A stellarator is a plasma device that relies primarily on external magnets to confine a plasma. Scientists researching

magnetic confinement fusion Magnetic confinement fusion is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, along with ...

aim to use stellarator devices as a vessel for nuclear fusion reactions. The name refers to the possibility of harnessing the power source of the stars, such as the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

. It is one of the earliest

fusion power Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices de ...

devices, along with the

z-pinch In fusion power research, the Z-pinch (zeta pinch) is a type of plasma confinement system that uses an electric current in the plasma to generate a magnetic field that compresses it (see pinch). These systems were originally referred to simp ...

and

magnetic mirror A magnetic mirror, known as a magnetic trap (магнитный захват) in Russia and briefly as a pyrotron in the US, is a type of magnetic confinement device used in fusion power to trap high temperature plasma using magnetic fields. T ...

. The stellarator was invented by American scientist

Lyman Spitzer Lyman Spitzer Jr. (June 26, 1914 – March 31, 1997) was an American theoretical physicist, astronomer and mountaineer. As a scientist, he carried out research into star formation, plasma physics, and in 1946, conceived the idea of telesco ...

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

in 1951, and much of its early development was carried out by his team at what became the

Princeton Plasma Physics Laboratory Princeton Plasma Physics Laboratory (PPPL) is a United States Department of Energy national laboratory for plasma physics and nuclear fusion science. Its primary mission is research into and development of fusion as an energy source. It is known ...

(PPPL). Lyman's Model A began operation in 1953 and demonstrated plasma confinement. Larger models followed, but these demonstrated poor performance, losing plasma at rates far worse than theoretical predictions. By the early 1960s, any hope of quickly producing a commercial machine faded, and attention turned to studying the fundamental theory of high-energy plasmas. By the mid-1960s, Spitzer was convinced that the stellarator was matching the

Bohm diffusion The diffusion of plasma across a magnetic field was conjectured to follow the Bohm diffusion scaling as indicated from the early plasma experiments of very lossy machines. This predicted that the rate of diffusion was linear with temperature and ...

rate, which suggested it would never be a practical fusion device. The release of information on the USSR's

tokamak A tokamak (; russian: токамáк; otk, 𐱃𐰸𐰢𐰴, Toḳamaḳ) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being ...

design in 1968 indicated a leap in performance. After great debate within the US industry, PPPL converted the Model C stellarator to the Symmetrical Tokamak (ST) as a way to confirm or deny these results. ST confirmed them, and large-scale work on the stellarator concept ended in the US as the tokamak got most of the attention for the next two decades. Research on the design continued in Germany and Japan, where several new designs were built. The tokamak ultimately proved to have similar problems to the stellarators, but for different reasons. Since the 1990s, the stellarator design has seen renewed interest. New methods of construction have increased the quality and power of the magnetic fields, improving performance. A number of new devices have been built to test these concepts. Major examples include

History

Previous work

In 1934,

Mark Oliphant Sir Marcus Laurence Elwin Oliphant, (8 October 1901 – 14 July 2000) was an Australian physicist and humanitarian who played an important role in the first experimental demonstration of nuclear fusion and in the development of nuclear weapon ...

Paul Harteck Paul Karl Maria Harteck (20 July 190222 January 1985) was an Austrian physical chemist. In 1945 under Operation Epsilon in "the big sweep" throughout Germany, Harteck was arrested by the allied British and American Armed Forces for suspicion of ...

and

Ernest Rutherford Ernest Rutherford, 1st Baron Rutherford of Nelson, (30 August 1871 – 19 October 1937) was a New Zealand physicist who came to be known as the father of nuclear physics. ''Encyclopædia Britannica'' considers him to be the greatest ...

were the first to achieve fusion on Earth, using a

particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle ...

to shoot

deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one ...

nuclei into a metal foil containing

lithium Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard conditions, it is the least dense metal and the least dense solid ...

or other elements. These experiments allowed them to measure the

nuclear cross section The nuclear cross section of a nucleus is used to describe the probability that a nuclear reaction will occur. The concept of a nuclear cross section can be quantified physically in terms of "characteristic area" where a larger area means a large ...

