contents=  Submitted to the Proceedings of the US Community Study on the
Future of Particle Physics (Snowmass 2021) ,
scale=1,placement=top,opacity=1,color=black,position=3.25in,1.2in

# A Strategic Approach to Advance Magnet Technology for Next Generation
Colliders

Authors (alphabetical)  G. Ambrosio  Fermi National Accelerator Laboratory,
Batavia IL 60510-5011, USA  K. Amm  Brookhaven National Laboratory, Upton, NY
11973-5000, USA  M. Anerella  Brookhaven National Laboratory, Upton, NY
11973-5000, USA  G. Apollinari  Fermi National Accelerator Laboratory, Batavia
IL 60510-5011, USA  D. Arbelaez  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  B. Auchmann  Paul Scherrer Insititue, Villigen,
Switzerland  S. Balachandran  ASC / NHMFL / Florida State University,
Tallahassee, FL 32310, USA  M. Baldini  Fermi National Accelerator Laboratory,
Batavia IL 60510-5011, USA  A. Ballarino  CERN, Geneva, Switzerland  S. Barua
ASC / NHMFL / Florida State University, Tallahassee, FL 32310, USA  E. Barzi
Fermi National Accelerator Laboratory, Batavia IL 60510-5011, USA  A. Baskys
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  C. Bird
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  J. Boerme
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  E. Bosque  ASC
/ NHMFL / Florida State University, Tallahassee, FL 32310, USA  L. Brouwer
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  S. Caspi
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  N. Cheggour
ASC / NHMFL / Florida State University, Tallahassee, FL 32310, USA  G.
Chlachidze  Fermi National Accelerator Laboratory, Batavia IL 60510-5011, USA
L. Cooley  ASC / NHMFL / Florida State University, Tallahassee, FL 32310, USA
D. Davis  ASC / NHMFL / Florida State University, Tallahassee, FL 32310, USA
D. Dietderich  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
J. DiMarco  Fermi National Accelerator Laboratory, Batavia IL 60510-5011, USA
L. English  ASC / NHMFL / Florida State University, Tallahassee, FL 32310, USA
L. Garcia Fajardo  Lawrence Berkeley National Laboratory, Berkeley, CA 94720,
USA  J.L. Rudeiros Fernandez  Lawrence Berkeley National Laboratory, Berkeley,
CA 94720, USA  P. Ferracin  Lawrence Berkeley National Laboratory, Berkeley,
CA 94720, USA  S. Gourlay  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  R. Gupta  Brookhaven National Laboratory, Upton, NY 11973-5000,
USA  A. Hafalia  Lawrence Berkeley National Laboratory, Berkeley, CA 94720,
USA  E. Hellstrom  ASC / NHMFL / Florida State University, Tallahassee, FL
32310, USA  H. Higley  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  I. Hossain  ASC / NHMFL / Florida State University, Tallahassee,
FL 32310, USA  M. Jewell  University of Wisconsin-Eau Claire, Eau Claire, WI
54702-4004  J. Jiang  ASC / NHMFL / Florida State University, Tallahassee, FL
32310, USA  GM. Juchno  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  F. Kametani  ASC / NHMFL / Florida State University, Tallahassee,
FL 32310, USA  V. Kashikhin  Fermi National Accelerator Laboratory, Batavia IL
60510-5011, USA  S. Krave  Fermi National Accelerator Laboratory, Batavia IL
60510-5011, USA  M. Kumar  Brookhaven National Laboratory, Upton, NY
11973-5000, USA  F. Kurian  Brookhaven National Laboratory, Upton, NY
11973-5000, USA  A. Lankford  University of California, Irvine, CA 92697-4575
D. Larbalestier  ASC / NHMFL / Florida State University, Tallahassee, FL
32310, USA  P. Lee  ASC / NHMFL / Florida State University, Tallahassee, FL
32310, USA  G. S. Lee  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  V. Lombardo  Fermi National Accelerator Laboratory, Batavia IL
60510-5011, USA  M. Marchevsky  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  V. Marinozzi  Fermi National Accelerator Laboratory,
Batavia IL 60510-5011, USA  C. Messe  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  J. Minervini  Massachusetts Institute of Technology,
Cambridge, Ma.  C. Myers  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  M. Naus  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  I. Novitski  Fermi National Accelerator Laboratory, Batavia IL
60510-5011, USA  T. Ogitsu  KEK, Tsukuba, Ibaraki, Japan  M. Palmer
Brookhaven National Laboratory, Upton, NY 11973-5000, USA  I. Pong  Lawrence
Berkeley National Laboratory, Berkeley, CA 94720, USA  S. Prestemon  Lawrence
Berkeley National Laboratory, Berkeley, CA 94720, USA  C. Runyan  Brookhaven
National Laboratory, Upton, NY 11973-5000, USA  G.L. Sabbi  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  T. Shen  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  S. Stoynev  Fermi National
Accelerator Laboratory, Batavia IL 60510-5011, USA  T. Strauss  Fermi National
Accelerator Laboratory, Batavia IL 60510-5011, USA  C. Tarantini  ASC / NHMFL
/ Florida State University, Tallahassee, FL 32310, USA  R. Teyber  Lawrence
Berkeley National Laboratory, Berkeley, CA 94720, USA  U. Trociewitz  ASC /
NHMFL / Florida State University, Tallahassee, FL 32310, USA  M. Turqueti
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  M. Turenne
Fermi National Accelerator Laboratory, Batavia IL 60510-5011, USA  D. Turrioni
Fermi National Accelerator Laboratory, Batavia IL 60510-5011, USA  G. Vallone
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  G. Velev
Fermi National Accelerator Laboratory, Batavia IL 60510-5011, USA  S. Viarengo
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  Politecnico di
Torino, Torino, Italy  L. Wang  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  X. Wang  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  X. Xu  Fermi National Accelerator Laboratory, Batavia
IL 60510-5011, USA  A. Yamamoto  KEK, Tsukuba, Ibaraki, Japan  CERN, Geneva,
Switzerland  S. Yin  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  A. Zlobin  Fermi National Accelerator Laboratory, Batavia IL
60510-5011, USA

(Accelerator Frontier (AF), Multi-TeV Colliders (AF4))

###### Contents

  1. 1 Executive Summary
  2. 2 Introduction
  3. 3 Magnet needs for future colliders
    1. 3.1 The energy frontier landscape - facilities under consideration
    2. 3.2 Hadron colliders - impact of magnet technology developments
    3. 3.3 Muon colliders - impact of magnet technology developments
  4. 4 Status of magnet R&D and future directions
    1. 4.1 Results in high-field superconducting magnet R&D
  5. 5 The DOE-OHEP US Magnet Development Program
    1. 5.1 Scale of investment
    2. 5.2 Vision and goals aligned with HEP needs
    3. 5.3 Managing magnetic forces in high-field accelerator magnets
      1. 5.3.1 Approaches to stress-management
      2. 5.3.2 Areas of investigation for stress-management methods
      3. 5.3.3 Development plans for stress-management methods
    4. 5.4 The promise of high-temperature superconductors for HEP
      1. 5.4.1 Bi2212
      2. 5.4.2 REBCO
    5. 5.5 Considerations for accelerator magnets beyond 20 T
      1. 5.5.1 Design Criteria
      2. 5.5.2 Magnetic Design
    6. 5.6 Technology underpinning the development of advanced magnet technology
  6. 6 Nurturing a strong industrial magnet ecosystem for science and society
    1. 6.1 Building and leveraging capabilities within US industry
  7. 7 Opportunities and challenges for international collaboration
  8. 8 Summary

##  1 Executive Summary

As the High Energy Physics community considers future discovery machines based
on circular colliders, the performance and cost drivers for such facilities
are of fundamental importance. The leading consideration for such a facility
is the magnet technology which steers and focuses the particle beams. As a
result of the last Snowmass and P5 process (2013-2014), DOE-OHEP initiated the
US Magnet Development Program (MDP), a general R$\&$D program that pulls
together longstanding individual HEP research groups at DOE laboratories and
University programs focused on magnet technology under a common collaboration,
with focused mission and goals and constructive review and guidance from a
Technical Oversight Committee.

The general magnet R$\&$D pursued by the MDP focuses on advancing magnet
technology irrespective of a specific project, and hence provides broad and
lasting value to the community as it explores future hadron colliders as well
as muon colliders. The combination of clarity in mission and goals, coupled
with the transparent, collaboration-friendly research paradigm of the MDP, has
led to internationally recognized leadership in the field, and to growing
synergies with the NSF-funded NHMFL; with other DOE offices, in particular
DOE-OFES; and with industry, for example through the SBIR program. These
synergies significantly enhance the effectiveness of the MDP. Furthermore,
international collaborations exist on specific technical topics, and we seek
to enhance collaborations with our European counterparts now that the European
Strategy document has been issued and the associated technology roadmaps have
been developed.

To explore long range opportunities for future HEP colliders, the MDP focuses
on high field magnet technology. All advanced superconductors of relevance to
HEP high field magnets, in particular the low-temperature superconductor Nb3Sn
and the high temperature superconductors REBCO and Bi2212, are strain
sensitive and brittle, characteristics that challenge magnet design,
fabrication, and operational performance. The MDP is exploring and developing
stress-managed design concepts to enable the use of these materials in high
field accelerator magnet configurations. We note that the magnet designs have
relevance to both hadron and muon collider needs. For muon colliders, there is
furthermore need to develop very high field solenoids for muon production and
for muon beam cooling. Expertise from MDP can be applied in these areas as
well, and we see strong synergies in that arena with ongoing development in
high field magnets for materials research, exemplified by the record solenoid
field developed and produced by the National High Magnetic Field Laboratory
(NHMFL), as well as advances in REBCO magnet technology by DOE-OFES and by
private industry in the nascent - but rapidly developing - compact fusion
realm.

A major element of the MDP is the development of technologies critical to the
understanding of magnet performance; these include advanced modeling
capabilities, the development and implementation of novel diagnostics, and the
exploration of new concepts that can impact the rate at which accelerator
magnets train up to full field. Advances in these areas provide lasting
benefit for HEP, and are highly valued by the broader superconducting magnet
community, both within the DOE Office of Science, and also in industry.

At the heart of superconducting magnet technology are the superconductors
themselves; the US has longstanding leadership in collaborating with industry
to develop new and improved superconductors, and it is critical that the
successful partnership be further grown and nurtured to support HEP’s future
needs. HEP is working closely with the new Accelerator R$\&$D and Production
Office (ARDAP) to develop a strategic plan that can strengthen US industry in
this arena and support HEP’s long term needs for conductor performance and
cost-effective conductor production.

General long range magnet R$\&$D is a critical foundation for HEP, providing a
strong basis to develop strategies for future colliders, growing the next
generation of scientists and engineers in the field of accelerator magnets, so
as to provide the foundation for directed-R$\&$D that will ultimately be
required to scale up and finalize magnet designs for a future collider
project. Currently the MDP is focused on exploring stress-managed structures
and in testing hybrid HTS/LTS accelerator magnets as a cost-effective means of
achieving high-field accelerator magnets; in parallel, designs are underway to
explore 20 T and beyond, which may be within reach in the next decade.

The HEP MDP collaboration is now well established, with a record of
achievements and a clear understanding of the opportunities and challenges
that lay ahead. General magnet R$\&$D , when well coordinated and managed and
fully leveraging synergistic activities, is an excellent investment for high
energy physics. The experience from MDP indicates that the scale of investment
needed to aggressively pursue magnet R$\&$D with the goal of enabling a
foundation for a future readiness program, and ultimately collider project, is
$\sim\$15M$ per year, with an additional $\sim\$20$% (i.e. $\$3$M) in
conductor procurement from industry to support the magnet development needs.
In summary, a long range magnet R$\&$D program, designed to advance magnet
technology while fully leveraging the broader community’s strengths, is vital
to HEP and the future of particle physics.

##  2 Introduction

Today’s colliders are built on a foundation of superconducting magnet
technology that provides strong dipole magnets to maintain the beam orbit and
strong focusing magnets to enable the extraordinary luminosity required to
probe physics at the energy frontier. The dipole magnet strength plays a
critical role in dictating the energy reach of a collider [1], and the
superconducting magnets are arguably the dominant cost driver for future
collider facilities. As the community considers opportunities to explore new
energy frontiers, the importance of advanced magnet technology – both in terms
of magnet performance and in the magnet technology’s potential for cost
reduction – is evident, as the technology status is essential for informed
decisions on targets for physics reach and facility feasibility.

