Editing Stellarator (section)

== History ==
=== Previous work ===
In 1934, [[Mark Oliphant]], [[Paul Harteck]] and [[Ernest Rutherford]] were the first to achieve fusion on Earth, using a [[particle accelerator]] to shoot [[deuterium]] nuclei into a metal foil containing [[deuterium]], [[lithium]] or other elements.<ref>{{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 |date= 17 March 1934 |issue= 3359 |page=413 |doi=10.1038/133413a0|bibcode= 1934Natur.133..413O |s2cid= 4078529 |doi-access=free }}</ref> These experiments allowed them to measure the [[nuclear cross section]] of various reactions of fusion between nuclei, and determined that the [[tritium]]–deuterium reaction occurred at a lower energy than any other fuel, peaking at about 100,000&nbsp;[[electronvolt]]s (100&nbsp;keV).{{sfn|McCracken|Stott|2012|p=35}}{{efn|Extensive studies in the 1970s lowered this slightly to about 70&nbsp;keV.}}

100&nbsp;keV corresponds to a temperature of about a billion [[kelvin]]s. Due to the [[Maxwell–Boltzmann statistics]], a bulk gas at a much lower temperature will still contain some particles at these much higher energies. Because the fusion reactions release so much energy, even a small number of these reactions can release enough energy to keep the gas at the required temperature. In 1944, [[Enrico Fermi]] demonstrated that this would occur at a bulk temperature of about 50&nbsp;million&nbsp;Celsius, still very hot but within the range of existing experimental systems. The key problem was ''confining'' such a plasma; no material container could withstand those temperatures. But because plasmas are electrically conductive, they are subject to electric and magnetic fields which provide a number of solutions.{{sfn|Stix|1998|p=3}}

In a magnetic field, the electrons and nuclei of the plasma circle the magnetic lines of force. One way to provide some confinement would be to place a tube of fuel inside the open core of a [[solenoid]]. A solenoid creates magnetic lines running down its center, and fuel would be held away from the walls by orbiting these lines of force. But such an arrangement does not confine the plasma along the length of the tube. The obvious solution is to bend the tube around into a torus (donut) shape, so that any one line forms a circle, and the particles can circle forever.{{sfn|Bromberg|1982|p=16}}

However, this solution does not actually work. For purely geometric reasons, the magnets ringing the torus are closer together on the inside curve, inside the "donut hole". Fermi noted this would cause the electrons to drift away from the nuclei, eventually causing them to separate and cause large voltages to develop. The resulting electric field would cause the plasma ring inside the torus to expand until it hit the walls of the reactor.{{sfn|Bromberg|1982|p=16}}

=== Stellarator ===
After [[World War II]], a number of researchers began considering different ways to confine a plasma. [[George Paget Thomson]] of [[Imperial College London]] proposed a system now known as [[z-pinch]], which runs a current through the plasma.{{sfn|Herman|1990|p=40}} Due to the [[Lorentz force]], this current creates a magnetic field that pulls the plasma in on itself, keeping it away from the walls of the reactor. This eliminates the need for magnets on the outside, avoiding the problem Fermi noted. Various teams in the UK had built a number of small experimental devices using this technique by the late 1940s.{{sfn|Herman|1990|p=40}}

Another person working on controlled fusion reactors was [[Ronald Richter]], a German scientist who moved to [[Argentina]] after the war. His ''thermotron'' used a system of electrical arcs and mechanical compression (sound waves) for heating and confinement. He convinced [[Juan Perón]] to fund development of an experimental reactor on an isolated island near the Chilean border. Known as the [[Huemul Project]], this was completed in 1951. Richter soon convinced himself fusion had been achieved in spite of other people working on the project disagreeing.{{sfn|Mariscotti|1992|pp=9–10}} The "success" was announced by Perón on 24 March 1951, becoming the topic of newspaper stories around the world.<ref>{{cite conference |first=Regis |last=Cabral |editor-first=Juan José |editor-last=Saldaña |chapter=The Perón-Richter Fusion Program: 1948–1953 |title=Cross Cultural Diffusion of Science: Latin America |year=1987 |location=Berkeley, California |page=85 }}</ref>

