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{{Short description|Magnetic confinement fusion device that confines plasma using external non-axisymmetric magnetic fields}}

{{Quantum book backlink|Plasma and fusion physics}}
'''Stellarator''' is a class of [[Physics:Quantum Magnetic confinement fusion|magnetic confinement fusion]] device that confines hot [[Software:Plasma|plasma]] almost entirely with externally generated magnetic fields. Unlike a [[Software:Tokamak|tokamak]], a stellarator does not rely on a large induced plasma current to create the rotational transform needed for confinement. This makes the stellarator intrinsically attractive for long-pulse or steady-state fusion operation, because it avoids many current-driven instabilities that complicate tokamak performance.<ref name="Spitzer1958">{{cite journal
|last=Spitzer
|first=Lyman
|date=1958
|title=The Stellarator Concept
|journal=Physics of Fluids
|volume=1
|issue=4
|pages=253–264
|bibcode=1958PhFl....1..253S
|doi=10.1063/1.1705883
}}</ref><ref name="ImbertGerard2024">{{cite book
|last1=Imbert-Gerard
|first1=Lise-Marie
|last2=Paul
|first2=Elizabeth
|last3=Wright
|first3=Adelle
|date=2024
|title=An Introduction to Stellarators: From Magnetic Fields to Symmetries and Optimization
|publisher=SIAM
|doi=10.1137/1.9781611978223
|url=https://math.arizona.edu/~lmig/AnIntroductiontoStellarators-Imbert-Ge%CC%81rard-et-al.pdf
|arxiv=1908.05360
|isbn=978-1-61197-821-6
}}</ref>

The concept was invented by [[Biography:Lyman Spitzer|Lyman Spitzer]] in 1951 at what became the [[Organization:Princeton Plasma Physics Laboratory|Princeton Plasma Physics Laboratory]] (PPPL). Early stellarators demonstrated the feasibility of magnetic confinement, but their transport losses were much larger than hoped. After the strong rise of the tokamak in the late 1960s, stellarator research declined in the United States, though it continued in Europe and Japan. Since the 1990s, advances in computation, coil design, and magnetic optimization have revived stellarators as serious reactor candidates, especially through devices such as [[Physics:Wendelstein 7-X|Wendelstein 7-X]], the [[Physics:Helically Symmetric Experiment|Helically Symmetric Experiment]] (HSX), and the [[Physics:Large Helical Device|Large Helical Device]] (LHD).<ref name="Stix1998">{{cite journal
|last=Stix
|first=Thomas
|date=1998
|title=Highlights in Early Stellarator Research at Princeton
|url=http://www.jspf.or.jp/JPFRS/PDF/Vol1/jpfrs1998_01-003.pdf
|journal=Journal of Plasma Fusion Research Series
|volume=1
|pages=3–8
}}</ref><ref name="Clery2015">{{cite journal
|last=Clery
|first=D.
|year=2015
|title=The bizarre reactor that might save nuclear fusion
|journal=Science
|doi=10.1126/science.aad4746
}}</ref><ref name="Beidler2021">{{cite journal
|last1=Beidler
|first1=C. D.
|last2=Smith
|first2=H. M.
|last3=Alonso
|first3=A.
|last4=Andreeva
|first4=T.
|last5=Baldzuhn
|first5=J.
|last6=Beurskens
|first6=M. N. A.
|last7=Borchardt
|first7=M.
|last8=Bozhenkov
|first8=S. A.
|last9=Brunner
|first9=K. J.
|last10=Damm
|first10=H.
|display-authors=1
|year=2021
|title=Demonstration of reduced neoclassical energy transport in Wendelstein 7-X
|journal=Nature
|volume=596
|issue=7871
|pages=221–226
|bibcode=2021Natur.596..221B
|doi=10.1038/s41586-021-03687-w
|pmc=8357633
|pmid=34381232
}}</ref>
[[File:Magnetic field stellarator yellow.jpg|thumb|400px|Schematic magnetic geometry of a stellarator, in which external coils generate rotational transform and confine plasma without requiring a large toroidal plasma current.]]
== Historical development ==

