Comptes Rendus Physique

Alain Aspect

Jacques Villain

C. R. Physique 18 (2017) 583–585Contents lists available at ScienceDirect
Comptes Rendus Physique
www.sciencedirect.com
The Comptes rendus de l’Académie des sciences throughout history / Les Comptes rendus de l’Académie des 
sciences à travers l’histoire
The birth of wave mechanics (1923–1926)
La naissance de la mécanique ondulatoire
Alain Aspect a, Jacques Villain b,∗
a Laboratoire Charles-Fabry, Institut d’optique, 2, avenue Augustin-Fresnel, 91127 Palaiseau, France
b Institut Laue-Langevin, 71, avenue des Martyrs, CS 20156, 38042 Grenoble cedex 9, France
a r t i c l e i n f o a b s t r a c t
Article history:
Available online 25 October 2017
Keywords:
Wave mechanics
Quantum mechanics
de Broglie
Schrödinger
Mots-clés :
Mécanique ondulatoire
Mécanique quantique
de Broglie
Schrödinger
In 1923, in three articles published in the Comptes Rendus of the Académie des Sciences, Louis 
de Broglie proposed the concept of wave–particle duality. Physicists from many countries 
seized upon this idea. In particular, Schrödinger developed de Broglie’s qualitative idea by 
writing down the equation that the wave must satisfy in the non-relativistic approximation. 
A relativistic version of this equation was proposed in 1926 by several scientists, and other 
ones found a solution to the Schrödinger equation as an expansion in powers of the Planck 
constant.
© 2017 Académie des sciences. Published by Elsevier Masson SAS. This is an open access 
article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
r é s u m é
En 1923, dans trois articles publiés dans les Comptes rendus de l’Académie des sciences, 
Louis de Broglie proposa le concept de dualité onde–particule. Les physiciens de multiples 
pays s’emparèrent de cette idée. En particulier, Schrödinger précisa l’idée qualitative de 
de Broglie en écrivant l’équation à laquelle l’onde doit satisfaire dans l’approximation non 
relativiste. Une version relativiste de cette équation fut proposée en 1926 par plusieurs 
chercheurs et, la même année, d’autres chercheurs obtinrent une solution de l’équation de 
Schrödinger comme série de puissances de la constante de Planck.
© 2017 Académie des sciences. Published by Elsevier Masson SAS. This is an open access 
article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Quantum physics was born in 1900, when Planck found a formula for the spectrum of the black-body radiation by making 
the hypothesis that the energy exchanged between radiation and material proceeds by quanta E = hν , and determined 
the value of the constant h by fitting the experimental results with his formula. But it was Einstein who realized the 
revolutionary character of the idea of quantization [1], and in 1905 he wrote the famous paper where he introduces the 
notion of Lichtquanten, quantum of light, which was named “photon” twenty years later. To accommodate the many optical 
phenomena that can be understood only assuming that light is a wave, as shown by Young, Fresnel, and Maxwell, he 
introduced the idea of wave–particle duality of light as early as 1911, in the famous Salzburg conference [2].
* Corresponding author.
E-mail address: villain@ill.fr (J. Villain).https://doi.org/10.1016/j.crhy.2017.10.007
1631-0705/© 2017 Académie des sciences. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
584 A. Aspect, J. Villain / C. R. Physique 18 (2017) 583–585After the groundbreaking discovery by Bohr, in 1913, that the idea of quantization allows one to render an account of 
the spectrum of the hydrogen atom, quantum mechanics developed as a heuristic science, which made use of various ad 
hoc assumptions to explain various phenomena. It was de Broglie who, in 1923, initiated a series of progress that would 
