PUB-19-400-TD
1
The 16 T Dipole Development Program for FCC and
HE-LHC
D. Schoerling, D. Arbelaez, B. Auchmann, M. Bajko, A. Ballarino, E. Barzi, G. Bellomo, M. Benedikt, S. Izquierdo
Bermudez, B. Bordini, L. Bottura, L. Brouwer, P. Bruzzone, B. Caiffi, S. Caspi, A. Chakraborti, E. Coatanea, G. de
Rijk, M. Dhalle, M. Durante, P. Fabbricatore, S. Farinon, H. Felice, A. Fernandez, I.S. Fernandez, P. Gao, B. Gold,
T. Gortsas, S. Gourlay, M. Juchno, V. Kashikhin, C. Kokkinos, S. Kokkinos, K. Koskinen, F. Lackner, C. Lorin, K.
Loukas, A. Louzguiti, K. Lyytikainen, S. Mariotto, M. Marchevsky, G. Montenero, J. Munilla, I. Novitski, T. Ogitsu, A.
Pampaloni, J. C. Perez, C. Pes, C. Petrone, D. Polyzos, S. Prestemon, M. Prioli, A. M. Ricci, J. M. Rifflet, E. Rochepault,
S. Russenschuck, T. Salmi, I. A. Santillana, F. Savary, C. Scheuerlein, M. Segreti, C. Senatore,M. Sorbi, M. Statera, A.
Stenvall, L. Tavian, T. Tervoort, D. Tommasini, F. Toral, R. Valente, G. Velev, A. P. Verweij, S. Wessel, F. Wolf,
F. Zimmermann, and A. V. Zlobin
Manuscript received October 26, 2018; accepted February 17, 2019.
This work was supported in part by the European Union’s Horizon 2020
research and innovation programme under Grant 654305, EuroCirCol project.
Work at LBNL was supported by the Director, Office of Science of the U.S.
Department of Energy (DOE) under Contract DE-AC02-05CH11231. Work
at NHMFL was supported by the U.S. DOE Office of High Energy Physics
(OHEP) under Grant DE-SC0010421. Work at FNAL was supported by
Fermi ResearchAl-liance, LLC, under Contract DE-AC02-07CH11359 with
the U.S. Department of Energy (OHEP). (Corresponding author: Daniel
Schoerling.)
D. Schoerling, M. Bajko, A. Ballarino, M. Benedikt, S. Izquierdo
Bermudez, B. Bordini, L. Bottura, G. de Rijk, I. S. Fernandez, F. Lackner, A.
M. Louzguiti, J. C. Perez, C. Petrone, M. Prioli, S. Russenschuck, I.A.
Santillana, F. Savary, C. Scheuerlein, L. Tavian, D. Tommasini, A. P.
Verweij, F. Wolf, and F. Zim-mermann are with the European Organization
for Nuclear Research (CERN), Geneva 1211, Switzerland (e-mail:
daniel.schoerling@cern.ch; marta.bajko@ cern.ch; amalia.ballarino@cern.ch;
michael.benedikt@cern.ch; susana. izquierdo.bermudez@cern.ch;
bernardo.bordini@cern.ch; luca.bottura@ cern.ch; gijs.derijk@cern.ch;
inigo.sancho.fernandez@cern.ch; friedrich. lackner@cern.ch;
alexandre.mehdi.louzguiti@cern.ch).
G. Bellomo, S. Mariotto, M. Sorbi, M. Statera, and R. Valente are with the
Istituto Nazionale di Fisica Nucleare (INFN), Milano 20133, Italy (e-mail:
giovanni.bellomo@mi.infn.it; samuele.mariotto@mi.infn.it; mmartchevskii@
lbl.gov).
M. Dhalle, P. Gao, and S. Wessel are with the University of Twente,
Twente 7500, The Netherlands (e-mail: m.m.j.dhalle@utwente.nl;
p.gao@utwente.nl).
