indirect cooling by liquid helium, a pure aluminum-
based stabilizer and a NbTi/Cu superconductor in the STCF superconducting
magnet. The overall dimensions of the magnet should be a length of 4.76 m,
with an inner diameter of 2.9 m and an outer diameter of 3.7 m; the coil
effective length is 4.0 m, and the coil mean diameter is 3.13 m.

Assuming the nominal current as _I_ =4000 A, _B 0=$\mu$0nI_, and _B 0_=1 T,
the number of turns in a 1 m long coil should be n $\approx$ 208, and the
width of the cable should be 4.67 mm. In total, 832 turns should be needed.
The energy stored by the solenoid is:

$\displaystyle E=(\frac{1}{2}H\cdot
B)V=\frac{1}{2}\cdot\frac{B^{2}}{\mu_{0}}\cdot S\cdot
l=\frac{1}{2}\cdot\frac{B^{2}}{\mu_{0}}\cdot\frac{\pi D^{2}}{4}\cdot l=12.3MJ$
(3.18)

The inductance can be derived as follows:

$\displaystyle\Phi=B\cdot S\cdot n=B\cdot\frac{\pi D^{2}}{4}\cdot n=6274.5WB$
(3.19)
$\displaystyle\frac{\mathrm{d}\Phi}{\mathrm{d}t}=L\frac{\mathrm{d}I}{\mathrm{d}t}$
(3.20) $\displaystyle L=\frac{\Phi}{I}$ (3.21)

which gives _L_ =1.68 H.

From the limitation of the maximum temperature rise of 70 K after quenching,
the enthalpy difference of the cable material can be obtained, and the height
of the superconductor should be 15 mm.

To address the hoop stress, an aluminum cylinder is necessary; material A5083,
which is good for welding and has high mechanical strength, is used; this
cylinder is the primary structural component of the cold mass, and coolant is
supplied through tubes attached to the outer surface of the restraining hoop
cylinder. This eliminates the large cryogen inventory and thick cryostat
necessary for cooled coils. The conductor is cooled by thermal conduction
through the thickness of the hoop restraint. Two coaxial aluminum cylinders
with close endplates cooled by liquid nitrogen act as the radiation heat
shield.

From calculations, the thickness of this support cylinder should be 18 mm.
After cooling-down and excite, the maximum equivalent stress on the support
cylinder is 23.9 MPa. The equivalent stress distribution in the coil is shown
in the Fig. 3.104, and the peak stress is 58.8 MPa. The total weight of the
cold mass is 4.6 tons, including the cable, the support cylinder, the end
flange and the cooling tube. Figure 3.105 shows the conceptual structure
layout of the solenoid magnet.

Figure 3.104: The equivalent stress distribution in the coil. Figure 3.105:
Conceptual structure layout of the solenoid.

The superconducting conductor is composed of NbTi/Cu (1:1) Rutherford cable
and a high purity ($>$99.99%, RRR$>$500) pure aluminum stabilizer. The
Rutherford cable contains 16 NbTi strands. The Main parameters of the
superconducting conductor are listed in Table 3.24. The cross section of the
superconductor is shown in the Fig. 3.106, the superconducting wire is located
in the center of the aluminum stabilizer. With this configuration, the coil
temperature kept below 70 K after quenching at operating current.

Table 3.24: Main parameters of the superconducting conductor. Rated current |  3820 A
---|---
Critical current at 4.2 k & 2 T |  $\geq$15000 A
Conductor length | 9.15 km
Cable dimension |  4.67 mm $\times$ 15 mm
Rutherford cable parameters |
Number of strands | 16
Cable transposition pitch |  100$\pm$5 mm
Cu:NbTi | 1:1
NbTi filament diameter |  30$\pm$5 $\mu$m
Number of filaments |  $\geq$600
N value@2T |  $\geq$35
Aluminum stabilizer parameters |
RRR@0T,4.2K |  $\geq$500
Yield<EMAIL_ADDRESS>|  $\geq$60MPa
Impurity content |  $\textgreater$1000ppm
Cross-section ratio of aluminum |  $\textgreater$80%
Figure 3.106: Cross-sectional view of the superconductor for the STCF detector
magnet.