=== Origins ===
The general fusion problem emerged from early nuclear reaction work in the 1930s, including the deuterium-fusion experiments of [[Biography:Mark Oliphant|Mark Oliphant]], Paul Harteck, and [[Biography:Ernest Rutherford|Ernest Rutherford]]. These studies helped establish that thermonuclear fusion would require extremely high particle energies and therefore temperatures far beyond those tolerated by ordinary material walls.<ref name="Oliphant1934">{{cite journal
|journal=Nature
|first1=Mark
|last1=Oliphant
|first2=Paul
|last2=Harteck
|first3=Ernest
|last3=Rutherford
|title=Transmutation Effects observed with Heavy Hydrogen
|volume=133
|issue=3359
|page=413
|date=1934-03-17
|doi=10.1038/133413a0
|bibcode=1934Natur.133..413O
|s2cid=4078529
|doi-access=free
}}</ref><ref name="McCrackenStott2012">{{cite book
|first1=Garry
|last1=McCracken
|first2=Peter
|last2=Stott
|title=Fusion: The Energy of the Universe
|publisher=Academic Press
|date=2012
|url=https://books.google.com/books?id=6Tud4RyMjlwC
|isbn=978-0-12-384657-0
}}</ref>

By the 1940s, it was understood that a sufficiently hot ionized gas, or plasma, might be confined magnetically rather than mechanically. But a straight magnetic tube allows plasma to escape from the ends, while a simple torus introduces gradient and curvature drifts that tend to separate charges and degrade confinement.<ref name="Bishop1958">{{cite book
|last=Bishop
|first=Amasa
|date=1958
|title=Project Sherwood; the U.S. program in controlled fusion
|publisher=Addison-Wesley
|series=Addison-Wesley books in nuclear science and metallurgy
|url=https://babel.hathitrust.org/cgi/pt?id=uc1.$b113483;view=1up;seq=21
}}</ref><ref name="Bromberg1982">{{cite book
|last=Bromberg
|first=Joan Lisa
|date=1982
|title=Fusion: Science, Politics, and the Invention of a New Energy Source
|publisher=MIT Press
|url=https://archive.org/details/fusionsciencepol0000brom
|url-access=registration
|isbn=978-0-262-02180-7
}}</ref>

=== Spitzer's stellarator ===
Spitzer's key insight was that these drifts could be reduced if the magnetic geometry were twisted so that a charged particle alternated between regions of stronger and weaker magnetic field. In the earliest conception, the plasma path resembled a figure-8, so upward and downward drifts would partly cancel over a full transit. This became the basis of the stellarator concept.<ref name="Spitzer1951">{{cite tech report
|last=Spitzer
|first=Lyman
|date=1951-07-23
|title=A Proposed Stellarator
|url=http://diglib.princeton.edu/pdfs/PPL001/c0002.pdf
|publisher=Project Matterhorn
}}</ref><ref name="Spitzer1958" />

Project Matterhorn at Princeton developed the first stellarator program through a sequence of Model A, B, and C devices. These experiments established that stellarator plasmas could be formed, heated, and magnetically confined, but they also revealed impurity radiation, anomalous transport, and confinement degradation far above the classical estimates.<ref name="Ellis1958">{{cite journal
|title=Experiments on the Ohmic Heating and Confinement of Plasma in a Stellarator
|first1=T.
|last1=Coor
|first2=S. P.
|last2=Cunningham
|first3=R. A.
|last3=Ellis
|first4=M. A.
|last4=Heald
|first5=A. Z.
|last5=Kran
|journal=Physics of Fluids
|date=1958-09
|volume=1
|issue=5
|pages=411–420
|doi=10.1063/1.1724358
|bibcode=1958PhFl....1..411C
|url=http://www-naweb.iaea.org/napc/physics/2ndgenconf/data/Proceedings%201958/papers%20Vol32/Paper25_Vol32.pdf
}}</ref><ref name="Stix1998" />

