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††thanks: ORCID: 0000-0003-3623-3335

# A very high energy hadron collider on the Moon

James Beacham<EMAIL_ADDRESS>Duke University, Durham, N.C., United States
Frank Zimmermann<EMAIL_ADDRESS>CERN, Meyrin, Switzerland

###### Abstract

The long-term prospect of building a hadron collider around the circumference
of a great circle of the Moon is sketched. A Circular Collider on the Moon
(CCM) of $\sim$11000 km in circumference could reach a proton-proton center-
of-mass collision energy of 14 PeV — a thousand times higher than the Large
Hadron Collider at CERN — optimistically assuming a dipole magnetic field of
20 T. Several aspects of such a project are presented, including siting,
construction, availability of necessary materials on the Moon, and powering,
as well as a discussion of future studies and further information needed to
determine the more concrete feasibility of each. Machine parameters and vacuum
requirements are explored, and an injection scheme is delineated. Other
unknowns are set down. Due to the strong interest from multiple organizations
in establishing a permanent Moon presence, a CCM could be the (next-to-) next-
to-next-generation discovery machine for high-energy particle physics and a
natural successor to next-generation machines, such as the proposed Future
Circular Collider at CERN or a Super Proton-Proton Collider in China, and
other future machines, such as a Collider in the Sea, in the Gulf of Mexico. A
CCM would serve as an important stepping stone towards a Planck-scale collider
sited in our Solar System.

##  I Introduction

After the discovery of the Higgs boson by the ATLAS and CMS collaborations at
the Large Hadron Collider (LHC) at CERN in 2012 Aad:2012tfa ;
Chatrchyan:2012ufa , high-energy particle physics finds itself with two main
goals for the future. The first is to accomplish a high-precision study of the
Higgs and other Standard Model (SM) particles and parameters. The second is to
attain higher center-of-mass collision energies with hadrons, to explore
unexplored parameter space and open up the prospect of new particle
discoveries. Both of these goals are the foci of the proposed next-generation
circular collider projects such as the Future Circular Collider (FCC)
Abada:2019lih ; Abada:2019zxq ; Benedikt:2018csr  at CERN; the Circular
Electron-Positron Collider (CEPC) and its potential successor, the Super
Proton-Proton Collider (SPPC) CEPC-SPPCStudyGroup:2015csa ; CEPC-
SPPCStudyGroup:2015esa ; CEPCStudyGroup:2018rmc ; CEPCStudyGroup:2018ghi  in
China; or, more exotically, a Collider in the Sea (CitS) floating in the Gulf
of Mexico, as has been proposed by a few U.S.-based collider experts
McIntyre:2017ibd . The FCC and the CEPC/SPPC projects could potentially be
realized sometime in the next few decades, as both initiatives have extensive
interest from the global community, as well as advanced conceptual design
reports (CDRs). The CitS idea could be potentially envisioned on a longer
time-frame, having relatively recently been conceptualized. The existence of
such ideas, whether in the form of more mature CDRs or as conceptual outlines,
indicates the strong interest by the particle physics community in reaching
higher collision energies. During eventual proton-proton collisions, these
machines could reach center-of-mass energies of 80–120 TeV (or 500 TeV in the
case of the CitS), a substantial increase over the current energy of 13 TeV at
the LHC.

The state of particle physics after the Higgs discovery, however, is such that
there are multiple unsolved mysteries of physics, but few (or no) hints as to
the mass scale of new particles or phenomena, that, if discovered, could help
solve these. The SM of particle physics, for all its successes, is known to be
incomplete. For example, it does not contain gravity, does not contain dark
matter, cannot explain dark energy, doesn’t account for the matter /
antimatter asymmetry of the universe, doesn’t account for the values of
neutrino masses, and offers no comprehensive explanation for why its structure
is the way it is. There are myriad excellent theoretical models or classes of
models that provide extensions to the SM to (at least partially) account for
these limitations and these models predict a wide variety of new particles
and/or forces to be discovered, at higher masses than are directly accessible
at current colliders or with small enough cross sections as to have eluded
existing datasets. Additionally, the SM itself makes a large number of
predictions, all of which, thus far, have been confirmed, but many of which
are either currently being tested with greater precision (such as the magnetic
moment of the muon Muong-2:2021vma ) or can only be tested with larger
datasets in the future, e.g., at the High-Luminosity LHC 2015hllh.book…..B  or
future machines like the FCC.

However, the existence of specific theoretical models is not the reason
higher-energy colliders should be built. The broader question to be addressed
by the particle physics community is as follows: At what energy does the
validity of the SM break down, if at all? In principle the SM could be valid
all the way to the Planck energy, $10^{16}$ TeV. Thus, a full and complete
understanding of the SM—and an identification of the point at which it becomes
invalid, thus providing a long-sought window toward new physics to explain the
open questions—will not be possible without a series of collider experiments
that test the SM at successively higher energies and simultaneously explore
the new parameter space searching for deviations from background expectation
or generic anomalies. New particles could appear at any energy up to the
Planck energy, and, as such, the full range of energies up to and including
the Planck scale must be tested. As a result of this, any future collider
experiment already has ample justification for its physics program. The future
of collider physics is exploratory and experimental, irrespective of specific
theory motivation, because the motivations are simple: There are a large
number of open questions to answer, and new particles to answer them could
arise at any energy. The physics cases for an FCC, a CEPC/SPPC, and a CitS are
clear, but stretching beyond those projects requires exploratory experiments
that reach as high a center-of-mass collision energy as possible.

Building a hadron collider much larger than those proposed for the next
generation (of $\sim$80–100 or 1900 km in circumference) on Earth will likely
prove politically and geographically challenging to a prohibitive degree.
While multiple potential circular tunnel trajectories on the order of 10,000
km in length can at least naively be identified on Earth, they each are
subject to significant drawbacks. (See Figure 1.)

Figure 1: Three potential Earth-based sites for a circular collider
approximately the same size as a collider encircling the Moon of $\sim$11000
km in circumference, represented by images of the Moon overlaid on a map of
the surface of the Earth. Each potential Earth-based site for such a large
collider project is accompanied by significant geographical, technological, or
political challenges. Adapted from Ref. openstreetmap  and Ref. wikimoon .

For example, the longer the circular tunnel, the more likely that multiple
access shafts will be located in populated areas on the surface that may
displace local residents or disrupt the local ecology. Additionally, for
potential sites on land — e.g., located entirely within Asia, traveling under
Russia, China, Mongolia, Kazakhstan, India, etc. — a 10,000-km tunnel would
likely traverse multiple types of rock, soil, and underground water sources
and would pass under large mountain ranges (e.g., the Himalayas), leading to
potentially insurmountable tunnel boring challenges, as well as a high
probability of disrupting water sources or other resources used by humans. The
challenges with siting a 10,000-km circular collider entirely within the
Pacific or Atlantic Oceans — in contrast to the CitS, which utilizes a likely
achievable neutral buoyancy in the Gulf of Mexico — should be clear.