The coil windings are wound by the inner winding technique with the aluminum-
alloy cylinder support, which acts as an external supporting mandrel and
removes part of the heat energy induced by quenching. To maintain the
operating temperature of the detector magnet, the cooling tubes for the
circular flow of liquid helium are welded on the outer surface of the
aluminum-alloy cylinder.

The titanium tie rods will be used for the coil suspension system and provide
axial and radial fixation, to ensure the precise and rigid suspension of the
cold mass inside the vacuum vessel. The loads to be supported are the self
weight of the cold mass and the magnetic forces due to the decentering and
misalignment of the coil with respect to the return yoke. The design must also
take into count the contraction of the coil during cooling and its deformation
under magnetic forces, with enough strengths and smallest heat conducting. 8
vertical rods are used to counteract the electromagnetic and cold shrinkage
forces, and the diameter of the rods is designed to be 25 mm.

####  3.10.3 Iron Yoke Design

The iron yoke has three functions. First, it provides a magnetic flux return
path to shield the leaked field. Second, it is used as the absorber material
for the muon detector, which is sandwiched between the multilayer iron plates.
Finally, it is the mechanical support structure of the overall detector.
Therefore, a high permeability material with high mechanical strength is
required for the yoke material to account for the mechanical and magnetic
field performance. Low-carbon steel is chosen for the yoke based on its
magnetic properties. However, this material has relatively low strength. Thus,
a balance between good magnetic properties and moderate strength must be
achieved. The yoke is divided into two main components, one barrel yoke and
two end-cap yokes. A detailed design would include data cables, cooling pipes,
and gas pipes passing through the yoke from the inner detectors. The total
weight of the iron yoke assembly is approximately 800 tons. Fig. 3.107 shows
the iron yoke configuration with the main dimensions.

Figure 3.107: Configuration of the iron yoke with pole tips for the STCF
detector.

The barrel yoke is an octagonal-shaped structure with a length of 4,760 mm.
The outer and inner heights of the octagon are 5,820 mm and 3,760 mm,
respectively. The barrel yoke supports the magnet cryostat. The inner vacuum
vessels of the cryostat host inner detectors. The barrel yoke is subdivided
into 10 layers, with 40 mm gaps between the layers for the muon detector. The
end-cap yoke also consists of 11 layers of steel plates. Used as the end door
of the detector, it is designed to slide apart to provide an opening for
access to the inner detectors. The end-cap muon chambers are mounted in the 4
cm gap between the vertical end-cap yoke disks and are normally inaccessible.
The details can be found in Sec. 3.11.

####  3.10.4 Quench Protection and Power Supply

The protection of the solenoid is based on the classical concept of the
extraction of stored energy by an external resistor. Approximately 12 MJ of
energy is stored in the magnet. Selected voltage signals from the STCF
detector magnet coil and power leads are monitored by a special quench
detection device. If a quench occurs, the power supply is switched off, and a
dump resistor is switched into the electrical circuit; the large stored energy
is extracted mainly by the dump resistor and partially by the coil itself. The
value of the dump resistor limits the maximum voltage across the solenoid
terminals. A 0.1 Ohms dump resistor is mounted in parallel to the breakers,
which are doubled for safety. As the operating current is approximately 3820
A, the maximum voltage is 382 V with respect to ground. The power supply is
designed to operate with 10 V and 4000 A, with a current stability of less
than 10 ppm within 8 hours, a current ripple of less than 10 ppm and an
accuracy of 20 ppm. The repeatability should reach 10 ppm.

