# Explore the possibility of advancing climate negotiations on the basis of
regional trade organizations: A study based on RICE-N

Wubo Dai
School of Smart Energy
Shanghai Jiao Tong University
Shanghai, 200240, China
<EMAIL_ADDRESS>

###### Abstract

Climate issues have become more and more important now. Although global
governments have made some progress, we are still facing the truth that the
prospect of international cooperation is not clear at present. Due to the
limitations of the Integrated assessment models (IAMs) model, it is difficult
to simulate the dynamic negotiation process. Therefore, using deep learning to
build a new agents based model (ABM) might can provide new theoretical support
for climate negotiations. Building on the RICE-N model, this work proposed an
approach to climate negotiations based on existing trade groups. Simulation
results show that the scheme has a good prospect.

##  1 Introduction

Climate change has significant impacts on the natural environment and human
society. Besides, the greenhouse gases causing climate change do not respect
national boundaries, their effects can be felt worldwide. Therefore,
collective action is required to address this global issue effectively.
Although we have made some progress such as the Paris Agreement and the recent
COP 27 meets, according to the latest IPCC 6 report [1], we are not doing
enough. The report [1] also notes that international cooperation is a critical
enabler for accelerated climate action. However, the prospect of international
cooperation is not clear at present. According to Nordhaus‘s research [2], the
main reason for the hindrance lies in the behavior of "free-ride", that is,
countries have an incentive to rely on the emissions reductions of others
without taking proportionate domestic abatement.

In order to use AI to provide a solution to this problem, the organizers used
Nordhaus‘s RICE model [3] as the climate and economic dynamics framework,
combined with ABM, created this RICE-N model that included 27 agents and their
negotiation mechanism [4]. Building on the official model, we adopted a form
similar to the customs unions, with added the requirement for mitigating
rates. Simulation results show that the scheme has a good prospect.

##  2 Methodology

Previous researchers have proposed a lot of solutions to the climate
negotiations. The Nordhaus Climate Club [2] is considered to be a very
promising climate negotiation mechanism, so our research is based on this
theory and real-world situations. Figure 1 illustrates the framework of the
default RICE-N model [4] and the model of this work.

Figure 1: Model structure of RICE-N and this work.

### Clubs

The first thing to do is to build clubs, we set a new parameter (an int
number) to represent the state of the group the agents are in at each step,
and allow them to choose their group state freely when a new step begin,
including setting up / joining in / changing or quitting a group. For example,
assume that the grouping state of agents A and B in time step one are 1 and 2,
that means they were in the different group now. If agent A still stay in
group 1 in time step two, then agent B can choose its grouping state to 1,
that means they will stay in the same group in this time step. Besides, B
could choose its grouping state to 0 (do not attend any group), 2 (stay in the
previous group) or 3(create a new group, assume no agent’s state is 3 in last
step).

In Nordhaus’s theory [2], the foundation of the club is a comparable carbon-
pricing mechanisms. Considering that countries cannot reach a consensus on the
carbon pricing mechanism at present, we choose to use the default tariff-
mitigation rate negotiation mechanism here. However, the negotiation will only
be carried out among members of the same group.

### Motivation

The motivation of the club has been described as sanction to non-members and
tariff-free border between members [2]. One of the sanction ways is a
countervailing duty on the carbon content of imports, just like the Carbon
Border Adjustment Mechanism of the EU [5]; However, it might be difficult to
achieve in the model now, so we chose another way Nordhaus mentioned: an extra
tariff on all imports from non-members.

As for tariff-free border between members, after referring to the situation of
some trade organizations, such as: North American Free Trade Area (NAFTA),
China-ASEAN Free Trade Area (CAFTA) [6], we found that their zero tariff
settings are gradually realized, so here we draw on this way, tariff for
members will decrease to zero over time.

### Critical mass

Another important principle in climate clubs is called critical mass, which
means it needs the participation of the major economic players, as they
represent 61% of global gross domestic product and 43% of goods imports [7].
This means we need to set an in initial group state to get these countries in
one club at the beginning. However, the real situation is it is difficult for
them to reach an agreement in one step, considering the complex international
relations.For example, China and the US ‘s ambiguity to the EU’s Carbon Border
Adjustment Mechanism [8].