Moreover, longer circular colliders on Earth lead to increasingly difficult
technological and geological challenges to ensure the stability of the
experiment. Creating and maintaining a 10,000-km-long vacuum for a proton
beam, while entirely possible, will be costly on Earth, whereas the vacuum on
and under the surface of the Moon is free. Additionally, as the Earth is
highly geologically active, a longer collider is more susceptible to the risk
of earthquakes and volcanic eruptions.

As a result, while a 10,000-km-scale circular collider on Earth is of course
technically possible, it carries with it a substantial number of prominent
issues that would make it less attractive compared to other potential basic
science projects here on Earth.

In contrast, the Moon presents a potentially ideal site for the next great
step forward in collider physics, primarily due to the fact that a return by
humans to the Moon has a high probability of being realized in the next
century. Both NASA and private companies are interested in establishing a
permanent presence on the Moon, and the U.S. Department of Energy has
encouraged the international particle physics community to collaborate in this
endeavor siegrist . This consideration evinces the possibility of a Moon-based
PeV-scale collider.

Indeed, through its Artemis program artemis , launched in 2017, NASA aims at
establishing a sustainable presence on the Moon by 2028. In preparation for
this, Moon deliveries are already starting as early as 2021, in the frame of
the Commercial Lunar Payload Services (CLPS) initiative CPLS . The near-term
goal is to explore the entire surface of the Moon with human and robotic
explorers. This exploration will provide relevant information for optimizing
the placements of future large-scale lunar infrastructures. Potential
materials and structural concepts for second-generation habitat construction
on the Moon are also rather well established already. For example, Ref.
doi:10.1061/0893  discusses a simple structural frame for erection and
concludes that a lunar habitat can be built with a reasonable factor of safety
and using existing technology.

We note that the United Nations Outer Space Treaty of 1976 ottr76  declares
that the Moon and other bodies “shall be free for exploration” and that the
Moon is “not subject to national appropriation by claim of sovereignty, by
means of use or occupations”. Therefore, a Moon-based collider could
potentially be built in the framework of a global effort, involving all, or
most, of the countries on Earth. Such a project might also serve as a natural
stepping stone towards future, larger space-based infrastructures.

In this document, we examine the prospect and challenges of building a hadron
collider around the $\sim$11000-km circumference of a great circle of the
Moon, a Circular Collider on the Moon (CCM). A CCM could be made 100 times
larger than the proposed FCC in the Lake Geneva Basin on Earth and would be
six times larger than a CitS. Optimistically assuming a dipole magnetic field
of 20 T botturasnowmass , a CCM could potentially reach a proton-proton
center-of-mass collision energy of 14 PeV, a thousand times more energetic
than the LHC.

##  II Construction and siting

Two primary considerations for a CCM are its method of construction and its
location on the Moon. The advantages, disadvantages, and costs of constructing
a tunnel a hundred to several hundred meters under the surface, fully
circumnavigating the Moon (“tunnelling”, i.e., using lunar tunnel boring
machines), vs. excavating a shallower trench and then covering it (“cut-and-
cover”) or constructing on the surface, would need to be studied, and an
appropriate placement to be identified. Presented here are initial
investigations as to the pros and cons of methods of construction and
locations for a CCM. For future refinement, using, for example, the Unified
Geological Map of the Moon UGMM  along with further information expected from
NASA’s Artemis program artemis , as an input, the placement on the Moon could
be optimised by applying the Tunnel Optimisation Tool, which was developed in
the frame for the FCC study Cook:2141838 .

###  II.1 Method of construction

Temperature extremes on the Moon present a challenge for a CCM. The dipole
magnets needed to accelerate protons must be superconducting, which requires
low temperatures compared to, e.g., room temperature on the surface of the
Earth. When exposed to the sun, the temperature on the lunar surface can reach
$\sim$127 °C nasamoontemp  ($\sim$400 K), too high to consider any
superconducting magnets. However, during Moon night, the temperature drops to
about $-173$ °C ($\sim$100 K). This is approximately the temperature at which
high-temperature superconductors (HTSs) could operate. This suggests one
possible CCM scenario, Scenario A: Build the collider on the surface, charge
an energy storage system during the lunar day, and operate the collider at
night when the magnets are superconducting. The challenge with this scenario
is that lunar days and nights last 13.5 Earth days each, leading to long
stretches of non-operation. Scenario A has the benefit of avoiding the need to
dig a tunnel, typically a large cost for any collider project.

Scenario A has a significant drawback because it would require a diameter $D$
smaller than twice the Moon radius $2R$ to ensure that the entire tunnel
experiences Moon night at the same time. The fraction of the Moon night
covering the entire collider can be estimated as $\left[\pi-2{\rm
arcsin}(D/(2R))\right]/\pi$, which vanishes for $D=2R$. The need to operate
the CCM during lunar night immediately decreases the circular size, and the
desire to operate for longer than, e.g., a few hours or one Earth-day, further
reduces the size. Such reductions lead to a collider circumference
significantly smaller than 11000 km and, hence, would lead to a smaller
center-of-mass collision energy, reducing the attractiveness of the Moon as a
site.

In addition to the above challenges, Scenario A also leaves the CCM exposed to
not just extreme temperatures, but also to meteoroid strikes, which could
potentially cause substantial damage to surface equipment. The Moon is
bombarded by smaller meteroids regularly, resulting in numerous strong impacts
each year that leave craters from a few centimeters to $\sim$10 m in diameter
spey2016 . (Impacts larger than this are rare.) A CCM constructed under
Scenario A, i.e., on the lunar surface, would need to be adequately shielded
to withstand impacts from small meteroids moving at up to 500 m per second
nasachurnurl . Because other long-term research projects have been discussed
to be located on the lunar surface LCRTNASA , such shielding should in
principle be possible to achieve, or the damage from such strikes mitigated,
though further study would be needed.

The drawbacks related to temperature variations and potential meteroid damage
could be obviated by other scenarios. For example, in Scenario B a CCM could
be constructed by digging and covering a trench a few meters deep (cut-and-
cover). According to measurements from the Apollo 15 and 17 missions
1977NASSP.370..283L , temperature fluctuations due to lunar day-night
temperature cycles are negligible once one reaches $\sim$50 cm below the lunar
surface, as shown in Figure 2.

Figure 2: Temperature, in K, of the lunar subsurface, as measured by the
Apollo 15 and 17 missions, taken directly from Ref. 1977NASSP.370..283L . The
striped regions for depths less than $\sim$70 cm show the variations in
temperature measured throughout a lunar month. At depths exceeding $\sim$50
cm, temperature fluctuations due to lunar day-night cycles are negligible.

However, the temperature of the lunar subsurface, while constant throughout
lunar day and night, is still too high for presently known HTS materials, at
255–256 K at a depth of 1–2 m. Thus, a cooling system will be needed to
maintain the HTS at a temperature of order 100 K and to enable CCM operation
during lunar day and night for any scenario other than Scenario A.
Additionally, it is possible that Scenario B by itself would not provide
adequate shielding to protect against damage from meteoroid strikes, and that
further surface shielding would need to be constructed anyway.

