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A spherical tokamak is a type of
fusion power Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion, nuclear fusion reactions. In a fusion process, two lighter atomic nucleus, atomic nuclei combine to form a heavier nucleus, whi ...
device based on the
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 d ...
principle. It is notable for its very narrow profile, or '' aspect ratio''. A traditional tokamak has a
toroid In mathematics, a toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its ...
al confinement area that gives it an overall shape similar to a
donut A doughnut or donut () is a type of food made from leavened fried dough. It is popular in many countries and is prepared in various forms as a sweet snack that can be homemade or purchased in bakeries, supermarkets, food stalls, and fra ...
, complete with a large hole in the middle. The spherical tokamak reduces the size of the hole as much as possible, resulting in a plasma shape that is almost spherical, often compared with a cored apple. The spherical tokamak is sometimes referred to as a spherical torus and often shortened to ST. The spherical tokamak is an offshoot of the conventional tokamak design. Proponents claim that it has a number of substantial practical advantages over these devices. For this reason the ST has generated considerable interest since the late 1980s. However, development remains effectively one generation behind traditional tokamak efforts like JET. Major experiments in the ST field include the pioneering
START Start can refer to multiple topics: *Takeoff, the phase of flight where an aircraft transitions from moving along the ground to flying through the air * Starting lineup in sports *Standing start, and rolling start, in an auto race Acronyms *St ...
and MAST at Culham in the UK, the US's
NSTX-U 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, ...
and Russian Globus-M. Research has investigated whether spherical tokamaks are a route to lower cost reactors. Further research is needed to better understand how such devices scale. Even in the event that STs do not lead to lower cost approaches to power generation, they are still lower cost in general; this makes them attractive devices for studying plasma physics, or as high-energy
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 ...
sources.


Background


Basic fusion physics

The basic idea behind fusion is to force two suitable atoms close enough together that the
strong force The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the n ...
pulls them together to make a single larger atom. This process releases a considerable amount of
binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
, typically in the form of high-speed subatomic particles like
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 or
beta particle A beta particle, also called beta ray or beta radiation (symbol β), is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, β ...
s. However, these same fuel atoms also experience the
electromagnetic force In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
pushing them apart. In order for them to fuse, they must be pressed together with enough energy to overcome this ''
coulomb barrier The Coulomb barrier, named after Coulomb's law, which is in turn named after physicist Charles-Augustin de Coulomb, is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo a ...
''. The simplest way to do this is to heat the fuel to very high temperatures, and allow 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 used ...
to produce a number of very high-energy atoms within a larger, cooler mix. For the fusion to occur, the higher speed atoms have to meet, and in the random distribution that will take time. The time will be reduced by increasing the temperature, which increases the number of high-speed particles in the mix, or by increasing the pressure, which keeps them closer together. The product of temperature, pressure and time produces the expected rate of fusion events, the so-called ''
fusion triple product The Lawson criterion is a figure of merit used in nuclear fusion research. It compares the rate of energy being generated by fusion reactions within the fusion fuel to the rate of energy losses to the environment. When the rate of production is ...
''. To be useful as a net energy exporter, the triple product has to meet a certain minimum condition, the
Lawson criterion The Lawson criterion is a figure of merit used in nuclear fusion research. It compares the rate of energy being generated by fusion reactions within the fusion fuel to the rate of energy losses to the environment. When the rate of production is ...
. In practical terms, the required temperatures are on the order of 100 million degrees. This leads to problems with the two other terms; confining the fuel at a high enough pressure and for a long enough time is well beyond the capabilities of any known material. However, at these temperatures the fuel is in the form of an electrically conductive
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...
, which leads to a number of potential ''confinement'' solutions using magnetic or electrical fields. Most fusion devices use variations of these techniques.
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 d ...
s are the most researched approach within the larger group of
magnetic fusion energy 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 i ...
(MFE) designs. They attempt to confine a plasma using powerful magnetic fields. Tokamaks confine their fuel at low pressure (around 1/millionth of atmospheric) but high temperatures (150 million Celsius), and attempt to keep those conditions stable for ever-increasing times on the order of seconds to minutes. Doing so, however, requires massive amount of power in the magnetic system, and any way to reduce this improves the overall energy efficiency of the system.