Based on these situations, we propose a concept: the major economic players do
need participate but will separately at the beginning; and the beginning group
state will be based on existing trade cooperation to make the negotiation
easier. And hopefully, this will finally lead to climate club of global scope.

To simulate this scenario, we ranked 27 agents according to their carbon
emissions and productions, The initial data comes from the previous work of
Tianyu et al [4]. Then we divided agents into high carbon emitting countries
(HC) and low carbon emitting countries (LC). You may see the Supplementary
Mater 1 for the detail calculation. Finally, we have two different initial
group state:

For HCs: we put the top five agents into one group, randomize other agents
into four other groups to simulate the ideal state where HC reach an agreement
at the beginning.

For HC with LC: we put the top five agents into five different groups, put
other agents into them evenly based on the rank to simulate the state
mentioned above.

### Real world situation

There are some other sets to close to real world situation, like for saving
rate and max export, choices are limited based on World Bank global average
data. You may see the Supplementary Mater 2 for the detail explanation.

##  3 Results and Discussion

The temperature rise and total gross output during 100 years in the simulation
under two scenarios are shown in Figure 2. From the figure, we can find that
the temperature rise of the HC with LC group is lower than that of the HCs by
more than 0.8 °C when the gross output has almost no difference.

Figure 2: temperature rise and total gross output.

To find out how this discrepancy aroused, We averaged the mitigating rates of
all agents in each stage, and displayed the data in Figure 3. According to the
Average mitigating rate of all regions, We found that in HCs, average
mitigating rate was lower than HC with LC in some periods, which led to a
higher temperature rise.

Figure 3: average mitigating rates of all agents.

Another thing we found was that according to the final group state, in HC with
LC, agents tended to cluster together at the end than the other scenario. It
also included more high carbon emitting agents.That was closer to the ideal
eventuality of a globally unified climate club. The results are shown in
Figure 4. However, There are still many aspects to explore and improve about
this research.

Figure 4: Group state during final time step.

##  4 Conclusions

In general, based on the Nordhaus’ Climate Club [2] theory and real-world
situation, this work proposed an approach to climate negotiations based on
existing trade groups. Current research suggested that the model can inform
real-world climate negotiations, but the underlying reasons remain to be
discovered.

## Supplementary Material

For the implementation of the above settings, please refer to the relevant
files in the Supplementary Materials.

## Acknowledgments

This work reused the AI4GCC code from MILA and Salesforce.

## References

[1] IPCC, 2023: Summary for Policymakers. In: Climate Change 2023: Synthesis
Report.A Report of the Intergovernmental Panel on Climate Change. Contribution
of Working Groups I, II and III to the Sixth Assessment Report of the
Intergovernmental Panel on Climate Change [Core Writing Team, H. Lee and J.
Romero (eds.)]. IPCC, Geneva, Switzerland.

[2] Nordhaus W. (2015) Climate Clubs: Overcoming Free-Riding in International
Climate Policy. American Economic Review 105(4):1339-70.

[3] Nordhaus W. (2018) Evolution of modeling of the economics of global
warming: changes in the DICE model, 1992–2017. Climatic Change 148(4):623–640.

[4] Tianyu Z, et al. AI for global climate cooperation: Modeling global
climate negotiations, agreements, and long-term cooperation in rice-n, 2022.
https://doi.org/10.48550/arXiv.2208.07004.

[5] Schippers M.L.,Wit W.De. (2022) Proposal for a Carbon Border Adjustment
Mechanism, Global Trade and Customs Journal 17(1):10-18

[6] He L-Y, Huang G. (2020) Tariff Reduction and Environment: Evidence from
CAFTA and Chinese Manufacturing Firms. Sustainability 12(5):2017.

[7] Norris J. G7 pins hopes on ‘climate club’ as the saviour of 1.5C target,
2022. https://chinadialogue.net/en/climate/g7-pins-hopes-on-climate-club-as-
the-saviour-of-1-5c-target.

[8] Eicke L,Weko S,Apergi M,Marian A. (2021) Pulling up the carbon ladder
Decarbonization,dependence,and third-country risks from the European carbon
border adjustment mechanism. Energy Res Social Sci 80:102240


A brief summary of ATAR R&D follows. A more detailed plan is presented in
Appendix D.1.

  * •

After initial sensor characterization and design optimization a PIONEER
specific prototype production should happen by the end of 2023. The
characterization includes studies on LGAD energy resolution and gain
suppression mechanism.