In a third scenario, Scenario C, a CCM tunnel could be bored a few tens to a
few hundred meters under the lunar surface. Such tunnel boring would add
substantial cost and time to the project and would still require a magnet
cooling system, but would definitely prevent damage from (most) meteoroid
strikes. Additionally, there has been much prior discussion of constructing
tunnels for lunar habitats mendell1985 , including the planned development of
lunar tunnel boring machines 1988tamu.rept…..A ; rostami2018 ; tunneltalk
operated remotely from Earth, and of the utilization of existing lunar lava
tubes 2017Icar..282…47B ; melosh2018 , and, thus, Scenario C would present key
opportunities for collaboration with other organizations and initiatives.

###  II.2 Placement and site

The Moon has been measured to be a slightly scalene spheroid garrick2014 , but
for our purposes we model it as a sphere with a radius of 1738 km lunarconst
and thus circumference of 10921 km, the equatorial circumference. More
significant for a CCM is the fact that the lunar surface is rather rough.
Local topographical deviations from an overall spherical shape can be large.
The side of the Moon facing the Earth (the near side) is much smoother than
the far side, where the largest deviations occur, with maximum elevations of
$\sim$10.8 km moonhigh  and minimum elevations of approximately $-9.1$ km
moonlow  relative to a reference sphere. (For reference, the highest mountain
on Earth is Mt. Everest at an elevation of 8.8 km and the deepest part of the
ocean is the Challenger Deep section of the Mariana Trench, at a depth of
$\sim$11 km. However, Earth’s radius is 3.7 times greater than the Moon’s.)

To ensure accessibility for maintenance and repairs, it will be beneficial to
identify a CCM trajectory that avoids large elevation changes as much as
possible. One such trajectory is shown schematically in Figure 3.

Figure 3: Schematic possible trajectory (black line) of a Circular Collider on
the Moon (CCM) that could potentially avoid several major elevation changes,
though not all. In the left image the north pole of the Moon is centered,
while in the right image the south pole is centered. In each image the side of
the Moon that faces the Earth is labeled “Near”. Original topographical images
were constructed with data collected by the Lunar Reconnaissance Orbiter
Camera 2010SSRv..150…81R ; 2016SSRv..200..431H ; 2016SSRv..200..393M ;
2012ISPAr39B4..511S ; LROC:EDR ; 2011JE003926 ; 2010GL043751 .

This trajectory circumnavigates the Moon approximately around the outer edge
seen from the Earth, but slightly displaced toward the Earth. Such a
trajectory appears to potentially avoid several major elevation changes,
although not all. Irrespective of whether a tunnel a few hundred meters
underground is bored (Scenario C) or a cut-and-cover approach is taken
(Scenario B), the construction of a CCM will likely require some tunneling.
Other major features, particularly the large mare (Mare Humboldtianum)
marehumboldt  in the northern lunar hemisphere, will likely require the CCM
beam pipe and tubular shielding structure to be suspended, potentially several
kilometers above the sunken surface. A detailed survey of this and other
potential CCM sites is left for future work.

##  III CCM machine parameters

Since the strong and electromagnetic cross sections decrease as $1/\gamma^{2}$
(where $\gamma$ is the Lorentz factor of the accelerated protons), the
luminosity should increase with the square of the energy. Extrapolating from
the FCC-hh (with a peak luminosity of about $3\times 10^{35}$ cm-2s-1 at
$\sqrt{s}=$ 100 TeV), a 14 PeV collider should aim at the much higher
luminosity of $6\times 10^{39}$ cm-2s-1. The collider luminosity can be
expressed as

$L=\frac{f_{\rm rev}n_{b}N_{b}}{4\pi\sigma_{x}^{\ast}\sigma_{y}^{\ast}}F_{\rm
geom}$ (1)

with
$\sigma_{x}^{\ast}=\sigma_{y}^{\ast}=\sqrt{\beta_{x,y}^{\ast}\varepsilon_{x,y}}$
the root-mean-square (rms) beam size at the interaction point (IP), $n_{b}$
the number of bunches per beam, $N_{b}$ the bunch population, $f_{\rm rev}$
the revolution frequency, and $F_{\rm geom}\approx 1$ a geometric factor
taking into account the so-called hourglass effect (variation of the beta
function across the luminous region), crossing angle, etc. We can rewrite the
luminosity by introducing the beam current $I_{\rm beam}=en_{b}N_{b}f_{\rm
rev}$ and the beam-beam tune shift $\xi$ for round beams colliding head-on,

$\xi=\frac{r_{p}N_{b}}{4\pi\varepsilon\gamma}\;,$ (2)

where $\gamma$ denotes the relativistic Lorentz factor (here $\gamma\approx
7.5\times 10^{6}$ for 7 PeV protons, i.e., a 14 PeV proton collider), and
$r_{p}$ the “classical proton radius” ($r_{p}\approx 1.5\times 10^{-18}$ m).
Equation (1) becomes

$L=\gamma\;\left(\frac{1}{er_{p}}\right)\;\frac{I_{\rm beam}}{\beta^{\ast}}\xi
F_{\rm geom}\;,$ (3)

with $\beta^{\ast}\equiv\beta_{x}^{\ast}=\beta_{y}^{\ast}$.

From (3), a linear increase with energy will be achieved naturally, thanks to
the adiabatic damping of the proton beam’s transverse geometric rms emittance
$\varepsilon$, for a constant normalized emittance ($\gamma\varepsilon$).

Fortunately, since the transverse radiation damping time is short, of order 30
s (compared with 1 day at the LHC), the emittance will shrink quickly until it
is balanced by an external transverse noise excitation that will need to be
applied in order to maintain stable collisions at a still acceptable value of
the beam-beam tune shift PhysRevSTAB.18.101002 .

For the CCM, the transverse damping decrement $\lambda_{d}=U_{0}/(2E_{\rm
beam}n_{\rm IP})$ is about $1.2\times 10^{-3}/n_{\rm IP}$ (200 turns damping
time), where $n_{\rm IP}$ designates the number of interaction points. The
value of the damping decrement is reminiscent of the e+e- collider LEP, where
the following approximate scaling law was established Assmann:453821 :

$\xi^{\rm max}\propto\lambda_{d}^{0.4}\;.$ (4)

From Ref. Assmann:453821 , we can expect a maximum tune shift $\xi$ between
0.05 and 0.08, depending on the number of interaction points. Recent
colliders, e.g., KEKB, have achieved higher tune shifts still. Conservatively
assuming a maximum tune shift of 0.06 yields another factor of 10 in
luminosity, compared with FCC-hh. We then arrive at an unprecedented
luminosity of $2\times 10^{38}$ cm-2s-1, which nevertheless falls short of our
ideal target by a factor $\sim$30\. Higher tune shift or smaller IP beta
functions would further boost the luminosity.

Based on the above considerations, Table 1 presents tentative proton-collider
parameters for the CCM, and compares them with those of the planned FCC-hh and
the HL-LHC. The CCM beam energy follows from $E_{\rm beam}=ceB_{\rm dip}F_{\rm
dip}C/(2\pi)$, where $c$ is the speed of light, $e$ the electron (proton)
charge, $C\approx 11,000$ km the ring circumference, $B_{\rm dip}=20$ T the
dipole field, and $F_{\rm dip}\approx 0.67$ the dipole filling factor, similar
to the LHC’s. Beam current and bunch spacing are kept roughly the same as for
the FCC-hh and the present LHC. Assuming that the CCM will operate at
$\xi=0.06$, the rms beam size at the interaction point (IP) is 120 nm, more
than two times larger than the vertical IP beam size at SuperKEKB.

