Spherical tokamak
Encyclopedia
A spherical tokamak is a type of fusion power
device based on the tokamak
principle. It is notable for its very narrow profile, or "aspect ratio
". A traditional tokamak has a toroid
al confinement area that gives it an overall shape similar to a donut
, complete with a large hole in the middle. The spherical tokamak reduces the size of the hole almost to zero, 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 practical advantages over these devices, some of them dramatic. For this reason the ST has seen considerable interest since it was introduced in the late 1980s. However, development remains effectively one generation behind mainline efforts like JET
. Major experiments in the field include the pioneering START
and MAST
at Culham in the UK, the US's NSTX
, and numerous others.
Further theoretical work has cast some doubt on the use of spherical tokamaks as a route to lower cost power producing reactors. Further research is needed to better understand the "scaling laws" associated with this design. Even in the event that spherical tokamaks do not lead to lower cost approaches to generation, they are still lower cost in general; this makes them attractive devices for general plasma physics uses, or as concentrated high-energy neutron
sources.
, ≥3 • 1021 keV • seconds / m³.
Tokamak
s are the leading approach within the larger group of magnetic fusion energy (MFE) designs, all of which attempt to confine a plasma using powerful magnetic fields. In the MFE approach, it is the time axis that is considered most important for ongoing development. 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 increasing times on the order of seconds to minutes.
A key measure of MFE reactor economics
is "beta
", β, the ratio of magnetic pressure to plasma 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. Tokamaks operate at relatively low betas, a few %, and generally require superconducting magnets in order to have enough field strength to reach useful densities.
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, 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.
(ORNL), led by Ben Carreras and Tim Hender, were studying the operations of tokamaks as A was reduced. They noticed, based on magnetohydrodynamic considerations, that tokamaks were inherently more stable at low aspect ratios. In particular, the classic "kink instability" was strongly suppressed. Other groups expanded on this body of theory, and found that the same was true for the high-order ballooning instability
as well. This suggested that a low-A machine would not only be less expensive to build, but have better performance as well.
One way to reduce the size of the magnets is to re-arrange them around the confinement area. This was the idea behind the "compact tokamak" designs, typified by the Alcator C-Mod
, Riggatron
and IGNITOR
. The later two of these designs place the magnets inside the confinement area, so 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, 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" designs, which include ITER
.
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.
The ST concept appeared to represent an enormous advance in tokamak design. However, it was being proposed during a period when US fusion research budgets were being dramatically scaled back. ORNL was provided with funds to develop a suitable central column built out of a high-strength copper alloy called "Glidcop
". However, they were unable to secure funding to build a demonstration machine, "STX".
machine to the ST layout.
Spheromaks are essentially "smoke ring
s" of plasma that are internally self-stable. They can, however, drift about within their confinement area. 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.
Machines 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 in the early 1980s, HSE was quickly converted to a ST in 1987 by adding new magnets to the outside of the confinement area and attaching them to its 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
and the SPHEX 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.
, of the United Kingdom Atomic Energy Authority
(UKAEA) fusion center at Culham
. What is today known as the Culham Centre for Fusion Energy
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
, 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
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
destabilizes the plasma. This so-called "Troyon limit" 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.
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
(NSTX) and Pegasus experiments in the US, Globus-M in Russia, and the UK's follow-on to START, MAST
. START itself found new life as part of the Proto-Sphera project in Italy, where experimenters are attempting to eliminate the central column by passing the current through a secondary plasma.
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.