  * •

Building of a first ATAR demonstrator (ATAR0) with a few planes of available
sensor prototypes (BNL strip LGADs, 2.5 cm with 500 $\mu$m pitch). An
electronics board with suitable characteristics needs to be designed and
produced. The prototype would be then tested in a pion/muon beamline either at
TRIUMF or PSI. This prototype may be produced by the end of 2023.

  * •

Identification of a suitable chips for the analog amplification and
digitization by 2024. The effect of a short flex between sensor and chip will
be studied within 2022.

  * •

The support mechanics and thermal load needs to be studied well with mock-up
prototypes and silicon heaters. These details needs to be fully understood by
2025.

  * •

Full production of sensors and readout ASIC, once identified, should take less
than a year given the modest area of the ATAR. Therefore final production and
subsequent assembly can start in 2025.

##  Appendix A  PIENU and PEN

Measurements of $R_{e/\mu}$ and associated exotic searches.

The PIENU experiment has provided the most precise measurement of the
branching ratio $R_{e/\mu}=(1.2344\pm 0.0023_{stat}\pm 0.0019_{sys})\times
10^{-4}$Aguilar-Arevalo  _et al._ (2015a); a further factor two improvement in
precision is anticipated. The $\pi\to e\nu$ branching ratio provides the best
test of electron–muon universality in charged current weak interactions
resulting in the ratio of weak interaction strengths
$\frac{g_{\mu}}{g_{e}}=1.0010\pm 0.0009$Bryman  _et al._ (2021). The PEN
experiment at PSI is aiming at comparable precision to PIENU.

Figure 24: The upper panel shows the positron energy spectrum with the red
line indicating $E_{cut}$. The lower panels show the time distributions for
events below and above $E_{cut}$. The black histograms are data, the red curve
is the $\pi^{+}\to\mu^{+}\to e^{+}$ signal, and the blue line is the
$\pi^{+}\to e^{+}\nu$ signal. The other histograms in various colors are the
background terms related to pile-up, muon DIF, and other effects discussed in
Ref. Aguilar-Arevalo  _et al._ (2015a).

PIENU obtained the branching ratio by first separating events into high- and
low-energy regions at an energy cut value ($E_{cut}$) as illustrated in Fig.
24. The time spectra were fit in each region with the $\pi^{+}\rightarrow
e^{+}\nu$ and $\pi^{+}\rightarrow\mu^{+}\rightarrow e^{+}$ shapes, plus
backgrounds originating from different sources including pion decays in
flight, contamination from old muon decays etc. The raw branching ratio
$R^{raw}_{e/\mu}$ was the ratio of the $\pi^{+}\rightarrow e^{+}\nu$ amplitude
to the $\pi^{+}\rightarrow\mu^{+}\rightarrow e^{+}$ amplitude. Corrections
such as the tail correction for low energy events below the Michel spectrum,
were subsequently applied to obtain the final value.

High precision pion decay experiments also provide a plethora of constraints
on exotic phenomena including heavy neutrinos and dark sector processes.
Extensions of the Standard Model postulate the existence of additional
(sterile) neutrinos Boyarsky  _et al._ (2009); Bryman and Shrock (2019b).
These additional states may contribute to the solution of outstanding puzzles
like the nature of dark matter, early cosmological processes like small scale
structure formation Bertoni  _et al._ (2015), and Mesogenesis Elahi  _et al._
(2021). Massive neutrino states $\nu_{H}$ are sought in the two-body pion
decays $\pi^{+}\rightarrow e^{+}\nu_{H}$ Aguilar-Arevalo  _et al._ (2018) and
$\pi^{+}\rightarrow\mu^{+}\nu_{H}$ Aguilar-Arevalo  _et al._ (2019).
Exploiting large data sets of pion decays and the resulting decay muons,
exotic two-body muon decays like $\mu^{+}\rightarrow e^{+}X$ can be sought
Aguilar-Arevalo  _et al._ (2020a), where X is a massive neutral boson (e.g. an
axion or a Majoron). Similarly, exotic particles have been searched for in
three body decays like $\pi^{+}\rightarrow l^{+}\nu X$ ($l=e^{+},\mu^{+}$)
Aguilar-Arevalo  _et al._ (2021). The PIENU experiment also obtained upper
limits for the rare decays $\pi^{+}\rightarrow e^{+}\nu_{e}\nu\bar{\nu}$ and
$\pi^{+}\rightarrow\mu^{+}\nu_{\mu}\nu\bar{\nu}$ at the $10^{-7}-10^{-6}$
level Aguilar-Arevalo  _et al._ (2020b).