While preparing for a ski trip to Aspen, Lyman Spitzer received a telephone call from his father, who mentioned an article on Huemul in ''[[The New York Times]]''.{{sfn|Ellis|1958|p=12}} Looking over the description in the article, Spitzer concluded it could not possibly work; the system simply could not provide enough energy to heat the fuel to fusion temperatures. But the idea stuck with him, and he began considering systems that would work. While riding the [[ski lift]], he hit upon the stellarator concept.<ref>{{cite web |last=Greenwald |first=J. |date=23 October 2013 |title=Celebrating Lyman Spitzer, the father of PPPL and the Hubble Space Telescope |url=http://www.pppl.gov/news/2013/10/celebrating-lyman-spitzer-father-pppl-and-hubble-space-telescope |publisher=Princeton Plasma Physics Lab |access-date=12 April 2017 |archive-date=25 April 2017 |archive-url=https://web.archive.org/web/20170425033914/http://www.pppl.gov/news/2013/10/celebrating-lyman-spitzer-father-pppl-and-hubble-space-telescope |url-status=dead }}</ref>{{efn|Sources disagree on when the stellarator concept emerged in its current form, Bromberg puts the figure-8 arrangement being part of later work after he returned to Princeton.}}

The basic concept was a way to modify the torus layout so that it addressed Fermi's concerns through the device's geometry. By twisting one end of the torus compared to the other, forming a figure-8 layout instead of a circle, the magnetic lines no longer travelled around the tube at a constant radius, instead they moved closer and further from the torus' center. A particle orbiting these lines would find itself constantly moving in and out across the minor axis of the torus. The drift upward while it travelled through one section of the reactor would be reversed after half an orbit and it would drift downward again. The cancellation was not perfect, but it appeared this would so greatly reduce the net drift rates that the fuel would remain trapped long enough to heat it to the required temperatures.{{sfn|Bromberg|1982|p=17}}

His 1958 description was simple and direct:
{{quotation|Magnetic confinement in the stellarator is based on a strong magnetic field produced by solenoidal coils encircling a toroidal tube. The configuration is characterized by a 'rotational transform', such that a single line of magnetic force, followed around the system, intersects a cross-sectional plane in points which successively rotate about the magnetic axis. ... A rotational transform may be generated either by a solenoidal field in a twisted, or figure-eight shaped, tube, or by the use of an additional transverse multipolar helical field, with helical symmetry.{{sfn|Spitzer|1958|p= 253}}}}

=== Matterhorn ===
While working at [[Los Alamos National Laboratory|Los Alamos]] in 1950, [[John Archibald Wheeler|John Wheeler]] suggested setting up a secret research lab at [[Princeton University]] that would carry on theoretical work on [[H-bomb]]s after he returned to the university in 1951. Spitzer was invited to join this program, given his previous research in interstellar plasmas.{{sfn|Bromberg|1982|p=14}}

But by the time of his trip to Aspen, Spitzer had lost interest in bomb design, and upon his return, he turned his attention full-time to fusion as a power source.{{sfn|Herman|1990|p=21}} Over the next few months, Spitzer produced a series of reports outlining the conceptual basis for the stellarator, as well as potential problems. The series is notable for its depth; it not only included a detailed analysis of the mathematics of the plasma and stability but also outlined a number of additional problems like heating the plasma and dealing with impurities.{{sfn|Stix|1998}}

With this work in hand, Spitzer began to lobby the [[United States Atomic Energy Commission]] (AEC) for funding to develop the system.{{sfn|Stix|1998}} He outlined a plan involving three stages. The first would see the construction of a Model A, whose purpose was to demonstrate that a plasma could be created and that its confinement time was better than a [[torus]]. If the A model was successful, the B model would attempt to heat the plasma to fusion temperatures. This would be followed by a C model, which would attempt to actually create fusion reactions at a large scale.{{sfn|Bromberg|1982|p=21}} This entire series was expected to take about a decade.{{sfn|Herman|1990|p=23}}

Around the same time, [[James L. Tuck|Jim Tuck]] had been introduced to the pinch concept while working at [[Clarendon Laboratory]] at [[Oxford University]]. He was offered a job in the US and eventually ended up at Los Alamos, where he acquainted the other researchers with the concept. When he heard Spitzer was promoting the stellarator, he also travelled to Washington to propose building a pinch device. He considered Spitzer's plans "incredibly ambitious". Nevertheless, Spitzer was successful in gaining $50,000 in funding from the AEC, while Tuck received nothing.{{sfn|Bromberg|1982|p=21}}