##  3 Magnet needs for future colliders

###  3.1 The energy frontier landscape - facilities under consideration

There are a large number of facilities under consideration to probe new realms
of the energy frontier, i.e. discovery machines, as well as a variety of
facilities focused on high beam intensity, i.e. machines focused on probing
known energy ranges with significant improvements in statistics to thoroughly
explore physics phenomena and identify rare events [2, 3]. Here we consider
those facilities that are ring-based, i.e. that seek to leverage recirculating
stored beams as a cost-effective means of achieving high energies and high
luminosities. Assuming the counter-rotating beams are at the same energy $E$,
the resulting center of mass energy is $E_{c.m.}=\sqrt{s}=2E$. Central to
ring-based accelerators are the magnets that bend the beams, as well as the
radio-frequency cavities that provide increase energy, and that maintain beam
energy to compensate for energy loss due to synchrotron radiation. The bend
radius $\rho$ for a beam of charge $e$ and momentum $p=mv$ is simply
$p=eB\rho$. Hence higher magnetic field enables proportionally higher energies
for the same ring radius. For any future high energy collider, magnet
technology arguably drives both the energy reach and the cost of the facility.

Discovery machines have historically used hadron beams, e.g. protons. The
world’s premier energy frontier facility, the Large Hadron Collider at CERN,
currently achieves a center of mass energy $E_{c.m.}\sim 13$ TeV, colliding
two counter-rotating proton beams of energy $6.5$ TeV. A natural approach to
reach new physics is to significantly enhance the beam energy and resulting
$E_{c.m.}$. The most aggressive example is the proposed ”Future Circular
Collider” (FCC), a facility advocated by CERN that would target $E_{c.m.}\sim
100$ TeV [4] in a new tunnel of circumference $\sim 100$ km. A competing
proposal, the Super proton-proton Collider (SppC) proposed by China, targets
an energy of $E_{c.m.}\sim 80$ TeV [5]. These machines are designed to access
new physics, in particular physics beyond the Standard Model, that promise
answers to questions related, for example, to the nature of dark matter, the
total absence of antimatter in the universe, and the peculiarities of
neutrinos.

An alternative approach to high energies is to leverage the large mass of
muons, while benefitting from their point-particle-like nature, i.e. Lepton
physics. The muon mass $m_{\mu}$ is $207$ times that of the electron; since
synchrotron radiation scales with $m^{-4}$, it is in principle feasible to
consider a ring-based muon collider at the energy frontier. Furthermore, for
new physics a hadron interaction requires $\sim 7$ times the $E_{c.m.}$
energy; for example, a $\sqrt{s}=14$ TeV muon collider is competitive with a
$\sqrt{s}=100$ TeV proton collider.

From an accelerator technology point of view, a high energy hadron collider,
although technically very challenging, is arguably well understood. A muon
collider, however, has unique challenges that must be understood and overcome
- these relate primarily to the production and control of the very short-lived
muon beams.

###  3.2 Hadron colliders - impact of magnet technology developments

For the main ring magnets, i.e. dipole magnets, of a hadron collider, the
linear relationship between beam energy, ring radius, and magnetic field
strength provide the basis for facility optimization for physics reach and for
cost. For site-limited facilities, e.g. when an existing tunnel will be re-
used, the magnet technology dictates the physics reach that can be obtained.
For a green-field facility, i.e. where a new tunnel and new magnets are being
considered, both the magnet technology and the ring circumference are
parameters that impact the physics reach; a reasonable estimate for the beam
energy is $E=0.3BR$, with energy $E$ in TeV, field $B$ in T, and radius $R$ in
km. The cost of the tunnel is arguable $\propto R$; the cost of magnets is
typically thought to scale $\propto B$, but we must recognize that the
required conductor mass scales $\propto B^{2}$, assuming the average current
density is roughly constant independent of field - this assumption appears to
be reasonably valid to-date. Furthermore, the scaling relation is
significantly impacted as the field strength approaches a superconductor’s
upper critical field $B_{c2}$. Figure 1 shows schematically the transition
from one superconductor to another as a function of field, and its relation to
hadron collider center of mass energy reach.

Figure 1: The center of mass energy for a hadron collider as a function of the
dipole magnet field strength, assuming the $E_{c.m.}=0.3B[T]R[km]$ scaling,
consistent with reasonable filling-factors of magnets on the ring
circumference.

###  3.3 Muon colliders - impact of magnet technology developments

The driving considerations for a muon collider relate to a) the short lifetime
of the muon ($\sim 2.2\mu$ s at rest), and b) the fact that muon production,
typically done by colliding a high energy proton beam on a target (resulting
in the production of pions which decay to muons) results in a large beam
emittance that requires cooling to achieve the beam properties needed for high
luminosity collisions [6].

The efficiency of muon production, via pion production at the target, requires
very strong solenoidal magnetic focusing field to maximize the number of pions
captured and to focus them as they are accelerated. The collision process
furthermore results in significant radiation by-products, further challenging
the requirements on the magnetic field system.

The short muon lifetime motivates novel magnet and optics schemes to enable
very rapid acceleration of the muons from target production to the storage
ring where collisions occur. Examples include very fast ramping magnets in a
synchronous multi-pass configuration, for example using high-temperature
superconductors in novel configurations [7], and/or large momentum acceptance
magnet optics, such as fixed-field alternating gradient (”FFAG”) designs that
enable the beam to be accelerated via multiple passes with fixed magnetic
field [8]. Finally, since even at relativistic velocities the lifetime of the
muon is limited, luminosity considerations motivate the most compact storage
ring possible, i.e. the highest field dipoles possible to minimize the ring
circumference.

The emittance consideration implies the need for significant beam cooling; the
most promising technique to date is ionization cooling, where the muon beam is
focused using strong solenoidal fields and passed through material, i.e.
absorber, resulting in (both transverse and longitudinal) momentum reduction;
the longitudinal momentum is then restored via (longitudinal) RF electric
fields [6]. Since the beam focusing drives the cooling rate and scales with
the magnetic field strength, very strong solenoidal fields are required. We
note that the large beam emittance also results in a large beam envelope,
which implies the need for relatively large apertures in the bending dipoles
of the high-energy acceleration stage.

The collider ring will require high field dipoles to maximize luminosity; for
example, at $2$ TeV the muon lifetime, though significantly extended, is only
$0.044$ s; the ring circumference then limits the number of turns before decay
and hence dictates the interaction opportunities. Furthermore, the collider
ring will need large aperture high-field magnets to accommodate absorbers to
dissipate the beam losses, estimated to be at the level of $\sim 500$ W/m.

We note that the solenoid fields required by a muon collider have some
similarities with magnet systems being developed for other applications. As
examples, the high field solenoids being developed at the NHMFL for condensed
matter experiments, including high-field NMR, have many similarities to the
solenoid technology needed for muon cooling channels. The larger bore high
field solenoid needed for the muon collider target has many commonalities with
a central solenoid for a compact fusion machine, and/or with hybrid
resistive/superconducting solenoids similar to the NHMFL’s 45 T flagship
facility, or the more recent series-connected hybrid solenoids built for high
field NMR.

Leveraging expertise and investments from other programs with common interests
leads to synergies that can significantly speed up magnet development and
mitigate risk for future projects.

Statement 1: High field magnets are critical to energy-frontier circular
colliders Advanced magnet technology is the driving technology for any energy-
frontier circular collider envisioned by the community, fundamentally
impacting both science reach and facility cost.

Statement 2: Muon colliders have additional magnet challenges that should be
addressed by HEP magnet R$\&$D in synergy with other DOE and NSF programs
There are significant accelerator magnet development efforts that are common
to any future circular collider and benefit from a general R$\&$D program.
Furthermore, in particular for a muon collider, there are significant
synergies with other DOE programs and with industry that should be leveraged
to more rapidly and efficiently develop critical magnet technology for HEP.

##  4 Status of magnet R&D and future directions

The dominant, commercially available conductors today are the low-temperature
superconductors (LTS) NbTi and Nb3Sn, and a suite of high temperature
superconductors (HTS) based on Bismuth Strontium oxides and on rare-earth
Barium Copper oxides (REBCO). We note that all superconducting colliders to-
date use the ”workhorse” superconductor NbTi; the LHC luminosity upgrade,
HiLumi, will include new interaction region focusing magnets that utilize -
for the first time in a collider - the superconductor Nb3Sn.

The HTS materials lack the maturity of their LTS counterparts, both in terms
of the scale of industrial production and uniformity and control of
properties, as well as in their application to magnets. Nevertheless they are
progressing rapidly, due both to potential applications at higher temperature,
and to the fact that they continue to carry significant transport current at
high field, well beyond that of their LTS counterparts, thereby promising
access to higher field superconducting magnets. The Bi family has two
commercial forms:

  * •

Bi$2223$ ($\mathrm{Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+x}}$), a multi-filamentary
superconductor in tape form that does not need further processing. A single
industrial supplier produces the tape. To date the material has had only
limited use in accelerator magnet applications due to its performance
characteristics as compared to other HTS materials.

  * •

Bi$2212$ ($\mathrm{Bi_{2}Sr_{2}CaCu_{2}O_{x}}$), a multi-filamentary round
wire that requires a high temperature reaction in an Oxygen environment to
create the superconducting state. The round wire is amenable to Rutherford
cabling, the primary scalable cable architecture used to-date in all HEP
colliders.

The REBCO family of superconductors are all produced in tape form, and do not
require further processing. However, they are not multifilamentary. The
primary rare-earth used is Yttrium (i.e.
$\mathrm{YBa_{2}Cu_{3}O_{7-\delta}}$).

An important characteristic of all advanced superconductors, including Nb3Sn
and the HTS conductors Bi2212 and REBCO, is that they are strain-sensitive.
The strain sensitivity manifests itself at low strain levels as a reversible,
intrinsic property, i.e. the critical current behaves as
$J_{c}=J_{c}(B,T,\epsilon)$. At larger strain levels the materials exhibit
irreversible reduction in transport current, i.e. degradation. Important goals
in high field magnet research include properly accounting for reversible
strain on the performance behavior of high field accelerator magnets, and
clarifying the acceptable strain state of the superconductor so as to design
magnets that do not exhibit degradation, while maximizing the field producing
potential of the superconductor.

Statement 3: Advanced superconductors are strain-sensitive High field
accelerator magnets must be designed to accommodate the strain limitations
intrinsic to the superconductors. The strain limits must be thoroughly
studied, understood, and quantified so that magnet designs avoid degradation
while maximally leveraging the superconductors properties.

HEP has long served as the driving force behind advances in commercial
superconductors, and in some cases those commercial products have enabled new
commercial applications to flourish - the development of more advanced NbTi
wire for the Tevatron, for example, provide critical performance that enabled
the - now ubiquitous - Magnetic Resonance Imaging (MRI) business to thrive.
Important developments in superconductors continue, both in Nb3Sn and in the
HTS materials; an excellent perspective on developments in that arena, as well
as challenges and possible avenues to strengthen and accelerate US
capabilities in commercial superconducting materials, is provided in a
complementary whitepaper [cooley1].

Statement 4: HEP leadership in driving advances in commecial superconductors
will require strategic planning and investments The properties of the
superconductors used in high field accelerator magnets are critical to the
magnet performance, and are a major element in the magnet cost. The ability to
continue to innovate new superconductor architectures, and to bring new
conductors to industrial maturity for projects, is a key component of magnet
development. Nurturing and maintaining a vibrant, competitive ecosystem for
superconductor development as well as for reliable, high quality production
capability, will require long term strategic planning and commitment from DOE,
in close collaboration with industry.

###  4.1 Results in high-field superconducting magnet R&D

The DOE office of High Energy Physics has sponsored research into high field
accelerator magnets at a number of laboratories over the years, most notably
LBNL, FNAL, and BNL, as well as programs at multiple Universities, including
most significantly FSU, TAMU, and OSU. The programs have probed a variety of
accelerator magnet concepts over the last three decades, with record dipole
fields in multiple configurations. As examples:

  * •

The Cosine-Theta approach, used in all colliders to-date. The D20 cosine-theta
magnet [9] was a flagship 4-layer magnet built in the late 1990’s that
achieved a peak field of $13.5$ T at $1.9$ K. Most recently, the MDPCT1
magnet, built at FNAL within the MDP program (see section 5), achieved the
record field of $14.5$ T at $1.9$ K in a $50$ mm bore, with excellent field
quality [10].

  * •

The Common Coil magnet configuration, wherein racetrack coils are energized in
reverse polarity so as to create a strong magnetic field between the coils,
yielding effectively twin apertures. Examples include the RD3c magnet built by
LBNL [11], the HFDC01 magnet developed by FNAL [12], and the DCC017 magnet
built and tested by BNL [13]. The latter continues to be in use, serving as a
magnet facility for a variety of high field ($\sim 10$ T) tests for
experiments for collaborators [14].

  * •

Block Dipole magnets; similar to the common-coil layout, but energized in same
polarity, resulting in a single, high field bore. To maximize field while
allowing access for the particle beam, the ends are flared. The concept was
most thoroughly explored by LBNL in the mid 2000’s, culminating in the HD3
magnet that achieved $13.8$ T at $4.2$ K [15]. The technology was ultimately
utilized in the CERN FRESCA-II magnet, which achieved $14.6$ T with a large,
$\sim 100$ mm bore [16]. The magnet is not designed as an accelerator magnet,
but rather serves as a test facility for superconducting cables.