PIONEER with two orders of magnitude more statistics has the potential to
improve the existing limits by at least an order of magnitude. Since the
searches are based on fits to the energy spectra of the visible final state
particles, an improved experiment can bring significant additional advantages
in lowering the limits and in reducing the systematic errors. For example, the
$\pi^{+}\rightarrow e^{+}\nu$ low energy tail represents the main background
for the $\pi\rightarrow e^{+}\nu_{H}$, $\pi^{+}\rightarrow e^{+}\nu X$, and
$\pi^{+}\rightarrow e^{+}\nu_{e}\nu\bar{\nu}$ searches: more precise knowledge
of the tail and its further reduction will significantly improve the upper
limits beyond the statistics. The search for rare and exotic decays involving
muons, like $\pi^{+}\rightarrow\mu^{+}\nu_{H}$, $\pi^{+}\rightarrow\mu^{+}\nu
X$, and $\pi^{+}\rightarrow\mu^{+}\nu_{\mu}\nu\bar{\nu}$ will benefit from an
improved stopping target and faster electronics, which will allow better
separation of muons from pions and thus further improve the sensitivity.

The PEN/PiBeta and PIENU experiments relied on inorganic scintillator
calorimetry. PIENU used a high-resolution ($\sigma=1\%$) crystal calorimeter
consisting of a single crystal NaI(Tl) detector surrounded by an array of 97
pure CsI crystals for shower leakage containment. The PIENU detector is shown
in Fig. 25a and described in Aguilar-Arevalo  _et al._ (2015b). The large
NaI(Tl) crystal was 19$X_{0}$ lengths thick and 19$X_{0}$ in diameter. The
high energy resolution and long radiation-lengths of the Na(Tl) crystal were
essential for reducing the low energy tail. However, the slow decay constant
of NaI(Tl) limited pile-up detection and rejection. The acceptance of the
PIENU detector was relatively small $<20\,\mathrm{\%}$ which resulted in an
important source of systematic uncertainty. The PEN experiment, on the
contrary, adopted a high solid angle geometry (see Fig. 25b). Its key
components were a highly segmented (240 elements) spherical pure CsI crystal
calorimeter covering $\sim 3\pi$ sr of solid angle around the pion stopping
target. The key limitations were related to the imperfect separation of
$\pi\rightarrow\mu\rightarrow e$ and $\pi\rightarrow e\nu$ decays. The primary
culprit was the 12$X_{0}$ thickness of the CsI calorimeter, which produced a
substantial low energy tail for 70 MeV positrons (and photons) extending well
under the $\pi\rightarrow\mu\rightarrow e$ spectrum.

The PIONEER approach using a high resolution, uniform response LXe calorimeter
with fast timing and high solid angle combines the assets of both experiments.

(a)

(b)

Figure 25: (a) Schematic view of the PIENU detector. Plastic scintillators are
shown in dark blue, wire chambers in green, silicon strip trackers in orange
and the calorimeter in light blue and red. (b) Schematic cross section of the
PEN detector, with a view of the CsI crystal calorimeter.