The Princeton program was officially created on 1 July 1951. Spitzer, an avid mountain climber,{{efn|The American Alpine Club has an annual Lyman Spitzer Cutting Edge Climbing Award.}} proposed the name "[[Project Matterhorn]]" because he felt that "the work at hand seemed difficult, like the ascent of a mountain".<ref>{{cite book |title= Project Matterhorn: An Informal History |first=Earl |last=Tanner |publisher= Princeton University |date=1982 |page=36}}</ref> Two sections were initially set up, S Section working on the stellarator under Spitzer, and B Section working on bomb design under Wheeler. Matterhorn was set up at Princeton's new Forrestal Campus, a {{convert|825|acre}} plot of land the University purchased from the Rockefeller Institute for Medical Research when Rockefeller relocated to [[Manhattan]].{{efn|Eventually becoming [[Rockefeller University]].}} The land was located about {{convert|3|miles}} from the main Princeton campus and already had sixteen laboratory buildings. Spitzer set up the top-secret S Section in a former rabbit hutch.{{sfn|Timeline}}

It was not long before the other labs began agitating for their own funding. Tuck had managed to arrange some funding for his [[Perhapsatron]] through some discretionary budgets at LANL, but other teams at LANL, [[Lawrence Berkeley National Laboratory|Berkeley]] and [[Oak Ridge National Laboratory|Oak Ridge]] (ORNL) also presented their ideas. The AEC eventually organized a new department for all of these projects, becoming "Project Sherwood".{{sfn|Bishop|1958}}

=== Early devices ===
With the funding from the AEC, Spitzer began work by inviting [[James Van Allen]] to join the group and set up an experimental program. Allen suggested starting with a small "tabletop" device. This led to the Model A design, which began construction in 1952. It was made from 5&nbsp;cm [[pyrex]] tubes about 350&nbsp;cm in total length, and magnets capable of about 1,000&nbsp;gauss.{{sfn|Stix|1998|p=6}} The machine began operations in early 1953 and clearly demonstrated improved confinement over the simple torus.{{sfn|Ellis|1958|p=13}}

This led to the construction of the Model B, which had the problem that the magnets were not well mounted and tended to move around when they were powered to their maximum capacity of 50,000&nbsp;gauss. A second design also failed for the same reason, but this machine demonstrated several-hundred-kilovolt X-rays that suggested good confinement. The lessons from these two designs led to the B-1, which used ohmic heating (see below) to reach plasma temperatures around 100,000 degrees.{{sfn|Ellis|1958|p=13}} This machine demonstrated that impurities in the plasma caused large [[x-ray]] emissions that rapidly cooled the plasma. In 1956, B-1 was rebuilt with an ultra-high vacuum system to reduce the impurities but found that even at smaller quantities they were still a serious problem. Another effect noticed in the B-1 was that during the heating process, the particles would remain confined for only a few tenths of a millisecond, while once the field was turned off, any remaining particles were confined for as long as 10 milliseconds. This appeared to be due to "cooperative effects" within the plasma.{{sfn|Ellis|1958|p=14}}

Meanwhile, a second machine known as B-2 was being built. This was similar to the B-1 machine but used pulsed power to allow it to reach higher magnetic energy and included a second heating system known as magnetic pumping. This machine was also modified to add an ultra-high vacuum system. Unfortunately, B-2 demonstrated little heating from the magnetic pumping, which was not entirely unexpected because this mechanism required longer confinement times, and this was not being achieved. As it appeared that little could be learned from this system in its current form, in 1958 it was sent to the [[Atoms for Peace]] show in [[Geneva]].{{sfn|Ellis|1958|p=14}} However, when the heating system was modified, the coupling increased dramatically, demonstrating temperatures within the heating section as high as {{val|1000|u=eV}}.{{sfn|Stix|1998|p=6}}{{efn|The bulk temperature of the plasma was much lower, this was the temperature only within the heating section.}}