Energy balance

Ideally, the energy needed to heat the fuel would be made up by the energy released from the reactions, keeping the cycle going. Anything over and above this amount could be used for power generation. This leads to the concept of the
Lawson criterion The Lawson criterion is a figure of merit used in nuclear fusion research. It compares the rate of energy being generated by fusion reactions within the fusion fuel to the rate of energy losses to the environment. When the rate of production is ...
, which delineates the conditions needed to produce net power. When the fusion fuel is heated, it will naturally lose energy through a number of processes. These are generally related to radiating terms like
blackbody radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spect ...
, and conduction terms, where the physical interaction with the surrounding carries energy out of the plasma. The resulting energy balance for any fusion power device, using a hot plasma, is shown below. :P_\text = \eta_\text\left(P_\text - P_\text - P_\text\right) where: * P_\text, is the net power out * \eta_\text, is the efficiency with which the plant captures energy, say through a steam turbine, and any power used to run the reactor * P_\text, is the power generated by fusion reactions, basically a function of the rate of reactions * P_\text, is the power lost through conduction to the reactor body * P_\text, is the power lost as light, leaving the plasma, typically through gamma radiation To achieve net power, a device must be built which optimizes this equation. Fusion research has traditionally focused on increasing the first ''P'' term: the fusion rate. This has led to a variety of machines that operate at ever higher temperatures and attempt to maintain the resulting
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...
in a stable state long enough to meet the desired triple product. However, it is also essential to maximize the ''η'' for practical reasons, and in the case of a MFE reactor, that generally means increasing the efficiency of the confinement system, notably the energy used in the magnets.


Beta number

A measure of success across the magnetic fusion energy world is the '' beta number''. Every machine containing plasma magnetically, can be compared using this number. \beta = \frac = \frac This is the ratio of the plasma pressure to the magnetic field pressure. Improving beta means that you need to use, in relative terms, less energy to generate the magnetic fields for any given plasma pressure (or density). The price of magnets scales roughly with β½, so reactors operating at higher betas are less expensive for any given level of confinement. Conventional tokamaks operate at relatively low betas, the record being just over 12%, but various calculations show that practical designs would need to operate as high as 20%.


Aspect ratio

The limiting factor in reducing beta is the size of the magnets. Tokamaks use a series of ring-shaped magnets around the confinement area, and their physical dimensions mean that the hole in the middle of the torus can be reduced only so much before the magnet windings are touching. This limits the aspect ratio, A = R/a, of the reactor to about 2.5; the diameter of the reactor as a whole could be about 2.5 times the cross-sectional diameter of the confinement area. Some experimental designs were slightly under this limit, while many reactors had much higher A.


History


Reducing aspect ratio

During the 1980s, researchers at
Oak Ridge National Laboratory Oak Ridge National Laboratory (ORNL) is a U.S. multiprogram science and technology national laboratory sponsored by the U.S. Department of Energy (DOE) and administered, managed, and operated by UT–Battelle as a federally funded research and ...
(ORNL), led by Ben Carreras and Tim Hender, were studying the operations of tokamaks as A was reduced. They noticed, based on
magnetohydrodynamic Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydro­magnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magneto­fluids include plasmas, liquid metals, ...
considerations, that tokamaks were inherently more stable at low aspect ratios. In particular, the classic "
kink instability A kink instability (also kink oscillation or kink mode), is a current-driven plasma instability characterized by transverse displacements of a plasma column's cross-section from its center of mass without any change in the characteristics of the p ...
" was strongly suppressed. Other groups expanded on this body of theory, and found that the same was true for the high-order
ballooning instability The ballooning instability (a.k.a. ballooning mode instability) is a type of internal pressure-driven plasma instability usually seen in tokamak fusion power reactors or in space plasmas. It is important in fusion research as it determines a set of ...
as well. This suggested that a low-A machine would not only be less expensive to build, but have better performance as well. In the traditional tokamak design, the confinement magnets are normally arranged outside a toroidal vacuum chamber holding the plasma. This chamber is known as the
first wall In nuclear fusion power research, the plasma-facing material (or materials) (PFM) is any material used to construct the plasma-facing components (PFC), those components exposed to the plasma within which nuclear fusion occurs, and particularly t ...
, and defines the minimum distance between the magnets and plasma. In a production design, another layer, the ''blanket'', sits between the first wall and magnets. The blanket serves two purposes, one is to protect the magnets from the high energy
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, which will damage them, and the other is to use those neutrons to breed tritium from lithium, producing more fuel for the reactor. However, this arrangement means there is considerable distance between the magnets and plasma, in most designs something on the order of a meter or more. This places significant limits on the achievable aspect ratio. One attempt to improve the reactor geometry was attempted by a class of designs known as the "compact tokamak", typified by the
Alcator C-Mod Alcator C-Mod was a tokamak (a type of magnetically confined fusion device) that operated between 1991 and 2016 at the Massachusetts Institute of Technology (MIT) Plasma Science and Fusion Center (PSFC). Notable for its high toroidal magnetic ...
(operational since 1991), the Riggatron (conceptual, unbuilt) and
IGNITOR Ignitor is the Italian name for a planned tokamak device, developed by ENEA. , the device has not been constructed. Started in 1977 by Prof. Bruno Coppi at MIT, Ignitor based on the 1970s Alcator machine at MIT which pioneered the high magnetic ...
(construction in progress ). The later two of these designs dispensed with the first wall and placed the magnets in direct contact with the plasma; in a production design the blanket would be outside the magnets. This greatly simplifies the physical design as well, as the toroidal vacuum vessel can be replaced with a cylinder. The decreased distance between the magnets and plasma leads to much higher betas, so conventional (non-superconducting) magnets could be used. The downside to this approach, one that was widely criticized in the field, is that it places the magnets directly in the high-energy neutron flux of the fusion reactions. In operation the magnets would be rapidly eroded, requiring the vacuum vessel to be opened and the entire magnet assembly replaced after a month or so of operation. Around the same time, several advances in plasma physics were making their way through the fusion community. Of particular importance were the concepts of elongation and triangularity, referring to the cross-sectional shape of the plasma. Early tokamaks had all used circular cross-sections simply because that was the easiest to model and build, but over time it became clear that C or (more commonly) D-shaped plasma cross-sections led to higher performance. This produces plasmas with high "shear", which distributed and broke up turbulent eddies in the plasma. These changes led to the "
advanced 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 ...
" designs, which include
ITER ITER (initially the International Thermonuclear Experimental Reactor, ''iter'' meaning "the way" or "the path" in Latin) is an international nuclear fusion research and engineering megaproject aimed at creating energy by replicating, on Earth ...
.