##  Appendix B PiBeta

Pion beta decay measurements

The branching ratio for pion beta decay was most accurately measured by the
PiBeta experiment444The PiBeta and PEN experiments shared much of the same
apparatus. at PSI Počanić  _et al._ (2006); Frlež  _et al._ (2004a); Počanić
_et al._ (2004); Frlež  _et al._ (2004b); Bychkov  _et al._ (2009) to be
$\frac{\Gamma(\pi^{+}\to\pi^{0}e^{+}\nu)}{\Gamma\textrm{(Total)}}=[1.036\pm
0.004\textrm{(stat)}\pm 0.004\textrm{(syst)}\pm 0.003(\pi\to e\nu)]\times
10^{-8}$, where the first uncertainty is statistical, the second systematic,
and the third is the $\pi\to e\nu$ branching ratio uncertainty. Pion beta
decay potentially provides the theoretically cleanest determination of the
magnitude of the CKM matrix element $\left|V_{ud}\right|$. With current input
one obtains $\left|V_{ud}\right|=0.9739(28)_{\textrm{exp}}(1)_{\textrm{th}}$,
where the experimental uncertainty comes almost entirely from the
$\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)$ branching ratio (BRPB). The theory
uncertainty has been reduced from $({\delta}V_{ud})_{\textrm{th}}=0.0005$
Sirlin (1978); Cirigliano  _et al._ (2003); Passera  _et al._ (2011) to
$({\delta}V_{ud})_{\textrm{th}}=0.0001$ via a lattice QCD calculation of the
radiative corrections Feng  _et al._ (2020). The current precision of 0.3 % on
$\left|V_{ud}\right|$ makes $\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)$ not
presently relevant for the CKM unitarity tests because super-allowed nuclear
beta decays provide a nominal precision of 0.03 %. In order to make
$\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)$ important for CKM unitarity tests,
two precision experimental stages can be identified: (1) As advocated in Ref.
Czarnecki  _et al._ (2019), a three-fold improvement in BRPB precision
compared to Ref. Počanić  _et al._ (2004) would allow for a 0.2% determination
of $\left|V_{us}/V_{ud}\right|$ improving on measurement of the following
ratio being currently $R_{V}=\frac{\Gamma\left(\textrm{K}\rightarrow\pi
l\nu(\gamma)\right)}{\Gamma\left(\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)\right)}=1.3367(25)$
, independent of the Fermi constant, short-distance, and structure-dependent
radiative corrections. This would match the precision of the current
extraction of $\left|V_{us}/V_{ud}\right|$ from the axial channels Marciano
(2004)
$R_{A}=\frac{\Gamma\left(\textrm{K}\rightarrow\mu\nu(\gamma)\right)}{\Gamma\left(\pi\rightarrow\mu\nu(\gamma)\right)}=1.9884(115)(42)$,
providing a new competitive constraint on the
$\left|V_{us}\right|$–$\left|V_{ud}\right|$ plane and probing new physics that
might affect vector and axial-vector channels in different ways. The
theoretical case for this approach was recently strengthened by improved
analysis of radiative corrections in $K\to\pi e\nu$ decays Seng  _et al._
(2021a). (2) In the second phase, an order of magnitude improvement in the
BRPB precision will be sought. This would provide the theoretically cleanest
extraction of $\left|V_{ud}\right|$ at the 0.02 % level.

##  Appendix C Alternative LYSO Calorimeter Considerations

A naturally segmented array of tapered LYSO crystals provides an attractive
alternative to our proposed LXe-based calorimeter. We are exploring a geometry
that matches that of the PEN pure CsI detector. The PEN crystals were limited
to 12$X_{0}$ depth, which is insufficient for an ideal $\pi\rightarrow e\nu$
measurement. However, the segmentation and fast response allows for various
trigger patterns and it is well-designed for the pion beta decay phase in the
PiBeta configuration. This detector has an inner radius of 26 cm, and an outer
radius of 48 cm. CsI has a radiation length of 1.86 cm. With the compact ATAR
geometry we are proposing, a sufficient volume exists to insert an inner array
of crystals between the ATAR and the existing PEN CsI array, see Fig. 25b and
Fig. 26a. On paper, LYSO crystals appear to be the ideal choice for such an
array. LYSO is a Cerium doped Lutetium based scintillator whose light output
is comparable to doped NaI(Tl). It has high density ($X_{0}$= 1.14 cm,
$R_{M}$=2.07 cm) and a light yield comparable to the highly luminous NaI(Tl),
but with much faster light signals. Its 420 nm typical scintillation light has
a 40 ns single exponential decay time and the spectrum is well matched to
conventional SiPM photosensors. LYSO is both radiation hard and non-
hygroscopic. To date, the main application for LYSO crystals has been in PET
medical scanners, where small crystals are needed with high light output to
resolve the 511 keV gammas from positron annihilation. The attractive
properties of these crystals suggest that larger arrays could be made for use
in particle physics applications and, indeed, several groups have explored
this possibility with small arrays and somewhat limited success.