We note that all of the above magnet concepts continue to be of interest, and
in fact all are being pursued to some degree by institutions around the world.
The lessons-learned from the research on these magnets formed the foundation
for the research goals and magnet development roadmap for the US Magnet
Development Program (MDP), which was created by DOE-OHEP in 2015 following the
last Snowmass and P5 process, and motivated in particular by recommendations
from the HEPAP Accelerator R$\&$D Subpanel Report [17].

It is important to note that the US Magnet Development Program was created as
a general R$\&$D program, within the research arm of DOE-OHEP, and tasked with
advancing accelerator magnet technology for future colliders, irrespective of
requirements of a specific collider. DOE-OHEP has an excellent track record of
supporting long range R&D, and initiating ”Directed” R$\&$D - essentially
technology readiness programs - when it becomes apparent that a specific
project, and hence project technology need, is on the horizon. The LHC
Accelerator Research Program (LARP), and its follow-on DOE 413.3b project, HL-
LHC AUP, serve as excellent examples (see Fig. 2). LARP benefitted
significantly from the expertise and experience from the magnet programs
described above, which had performed critical exploratory research into the
use of Nb3Sn for accelerator magnets, with many of the record dipole magnets
described above having occurred prior to the onset of LARP. Of course the HL-
LHC AUP project, currently underway, depended intimately on the developments
from LARP, which largely developed and solidified the design and early
demonstrations of the quadrupole magnets for the project.

Here we advocate for a strong, effective general R$\&$D magnet program that
develops high field magnet technology, guides the developments of advanced
superconductors, and lays a foundation of scientific and engineering knowledge
that provides lasting value for any future HEP collider - i.e. the US Magnet
Development Program. A strong R$\&$D program serves as the foundation needed
for future directed R$\&$D programs that target specific collider designs or
that focus on cost reduction and scale-up. Examples of possible directed
R$\&$D programs are provided in complementary whitepapers [18], [19].

Figure 2: The DOE approach to advanced superconducting magnet technology has
supported long-term R$\&$D as well as, when appropriate, directed R$\&$D; an
example of the latter was LARP, which, among other accelerator developments,
prepared Nb3Sn quadrupole technology to enable the LHC luminosity upgrade
(HiLumi) currently underway. DOE-OHEP is now contributing quadrupole magnets
for HiLumi under the HL-LHC AUP project.

Statement 5: Complementarity of General and Directed R$\&$D The DOE-OHEP
paradigm of long-range R$\&$D to advance magnet technology, coupled, when
appropriate, with Directed-R$\&$D that demonstrates feasibility and prepares
magnet technologies for projects, has proven extremely effective.

##  5 The DOE-OHEP US Magnet Development Program

The DOE-OHEP created the US Magnet Development Program in late 2015, pulling
together experienced teams from DOE laboratories and the National High
Magnetic Field Laboratory in a collaboration to advance accelerator magnet
technology for HEP needs. As an element of the HEP General Accelerator R$\&$D
program, MDP is tasked with exploring the limits of high field accelerator
magnet technology, without being constrained by the specific requirements of
any given potential project.

The MDP is funding-limited and has by necessity - and appropriately -
developed a focused mission and prioritized set of goals. Many excellent
additional goals and research directions have been identified, but by
necessity are not currently supported. Since its inception, the program has
worked to streamline its operations and demonstrate an efficient and effective
R$\&$D operation, leveraging significantly synergistic activities, e.g. with
Fusion Energy Sciences (FES), with the magnet R$\&$D activities of the NHMFL
supported by NSF, and with industry, in particular DOE’s Small Business
Innovation Research (SBIR), as well as international collaborations. The
program has oversight through a longstanding Technical Advisory Committee,
composed of internationally recognized - and international - membership, as
well as a Steering Council composed of laboratory leadership from the MDP
collaborating institutions.

###  5.1 Scale of investment

The MDP has made significant technical advances and has demonstrated
leadership in the field. Moving forward, based on our experience to-date, a
general R$\&$D program, i.e. MDP, would be most effective if funded at a level
of $\sim\$15$M per year; to support the program’s needs for superconductor, an
additional $\sim 20$%, i.e. $\sim\$3$M, should be allocated for procurement of
industrial superconductor. Alternative mechanisms to obtain superconductor for
programs such as MDP are explored in a companion whitepaper [cooley1]. This
investment is less than that proposed - and needed - by associated directed
R$\&$D programs, since directed R$\&$D must address critical elements such as
technology scale-up, value engineering, and reproducibility, all of which
require more investment. We note that general R$\&$D - MDP - invests heavily
in resources - people - and hence serves as an incubator and repository of
expertise for the community.

###  5.2 Vision and goals aligned with HEP needs

As a National Program composed of multiple DOE Laboratories and University
members, the US Magnet Development Program (MDP) aspires to provide broad
leadership in accelerator magnet technology [20]. The vision of the MDP is to:

  1. 1.

Maintain and strengthen US Leadership in high-field accelerator magnet
technology for future colliders;

  2. 2.

Further develop and integrate magnet research teams across the partner
laboratories and US Universities for maximum value and effectiveness to MDP;

  3. 3.

Identify and nurture cross-cutting / synergistic activities with other
programs (e.g. Fusion), to more rapidly advance progress towards our goals.

These three core vision elements provide focus and direction to the program,
while guiding interaction with other DOE-SC offices, international partners,
and industry, to further the mission of the MDP. The overarching goals of the
program remain unchanged after the program’s first four years:

  * •

Explore the performance limits of Nb3Sn accelerator magnets, with a sharpened
focus on minimizing the required operating margin and significantly reducing
or eliminating training

  * •

Develop and demonstrate an HTS accelerator magnet with a self-field of 5 T or
greater, compatible with operation in a hybrid HTS/LTS magnet for fields
beyond 16 T

  * •

Investigate fundamental aspects of magnet design and technology that can lead
to substantial performance improvements and magnet cost reduction

  * •

Pursue Nb3Sn and HTS conductor R$\&$D with clear targets to increase
performance, understand present performance limits, and reduce the cost of
accelerator magnets

The original 2015 MDP roadmaps were updated in 2020 [21], to take into account
progress that had been made by the program and to further strengthen and
integrate the multi-lab collaboration. The major themes for the updated
roadmaps include:

  * •

Explore the potential for stress-managed structures to enable high-field
accelerator magnets, i.e. structures that mitigate degradation to strain-
sensitive Nb3Sn and HTS superconductors in high-field environments;

  * •

Explore the potential for hybrid HTS/LTS magnets for cost-effective high field
accelerator magnets that exceed the field strengths achievable with LTS
materials;

  * •

Advance magnet science through the rapid development and deployment of unique
diagnostics and modeling tools to inform and accelerate magnet design
improvements;

  * •

Perform design studies on high field accelerator magnet concepts to inform
DOE-OHEP on further promising avenues for magnet development;

  * •

Advance superconductors through enhanced performance, improved production
quality, and reduction in cost - all critical elements for future collider
applications.

These themes are consistent with the original US MDP goals and leverage the
major advances the US MDP has achieved to date in advancing superconductors,
developing core HTS magnet technologies, and demonstrating record Nb3Sn
accelerator magnet performance. Together, the themes form the foundation for a
program that will maintain US leadership in developing advance accelerator
magnet technology for the years to come.

Statement 6: The US MDP is the result of a recommendation from the 2015 HEPAP
Accelerator R$\&$D Subpanel The US MDP is a long-term HEP GARD funded program
that integrates leading DOE laboratory and University teams to advance
accelerator magnet technology in support of HEP mission needs, addressing
recommendations from the last Snowmass process and in particular the follow-on
2015 HEPAP Accelerator R$\&$D Subpanel report.

Statement 7: A general magnet R$\&$D program is a cost-effective investment
for DOE-OHEP General magnet R&D, when well coordinated and managed and fully
leveraging synergistic activities, is an excellent investment for high energy
physics. The experience from MDP indicates that the scale of investment needed
is $\sim\$15M$ per year, with an additional $\sim\$20$% (i.e. $\$3$M) in
conductor procurement from industry to support the magnet needs.

###  5.3 Managing magnetic forces in high-field accelerator magnets

To mitigate coil stress values at high fields and/or large apertures, stress-
management (SM) concepts for various magnet coil geometries have been proposed
[22, 23, 24, 25]. The Canted-Cosine-Theta (CCT) dipole concept, under
development at LBNL and PSI, is based on tilted solenoid coils. A Stress-
Management Cosine-Theta (SMCT) dipole concept, in progress at FNAL, is built
on the traditional cosine-theta magnet technology. The SMCT and CCT designs
complement each other and address the question of whether stress-managed
structures can fulfill their promise of breaking the traditional scaling of
coil stress with field. If so, SM would enable high field magnet technology
with stress/strain sensitive Nb3Sn . The same principle could be then applied
to other stress/strain sensitive superconductors, such as High Temperature
Superconductors (HTS). Together, the stress-managed magnet concepts are
designed to address the key questions and provide capabilities – i.e. strong
dipole fields and large bore – needed for HEP accelerator facilities. These
concepts are also important for the development of very high-field hybrid
dipole magnets with HTS coils as inserts and Nb3Sn coils as outserts.
Integration of technical expertise and capabilities from the U.S. and EU
laboratories, including areas such as magnet design, fabrication
infrastructure, instrumentation, test facilities and test data analysis, will
increase the efficiency and outcome of each magnet program.

####  5.3.1 Approaches to stress-management

Currently, as part of the US Magnet Development Program, two different stress-
management approaches are being pursued. These are the Canted-Cosine-Theta
(CCT) and Stress-Management Cosine-Theta (SMCT) approaches. These approaches
share the common stress interception scheme of using ribs to transfer Lorentz
forces to the spar portion of the mandrel. The SMCT method intercepts the
force on blocks of conductor while the CCT method intercepts the force on
every turn of the coil. The SMCT winding geometry resembles that of a
conventional cosine-theta magnet, while the CCT geometry consists of pairs of
canted solenoids with opposing canting direction. The key features of each
design are further described in the following sections.

##### 5.3.1.1 Canted Cosine Theta (CCT)

Figure 3 (left) shows the winding geometry for the CCT configuration. This
consists of two tilted solenoids with opposing tilt orientation. The current
direction is such that the dipole field component of each layer is additive,
while the solenoidal field component is canceled. Figure 3 (right) shows the
cross-section of the coils. The intrinsic Cos($\theta$) nature of the
conductor distribution leads to excellent field quality in the CCT dipoles.
The internal support structure of the CCT dipole can also be seen in Figure 3
(right). The Lorentz force at each turn is intercepted and partially
transferred to the spar (the area in the mandrel below the ribs). This can
lead to a significant reduction in the peak stress on the conductor. Another
key advantage of CCT magnet technology is the ease of fabrication. A minimal
number of parts are required, since many key features are incorporated into
the mandrels. Since the mandrel also defines the basic geometry, this leads to
greatly simplified reaction and impregnation tooling. The simplification of
the manufacturing process could lead to significant cost reductions as the
technology is further developed.

Figure 3: The ”Canted Cosine Theta” (CCT) concept, wherein the Rutherford
cable is directly supported in grooves machined into a support structure. The
tilted winding results in a solenoidal field component, which is compensated
by the next layer in the structure. The cross-section (right) shows the
intrinsic “Cos($\theta$)” nature of the resulting current distribution,
resulting in excellent field quality.

##### 5.3.1.2 Stress-Managed Cosine Theta (SMCT)

The winding geometry for SMCT magnets follows a traditional Cosine theta
approach with conductor blocks that are separated by wedges. However, the
necessary parts are incorporated into a solid mandrel internal structure as
shown in Figure 4. The mandrel contains the ribs / wedges and a spar to
partially intercept the azimuthal Lorentz force on the coil blocks. As with
the CCT concept, this can lead to significant reduction in the peak conductor
stress. The two-dimensional nature of the straight section in the SMCT leads
to improved conductor efficiency when compared to the CCT approach. As is the
case for CCT, the SMCT method consolidates the significant quantity of parts,
common in more traditional magnet approaches, into one mandrel structure. This
can lead to simplified winding, reaction, and impregnation processes and
tooling. As with CCT, this could lead to significant cost savings as the
technology becomes more mature.

Figure 4: The Stress Managed Cosine Theta (SMCT) concept, wherein groups of
Rutherford cables are directly supported in grooves machined into a support
structure. The groupings are designed such that the cross-section (right)
emulates a Cos($\theta$) current distribution, resulting in excellent field
quality.

