Stellarator

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Example of a stellarator design, as used in the Wendelstein 7-X experiment: A series of magnet coils (blue) surrounds the plasma (yellow). A magnetic field line is highlighted in green on the yellow plasma surface. W7X-Spulen Plasma blau gelb.jpg
Example of a stellarator design, as used in the Wendelstein 7-X experiment: A series of magnet coils (blue) surrounds the plasma (yellow). A magnetic field line is highlighted in green on the yellow plasma surface.
Wendelstein 7-X in Greifswald, Germany. Coils are prepared for the experimental stellarator. Stellarator Wendelstein 7-X Planar-Spulen Vermessung.jpg
Wendelstein 7-X in Greifswald, Germany. Coils are prepared for the experimental stellarator.
HSX stellarator HSX picture.jpg
HSX stellarator

A stellarator is a device used to confine hot plasma with magnetic fields in order to sustain a controlled nuclear fusion reaction. The name refers to the possibility of harnessing the power source of the sun, a stellar object. [1] It is one of the earliest fusion power devices, along with the z-pinch and magnetic mirror.

Plasma (physics) plasma object

Plasma is one of the four fundamental states of matter, and was first described by chemist Irving Langmuir in the 1920s. Plasma can be artificially generated by heating or subjecting a neutral gas to a strong electromagnetic field to the point where an ionized gaseous substance becomes increasingly electrically conductive, and long-range electromagnetic fields dominate the behaviour of the matter.

Magnetic field spatial distribution of vectors allowing the calculation of the magnetic force on a test particle

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.

Nuclear fusion process where atomic nuclei combine and release energy

In nuclear chemistry, nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles. The difference in mass between the reactants and products is manifested as either the release or absorption of energy. This difference in mass arises due to the difference in atomic "binding energy" between the atomic nuclei before and after the reaction. Fusion is the process that powers active or "main sequence" stars, or other high magnitude stars.

Contents

The stellarator was invented by Lyman Spitzer of Princeton University in 1951, and much of its early development was carried out by his team at what became the Princeton Plasma Physics Laboratory (PPPL). The basic concept is to lay out the magnetic fields so that particles circulating around the long axis of the machine follow twisting paths, which cancels out instabilities seen in purely toroidal machines. This would keep the fuel confined long enough to allow it to be heated to the point where fusion would take place.

Lyman Spitzer American astronomer

Lyman Strong Spitzer, Jr. 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 telescopes operating in outer space. Spitzer invented the stellarator plasma device and is the namesake of NASA's Spitzer Space Telescope. As a mountaineer, he made the first ascent of Mount Thor, with Donald C. Morton.

Princeton University University in Princeton, New Jersey

Princeton University is a private Ivy League 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 nine colonial colleges chartered before the American Revolution. The institution moved to Newark in 1747, then to the current site nine years later, and renamed itself Princeton University in 1896.

Princeton Plasma Physics Laboratory research institute

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.

The first Model A started operation in 1953 and proved the basic layout worked. Larger models followed, but these demonstrated poor performance, suffering from a problem known as pump-out that caused them to lose 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 rate, which suggested it would never be a practical fusion device.

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 inversely linear with the strength of the confining magnetic field.

The release of information on the USSR's tokamak design in 1968 indicated a leap in performance. This led to the Model C stellarator being converted 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 as the tokamak got most of the attention. The tokamak ultimately proved to have similar problems to the stellarators, but for different reasons. Since the 1990s, this has led to renewed interest in the stellarator design. [2] 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 Wendelstein 7-X in Germany, the Helically Symmetric Experiment (HSX) in the USA, and the Large Helical Device in Japan.

Tokamak device using a magnetic field to confine a plasma in the shape of a torus

A tokamak is a device which uses a powerful magnetic field to confine a hot plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being developed to produce controlled thermonuclear fusion power. As of 2016, it is the leading candidate for a practical fusion reactor.

Wendelstein 7-X experimental fusion reactor

The Wendelstein 7-X (W7-X) reactor is an experimental stellarator built in Greifswald, Germany, by the Max Planck Institute of Plasma Physics (IPP), and completed in October 2015. Its purpose is to advance stellarator technology and though this experimental reactor will consume far more power than it generates, it is used to evaluate the main components of a future fusion power plant; it was developed based on the predecessor Wendelstein 7-AS experimental reactor.

Helically Symmetric Experiment

The Helically Symmetric Experiment (HSX), stylized as Helically Symmetric eXperiment, is an experimental plasma confinement device at the University of Wisconsin-Madison, with design principles that are hoped to be incorporated into a fusion reactor. The HSX is a modular coil stellarator which is a toroid-shaped pressure vessel with external electromagnets which generate a magnetic field for the purpose of containing a plasma.