Two additional machines were built to study pulsed operation. B-64 was completed in 1955, essentially a larger version of the B-1 machine but powered by pulses of current that produced up to 15,000&nbsp;gauss. This machine included a [[divertor]], which removed impurities from the plasma, greatly reducing the x-ray cooling effect seen on earlier machines. B-64 included straight sections in the curved ends which gave it a squared-off appearance. This appearance led to its name, it was a "figure-8, squared", or 8 squared, or 64. This led to experiments in 1956 where the machine was re-assembled without the twist in the tubes, allowing the particles to travel without rotation.{{sfn|Stix|1998|p=7}}

B-65, completed in 1957, was built using the new "racetrack" layout. This was the result of the observation that adding helical coils to the curved portions of the device produced a field that introduced the rotation purely through the resulting magnetic fields. This had the added advantage that the magnetic field included ''shear'', which was known to improve stability.{{sfn|Stix|1998|p=7}} B-3, also completed in 1957, was a greatly enlarged B-2 machine with ultra-high vacuum and pulsed confinement up to 50,000&nbsp;gauss and projected confinement times as long as 0.01 second. The last of the B-series machines was the B-66, completed in 1958, which was essentially a combination of the racetrack layout from B-65 with the larger size and energy of the B-3.{{sfn|Ellis|1958|p=14}}

Unfortunately, all of these larger machines demonstrated a problem that came to be known as "[[pump out]]". This effect was causing plasma drift rates that were not only higher than classical theory suggested but also much higher than the Bohm rates. B-3's drift rate was a full three times that of the worst-case Bohm predictions, and failed to maintain confinement for more than a few tens of microseconds.{{sfn|Stix|1998|p=7}}

=== Model C ===
{{main|Model C stellarator}} 
As early as 1954, as research continued on the B-series machines, the design of the Model C device was becoming more defined. It emerged as a large racetrack-layout machine with multiple heating sources and a divertor, essentially an even larger B-66. Construction began in 1958 and was completed in 1961. It could be adjusted to allow a plasma minor axis between {{val|5|and|7.5|u=cm}} and was {{val|1,200|u=cm}} in length. The toroidal field coils normally operated at 35,000&nbsp;gauss.{{sfn|Stix|1998|p=7}}

By the time Model C began operations, information collected from previous machines was making it clear that it would not be able to produce large-scale fusion. Ion transport across the magnetic field lines was much higher than classical theory suggested. Greatly increased magnetic fields of the later machines did little to address this, and confinement times simply were not improving. Attention began to turn to a much greater emphasis on the theoretical understanding of the plasma. In 1961, [[Melvin B. Gottlieb]] took over the Matterhorn Project from Spitzer, and on 1 February the project was renamed as the [[Princeton Plasma Physics Laboratory]] (PPPL).{{sfn|Timeline}}

Continual modification and experimentation on the Model C slowly improved its operation, and the confinement times eventually increased to match that of Bohm predictions. New versions of the heating systems were used that slowly increased the temperatures. Notable among these was the 1964 addition of a small [[particle accelerator]] to accelerate fuel ions to high enough energy to cross the magnetic fields, depositing energy within the reactor when they collided with other ions already inside.{{sfn|Timeline}} This method of heating, now known as [[neutral beam injection]], has since become almost universal on [[magnetic confinement fusion]] machines.<ref>{{cite web |date=9 July 2012 |title=Neutral beam powers into the record books |url=http://www.ccfe.ac.uk/news_detail.aspx?id=166 |url-status=dead |archive-url=https://web.archive.org/web/20170324043543/http://www.ccfe.ac.uk/news_detail.aspx?id=166 |archive-date=24 March 2017 }}</ref>

Model C spent most of its history involved in studies of ion transport.{{sfn|Timeline}} Through continual tuning of the magnetic system and the addition of the new heating methods, in 1969, Model C eventually reached electron temperatures of 400&nbsp;eV.{{sfn|Johnson|1982|p=4}}

=== Other approaches ===
Through this period, a number of new potential stellarator designs emerged, which featured a simplified magnetic layout. The Model C used separate confinement and helical coils, as this was an evolutionary process from the original design which had only the confinement coils. Other researchers, notably in Germany, noted that the same overall magnetic field configuration could be achieved with a much simpler arrangement. This led to the '''torsatron''' or '''heliotron''' layout.