put the formalism of quantum mechanics on a solid ground, by introducing the concept of matter waves.
In the year 1923, the 31-year-old Louis de Broglie wished to “extend to all particles the coexistence of waves and 
particles discovered by Einstein about light.” In three notes [3] indeed, he justified this duality statement and established 
the relation between the momentum p of a freely propagating particle and the wavelength λ of the associated wave, now 
known as the de Broglie relation1:
λ = h/p (1)
where h is the Planck constant.
The derivation given by de Broglie, based on special relativity, is quite different from that given in modern textbooks. It 
is more clearly explained in his thesis [4] and more clearly yet, in English, in his Nobel lecture [5]. It will be summarized 
now.
In analogy with Einstein’s postulate that relates the energy E of a photon with its frequency ν by the relation E = hν , 
de Broglie associates with a particle at rest a wave function
Ψ = exp
(
2πi
h
m0c
2t
)
(2)
which makes use of the relativistic energy at rest m0c2. If the particle moves at velocity v , the wave function has the same 
expression, except that the time t is to be replaced by the time t′ in the moving frame. Introducing the coordinates x and t
in the fixed frame through a Lorentz transformation, the wave function takes the form
Ψ = exp
[
2πi
h
m0v√
1 − β2
(
c2t
v
− x
)]
(3)
where β = v/c.
Since the relativistic expression of the momentum is p = m0/
√
1 − β2, formula (3) corresponds to a wavelength λ = h/p, 
which is relation (1). The phase velocity c2/v is larger than the speed of light c and physically meaningless, but it can be 
checked [3] that the group velocity U = dν/d(ν/v) is equal to v .
After the serendipitous discovery by Davisson and Germer of electron diffraction on a crystal lattice of nickel [6], an 
undulatory phenomenon associated with a wavelength in agreement with the de Broglie relation (1), de Broglie obtained 
the Nobel prize, in 1929 (and Davisson got it in 1937).
De Broglie’s first two notes [3a,3b] were presented by Jean Perrin, who was going to be awarded the Nobel Prize in 
1926. Despite this distinguished support, one may doubt that de Broglie’s notes would have been easily accepted by other 
scientific journals. Indeed, de Broglie’s basic idea was to apply his relation to the photon considered as an “atom of light” 
(atome de lumière), supposed to have a very weak, but non-vanishing mass! When de Broglie wanted to transform his theory 
into a doctoral thesis, the principal examiner was Paul Langevin. According to Whitaker [7] Langevin was skeptical and asked 
for Einstein’s opinion. Einstein’s advice was positive, but perhaps not on all points. Eventually, there were no “atoms of light” 
in de Broglie’s thesis [4].
De Broglie’s ambition was not restricted to freely propagating particles. He immediately applied the wave description to 
the electrons in the atom, and re-derived Bohr’s quantization rules [3]. Indeed, for a classical motion of a charge −e on a 
circular orbit with radius r, around the nucleus with charge +e, the Coulomb force e2/(πε0r2) equilibrates the centrifugal 
force p2/(mr) (in the non-relativistic limit). This yields a relation between the radius and the momentum, which can be 
expressed as h/λ, according to (1). Now, de Broglie imposes the condition that the length of the orbit be an integer number 
of wavelengths, an “almost necessary” condition of stability of the orbit, as written in the first paper. This selects a discrete 
series of radii, which are the same as that found by imposing Bohr’s quantization condition. This is a remarkable result, 
which justifies Einstein’s positive appreciation of de Broglie’s thesis work.
Having a wave, it was natural to ask the question of the wave equation governing the evolution of that wave. It is 