####  3.10.5 Magnet Cryogenics

Solenoid cryogenics cooling is based on the thermosiphon cooling method, where
the superconducting coil is indirectly cooled with saturated liquid helium.
The thermosiphon circuit consists of a helium phase separator located in an
elevated position and cooling tubes. A horizontal cryostat is designed,
including a vacuum tank, an inner thermal shield, and an outer thermal shield.
The stainless steel vacuum vessel is a cylinder with a length of 4.76 m. The
thickness of the inner wall, outer wall, and endplates is 6 mm, 16 mm, and 32
mm, respectively. Figure 11.5.1 presents the vacuum vessel stress and
deformation near the endplate, indicating a 41.80 MPa stress and 0.23 mm
strain in the middle of the inner vessel.

Figure 3.108: Stress and deformation of vacuum vessel(2D 1/2 Model).

The service tower is designed on the top section of the barrel iron yoke.
Table 3.25 shows the heat load estimation of the magnet.

Table 3.25: Heat load estimation. Heat Load Components | 77 K | 4.5 K
---|---|---
Caused by the support rods in cryostat | 27 W | 1.0 W
Caused by the radiation in cryostat | 74 W | 3.2 W
Caused by the current leads | —— | 7.9 W + 0.4 g/s
Caused by the radiation in chimney & SP | 10 W | 0.4 W
Caused by the support rods in chimney & SP | 4 W | 0.1 W
Caused by the bayonet and valves in SP | 46 W | 13 W
Caused by the measuring wires | 5 W | 0.8 W
Total | 166 W 26.4 W + 0.4 g/s |
Adopted heat load ($\times 1.5$) | 249 W | 39.6 W + 0.6 g/s

The STCF detector cryogenic system consists of a helium refrigerator, liquid
and gas transfer lines, liquid and gas storage, and a nitrogen system. The
major components include compressors, oil removal systems, cold boxes and
control systems. All the helium supplied by this system, except for normal
leakage and necessary venting, is circulated and reliquefied. Liquid nitrogen
usage includes the cooling of the transfer line thermal shield, the cooling of
the thermal shield and thermal intercepts in the superconducting solenoid
magnet, and the cooling of the high-pressure helium feed stream in the
refrigerator.

###  3.11 Iron Yoke and Mechanical Structure

####  3.11.1 Mechanical Structure of the Iron Yoke

The iron yoke is the base structure of the MUD and the base support of the
subdetector components attached to it. It has two important functions: one is
absorbing all the high-energy particles except muons in the MUD, and the other
is conducting a magnetic field from the superconducting solenoid that serves
as leak shielding. The iron yoke material and structure must be magnetically
permeable and have high mechanical strength. Low carbon steel is selected as
the baseline iron yoke material and is measured piece by piece with strict
requirements for permeability before machining.

The iron yoke consists of a barrel part and an endcap part, both of which have
a multilayer structure. The barrel yoke, as shown in Fig. 3.109(a), has ten
layers with thicknesses of 40, 40, 45, 45, 60, 60, 60, 80, 80, and 150 mm from
the innermost layer to the outermost layer. Every layer has an octagonal
column configuration and is formed by eight pieces of separate iron plates.
The net inner height of the 1st layer is 3.78 m and that of the 10th layer is
5.52 m.

The endcap yoke, as shown in Fig. 3.109(b), consists of eleven layers of iron
plates in an octagonal shape. Every layer is formed by two half-octagonal iron
plates. The thicknesses of the endcap yoke layers are 40, 40, 40, 45, 45, 60,
60, 60, 80, 80, and 150 mm along the beampipe direction. Polar iron is
situated in the center area of the endcap yoke and is separated into two
halves: one half is fixed to the endcap iron, and the other half can be pushed
and pulled during installation and maintenance. An adequate gap between iron
plates is maintained for the installation of cables and pipes.

(a)

(b)

Figure 3.109: A schematic view of the iron yoke in the (a) barrel and (b)
endcap regions.

The total weight of the iron yoke is up to approximately 800 tons. The iron
yoke is subject to a large electrodynamic force when the superconducting
solenoid is in operation. The structure of the iron yoke should be strong
enough to resist this strong force. Welding is avoided in the iron plate
connections to mitigate deformation effects. Bolting is convenient for
position adjustment. The dead zone of the MUD should be minimized when
considering connections.