=== Decline and return ===
In 1968, the high-performance Soviet tokamak results changed the direction of magnetic-confinement research. PPPL converted Model C into the Symmetric Tokamak, confirming that tokamaks had a major confinement advantage at that time. Large-scale stellarator work in the United States then largely gave way to tokamak development.<ref name="Bromberg1982" /><ref name="Stix1998" />

Interest in stellarators returned when it became clear that tokamaks also faced severe challenges, especially current-driven disruptions, pulsed operation, and reactor control complexity. Modern stellarators benefited from computer-aided optimization of three-dimensional magnetic fields, making it possible to design devices with much better neoclassical transport properties than the classical Princeton machines.<ref name="Clery2013">{{cite journal
|last=Clery
|first=D.
|date=2013-01-17
|title=After ITER, Many Other Obstacles for Fusion Power
|journal=Science
|url=https://www.science.org/content/article/after-iter-many-other-obstacles-fusion-power
}}</ref><ref name="GatesNSCC">{{cite book
|last=Gates
|first=David A.
|title=Stellarator Research Opportunities: A Report of the National Stellarator Coordinating Committee
|oclc=1187827940
}}</ref><ref name="ImbertGerard2024" />

== Physical principles ==

=== Magnetic confinement and rotational transform ===
A stellarator confines plasma in a toroidal vacuum vessel using non-axisymmetric magnetic fields generated by external coils. Its defining feature is that the field lines wrap around the torus helically even without a large toroidal plasma current. This field-line twist is known as '''rotational transform'''.<ref name="Spitzer1958" /><ref name="ImbertGerard2024" />

Because the transform is created externally, stellarators can in principle operate in steady state. This distinguishes them from tokamaks, in which much of the transform is produced by plasma current and therefore by transformer action or non-inductive current-drive systems.<ref name="LandremanBoozer2017">{{cite journal
|last1=Landreman
|first1=Matt
|last2=Boozer
|first2=Allen H.
|title=Stellarator design challenges
|journal=Physics of Plasmas
|date=2017
|volume=24
|issue=8
|doi=10.1063/1.4993056
}}</ref>

=== Drift reduction and transport ===
The original motivation for the stellarator was to reduce the outward particle drifts that arise in a simple toroidal field. In modern language, stellarator optimization aims to reduce neoclassical transport and improve energetic-particle confinement by shaping the magnetic field so that orbit-averaged radial drifts are minimized.<ref name="Spitzer1958" /><ref name="ImbertGerard2024" />

One major challenge in stellarator physics is that magnetic-field strength varies strongly along three-dimensional field lines. Some particles become magnetically trapped, and these trapped-particle effects can enhance radial transport. This was one of the main reasons early stellarators performed poorly. Modern devices therefore target properties such as quasi-symmetry or omnigeneity to reduce these losses.<ref name="Canik2007">{{cite journal
|last1=Canik
|first1=J. M.
|display-authors=0
|date=2007
|title=Experimental Demonstration of Improved Neoclassical Transport with Quasihelical Symmetry
|journal=Physical Review Letters
|volume=98
|issue=8
|article-number=085002
|bibcode=2007PhRvL..98h5002C
|doi=10.1103/PhysRevLett.98.085002
|pmid=17359105
|s2cid=23140945
}}</ref><ref name="Dinklage2018">{{cite journal
|last1=Dinklage
|first1=A.
|last2=Beidler
|first2=C. D.
|last3=Helander
|first3=P.
|last4=Fuchert
|first4=G.
|last5=Maaßberg
|first5=H.
|last6=Rahbarnia
|first6=K.
|last7=Sunn Pedersen
|first7=T.
|last8=Turkin
|first8=Y.
|last9=Wolf
|first9=R. C.
|display-authors=1
|year=2018
|title=Magnetic configuration effects on the Wendelstein 7-X stellarator
|journal=Nature Physics
|volume=14
|issue=8
|pages=855–860
|bibcode=2018NatPh..14..855D
|doi=10.1038/s41567-018-0141-9
}}</ref>