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. [3] This system allowed them to measure the nuclear cross section of various fusion reactions, and determined that the tritium-deuterium reaction occurred at a lower energy than any other fuel, peaking at about 100,000  electronvolts (100 keV). [4] [lower-alpha 1]

Mark Oliphant 27th Governor of South Australia

Sir Marcus Laurence Elwin "Mark" Oliphant 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 weapons.

Paul Harteck German chemist

Paul Karl Maria Harteck was a German 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 aiding the Nazis in their nuclear weapons program and he was incarcerated at Farm Hall, an English house fitted with covert electronic listening devices, for six months.

Ernest Rutherford New Zealand-born British chemist and physicist

Ernest Rutherford, 1st Baron Rutherford of Nelson, HFRSE LLD, was a New Zealand-born British physicist who came to be known as the father of nuclear physics. Encyclopædia Britannica considers him to be the greatest experimentalist since Michael Faraday (1791–1867).

100 keV corresponds to a temperature of about a billion kelvins. 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 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. [5]

The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is the base unit of temperature in the International System of Units (SI).

Maxwell–Boltzmann statistics Statistical distribution used in many-particle mechanics

In statistical mechanics, Maxwell–Boltzmann statistics describes the average distribution of non-interacting material particles over various energy states in thermal equilibrium, and is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.

Enrico Fermi Nuclear physicist

Enrico Fermi was an Italian and naturalized-American physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb". He was one of very few physicists to excel in both theoretical physics and experimental physics. Fermi held several patents related to the use of nuclear power, and was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and for the discovery of transuranium elements. He made significant contributions to the development of statistical mechanics, quantum theory, and nuclear and particle physics.

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 a 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. [6]

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. [6]

Stellarator

In the post-war era, 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. [7] 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. [7]

Another person working on controlled fusion reactors was Ronald Richter, a former 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. [8] The "success" was announced by Perón on 24 March 1951, becoming the topic of newspaper stories around the world. [9]

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 . [10] 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. [11] [lower-alpha 2]

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. [12]

His 1958 description was simple and direct:

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. [13]

Matterhorn

While working at Los Alamos in 1950, John Wheeler suggested setting up a secret research lab at Princeton University that would carry on theoretical work on H-bombs after he returned to the university in 1951. Spitzer was invited to join this program, given his previous research in interstellar plasmas. [14]

But by the time of his trip to Aspen, Spitzer had lost interest in bomb design and he turned his attention full-time to fusion as a power source. [15] 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. [16]

With this work in hand, Spitzer began to lobby the Department of Energy (DOE) for funding to develop the system. [16] 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. [17] This entire series was expected to take about a decade. [18]

Around the same time, 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 DOE, while Tuck received nothing. [17]

The Princeton program was officially created on 1 July 1951. Spitzer, an avid mountain climber, [lower-alpha 3] proposed the name "Project Matterhorn" because he felt "the work at hand seemed difficult, like the ascent of a mountain." [19] 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 825 acres (334 ha) plot of land the University purchased from the Rockefeller Institute for Medical Research when Rockefeller relocated to Manhattan. [lower-alpha 4] The land was located about 3 miles (4.8 km) from the main Princeton campus and already had sixteen laboratory buildings. Spitzer set up the top-secret S Section in a former rabbit hutch. [20]

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 DOE eventually organized a new department for all of these projects, becoming "Project Sherwood". [21]

Early devices

With the funding from the DOE, 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-centimetre (2.0 in) pyrex tubes about 350 cm (11.5 ft) in total length, and magnets capable of about 1,000 gauss. [22] The machine began operations in early 1953 and clearly demonstrated improved confinement over the simple torus. [23]

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. [23] 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. [24]

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. [24] However, when the heating system was modified, the coupling increased dramatically, demonstrating temperatures within the heating section as high as 1,000 electronvolts (160 aJ). [22] [lower-alpha 5]

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 diverter, 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. [25]

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. [25] 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. [24]

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. [25]

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 diverter, 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 5 and 7.5 centimetres (2.0 and 3.0 in) and was 1,200 cm (470 in) in length. The toroidal field coils normally operated at 35,000 gauss. [25]

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). [20]

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. [20] This method of heating, now known as neutral beam injection, has since become almost universal on magnetic confinement fusion machines. [26]

Model C spent most of its history involved in studies of ion transport. [20] 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. Through this period, a number of new potential stellarator designs emerged, using a single set of magnetic coils. The Model C used separate confinement and helical coils, but it was seen that these could be combined, and this led to the torsitron concept. [27] [lower-alpha 6]

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 reactor in England, verified the Soviet claims of electron temperatures of 1,000 eV. What followed was a "veritable stampede" of tokamak construction worldwide. [28]

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 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 13, 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, there was renewed interest in the stellarator approach. [2] This coincided with the development of advanced computer aided design tools that allowed the construction of complex magnets that were previously known but considered too difficult to design and build.