M. Durante, H. Felice, C. Lorin, C. Pes, J. M. Rifflet, E. Rochepault, and
M. Segreti are with the CEA, Saclay 91400, France (e-mail:
maria.durante@cea.fr; helene.felice@cea.fr; clement.lorin@cea.fr).
B. Caiffi, P. Fabbricatore, S. Farinon, A. Pampaloni, and A. M. Ricci are
with the Istituto Nazionale di Fisica Nucleare (INFN), Genova 16146, Italy
(e-mail:barbara.caiffi@ge.infn.it; fabbric@ge.infn.it;
stefania.farinon@ge.infn.it).
A. Fernandez, J. Munilla, and F. Toral are with the Centre for Energy,
Envi-ronment and Technology (CIEMAT), Madrid 28040, Spain (e-mail:
alejandro. fernandez@ciemat.es; javier.munilla@ciemat.es).
T. Ogitsu is with KEK, Tsukuba 305-0801, Japan (e-mail: toru.ogitsu@
kek.jp).
B. Auchmann and G. Montenero are with the Paul Scherrer Insti-tut (PSI),
Villigen 5232, Switzerland (e-mail: bernhard.auchmann@psi.ch;
giuseppe.montenero@psi.ch).
A. Chakraborti, E. Coatanea, K. Koskinen, K. Lyytikainen, T. Salmi, and
A. Stenvall are with the Tampere University of Applied Sciences (TAMK),
Tam-pere 33100, Finland (e-mail: ananda.chakraborti@tut.fi;
eric.coatanea@tut.fi; kari.t.koskinen@tut.fi; kari.lyytikainen@tut.fi).
C. Senatore is with the Faculty of Science, University of Geneva (UoG),
Geneva 1211, Switzerland.
Abstract—A future circular collider (FCC) with a center-of-
mass energy of 100 TeV and a circumference of around 100 km,
or an energy upgrade of the LHC (HE-LHC) to 27 TeV require
bending magnets providing 16 T in a 50-mm aperture. Several
development programs for these magnets, based on Nb
3
Sn
technology, are being pursued in Europe and in the U.S. In these
programs, cos–theta, block-type, common-coil, and canted–cos–
theta magnets are ex-plored; first model magnets are under
manufacture; limits on con-ductor stress levels are studied; and a
conductor with enhanced characteristics is developed. This paper
summarizes and discusses the status, plans, and preliminary
results of these programs.
Index Terms—FCC, Nb
3
Sn, superconducting, 16 T.
I. INTRODUCTION
THE Future Circular Collider (FCC) and the High-Energy
Large Hadron Collider (HE-LHC), an LHC energy-doubler,
aim at reaching 100 TeV and 27 TeV, respectively. The
D. Arbelaez, L. Brouwer, S. Caspi, S. Gourlay, M. Juchno, M. Martchevsky,
and S. Prestemon are with Lawrence Berkeley National Laboratory (LBNL),
Berkely, CA 94720 USA (e-mail: darbelaez@lbl.gov; lnbrouwer@lbl.gov;
s_caspi@lbl.gov; sagourlay@lbl.gov; mjuchno@lbl.gov).
E. Barzi, V. Kashikhin, I. Novitski, G. Velev, and A. V. Zlobin are with
Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510 USA (e-
mail: barzi@fnal.gov; vadim@fnal.gov; novitski@fnal.gov).
´
P. Bruzzone is with Ecole Polytechnique Fed´erale´ de Lausanne (EPFL),
Lau-sanne 1015, Switzerland (e-mail: pierluigi.bruzzone@psi.ch).
B. Gold and T. Tervoort are with Eidgenossische¨ Technische Hochschule
Zurich,¨ Zurich¨ 8092, Switzerland (e-mail: barbara.gold@mat.ethz.ch).