=== Heating ===
Because a stellarator lacks the large plasma current of a tokamak, it cannot rely on current-driven ohmic heating as its main high-temperature heating mechanism. Instead, stellarators use combinations of:

* initial ohmic or startup methods in some devices,
* radio-frequency heating such as electron-cyclotron or ion-cyclotron resonance heating,
* neutral beam injection,
* and auxiliary microwave systems.<ref name="Spitzer1958" /><ref name="Johnson1982">{{cite tech report
|last=Johnson
|first=John
|date=1982-12
|title=The Stellarator Approach to Toroidal Plasma Confinement
|url=http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/13/690/13690529.pdf
|publisher=Princeton University, Plasma Physics Laboratory
}}</ref>

This separation between confinement and current drive is both an advantage and a complication: the machine gains steady-state potential, but coil geometry and heating access become more demanding.<ref name="LandremanBoozer2017" />

== Modern optimized stellarators ==

=== HSX and quasi-symmetry ===
A major milestone came from the [[Physics:Helically Symmetric Experiment|HSX]] at the University of Wisconsin, which demonstrated that quasi-helical symmetry can substantially reduce neoclassical transport. Experiments showed improved particle and heat confinement when the configuration was tuned toward quasi-symmetry compared with intentionally symmetry-broken cases.<ref name="Canik2007" />

=== Wendelstein 7-X ===
The most advanced optimized stellarator currently in operation is [[Physics:Wendelstein 7-X|Wendelstein 7-X]] in Greifswald, Germany. W7-X was designed to test whether careful magnetic optimization can suppress neoclassical transport to reactor-relevant levels while supporting long-pulse operation.<ref name="Clery2015" /><ref name="Dinklage2018" />

Results from W7-X have shown reduced neoclassical energy transport, effective magnetic optimization, and strong control over bootstrap current, supporting the stellarator strategy of achieving confinement quality through three-dimensional field design rather than large plasma current.<ref name="Beidler2021" /><ref name="Dinklage2018" />

W7-X has also demonstrated the performance of the island divertor concept, including detached operating scenarios and reduced heat loads at the targets, which are crucial for any steady-state fusion device.<ref name="Pedersen2022">{{cite journal
|last1=Pedersen
|first1=T. S.
|display-authors=0
|date=2022
|title=Experimental confirmation of efficient island divertor operation and successful neoclassical transport optimization in Wendelstein 7-X
|journal=Nuclear Fusion
|volume=62
|issue=4
|page=042022
|bibcode=2022NucFu..62d2022S
|doi=10.1088/1741-4326/ac2cf5
}}</ref><ref name="Schmitz2021">{{cite journal
|last1=Schmitz
|first1=Oliver
|last2=Feng
|first2=Yuhe
|last3=Jakubowski
|first3=Marcin
|last4=König
|first4=Ralf
|last5=Krychowiak
|first5=Maciej
|last6=Otte
|first6=Matthias
|last7=Reimold
|first7=Felix
|display-authors=1
|date=2021
|title=Island divertor control and heat-flux mitigation studies in Wendelstein 7-X
|journal=Nuclear Fusion
|volume=61
|issue=1
|doi=10.1088/1741-4326/abb51e
|url=https://www.osti.gov/biblio/1814444
}}</ref>