####  5.3.2 Areas of investigation for stress-management methods

In order to reduce conductor stress, stress-management approaches introduce
internal structures and additional interfaces when compared to more
traditional magnet designs. Furthermore, the mandrels which incorporate this
structure can have fairly complex geometries. In order to take full advantage
of these technologies, further understanding and development in several areas
is necessary. Below is a list of some of the primary issues that are being
investigated to develop these stress-management approaches:

  * •

Continue development of mandrel fabrication methods including exploration of
conventional machining methods as well as additive manufacturing approaches;

  * •

Investigate approaches for scale up to larger magnets including segmentation
approaches;

  * •

Explore new methods for layer-to-layer interface coupling, especially for the
CCT approach where the coils have a closed structure;

  * •

Investigate and optimize external structures for use in stress-managed magnets
with increases internal structure rigidity.

  * •

Understand the influence of additional interfaces on stress-limits and
training under different interface conditions;

  * •

Understand the evolution of interface behavior, and the influence on training,
due to interface damage in current and past magnet tests;

  * •

Develop methods to improve control over interfaces for the desired behavior to
reduce training and avoid unwanted stress re-distribution onto the conductor;

  * •

Develop efficient and cost effective fabrication methods using minimal tooling
to reduce overall magnet fabrication cost and complexity;

  * •

Explore the limits of stress-management approaches on high field / large bore
demonstrators.

####  5.3.3 Development plans for stress-management methods

The design of several magnet configurations using SMCT technology has been
performed over the last few years [24, 25]. This includes the magnetic and
mechanical design and analysis. Significant developments have also been made
on fabrication technologies, specifically with regards to additive mandrel
manufacturing [26] and winding methodologies.

The CCT program has been ongoing since the start of the US MDP. The early
focus has been on developing the methods and technology for CCT magnet design,
analysis, fabrication, and testing. This early effort has culminated in the
test of three two-layer Nb3Sn CCT dipoles with 90 mm aperture and a bore field
of approximately 10 T at the short sample limit [27]. Each magnet in the
series led to improved understanding and methods for CCT technology. The last
magnet in the series reached approximately 88% of the short sample limit. This
effort has led to the next steps in CCT magnet development which are focused
on demonstrating higher field / larger aperture operation and training
understanding / reduction.

##### 5.3.3.1 Small Scale Testing

The additional interfaces that are introduced in stress-management approaches
can be a source for energy release during magnet operation, which can lead to
training quenches. Furthermore, if the interfaces evolve as the magnet is
trained (i.e. by debonding and / or sliding of the conductor) this can lead to
a redistribution of stress on the conductor. For example, a debonding event
can lead to a reduction in shear stress and an increase in normal stress on
the edge of the conductor. In order to probe / understand this behavior, small
scale experiments that allow for systematic investigation of different
parameters are desirable. Such experiments are currently ongoing with two
different platforms. The BOX experiments being carried out at PSI and the
University of Twente [28] use cable in groove samples that are arranged in a
serpentine pattern. The samples are then tested in a background field provided
by an solenoid magnet. The focus of these experiments has been on probing
training behavior with different impregnation materials and interface
conditions. A complementary effort is going on at LBNL with subscale CCT
magnets [27]. The subscale CCT magnets are designed to achieve stress levels
that ensure training at a similar load line margin when compared to the
previously described two-layer Nb3Sn CCT series. This platform produces more
comparable stress levels to larger CCT magnets than the BOX platform; however,
this comes at the expense of higher complexity and slower turn around time.
Similar to the BOX experiments, the aim of the subscale CCT program is to
investigate how changes to structural conditions, impregnation materials, and
interface conditions affect training and performance limits. Future testing at
a subscale level could also include the SMCT geometry, in order to probe how
training is affected when multiple turns lie inside of the mandrel grooves in
a more traditional Cos($\theta$) geometry.

##### 5.3.3.2 Large Scale Demonstrators

Large scale demonstrators for stress-managed magnets are currently planned as
part of the 2020 updated US MDP roadmap. For the SMCT approach, the roadmap
R&D goals are to demonstrate a bore field up to 11 T at 1.9 K with 120-mm
aperture in two-layer Nb3Sn dipole magnets with stress-managed coils; and to
demonstrate up to 17 T at 1.9 K with a 60-mm aperture in a four-layer Nb3Sn
dipole magnet with stress-managed outer coils [24, 25, 29]. For the CCT
approach, the roadmap R&D goals are to demonstrate bore field up to 13 T in a
120-mm aperture in a four-layer Nb3Sn CCT model magnet [30]. Both of these
efforts are closely aligned with the HTS programs as they can serve as the
background field for HTS insert tests. This will allow for probing of HTS
magnet behavior under high magnetic field and high stress states. The
technology development of stress-management techniques for Nb3Sn is highly
applicable to HTS conductors due to their similarly brittle nature. Stress-
management methods are also currently being applied to HTS conductors [31],
[32], and will be critical for high field hybrid dipole magnets.

Statement 8: Limiting magnetic force accumulation is essential to access high
field magnets The concept of stress-management, i.e. intercepting magnetic
forces to structural members before they can accumulate to damaging levels,
promises a path towards very high field accelerator magnets.

###  5.4 The promise of high-temperature superconductors for HEP

High Temperature Superconductors (HTS) have unique properties that are of
particular interest to high energy physics applications. First, the ability to
carry transport current at elevated temperature, above the traditional $1.8$ K
or $4.2$ K associated with the liquid helium operation of low-temperature
superconductors, opens the possibility of magnets operating at temperatures
associated with other liquid cryogens, or in special cases with the use of
cryogen-free cryostats cooled with cryocooler systems. The advantage of higher
temperature operation may include higher overall efficiency (i.e. associated
with Carnot efficiency), which can be particularly important in cases where
heat loads on the magnet cold mass are significant.

Second, and perhaps most importantly for collider applications, HTS materials
have the additional property of a very high upper critical field $B_{c2}$;
both Bi2212 and REBCO have $B_{c2}\sim 100$ T, which opens the door to
potentially very high field magnets. Attaining these high fields, however,
requires surmounting significant challenges - learning how to work with the
materials, understanding their behavior under stress and strain, managing the
tremendous forces that are created at high magnetic field, and developing
methods to protect the magnets from damage if and when some part of the
superconductor loses its superconducting state (i.e. a ”quench”). Addressing
these challenges is a central theme of the US MDP.

While active material research continues increasing the potential of Nb3Sn
conductors towards generating a dipole field of $20$ T at $4.2$ K [33], [34],
[35], high-temperature superconductors (HTS) [36] are required to generate
dipole fields at and beyond $20$ T. Two main candidate HTS conductors are
Bi-2212 round wires [37] and REBCO coated conductors [38].

####  5.4.1 Bi2212

The superconductor Bi2212 is manufactured using a powder-in-tube technique, a
well-established superconductor architecture that allows for a multi-filament
composite wire to be manufactured [37]. This has a number of advantages:

  * •

Because it is multifilamentary and isotropic, magnetization losses are
controlled and the conductor is ”well-behaved” for accelerator applications
where field quality is a concern.

  * •

because it is a round wire, the well established HEP route to scale up
current, through the use of Rutherford cables, can be applied. Rutherford
cables enable efficient use of superconductors while minimizing the number of
turns in a magnet, thereby reducing the magnet inductance; the inductance is
critical parameter in magnet protection, i.e. the ability to extract the
stored magnetic energy in the case of a quench.

  * •

Because it builds on established wire drawing fabrication processes, there is
potential for some degree of scale-up in the production capacity, and industry
has tooling and procedures that can be readily applied to Bi2212 wire
production.

Furthermore, the transport current of Bi2212 has seen significant improvement
over the last decade, and the wire is now competitive with Nb3Sn above $\sim
14$ T, making it a very attractive candidate for accelerator magnets beyond
$\sim 16$ T.

Despite these advantages, the conductor currently is being actively developed
almost exclusively by HEP and by the high field NMR community. This is
primarily due to complexities in its implementation in magnets - Bi2212
requires a high temperature heat treatment ($\sim 890$ $\degree C$) in a 1-bar
Oxygen environment. Furthermore, to access the highest performance, the heat
treatment must be performed at overpressure, e.g. at $\sim 50$ bar (still at
1-bar $O_{2}$). Finally, like all advanced superconductors, once formed the
superconductor is strain sensitive and brittle, so handling of the
superconductor must be minimized; for this reason magnet research leans
towards a ”wind-and-react” approach. Evaluating the transport current strain
sensitivity and degradation limits, in particular under transverse pressure,
is important for accelerator application. The combination of issues described
above puts constraints on the tooling design and material.

We are steadily progressing on addressing the technical challenges associated
with the use of Bi2212 superconductor for accelerator magnets, including
issues related to the reaction process such as insulations and conductor
treatments that avoid Bi2212 leakage during heat-treatment, and magnet and
tooling materials that are compatible with the reaction temperature and
environment, and are now working towards first implementation of Bi2212 in a
hybrid HTS/LTS magnet, where Bi2212 is applied in the inner coils that are
subjected to high field, and the outer coils utilize Nb3Sn, due to their
higher efficiency at lower field.

A review of the status of Bi2212 accelerator magnet research, and how the
material can play an essential role for HEP in the coming decades, is provided
in a companion whitepaper [39].

Statement 9: Bi2212 is a leading HTS material candidate for accelerator
magnets that benefits from many of the conductor characteristics proven
effective by HEP over the last decades Key characteristics, including the fact
it is produced as a multifilamentary round wire that can be readily made into
a Rutherford cable, make Bi2212 a leading HTS candidate material for HEP
applications. The challenge now is to translate the impressive progress in
transport current achieved from commercial wires over the last decade into
accelerator magnet performance.

####  5.4.2 REBCO

Of the two HTS candidate conductors, REBCO is the greater departure from LTS
cconductors because coated conductors are available only in tape form, with a
high aspect ratio of at least 10. The brittle REBCO layer is already in the
conductor that is delivered from vendor to magnet builders. Handling of the
tape for magnet fabrication and operation must be performed carefully so as
not to exceed a tensile strain of only about 0.6%. There are several reasons
why we painstakingly learn how to use this material:

  * •

Potential low cost due to the low raw material cost, even if today’s cost
remains very high;

  * •

Capability to generate high magnetic fields over a broad temperature range of
1.9 – 40 K.

These two factors could have a profound impact on future collider projects
that require high-field magnets. The recent European Accelerator R$\&$D
Roadmap has well explained the rationale for their focus on REBCO [40]. In a
companion white paper submitted to the Snowmass Community Study, we will
explore these topics in some details and offer additional opinions [41]. The
U.S. MDP has long recognized the potential of REBCO. One of the overarching
goals of MDP is to demonstrate a dipole field of $5$ T or greater, and measure
its field quality [20]. The recently updated MDP roadmap has pointed to the
hybrid LTS/HTS dipole magnet as a vehicle to further study, develop and
exploit the potential of HTS insert magnet technology [42]. To reach these
goals, we plan the following strategy for REBCO magnet technology development,
recognizing that REBCO is the least familiar one among all the existing
technical conductors for HEP applications:

  * •

Strongly couple the development of REBCO conductor and magnet technology. Use
the magnet results as a critical feedback to the conductor vendor that, in
turn, will help improve the magnet performance. Conductor architecture that is
most suitable for high-field dipole magnets is a question to be addressed (see
Fig. 5). We currently focus on the round-wire cable architectures that are
pursued by U.S. technology startups, but keep an eye on alternative conductor
architectures that are pursued by our European colleagues. The round wire
architecture is essentially isotropic in terms of mechanics and magnetics,
making it more readily scalable and transportable to new magnet architectures.

  * •

Take incremental but, hopefully, fast steps to grow the magnet technology.
Stick to the concept of minimum viable magnet with a focus on generating
higher dipole fields. Understanding implications but avoiding premature
optimization on important issues such as field quality and quench protection.
Building upon the experience and lessons learned from the previous steps,
introduce and explore a limited number of new features in the next magnets
towards a full set of magnet technology that can yield the ultimate dipole
fields.

  * •

Leverage MDP/CPRD, DOE SBIR and synergetic fusion programs to collaborate with
potential vendors to advance their product towards magnet conductors and to
develop relevant and critical magnet technologies that can help MDP succeed in
its mission.

Figure 5: REBCO technology has a unique challenge: we need to build multi-tape
conductor from a highly-aspected tape. Several concepts exist for a multi-tape
REBCO cable that can be used for high-field dipole magnets. A detailed
comparison regarding the merits and drawbacks of each concept is not yet
available, partially due to limited magnet results, and a down-select is not
yet feasible. The U.S. MDP is focused on the round-wire architecture while the
European counterpart has been traditionally focused on the rectangular cable
architecture based on stack of tapes.  Figure 6: Three magnet configurations
that are currently being pursued by collaborating laboratories at MDP. Left:
common coil. Middle: COMB. Right: CCT. All three configurations feature stress
management and are developed for round REBCO wires.