Schrödinger who solved the problem, in a series of papers [8] published in 1926, just after Heisenberg [9], on the one hand, 
Born and Jordan [10], on the other one, published their matrix version of quantum mechanics. Modern quantum mechanics 
was born when Schrödinger demonstrated the equivalence between the matrix formalism and his wave formulation. A re-
markable feature of Schrödinger’s formalism is the fact that it also yields a treatment of several particles systems, however 
only in the non-relativistic approximation.
What about relativity? As early as 1926, a relativistic treatment, valid only for a single particle with spin zero, was 
obtained independently by various authors from seven different countries. Five articles were in German [8d,11–14] and two 
1 Actually relation (1) was not explicitly written in 1923. In Ref. [2b], it was said that the wave has the phase velocity V = c2/v and the frequency 
ν = m0c2(1 − v2/c2)−1/2/h, where m0 is the mass of the particle at rest and c is the velocity of light. Since V = λν and p = m0v(1 − v2/c2)−1/2, relation 
(1) results. It is explicitly written in de Broglie’s Nobel lecture [3].
A. Aspect, J. Villain / C. R. Physique 18 (2017) 583–585 585in French [15,16]. The result is generally known as the Klein–Gordon or Klein–Gordon–Fock equation,2 though Shiff [17]
calls it Schrödinger’s relativistic equation. For a free particle (in the absence of potential), the wave function Ψ (x, y, z, t)
satisfies
∇2Ψ − 1
c2
∂2
∂t2
Ψ = 4π
2m2c2
h2
Ψ (4)
where m and c have their usual meaning. This relation can be written pμpμΨ = (m2/c2)Ψ where μ denotes the four 
space-time coordinates. For a particle of charge e in a quadrivector potential Aμ , the momentum pμ is just to be replaced 
by pμ − e Aμ . The case of the Coulomb interaction created by a point charge can be treated exactly [17]. It corresponds 
to a π− meson bound to a nucleus [18]. The resulting fine structure is quite different from that observed in the hydrogen 
atom (where the particle is an electron and has a spin!) The correct relativistic treatment of the hydrogen atom was made 
possible in 1928 by Dirac’s equation.
In the same year 1926, the solution to Schrödinger’s equation as an expansion in powers of the Planck constant h was 
proposed nearly at the same time by three authors: Wentzel [19], Brillouin [20], and Kramers [21]. Wentzel’s and Kramers 
illustrated their articles by various examples, while Brillouin’s note was restricted to the principle of the series expansion, 
as was usual among French physicists.
It is remarkable that de Broglie, 50 years after his discovery, despite the fantastic success of Schrödinger’s equation 
in theoretical chemistry and atomic physics, was still reluctant to accept Born’s probabilistic views [22]. “Usual quantum 
mechanics gives us but an exact statistical view without revealing us the true nature” [of the coexistence of waves and 
particles]. The “true nature” that de Broglie had in mind, was the pilot wave theory, outlined in a note in 1927 [23] and 
then elaborated by de Broglie himself and by David Bohm. The de Broglie–Bohm theory is philosophically gratifying for 
those who would like a deterministic world, and many scientists are still investigating its consequences. However, the 
probabilistic formalism of quantum mechanics is sufficient for all known applications. Moreover, experimental violations 
of Bell’s inequalities prove that interpretations in the spirit of de Broglie’s or Einstein’s views either must be rejected, 
or have a fundamental non-locality built into them [24]. Far from being useless, this fundamental debate has drawn the 
attention of physicists onto the extraordinary character of the behavior of individual quantum objects, and lead to the 