Spherical tokamaks

In 1984, Martin Peng of
ORNL Oak Ridge National Laboratory (ORNL) is a U.S. multiprogram science and technology national laboratory sponsored by the U.S. Department of Energy (DOE) and administered, managed, and operated by UT–Battelle as a federally funded research and ...
proposed an alternate arrangement of the magnet coils that would greatly reduce the aspect ratio while avoiding the erosion issues of the compact tokamak. Instead of wiring each magnet coil separately, he proposed using a single large conductor in the center, and wiring the magnets as half-rings off of this conductor. What was once a series of individual rings passing through the hole in the center of the reactor was reduced to a single post, allowing for aspect ratios as low as 1.2. This means that STs can reach the same operational
triple product In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector- ...
numbers as conventional designs using one tenth the magnetic field. The design, naturally, also included the advances in plasma shaping that were being studied concurrently. Like all modern designs, the ST uses a D-shaped plasma cross section. If you consider a D on the right side and a reversed D on the left, as the two approach each other (as A is reduced) eventually the vertical surfaces touch and the resulting shape is a circle. In 3D, the outer surface is roughly spherical. They named this layout the "spherical tokamak", or ST. These studies suggested that the ST layout would include all the qualities of the advanced tokamak, the compact tokamak, would strongly suppress several forms of turbulence, reach high β, have high self-magnetism and be less costly to build.Y-K Martin Peng, "Compact DT Fusion Spherical Tori at Modest Fields", CONF-850610-37 (December 1985) The ST concept appeared to represent an enormous advance in tokamak design. In 1985 ORNL proposed the Spherical Torus Experiment (STX). However, this was during a period when US fusion research budgets were being dramatically scaled back. ORNL was provided with funds to develop and test a prototype central solenoid column built with 6 layers of turns of a high-strength copper alloy called "
Glidcop Glidcop is a family of copper-based metal matrix composite (MMC) alloys mixed primarily with small amounts of aluminum oxide ceramic particles. It is a trademark of North American Höganäs. The name is sometimes written GlidCop or GLIDCOP. The ...
" (each layer with water cooling).T.J. McManamy et al.
"STX Magnet Fabrication and Testing to 18T"
Martin Marietta Energy Systems, December 1988
However, they were unable to secure funding to build the complete STX design.