The general structure specifications of the iron yoke are as follows:

  * •

The center of the iron yoke geometry should be below 3.9 m.

  * •

The final assembly of the iron yoke will be completed in the detector hall,
and the yoke will be transported to and positioned at the positron-electron
collision point.

  * •

The interior areas of the iron yoke should be easily accessible, and the
vacuum conditions should be maintained during maintenance.

  * •

The support structure of the solenoid should guarantee that the magnetic field
is reproducible after detector maintenance. Electric cables should be routed
along magnetic lines to avoid additional stray magnetic fields.

  * •

Enough space should be left for electric cables and media coming in and out of
the iron yoke.

####  3.11.2 Mechanical Movement of the Iron Yoke

The iron yoke assembly stands on a steel base support that includes the main
frame, a guiding frame, an enforcement frame and a lifting jack. The
mechanical support allows the detector to move in both horizontal and vertical
direction. In the final positioning step, the detector is transported
horizontally to the collision point on a guiding rail and raised in the
vertical direction on the hydraulically driven jack system. The position
precision is guaranteed by the straightness of the guiding rail and the
accuracy of the motor controller system. The base support structure should be
strong enough to withstand the load of the whole detector, which may be as
heavy as 800 tons. At the end of the guiding rail, a disc spring is mounted as
a buffer to prevent the detector from going out of range.

The endcap iron yoke can be opened and closed to allow people to enter the
detector to perform maintenance. To make this easy, half of the polar ring
iron in the center is pulled out before the endcap iron opens, and the four
endcap iron yokes move independently and are controlled by servo motors. On
the top of the detector, extra guiding rails are mounted to increase the
position precision and stability of the movement.

####  3.11.3 Detector Hall and Infrastructure

The detector hall is the main place where the whole setup will be assembled
and the detector will be positioned in its final working location. The
requirements of the detector hall are as follows:

  * •

The detector hall dimensions should be be no less than 20 m along the beam
direction, 7 m in height, and 30 m in the transverse beam direction.

  * •

The collision point should be approximately 3.9 m above the ground floor.

  * •

The load capacity of the ground floor should be 400 kN/m2.

  * •

The sum of the floor vibration amplitude should be less than a $\mu$m in the
range of $1\sim 60$ Hz.

  * •

The ceiling crane should have a 50 ton lifting load capacity.

  * •

The main gate should be no less than 5.5 m in width and 6.0 m in height. The
dimensions of the detector component and subsystem that need to be brought
into the hall through the main gate are restricted by the gate size.

Figure 3.110: A cross-sectional view of the detector (upper) and an overall
view of the detector (lower).

###  3.12 Trigger, Clock and Data Acquisition

The c.m. energy region of the STCF spans from 2.0 to 7.0 GeV, and the
corresponding event rate varies with respect to different c.m. energies. The
event rates of different c.m. energies can be divided into two categories:
on-$J/\psi$ peak and off-$J/\psi$ peak. The total cross-sections and event
rates at the on-$J/\psi$ peak, $\sqrt{s}=3.097$ GeV, is approximately one
magnitude larger than that at the off-$J/\psi$ peak due to the large
production cross-section of $J/\psi$. Table 3.26 summarizes the cross-sections
and event rates at $\sqrt{s}=3.097$ GeV and 3.773 GeV, respectively. The
production cross-section of $J/\psi$ is related to the energy spread of the
beams. According to the designed machine parameters of the STCF, which are
described in Sec. 3.2, the beam energy spread is $4.0\times 10^{-4}$,
corresponding to a beam energy spread of $\Delta E_{\rm beam}=$0.6 MeV and a
total energy spread of $\Delta E=\sqrt{2}\cdot\Delta E_{\rm beam}=0.848$ MeV
at $\sqrt{s}=3.097$ GeV. The event rate is calculated from the product of the
cross-section and luminosity, which is supposed to be 75% of the peaking
luminosity at the optimized c.m energy $\sqrt{s}=4.0$ GeV, that is $0.75\times
10^{35}$ cm-2s-1 at $\sqrt{s}=3.097$ GeV. The total rate of physics events is
expected to be approximately $400~{}\rm kHz$ at the on-$J/\psi$ peak and to be
approximately 60 kHz at the off-$J/\psi$ peak.