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

electronvolt In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum ...

s (100 keV). 100 keV corresponds to a temperature of about a billion

kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...

s. Due to the

Maxwell–Boltzmann statistics In statistical mechanics, Maxwell–Boltzmann statistics describes the distribution of classical material particles over various energy states in thermal equilibrium. It is applicable when the temperature is high enough or the particle density ...

, 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 million 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. 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. 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.

Stellarator

After

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

, a number of researchers began considering different ways to confine a plasma.

George Paget Thomson Sir George Paget Thomson, FRS (; 3 May 189210 September 1975) was a British physicist and Nobel laureate in physics recognized for his discovery of the wave properties of the electron by electron diffraction. Education and early life Thomso ...

Imperial College London Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...

proposed a system now known as

, which runs a current through the plasma. 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. Another person working on controlled fusion reactors was

Ronald Richter Ronald Richter (1909–1991) was an Austrian-born German, later Argentine citizen, scientist who became infamous in connection with the Argentine Huemul Project and the National Atomic Energy Commission (CNEA). The project was intended to generat ...

, a German scientist who moved to

Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the second-largest country in South America after Brazil, th ...

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 The Huemul Project ( es, Proyecto Huemul) was an early 1950s Argentine effort to develop a fusion power device known as the Thermotron. The concept was invented by Austrian scientist Ronald Richter, who claimed to have a design that would produc ...

, this was completed in 1951. Richter soon convinced himself fusion had been achieved in spite of other people working on the project disagreeing. The "success" was announced by Perón on 24 March 1951, becoming the topic of newspaper stories around the world. 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 ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid d ...

''. 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 A ski lift is a mechanism for transporting skiers up a hill. Ski lifts are typically a paid service at ski resorts. The first ski lift was built in 1908 by German Robert Winterhalder in Schollach/Eisenbach, Hochschwarzwald. Types * Aerial ...

, he hit upon the stellarator concept. The basic concept was a way to modify the torus layout so that it addressed Fermi's concerns though 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. His 1958 description was simple and direct:

Matterhorn

While working at Los Alamos in 1950, John Wheeler suggested setting up a secret research lab at

that would carry on theoretical work on

H-bomb A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lowe ...

s after he returned to the university in 1951. Spitzer was invited to join this program, given his previous research in interstellar plasmas. 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. 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. With this work in hand, Spitzer began to lobby the

United States Atomic Energy Commission The United States Atomic Energy Commission (AEC) was an agency of the United States government established after World War II by U.S. Congress to foster and control the peacetime development of atomic science and technology. President ...

(AEC) for funding to develop the system. 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 In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not tou ...

. 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. This entire series was expected to take about a decade. Around the same time, Jim Tuck had been introduced to the pinch concept while working at

Clarendon Laboratory The Clarendon Laboratory, located on Parks Road within the Science Area in Oxford, England (not to be confused with the Clarendon Building, also in Oxford), is part of the Department of Physics at Oxford University. It houses the atomic and ...

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to th ...

. 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. The Princeton program was officially created on 1 July 1951. Spitzer, an avid mountain climber, proposed the name " Project Matterhorn" because he felt "the work at hand seemed difficult, like the ascent of a mountain." 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 plot of land the University purchased from the Rockefeller Institute for Medical Research when Rockefeller relocated to

Manhattan Manhattan (), known regionally as the City, is the most densely populated and geographically smallest of the five boroughs of New York City. The borough is also coextensive with New York County, one of the original counties of the U.S. state ...

. The land was located about from the main Princeton campus and already had sixteen laboratory buildings. Spitzer set up the top-secret S Section in a former rabbit hutch. 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, Berkeley and Oak Ridge (ORNL) also presented their ideas. The AEC eventually organized a new department for all of these projects, becoming "Project Sherwood".