In these designs, the primary field is produced by a single helical magnet, similar to one of the helical windings of the "classical" stellarator. In contrast to those systems, only a single magnet is needed, and it is much larger than those in the stellarators. To produce the net field, a second set of coils running poloidally around the outside of the helical magnet produces a second vertical field that mixes with the helical one. The result is a much simpler layout, as the poloidal magnets are generally much smaller and there is ample room between them to reach the interior, whereas in the original layout the toroidal confinement magnets are relatively large and leave little room between them.{{sfn|Johnson|1982|p=4}}{{sfn|Johnson|1982|p=58|loc=diagram}}

A further update emerged from the realization that the total field could be produced through a series of independent magnets shaped like the local field. This results in a series of complex magnets that are arranged like the toroidal coils of the original layout. The advantage of this design is that the magnets are entirely independent; if one is damaged it can be individually replaced without affecting the rest of the system. Additionally, one can re-arrange the overall field layout by replacing the elements. These "modular coils" are now a major part of ongoing research.

=== Tokamak stampede ===
In 1968, scientists in the [[Soviet Union]] released the results of their [[tokamak]] machines, notably their newest example, T-3. The results were so startling that there was widespread scepticism. To address this, the Soviets invited a team of experts from the United Kingdom to test the machines for themselves. Their tests, made using a [[laser]]-based system developed for the [[ZETA (fusion reactor)|ZETA]] reactor in England, verified the Soviet claims of electron temperatures of 1,000&nbsp;eV. What followed was a "veritable stampede" of tokamak construction worldwide.{{sfn|Kenward|1979b}}

At first the US labs ignored the tokamak; Spitzer himself dismissed it out of hand as experimental error. However, as new results came in, especially the UK reports, Princeton found itself in the position of trying to defend the stellarator as a useful experimental machine while other groups from around the US were clamoring for funds to build tokamaks. In July 1969 Gottlieb had a change of heart, offering to convert the Model C to a tokamak layout. In December it was shut down and reopened in May as the [[Symmetric Tokamak]] (ST).

The ST immediately matched the performance being seen in the Soviet machines, besting the Model C's results by over ten times. From that point, PPPL was the primary developer of the tokamak approach in the US, introducing a series of machines to test various designs and modifications. The [[Princeton Large Torus]] of 1975 quickly hit several performance numbers that were required for a commercial machine, and it was widely believed the critical threshold of [[breakeven (fusion)|breakeven]] would be reached in the early 1980s. What was needed was larger machines and more powerful systems to heat the plasma to fusion temperatures.

Tokamaks are a type of pinch machine, differing from earlier designs primarily in the amount of current in the plasma: above a certain threshold known as the ''[[safety factor]]'', or ''q'', the plasma is much more stable. ZETA ran at a ''q'' around {{frac|3}}, while experiments on tokamaks demonstrated it needs to be at least 1. Machines following this rule showed dramatically improved performance. However, by the mid-1980s the easy path to fusion disappeared; as the amount of current in the new machines began to increase, a new set of instabilities in the plasma appeared. These could be addressed, but only by greatly increasing the power of the magnetic fields, requiring [[superconducting]] magnets and huge confinement volumes. The cost of such a machine was such that the involved parties banded together to begin the [[ITER]] project.

=== Stellarator returns ===
As the problems with the tokamak approach grew, interest in the stellarator approach reemerged.<ref name="Clery2013"/> This coincided with the development of advanced [[computer aided design|computer aided]] planning tools that allowed the construction of complex magnets that were previously known but considered too difficult to design and build.<ref>{{cite web|url=https://projects.research-and-innovation.ec.europa.eu/en/horizon-magazine/twisting-design-fusion-reactor-thanks-supercomputers|title=Twisting design of fusion reactor is thanks to supercomputers|last=Bilby|first=Ethan|date=14 April 2016|website=Horizon: the EU Research & Innovation magazine|language=en|access-date=3 May 2024|archive-date=13 April 2024|archive-url=https://web.archive.org/web/20240413025231/https://projects.research-and-innovation.ec.europa.eu/en/horizon-magazine/twisting-design-fusion-reactor-thanks-supercomputers|url-status=live}}</ref><ref>{{cite web|url=https://newatlas.com/wendelstein7x-fusion-stellarator-plasma-tests/40014/|title=Wendelstein 7-x stellarator puts new twist on nuclear fusion power|last=Jeffrey|first=Colin|date=26 October 2015|website=New Atlas|language=en|access-date=22 December 2019}}</ref>