From spheromak to ST

Failing to build an ST at ORNL, Peng began a worldwide effort to interest other teams in the ST concept and get a test machine built. One way to do this quickly would be to convert a
spheromak 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 s ...
machine to the ST layout. Spheromaks are essentially " smoke rings" of plasma that are internally self-stable. Typical reactors use gas puffers and magnets to form the spheromak and inject it into a cylindrical confinement area, but as the magnetic fields are confined within the plasma, they are free to drift about the confinement area and collide with the first wall. The typical solution to this problem was to wrap the area in a sheet of copper, or more rarely, place a copper conductor down the center. When the spheromak approaches the conductor, a magnetic field is generated that pushes it away again. A number of experimental spheromak machines were built in the 1970s and early 80s, but demonstrated performance that simply was not interesting enough to suggest further development. Spheromaks with the central conductor had a strong mechanical resemblance to the ST design, and could be converted with relative ease. The first such conversion was made to the Heidelberg Spheromak Experiment or HSE. Built at
Heidelberg University } Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, ...
in the early 1980s, HSE was quickly converted to a ST in 1987 by adjusting its magnetic coils at the outside of the confinement area and attaching them to a new central conductor. Although the new configuration only operated "cold", far below fusion temperatures, the results were promising and demonstrated all of the basic features of the ST. Several other groups with spheromak machines made similar conversions, notably the rotamak at the
Australian Nuclear Science and Technology Organisation The Australian Nuclear Science and Technology Organisation (ANSTO) is a statutory body of the Australian government, formed in 1987 to replace the Australian Atomic Energy Commission. Its head office and main facilities are in southern outs ...
and the
SPHEX Wasps of the genus ''Sphex'' (commonly known as digger wasps) are cosmopolitan predators that sting and paralyze prey insects. ''Sphex'' is one of many genera in the old digger wasp family Sphecidae ('' sensu lato''), though most apart from the ...
machine. In general they all found an increase in performance of a factor of two or more. This was an enormous advance, and the need for a purpose-built machine became pressing.


START and newer systems

Peng's advocacy also caught the interest of Derek Robinson, of the
United Kingdom Atomic Energy Authority The United Kingdom Atomic Energy Authority is a UK government research organisation responsible for the development of fusion energy. It is an executive non-departmental public body of the Department for Business, Energy and Industrial Strategy ...
(UKAEA) fusion center at
Culham Culham is a village and civil parish in a bend of the River Thames, south of Abingdon in Oxfordshire. The parish includes Culham Science Centre and Europa School UK (formerly the European School, Culham, which was the only Accredited Europe ...
. What is today known as the
Culham Centre for Fusion Energy The Culham Centre for Fusion Energy (CCFE) is the UK's national laboratory for fusion research. It is located at the Culham Science Centre, near Culham, Oxfordshire, and is the site of the Joint European Torus (JET), Mega Ampere Spherical Tokam ...
was set up in the 1960s to gather together all of the UK's fusion research, formerly spread across several sites, and Robinson had recently been promoted to running several projects at the site. Robinson was able to gather together a team and secure funding on the order of 100,000 pounds to build an experimental machine, the
Small Tight Aspect Ratio Tokamak The Small Tight Aspect Ratio Tokamak, or START was a nuclear fusion experiment that used magnetic confinement to hold plasma. START was the first full-sized machine to use the spherical tokamak design, which aimed to greatly reduce the aspect ...
, or START. Several parts of the machine were recycled from earlier projects, while others were loaned from other labs, including a 40 keV neutral beam injector from ORNL. Before it started operation there was considerable uncertainty about its performance, and predictions that the project would be shut down if confinement proved to be similar to spheromaks. Construction of START began in 1990, it was assembled rapidly and started operation in January 1991. Its earliest operations quickly put any theoretical concerns to rest. Using ohmic heating alone, START demonstrated betas as high as 12%, almost matching the record of 12.6% on the
DIII-D DIII-D is a tokamak that has been operated since the late 1980s by General Atomics (GA) in San Diego, USA, for the U.S. Department of Energy. The DIII-D National Fusion Facility is part of the ongoing effort to achieve magnetically confined fusio ...
machine. The results were so good that an additional 10 million pounds of funding was provided over time, leading to a major re-build in 1995. When neutral beam heating was turned on, beta jumped to 40%, beating any conventional design by 3 times. Additionally, START demonstrated excellent plasma stability. A practical rule of thumb in conventional designs is that as the operational beta approaches a certain value normalized for the machine size,
ballooning instability The ballooning instability (a.k.a. ballooning mode instability) is a type of internal pressure-driven plasma instability usually seen in tokamak fusion power reactors or in space plasmas. It is important in fusion research as it determines a set of ...
destabilizes the plasma. This so-called "
Troyon limit The beta of a plasma, symbolized by ''β'', is the ratio of the plasma pressure (''p'' = ''n'' ''k''B ''T'') to the magnetic pressure (''p''mag = ''B''²/2 ''μ''0). The term is commonly used in studies of the Sun and Earth's magnetic field, an ...
" is normally 4, and generally limited to about 3.5 in real world machines. START improved this dramatically to 6. The limit depends on size of the machine, and indicates that machines will have to be built of at least a certain size if they wish to reach some performance goal. With START's much higher scaling, the same limits would be reached with a smaller machine.