Early devices

With the funding from the AEC, Spitzer began work by inviting

James Van Allen James Alfred Van Allen (September 7, 1914August 9, 2006) was an American space scientist at the University of Iowa. He was instrumental in establishing the field of magnetospheric research in space. The Van Allen radiation belts were named aft ...

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

pyrex Pyrex (trademarked as ''PYREX'' and ''pyrex'') is a brand introduced by Corning Inc. in 1915 for a line of clear, low-thermal-expansion borosilicate glass used for laboratory glassware and kitchenware. It was later expanded to include kitchenwa ...

tubes about in total length, and magnets capable of about 1,000 gauss. The machine began operations in early 1953 and clearly demonstrated improved confinement over the simple torus. 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 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. This machine demonstrated that impurities in the plasma caused large

x-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...

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. 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 "Atoms for Peace" was the title of a speech delivered by U.S. President Dwight D. Eisenhower to the UN General Assembly in New York City on December 8, 1953. The United States then launched an "Atoms for Peace" program that supplied equipment ...

show in

Geneva , neighboring_municipalities= Carouge, Chêne-Bougeries, Cologny, Lancy, Grand-Saconnex, Pregny-Chambésy, Vernier, Veyrier , website = https://www.geneve.ch/ Geneva ( ; french: Genève ) frp, Genèva ; german: link=no, Genf ; it, Ginevr ...

. However, when the heating system was modified, the coupling increased dramatically, demonstrating temperatures within the heating section as high as . 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 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. 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. B-3, also completed in 1957, was a greatly enlarged B-2 machine with ultra-high vacuum and pulsed confinement up to 50,000 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. 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.

Model C

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 and was in length. The toroidal field coils normally operated at 35,000 gauss. 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

(PPPL). 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

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. This method of heating, now known as

neutral beam injection Neutral-beam injection (NBI) is one method used to heat plasma inside a fusion device consisting in a beam of high-energy neutral particles that can enter the magnetic confinement field. When these neutral particles are ionized by collision with ...

, has since become almost universal on

machines. Model C spent most of its history involved in studies of ion transport. 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 eV.

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 torastron 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. 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 The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

released the results of their

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 A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fi ...

-based system developed for the

ZETA Zeta (, ; uppercase Ζ, lowercase ζ; grc, ζῆτα, el, ζήτα, label= Demotic Greek, classical or ''zē̂ta''; ''zíta'') is the sixth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 7. It was derived f ...

reactor in England, verified the Soviet claims of electron temperatures of 1,000 eV. What followed was a "veritable stampede" of tokamak construction worldwide. 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 The Princeton Large Torus (or PLT), was an early tokamak built at the Princeton Plasma Physics Laboratory (PPPL). It was one of the first large scale tokamak machines, and among the most powerful in terms of current and magnetic fields. Originally ...

of 1975 quickly hit several performance numbers that were required for a commercial machine, and it was widely believed the critical threshold of 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 In engineering, a factor of safety (FoS), also known as (and used interchangeably with) safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety factors are often calculated using detailed analy ...

'', or ''q'', the plasma is much more stable. ZETA ran at a ''q'' around , 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 Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...

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. This coincided with the development of advanced computer aided planning tools that allowed the construction of complex magnets that were previously known but considered too difficult to design and build. 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 The Wendelstein 7-X (abbreviated W7-X) reactor is an experimental stellarator built in Greifswald, Germany, by the Max Planck Institute for Plasma Physics (IPP), and completed in October 2015.Helically Symmetric Experiment (HSX) in the US, and the Large Helical Device in Japan. W7X and LHD use superconducting magnetic coils. 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 advantages from an engineering standpoint.

Underlying concepts

Requirements for fusion

Heating a gas increases the energy of the particles within it, so by heating a gas into hundreds of millions of degrees, the majority of the particles within it reach the energy required to fuse. According to the

Maxwell–Boltzmann distribution In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and use ...

, some of the particles will reach the required energies at much lower average temperatures. Because the energy released by the fusion reaction is much greater than what it takes to start it, even a small number of reactions can heat surrounding fuel until it fuses as well. In 1944, Enrico Fermi calculated the D-T reaction would be self-sustaining at about . Materials heated beyond a few tens of thousand degrees ionize into their

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

s and nuclei, producing a gas-like

state of matter In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, ...

known as plasma. According to the

ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...