present development of quantum technologies.
The authors are grateful to Franck Laloë for a critical reading of the manuscript.
References
[1] (a) A. Douglas Stone, Einstein and the Quantum, Princeton University Press, 2013;
(b) F. Balibar, O. Darrigol, B. Jech (Eds.), Albert Einstein Œuvres choisies, tome 1 – Quanta, Éditions du Seuil et du CNRS, 1989.
[2] A. Einstein, Zum gegenwärtigen Stand der Strahlungsproblems, Phys. Z. 10 (1909) 185–193.
[3] (a) L. de Broglie, Ondes et quanta, C. R. hebd. Séanc. Acad. Sci. Paris 177 (1923) 507–510;
(b) Quanta de lumière, diffraction et interférences, C. R. hebd. Séanc. Acad. Sci. Paris 177 (1923) 548–551;
(c) L. de Broglie, Les quanta, la théorie cinétique des gaz et le principe de Fermat, C. R. hebd. Séanc. Acad. Sci. Paris 177 (1923) 630–632.
[4] L. de Broglie, PhD Thesis, 1925, https://tel.archives-ouvertes.fr/tel-00006807/document.
[5] L. de Broglie, Nobel lecture, https://www.nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf, 1929.
[6] C.J. Davison, Nobel lecture, https://www.nobelprize.org/nobel_prizes/physics/laureates/1937/davisson-lecture.pdf, 1929.
[7] A. Whitaker, Einstein, Bohr and the Quantum Dilemma, Cambridge University Press, 2006.
[8] (a) E. Schrödinger, Quantisierung als Eigenwertproblem, Ann. Phys. (Berlin) 79 (1926) 361–376;
(b) E. Schrödinger, Quantisierung als Eigenwertproblem, Ann. Phys. (Berlin) 79 (1926) 489–527;
(c) E. Schrödinger, Quantisierung als Eigenwertproblem, Ann. Phys. (Berlin) 79 (1926) 734–756;
(d) E. Schrödinger, Quantisierung als Eigenwertproblem, Ann. Phys. (Berlin) 81 (1926) 109, Long and clear English summary in Phys. Rev. 28, 1049–1070. 
These articles can be found on the site http://dieumsnh.qfb.umich.mx/archivoshistoricosMQ/ModernaHist/Schrodinger1926a.pdf (and similar sites ob-
tained by changing 1926a into 1926b, etc.) and/or on the site http://gallica.bnf.fr/ark:/12148/cb34462944f/date.
[9] W. Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen, Z. Phys. 33 (1925) 879.
[10] M. Born, P. Jordan, Zur Quantenmechanik, Z. Phys. 34 (1925) 858.
[11] O. Klein, Quantentheorie und fünfdimensionale Relativitätstheorie, Z. Phys. 37 (1926) 895.
[12] W. Gordon, Der Comptoneffekt nach der Schrödingerschen Theorie, Z. Phys. 40 (1926) 117.
[13] V. Fock, Zur Schrödingerschen Wellenmechanik, Z. Phys. 38 (1926) 242.
[14] J. Kudar, Zur vierdimensionalen Formulierung der undulatorischen Mechanik, Ann. Phys. (Berlin) 81 (1926) 632.
[15] T. de Donder, H. van den Dungen, La quantification déduite de la gravifique einsteinienne, C. R. hebd. Séanc. Acad. Sci. Paris (Paris) 183 (1926) 22–25.
[16] L. de Broglie, Remarques sur la nouvelle mécanique ondulatoire, C. R. hebd. Séanc. Acad. Sci. Paris 183 (1926) 272–273.
[17] L.I. Shiff, Quantum Mechanics, McGraw–Hill, 1949.
[18] G. Velo, Meccanica statistica relativistica, in: Enciclopedia Delle Scienze Fisiche, 1993.
[19] G. Wentzel, Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik, Z. Phys. 38 (1926) 518–529.
[20] L. Brillouin, La mécanique ondulatoire de Schrödinger : une méthode générale de résolution par approximations successives, C. R. hebd. Séanc. Acad. 
Sci. Paris 183 (1926) 24–26.
[21] H.A. Kramers, Wellenmechanik und halbzahlige Quantisierung, Z. Phys. 39 (1926) 828–840.
[22] L. de Broglie, Sur les véritables idées de base de la mécanique ondulatoire, C. R. hebd. Séanc. Acad. Sci. Paris 277B (1973) 71.
[23] L. de Broglie, La structure atomique de la matière et du rayonnement et la mécanique ondulatoire, C. R. hebd. Séanc. Acad. Sci. Paris 184 (1927) 273.
[24] F. Laloe, Do we really understand quantum mechanics?, Am. J. Phys. 69 (2001) 655.2 Actually the first published article seems to be that of Klein, while Gordon’s and Fock’s articles are illustrated by applications that are lacking in the 
other versions.