Rush to build STs

START proved Peng and Strickler's predictions; the ST had performance an
order of magnitude An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic dis ...
better than conventional designs, and cost much less to build as well. In terms of overall economics, the ST was an enormous step forward. Moreover, the ST was a new approach, and a low-cost one. It was one of the few areas of mainline fusion research where real contributions could be made on small budgets. This sparked off a series of ST developments around the world. In particular, the
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, ...
(NSTX) and
Pegasus Pegasus ( grc-gre, Πήγασος, Pḗgasos; la, Pegasus, Pegasos) is one of the best known creatures in Greek mythology. He is a winged divine stallion usually depicted as pure white in color. He was sired by Poseidon, in his role as hor ...
experiments in the US, Globus-M in Russia, and the UK's follow-on to START, MAST. Meanwhile START itself found new life as part of the revolutionary
Proto-Sphera Proto-Sphera is an Italian experiment to develop a spherical fusion reactor using a plasma to replace the usual central column.https://www.afs.enea.it/project/protosphera/ The device used is the repurposed Small Tight Aspect Ratio Tokamak The Smal ...
project in Italy, where experimenters are attempting to eliminate the central column by passing the current through a secondary plasma. The
Proto-Sphera Proto-Sphera is an Italian experiment to develop a spherical fusion reactor using a plasma to replace the usual central column.https://www.afs.enea.it/project/protosphera/ The device used is the repurposed Small Tight Aspect Ratio Tokamak The Smal ...
project also removes the need of a
divertor In nuclear fusion power research, a divertor is a device within a tokamak or a stellarator that allows the online removal of waste material from the plasma while the reactor is still operating. This allows control over the buildup of fusion pro ...
, since plasma instabilities are exploited rather than avoided.


Design

Tokamak reactors consist of a toroidal vacuum tube surrounded by a series of magnets. One set of magnets is logically wired in a series of rings around the outside of the tube, but are physically connected through a common conductor in the center. The central column is also normally used to house the
solenoid upright=1.20, An illustration of a solenoid upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whose ...
that forms the inductive loop for the ohmic heating system (and pinch current). The canonical example of the design can be seen in the small tabletop ST device made at Flinders University, which uses a central column made of copper wire wound into a solenoid, return bars for the toroidal field made of vertical copper wires, and a metal ring connecting the two and providing mechanical support to the structure.


Stability within the ST

Advances in plasma physics in the 1970s and 80s led to a much stronger understanding of stability issues, and this developed into a series of "scaling laws" that can be used to quickly determine rough operational numbers across a wide variety of systems. In particular, Troyon's work on the critical beta of a reactor design is considered one of the great advances in modern plasma physics. Troyon's work provides a beta limit where operational reactors will start to see significant instabilities, and demonstrates how this limit scales with size, layout, magnetic field and current in the plasma. However, Troyon's work did not consider extreme aspect ratios, work that was later carried out by a group at 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 ...
. This starts with a development of a useful beta for a highly asymmetric volume: : \beta=\frac. Where \langle B^2\rangle is the volume averaged magnetic field \scriptstyle\langle B^2\rangle = \langle B_^2 + B_^2\rangle (as opposed to Troyon's use of the field in the vacuum outside the plasma, \scriptstyle B_0). Following Freidberg, this beta is then fed into a modified version of 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 ...
: : q_\star= \frac \left( \frac \right). Where \scriptstyle B_0 is the vacuum magnetic field, a is the minor radius, \scriptstyle R the major radius, \scriptstyle I the plasma current, and \scriptstyle \kappa the elongation. In this definition it should be clear that decreasing aspect ratio, \scriptstyle R/a, leads to higher average safety factors. These definitions allowed the Princeton group to develop a more flexible version of Troyon's critical beta: : \beta_\text = 5\langle B_N\rangle \left( \frac\right) \frac. Where \epsilon is the inverse aspect ratio 1/A and \langle B_N\rangle is a constant scaling factor that is about 0.03 for any q_\star greater than 2. Note that the critical beta scales with aspect ratio, although not directly, because q_\star also includes aspect ratio factors. Numerically, it can be shown that \beta_\text is maximized for: : q_\star = 1 + \left(\frac\right)^ \approx 1.8. Using this in the critical beta formula above: : \beta_\text = 0.072 \left(\frac\right)\epsilon. For a spherical tokamak with an elongation \kappa of 2 and an aspect ratio of 1.25: : \beta_\text = 0.072 \left(\frac\right)\frac = 0.14. Now compare this to a traditional tokamak with the same elongation and a major radius of 5 meters and minor radius of 2 meters: : \beta_\text = 0.072 \left(\frac\right)\frac = 0.072. The linearity of \beta_\text\, with aspect ratio is evident.