T. Gortsas, C. Kokkinos, S. Kokkinos, K. Loukas, and D. Polyzos are with
the Department of Mechanical Engineering & Aeronautics, Univer-sity of
Patras, Patras 26504, Greece (e-mail: thodoris.gortsas@gmail.com;
charilaos.kokkinos@feacomp.com; sotiris.kokkinos@feacomp.com;
konstanti-nos.loukas@feacomp.com).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TASC.2019.2900556
FERMILAB-PUB-19-400-TD
This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S.
Department of Energy, Office of Science, Office of High Energy Physics.
2 PUB-19-400-TD
TABLE I
MAIN TARGET PARAMETERS OF THE BASELINE COS-THETA
DIPOLE MAGNET FOR FCC AND HE-LHC
magnet systems of both colliders are based on twin-aperture 16 T
Nb
3
Sn dipole magnets with an aperture of 50 mm. The main
target parameters of the cos-theta baseline Nb
3
Sn dipole magnet
design are provided in Table I.
The design, manufacturing and operation of such dipoles in
accelerator quality in large quantities is a large step forward and
requires a dedicated development program. The program prof-its
largely from the experience gained through CERN’s High-
Luminosity LHC (HL-LHC) program with Nb
3
Sn magnets [1],
[2]. Critical aspects identified as essential for succeeding in de-
signing, cost-effectively manufacturing and reliably operating 16
T dipole magnets in large colliders are: (a) the improvement of
the state of the art conductor performance towards 1500 A/mm
2
and a cost of 5 EUR/kA.m at 16 T and 4.2 K com-pared to 1000
A/mm
2
and 20 EUR/kA.m at 16 T and 4.2 K in the HL-LHC
project (b) the design of cost-effective 16 T dipole magnets with
adequate electromagnetic and structural designs, and (c) the
improvement of training. These points are addressed in a
worldwide collaboration through different programs.
In Europe the work started in 2013, after the approval of the
CERN council, and is dedicated to achieving the target
parameters of the FCC dipole magnets [3]. In the US the 2014
Particle Physics Project Prioritization Panel (P5) identified a
critical need for high-field magnet R&D focused on substantially
increasing performance and reducing the cost per T.m, which
triggered the US Magnet Development Program (MDP) [4]. The
US program started in June 2016 with the goal of exploring the
performance limits of Nb
3
Sn accelerator magnets, pursuing
Nb
3
Sn conductor R&D towards increased performance and
reduced cost and investigating fundamental aspects of magnet
design and technology for substantially improving their
performance and reducing magnet cost.
Both in the US and Europe the conductor development is seen
as key. The CERN managed program is developed in three
phases. In the first phase the focus is devoted to the in-crease of
the critical current by 50% with respect to HL-LHC (1500 A/mm
2
at 4.2 K and 16 T), maintaining a high residual resistivity ratio
(RRR) of 150. Achieving this goal requires a major breakthrough
and work on novel methods, as Artificial Pinning Centres (APC),
grain refinement and architectures. In the second phase the
conductor will be optimized for the reduction of magnetization,
in particular at low fields, by acting on the effective filament
diameter and possibly on APC. The third phase can be considered
the preparation to industrialization, with focus on achieving long
unit length (5 km) and competitive cost (5 kEuro/kAm at 4.2 K
and 16 T). The US program is synergic to the CERN program and
is tackling similar targets.
To be able to sustain the European magnet program until 2020
up to around 500 km Nb
3
Sn wire of different diameters in the
range of 0.7 mm to 1.1 mm will be procured from dif-ferent
suppliers within the framework of CERN’s technology
companion conductor program. Moreover, CERN established bi-
lateral agreements with collaborating institutes and compa-nies in
Europe and Asia for conductor development and characterization
namely with the High Energy Accelerator Research Organization
KEK (Japan), the University of Geneva (Switzer-land), the
University of Freiberg (Germany) and the companies Kiswire
Advanced Technology (Korea), TVEL (Russia), Bruker
(Germany), and Luvata (Finland).
In the US, conductor development for high field accelerator
magnets is organized primarily through the Conductor Procure-
ment and R&D (CPRD) program, an element of the US Magnet
Development Program (MDP) focusing on advancing LTS and
HTS industrial conductors. For Nb
3
Sn, the program focuses on
determining the performance limits, future scalability,
industrialization and cost reduction.