, like any hot gas, plasma has an internal

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

and thus wants to expand. For a fusion reactor, the challenge is to keep the plasma contained. In a magnetic field, the electrons and nuclei orbit around the magnetic field lines, confining them to the area defined by the field.

Magnetic confinement

A simple confinement system can be made by placing a tube inside the open core of a solenoid. The tube can be evacuated and then filled with the requisite gas and heated until it becomes a plasma. The plasma naturally wants to expand outwards to the walls of the tube, as well as move along it, towards the ends. The solenoid creates magnetic field lines running down the center of the tube, and the plasma particles orbit these lines, preventing their motion towards the sides. Unfortunately, this arrangement would not confine the plasma along the ''length'' of the tube, and the plasma would be free to flow out the ends. The obvious solution to this problem is to bend the tube around into a

(a ring or donut) shape. Motion towards the sides remains constrained as before, and while the particles remain free to move along the lines, in this case, they will simply circulate around the long axis of the tube. But, as Fermi pointed out, when the solenoid is bent into a ring, the electrical windings would be closer together on the inside than the outside. This would lead to an uneven field across the tube, and the fuel will slowly drift out of the center. Since the electrons and ions would drift in opposite directions, this would lead to a charge separation and electrostatic forces that would eventually overwhelm the magnetic force. Some additional force needs to counteract this drift, providing long-term ''confinement''.

Stellarator concept

Spitzer's key concept in the stellarator design is that the drift that Fermi noted could be canceled out through the physical arrangement of the vacuum tube. In a torus, particles on the inside edge of the tube, where the field was stronger, would drift up, while those on the outside would drift down (or vice versa). However, if the particle were made to alternate between the inside and outside of the tube, the drifts would alternate between up and down and would cancel out. The cancellation is not perfect, leaving some net drift, but basic calculations suggested drift would be lowered enough to confine plasma long enough to heat it sufficiently. Spitzer's suggestion for doing this was simple. Instead of a normal torus, the device would essentially be cut in half to produce two half-tori. They would then be joined with two straight sections between the open ends. The key was that they were connected to alternate ends so that the right half of one of the tori was connected to the left of the other. The resulting design resembled a figure-8 when viewed from above. Because the straight tubes could not pass through each other, the design did not lie flat, the tori at either end had to be tilted. This meant the drift cancellation was further reduced, but again, calculations suggested the system would work. To understand how the system works to counteract drift, consider the path of a single particle in the system starting in one of the straight sections. If that particle is perfectly centered in the tube, it will travel down the center into one of the half-tori, exit into the center of the next tube, and so on. This particle will complete a loop around the entire reactor without leaving the center. Now consider another particle traveling parallel to the first, but initially located near the inside wall of the tube. In this case, it will enter the ''outside'' edge of the half-torus and begin to drift down. It exits that section and enters the second straight section, still on the outside edge of that tube. However, because the tubes are crossed, when it reaches the second half-torus it enters it on the ''inside'' edge. As it travels through this section it drifts back up. This effect would reduce one of the primary causes of drift in the machine, but there were others to consider as well. Although the ions and electrons in the plasma would both circle the magnetic lines, they would do so in opposite directions, and at very high rotational speeds. This leads to the possibility of collisions between particles circling different lines of force as they circulate through the reactor, which due to purely geometric reasons, causes the fuel to slowly drift outward. This process eventually causes the fuel to either collide with the structure or cause a large charge separation between the ions and electrons. Spitzer introduced the concept of a ''divertor'', a magnet placed around the tube that pulled off the very outer layer of the plasma. This would remove the ions before they drifted too far and hit the walls. It would also remove any heavier elements in the plasma. Using classical calculations the rate of diffusion through collisions was low enough that it would be much lower than the drift due to uneven fields in a normal toroid. But earlier studies of magnetically confined plasmas in 1949 demonstrated much higher losses and became known as

. Spitzer spent considerable effort considering this issue and concluded that the anomalous rate being seen by Bohm was due to instability in the plasma, which he believed could be addressed.