New materials and 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 Wendelstein 7-X in Germany, the Helically Symmetric Experiment (HSX) in the USA, 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 no confinement is 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 the hundreds of millions of degrees, the majority of the particles within it would reach the energy required to fuse. According to the Maxwell–Boltzmann distribution, some of the particles will reach the required energies at much lower average temperatures. Because the energy released by the 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 50,000,000 degrees Celsius (90,000,000 degrees Fahrenheit). [29]

Materials heated beyond a few tens of thousand degrees ionize into their electrons and nuclei, producing a gas-like state of matter known as plasma. According to the ideal gas law, like any hot gas, plasma has an internal pressure and thus wants to expand. [30] For a fusion reactor, the challenge is to keep the plasma contained; any known substance would melt at these temperatures. But because a plasma is electrically conductive, it is subject to electric and magnetic fields. In a magnetic field, the electrons and nuclei orbit around the magnetic field lines, confining them to the area defined by the field. [31] [32]

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. [33]

The obvious solution to this problem is to bend the tube around into a torus (a ring or donut) shape. [33] 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, [lower-alpha 7] 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. [6] [33]

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 simple 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 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 lay 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 studies in 1949 demonstrated much higher losses and became known as Bohm diffusion. 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. [35]

Complications, alternative designs

Practical complications make the original figure-8 device less than ideal. This led to alternative designs and additions.

One of the major concerns 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 be 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 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.

Heating

Unlike the z-pinch designs being explored in the UK and other US labs, 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, and the later tokamaks, 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, 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. [36]

To heat the plasma to higher temperatures, a second heat source was added, 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 . 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. [37] According to the ideal gas law, this results in an increase in temperature. Like the 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-cycloron resonance heating, [38] although this name is not widely used.

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:

Spacial 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 coils. It can also have the continuous coils replaced by a number of discrete coils producing a similar field.
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. [39] 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 [40] (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. [41] 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.[ citation needed ] The Wendelstein 7-X device is based on a five field-period Helias configuration.

Recent results

Optimization to reduce transport losses

The goal of magnetic confinement devices is to minimise 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 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. [42] [43]

The newer Wendelstein 7-X in Germany was designed to be close to 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; [44] that is, all quasisymmetric magnetic fields are omnigenous, but not all omnigenous magnetic fields are quasisymmetric.

See also

Notes

  1. Extensive studies in the 1970s lowered this slightly to about 70 keV.
  2. 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.
  3. The American Alpine Club has an annual Lyman Spitzer Cutting Edge Climbing Award.
  4. Eventually becoming Rockefeller University.
  5. The bulk temperature of the plasma was much lower, this was the temperature only within the heating section.
  6. See diagram, Johnson page 58.
  7. Andrei Sakharov also came to the same conclusion as Fermi as early as 1950, but his paper on the topic was not known in the west until 1958. [34]

Related Research Articles

Fusion power

Fusion power is a theoretical form of power generation in which energy will be generated by using nuclear fusion reactions to produce heat for electricity generation. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, and at the same time, they release energy. This is the same process that powers stars like our Sun. Devices designed to harness this energy are known as fusion reactors.

Reversed field pinch

A reversed-field pinch (RFP) is a device used to produce and contain near-thermonuclear plasmas. It is a toroidal pinch which uses a unique magnetic field configuration as a scheme to magnetically confine a plasma, primarily to study magnetic fusion energy. Its magnetic geometry is somewhat different from that of the more common tokamak. As one moves out radially, the portion of the magnetic field pointing toroidally reverses its direction, giving rise to the term "reversed field". This configuration can be sustained with comparatively lower fields than that of a tokamak of similar power density. One of the disadvantages of this configuration is that it tends to be more susceptible to non-linear effects and turbulence. This makes it a perfect laboratory for non-ideal (resistive) magnetohydrodynamics. RFPs are also used in the study of astrophysical plasmas as they share many features.

Tokamak Fusion Test Reactor

The Tokamak Fusion Test Reactor (TFTR) was an experimental tokamak built at Princeton Plasma Physics Laboratory (PPPL) circa 1980 and entering service in 1982. TFTR was designed with the explicit goal of reaching scientific breakeven, the point where the heat being released from the fusion reactions in the plasma is equal or greater than the heating being supplied to the plasma by external devices to warm it up.

Magnetic confinement fusion approach to generating fusion power that uses magnetic fields to confine fuel

Magnetic confinement fusion is an approach to generate thermonuclear fusion power that uses magnetic fields to confine the hot fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, the other being inertial confinement fusion. The magnetic approach dates into the 1940s and has seen the majority of development since then. It is usually considered more promising for practical power production.