The design and technology development towards 16 T dipole
magnets is carried out within the European Program EuroCirCol
WP5 (2015-2019), CERN’s FCC Magnet Technology
Companion Program (started in 2015), and the U.S. Magnet
Development Program (started in 2016, focused on general R&D
for high field accelerator magnet technology, consistent with the
FCC goals).
Within EuroCirCol WP5, the program is focused on cost-
effective cos-theta, block-type and common-coil electromagnetic
and structural designs and Nb
3
Sn strand and cable
characterization. The work performed within this program is the
base for the Conceptual Design Reports (CDRs) for FCC and
HE-LHC.
Within CERN’s FCC Magnet Technology Companion Pro-
gram the following initiatives are pursued: the design and
manufacture of flat-racetrack coils accessing the 16 T field range
with margin, coil manufacturing and property characterization
focused on enhancing the understanding of the irreversible
degradation, the windability of Rutherford cables and the material
characterization of Nb
3
Sn coil packs. In the last years these
programs have been substantially complemented with bi-lateral
collaboration agreements between CERN and institutes covering
aspects not yet treated in other programs. CEA
PUB-19-400-TD
3
(Commissariat a` l’energie´ atomique et aux energies´
alternatives, France), INFN (Istituto Nazionale di Fisica
Nucleare, Italy) and CIEMAT (Centro de Investigaciones
Energeticas,´ Medioambientales y Tecnologicas,´ Spain) aim at
designing and manufacturing 16 T block-type, cos-theta and
common-coil dipole models, respectively. Other agreements have
been established with Budker Institute of Nuclear Physics
(Russia) on the design and manufacture of a 16 T dipole model;
with the Paul Scherrer Institute (Switzerland) on the design of a
CCT 16 T demonstrator and manufacture of an 11 T technology
demonstrator; with EPFL (Ecole polytechnique fed´erale´ de
Lausanne, Switzerland) on Nb
3
Sn splices; with the ETHZ
(Eidgenossische¨ Technische Hochschule Zurich,¨ Switzerland)
on the characterization of impregnation systems for Nb
3
Sn coils;
with the Tampere University of Technology (Finland) on quench
protection of Nb
3
Sn magnets and the industrialization of the
production of 16 T Nb
3
Sn magnets and with the University of
Patras (Greece) on compact mechanical structures for 16 T
dipoles.
The U.S. Magnet Development Program is initially focused on
a strong technology development effort, along with a two-
pronged approach towards high field magnet design and testing
currently including: a) the design, fabrication and test of building
a 4-layer 15 T cos-theta dipole demonstrator with an aperture of
60 mm, which is scheduled to be tested in 2018; and b) the devel-
opment and testing of the Canted Cosine-theta concept (CCT),
initially through the design, manufacture and test of 2-layer 10 T
magnets. The program will proceed towards higher-field concepts
based on results from these first tests. On the technology front,
areas of focus include a) detailed characterization and
comparison of epoxies and interfaces b) development of
characterization and novel diagnostics including quench anten-
nae and passive and active acoustic instrumentation to advance
the understanding and mitigation of training behavior, and c)
advanced modeling techniques utilizing computer clusters and
parallel computing to enable multiphysics modeling of magnet
systems. Under the Small Business Innovation Research (SBIR)
and Small Business Technology Transfer (STTR) programs of
the US Department of Energy (DOE) [5] synergic developments
on conductor and magnet technology are performed.
The CCT design is also being explored by PSI, where the
R&D focuses on particular design elements that render CCT
magnets more compact and competitive in conductor usage, the
ultimate goal being a 4-layer 16 T magnet.