Alternative designs

One of the major concerns for the original stellarator concept is that the magnetic fields in the system will only properly confine a particle of a given mass traveling at a given speed. Particles traveling faster or slower will not circulate in the desired fashion. Particles with very low speeds (corresponding to low temperatures) are not confined and can drift out to the tube walls. Those with too much energy may hit the outside walls of the curved sections. To address these concerns, Spitzer introduced the concept of a ''divertor'' that would connect to one of the straight sections. This was essentially a

mass spectrometer Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a '' mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is us ...

that would remove particles that were moving too fast or too slow for proper confinement. The physical limitation that the two straight sections cannot intersect means that the rotational transform within the loop is not a perfect 180 degrees, but typically closer to 135 degrees. This led to alternate designs in an effort to get the angle closer to 180. An early attempt was built into the Stellarator B-2, which placed both curved sections flat in relation to the ground, but at different heights. The formerly straight sections had additional curves inserted, two sections of about 45 degrees, so they now formed extended S-shapes. This allowed them to route around each other while being perfectly symmetrical in terms of angles. A better solution to the need to rotate the particles was introduced in the Stellarator B-64 and B-65. These eliminated the cross-over and flattened the device into an oval, or as they referred to it, a racetrack. The rotation of the particles was introduced by placing a new set of magnetic coils on the half-torus on either end, the ''corkscrew windings''. The field from these coils mixes with the original confinement fields to produce a mixed field that rotates the lines of force through 180 degrees. This made the mechanical design of the reactor much simpler, but in practice, it was found that the mixed field was very difficult to produce in a perfectly symmetrical fashion. Modern stellarator designs generally use a more complex series of magnets to produce a single shaped field. This generally looks like a twisted ribbon. Differences between the designs generally come down to how the magnets are arranged to produce the field, and the exact arrangement of the resulting field. A wide variety of layouts have been designed and some of these have been tested.

Heating

Unlike the

or tokamak, the stellarator has no induced electrical current within the plasma – at a macroscopic level, the plasma is neutral and unmoving, in spite of the individual particles within it rapidly circulating. In pinch machines, the current itself is one of the primary methods of heating the plasma. In the stellarator, no such natural heating source is present. Early stellarator designs used a system similar to those in the pinch devices to provide the initial heating to bring the gas to plasma temperatures. This consisted of a single set of windings from a

transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...

, with the plasma itself forming the secondary set. When energized with a pulse of current, the particles in the region are rapidly energized and begin to move. This brings additional gas into the region, quickly ionizing the entire mass of gas. This concept was referred to as ''ohmic heating'' because it relied on the resistance of the gas to create heat, in a fashion not unlike a conventional resistance heater. As the temperature of the gas increases, the conductivity of the plasma improves. This makes the ohmic heating process less and less effective, and this system is limited to temperatures of about 1 million kelvins. To heat the plasma to higher temperatures, Spitzer proposed a second heat source, the ''magnetic pumping'' system. This consisted of radio-frequency source fed through a coil spread along the vacuum chamber. The frequency is chosen to be similar to the natural frequency of the particles around the magnetic lines of force, the ''

cyclotron frequency Cyclotron resonance describes the interaction of external forces with charged particles experiencing a magnetic field, thus already moving on a circular path. It is named after the cyclotron, a cyclic particle accelerator that utilizes an oscillati ...

''. This causes the particles in the area to gain energy, which causes them to orbit in a wider radius. Since other particles are orbiting their own lines nearby, at a macroscopic level, this change in energy appears as an increase in pressure. According to the

, this results in an increase in temperature. Like ohmic heating, this process also becomes less efficient as the temperature increases, but is still capable of creating very high temperatures. When the frequency is deliberately set close to that of the ion circulation, this is known as ''ion-cyclotron resonance heating'', although this term was not widely used at the time.