=== Divertor and edge physics ===
In stellarators such as W7-X, the edge magnetic topology can be exploited deliberately through magnetic islands to manage fueling, recycling, impurity radiation, and heat exhaust. This is a major area of current stellarator research because steady-state fusion operation depends on controlling plasma–wall interactions over long durations.<ref name="Jakubowski2021">{{cite journal
|last1=Jakubowski
|first1=M.
|display-authors=0
|date=2021
|title=Overview of the results from divertor experiments with attached and detached plasmas at Wendelstein 7-X and their implications for steady-state operation
|journal=Nuclear Fusion
|volume=61
|issue=10
|bibcode=2021NucFu..61j6003J
|doi=10.1088/1741-4326/ac1b68
|url=https://publikationen.bibliothek.kit.edu/1000140073/133022842
}}</ref><ref name="Stephey2018">{{cite journal
|display-authors=1
|year=2018
|title=Impact of magnetic islands in the plasma edge on particle fueling and exhaust in the HSX and W7-X stellarators
|journal=Physics of Plasmas
|volume=25
|issue=6
|article-number=062501
|bibcode=2018PhPl...25f2501S
|doi=10.1063/1.5026324
|author1-first=L.
|author1-last=Stephey
|author2-first=A.
|author2-last=Bader
|author3-first=F.
|author3-last=Effenberg
|author4-first=O.
|author4-last=Schmitz
|author5-first=G.
|author5-last=Wurden
|author6-first=D.
|author6-last=Anderson
}}</ref>

== Configurations ==
Several major stellarator configurations exist.

=== Classical and figure-8 stellarators ===
The earliest Princeton machines used figure-8 or racetrack-like geometries to generate rotational transform through the shape of the confinement path itself. These were historically decisive but were eventually superseded by more flexible magnetic layouts.<ref name="Spitzer1958" /><ref name="Stix1998" />

=== Torsatron and heliotron ===
A torsatron uses continuous helical windings to generate the confining field. A heliotron is a closely related configuration, developed especially in Japan, that combines helical coils with additional poloidal-field coils. The [[Physics:Large Helical Device|Large Helical Device]] is a leading heliotron example.<ref name="Johnson1982" /><ref name="Wakatani1998">{{cite book
|last=Wakatani
|first=M.
|year=1998
|title=Stellarator and Heliotron Devices
|url=https://books.google.com/books?id=MxttViyhaaEC
|publisher=Oxford University Press
|isbn=978-0-19-507831-2
}}</ref>

=== Modular stellarator and HELIAS ===
Modern reactor-oriented stellarators often use modular, non-planar coils shaped to produce a highly optimized magnetic field. The HELIAS family is a prominent example, and W7-X is based on a five-field-period HELIAS configuration. These designs aim to combine low neoclassical transport, manageable bootstrap currents, and favorable divertor structure.<ref name="ImbertGerard2024" /><ref name="Dinklage2018" />

== Advantages and challenges ==

=== Advantages ===
The main attraction of stellarators is that they can operate without a large plasma current, which reduces the risk of major current-driven disruptions and makes true steady-state operation physically natural. This is one of the strongest reactor-level arguments in their favor.<ref name="LandremanBoozer2017" /><ref name="Clery2015" />

=== Challenges ===
The price of this stability is geometric complexity. Stellarators generally require large, precisely positioned three-dimensional coils, sophisticated optimization, and challenging engineering tolerances. They have historically tended to be larger than tokamaks of similar confinement scale, and reactor designs must also manage neutron shielding, blanket thickness, alpha-particle losses, and manufacturing complexity.<ref name="LandremanBoozer2017" /><ref name="Bromberg1982" />

== Significance ==
Stellarators are now regarded as one of the main alternative paths to practical fusion power. Their modern importance lies not in replacing tokamaks outright, but in offering a complementary route to stable, continuous operation. The success of HSX and especially W7-X has shown that the old stellarator problems were not fundamental flaws of the concept, but challenges of magnetic optimization and engineering that can be substantially improved with modern design methods.<ref name="Canik2007" /><ref name="Beidler2021" /><ref name="Clery2015" />

==See also==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}
{{Author|Harold Foppele}}

{{Sourceattribution|Quantum Stellarator|1}}

Physics:Quantum Stellarator - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

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