The birth of wave mechanics (1923–1926)

Jean-Claude Garreau

Quantum simulation of disordered systems with cold atoms

Aurélien Barrau

Tome 18 (2017) – N◦ 3–4 – mars–avril 
This artist’s illustration depicts how the foamy structure of space-time may appear, showing tiny bubbles 
quadrillions of times smaller than the nucleus of an atom, which are constantly fluctuating and last for only 
infinitesimal fractions of a second. NASA/CXC/M. Weiss. Public domain.
Cette vue d’artiste représente comment la structure en mousse de l’espace-temps peut se manifester. Elle montre 
des bulles minuscules, des quadrillons de fois plus petites que le noyau d’un atome, qui fluctuent en permanence 
et ont une durée de vie de l’ordre de fractions infinitésimales de seconde. NASA/CXC/M. Weiss. Domaine public.
DOSSIER
Testing different approaches to quantum gravity with cosmology / Tester les théories
de la gravitation quantique à l’aide de la cosmologie
Coordinator / Coordinateur : Aurélien Barrau
• Testing different approaches to quantum gravity with cosmology: An overview
Aurélien Barrau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
• String cosmology and the landscape
Iosif Bena, Mariana Graña . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
• Testing loop quantum cosmology
Edward Wilson-Ewing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
• Spectral action gravity and cosmological models
Matilde Marcolli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
• The universe as a quantum gravity condensate
Daniele Oriti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
• Evolution of universes in causal set cosmology
Fay Dowker, Stav Zalel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
• Asymptotically safe cosmology – A status report
Alfio Bonanno, Frank Saueressig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
Continued on the next page
Contents (continued)
• CDT and cosmology
Lisa Glaser, Renate Loll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
• Do we really understand the cosmos?
Thanu Padmanabhan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
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Testing different approaches to quantum gravity with cosmology: An overview