Experts in the field, such as Ren-Yuan Zhu from Caltech, have advised our
collaboration on the pros and cons and experiences of other groups, see for
example Zhu (2021). The growth of relatively long LYSO crystals is a fairly
new and expensive R&D effort, not easily justified without a demanding end-use
application. The Mu2e Collaboration built a $5\times 5$ array of $3\times
3\times 20\,$cm3 crystals and subjected the array to test beams at Frascati
and Mainz Atanov  _et al._ (2016). At 100 MeV, the resolution was in the range
of 3–4%, dominated by a 2.5% constant term indicative of non-uniformity in
light transmission and possibly crystal to crystal calibrations and surface
preparation. That performance met the specifications for Mu2e, but they did
not push it further, choosing eventually to use undoped CsI based on an
overall cost analysis.

Figure 26: Possible use of an inner array of tapered LYSO crystals within the
open volume of the existing PEN CsI calorimeter. a) Opened view showing in
blue the array of LYSO crystals that matches one-to-one to the existing
geometry of the PEN crystals shaded in gray. b) An example array ideal for
testing the concept. c) An individual pentagonal crystal, 16$X_{0}$ in depth.
Each such crystal would be read out by a thin array of SiPMs.

Dr. Zhu has investigated crystals from various companies and published
properties that will guide us going forward. An example of a study of a
25$X_{0}$ crystal’s longitudinal transmission and how to improve it is found
in Mao  _et al._ (2012). It is imperative to improve on the uniformity of
light production and transmission along the length of the crystal. Experience
has shown – as it has for CsI – that custom surface preparation on tapered
crystals is also important and can be realized with careful lab bench work. We
aim to investigate the possibilities of using LYSO for PIONEER, but would not
now claim this to be defensible until proper bench tests and manufacturer
quotes are in hand. Figures 26b and c indicated prototype geometries that are
designed to fit inside the PEN calorimeter. We will issue requests to a
variety of companies for quotes to see if these crystal shapes can be made to
meet our specifications. If tests are successful — principally achieving the
needed energy resolution below 3% – then a careful side-by-side comparison of
costs and performance against our leading calorimeter candidate based on LXe
can be made.

##  Appendix D ATAR technical details

As introduced in Sec. III.3, the highly segmented active target (ATAR) is a
key new feature of the proposed PIONEER experiment which will define the
fiducial pion stop region, provide high resolution timing information, and
furnish selective event triggers. Further technical details will be covered by
this Appendix.

###  D.1 ATAR R&D plan

The ATAR is a small project in terms of production (roughly 0.01 m2 of sensor
area) but still requires significant R&D for sensors, electronics,
digitization and mechanics. An envisioned path forward for this project is the
following:

  * •

Sensor characterization and design optimization is the top priority, LGAD
prototypes from BNL and FBK are being studied. A PIONEER-specific prototype
production is expected to happen within 2 years from now at BNL. Introduction
to the LGAD technology is shown in Appendix D.2 and studies on available high
granularity LGAD prototypes are shown in Appendix D.3. To steer the design
effort, TCAD (Silvaco and Sentaurus) simulations are crucial (see Appendix
D.3.1). An important aspect to understand is the energy resolution of LGAD
devices as well as the gain suppression mechanism E. Rivera (2021). A test
beam at the the ion beam line at the University of Washington (CENPA) will be
used to study the response of LGADs to high ionizing particles. This will
tentatively happen in 2022 with available sensor prototypes and analog
amplifier boards.

  * •

Having the amplifier chip several cm away from the LGAD sensor is rather
unconventional and the effect on the response needs to be understood; a first
connection flex prototype was produced and will be thoroughly tested within
2023. Likely a second flex production with the lesson learned will happen in
the same year.

  * •

The building of a first ATAR demonstrator (ATAR0) is foreseen within the end
of 2023 with available sensor prototypes. The project is described in Appendix
D.5.

  * •

Identification of a suitable chip for the analog amplification; the ideal path
would be to find an already existing chip (e.g. FAST2) and characterize it
with LGAD prototypes. In parallel an effort to produce a new chip can be
pursued through external companies (SBIR-like funding). A prototype readout
chip needs to be ready by 2024.

  * •

Identification of a digitizer chip: currently available digitizers are too
expensive for the number of channels in the ATAR. Small companies might be
available to develop a new chip with the needed performance by modifying
existing designs. A suitable digitizer chip needs to be identified/developed
by 2024.