The status of development is presented in the HE-LHC and
FCC CDRs [6]. These CDRs are a major input for the Update of
the European Strategy for Particle Physics (ESPP), which are
planned to be approved by the CERN council in May 2020 after a
bottom-up process that starts with the broad consultation of all
stakeholders in Europe’s particle physics community and
culminates in a dedicated meeting of the European Strategy
Group. In this review the ESPP for the next years is defined. It is
planned to update the ESPP again in around five years.
The overall aim of these programs and collaborations is to
enable the required technology development, design and man-
ufacture of cost effective high-field Nb
3
Sn dipole model mag-nets
accessing the 16 T field range. The results and lessons learned
will enable validating and testing the specific interesting
characteristics of the different design options and allow a down-
selection of the design option, to be able to formulate a clear
vision for the construction of long models (2023-2027) at the
time of the next but one ESPP and for industry proto-types (2027-
2032), pre-series magnets (2032-2036), and series magnets
(2036-2041).
In this paper the main results of the work performed in the
different programs is discussed. We believe that the work per-
formed, will allow us to submit a credible 16 T dipole magnet
CDR to the European Strategy Group.
II. CONDUCTOR DEVELOPMENT AND
PROCUREMENT
Despite the short time span of the programs, high-performing
Nb
3
Sn conductors have been already produced by new collab-
orating partner institutes and companies, achieving a J
c
per-
formance in the order of the specification for HL-LHC [7]. Work
performed on grain refinement and APC has shown very
promising results, achieving the FCC specification in critical
current density on small samples [8], [9]. To improve the train-
ing of magnets the addition of materials with high heat capacity
(Gd
2
O
3
) incorporated directly within the Nb
3
Sn wire is being
investigated, preliminary results already indicate a much in-
creased minimum quench energy (MQE) [10] and, thus, may
allow significant reduction of magnet training.
As next step, the conductor optimization for the reduction of
magnetization, in particular at low fields, by acting on the
effective filament diameter and possibly on APC. After being
able to produce wire with the required technical specification, an
industrialization phase is planned focusing on achieving long unit
length (5 km) and competitive cost (5 EUR/kA.m at 4.2 K and 16
T).
III. MAGNET DESIGN
Cos-theta [11], block type [12], common-coil [13], canted-cos
theta (CCT) [14], [15] and cos-theta magnets with stress
management [16] are being studied as design options for twin-
aperture dipole magnets accessing the 16 T field range. The
electromagnetic design of the different design options is shown in
Fig. 1. The cos-theta design was chosen as baseline design, as
among these four optimized designs, it was found to be the most
efficient in terms of amount of conductor used for a given
integrated field strength and the same margin on the load-line;
with respect to the conductor amount required for the cos-theta
the block requires 3.7%, the common-coil 25.4% and the CCT
27.7% more conductor. Each design option was optimized using
the same assumptions in terms of conductor, load margin, field
quality and quench. The relative difference in conductor usage
may change if each design is allowed to optimize conductor for
its own efficiency and quench performance.
The cos-theta was also the design option of choice for all
colliders with SC magnets so far. Each of the alternative designs
features specific interesting characteristics, which may have the
potential to become competitive with the baseline cosine-theta
design in terms of performance. Therefore, their designs are
being fully developed and it is planned to explore them through
model magnets.
4 PUB-19-400-TD
Fig. 1. Electromagnetic design of the different design options.
TABLE II
BASELINE TARGET PARAMETERS OF THE CONDUCTOR FOR THE MAIN DIPOLES
To keep the magnet size and mass within reasonable limits, it
has been decided to accept a fringe field outside the cryostat of
up to 0.1 T, which is considered safe for other equipment. This
decision allowed to reduce the cold mass diameter to 800 mm and
to fit the cold mass into a cryostat with an outer diameter of 1250
mm; compatible with an installation in both the FCC and HE-
LHC. Studies are on-going to further optimize the structure
towards compactness.