A spheromak is an arrangement of plasma formed into a toroidal shape similar to a smoke ring. The spheromak contains large internal electric currents and their associated magnetic fields arranged so the magnetohydrodynamic forces within the spheromak are nearly balanced, resulting in long-lived (microsecond) confinement times without external fields. Spheromaks belong to a type of plasma configuration referred to as the compact toroids.

ZETA (fusion reactor) Experimental fusion reactor in the United Kingdom

ZETA, short for "Zero Energy Thermonuclear Assembly", was a major experiment in the early history of fusion power research. Based on the pinch plasma confinement technique, and built at the Atomic Energy Research Establishment in the United Kingdom, ZETA was larger and more powerful than any fusion machine in the world at that time. Its goal was to produce large numbers of fusion reactions, although it was not large enough to produce net energy.

National Spherical Torus Experiment

The National Spherical Torus Experiment (NSTX) is a magnetic fusion device based on the spherical tokamak concept. It was constructed by the Princeton Plasma Physics Laboratory (PPPL) in collaboration with the Oak Ridge National Laboratory, Columbia University, and the University of Washington at Seattle.

National Compact Stellarator Experiment

The National Compact Stellarator Experiment (NCSX) was a magnetic fusion energy experiment based on the stellarator design being constructed at the Princeton Plasma Physics Laboratory (PPPL). NCSX was one of a number of new stellarator designs from the 1990s that arose after studies illustrated new geometries that offered better performance than the simpler machines of the 1950s and 1960s. Compared to the more common tokamak, these were much more difficult to design and build, but produced far more stable plasma, the main problem with successful fusion.

Tokamak à configuration variable

The Tokamak à configuration variable is a Swiss research fusion reactor of the École polytechnique fédérale de Lausanne. Its distinguishing feature over other tokamaks is that its torus section is three times higher than wide. This allows studying several shapes of plasmas, which is particularly relevant since the shape of the plasma has links to the performance of the reactor. The TCV was set up in November 1992.

Trisops was an experimental machine for the study of magnetic confinement of plasmas with the ultimate goal of producing fusion power. The configuration was a variation of a compact toroid, a toroidal (doughnut-shaped) structure of plasma and magnetic fields with no coils penetrating the center. It lost funding in its original form in 1978.

Magnetically confined fusion plasmas such as those generated in tokamaks and stellarators are characterized by a typical shape. Plasma shaping is the study of the plasma shape in such devices, and is particularly important for next step fusion devices such as ITER. This shape is conditioning partly the performance of the plasma. Tokamaks, in particular, are axisymmetric devices, and therefore one can completely define the shape of the plasma by its cross-section.

Safety factor (plasma physics)

In a toroidal fusion power reactor, the magnetic fields confining the plasma are formed in a helical shape, winding around the interior of the reactor. The safety factor, labeled q or q(r), is the ratio of the times a particular magnetic field line travels around a toroidal confinement area's "long way" (toroidally) to the "short way" (poloidally).

Hybrid Illinois Device for Research and Applications

The Hybrid Illinois Device for Research and Applications (HIDRA) is a medium-sized toroidal magnetic fusion device currently being assembled within the Center for Plasma Material Interactions in the Department of Nuclear, Plasma and Radiological Engineering at the University of Illinois at Urbana–Champaign, United States. It is anticipated that HIDRA will have first plasma by mid-September 2015 and start full experimental campaigns by December of that year. HIDRA is the former WEGA classical stellarator that was operated at the Max-Planck Institut für Plasmaphsyik in Greifswald Germany from 2001 to 2013.

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 really large scale tokamak machines, and among the most powerful in terms of current and magnetic fields. A key feature was the use of external heating systems to raise the temperature of the plasma fuel, a requirement of any practical fusion power device.

The Model C stellarator was the first large-scale stellarator to be built, during the early stages of fusion power research. Planned since 1952, construction began in 1961 at what is today the Princeton Plasma Physics Laboratory (PPPL). The Model C followed the table-top sized Model A, and a series of Model B machines that refined the stellarator concept and provided the basis for the Model C, which intended to reach break-even conditions. Model C ultimately failed to reach this goal, producing electron temperatures of 400 eV when about 100,000 were needed. In 1969, after UK researchers confirmed that the USSR's T-3 tokamak was reaching 1000 eV, the Model C was converted to the Symmetrical Tokamak, and stellarator development at PPPL ended.

References

Citations

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  34. Furth 1981, p. 275.
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  37. Spitzer 1958, p. 188.
  38. Spitzer 1958, p. 189.
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