Parameter | CCM | FCC-hh | HL-LHC
---|---|---|---
Maximum beam energy $E_{\rm beam}$ [TeV] | 7,000 | 50 | 7
Circumference $C$ [km] | 11,000 | 97.8 | 26.7
Arc dipole magnet field $B_{\rm dip}$ [T] | 20 | 16 | 8.3
Beta function at interaction point (IP) $\beta_{x,y}^{\ast}$ [m] | 0.5 | 0.3 | 0.15
Transverse normalized rms emittance $\varepsilon_{n}$ [$\mu$m] | 0.2 | 2.2 | 2.5
Rms interaction-point beam size [$\mu$m] | 0.12 | 3.5 | 7
Beam current [A] | 0.5 | 0.5 | 1.12
Bunches per beam $n_{b}$ | 1,200,000 | 10,400 | 2,760
Bunch spacing [ns] | 25 | 25 | 25
Bunch population $N_{b}$ [$10^{11}$] | 1.0 | 1.0 | 2.2
Energy loss per turn $U_{0}$ [MeV] | $1.7\times 10^{7}$ | 4.67 | 0.007
Synchrotron radiation power $P_{\rm SR}$ [MW] | $8.5\times 10^{6}$ | 4.8 | 0.014
Critical photon energy $E_{\rm cr}$ [keV] | 105,000 | 4.3 | 0.044
Transverse emittance damping time $\tau_{x,y}$ [h] | 0.004 | 1.0 | 25.8
Beam-beam parameter per interaction point, $\xi$ [$10^{-3}$] | 60 | 5.4 | 8.6
Luminosity per interaction point $L$ [$10^{34}$ cm-2s-1] |  $\sim$20,000 |  $\sim$30 | 5 (leveled)
Number of events per bunch crossing (pile-up) |  $\sim$106 |  $\sim$1000 | 135
Maximum integrated luminosity per experiment [ab-1/y] |  $\sim$2000 | 1.0 | 0.35
Table 1: Tentative proton-proton parameters for CCM, compared with FCC-hh and
HL-LHC bordry2018machine .

Quantities of interest are the beam lifetime, the synchrotron radiation, and
the power consumption. The beam lifetime is PhysRevSTAB.18.101002

$\tau_{\rm beam}=\frac{n_{b}N_{b}}{Ln_{IP}\sigma_{\rm tot}}\;,$ (5)

where the total cross section $\sigma_{\rm tot}$ can be approximated as
Menon:2012dr

$\sigma_{\rm tot}\;[{\rm mbarn}]\approx
42.1s^{-0.467}-32.19s^{-0.540}+35.83+0.315{\rm\ln}^{2}\left(\frac{s}{34}\right)\;,$
(6)

and $s$ designates the square of the center-of-mass energy in units of GeV2.
For the collision energy of the CCM we find $\sigma_{\rm tot}\approx 283$
mbarn. With $n_{\rm IP}=2$ IPs, the beam lifetime (5) is only about 18
minutes.

Therefore, we could require rapid top-up injection in order to maintain a
constant beam current. For example, injecting every 100 seconds would keep the
beam current constant to within 10%.

The integrated luminosity can now be estimated under assumptions similar to
those adopted for proposed future colliders at CERN bordry2018machine . With
160 days scheduled for physics per year, and assuming a 70% availability of
the complex, we estimate an integrated luminosity of $\sim$2000 ab-1 per
experiment and per year.

Critical photon energies in the arcs, $(3/2)\hbar c\gamma^{3}/\rho$ with
$\rho\approx F_{\rm dip}C/(2\pi)$, reach the level of 100 MeV. Fortunately, in
the excellent vacuum on the Moon no beam pipe would be needed. With a residual
molecular or atomic density of order $10^{12}$/m3 or less MFS , the vacuum
quality on the Moon surface is at least 100 times better than the vacuum in
the beam pipes of the LHC of $10^{15}$ H2/m3 (Bruning:782076, , Chapter 12).
Therefore, the charged particles of the CCM could circulate without a
dedicated vacuum system, shielding, beam pipe, and pumping system, resulting
in a great cost saving. Open plane dipole magnets would allow the photons to
escape into the tunnel wall or into the Moon sky, depending on the scenario.

##  IV Powering

A prominent concern for the CCM is identifying a power source substantial
enough to both sustain the machine and compensate for energy lost due to
synchrotron radiation. The energy loss per turn increases as $\gamma^{4}$ and
decreases with circumference $C$ (or radius) only inversely linearly, as
$1/C$. It also rises linearly with beam current. Doing the algebra, and
starting from 4.8 MW emitted at the FCC-hh, we arrive at the interesting
number of 8,500 GW or 8.5 TW. This power must be sustained by a distributed
radiofrequency system, or by an alternative acceleration mechanism. A power
source at the level of 10 TW would thus appear to be required. For comparison,
the total energy consumption for the entire Earth in 2019 corresponded to a
source of $\sim$18–20 TW globalpower .

Fortunately, a number of possible powering scenarios for lunar habitats and
other projects on the Moon have already been explored, since a major
consideration of any project proposed for the Moon is power. (See, for
example, Ref. CLIMENT2014352 .) Some combination of these could in principle
be utilized for a CCM.

For example, NASA and the U.S. Department of Energy have begun studies of
fission surface power nasafission ; doefission1 ; doefission2  to be deployed
for small-scale projects with minimal power needs on the Moon mitnuclear .
Since such studies target power outputs in the kW range, these are, however,
unlikely to be useful for a CCM as currently envisioned.

An alternative option would be the construction of full-scale fission reactors
on the Moon like those on Earth. Even if this proved possible, it is unclear
whether the power output could meet the needs of a CCM. As of this writing,
there are 444 operable fission power reactors used for non-military purposes
in the world, with a combined power output of 394 GW iaea . Achieving tens of
TW with existing fission technology will, thus, be potentially challenging.

Fusion power is in principle more promising, but there are challenges
associated with fusion reactors, as well. The target power output of ITER iter
is 500 MW, from 50 MW of injected power, and, thus, a CCM would require a
power output equivalent to $\sim$20k ITER reactors. Clearly fusion power
technology will advance significantly in the next several decades, but it
remains unclear when it could be harnessed to reach the 10s of TW level. As a
result, alternative powering methods for the CCM should be examined.