A. Baseline Conductor Parameters
Two distinct conductors are foreseen for the 16 T dipoles: a
high-field (HF) conductor used for the inner coil and a low-field
(LF) conductor used for the outer coil. The target parameters of
the HF and LF conductor are summarized in Table II. It is
assumed in the magnet design that the insulated cable can be sub-
mitted to pressures of up to 150 MPa at ambient temperature and
200 MPa when cold, without experiencing an irreversible degra-
dation of its characteristics. Based on the information coming
Fig. 2. FCC and HE-LHC baseline cross-section (left: Coil cross-section
slightly left/right asymmetric to compensate b
2
, right: cold mass with an
outer diameter of 800 mm).
from tailored experiments and from magnet tests, these values are
considered to be challenging but realistic (see Section IV. A).
Due to the high J
c
, the large filament diameter and the large
amplitude of a magnet cycle, the magnetization losses of these
magnets have a considerable impact on the design of the cryo-
genic system (see next Section III. B). This limit can be respected
with filament diameters up to around 20 µm, grain refinement,
the introduction of APC, and with the optimization of the re-set
current during the machine powering cycle. R&D work for
achieving small sub-elements with reasonable heat treatment
cycles is planned.
B. Baseline Dipole Design
The baseline dipole is foreseen to be assembled in a helium
tight cold mass (CM) structure, integrated in a cryostat: a cross
section of the coil and cross-section is presented in Fig. 2.
The CM for the FCC main dipole (MD) is straight and has a
total length between the two extremities of the beam pipe flanges
of 15.8 m and a magnetic length of 14.069 m. The CM for HE-
LHC follows the beam’s path and is therefore curved with a
sagitta of around 9 mm. The CM external diameter is of 800 mm.
Its cryostat structure is composed of a radiation shield, a thermal
screen and a vacuum vessel. The CM is supported by three feet
made from a composite material. All parts between the beam pipe
and the shrinking cylinder (defining the outer envelope of the
cold mass) are immersed in superfluid helium at atmospheric
pressure and are cooled by a heat-exchanger tube. In the heat
exchanger tube two-phase low-pressure helium circulates. The
next temperature stage is that of the beam screen, cooled at a
reference temperature of 50 K, which also corresponds to the
temperature level for cooling the thermal screen and the support
posts. The fact that the additional intermediate temperature level
used in the LHC, in the range of 4 to 20 K is missing, results in
larger static losses from the cold mass and the support posts than
in the LHC. The total heat loads of a cryodipole operating in
steady state mode are estimated to be about 0.5 W/m at 1.9 K and
about 10 W/m at 50 K. The target losses during a full cycle from
nominal field, down to injection and up to nominal field again,
for which a large portion comes from the magnetization of the
superconductor, are set to 5 kJ/m at 1.9 K for the two apertures,
such that the cryogenic system can reset the temperature within 2
h. The design field of 16 T is generated by a current of 11,390 A
in a coil which has a physical aperture of 50 mm and the distance
between the axis of the two apertures is 250 mm.
PUB-19-400-TD
5
Each MD aperture has 200 cable turns distributed in one upper
and one lower coil, and each coil comprises two double layer
(inner and outer) coils. Since the magnetic flux density varies
considerably in the coil (it is much higher in the inner than in the
outer coil), the design exploits the principle of grading (see
below). The inner coil comprises 32 turns of a 0.5° keystoned
Rutherford cable, made from 22 strands of 1.1 mm diameter, the
outer coil has 68 turns of a 0.5° keystoned Rutherford cable,
made from 38 strands of 0.7 mm diameter.
The current density in the outer coil is larger than that in the
inner coil because the two coils are connected in series and the
inner layers cable has a larger conductor area than the outer
layers cable. This design exploits the concept of grading, which
consists of increasing the current density where the magnet field
is lower, resulting in a considerable saving of conductor for a
given margin on the load-line, which for the FCC MD has been
set to 14%. The structure is based on the so-called key and
bladders concept together with the use of an aluminum cylinder
surrounded by a stainless steel welded shell. The aluminum shell
provides an increase of coil loading, as required from assembly to
the operational temperature and during magnet energization. This
design choice, compared to a traditional collared magnet, allows
keeping the stress at all steps (assembly, cool-down, powering to
16 T) below the stipulated limits, at which the conductor would
start degrading irreversibly. The stainless shell, in addition to
increasing the stiffness of the structure, provides helium
tightness, alignment and support for the magnet end covers.