In the past few years, the REBCO community has investigated different dipole
magnet configurations using CORC® wires and progressed towards a high-field
dipole magnet technology. The three magnet configurations are common coil
being developed at BNL [43], Conductor on Molded Barrels (COMB) at FNAL [44],
and CCT at LBNL [45], [46], [47]. Figure 6 shows the three concepts. All
magnet configurations feature stress-management to better enable high-field
applications. Subscale models of both common coil and COMB concepts are being
developed with magnets of a larger scale planned for development and testing
within the next 12 months. The latest CCT magnet generated a peak dipole field
of 2.9 T at 4.2 K in [47], with ongoing work to develop a magnet to 5 T at 4.2
K.

MDP is currently collaborating with the Colorado-based Advanced Conductor
Technologies, LLC, the vendor of CORC® wires to develop the various dipole
magnet configurations. MDP is also evaluating the potential of STAR® conductor
from the Texas-based AMPeers LLC as an alternative round-wire architecture for
REBCO tapes. In the coming years, the REBCO teams will continue focusing on
increasing the dipole field that a REBCO magnet can generate as the single
most important goal for two reasons. First, a higher dipole field is critical
to support the strategic hybrid LTS/HTS dipole magnet configuration towards a
dipole field of 20 T. The ongoing design analysis of the 20 T hybrid dipole
magnet shows that to generate a 5 T dipole field from an HTS insert in a
background field of 15 T, the insert needs to generate at least 10 T dipole
field when being tested stand-alone [48]. This is nontrivial, considering
today we are capable of generating no more than 5 T.

Second, a REBCO magnet capable of higher dipole fields can emerge as a strong
candidate for stand-alone applications. As mentioned earlier, REBCO magnets
can in theory generate strong field ($>10$ T) at elevated temperatures. This
has two implications. First, it opens the possibility to operate without
liquid helium, e.g. with cryocoolers. Second, a higher efficiency to extract
heat compared to operation at 1.9 or 4.2 K. This can be very appealing for
applications with high heat load, such as the proposed pp machine and muon
colliders [40]. We also note that REBCO is a focus of the rising fusion
technology development as one of the enabling technologies for fusion [49].
REBCO is at the heart of the compact high-field fusion magnets that are being
actively developed by several fusion technology companies that have attracted
unprecedented public attention and private investment. A strong synergy
between HEP and Fusion magnets naturally appears. The fusion application, if
successful, can establish a sustainable market for REBCO conductors, which can
help reduce today’s high conductor cost. The MDP recognizes the strong synergy
and seeks to collaborate with our fusion colleagues in both public and private
sectors to address the technology needs for high-field REBCO magnets. An
excellent example is the development of a test facility dipole magnet that is
jointly supported by DOE OFES and HEP. The magnet for the facility will be a
state-of-art Nb3Sn block-design high-field dipole magnet that will provide a
15 T dipole background field for HTS insert and fusion cable testing.

Statement 10: REBCO has strong potential for HEP applications Continuation and
increase of the strategic investment in REBCO conductor and magnet technology
development will be critical to establish U.S. leadership in this future cost-
effective high-field magnet technology that can benefit both HEP and fusion
energy applications.

###  5.5 Considerations for accelerator magnets beyond 20 T

In superconducting dipole magnets, bore fields at the $15$ to $16$ T level are
considered as the practical limit for Nb3Sn superconductor [50]. To further
push the magnetic field of dipole magnets beyond the Nb3Sn limits, High
Temperature Superconductors (HTS) need to be considered in the magnet design.
For accelerator magnets, the most promising HTS materials currently under
consideration are Bi2212 [37] and REBCO [51]. However, their outstanding
performance still comes with a significantly higher cost than Nb3Sn.
Therefore, an economically viable option of 20 T dipole magnets has to involve
a hybrid approach, where HTS materials are used in the high field part of the
coil with so-called insert coils, and Nb3Sn and Nb-Ti superconductors are
adopted in the lower field region with so-called outsert coils. Preliminary
design studies of 20 T hybrid dipole magnets were carried out in 2005 [52] and
in 2014-2016 [53, 54, 55], whereas a full HTS option was analyzed in 2018
[56]. In 2015, a 20 T hybrid block-type design was presented by G. Sabbi, et
al. in [57]. A hybrid magnet was recently attempted by inserting a REBCO coil
inside the FRESCA2 dipole magnet [58]. Finally, REBCO inserts based on Roebel
cables were fabricated and tested as part of the EUCARD2 Collaboration [59],
[60].

Here we describe a preliminary conceptual magnetic design analysis of a $20$ T
hybrid dipole magnet for particle accelerators implementing Nb3Sn and HTS
coils (Nb-Ti is not considered in this study). First, a description of the
superconducting material properties and the criteria used in the different
designs is provided. Then, the magnetic analysis of 3 types of coil lay-outs,
1) cos-theta, with and without stress management, 2) block-type, with and
without stress management, and 3) common-coil, are presented.

An example of the superconducting material properties considered for this
preliminary analysis is shown in Fig. 7, with a Nb3Sn Rod restack Process
(RRP) and a Bi2212 strand produced by Bruker-OST, and a REBCO CORC™ wire
produced by ACT LLC. For each material, the engineering current density
$J_{e}$ used in the computations, where $J_{e}$ is the critical strand current
divided by the strand cross-section area, is given in Table 1.

,

Figure 7: Cross-sections, not in scale, of Nb3Sn (left, $0.85$ mm ⌀), and Bi2212 (center, $0.8$ mm ⌀) composite wires produced by Bruker-OST, and a REBCO CORC® wire (right, $3.4$ mm ⌀) by ACT LLC. Table 1: Superconductor Strand and Cable Properties Assumed Parameter | Unit | Nb3Sn | Bi2212 | REBCO
---|---|---|---|---
Strand diameter | mm | $0.7-1.1$ | $0.7-1.1$ | $1.2-4.0$
Cable width | mm | $7.8-26.2$ | $7.8-26.2$ | NA
Cable thickness mm | $1.2-2.0$ | $1.2-2.0$ | NA |
$J_{e}$ (at $1.9$ K, $16$ T) | A/mm2 | 870 | 800 | 700
$J_{e}$ (at 1.9 K, 20 T) | A/mm2 | 360 | 740 | 590
$J_{0}$ / $J_{e}$ | $0.67$ | $0.67$ | $0.54$ |

####  5.5.1 Design Criteria

The criteria defined in the conceptual design are summarized in Table 2. The
magnet must be able to produce 20 T in a 50 mm clear aperture with at least
15% of load-line margin. This means that the short-sample bore field, i.e. the
bore field achieved when the magnet reaches the current limits established by
the conductor critical surface, is at least 23.5 T. The design must have all
the geometrical harmonics field below 5 units at the nominal field and at 2/3
of the aperture radius (magnetization effects are not included at this stage).
All the coils are assumed to be powered in series (a condition which impacts
both the magnetic design and the quench protection system), and the hot spot
temperature at quench is assumed to be limited to 350 K, both in the Nb3Sn
[61] and in the HTS coils [62], [63], [64]. In terms of stress limits, for the
Nb3Sn we chose 150 and 180 MPa at 293 K and 1.9 K respectively, consistently
with results published in [65], whereas for the HTS we defined a preliminary
and more conservative value of 120 MPa [66], [67].

Table 2: Magnet design parameters used in the study Parameter | Unit | Value
---|---|---
Operational temperature | K | $1.9$
Operational bore field $B_{0_{o}p}$ | T | $20$
Load-line margin | % | $15$
Geometrical harmonics ($20$ T, $R_{ref}=17$ mm) | unit | $<5$
Maximum Nb3Sn coil eq. stress ($293$ K) | MPa | $150$
Maximum Nb3Sn coil eq. stress ($1.9$ K) | MPa | $180$
Maximum HTS coil eq. stress ($293$ K, $1.9$ K) | MPa | 120
Maximum hot spot temperature | K | $350$

####  5.5.2 Magnetic Design

For a preliminary magnetic analysis of the 20 T hybrid magnet, we investigated
different coil design options, all shown in Fig. 8. In particular, the
following lay-outs were considered: traditional Cos-theta (CT) design, Stress
Management Cos-theta(SMCT) design, Canted Cos-theta (CCT) design, Block (BL)
design, and Common-Coil (CC) design. The main parameters are given in Table 3.
The cables considered range from 9.1 to 21.6 mm width and from 1.5 to 2.1 mm
thickness (including insulation). All the designs implement HTS Bi2212
Rutherford cables; REBCO CORC® wire, with an assumed 7.5 x 7.5 mm2 of
dimension with insulation, was considered only for the common-coil, given the
large bending radius of the latter. With a 20 T bore field, the operational
current varies from 10.7 to 17.8 kA, and the peak field in the HTS and LTS
coils is respectively 20.2-21.0 T and 12.7-17.0 T. The target load-line margin
is achieved in the CT, SMCT, and BL designs, while in the others the margin is
a few percentage points below target. In terms of field quality, design
criteria are met by all the designs except the BL, which features geometric
harmonics up to the 10 units level. Finally, it is important to point out that
only a preliminary investigation of the accumulated electro-magnetic (e.m.)
forces in some of the designs was carried out, and a complete mechanical
analysis aimed at bringing the stress in the HTS and LTS below the limits
fixed in Table II has not been performed yet. Similarly, a full field quality
and quench protection analysis has not been performed. Therefore, the designs
depicted in Fig. 8 represent only a first iteration and a starting point of
the design, and, since they meet only part of the criteria, they are not yet
comparable.

Figure 8: Cross-sections of 20 T hybrid dipole coils. The designs use
consistent conductor properties, but are at different stages of the analysis
in terms of field quality, mechanics, and quench protection: therefore, they
are not comparable among them. From left two right: Cos-theta (CT) design,
with 4 (top) and 2 (bottom) layer Bi2212 coils; Stress management Cos-theta
(SMCT) design, with 4 (top) and 2 (bottom) layers Bi2212 coils; Canted Cos-
theta (CCT) design, with 4-layer Bi2212 coil; Block (BL) design, with and
without stress management; Common Coil (CC) design, with Bi2212 (top, with 3
external Nb3Sn layers, and center, with 5 external Nb3Sn layers) and REBCO
CORC® coils (bottom, with 4 external Nb3Sn layers). For all the CC designs,
only one aperture is shown. Table 3: 20 T Hybrid Magnet Parameters.
Definitions: ”w”=width, ”t”=thickness, ”op”=operational, ”ss”=short-sample. Parameter | Unit | CT I | CT II | SMCT I | SMCT II | CCT | BL I | BL II | CC I | CC II | CC III
---|---|---|---|---|---|---|---|---|---|---|---
Cable I w/t | mm | 18.7/1.5 | 20.9/1.7 | 21.4/1.5 | 21.4/1.5 | 18.7/1.9 | 17.1/2.1 | 17.1/2.1 | 18.7/1.8 | 18.7/1.8 | 7.5/7.5
Cable II w/t | mm | 16.4/1.5 | 24.7/2.1 | 8.7/1.5 | 24.2/1.5 | - | 17.1/2.1 | 17.1/2.1 | 13.6/1.9 | 13.6/1.9 | 21.6/1.9
Cable III w/t | mm | 16.3/1.5 | 18.0/1.5 | 15.8/1.5 | 15.8/1.5 | - | - | - | - | - | -
Current${}_{\textit{op}}$ | kA | 10.7 | 13 | 11.4 | 11.8 | 12.8 | 12.6 | 12.2 | 14 | 13.9 | 17.8
B${}_{\textit{bore}}^{\textit{op}}$ | T | 20 | 20 | 20.1 | 20 | 20 | 20 | 20 | 20 | 20 | 20
B${}_{\textit{peak}}^{\textit{op}}$ HTS/LTS | T | 20.5/12.7 | 20.3/16.1 | 20.6/13.6 | 20.6/16.0 | 20.2/13.2 | 20.6/15.1 | 20.9/15.2 | 20.4/13.8 | 20.2/13.7 | 21.0/17.0
B${}_{\textit{bore}}^{\textit{ss}}$ | T | 24.4 | 23.5 | 24.4 | 23.2 | 23.4 | 23.6 | 23.6 | 22.9 | 23 | 21.7
B${}_{\textit{peak}}^{\textit{ss}}$ HTS/LTS | T | 24.9/15.4 | 23.8/17.7 | 24.9/16.4 | 23.8/18.4 | 23.6/12.9 | 24.3/17.7 | 24.7/18.0 | 23.3/15.7 | 23.3/15.7 | 24.7/18.2
Margin | % | 18/25 | 21/15 | 22/18 | 20/15 | 14/14 | 21/17 | 22/17 | 13/13 | 13/13 | 15/7
Area cable HTS |  mm2 | 3241 | 1494 | 2091 | 1527 | 4490 | 1360 | 1500 | 1290 | 1154 | 1012
Area cable LTS |  mm2 | 2150 | 6106 | 3780 | 5148 | 4915 | 4740 | 4640 | 2326 | 2558 | 4191
Coil width | mm | 105 | 129 | 144 | 149 | 135 | 80 | 112 | 70 | 104 | 106
Coil inner rad | mm | 25 | 25 | 30 | 30 | 30 | 35 | 35 | 25 | 25 | 25