Table 3.26: Summary of the cross-sections and event rates from physics processes at $\sqrt{s}=3.097$ GeV and $\sqrt{s}=3.773$ GeV.  Physics Process |  Cross-section (nb) |  Rate (Hz)
---|---|---
$\sqrt{s}=3.097$ GeV, $\mathcal{L}=0.75\times 10^{35}$ cm-2s-1, $\Delta
E=0.848$ MeV
$J/\psi$ | 4500 | 337500
$\to e^{+}e^{-}$ |  270 |  20000
$\to\mu^{+}\mu^{-}$ |  270 |  20000
Bhabha $(\theta\in(20^{\circ},160^{\circ})$ | 734 | 55000
$\gamma\gamma$ $(\theta\in(20^{\circ},160^{\circ})$ | 36 | 2700
$\mu^{+}\mu^{-}$ | 11.4 | 900
Hadronic from continuum | 25.6 | 2000
$2\gamma$ process $(\theta\in(20^{\circ},160^{\circ}),E>0.1$ GeV |  $\sim$23.3 | $1740$
Total |  $\sim$5300 |  $\sim$400000
$\sqrt{s}=3.773$ GeV, $\mathcal{L}=1.0\times 10^{35}$cm-2s-1
$\psi(3770)$ | 9 | 900
Bhabha $(\theta\in(20^{\circ},160^{\circ})$ | 517 | 51700
$\gamma\gamma$ $(\theta\in(20^{\circ},160^{\circ})$ | 24.5 | 2450
$\mu^{+}\mu^{-}$ | 7.9 | 790
Hadronic from continuum | 18 | 1800
$2\gamma$ process $(\theta\in(20^{\circ},160^{\circ}),E>0.1$ GeV |  $\sim$25 | $2500$
Total |  $\sim$601 |  $\sim$60100

####  3.12.1 Trigger

##### Trigger System

The expected peak event rate at the STCF of $400~{}\rm kHz$places challenging
requirements on the trigger system. The baseline design of the STCF trigger
system is based on a two-level trigger concept: a hardware-based (Level 1, L1)
trigger and a software-based high-level trigger (HLT), as shown in Fig. 3.111.
The L1 trigger mainly utilizes the information from the MDC and EMC
subdetectors. The MDC provides charged track information (momentum, position,
charge, multiplicity, and so on). The EMC gives energy deposit information and
alternative cluster information (position, energy, size, multiplicity, and so
on). The trigger signal generated by L1 will be send back to each sub-detector
system. The HLT uses infomation from all sub-detector systems. Typically, the
MUD provides the fast reconstructed cluster information (layer number, hit
number, and position). EMC also calculates the cluster shape information and
gets used in HLT. In this level, the reconstructed tracks and clusters will be
marked with a preliminary tab and get identified as various trigger types. The
HLT will be implemented as part of the DAQ system.

Figure 3.111: The schematic of STCF trigger system.