More promising for a CCM is power from the sun. Due to its lack of atmosphere,
solar power would be plentiful on the Moon. Solar power on the Moon has the
additional benefit that the materials needed for manufacturing photovoltaic
cells are likely already present in the rocks and dust of the Moon (as
discussed in, e.g., Ref. 1367615 ). One possible powering solution for the CCM
could, thus, be a large-scale harnessing of solar power in the form of the
construction of a small patch of a Dyson sphere Dyson1667  around the sun, on
or near the Moon. The total power emitted by the sun is about 400 yottawatt
($4\times 10^{26}$ W) NSFS . Therefore, less than a thirtieth of a part per
trillion of the sun power would be needed to operate the CCM. Indeed,
considering the distance between the Moon and the sun of about 150 million km,
the power required corresponds to $\sim$0.07% of the sun power incident on the
Moon surface. Assuming 100% efficient solar panels, a CCM would thus require
the construction of a solar power array of $\sim$6.7$\times 10^{3}$ km2 on the
lunar surface, an area slightly larger than the size of the U.S. state of
Delaware. Current solar power technology achieves $\sim$20% efficiency on
Earth, and so the total array on the Moon would need to be larger. Solar power
on the Moon will also likely be complicated by the fact that radiation
exposure and the high temperatures during lunar day can severely degrade and
damage solar panels. NASA is currently studying ways to address these
challenges nasasolar .

The other major limitation related to using solar power in the form of a Dyson
patch is that there is no part of the Moon that is constantly exposed to the
sun. A solution to address both the issue with solar panel efficiency for a
CCM and the issue with sun exposure would be to build a Dyson band or belt
around the equator of the Moon to continuously collect sun power. Both a Dyson
patch of $\sim$6.7$\times 10^{3}$ km2 and a Dyson belt of 100 km in width are
shown schematically in Figure 4.

Figure 4: Schematic demonstration of the relative size on the Moon (large gray
circle) of a Dyson patch of $\sim$6.7$\times 10^{3}$ km2 (small blue dot) that
could potentially collect enough solar power to provide the $\sim$10 TW
estimated to be needed by a CCM, assuming the patch could be constantly in
sunlight. The patch is slightly larger than the size of the U.S. state of
Delaware. Because such a spot that is constantly exposed to the sun does not
exist on the Moon, also shown is the size of a Dyson belt of 100 km in width,
circumnavigating the Moon around the lunar equator. Such a Dyson belt would
always have a portion of the solar panels exposed to the sun. The concept is
similar to the Luna Ring concept proposed by the Shimizu Corporation shimizu .

Such a Dyson belt would additionally easily provide ample power to multiple
lunar projects, as well as potentially send power back to Earth. Such an idea
was championed by David Criswell for many decades criswellLSP  and has been
recently studied in detail by the Shimizu Corporation with the Luna Ring
concept shimizu  and by the Japan Aerospace Exploration Agency (JAXA) for the
Space Solar Power Systems (SSPS) SSPS .

##  V Injector

For the design beam lifetime of 18 minutes, a top-up injection at time
intervals of 100 s for each ring would assure that the beam current stays
approximately constant, within $\pm 5\%$ of the average value, translating
into fairly constant luminosity and acceptable charge-imbalances between
colliding bunches. This top-up injection at a rate of 0.02 Hz for the two
beams could be achieved with a rapid cycling “conventional” full energy
booster (though achieving the implied ramp rate with 20 T magnets might be
non-trivial). The full-energy booster injector must have the same size and the
same peak dipole field of 20 T as the collider. The booster can be preceded by
a series of lower-energy and perhaps lower field circular accelerators. Each
synchrotron could increase the beam energy by about a factor of 20, as for
example is done with the PS, SPS, and LHC at CERN. Field is balanced with the
circumference and number of cycles required to fill the subsequent machine. As
cycle times for the lower-energy machines become rather short, injecting into
the first synchrotron of the chain at an energy of around 1 TeV, from a
superconducting proton linac, could be an interesting option. Table 2 presents
parameters of an example configuration sketched in Fig. 5. It is evident that
the complex could be constructed in stages, and both the proton linac and the
first synchrotron be initially used for other applications, while the
downstream accelerators are being constructed.

Incidentally, the high-power linac could also be an excellent proton driver to
produce the muons for a muon collider. (See Ref. muoncollider2020  and
references therein for a recent discussion of potential muon colliders.) If
constructed on the Moon, the collision energy would no longer be limited, by
the neutrino radiation hazard, to a few tens of TeV King:1999gb , as an earth-
based muon machine would be.

Table 2: Parameters for a possible CCM injector chain. Synchrotron | Circumference [km] | Max. Dipole field [T] | Cycle time [s] | Extr. / Inj. Energy
---|---|---|---|---
Top-Up Booster | 11,000 | 20 | 50 | 7 PeV / 350 TeV
Pre-Booster | 2,750 | 4 | 12.5 | 350 TeV / 17.5 TeV
First Synchrotron | 550 | 1 | 2.5 | 17.5 TeV / 0.9 TeV
Superconducting linac | 50 (length) | — | CW | 0.9 TeV / $\sim$0
Figure 5: Sketch of a possible CCM injector chain, with parameters as listed
in Table 2. The “First Synchrotron” circle (light green) is twenty times
larger in circumference than the LHC.

##  VI Dipole magnets

An important consideration for the CCM is the identification and sourcing of
sufficient raw materials to constitute the dipole magnets needed. In contrast
to the more than 1200 dipole magnets of the LHC and the planned $\sim$5000
dipole magnets of the FCC, each about $14$ meters long, the CCM will require
$\sim$5.5$\times 10^{5}$ dipole magnets for the full, 11000-km accelerator
alone, assuming a similar magnet length. (Additional magnets will be needed
for the supporting accelerators in the injector complex; for simplicity we
consider the CCM itself in the following.)

As discussed in Section II.1, the dipole magnets of the CCM will likely be
high-temperature superconductors (HTSs) targeting a magnetic field of at least
$\sim$20 T. Two HTS approaches and technologies present themselves as
possibilities for the CCM.

The first is to use HTSs based on tapes of rare-earth elements (REEs) combined
with barium-copper-oxide, collectively referred to as ReBCO. (See Ref.
vanNugteren:2018xal  for a recent review of ReBCO technology and prospects for
use in magnets for future colliders.) In practice, HTSs for accelerators are
composed of both superconducting material and some amount of stabilizer, such
as copper. In the case of ReBCO-based HTSs, the ReBCO layer is a small
fraction of the entire material, $\sim$2–3%, and the REE component is
$\sim$30–40% of the ReBCO, a comparably small fraction of the total. A
sufficient quantity of usable REEs such as yttrium or gadolinium would need to
be identified for the dipoles of the CCM, presenting a challenge because, as
their name implies, such elements are rare. Moreover, a 1–2 $\mu$m silver
layer might be needed on top of, or underneath, the ReBCO HTS material in
addition to 50–100 $\mu$m copper stabilizer Bonura_2014 .

As a benchmark, we consider a CCM constructed of a series of 14-m dipoles,
each of which consists of 2 tons of conductor total. This corresponds to
$\sim$24 kg of REE needed per dipole, and a corresponding total amount of REE
needed for the CCM of $\sim$1.32$\times 10^{7}$ kg, or $\sim$13200 tons.

However, hybrid magnets could be constructed from some combination of ReBCO-
based HTS as an inner high-field layer and other, more conventional materials,
such as Nb3Sn, envisioned for the FCC-hh, or Nb-Ti, as for the LHC, for the
outer lower-field layers. For example, a 20 T hybrid magnet consisting of
three layers was considered in Ref. Assmann:1284326 . Under the assumption of
CCM dipole magnets consisting of, e.g., 50% Nb3Sn and 50% ReBCO, and given the
benchmark above, this corresponds to $\sim$6600 tons of REE needed.