New materials and construction methods have increased the quality and power of the magnetic fields, improving performance. New devices have been built to test these concepts. Major examples include [[Wendelstein 7-X]] in Germany, the [[Helically Symmetric Experiment]] (HSX) in the US, and the [[Large Helical Device]] in Japan. W7X and LHD use [[superconducting magnet|superconducting magnetic coil]]s.

<!-- this paragraph should probably be moved elsewhere -->
The lack of an internal current eliminates some of the instabilities of the tokamak, meaning the stellarator should be more stable at similar operating conditions. On the downside, since it lacks the confinement provided by the current found in a tokamak, the stellarator requires more powerful magnets to reach any given confinement. The stellarator is an inherently steady-state machine, which has several engineering advantages.

In 2023 PPPL built an experimental device using mainly commercial components at a cost of $640,000. Its core is a glass vacuum chamber surrounded by a [[3D printing|3D-printed]] nylon shell that anchors 9,920 [[permanent magnets]]. Sixteen electromagnets wrap the shell.<ref>{{cite web |last=Clynes |first=Tom |date=28 October 2024 |title=Stellarators and AI: The Future of Fusion Energy Research – IEEE Spectrum |url=https://spectrum.ieee.org/the-off-the-shelf-stellarator |access-date=2024-12-09 |website=spectrum.ieee.org |language=en}}</ref>

=== Private sector stellarators ===
Private sector stellarator projects began emerging in 2018.<ref>{{cite book |last=Fusion Industry Association |title=The global fusion industry in 2023 |publisher=Fusion Industry Association |year=2023}}</ref> Participants include Renaissance Fusion,<ref>{{cite web |date=2023-09-18 |title=Revolutionizing Energy: Renaissance Fusion's Quest for Sustainable Nuclear Fusion |url=https://innovationorigins.com/en/revolutionizing-energy-renaissance-fusions-quest-for-sustainable-nuclear-fusion/ |access-date=2024-05-11 |website=IO |language=en-GB}}</ref> Proxima Fusion, a Munich-based spin-off from the [[Max Planck Institute for Plasma Physics]], which steered the W7-X experiment,<ref name=":0">{{cite web |last=Butcher |first=Mike |date=2024-04-09 |title=Proxima Fusion raises $21M to build on its 'stellarator' approach to nuclear fusion |url=https://techcrunch.com/2024/04/09/proxima-fusion-raises-21m-to-build-on-its-stellarator-approach-to-nuclear-fusion/ |access-date=2024-05-11 |website=TechCrunch |language=en-US}}</ref> Type One, and Thea Energy.<ref name=":1">{{Cite web |last=Clery |first=Daniel |date=1 Apr 2025 |title=Stellarators, once fusion's dark horse, hit their stride |url=https://www.science.org/content/article/stellarators-fusions-dark-horse-hit-stride |access-date=2025-04-03 |website=www.science.org |language=en}}</ref>

Proxima Fusion is a Munich-based spin-off from the [[Max Planck Institute for Plasma Physics]], which steered the W7-X experiment.<ref name=":0" /> In February 2025, it announced plans to build a test magnet from high-temperature superconductors in 2027 and a demo unit in 2031.<ref>{{Cite web |title=German stellarator fusion design concept unveiled |url=https://www.world-nuclear-news.org/articles/german-stellarator-fusion-design-concept-unveiled |access-date=2025-04-29 |website=World Nuclear News |language=en}}</ref><ref name=":1" />

Type One is seeking $200 million in investment to add to $82 million raised in 2024. Its Infinity One system is intended to validate the design, with construction beginning in 2026. Infinity Two is intended to produce net power. That machine is designed to cover 14 meters and generate 800 MWt, resulting in 350 MWe.<ref name=":1" />

PPPL spinout Thea Energy plans to shape its fields with angled circular coils finetuned with flat magnets.<ref name=":1" />