It is worth noting that the $400~{}\rm kHz$ event rate only occurs at the
$J/\psi$ peak. At other c.m. energies, the event rate would be much lower. For
instance, according to Table 3.26, the expected event rate is approximately 60
kHz at $\sqrt{s}=3.773$ GeV ($\psi(3770)$). At the event rate of $400~{}\rm
kHz$ expected on the $J/\psi$ peak, the probability of more than one physics
event occuring within a time window of 200 (500) ns is approximately 8 (18)%.
This poses major challenges to the STCF detector in terms of separating the
physics events close in time. This calls for fast detector response to
minimize the event overlapping probability. The MDC is the part of the STCF
detector that is most susceptible to the high event rate given its rather long
drift time and hence a long integration time window (up to 1 $\mu$s). However,
timing capability of other components of the STCF detector (for example, the
CMOS-ITK and EMC) can be exploited to resolve the overlapping events recorded
by the MDC as described in Sec. 3.5.5. It should be noted that the current
conceptual design of the STCF detector has not been fully optimized to
effectively distinguish close-by events at a $400~{}\rm kHz$ event rate.
Further design studies of both detectors and readout electronics are needed to
fully meet the challenge posed by the very high event rate.

##### Trigger Electronics

As shown in Fig. 3.112, the trigger electronics are organized into several
hierarchies. The first step of trigger processing is finished within the
electronics of each subdetector (i.e., in “trigger logic” in each readout unit
of Fig. 3.112), which contributes to the generation of the “global trigger”
signal. The results (marked as “InfHIT” in Fig. 3.112) are then sent to the
subtrigger unit (STU) for further processing, and the final information is
gathered by the global trigger unit (GTU) for the decision of whether to
generate a global trigger (marked as “TrgG” in Fig. 3.112). Actually, there
may be several layers of STUs, according to the final system scale. Optical
fibers will be used for communication between the RU, STU, and GTU, as this is
suitable for signal transmission over long distances and can isolate the
ground of different modules over a large area. Based on the wavelength
division multiplexing (WDM) technique, bidirectional signal transmission can
be performed over one optical fiber. As for the downlink distribution of TrgG,
TrgG is fanned out through the same optical fiber path for the uplink from the
RU to the STU and finally to the GTU, just backward. Once the FEE receive
TrgG, the “trigger match” function is executed to locate the valid data, which
are then read out to the DAQ. This “trigger match” process would be conducted
in the RU or in FEE, according to the electronics designs of different
subdetectors. The uplink delay from the subdetector electronics to GTU and the
downlink delay backwards contribute to the final trigger latency. Besides, a
proper trigger match window should be selected to perform the “trigger match”
process. According to the trigger latency and match window size, the times
tamp region of valid data can be calculated, and then the trigger match
process is accomplished by searching data within the caches of the subdetector
electronics.

Figure 3.112: Block diagram of the trigger electronics for the STCF.

####  3.12.2 Clock System for the Readout Electronics

The structure of the clock system for the readout electronics in the STCF is
shown in Fig. 3.113. The readout electronics should be synchronized for time
measurement or event building. This is achieved in two steps. First, all the
FEE should be synchronized to a system clock which functions as the global
reference for the time stamping or precise time measurement in all the
subdetector electronics, and this system clock will be imported from the clock
system of the accelerator in STCF; second, the time stamp should be started
(or cleared) at the same time point. For the first step, as shown in Fig.
3.113, the global clock unit (GCU) receives the system clock and then fans it
out to multiple subclock units (SCUs). These SCUs further send the
synchronized clocks to the Common ReadOut Board based on PXI (CROB-PXI)
modules in the DAQ and then finally transmit them to the RUs & FEE of
different subdetector electronics. Considering the large scale of electronics,
optical fibers will also be used to guarantee high-quality clock signal
transmission over long distances.

For the second step (i.e., the synchronous starting of the time stamp), once
the DAQ receives a command from the operator, it transmits this command to the
GTU, as shown in Fig. 3.112. The GTU translates this command and generates a
“Start” signal, and then distributes this signal through the same path for the
global trigger signal in normal working mode. When the FEE receive this
“Start” signal, the counters within all the FEEs are cleared to zero, and then
start counting driven by the aforementioned system clock. The outputs of the
counters are used as the time stamps, which are well synchronized among all
the FEEs. Besides, a periodic checking process will also be implemented: the
GTU sends out global time stamp information which is compared with the local
time stamps within the FEEs. Errors detected in this checking process will be
reported in time, and the local time stamp will be corrected simultaneously.
The time stamp information is added to the data packages from the FEEs, which
will be further used in event building.