The total amount of all REEs on Earth is estimated to correspond to 120
million tons globalREE . Sourcing REEs for the CCM on Earth and then
transporting them to the Moon could, in principle, be feasible, though Earth-
to-Moon material transport should likely be avoided or kept to a minimum due
to the cost involved. Sourcing REEs on the Moon, instead, would alleviate the
need for transport. However, currently it is unclear whether REEs are
plentiful enough on the Moon to be collected and used. Recent estimates
suggest that lunar REEs could be abundant, but it remains to be confirmed
whether they would exist in usable amounts for a CCM. (See, e.g., Ref.
resources6030040 .) In principle, however, irrespective of their source,
$\sim$6600 tons of REE could be collected over the decades prior to and during
the construction of the CCM.

Moreover, ancillary material such as copper or silver will need to be sourced,
as mentioned above. Evidence from lunar missions indicates the possible
presence of silver on the Moon, as described in, e.g., Ref. Schultz468 , along
with oxygen, hydrogen, sodium, and other elements, but the question as to
whether such elements are present in quantities sufficient for ReBCO-based
HTSs for the CCM remains open.

The second option would be to deploy magnets that utilize iron-based
superconductor (IBS) ironhts , as is foreseen to be used for the 12–24 T
magnets of the SPPC. IBSs based on iron and pnictides (typically arsenic (As)
and phosphorus (P)) would alleviate the need to source thousands of tons of
REE, instead requiring the sourcing of something on the order of a million
tons of iron, arsenic and phosphorus. The total amount of usable metals and
other elements (including iron and pnictides) on the Moon is the subject of
much study, with current estimates suggesting that accessible iron could be
plentiful crawford2014lunar ; HEGGY2020116274 . Further studies of the lunar
composition will be needed to determine whether sufficient iron and pnictides
for a CCM could be sourced on the Moon.

Magnet R&D for IBS technology is developing Zhang_2021 ; Wang_2019 ;
doi:10.1142/S0217751X19400037 ; Tang2017  and IBS could likely prove an
appealing alternative to ReBCO-based HTS. A rough price estimate for the SPPC
IBS magnets is 200k RMB (or $\sim$28k CHF as of May 2021) per meter, roughly
shared between the cost of the IBS conductor and the mechanical components of
the magnet QingjinXu . Assuming the same cost, the dipole magnets of the CCM
would amount to about 200 billion CHF, not including any possibly required
material transport from Earth to Moon. Such cost estimates will likely be
greatly affected by cooperative mining and manufacturing systems on the Moon
that could serve multiple projects, including the CCM, potentially lowering
the overall magnet expenses.

A more extensive study of the availability of the materials needed and
construction costs for the magnets of the CCM and the supporting injector
complex is left for future work.

##  VII Duration of construction, installation, and commissioning

As discussed in Section II.1, Scenario C — which involves excavating tunnels a
few dozen to a few hundred meters under the lunar surface to avoid temperature
variations, radiation damage to workers and facilities, and meteoroid strikes
— likely presents the best option for the CCM. The completion of the tunneling
complex needed for both the main, $\sim$11000-km tunnel of the CCM and the
additional tunnels needed to house the other accelerators of the injection
complex (as described in Section V) — as well as the shafts from the lunar
surface to the CCM tunnel, auxiliary tunnels, caverns, and alcoves — could
target a seven-to-ten-year schedule. Such a tunneling schedule relies upon the
construction, availability, and operation of a number of lunar tunnel boring
machines (LTBMs) working simultaneously and in parallel and, thus, relies upon
technology mature enough to allow for remote handling.

Construction of manufacturing centers, factories, underground buildings for
support personnel, data centres, communication systems, and various
infrastructure pieces, as well as construction of the dipole magnets and CCM
machine components, could also proceed in parallel with tunnel excavation. As
tunnel excavation would necessarily displace a large amount of rock from the
lunar regolith, such resources could potentially be used in the construction
of the accelerator components or detectors, and could be made available to
other projects on the Moon.

Additional time — perhaps five years — will be needed for installation of the
machine, commissioning, and the construction and installation of the
detectors, which would bring the total time from the beginning of construction
to the beginning of data-taking to about 15 years.

Prior to the beginning of CCM construction, several broader developments must
occur. Reliable systems for transporting humans and some resources between the
Earth and the Moon would need to be robust, regular, and affordable. Remotely-
operated LTBMs must be mature, industry-quality, and available, something that
may be feasible by the 2040s, depending upon several factors rostamipriv .
Detailed studies of the geological composition of the lunar regolith, as well
as surveys of the lunar subsurface, to ensure the accessibility of sufficient
resources to construct all components of the CCM, would need to be performed.
A powering system such as the Dyson belt / Luna Ring solar powering system
discussed in Section IV would need to be constructed; under the assumption
that such a project would begin construction by 2035 at the soonest (according
to a projection by the Shimizu Luna Ring team), it could potentially be able
to provide power to other lunar projects by the 2040s or 2050s. Underground
facilities for longer-term stays by researchers would need to be built and
installed.

Given the multiple technological unknowns and large uncertainties associated
to them, it is challenging to arrive at a concrete estimate as to the timeline
for a project such as the CCM. However, the uncertainties and unknowns
associated to each of the needed technological advancements vary widely in
size and scope. Some of the needed advancements are being currently pursued
and are clearly foreseen for the future, while others are decidedly more
ambitious and the timelines more speculative. For example, in a few decades
from now, 20-T magnet technology can be taken for granted botturasnowmass ,
whereas it is much more challenging to assign a concrete timeline to the
availability of, e.g., remotely-operated LTBMs. The time scale for a CCM is
not defined by accelerator technology (because such development continues and
will continue apace here on Earth, irrespective of any potential utilization
on the Moon), but rather by the advances in the construction of lunar
habitats, lunar mining and production capabilities, and suitable large-scale
solar energy generation.

The NASA Artemis program artemis  aims at establishing a Base Camp on the Moon
surface by the end of the 2020s, and a “Gateway” in lunar orbit. These
elements will support robots and astronauts in explorations and science
missions. In parallel, China and Russia plan the joint construction of an
International Lunar Research Station (ILRS) spectrumilrs , which, similar to
Artemis, will include both a space station in lunar orbit and a Moon base on
the surface. The ILRS is expected to become operational a few years after the
Artemis base, namely from 2036 onwards, and to provide a range of scientific
facilities and equipment for studying lunar topography, geomorphology,
chemistry, geology and internal structure of the Moon ilrsspace . The ILRS
will explore and advance the potential extraction of helium-3 from the Moon’s
surface, and the 3D printing of solar panels at the Moon’s equator. The lunar
solar panels would capture solar energy, that could be transmitted to Earth by
lasers or microwaves, or, more easily, be consumed directly on the Moon
spectrumilrs .