Prior to installation each magnet will be cold tested. De-
pending on its training performance, the magnet may be also
submitted to a thermal cycle to confirm that, once installed in the
tunnel, the target to power the magnets to nominal field without
experiencing training quenches can be achieved. Concerning
magnetic measurements, a warm-cold correlation will be
established based on the statistics on pre-series magnets, as it was
successfully done for the LHC. All series magnets will be then
magnetically measured warm and only a small percentage of
them also measured cold.
C. Quench Protection
The magnet and its protection system are conceived to limit
the hot spot temperature in the case of a quench to below 350 K
and the peak voltage to ground in the coil below 2.5 kV. This
voltage limit comprises up to 1.2 kV due to the quench evolution
in the magnet itself and up to 1.3 kV from the circuit. The protec-
tion system can be based on the coupling-loss-induced quench
method (CLIQ), on quench heaters alone or on a combination of
both. On paper all options effectively protect the magnets within
the above limits [17]. Experiments on the FCC models and pro-
totypes will allow to understand in real conditions if CLIQ can be
implemented with the required reliability and redundancy for
every quench condition. For the reasons above, though it is
believed that CLIQ has the potential to quench the entire magnet
in 30 ms after the initiation of a quench (time delay), the 16 T
magnets have been designed assuming a time margin of at least
40 ms, which is compatible with the use of quench-heaters.
D. Field Quality
The field error naming convention follows the one adopted for
the LHC [18]. The systematic field error values are deterministic
and computed with ROXIE: they are made of a geometric con-
tribution, a contribution coming from persistent currents and the
effect of saturation of the ferromagnetic yoke (see Table I). The
contribution of the persistent currents [19] has been computed
considering the conductor characteristics of Table II.
The coils are slightly asymmetric to compensate for the b
2
component and to bring this component well below the target
specification. Further optimization is on-going to passively cor-
rect the b
3
error from persistent current by using iron shims. The
yoke shape will also be further optimized to minimize the
saturation effects.
E. Cost Estimate
The magnet cost has been split in three main contributions: the
conductor cost, the assembly cost, and the cost of the magnet
parts [20]. The main contributor is the conductor cost, which is of
about 670 kEUR/magnet considering the FCC target conductor
cost of 5 EUR/kA.m at 4.2 K and 16 T. This cost is between three
and four times lower than the present cost considered for
conductor procured for HL-LHC, noting that the expected 50% J
c
increase has a direct impact on the cost reduction. Due to the
limited number of suppliers and limited demand on the market at
this stage, this cost is considered the most uncertain.
The cost of the parts amount to 450 kEUR/magnet, is based on
present costs and is estimated to be solid as production can be
performed by standard manufacturing industry.
The cost for the assembly has been set to 600 kEUR, which is
about twice the cost of the assembly of the LHC magnets. This
cost is dominated by the number of coils to be made in a magnet
(twice than for the LHC) and by their increased complexity. The
production will require a tailor-made production line and the final
cost will depend on the degree of industrialization that can be
achieved during the series production. A study on how to
industrialize this production has therefore already been initiated
with the University of Tampere (UoT), taking the present
production for HL-LHC as test bed, first results are expected
soon.
Mainly due to the uncertainty of the cost of the conductor, and
also to the opportunities that a R&D program may provide to
simplify the magnet manufacture, we believe that it is more
reasonable to give a range than a given number, between 1.7 and
2.0 MEUR/magnet.
IV. MAGNET TECHNOLOGY DEVELOPMENT
Magnet technology development is seen as key for succeeding
in building 16 T dipole magnets. Dedicated tests and studies en-
able the possibility of exploring different critical aspects within
shorter time and with lower cost compared to model magnets.