Inherent problems

Work on the then-new tokamak concept in the early 1970s, notably by

Tihiro Ohkawa was a Japanese physicist whose field of work was in plasma physics and fusion power. He was a pioneer in developing ways to generate electricity by nuclear fusion when he worked at General Atomics. Ohkawa died September 27, 2014 in La Jolla, Cal ...

General Atomics General Atomics is an American energy and defense corporation headquartered in San Diego, California, specializing in research and technology development. This includes physics research in support of nuclear fission and nuclear fusion energy. Th ...

, suggested that toroids with smaller '' aspect ratios'' and non-circular plasmas would have much-improved performance. The aspect ratio is the comparison of the radius of the device as a whole to the radius of the cross-section of the vacuum tube. An ideal reactor would have no hole in the center, minimizing the aspect ratio. The modern

spherical tokamak A spherical tokamak is a type of fusion power device based on the tokamak principle. It is notable for its very narrow profile, or '' aspect ratio''. A traditional tokamak has a toroidal confinement area that gives it an overall shape similar to ...

takes this to its practical limit, reducing the center hole to a single metal post, elongating the cross-section of the tubing vertically, producing an overall shape that is nearly spherical and has a ratio less than 2. The MAST device in the UK, among the most powerful of these designs, has a ratio of 1.3. Stellarators generally require complex magnets to generate the desired field. In early examples, this was often in the form of several different sets of magnets, and while modern designs combine these together, the designs that result often require a considerable working volume. As a result, stellarators require a fair amount of working room in the center of the torus, and as a result, they also have relatively large aspect ratios. For instance, W7-X has an aspect ratio of 10, which leads to a very large overall size. There are some new layouts that aim to reduce the aspect ratio, but these remain untested and the reduction is still nowhere near the level seen in modern tokamaks. In a production design, the magnets would need to be protected from the 14.1 MeV

neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...

s being produced by the fusion reactions. This is normally accomplished through the use of a

breeding blanket The tritium breeding blanket (also known as a fusion blanket, lithium blanket or simply blanket), is a key part of many proposed fusion reactor designs. It serves several purposes; one is to act as a cooling mechanism, absorbing the energy from the ...

, a layer of material containing large amounts of

. In order to capture most of the neutrons, the blanket has to be about 1 to 1.5 meters thick, which moves the magnets away from the plasma and therefore requires them to be more powerful than those on experimental machines where they line the outside of the vacuum chamber directly. This is normally addressed by scaling the machine up to extremely large sizes, such that the ~10 centimetre separation found in smaller machines is linearly scaled to about 1 meter. This has the effect of making the machine much larger, growing to impractical sizes. Designs with smaller aspect ratios, which scale more rapidly, would address this effect to some degree, but designs of such systems, like ARIES-CS, are enormous, about 8 meters in radius with a relatively high aspect ratio of about 4.6. The stellarator's complex magnets combine together to produce the desired field shape. This demands extremely high positioning tolerances which drive up construction costs. It was this problem that led to the cancellation of the US's National Compact Stellarator Experiment, or NCSX, which was an experimental low-aspect design with a ratio of 4.4. To work properly, the maximum deviation in placement across the entire machine was . As it was assembled this was found to be impossible to achieve, even the natural sagging of the components over time was more than the allowed limit. Construction was cancelled in 2008, throwing the future of the PPPL into doubt. Finally, stellarator designs are expected to leak around 5% of the generated

alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be pr ...

s, increasing stress on the plasma-facing components of a reactor.

Plasma heating

There are several ways to heat the plasma (which must be done before ignition can occur). ;Current heating: The plasma is electrically conductive, and heats up when a current is passed through it (due to electrical resistance). Only used for initial heating, as the resistance is inversely proportional to the plasma temperature. ;High-frequency electromagnetic waves: The plasma absorbs energy when electromagnetic waves are applied to it (in the same manner as food in a microwave). ;Heating by neutral particles: A neutral particle beam injector makes ions and accelerates them with an electric field. To avoid being affected by the Stellarator's magnetic field, the ions must be neutralised. Neutralised ions are then injected into the plasma. Their high kinetic energy is transferred to the plasma particles by collisions, heating them.