Various encouraging studies and forecasts for the second half of the 21st
century also exist. For example, working groups at the NASA’s Marshall Space
Flight Center (MSFC) developed estimates of the operations and economics of
space activities in the vicinity of the Earth and Moon in the 2050 time frame,
along with a picture for 2100 7119255 . A scenario for the 2050 “cis-lunar
econosphere” identifies In Situ Resource Utilization (ISRU) and on-site, 3D
manufacturing as critical technologies. Other MSFC predictions or assumptions
are that, “Mining operations on the moon’s surface … will be robotic in
nature, with human oversight”, and that a 300-person habitat in the Moon’s
vicinity, “will house personnel to run mining operations, way stations, and
construction of a large habitat” on the Moon itself. A report from the US Air
Force Space Command, published in 2019, predicts that, in a positive scenario,
by 2060, “Multiple nations have [M]oon bases or colonies competing … in
providing key infrastructure for commercial exploitation of the [M]oon and
continued development of manufacturing and facilities across cislunar space”
usaf .

Given these plans, and under the assumption that the already excellent
progress on the necessary base technologies, e.g. lunar mining, lunar
tunneling, in-situ fabrication, and lunar/spatial energy production, continues
as predicted, it is reasonable to estimate that the CCM could begin initial
construction at the earliest in the 2070s or 2080s. It is therefore to be
expected that the CCM might start producing data not before the beginning of
the 22nd century, if not much later.

##  VIII Other considerations and opportunities

There are several important aspects, considerations, and opportunities
associated with and presented by the CCM that are left for future work. The
following is a partial list of these aspects.

  * •

Detectors: As discussed in Section III, the beam lifetime of the CCM is
already very short, at around 18 minutes. This suggests two interaction points
(IPs) and, hence, two detectors. A larger number of IPs would require a more
powerful injector, which is a challenging prospect, given the conditions
discussed. Two IPs and two detectors suggests that the detectors both be
designed in a general-purpose manner, similar to the way ATLAS and CMS were
designed at the LHC. However, detector technology and hardware needed for
operation under the extreme conditions of the CCM (e.g., performing tracking
and triggering when the average number of events per proton bunch crossing is
on the level of 106) would need to be developed. Construction of the detectors
would need to be conducted on the Moon, to avoid costly and potentially
damaging transport from the Earth to the Moon, and could proceed within the
same facilities built for the construction of the CCM accelerator complex.

  * •

Data management and transfer: The collision data produced at the CCM and
collected by the detectors would likely be initially stored at a data centre
located on the Moon itself. Initial reconstruction of the data could take
place at the lunar data centre before being transmitted to multiple data
centres on the Earth for redundant storage and further analysis by physicists,
similar in spirit to the Worldwide LHC Computing Grid wlcg . In the event that
a sizable percentage of the CCM physicists were based on the Moon (see below),
an alternate, Moon-based grid (a Lunar CCM Computing Grid) system could be
employed, e.g., if habitats were constructed within multiple lunar lava tubes.
Data transfer between the Moon and Earth should be relatively straightforward
to accomplish, at high rates, given the advanced state of current deep space
communications research at, e.g., NASA NASASCAN , the ESA ESAcomm , and JAXA
JAXAcomm , and the likely major progress in space communications in the next
50 years.

  * •

Physics program: The physics program for the detectors at the CCM would likely
have three pillars. The first would be a general search program for new
particles and fields, including any deviations from Standard Model (SM)
expectations as well as more specific, model-dependent searches for beyond the
SM phenomena at an unprecedented center-of-mass proton-proton collision energy
of 14 PeV. The second would be precision study of SM predictions and
properties at such high energies. The third pillar of the CCM research program
would be informed by what is observed by preceding collider projects such as
the FCC, the SPPC, or the CitS.

  * •

Heavy ion collisions: The physics program of the CCM could — and of course
should — be extended to include heavy-ion collisions in addition to proton-
proton collisions, at the equivalent centre-of-mass energy. The searches for
new physics in heavy-ion collisions carried out at the LHC lhcions , and
envisioned for the FCC-hh fcchhions , could be expanded into a much higher
energy range.

  * •

Muon collider: As mentioned in Section V, the high-power linac of the CCM
could also be an excellent proton driver to produce the muons for a muon
collider. (See Ref. muoncollider2020  and references therein for a recent
discussion of potential muon colliders.) If constructed on the Moon, the
collision energy would no longer be limited, by the neutrino radiation hazard,
to a few tens of TeV King:1999gb , as an earth-based muon machine would be.

  * •

Detectors as cosmic ray observatory: The detectors of the CCM could in
principle be used as cosmic-ray observatories during commissioning and non-
operation.

  * •

Remote operation vs. on-site intervention: The prospect of thousands of CCM
maintenance staff members and researchers residing permanently on the Moon is
sub-optimal, owing to the likely costs associated to travel between the Earth
and the Moon. Thus, a full examination of the needs of a largely remotely-
operated accelerator and detector complex needs to be conducted. However,
given the complexity of both the CCM accelerator complex and the two detectors
— and the fact that current high-energy physics projects require significant
manual operation and occasional intervention — it’s probable that some number
of physicists, technicians, engineers, and support staff for the CCM will be
stationed on the Moon. In the interests of keeping this number to a minimum,
as mentioned above, a full study of the operational needs of the CCM will be
necessary.

  * •

Lunar Particle and Astrophysics Research Center (LPARC): The construction of
the CCM will require global collaboration similar in spirit to that of the LHC
and FCC at CERN, but much larger in scale. Because of its remote location and
unique circumstances, the CCM could be constructed as one component of an
entire Lunar Particle and Astrophysics Research Center (LPARC). In addition to
the CCM, an LPARC could feature multiple other projects and experiments such
as observational astronomy LCRTNASA , gravitational wave detectors, a very-
long-baseline neutrino detector between Earth and Moon 1992LPI….23.1537W ,
dark matter experiments, precision measurements (in low-gravity conditions),
quantum computing, a quantum technology center, a large data centre (see
above), etc. Many such projects have been proposed over the years and all
could benefit from collaboration and synergy with the CCM.

##  IX Classification of unknowns

As mentioned in previous sections, there are several prominent technological
developments that need to occur before the realistic feasibility of the
construction of the CCM, sometime in the next century, can be determined. Some
of these developments will clearly occur, while others are of a more
speculative nature. Below we list the major developments needed and classify
them as either _inevitable, highly likely, likely, speculative,_ or _highly
speculative_.

  * •

Magnet technology: As discussed in Section VII, dipole magnets of 20 T can be
taken for granted within the next few decades botturasnowmass . Thus, such a
development, necessary for the CCM, can be classified as _inevitable_.

  * •

Transportation: As mentioned, there is strong interest from both public
agencies and private companies in returning to the Moon, in order to establish
bases or commercial operations, and there are multiple projects working toward
this goal. It is possible that such projects will prove too difficult to make
reliable and dependable, but there appears to be a strong enough interest to
sustain such endeavors for the foreseeable future. Thus, reliable
transportation between the Earth and the Moon in the next few decades seems
_highly likely_.

  * •

Robust Moon-to-Earth communication: As discussed in Section VIII, there are
multiple advanced projects ongoing to facilitate and improve deep space
communication. Thus, robust communication between the Moon and Earth,
necessary for CCM operations and data transfer, seems _highly likely_.