Figure 3.113: Block diagram of the clock system for the readout electronics in
the STCF.

####  3.12.3 Data Acquisition System

##### Data Size Requirements

The data size requirements are based on requests from subdetectors, as
summarized in Table 3.27.

Table 3.27: Estimated data size of each detector system. The readout time window is adjusted for each detector system to collect the stored events after receiving the trigger. A 50 ns jitter for the event starting time is assumed. The estimated event size includes both the physics events and the background contribution within the corresponding readout time. Component | Num. of channels | Readout time window | Event size (B) | Total (B/s)
---|---|---|---|---
ITK (Silicon) | 50M | 500 ns | 14300 | 5.72G
ITK ($\mu$RWELL) | 10552 | 500 ns | 17232 | 6.89G
MDC | 11520 |  1 $\mu$s | 20400 | 8.16G
PID (RICH) | 518400 | 500 ns | 15600 | 6.24G
PID (DTOF) | 6912 | 500 ns | 7380 | 2.95G
EMC | 8670 | 500 ns | 15000 | 6.00G
MUD | 41280 | 500 ns | 262 | 105M
Total(Silicon) | 50.6M | – | 72.9k | 29.2G
Total($\mu$RWELL) | 594k | – | 75.9k | 30.4G

##### Design Goal

The data acquisition (DAQ) system performs data processing and system control
in the STCF experiment. The main functionalities of the STCF DAQ system are as
follows:

  * •

Reads out the detector data after the Level-1 (L1) trigger matching from the
front-end electronics (FEE) or the merged L1 triggered data from the FEE
readout unit (RU).

  * •

Implements several steps of the data processing, including event building,
event data compression or information extraction, and high-level trigger (HLT)
computing, before the physics events of interest are ultimately saved to the
storage system.

  * •

Organizes and manages the FEE modules, configures the FEE working parameters,
and controls the working flow of the system.

  * •

Monitors the running status online, including the FEE working status, the
status of the link, etc.

  * •

Decimates and analyzes the event data to assess the working status of the
system when needed.

Of the points mentioned above, the reading out and processing of FEE data is
the most significant functionality of a DAQ system.

In the STCF, as shown in Table 3.27, the total trigger rate is expected to be
approximately $400~{}\rm kHz$, which produces a total data rate of
approximately $30.4~{}\rm GB/s$ when the average event size is $75.9~{}\rm
KB$. Furthermore, the design of the DAQ architecture should consider other
factors, such as the budget, the development time, the difficulty of
development, the scalability, and the maintenance cost in hardware, software
and human resources.

##### Conceptual Hardware Architecture of the DAQ System

The conceptual DAQ system is composed of two layers. One is the FPGA-based
processing layer (FPGA layer, FL), where the FEE data reading, preprocessing
and merging are performed in real time with low time latency by the FPGA. The
other part is the CPU/GPU-based processing layer (software layer, SL), where
the software part of the DAQ, such as event building, data
compressing/information extracting, high-level trigger (HLT) computing, is
running, The FPGA layer is described in Fig. 3.114:

Figure 3.114: Conceptual hardware architecture (FL).

As shown in Fig. 3.114, a data merging stage named readout units (RUs) is used
to collect the data from the FEE, extract the trigger information, send the
trigger information to the trigger system (TS), receive the trigger signals
(from the trigger system) and the commands (from the DAQ system), and forward
them to the FEE. The RUs are connected to the FEE through cables, such as
twisted pairs or coaxial cables, at a typical data rate of 80/160/320 Mbps,
through which a typical merging ratio of 1:32 or 1:64 can be provided.