Power scaling

Beta is an important measure of performance, but in the case of a reactor designed to produce electricity, there are other practical issues that have to be considered. Among these is the
power density Power density is the amount of power (time rate of energy transfer) per unit volume. In energy transformers including batteries, fuel cells, motors, power supply units etc., power density refers to a volume, where it is often called volume p ...
, which offers an estimate of the size of the machine needed for a given power output. This is, in turn, a function of the plasma pressure, which is in turn a function of beta. At first glance it might seem that the ST's higher betas would naturally lead to higher allowable pressures, and thus higher power density. However, this is only true if the magnetic field remains the same – beta is the ratio of magnetic to plasma density. If one imagines a toroidal confinement area wrapped with ring-shaped magnets, it is clear that the magnetic field is greater on the inside radius than the outside - this is the basic stability problem that the tokamak's electric current addresses. However, the ''difference'' in that field is a function of aspect ratio; an infinitely large toroid would approximate a straight solenoid, while an ST maximizes the difference in field strength. Moreover, as there are certain aspects of reactor design that are fixed in size, the aspect ratio might be forced into certain configurations. For instance, production reactors would use a thick "blanket" 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 el ...
around the reactor core in order to capture the high-energy neutrons being released, both to protect the rest of the reactor mass from these neutrons as well as produce
tritium Tritium ( or , ) or hydrogen-3 (symbol T or H) is a rare and radioactive isotope of hydrogen with half-life about 12 years. The nucleus of tritium (t, sometimes called a ''triton'') contains one proton and two neutrons, whereas the nucleus o ...
for fuel. The size of the blanket is a function of the neutron's energy, which is 14 MeV in the D-T reaction regardless of the reactor design, Thus the blanket would be the same for a ST or traditional design, about a meter across. In this case further consideration of the overall magnetic field is needed when considering the betas. Working inward through the reactor volume toward the inner surface of the plasma we would encounter the blanket, "first wall" and several empty spaces. As we move away from the magnet, the field reduces in a roughly linear fashion. If we consider these reactor components as a group, we can calculate the magnetic field that remains on the far side of the blanket, at the inner face of the plasma: : B_= () .\, Now we consider the average plasma pressure that can be generated with this magnetic field. Following Freidberg: : = \beta_\text\left (1 + \kappa^2\right) \epsilon \left(\right)^2 G(\epsilon) \left(B_\text\right)^2. In an ST, where we are attempting to maximize B_0 as a general principle, one can eliminate the blanket on the inside face and leave the central column open to the neutrons. In this case, \epsilon_0 is zero. Considering a central column made of copper, we can fix the maximum field generated in the coil, B_\text to about 7.5 T. Using the ideal numbers from the section above: : = 0.14 \left(1 + 2^2\right) \left(\frac\right) \left(1 - \frac\right)^2 2.5 \cdot 7.5^2 = 2.6 \text. Now consider the conventional design as above, using superconducting magnets with a B_\text of 15 T, and a blanket of 1.2 meters thickness. First we calculate \epsilon to be 1/(5/2) = 0.4 and \epsilon_b to be 1.5/5 = 0.24, then: : = 0.072 \left(1 + 2^2\right) \left(\frac\right) \left(1 - \frac - \frac\right)^2 1.2 \cdot 15^2 = 7.7 \text. So in spite of the higher beta in the ST, the overall power density is lower, largely due to the use of superconducting magnets in the traditional design. This issue has led to considerable work to see if these scaling laws hold for the ST, and efforts to increase the allowable field strength through a variety of methods. Work on START suggests that the scaling factors are much higher in STs, but this work needs to be replicated at higher powers to better understand the scaling. Research using data from
NSTX The National Spherical Torus Experiment (NSTX) is a Magnetic fusion energy, magnetic fusion device based on the ''spherical tokamak'' concept. It was constructed by the Princeton Plasma Physics Laboratory (PPPL) in collaboration with the Oak Ridg ...
and MAST appears to confirm the supposition that for similar values of field and fusion power, but smaller volume, STs can demonstrate a fusion triple product of up to a factor of three higher and a fusion power gain of an order of magnitude higher than tokamaks.