  * •

Lunar habitats, mining, and construction capabilities: As discussed in Section
VII, there are several projects underway that are pursuing clear goals for
establishing habitats, conducting geological studies, and facilitating mining
and construction operations on the Moon. Such projects are very ambitious and,
as such, could be subject to delays. Because of this, the establishment, in
the next century, of the lunar habitats, mining, and construction capabilities
needed for the CCM is classified as _likely_.

  * •

Lunar tunnel boring machines: As discussed in Section VII, much work is
currently ongoing in support of applying humanity’s extensive experience with
terrestrial tunnel boring machines to the geology of the Moon. Because such
tunneling technology is well advanced, the eventual usage of LTBMs within the
next 50 years seems _likely_.

  * •

Remotely-operated lunar tunnel boring machines: However, there are major
challenges inherent to operating complex machines such as LTBMs remotely from
the Earth, under the unusual conditions on the Moon (where unexpected
difficulties seem inevitable). As such, the prospect of remotely-operated
lunar tunnel boring machines in the next 50–100 years seems _speculative_.

  * •

Lunar raw materials: As discussed in Section VI, initial studies of the lunar
regolith suggest that sufficient raw materials — particularly iron, silver,
rare-earth elements, and pnictides — could potentially be present. However,
extensive studies can only be conducted once humans (or advanced surveying
robots) return to the Moon. Thus, while the existence of raw materials needed
to construct the HTS magnets of the CCM seems likely, it is more accurate to
currently classify this prospect as _speculative_.

  * •

Solar power on the Moon: As discussed in Section IV, the most likely candidate
for a power source sufficient to power the CCM, on the level of 10 TW, is a
solar panel Dyson belt around the equator of the Moon. The concept has been
discussed for many decades and has been recently put on firmer conceptual and
technological footing by the Shimizu Corporation, with their Luna Ring
proposal shimizu , and also by JAXA, through the development of the Space
Solar Power Systems SSPS , but much further work needs to be done. Given the
highly ambitious nature of this proposal, the prospect of a Dyson belt around
the equator of the Moon in the next 50 years to power (among other
apparatuses) a CCM using 10 TW can be classified as _highly speculative_.
Because such a powering scheme is of the utmost importance for the CCM, and
possibly for humankind in general, this prospect can also be determined as the
highest priority for future research and development.

##  X Conclusions

The construction of a very large hadron collider around the $\sim$11000-km
circumference of a great circle of the Moon — a Circular Collider on the Moon
(CCM) — is an attractive prospect for the (next-to-)next-to-next-generation of
particle physics project, a potential successor to the proposed FCC at CERN,
SPPC in China, or CitS in the Gulf of Mexico. The CCM could achieve an
unprecedented center-of-mass proton-proton collision energy of 14 PeV, a
thousand times more energetic than the LHC, utilizing dipole magnets that
optimistically reach $\sim$20 T botturasnowmass .

The CCM would require $\sim$5.5$\times 10^{5}$ dipole magnets, which could be
either ReBCO-based, requiring $\sim$7–13 k tons of rare-earth elements, or
iron-based, requiring something on the order of a million tons of IBS,
containing iron and pnictides. Many of the raw materials required to construct
the machine, injector complex, detectors, and facilities of the CCM can
potentially be sourced directly on the Moon.

Of the various scenarios for CCM construction discussed, Scenario C is the
most compelling, which involves drilling shafts and excavating a nearly
11000-km tunnel — along with additional tunneling for the injector complex and
auxiliary tunnels — a few dozen to a few hundred meters under the lunar
surface to avoid lunary day-night temperature variations, cosmic radiation
damage, and meteoroid strikes.

One plausible trajectory for the CCM would be to position it as
circumnavigating the Moon approximately around the outer edge seen from the
Earth, slightly displaced toward the Earth. This trajectory appears to avoid
major elevation changes, and will be modified with more sophisticated tunnel-
siting tools in the future.

Due to the extraordinary conditions of such a machine, including an energy
loss per turn of $\sim$107 MeV and a synchrotron radiation power of 8.5 TW, a
CCM powering system that relies upon abundant solar power will be needed. This
could be achieved by constructing a belt of solar panels around the lunar
equator at least 100 km in width, similar to what has been studied by, e.g.,
the Shimizu Corporation with the Luna Ring proposal.

The physics program of the CCM would be focused on exploring the unknown,
searching for new physics beyond the Standard Model (BSM), as the scale of BSM
physics is not concretely predictable and requires a purely exploratory
mindset. The research at the CCM will be conducted by two detectors at the two
interaction points, which could be built in a general-purpose manner, similar
to ATLAS and CMS at the LHC. The detector design and technology required would
be driven by the extreme conditions of the CCM such as an average number of
proton interactions per bunch crossing on the level of $10^{6}$, orders of
magnitude larger than the $\sim$200 at the HL-LHC.

A project such as the CCM will require global collaboration and could be one
component of an entire Lunar Particle and Astrophysics Research Center (LPARC)
hosting multiple experiments and projects.

Several large unknowns exist that will need to be addressed in detail before
the ultimate feasibility of the CCM can be determined. The two most prominent
among these are 1) whether the mineral composition of the lunar regolith
contains sufficient raw materials (particular iron and rare-earth elements) to
facilitate lunar-based construction of the components of the CCM; and 2)
whether a large-scale solar power Dyson belt around the equator of the Moon
can be constructed and operated realistically.

Under the assumption that the already excellent progress made in the
development of industry-quality lunar tunnel boring machines, transport
between Earth and Moon, detailed studies of lunar geology, solar powering on
the Moon, and the construction of underground facilities for humans on the
Moon continues apace during the next few decades, an 11000-km, 14-PeV Circular
Collider on the Moon could, optimistically, start being constructed towards
the end of the 21st century, and might then begin delivering data in the first
half of the 22nd century.

Such a project will be a very large step forward into the unknown, revealing
unparalleled information about the universe, as well as providing vital
experience building large, non-terrestrial structures for humanity. The CCM
will be an important stepping stone toward an ultimate Planck-scale collider,
with a centre-of-mass energy of $\sim$1016 TeV, that would require a minimum
size equal to a tenth of the distance from Earth to Sun Chen:1997ai ;
Zimmermann:2018koi .

##  XI Acknowledgments

We thank Mark Robinson for helpful discussions and guidance about the surface
and temperature profile of the Moon. We also thank Lucio Rossi and Davide
Tommasini for enlightening discussions about high-temperature superconductors
for use in accelerators. We are grateful to Qingjin Xu and Xinchou Lou for
helpful information on the SPPC IBS magnet development program. With a
considerable degree of scepticism, Fritz Caspers has alerted us of the JAXA
study. We further thank Jamal Rostami for illuminating discussions of the
timeline for lunar tunnel boring machines.

This work was supported, in part, by the European Union’s Horizon 2020
Research and Innovation Programme under grant agreement No. 101004730
(I.FAST). J. Beacham acknowledges support from the U.S. Department of Energy’s
Office of Science under grant number DE-SC0010007.

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