##### 5.5.2.1 Cos-theta (CT), Stress Management Cos-theta (SMCT), and Canted
Cos-theta (CCT) Designs

For the CT options we considered a design with double layers coils, each wound
with the same cable. This design choice avoids interlayer splices and has been
implemented in most of the Nb3Sn CT coils fabricated so far (the only
exception being the CERN-ELIN and UT-CERN dipole magnets [50]). The first
design (top CT in Fig. 8) has 4 Bi2212 layers and 2 Nb3Sn layers, with a peak
field in the Nb3Sn of 12.7 T and a total coil width of 105 mm. In a second
design (bottom CT in Fig. 8) we reduced the Bi2212 layers from 4 to 2 by
increasing the width of the Nb3Sn coils. As a result, the peak field in the
Nb3Sn rose to 16.1 T and the total coil width rose to 129 mm. As shown in
sector coils, a traditional CT design magnet aiming at 20 T is characterized
by high coil stress in the azimuthal and radial directions. A possible
alternative solution is the SMCT, where each layer is separated by 5 mm thick
spars (or mandrels) and each cable block is separated by ribs, connected to
the mandrel [25]. The implementation of stress intercepting elements results
in an overall increase of coil width from 102-129 mm in the CT to 144-149 mm,
and in the conductor area. A further step towards the reduction of the stress
is done with the CCT design, where each turn is separated by spars and ribs
[29]-[31]. The field quality is naturally achieved by superimposing the two
tilted solenoids (see Fig. 8 center). For the 20 T hybrid we chose a simple
design with 4 Bi2212 layers and 2 Nb3Sn layers, all wound with a MQXF cable.
The total area of the insulated cable (taken from a simple cross-section of
the 3D design) is, as expected, larger than in the previous CT and SMCT
designs. However, since the layer-to-layer splices are located in the coil
ends, a full graded coil, with cables progressively smaller from the inserts
to the outserts, can reduce significantly the coil size, and it will be the
goal of the next step in the optimization.

##### 5.5.2.2 Block (BL) Design

The Block design [68], [69], [70] allows for a very efficient subdivision
between the HTS and LTS coils, since the cables are aligned with the flux
lines. Therefore, the area of Bi2212 in the block design shown in Fig 8 (BL
top design), is smaller than for the CT, SMCT and CCT options (see Table 3).
Also, in terms of total conductor area the design is very compacted, despite
the inclusion of a 10 mm thick internal support in the inner coil that
increases the coil aperture to 70 mm (similarly to the coil design of FRESCA2
[71] and TFD [71] magnets). However, as shown in [72], the peak stress in the
coil, in particular because of the horizontal e.m. forces, can be as high as
280 MPa in the Nb3Sn and 160 MPa in the Bi2212 at 20 T. Therefore, an
alternative has been considered where vertical and horizontal plates are
included to intercept part of the e.m. forces. In the bottom BL design in Fig.
8, intercepting plates separates Bi2212 and Nb3Sn coils: consequently, the
coil in-creases in size, but the stress in the Nb3Sn and in the Bi2212 coils
decreases to about 160 MPa and 140 MPa respectively at 20 T.

##### 5.5.2.3 Common-coil design

On Fig. 8, 3 different common coil designs for the 20 T hybrid are shown. The
common-coil design [73], [74], [75] is based on racetrack coils that, with a
large bending radius in the ends, cover both magnet apertures (in Fig. 8 only
one aperture is shown). The large bending radius opens the possibility not
only of implementing the react-and-wind technique, but also to utilize REBCO
CORC® cable, whose rigidity makes small bending radius a possible source of
conductor degradation. Similar to the block design, the common-coil allows
aligning the block with the flux lines, thus minimizing the HTS conductor use.
Also, by having the layer-to-layer splice inside the winding pole at the
center of the coil, one can wind and react individual layers, and grade each
layer to maximize efficiency. The two top designs in Fig. 8 use Bi2212 cables
in the small blocks around the aperture and in the first layer, followed by
either 3 or 5 layers of Nb3Sn cables. In both designs, the coil area and width
are small compared to the previous designs; however, it is important to point
out that the load-line margins are below the 15% criteria. In the third
design, we implement a large CORC® wire, in series with 4 layers of HTS. Also
in this case further magnetic analysis will be carried out to bring the load-
line margin to the design criteria. Regarding the coil stress, the common coil
design allows the insertion of vertical plates to intercept the horizontal
e.m. forces, and as in the BL design, horizontal bars can be used to intercept
the vertical force. As a next step, a mechanical analysis will be performed to
verify the stress, and the magnetic design will be updated accordingly.

##### 5.5.2.4 Conclusions - 20T design concepts

We presented in this section a preliminary investigation of a hybrid 20 T
dipole, which we consider a promising option for a dipole magnet operating
beyond the limits of Nb3Sn and aimed at minimizing the HTS volume. Two HTS
conductors are considered: Bi2212, in the form of a Rutherford cable with
$J_{e}$ of $740$ A/mm2 at $20$ T, and REBCO tape in a CORC®/STAR® wire with
$J_{e}$ of $590$ A/mm2 at $20$ T. As part of the design criteria, we target a
bore field of $20$ T with a load-line margin of at least 15% for both LTS and
HTS coils. Also, all the coils are assumed powered in series, and stress must
be kept below $150-180$ MPa in the Nb3Sn and below $120$ MPa in the HTS. A
preliminary analysis done with sector coils indicated that 1) with identical
$J_{0}$ in both HTS and LTS, we have a coil width of $\sim 70$ mm, 2) radial
stresses of about $200$ MPa are generated by the radial/horizontal e.m.
forces, and 3) a significant reduction of HTS area can be obtained by anti-
grading, i.e. by increasing the size of the Nb3Sn outsert. Finally, we
performed a preliminary analysis of a $20$ T hybrid with different coil design
options, all shown in Fig. 8. The designs are not yet comparable since they do
not meet all the specifications, but they provide a first idea of the overall
coil features, and they constitute a starting point for further analysis.

Statement 11: 20 T accelerator dipoles may be within reach Judicious magnet
design, incorporating concepts such as stress management and optimized pre-
stressing, indicates 20 T dipole fields may be achievable with existing
superconducting materials in a variety of magnet configurations.

###  5.6 Technology underpinning the development of advanced magnet technology

There are many elements of technology development that lie at the heart of
advanced magnet R$\&$D . Advances in modeling are providing more detailed
insight into stress and strain states in magnets, including full 3D effects
and taking into account complex nonlinear material and interface behavior. We
are now seeing synergies with the broader Accelerator Modeling community (see
associated whitepaper [76]). Advances in diagnostics provide new and unique
insight into the timescales and energy scales of perturbations that may lead
to quenches and to magnet training, and to their location in the magnet.
Advances in materials and testing techniques may lead to reduction in
training. These elements are a significant part of the US MDP and provide
lasting progress for the broader superconducting magnet community. Campanion
whitepapers that explore these areas in more detail include [77], [78], [79],
and [80].

Advancing magnet technology requires a detailed understanding of magnet
performance and insight into magnet behavior and performance limitations
through optimized diagnostics. A key element of the US MDP approach is the
development and implementation of an integrated diagnostics package of novel
sensor hardware, electronics and data analysis techniques for real-time, non-
invasive monitoring of LTS, HTS and hybrid magnets. This entails synchronous
acquisition of voltages, acoustic, magnetic and optical data for magnets under
test, and a synergistic data analysis. The end goal of such development would
be the application of this advanced diagnostic system to existing and future
accelerator magnets and magnet test facilities. Current MDP R$\&$D elements
for superconducting magnet diagnostics include the following:

  * •

Develop a next-generation acoustic emission diagnostic hardware capable of
self-calibration to drastically improve disturbance triangulation accuracy and
fingerprinting. Use it to study physics of quench-triggering disturbances and
mechanisms of mechanical memory and training in Nb3Sn magnets.

  * •

Establish fiber-optic based diagnostic capabilities through the use of Fiber
Bragg Grating (FBG) and Rayleigh scattering-based sensors to measure elastic
deformations, localize hot spots (especially in HTS magnets) and probe
mechanical disturbances in SC cables.

  * •

Improve accuracy of voltage, magnetic and acoustic-based diagnostics through
calibration using distributed spot heater and piezo-transducer arrays.

  * •

Bring magnetic diagnostics to the next level through development and use of
flexible multi-element quench antennas, large-scale Hall sensor arrays and
non-rotating field quality probes, aiming at understanding electromagnetic
instabilities in LTS magnets and imaging current-sharing patterns in
superconducting cables and HTS magnet coils. Develop new algorithms for
current flow reconstruction and disturbance localizations.

  * •

Design and conduct innovative small-scale experiments to probe training
behavior and energy release in impregnated cables under similar loads as in
the magnets.

  * •

Develop new methods for reliable and robust quench detection and localization
for HTS magnets and hybrid LTS/HTS magnets.

  * •

Use diffuse field ultrasonic techniques to enable targeted delivery of
vibrational excitation to the conductor, for a non-invasive structural local
probing of SC coils and mitigation of their training behavior.

  * •

Apply machine learning and deep learning approaches to process diagnostic data
and identify real-time predictors of magnet quenching

  * •

Develop cryogenic digital and analog electronics to facilitate, simplify and
improve reliability of diagnostic instrumentation by enabling pre-processing
of magnet diagnostic data in the cryogenic environment.

A synergistic analysis of data acquired by these diverse diagnostic techniques
will bring us closer to answering key technical questions that define SC
magnet performance. It is an ample and comprehensive program with the aim of
developing an integrated system of hardware and software solutions applicable
not only to the U.S. MDP SC magnets, but to any other SC accelerator magnet
and also magnets for test facilities. The effort should extend well beyond MDP
and engage instrumentation experts across national and international labs.

In addition to the diagnostics that provide critical insight into magnet
behavior, a number of potential techniques aiming to affect the training rate
before or during magnet powering are under investigation:

  * •

High-Cp conductor and insulation development that can lead to conductors and
coils with optimized characteristics enabling stable operation against
perturbations [81], [82];

  * •

Artificially increasing the coil current during a quench by discharging a
large capacitor at quench detection. The overcurrent transient will generate
forces beyond the nominal quench current, possibly significantly increasing
the rate at which the magnet trains and hence reducing the total number of
training quenches;

  * •

Inducing ultrasonic vibrations into the conductor and coil parts during ramp
up. This may allow for gradual energy discharges, avoiding accumulation of
energy (notably due to friction) in areas around the coil/conductor and
potentially improving the rate at which magnets train;

  * •

Performing fast-turn-around cable/stack training R$\&$D in a controllable
configuration, thereby providing more quantitative insight into training
mechanisms and means to influence them.

These approaches complement other technology areas that are focused on
understanding the disturbance spectrum and on mitigating their sources.

Statement 12: Advanced diagnostics provide ”science” of magnets New
diagnostics and testing techniques are providing extraordinary insight into
magnet behavior and provide critical feedback to conductor and magnet
designers. The techniques and knowledge gained are valuable to the broader
superconducting magnet community.

##  6 Nurturing a strong industrial magnet ecosystem for science and society

Science facilities, particularly those of the scale of a future collider for
high energy physics, depend fundamentally on industry. A strong industrial
capacity can be very effective at reducing cost of components, and enables
timely delivery to meet project schedules.

The HEP community recognizes that the timescales for the germination of a
future collider project are inconsistent with the timescales of industry;
hence an approach that focuses on nurturing an ecosystem of industrial
capability and expertise, rather than on industrial capacity, is more viable
between HEP projects.

###  6.1 Building and leveraging capabilities within US industry

Nurturing the industrial ecosystem can, and should, be pursued on multiple
fronts:

  * •

Support technology transfer and public private partnerships related to HEP
technology, e.g. advanced magnet systems, that have potential to seed new
applications in society. Examples include medical gantries, compact fusion,
superconducting magnets for wind generation, etc. An excellent example of a
DOE program that targets this avenue to nurturing the ecosystem is the DOE
Accelerator Stewardship program.

  * •

Align DOE investments in small businesses with HEP community needs. The DOE
SBIR program strives to nurture the industry ecosystem, and HEP programs, such
as the MDP, can work to encourage industry involvement in the program around
topics and capabilities that support future collider technologies.

  * •

The industry ecosystem depends on a pipeline of talent and expertise. HEP can
work with labs and Universities to make sure a steady stream of scientists and
engineers are produced that can support industry needs.