Fay Dowker

Stav Zalel

Evolution of universes in causal set cosmology

Alessandro Monfardini

Superconducting millimetre-wave cameras

Bernard Bigot

C. R. Physique 18 (2017) 367–371Contents lists available at ScienceDirect
Comptes Rendus Physique
www.sciencedirect.com
Demain l’énergie – Séminaire Daniel-Dautreppe, Grenoble, France, 2016
ITER: A unique international collaboration to harness the 
power of the stars
ITER : une collaboration internationale inédite pour puiser l’énergie des 
étoiles
Bernard Bigot
ITER Organization, route de Vinon-sur-Verdon, CS 90 046, 13067 Saint-Paul-lès-Durance, France
a r t i c l e i n f o a b s t r a c t
Article history:
Available online 19 September 2017
Keywords:
ITER
Energy
Thermonuclear fusion
Tokamak
Plasma
Superconducting magnets
Mots-clés :
ITER
Énergie
Fusion thermonucléaire
Tokamak
Plasma
Électro-aimant supraconducteur
Harnessing the energy of thermonuclear fusion reactions is one of the greatest challenges 
of our time. Fusion, the nuclear reaction that powers the Sun and stars would provide 
mankind with a safe, environmentally benign, and virtually limitless source of energy.
© 2017 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.
r é s u m é
Exploiter l’énergie libérée par les réactions de fusion thermonucléaire est l’un des plus 
grands défis de notre temps. En imitant les réactions physiques qui alimentent le Soleil et 
les étoiles, l’humanité pourrait accéder à une source d’énergie virtuellement inépuisable, 
sûre et respectueuse de l’environnement.
© 2017 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.
In the 1920s, physicists began unravelling the nuclear cycles by which Sun-like stars have been producing prodigious 
amounts of energy for billions of years. Three decades later, most developed nations had joined in the ambition to create a 
comparable reaction in a manmade machine.
In the core of Sun-like stars, gravitational forces create conditions of temperature, pressure and density that allow hy-
drogen nuclei to overcome electrostatic forces and fuse.
The fusion process is a mass-to-energy conversion reaction. In Sun-like stars, it is extremely slow – it takes about one 
billion years for a hydrogen nucleus to “get a chance” to fuse with another and initiate the complex chain of reactions that 
will eventually produce a helium nucleus and a considerable liberation of energy (see Fig. 1).
E-mail address: Bernard.Bigot@iter.org.http://dx.doi.org/10.1016/j.crhy.2017.09.002
1631-0705/© 2017 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.
368 B. Bigot / C. R. Physique 18 (2017) 367–371Fig. 1. (a) The “proton–proton chain” that was identified in the 1920s (Eddington) and fully described in the following decade (Bethe) is the complex and 
lengthy process that enables Sun-like stars to generate energy. (b) In a fusion reactor, the deuterium–tritium reaction is much simpler than in Sun-like 
stars, but produces the same result: two light nuclei fuse into one heavier one (helium), producing large amounts of energy in the process.
The fusion process as it occurs in the core of Sun-like stars cannot be replicated on Earth. But it can be imitated.
Physicists soon determined that a hot, ultra-low-density plasma (in the range of 150,000,000 ◦C) comprised of equal parts 
of deuterium and tritium (the two heavy isotopes of hydrogen) and confined by intense magnetic fields would provide an 
environment in which fusion reactions can occur (see Appendix A).
As early as the mid-1960s, “fusion machines” of various shapes, sizes and performance levels – such as pinch and mirror 
devices, stellarators, and tokamaks (a Russian acronym for Toroidal Chamber, Magnetic Coils) – were operating in the Soviet 
Union, the USA, the United Kingdom, Germany, France, and Japan.
However, the way to fusion power was to prove considerably more difficult, complex, and costly than anticipated.
As they explored the mind-boggling complexity of plasma physics and faced the technological challenges of building 
and operating fusion devices, physicists and engineers realized that no single nation, whatever its human, scientific and 
technological resources, could address the magnitude of the task alone.
In the 1970s, as large and promising tokamak projects were being developed in Europe (Joint European Torus), the 
US (Tokamak Fusion Test Reactor) Japan (JT-60) and the USSR (T-15), the international fusion community engaged in an 
international effort to design an even larger experimental machine – INTOR, the International Tokamak Reactor.
INTOR never saw the light of day, but paved the way to ITER, the International Thermonuclear Experimental Reactor 
(and the Latin word for “the way”), which is currently under construction in Saint-Paul-lès-Durance, some 40 km north of 
Aix-en-Provence, in southern France.
The ITER Project received a decisive political push in November 1985 when President Reagan and Secretary General 
Gorbachev met in Geneva and agreed on launching “the widest practicable development of international cooperation in obtaining
[fusion] energy, which is essentially inexhaustible, for the benefit for all mankind.”
Two decades of collaborative work ensued as the project’s members – the USA, the USSR (later Russia), Europe (Euratom) 
and Japan, joined by China and Korea in 2003 and by India in 2005 – fine-tuned the design of the installation and eventually 