Advantages

STs have two major advantages over conventional designs. The first is practical. Using the ST layout places the toroidal magnets much closer to the plasma, on average. This greatly reduces the amount of energy needed to power the magnets in order to reach any particular level of magnetic field within the plasma. Smaller magnets cost less, reducing the cost of the reactor. The gains are so great that superconducting magnets may not be required, leading to even greater cost reductions. START placed the secondary magnets inside the vacuum chamber, but in modern machines these have been moved outside and can be superconducting. The other advantages have to do with the stability of the plasma. Since the earliest days of fusion research, the problem in making a useful system has been a number of
plasma instabilities The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it ...
that only appeared as the operating conditions moved ever closer to useful ones for fusion power. In 1954
Edward Teller Edward Teller ( hu, Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist who is known colloquially as "the father of the hydrogen bomb" (see the Teller–Ulam design), although he did not care fo ...
hosted a meeting exploring some of these issues, and noted that he felt plasmas would be inherently more stable if they were following convex lines of magnetic force, rather than concave. It was not clear at the time if this manifested itself in the real world, but over time the wisdom of these words became apparent. In the tokamak, stellarator and most pinch devices, the plasma is forced to follow helical magnetic lines. This alternately moves the plasma from the outside of the confinement area to the inside. While on the outside, the particles are being pushed inward, following a concave line. As they move to the inside they are being pushed outward, following a convex line. Thus, following Teller's reasoning, the plasma is inherently more stable on the inside section of the reactor. In practice the actual limits are suggested by 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 ...
", ''q'', which vary over the volume of the plasma. In a traditional circular cross-section tokamak, the plasma spends about the same time on the inside and the outside of the torus; slightly less on the inside because of the shorter radius. In the advanced tokamak with a D-shaped plasma, the inside surface of the plasma is significantly enlarged and the particles spend more time there. However, in a normal high-A design, ''q'' varies only slightly as the particle moves about, as the relative distance from inside the outside is small compared to the radius of the machine as a whole (the definition of aspect ratio). In an ST machine, the variance from "inside" to "outside" is much larger in relative terms, and the particles spend much more of their time on the "inside". This leads to greatly improved stability. It is possible to build a traditional tokamak that operates at higher betas, through the use of more powerful magnets. To do this, the current in the plasma must be increased in order to generate the toroidal magnetic field of the right magnitude. This drives the plasma ever closer to the Troyon limits where instabilities set in. The ST design, through its mechanical arrangement, has much better ''q'' and thus allows for much more magnetic power before the instabilities appear. Conventional designs hit the Troyon limit around 3.5, whereas START demonstrated operation at 6.


Disadvantages

The ST has three distinct disadvantages compared to "conventional" advanced tokamaks with higher aspect ratios. The first issue is that the overall pressure of the plasma in an ST is lower than conventional designs, in spite of higher beta. This is due to the limits of the magnetic field on the inside of the plasma, B_\text. This limit is theoretically the same in the ST and conventional designs, but as the ST has a much lower aspect ratio, the effective field changes more dramatically over the plasma volume. The second issue is both an advantage and disadvantage. The ST is so small, at least in the center, that there is little or no room for superconducting magnets. This is not a deal-breaker for the design, as the field from conventional copper wound magnets is enough for the ST design. However, this means that power dissipation in the central column will be considerable. Engineering studies suggest that the maximum field possible will be about 7.5 T , much lower than is possible with a conventional layout. This places a further limit on the allowable plasma pressures. However, the lack of superconducting magnets greatly lowers the price of the system, potentially offsetting this issue economically. The lack of shielding also means the magnet is directly exposed to the interior of the reactor. It is subject to the full heating flux of the plasma, and the neutrons generated by the fusion reactions. In practice, this means that the column would have to be replaced fairly often, likely on the order of a year, greatly affecting the availability of the reactor. In production settings, the availability is directly related to the cost of electrical production. Experiments are underway to see if the conductor can be replaced by a
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 ...
plasma or liquid metal conductor in its place. Finally, the highly asymmetrical plasma cross sections and tightly wound magnetic fields require very high toroidal currents to maintain them. Normally this would require large amounts of secondary heating systems, like neutral beam injection. These are energetically expensive, so the ST design relies on high
bootstrap current In a toroidal fusion power device, a plasma is confined within a donut-shaped cylinder. If the gas pressure of the plasma varies across the radius of the cylinder, a self-generated current will spontaneously arise within the plasma, due to collisi ...
s for economical operation. Luckily, high elongation and triangularity are the features that give rise to these currents, so it is possible that the ST will actually be more economical in this regard. This is an area of active research.