The success of the DOE-OHEP Accelerator Stewardship Program, initiated
following the report Accelerators for America’s Future [83], catalyzed the
creation of a new program office in DOE, the Office of Accelerator R$\&$D and
Production (ARDAP). Its mission is to …help coordinate Office of Science (SC)
accelerator R&D, foster public-private partnerships to develop and deploy
accelerator technology, support workforce development and improve its
diversity, and provide resources for accelerator design and engineering. The
overarching goal is to ensure a robust pipeline of innovative accelerator
technology, train an expert workforce, and reduce significant supply chain
risks by re-shoring critical accelerator technology. ARDAP is therefore
ideally suited to support the industrial ecosystem described above, that is so
essential to deliver on future collider opportunities.

Statement 13: Work with ARDAP to strengthen the magnet ecosystem The newly
minted Office of Accelerator R$\&$D and Production (ARDAP) is ideally suited
to work with, and support, DOE-OHEP needs in terms of domestic industrial
expertise and capabilities for future colliders. MDP can support HEP by
clearly identifying critical needs, both near and long-term, for HEP
accelerator magnet development and production.

##  7 Opportunities and challenges for international collaboration

High Energy Physics is fundamentally an international endeavor, and the
development of critical technologies enabling new colliders is similarly
advanced through the combined efforts of international scale. All areas of the
MDP benefit from close communication and collaboration with magnet and
conductor R$\&$D partners outside the US. Well-established communication
channels ensure that we maximize progress through programs that are both
competitive but also complementary.

Ties with international laboratories and universities have been, and we expect
will continue to be, a critical element of our program. The US MDP leadership
strives to foster a diverse, inclusive, and innovative culture that motivates
innovation and open communication. Transparency in our purpose and research
approach has proven to be effective in supporting the development of strong
collaborations with international partners.

Furthermore, we note that a significant fraction of MDP staff were educated,
wholly or partially, at international institutions. Exchanges of ideas,
concepts, and results with international collaborators is central to our
approach to research.

The European Strategy process has recently been completed, resulting in a
suite of recommendations related to investments in critical technologies for
future colliders. The implementation of those recommendations is currently
underway; the European Laboratory Directors Group (LDG) initiated the
development of roadmaps for each area, including magnet technology - the
European High Field Magnet program (HFM) [40], [84]. That process is now
completed, and teams from multiple European laboratories and Universities are
currently organizing to deliver on the European magnet roadmap.

The US MDP was actively engaged in the European roadmapping process, and we
now have the opportunity to collaborate with the HFM through our established
programs. A major consideration is to document collaboration topics to make
sure efforts are equitable, and to insist on transparency and openness among
the teams, while encouraging innovation and recognizing individual’s
contributions to the programs.

Statement 14: High Energy Physics is an international endeavor High Energy
Physics is an international endeavor, and magnet technology research for the
field is accordingly international in nature. Equity and openness are sought
with collaborators with common interests and relevant expertise and
capabilities.

##  8 Summary

High field magnet technology is essential to the mission of High Energy
Physics. A robust long range R$\&$D program serves as an investment in the
field’s future, providing lasting advances and understanding in magnet
performance, with innumerable benefits to the broader superconducting magnet
community. Furthermore, such a longstanding R$\&$D effort serves to lead and
align industry, in particular small businesses, with the field, and
potentially to initiate and incubate new applications of superconducting
technology for society.

A long range R$\&$D magnet program, i.e. the MDP, is a highly leveraged
investment that provides advanced technology that paves the way for future
collider projects, providing a solid foundation of knowledge and expertise for
directed R$\&$D programs when opportunities arise. We note that the MDP serves
as an excellent venue for nurturing new talent and maintaining expertise that
is critical to HEP’s future; the program is highly sought after by early
career scientists, and is designed and led with the intention of growing the
next generation of magnet scientists, providing continuity and promise for our
field.