agreed on the location for its construction.
In October 2007, the ITER International Fusion Energy Organization (in short the ITER Organization) was officially estab-
lished, and the dream of three generations of fusion physicists and engineers at last had a legal framework and a home to 
become reality.
ITER’s mission is to build and operate a very large tokamak that will confirm the feasibility of exploiting fusion reactions 
for the production of energy by providing an integrated demonstration of the physics and technology required for a fusion 
power plant.
The ITER tokamak will be by far the largest fusion machine ever built (23,000 t, approximately 30 m high and 30 m in 
diameter) and the first to sustain a “burning plasma” in which the energetic helium nuclei (α particles) resulting from the 
fusion reactions dominate all other forms of plasma heating (Fig. 2).
Reaching the conditions necessary for fusion reactions to occur will require approximately 50 MW of heating power in 
the form of radiofrequency and microwaves, and neutral particle injection. Once fusion reactions are initiated, the “burning 
plasma” will deliver 500 MW of fusion power for durations of 300 to 500 seconds (see insert 2).
ITER is also designed to explore the physics basis for the continuous operation of fusion power plants by investigating 
“steady-state” plasma operation.
Strong magnetic fields, produced by a massive array of superconducting coils (10,000 t) will shape and confine the hot 
plasma within the tokamak’s vacuum vessel (Fig. 3).
And like the ITER machine, the ITER collaboration is unique.
B. Bigot / C. R. Physique 18 (2017) 367–371 369Fig. 2. (a) Little free space remains on the 42 hectares of the ITER platform. Sandwiched between the cooling tower zone and concrete batching plant at 
the northern end (far left) and the electrical switchyard to the south (far right) are the work areas for the Tokamak Complex (centre crane), the cryoplant 
(middle right, all grey) and the buildings for magnet power conversion (twin structures, right). Any free space is used for storage. At the top of the image, 
manufacturing is underway in on-site facilities for the cryostat and four of the machine’s six poloidal field coils, too large to be transported by road. (b) The 
ITER tokamak will be assembled in this “well” at the centre of the Tokamak Complex building. The large openings in the walls of the “bioshield” – the thick 
steel and concrete structure that surrounds the machine – are “penetrations” that will allow system equipment such as magnet feeders, remote handling, 
heating and diagnostics to reach the machine.
Fig. 3. (a) Six ring-shaped coils circle the tomakak to create the poloidal magnetic field. Four of them, ranging from 17 to 24 m in diameter will be 
manufactured by Europe on the ITER site. Fabrication for poloidal field coil # 5 began in April 2017. (b) In La Seyne-sur-Mer, in the Var département, the 
French Company CNIM has produced 35 of the 70 needed “radial plates” for the tokamak’s toroidal field coils.
It is the largest scientific cooperation project ever established, bringing together 35 nations representing more than half 
of the world’s population and 85% of the planet’s gross domestic product.
The contribution of the seven ITER Members is done essentially in-kind – China, the European Union, India, Japan, Korea, 
Russia, and the United States have each established a Domestic Agency that contracts with the industry to manufacture 
machine components and installation systems.
With the exception of the European Union, each Member’s contribution represents approximatively 9% of the total value 
of the project. As “host Member”, the European Union not only procures its share of components and systems; it is also 
responsible for delivering the 39 permanent buildings of the installation, which brings its contribution to approximately 
45%.
Ten years have passed now since scrapers and earth-moving equipment began transforming a large stretch of national 
forest, granted by France to the ITER Organization, into the perfectly flat platform that would accommodate the ITER instal-
lation.
In the summer of 2010, building construction began in earnest. Seven years later, the progress accomplished, both on 
the construction site in Saint-Paul-lès-Durance and in factories throughout the world, is spectacular.
On the construction site, 2,000 workers are busy erecting and equipping the installation’s buildings. Close to 6 billion 
euros in contracts (mainly for civil works) have already been awarded, half of them to French companies.
Visible from afar, the stainless-steel-clad Assembly Hall, rising 60 m high, and the adjacent Tokamak Complex, which 
form the heart of the installation, are now distinct features of the Durance Valley landscape.
A cryoplant (see Appendix B) – the largest in the world – to provide cooling fluids for the tokamak’s superconducting 
magnetic system; twin buildings, 150 m long, for the magnet power conversion equipment; a 400-kV switchyard and its set 
of giant transformers along with several other buildings have all reached different stages of completion. Night and day, the 
ITER worksite is swarming with activity.
Activity is also intense in factories on three continents where the ITER components and systems are being manufactured. 