After the RUs, two other data merging stages (CROB-PXI and CROB-PCIe) are used
to merge the data from the RUs, transmit the commands, and distribute the
clock and trigger signal (optional) to the RUs and FEE. By using GTX/GTH
transceivers in the FPGA, each fiber link in CROB-PXI and CROB-PCIe can
transfer data at a rate up to 10 Gb/s, while each PCIe Gen2$\times$8 interface
can provide a theoretical transmission capability of 32 Gb/s. Additionally,
the FPGAs on CROB-PXI and CROB-PCIe can perform real-time data preprocessing
and data merging in the pipeline, so the entire FL can provide sufficient
transfer bandwidth, processing ability, and scalability for the FEE of
different detectors.

The SL is mainly composed of workstations or servers, and the conceptual
hardware architecture of the SL is shown in Fig. 3.115.

Figure 3.115: Conceptual hardware architecture (SL).

There are 3 main types of server nodes in the SL: the readout servers (ROS),
the event builders (EBs), and the NAS nodes. All the nodes are interconnected
with 10G/25G/40G Ethernet. The ROSs are equipped with CROB-PCIe boards, acting
as the entrance of the uplink streams (such as the data stream, the status
stream) and the output port of the downlink streams (such as the command
stream). The EBs perform high-performance computing (HPC) in terms of data
compression, information extraction, and event building by integrating all
kinds of computing resources, including CPUs, GPUs, and FPGA hardware
accelerators. The NAS provides the necessary storage capacity and bandwidth
for the STCF experiment.

In addition to the server nodes mentioned above, there are some other servers
in the SL. The LOG/DB server (LOG) provides the system database for recording
the system log information, including the system topology, running status,
working parameters, and warning and error messages. The online/control server
(OLC) is the command hub of the whole system and can receive, process, and
forward the commands sent by the remote control server (RCS). It is also an
online information controller that can merge the status stream, extract the
online information for each detector system, and decimate the event data. All
of this online information is processed in the remote online server (ROL) and
the remote event analysis server (REA).

##### Conceptual Architecture of the Firmware and Software

The firmware and the software of the STCF conceptual DAQ system are based on a
generic stream-processing DAQ framework named the D-Matrix. The design
philosophies of the D-Matrix are as follows:

  * •

The workflows of a DAQ system are abstracted into several independent streams,
such as the data stream, the command stream, the command feedback stream, the
status stream, the online information stream, the log stream, and the
emergency message stream, etc.

  * •

Each stream has its own processing map constructed by the cascading of some
standard or custom stream processing nodes named “logic nodes” (LNs). LNs can
be FPGA firmware modules or software processes, work in the application layer
of the OSI model, and can be distributed to “physical nodes (PNs)”, which
means the hardware entities where the LNs run, such as FPGAs or servers. The
distribution of an LN to a PN is based on the factors including the LN type,
the resources and the processing ability that PN can provide and the real
connection map among PNs. With a feasible function abstract, most of the LNs
can be reused in different streams with different working parameters. With the
standard interface and the standard data structure definition, the LNs with
matched parameters can be connected freely.

  * •

For the transport layer interfaces between two PNs, the “multiple point-to-
point” (MPP) model is used, which means that the interfaces based on different
mediums and different protocols are encapsulated to a unified model, as shown
in Fig. 3.116. Under this model, each stream crossing the PNs has a channel
“independent” from other streams, and the interface between PNs seems to be
“transparent” for each stream. In this way, the connection of the LNs for each
stream is independent of the transport layer, the link layer and the physical
layer of the hardware.

Figure 3.116: Multiple point-to-point (MPP) model.

Taking the data stream as an example.

One of the core functionalities of a DAQ system is the event building. In
D-Matrix, this functionality is implemented by the cascading of the “Merge”
nodes, which can merge the data fragments for some continuous small spatio-
temporal ranges into an intact data frame. The process of the event building
can be divided into multiply steps, shown as Figure 3.117. In the CROB-PXI and
CROB-PCIe, a firmware “Merge” node is used severally to aggregate the data
with same trigger number from multiple RUs. In the Readout Server, the data
from multiply CROB-PCIe boards can be packaged in a software “Merge” node and
then be distributed to diverse EBs according to the trigger number by a