  * •

The support mechanics and thermal transport calculation needs to be studied
well for the success of the ATAR. The support needs to introduce as little
dead material as possible to avoid degradation of the positron energy. A
discussion is ongoing between technicians from UCSC and UW for the design of
the mechanic support and mounting procedure. Thermal load tests can be
conducted with an ATAR mock-up made with Silicon heaters, thermal calculations
are also foreseen. The radiation damage during the $\pi\to e\nu$ phase of the
experiments is low enough that the heat dissipation of the sensors is not a
concern.

###  D.2 Sensor technology

The chosen technology for the ATAR is based on Low Gain Avalanche Detectors
(LGAD) Pellegrini  _et al._ (2014), thin silicon detectors with moderate
internal gain. Due to the internal gain and thin bulk, LGADs have fast rise
time and short full charge collection time. The best estimate at present for
the sensor thickness is around 120 $\mu$m to avoid support structures for the
sensor, which would introduce dead areas and inactive material within the
beam. Using fast electronics is expected to result in a pulse rise time of
about 1 ns for an LGAD of this thickness. Such a sensor would be able to
separate two closely overlapping hits if they arrive more than 1.5 ns apart.
The time resolution on the rising edge should be less than 100 ps for a
minimum ionizing signal, down to much better time resolution for large
$\pi/\mu$ signals.

Current standard LGADs are limited in terms of granularity to the mm scale. To
achieve a 100% active area, several technologies still at prototype level are
being evaluated for PIONEER, such as AC-LGADs Apresyan  _et al._ (2020)
(studies shown in Appendix D.3.1), TI-LGADs Paternoster  _et al._ (2020)
(studies shown in Appendix D.3.2) and DJ-LGAD Ayyoub  _et al._ (2021) (a
prototype run is expected to be finished and tested by Q1 2022).

Preliminary data taken at the Stanford Light source (SSRL) Galloway  _et al._
(2019) show that LGADs can detect low energy X-rays with a reasonable energy
resolution (8% to 15%) thanks to the internal gain. The beamline at SSRL had a
2 ns repetition rate and single pulses were completely separated with 50
$\mu$m thick LGADs.

A dynamic range from MIP (positron) to several MeV (pion/muon) of deposited
charge is expected in the ATAR. Since the event reconstruction relies on
temporal pulse separation, the response to successive MiP and high charge
deposition have to be studied Ryan (2021). Furthermore the effect of gain
suppression for large charge deposition in LGADs has to be taken into account
E. Rivera (2021). To study these effects a test beam will be organized at the
ion beam line of the University of Washington (CENPA) in 2022 to study the
response of the aforementioned sensors to high ionizing events. Furthermore,
laboratory tests will be conducted with an alpha source.

###  D.3 High granularity LGAD ongoing R&D

####  D.3.1 AC-LGADs

Figure 27: Left: prototype BNL AC-LGAD strip sensor with 80 $\mu$m wide strips
and pitch of (left to right) 100, 150, 200 $\mu$m. Right: sensor response
($P_{max}$) as a function of position (perpendicular to the strip) of two
strips with 200 $\mu m$ of pitch H. Sadrozinski (2021). The dashed lines
highlight the position of the two strips in the plot. Data taken at the FNAL
120 GeV proton test beam facility.

AC-LGADs overcome the granularity limitation of traditional LGADs and have
been shown to provide spatial resolution of the order of tens of $\mu$m
Tornago  _et al._ (2021). AC-LGAD design also allows to have a completely
active sensor with no dead regions. Studies were conducted on strip AC-LGAD
prototypes from Brookhaven National Lab (BNL) (Fig. 27, Left). The sensors
have been tested with a laboratory IR laser TCT station Par  and at a Fermilab
(FNAL) test beam H. Sadrozinski (2021). The response of two strips of a 200
$\mu$m pitch BNL AC-LGAD as a function of position can be seen in Fig. 27
(Right). The position resolution of this prototype sensor varies between 5-15
$\mu m$ in the direction perpendicular to the strip. In the next few years
several prototypes will be tested in laboratories and test beams to identify
the right parameter configuration, then a PIONEER-specific production will be
made at Brookhaven.

The envisioned metal size for the 200 $\mu$m pitch strips, as well as other
parameters of interest for the sensor such as the doping profile, needs to be
confirmed after a testing R&D campaign and TCAD simulations. These parameters
have been studied with the TCAD Silvaco Sil  to have a good representation of
the observed sensor performance. Simulations with TCAD software are important
to compare with existing prototype data and to help in optimizing the design,
currently the simulated sensor response show a reasonably good match with FNAL
TB data. Studies made with simulations tools will provide crucial input for
the future PIONEER sensor production.