Configurations

Several different configurations of stellarator exist, including: ;Spatial stellarator: The original figure-8 design that used geometry to produce the rotational transform of the magnetic fields. ;Classical stellarator: A toroidal or racetrack-shaped design with separate helical coils on either end to produce the rotation. ;Torsatron: A stellarator with continuous

helical Helical may refer to: * Helix, the mathematical concept for the shape * Helical engine, a proposed spacecraft propulsion drive * Helical spring, a coilspring * Helical plc, a British property company, once a maker of steel bar stock * Helicoil A t ...

coils. It can also have the continuous coils replaced by a number of discrete coils producing a similar field. The Compact Auburn Torsatron at Auburn University is an example. ;Heliotron: A stellarator in which a helical coil is used to confine the plasma, together with a pair of poloidal field coils to provide a vertical field. Toroidal field coils can also be used to control the magnetic surface characteristics. The Large Helical Device in Japan uses this configuration. ;Modular stellarator: A stellarator with a set of modular (separated) coils and a twisted toroidal coil. e.g. Helically Symmetric Experiment (HSX) (and Helias (below)) ;Heliac: A ''helical axis stellarator'', in which the magnetic axis (and plasma) follows a helical path to form a toroidal helix rather than a simple ring shape. The twisted plasma induces twist in the magnetic field lines to effect drift cancellation, and typically can provide more twist than the Torsatron or Heliotron, especially near the centre of the plasma (magnetic axis). The original Heliac consists only of circular coils, and the flexible heliac ( H-1NF, TJ-II, TU-Heliac) adds a small helical coil to allow the twist to be varied by a factor of up to 2. ;Helias: A ''helical advanced stellarator'', using an optimized modular coil set designed to simultaneously achieve high plasma, low Pfirsch–Schluter currents and good confinement of energetic particles; i.e., alpha particles for reactor scenarios. The Helias has been proposed to be the most promising stellarator concept for a power plant, with a modular engineering design and optimised plasma, MHD and magnetic field properties. The

Wendelstein 7-X The Wendelstein 7-X (abbreviated W7-X) reactor is an experimental stellarator built in Greifswald, Germany, by the Max Planck Institute for Plasma Physics (IPP), and completed in October 2015.energy transport across a magnetic field. Toroidal devices are relatively successful because the magnetic properties seen by the particles are averaged as they travel around the torus. The strength of the field seen by a particle, however, generally varies, so that some particles will be trapped by the mirror effect. These particles will not be able to average the magnetic properties so effectively, which will result in increased energy transport. In most stellarators, these changes in field strength are greater than in tokamaks, which is a major reason that transport in stellarators tends to be higher than in tokamaks. University of Wisconsin electrical engineering Professor David Anderson and research assistant John Canik proved in 2007 that the Helically Symmetric eXperiment (HSX) can overcome this major barrier in plasma research. The HSX is the first stellarator to use a quasisymmetric magnetic field. The team designed and built the HSX with the prediction that

quasisymmetry In magnetic confinement fusion, quasisymmetry (sometimes hyphenated as quasi-symmetry) is a type of continuous symmetry in the magnetic field strength of a stellarator. Quasisymmetry is desired, as Noether's theorem implies that there exists a cons ...

would reduce energy transport. As the team's latest research showed, that is exactly what it does. "This is the first demonstration that quasisymmetry works, and you can actually measure the reduction in transport that you get," says Canik. The newer

Wendelstein 7-X The Wendelstein 7-X (abbreviated W7-X) reactor is an experimental stellarator built in Greifswald, Germany, by the Max Planck Institute for Plasma Physics (IPP), and completed in October 2015.omnigeneity (a property of the magnetic field such that the mean radial drift is zero), which is a necessary but not sufficient condition for quasisymmetry; that is, all quasisymmetric magnetic fields are omnigenous, but not all omnigenous magnetic fields are quasisymmetric.