More than 40% (in value) of the total components and systems needed for First Plasma in 2025 have already been produced.
370 B. Bigot / C. R. Physique 18 (2017) 367–371Buildings, components, systems, will soon coalesce into one the most complex installations ever conceived and con-
structed.
ITER, which will enter into operation in 2025, marks both the culmination of six decades of fusion research and the 
opening of a whole new chapter in the quest for unlimited energy. It is an opportunity to change the course of our civiliza-
tion.
Building ITER is also a demonstration that nations, when confronted with a global challenge, can establish a completely 
new model for international collaboration. In ITER, scientists, engineers and administrators from 35 nations have demon-
strated their ability to work together across national and cultural boundaries to accomplish a common goal.
Conclusion
ITER marks both the culmination of six decades of international scientific and technological effort and the opening of 
a new and decisive chapter in the history of fusion research. By demonstrating the feasibility of fusion energy, ITER will 
answer the question that has obsessed three generations of physicists and engineers. It will realize the Promethean dream 
of bringing the fire of the Sun down to Earth.
Acknowledgements
We would like to thank Robert Arnoux, co-author, with Jean Jacquinot, of the book ITER, le chemin des étoiles ?, edited by 
Édisud, 2006.
Appendix A. Power ratio Q ≥ 10
Creating conditions for fusion in a deuterium–tritium plasma in ITER requires a considerable input of heating power 
(∼50 MW) in the form of radio-waves, microwaves, and neutral particle injection.
The fusion of a deuterium nucleus (one proton, one neutron) with a tritium nucleus (one proton, two neutrons) produces 
a helium nucleus (two protons, two neutrons) and a neutron (see Fig. 1b).
The helium nucleus, or alpha particle, which carries 20% of the energy released (3.5 MeV), remains trapped inside the 
magnetic cage and transfers its energy to the plasma – “alpha heating” becomes dominant, a condition referred to as a 
‘burning plasma’.
The neutron, which carries 80% of the energy released (14.1 MeV) escapes and hits the inner walls of the vacuum vessel, 
where the kinetic energy of its impact is transformed into heat.
If ITER were an industrial fusion plant, the heat generated by the burning plasmas would be used to produce pressurized 
steam and, by way of turbines and generators, electricity. Only residual heat would need to be dissipated.
But as an experimental installation, not designed to produce electricity, ITER will need to evacuate and dissipate all the 
power the fusion reactions generate.
The primary mission of the ITER project is to produce ∼500 MW of fusion power for durations of 300–500 s with a ratio 
of fusion output power to input heating power (fusion gain), Q , of at least 10.
If plasma confinement characteristics are favourable, ITER would also be capable of exploring the ‘controlled ignition’ 
regime of tokamak operation (with Q ∼ 30) in which power plant plasmas are expected to operate.
Heat will be removed from the vacuum vessel and its components by a closed-loop pressurized water circuit and even-
tually dissipated by the heat rejection system that comprises cold and hot basins with a total volume of 20,000 m3 as well 
as an induced-draft cooling tower installation.
Appendix B. A large and complex cryogenic system
The ITER machine will rely on a large and complex cryogenic system comprising the cryoplant, which will produce the 
required cooling power, and a five-kilometre long cryodistribution system to distribute the cooling fluids. The cryogenic 
system will guarantee cooling and stable operation for the tokamak’s magnets, its cryopumps, and its thermal shields over 
a wide range of plasma scenarios.
The magnets, all 10,000 tons of them, operate at high magnetic fields to confine and stabilize the plasma and require 
cooling with supercritical helium at 4 K (−269 ◦C). They will be surrounded by a large cylindrical cryostat (30 m in height, 
30 m in diameter) and an actively-cooled silver-coated thermal shield with a forced flow of helium at 80 K (see Fig. 4).
Large cryosorption panels cooled by 4 K supercritical helium are used to achieve the high pumping rates and vacuum 
levels.
The cryoplant system is comprised of three helium and two nitrogen refrigerators combined with an 80 K helium loop. 
Storage and recovery of the large helium inventory (25 t) is provided in warm and cold (4 K and 80 K) gaseous helium 
tanks.
B. Bigot / C. R. Physique 18 (2017) 367–371 371Fig. 4. A large “thermos”, the cryostat, will encase the machine and prevent heat exchanges between the ultra-cold superconducting magnet system and 
the environment. Procured by India, this 30-metre high, 30-metre in diameter is being assembled and welded in a dedicated workshop on the ITER site.
Three parties are associated in the procurement of the ITER cryoplant: Europe (the liquid nitrogen facility and auxiliary 
systems), India (the interconnecting lines and cryodistribution equipment), and the ITER Organization (responsible for the 
direct procurement of the liquid helium plant).


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