####  D.3.2 TI-LGADs

Trench Isolated (TI) LGADs are a novel silicon sensor technology that utilizes
a deep narrow trench to electrically isolate neighboring pixels to prevent
breakdown, as opposed to standard LGADs which use a junction termination
extension to prevent breakdown at the pixel edges Paternoster  _et al._
(2020). By utilizing the deep trench isolation technology, the no-gain region
is reduced to a few micrometers, thus achieving a higher fill factor than
regular LGADs. Prototypes TI-LGADs sensors from Fondazione Bruno Kessler (FBK)
Paternoster  _et al._ (2020) were studied at UCSC. TI-LGADs show the standard
response of a conventional LGAD and exhibits a small amount of “cross-talk”.
Furthermore the response of the sensor is constant along the strip. The
maximum values of the pulse shape for the neighbor strips correspond to 3$\%$
of the maximum value of the red pulse showing there is good isolation between
strips. New TI-LGADs productions are envisioned at FBK and other vendors, the
prototypes will be tested in laboratories and test beams to find a suitable
alternative sensor technology for PIONEER.

###  D.4 Electronics and readout chain

To read out the ATAR sensors, two crucial electronic components need to be
identified: an amplifier chip and a digitizer board. The ASIC needs to be fast
enough for the sensor in use; for the signal rise time in the 120 $\mu$m-thick
prototype sensors, a bandwidth of 1 GHz should be sufficient. However, the
high dynamic range (2000) requirement for the ATAR brings major complications
to the readout. Current fast readout chips usually have a dynamic range of $<$
1000, since they are targeted at MIPs-only detection in tracker sub-systems.
One possibility is to develop an amplifier chip with logarithmic response or
dynamic gain switching as well as a high enough bandwidth, currently no such
chip exists with the necessary characteristics. Already available integrated
chips, such as FAST Olave  _et al._ (2021) and FAST2, are being evaluated.
Some new ASIC technologies that are being developed at UCSC in collaboration
with external companies can run with 2.5V maximum signal, this allows for an
increased dynamic range.

Since the amplification chip has to be positioned away from the active region,
the effect of placing a short (5 cm) flex cable between the sensor and the
amplification stage has to be studied. To study this a prototype flex was
produced and the effect on LGAD signals will be studied.

To successfully reconstruct the decay chains, the ATAR is expected to be fully
digitized at each event. To achieve this goal, a high bandwidth digitizer with
sufficient bandwidth and sampling rate have to be identified. The same issue
afflicting the amplifier, the high dynamic range, is also problematic for the
digitization stage. A digitizer that would suit PIONEER’s requirements needs
to be identified, a ready commercial solution would be the best option but the
cost per channel might be prohibitive. For this reason the collaboration is
exploring the possibility to develop a new kind of digitizer specific to this
application.

###  D.5 ATAR0 prototype

A first ATAR demonstrator (ATAR0) is foreseen with available sensor
prototypes: the current BNL AC-LGAD production has 2.5 cm long strips with a
pitch of 500 $\mu$m, which is close to the final 200 $\mu$m 2x2 cm2 ATAR
design (however the sensor thickness is 50 $\mu$m instead of the final design
120 $\mu$m). Since a 50 $\mu$m thick sensor is fabricated on a support wafer
of a few 100s $\mu$m, the devices would need to undergo an etching procedure
to have full active volume, the thinning procedure can be executed at BNL. The
BNL sensor group has experience with wafer lapping and chemical mechanical
planarization (CMP). The sensor would be initially lapped to remove most of
the thickness of the handling thick substrate, followed by CMP for final
polish. The etching rate would be determined on dummy wafers and the process
would be optimized to reach the required final thickness. The prototype would
have a few layers (5-10) with a reduced number of channels to detect the
temporal development of a muon or pion decay. As the layers would need to be
very close to each other, a suitable readout board needs to be developed. The
board might be built with discrete components or using a chip such as FAST2.
The prototype would be then tested in a pion/muon beamline either at TRIUMF or
a PSI. Hopefully such a prototype can be produced by the end of 2023.

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