List of ST machines


Retired

*
Small Tight Aspect Ratio Tokamak The Small Tight Aspect Ratio Tokamak, or START was a nuclear fusion experiment that used magnetic confinement to hold plasma. START was the first full-sized machine to use the spherical tokamak design, which aimed to greatly reduce the aspect ...
(START), UK. Hardware used for Proto-Sphera, Italy


Operational


ST25 website
Tokamak Energy Tokamak Energy is a fusion power research company based in the United Kingdom, established in 2009. The company employs over 200 people and holds over 50 families of patent applications. It has built several versions of tokamaks, in the form of sp ...
, UK *
Mega Ampere Spherical Tokamak Mega Ampere Spherical Tokamak (MAST) was a nuclear fusion experiment, testing a spherical tokamak nuclear fusion reactor, and commissioned by EURATOM/UKAEA. The original MAST experiment took place at the Culham Centre for Fusion Energy, Oxford ...

MAST website
Culham Centre for Fusion Energy The Culham Centre for Fusion Energy (CCFE) is the UK's national laboratory for fusion research. It is located at the Culham Science Centre, near Culham, Oxfordshire, and is the site of the Joint European Torus (JET), Mega Ampere Spherical Tokam ...
,
United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales and North ...

Globus-M website
Ioffe Institute The Ioffe Physical-Technical Institute of the Russian Academy of Sciences (for short, Ioffe Institute, russian: Физико-технический институт им. А. Ф. Иоффе) is one of Russia's largest research centers specialized ...
,
Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
*
NSTX The National Spherical Torus Experiment (NSTX) is a Magnetic fusion energy, magnetic fusion device based on the ''spherical tokamak'' concept. It was constructed by the Princeton Plasma Physics Laboratory (PPPL) in collaboration with the Oak Ridg ...

NSTX website
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 ...
,
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

Proto-Sphera website
(using hardware from START), ENEA,
Italy Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...

TST-2
University of Tokyo , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...
,
Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...

QUEST
Kyushu University , abbreviated to , is a Japanese national university located in Fukuoka, on the island of Kyushu. It was the 4th Imperial University in Japan, ranked as 4th in 2020 Times Higher Education Japan University Rankings, one of the top 10 Design ...
,
Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...

SUNIST
Tsinghua University Tsinghua University (; abbreviation, abbr. THU) is a National university, national Public university, public research university in Beijing, China. The university is funded by the Ministry of Education of the People's Republic of China, Minis ...
,
China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...
*
PEGASUS Pegasus ( grc-gre, Πήγασος, Pḗgasos; la, Pegasus, Pegasos) is one of the best known creatures in Greek mythology. He is a winged divine stallion usually depicted as pure white in color. He was sired by Poseidon, in his role as hor ...

PEGASUS website
University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...
,
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

ETE website
National Institute for Space Research The National Institute for Space Research ( pt, Instituto Nacional de Pesquisas Espaciais, INPE) is a research unit of the Brazilian Ministry of Science, Technology and Innovations, the main goals of which are fostering scientific research an ...
,
Brazil Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area ...


Under construction

* URANIA upgrade from
Pegasus Pegasus ( grc-gre, Πήγασος, Pḗgasos; la, Pegasus, Pegasos) is one of the best known creatures in Greek mythology. He is a winged divine stallion usually depicted as pure white in color. He was sired by Poseidon, in his role as hor ...


Proposed

*
Spherical Tokamak for Energy Production Spherical Tokamak for Energy Production (STEP) is a spherical tokamak fusion plant concept proposed by the United Kingdom Atomic Energy Authority and funded by UK government. The project is a proposed DEMO-class successor device to the ITER tokamak ...
(STEP), UK * China Fusion Engineering Testing Reactor (CFETR)


References


Citations


Bibliography

* * * * * 61 slides


External links


Spherical Tokamaks
– list of ST experiments at tokamak.info (DEAD link Jan 2015)
2012 list of STsCulham Centre for Fusion Energy
– spherical tokamaks at Culham, UK, including details of the MAST and START experiments {{fusion methods Tokamaks