## References

  * [1] William Barletta et al.  “High Energy Hadron Colliders - Report of the Snowmass 2013 Frontier Capabilities Hadron Collider Study Group” 28 pages, 18 figures. This document was prepared as the final report of the Frontier Capabilities Hadron Collider Study Group at the 2013 Community Summer Study ”Snowmass 2013”, Minneapolis, MN, July-August 2013  In _arXiv.org_ physics.acc-ph, 2013  URL: arXiv.org
  * [2] Michael Benedikt and Frank Zimmermann  “Proton colliders at the energy frontier”  In _Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment_ , 2018  DOI: 10.1016/j.nima.2018.03.021
  * [3] V Shiltsev and F Zimmermann  “Modern and future colliders”  In _Reviews of Modern Physics_ 93.1, 2021, pp. 015006  DOI: 10.1103/revmodphys.93.015006
  * [4] Michael Benedikt and Frank Zimmermann  “The physics and technology of the Future Circular Collider”  In _Nature Reviews Physics_ 1.4, 2019, pp. 238–240  DOI: 10.1038/s42254-019-0048-0
  * [5] Jie Gao  “CEPC and SppC Status — From the completion of CDR towards TDR”  In _International Journal of Modern Physics A_ 36.22, 2021, pp. 2142005  DOI: 10.1142/s0217751x21420057
  * [6] M. Bogomilov et al.  “Demonstration of cooling by the Muon Ionization Cooling Experiment”  In _Nature_ 578.7793, 2020, pp. 53–59  DOI: 10.1038/s41586-020-1958-9
  * [7] Henryk Piekarz et al.  “Record High Ramping Rates in HTS Based Super-conducting Accelerator Magnet”  In _arXiv_ , 2021  eprint: 2111.06459
  * [8] J.S. Berg et al.  “Acceleration stages for a muon collider”  In _Proceedings of the 1999 Particle Accelerator Conference (Cat. No.99CH36366)_ 5, 1999, pp. 3152–3154 vol.5  DOI: 10.1109/pac.1999.792233
  * [9] A. al.  “Test results for a high field (13T) Nb3Sn dipole”  In _Proceedings of Particle Accelerator Conference_ , 1997, pp. 3212
  * [10] Alexander V. Zlobin et al.  “Reassembly and Test of High-Field Nb3Sn Dipole Demonstrator MDPCT1”  In _IEEE Transactions on Applied Superconductivity_ 31.5, 2020, pp. 1–6  DOI: 10.1109/tasc.2021.3057571
  * [11] A F Lietzke et al.  “Test results of RD3c, a Nb¡sub¿3¡/sub¿Sn common-coil racetrack dipole magnet”  In _IEEE Trans. Appl. Supercond_ 13.2, 2003, pp. 1292 1296  DOI: 10.1109/tasc.2003.812652
  * [12] V.S. Kashikhin et al.  “Development and test of single-layer common coil dipole wound with reacted Nb/sub 3/Sn cable”  In _IEEE Transactions on Applied Superconductivity_ 14.2, 2004, pp. 353–356  DOI: 10.1109/tasc.2004.829128
  * [13] R Gupta et al.  “React and Wind Nb3Sn common coil dipole”  In _IEEE Trans. Appl. Supercond_ 17.2, 2007, pp. 1130 1135  DOI: 10.1109/tasc.2007.898139
  * [14] Ramesh Gupta et al.  “New Approach and Test Facility for High-Field Accelerator Magnets R&D”  In _IEEE Transactions on Applied Superconductivity_ 30.4, 2019, pp. 1–6  DOI: 10.1109/tasc.2019.2961064
  * [15] M Marchevsky et al.  In _IEEE Trans. Appl. Supercond_ 24.3, 2014, pp. 1 6  DOI: 10.1109/tasc.2013.2285881
  * [16] Gerard Willering et al.  “Tests of the FRESCA2 100 mm Bore Nb3Sn Block-Coil Magnet to a Record Field of 14.6 T”  In _IEEE Transactions on Applied Superconductivity_ 29.5, 2019, pp. 1–6  DOI: 10.1109/tasc.2019.2907280
  * [17] “science.energy.gov/media/hep/hepap/pdf/Reports/Accelerator_RD_Subpanel/Report.pdf”  URL: http://science.energy.gov/media/hep/hepap/pdf/Reports/Accelerator%5C_RD%5C_Subpanel%5C_Report.pdf
  * [18] G. Ambrosio, G. Apollinari, M. Baldini and R. Carcagno  “Leading-Edge technology And Feasibility-directed (LEAF) Program aimed at readiness demonstration for Energy Frontier Circular Colliders by the next decade”  In _arxiv:2203.07654_ URL: https://arxiv.org/abs/2203.07654
  * [19] Giorgio Ambrosio et al.  “Development and demonstration of next generation technology for Nb3Sn accelerator magnets with lower cost, improved performance uniformity, and higher operating point in the 12-14 T range”  In _arXiv:2203.07352_ URL: https://arxiv.org/abs/2203.07352
  * [20] Stephen A Gourlay et al.  “The US magnet development program plan”, 2016
  * [21] Soren Prestemon et al.  “The 2020 Updated Roadmaps for the US Magnet Development Program”  In _arXiv_ , 2020  eprint: 2011.09539
  * [22] N. Diaczenko et al.  “Stress management in high-field dipoles”  In _Proceedings of the 1997 Particle Accelerator Conference (Cat. No.97CH36167)_ 3, 1997, pp. 3443–3445  DOI: 10.1109/pac.1997.753236
  * [23] S Caspi et al.  “Canted–Cosine–Theta Magnet (CCT)—A Concept for High Field Accelerator Magnets”  In _IEEE Transactions on Applied Superconductivity_ 24.3, 2014, pp. 1–4  DOI: 10.1109/tasc.2013.2284722
  * [24] A.V. Zlobin, V.. Kashikhin and I. Novitski  “LARGE-APERTURE HIGH-FIELD Nb3Sn DIPOLE MAGNETS”  In _9th International Particle Accelerator Conference_ DOI: 10.18429/jacow-ipac2018-wepml026
  * [25] A.V. Zlobin, V.. Kashikhin and I. Novitski  “LARGE-APERTURE HIGH-FIELD Nb3Sn DIPOLE MAGNETS”  In _9th International Particle Accelerator Conference_ DOI: 10.18429/jacow-ipac2018-wepml026
  * [26] I. Novitski et al.  “Using Additive Manufacturing technologies in high-field accelerator magnet coils”  In _Cryogenic Engineering Conference and International Cryogenic Materials Conference_ , 2021
  * [27] Diego Arbelaez et al.  “Status of the Nb3Sn Canted-Cosine-Theta Dipole Magnet Program at Lawrence Berkeley National Laboratory” Conference Name: IEEE Transactions on Applied Superconductivity  In _IEEE Transactions on Applied Superconductivity_ , 2022, pp. 1–1  DOI: 10.1109/TASC.2022.3155505
  * [28] Michael Daly et al.  “BOX: an efficient benchmark facility for the study and mitigation of interface-induced training in accelerator type high-field superconducting magnets” Publisher: IOP Publishing  In _Supercond. Sci. Technol._ 34.11, 2021, pp. 115008  DOI: 10.1088/1361-6668/ac2002
  * [29] Mariusz Juchno et al.  “Mechanical Utility Structure for Testing High Field Superconducting Dipole Magnets” Conference Name: IEEE Transactions on Applied Superconductivity  In _IEEE Transactions on Applied Superconductivity_ 29.5, 2019, pp. 1–4  DOI: 10.1109/TASC.2019.2896044
  * [30] Lucas Brouwer et al.  “Design of CCT6: a Large-Aperture, Nb3Sn Dipole Magnet for HTS Insert Testing” Conference Name: IEEE Transactions on Applied Superconductivity  In _IEEE Transactions on Applied Superconductivity_ , 2022, pp. 1–1  DOI: 10.1109/TASC.2022.3151723
  * [31] Tengming Shen and Laura Garcia Fajardo  “Superconducting Accelerator Magnets Based on High-Temperature Superconducting Bi-2212 Round Wires”  In _Instruments_ 4.2, 2020, pp. 17  DOI: 10.3390/instruments4020017
  * [32] V.. Kashikhin, V. Lombardo and G. Velev  “Magnet Design Optimization for Future Hadron Colliders”, 2019  URL: https://www.osti.gov/biblio/1545078
  * [33] X Xu, M Sumption, X Peng and E W Collings  “Refinement of Nb3Sn grain size by the generation of ZrO2 precipitates in Nb3Sn wires”  In _Applied physics letters_ 104.8 American Institute of Physics, 2014, pp. 082602  DOI: 10.1063/1.4866865
  * [34] Shreyas Balachandran et al.  “Beneficial influence of Hf and Zr additions to Nb4at%Ta on the vortex pinning of Nb3Sn with and without an O source”  In _Superconductor Science and Technology_ 32.4 IOP Publishing, 2019, pp. 044006  DOI: 10.1088/1361-6668/aaff02
  * [35] G Sabbi et al.  “Performance Characteristics of Nb3Sn Block-Coil Dipoles for a 100 TeV Hadron Collider”  In _IEEE Transactions on Applied Superconductivity_ 25.3, 2015, pp. 4001407  DOI: 10.1109/TASC.2014.2365471
  * [36] K. Marken  “Fundamental issues in high temperature superconductor (HTS) materials science and engineering”  In _High Temperature Superconductors (HTS) for Energy Applications_ , Woodhead Publishing Series in Energy  Woodhead Publishing, 2012, pp. 3–33  DOI: 10.1533/9780857095299.1.3
  * [37] D C Larbalestier et al.  “Isotropic round-wire multifilament cuprate superconductor for generation of magnetic fields above 30 T”  In _Nature materials_ 13.4, 2014, pp. 375–381  DOI: 10.1038/nmat3887
  * [38] V. Selvamanickam  “High temperature superconductor (HTS) wires and tapes”  In _High Temperature Superconductors (HTS) for Energy Applications_ , Woodhead Publishing Series in Energy  Woodhead Publishing, 2012, pp. 34–68  DOI: 10.1533/9780857095299.1.3
  * [39] T. Shen, A. Zlobin and D. Larbalestier  “High Temperature Superconducting $Bi-2212$ Magnets for Energy Frontier Circular Colliders”  In _arXiv:2203.10564_ URL: https://arxiv.org/abs/arXiv:2203.10564
  * [40] P. Védrine et al.  “High-field magnets”  In _European Strategy for Particle Physics - Accelerator R &D Roadmap_, 2022, pp. 11–61
  * [41] Xiaorong Wang et al.  “REBCO – a silver bullet for our next high-field magnet and collider budget?”  In _arXiv:2203.08736_ URL: https://arxiv.org/abs/2203.08736
  * [42] Soren Prestemon et al.  “The 2020 Updated Roadmaps for the US Magnet Development Program”, 2020
  * [43] D. Laan, J. Weiss, D. Hazelton and R. Gupta  “Recent progress on CORC cable, wire and magnet development” Presentation at EUCAS 2019, 2019  URL: https://www.advancedconductor.com/wp-content/uploads/2020/03/Van-der-Laan-EUCAS-2019.pdf
  * [44] Vadim Kashikhin, Vito Lombardo and Gueorgui Velev  “Magnet Design Optimization for Future Hadron Colliders”  Melbourne, Australia: JACOW Publishing, Geneva, Switzerland, 2019, pp. 4307–4310  DOI: 10.18429/JACoW-IPAC2019-THPTS084
  * [45] Xiaorong Wang et al.  “A viable dipole magnet concept with REBCO CORC® wires and further development needs for high-field magnet applications”  In _Superconductor Science and Technology_ 31.4 IOP Publishing, 2018, pp. 045007  DOI: 10.1088/1361-6668/aaad8f
  * [46] Xiaorong Wang et al.  “A 1.2 T canted cos$\vartheta$ dipole magnet using high-temperature superconducting CORC® wires”  In _Superconductor Science and Technology_ 32.7 IOP Publishing, 2019, pp. 075002  DOI: 10.1088/1361-6668/ab0eba
  * [47] Xiaorong Wang et al.  “Development and performance of a 2.9 Tesla dipole magnet using high-temperature superconducting CORC® wires”  In _Superconductor Science and Technology_ 34.1 IOP Publishing, 2020, pp. 015012  DOI: 10.1088/1361-6668/abc2a5
  * [48] P Ferracin et al.  “Towards 20 T Hybrid Accelerator Dipole Magnets”  In _IEEE Transactions on Applied Superconductivity_ 32.6, 2022, pp. 4000906  DOI: 10.1109/TASC.2022.3152715
  * [49] R Maingi et al.  “Summary of the FESAC transformative enabling capabilities panel report”  In _Fusion Science and Technology_ 75.3 Taylor & Francis, 2019, pp. 167–177  DOI: 10.1080/15361055.2019.1565912
  * [50] “Nb3Sn Accelerator Magnets”  Springer Open, 2019
  * [51] V. Selvamanickam  “High Temperature Superconductors (HTS) for Energy Applications”  In _Part I: Fundamental science and engineering of high temperature superconductor (HTS) materials and components_ , 2012, pp. 34–68  DOI: 10.1533/9780857095299.1.34
  * [52] P. McIntyre and A. Sattarov  “ON THE FEASIBILITY OF A TRIPLER UPGRADE FOR LHC**Work supported by US Dept. of Energy, grant # DE-FG03-95ER40924,and by EC Research Infrastructure Activity FP6: ’Structuring. the European Research Area’ program, CARE-RI13-CT-3003-506395.”  In _Proceedings of the 2005 Particle Accelerator Conference_ , 2005, pp. 634–636  DOI: 10.1109/pac.2005.1590511
  * [53] L Rossi and E Todesco  “Conceptual design of 20 T dipoles for high-energy LHC”  In _arXiv_ , 2011  eprint: 1108.1619
  * [54] E. Todesco and et  “Dipoles for High-Energy LHC”  In _IEEE Trans. Appl. Supercond_ 24, 3, 2014
  * [55] Qingjin Xu et al.  “20-T Dipole Magnet With Common-Coil Configuration: Main Characteristics and Challenges”  In _IEEE Transactions on Applied Superconductivity_ 26.4, 2016, pp. 1–4  DOI: 10.1109/TASC.2015.2511927
  * [56] Jeroen van Nugteren et al.  “Toward REBCO 20 T+ Dipoles for Accelerators”  In _IEEE Transactions on Applied Superconductivity_ 28.4, 2018, pp. 1–9  DOI: 10.1109/tasc.2018.2820177
  * [57] GianLuca Sabbi et al.  In _IEEE Transactions on Applied Superconductivity_ 25.3, 2015, pp. 1–7  DOI: 10.1109/tasc.2014.2365471
  * [58] Douglas Martins Araujo et al.  “Preliminary Integration for Testing HTS Feather-M2 in the FRESCA2 Dipole Magnet”  In _IEEE Transactions on Applied Superconductivity_ 30.4, 2019, pp. 1–5  DOI: 10.1109/tasc.2020.2979393
  * [59] Maria Durante et al.  “Manufacturing of the EuCARD2 Roebel-Based Cos-Theta Coils at CEA Saclay”  In _IEEE Transactions on Applied Superconductivity_ 30.4, 2019, pp. 1–5  DOI: 10.1109/tasc.2020.2978788
  * [60] Lucio Rossi et al.  “The EuCARD2 Future Magnets Program for Particle Accelerator High-Field Dipoles: Review of Results and Next Steps”  In _IEEE Transactions on Applied Superconductivity_ 28.3, 2018, pp. 1–10  DOI: 10.1109/tasc.2017.2784357
  * [61] G. Ambrosio  “Maximum allowable temperature during quench in Nb3Sn accelerator magnets”  In _CERN Yellow Report, CERN-2013-006_ , 2013, pp. 43.
  * [62] Liyang Ye, Pei Li, Tengming Shen and Justin Schwartz  “Quench degradation limit of multifilamentary Ag/Bi2Sr2CaCu2O x round wires”  In _Superconductor Science and Technology_ 29.3, 2016, pp. 035010  DOI: 10.1088/0953-2048/29/3/035010
  * [63] A Ishiyama et al.  “Degradation of YBCO Coated Conductors Due to an Over-Current Pulse”  In _IEEE Transactions on Applied Superconductivity_ 21.3, 2011, pp. 3025–3028  DOI: 10.1109/tasc.2010.2092396
  * [64] X Wang, Ulf Trociewitz and Justin Schwartz  “Critical current degradation of short YBa2Cu3O7 - δ coated conductor due to an unprotected quench”  In _Superconductor Science and Technology_ 24, 2010, pp. 035006  DOI: 10.1088/0953-2048/24/3/035006
  * [65] Patrick Ebermann et al.  “Irreversible degradation of Nb3Sn Rutherford cables due to transverse compressive stress at room temperature”  In _Superconductor Science and Technology_ 31.6, 2018, pp. 065009  DOI: 10.1088/1361-6668/aab5fa
  * [66] D.R. Dietderich, T. Hasegawa, Y. Aoki and R.M. Scanlan  “Critical current variation of Rutherford cable of Bi-2212 in high magnetic fields with transverse stress”  In _Physica C: Superconductivity_ 341, 2000, pp. 2599–2600  DOI: 10.1016/s0921-4534(00)01371-x
  * [67] D C van der Laan, D M McRae and J D Weiss  “Effect of transverse compressive monotonic and cyclic loading on the performance of superconducting CORC® cables and wires”  In _Superconductor Science and Technology_ 32.1, 2018, pp. 015002  DOI: 10.1088/1361-6668/aae8bf
  * [68] Gianluca Sabbi et al.  “Design Study of a 16-T Block Dipole for FCC”  In _IEEE Transactions on Applied Superconductivity_ 26.3, 2016, pp. 1–5  DOI: 10.1109/tasc.2016.2537538
  * [69] Michel Segreti et al.  “2-D and 3-D Design of the Block-Coil Dipole Option for the Future Circular Collider”  In _IEEE Transactions on Applied Superconductivity_ 29.5, 2019, pp. 1–4  DOI: 10.1109/TASC.2019.2892058
  * [70] Etienne Rochepault et al.  “The Use of Grading in Nb3Sn High-Field Block-Coil Dipoles”  In _IEEE Transactions on Applied Superconductivity_ 31.4, 2021, pp. 1–10  DOI: 10.1109/tasc.2021.3061246
  * [71] P. Ferracin et al.  “Development of the EuCARD $\hbox{Nb}_{3}\hbox{Sn}$ Dipole Magnet FRESCA2”  In _IEEE Transactions on Applied Superconductivity_ 23.3, 2013, pp. 4002005–4002005  DOI: 10.1109/TASC.2013.2243799
  * [72] Etienne Rochepault, Paolo Ferracin and Giorgio Vallone  “20 T Hybrid Nb3Sn-HTS Block-coil Designs for a Future Particle Collider”  In _IEEE Transactions on Applied Superconductivity_ PP.99, 2022, pp. 1–1  DOI: 10.1109/TASC.2022.3158643
  * [73] Ramesh Gupta et al.  “Common Coil Dipoles for Future High Energy Colliders”  In _IEEE Transactions on Applied Superconductivity_ 27.4, 2017, pp. 1–5  DOI: 10.1109/TASC.2016.2636138
  * [74] Fernando Toral, Javier Munilla and Tiina Salmi  “Magnetic and Mechanical Design of a 16 T Common Coil Dipole for an FCC”  In _IEEE Transactions on Applied Superconductivity_ 28.3, 2018, pp. 1–5  DOI: 10.1109/TASC.2018.2797909
  * [75] Emmanuele Ravaioli and GianLuca Sabbi  “Design of a Compact 16 T Common-Coil Dipole for Future Colliders”  In _IEEE Transactions on Applied Superconductivity_ 28.4, 2018, pp. 1–5  DOI: 10.1109/TASC.2018.2813518
  * [76] S. Biedron, L. Brouwer, a. and b.  “Accelerator Modeling Community White Paper”  URL: https://arxiv.org/abs/2203.08335
  * [77] M. Baldini et al.  “Fiber-optic diagnostic system for future accelerator magnets”  In _arXiv:2203.08309_ URL: https://arxiv.org/abs/arXiv:2203.08309
  * [78] M. Marchevsky, R. Teyber, b. and c.  “Advancing Superconducting Magnet Diagnostics for Future Colliders”  In _arXiv:2203.08869_ URL: https://arxiv.org/abs/2203.07274
  * [79] Maxim Marchevsky  “Understanding training in superconducting accelerator magnets using acoustic emission diagnostics”  In _arXiv:2203.08871_ URL: https://arxiv.org/abs/arXiv:2203.08871
  * [80] Stoyan Stoynev  “Test samples and infrastructure for accelerator magnet developments”  In _arXiv:2203.07274_
  * [81] Xingchen Xu, Alexander V. Zlobin, Xuan Peng and Pei Li  “Development and Study of Nb¡sub¿3¡/sub¿Sn Wires With High Specific Heat”  In _IEEE Transactions on Applied Superconductivity_ 29.5, 2019, pp. 1–4  DOI: 10.1109/tasc.2019.2892325
  * [82] E. Barzi et al.  “Test of Superconducting Wires and Rutherford Cables With High Specific Heat”  In _IEEE Transactions on Applied Superconductivity_ 31.5, 2021, pp. 1–8  DOI: 10.1109/TASC.2021.3069047
  * [83] “Accelerators for America’s Future”  URL: https://science.osti.gov/-/media/hep/pdf/accelerator-rd-stewardship/Report.pdf
  * [84] Pierre Védrine et al.  “High Field Magnet Development for HEP in Europe : A Proposal from LDG HFM Expert Panel”  In _arXiv:2203.08054_ URL: https://arxiv.org/abs/2203.08054

cooley1