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
. This starts with a development of a useful beta for a highly asymmetric volume:
Where
is the volume averaged magnetic field 
(as opposed to Troyon's use of the field in the vacuum outside the plasma, 
). Following Freidberg, this beta is then fed into a modified version of the safety factor
:
Where
is the vacuum magnetic field, a is the minor radius, 
the major radius, 
the plasma current, and 
the elongation. In this definition it should be clear that decreasing aspect ratio, 
leads to higher average safety factors. These definitions allowed the Princeton group to develop a more flexible version of Troyon's critical beta:
Where
is the inverse aspect ratio 
and 
is a constant scaling factor that is about 0.03 for any 
greater than 2. Note that the critical beta scales with aspect ratio, although not directly, because 
also includes aspect ratio factors. Numerically, it can be shown that 
is maximized for:
Using this in the critical beta formula above:
For a spherical tokamak with an elongation
of 2 and an aspect ratio of 1.25:
Now compare this to a traditional tokamak with the same elongation and a major radius of 5 meters and minor radius of 2 meters:
The linearity of
with aspect ratio is evident.
, 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 electrical 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
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
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:
Now we consider the average plasma pressure that can be generated with this magnetic field. Following Freidberg:
In an ST, where were are attempting to maximize
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, 
is zero. Considering a central column made of copper, we can fix the maximum field generated in the coil, 
to about 7.5 T. Using the ideal numbers from the section above:
Now consider the conventional design as above, using superconducting magnets with a
of 15 T, and a blanket of 1.2 meters thickness. First we calculate 
to be 1/(5/2) = 0.4 and 
to be 1.5/5 = 0.24, then:
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 ST's, but this work needs to be replicated at higher powers to better understand the scaling.
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
that only appeared as the operating conditions moved ever closer to useful ones for fusion power. In 1954 Edward Teller
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 become 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
", 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.
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,
This limit is theoretically the same in the ST and conventional designs, but as the ST has a much higher 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 fields 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
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. 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
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.
Fusion power
Fusion power is the power generated by nuclear fusion processes. In fusion reactions two light atomic nuclei fuse together to form a heavier nucleus . In doing so they release a comparatively large amount of energy arising from the binding energy due to the strong nuclear force which is manifested...
device based on the tokamak
Tokamak
A tokamak is a device using a magnetic field to confine a plasma in the shape of a torus . Achieving a stable plasma equilibrium requires magnetic field lines that move around the torus in a helical shape...
principle. It is notable for its very narrow profile, or "aspect ratio
Aspect ratio
The aspect ratio of a shape is the ratio of its longer dimension to its shorter dimension. It may be applied to two characteristic dimensions of a three-dimensional shape, such as the ratio of the longest and shortest axis, or for symmetrical objects that are described by just two measurements,...
". A traditional tokamak has a toroid
Toroid
Toroid may refer to*Toroid , a doughnut-like solid whose surface is a torus.*Toroidal inductors and transformers which have wire windings on circular ring shaped magnetic cores.*Vortex ring, a toroidal flow in fluid mechanics....
al confinement area that gives it an overall shape similar to a donut
DONUT
DONUT was an experiment at Fermilab dedicated to the search for tau neutrino interactions. Even though the detector operated only during a few months in the summer of 1997, it was largely successful. By detecting the tau neutrino, it confirmed the existence of the last lepton predicted by the...
, complete with a large hole in the middle. The spherical tokamak reduces the size of the hole almost to zero, 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 practical advantages over these devices, some of them dramatic. For this reason the ST has seen considerable interest since it was introduced in the late 1980s. However, development remains effectively one generation behind mainline efforts like JET
Joint European Torus
JET, the Joint European Torus, is the largest magnetic confinement plasma physics experiment worldwide currently in operation. Its main purpose is to open the way to future nuclear fusion experimental tokamak reactors such as ITER and :DEMO....
. Major experiments in the field include the pioneering START
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. The experiment began at the Culham Science Centre in the United Kingdom in 1991 and was retired in 1998. It was built as a low cost design, largely using parts already...
and MAST
Mega Ampere Spherical Tokamak
The Mega Ampere Spherical Tokamak, or MAST experiment is a nuclear fusion experiment in operation at Culham, Oxfordshire, England since December 1999. It follows the highly successful START experiment...
at Culham in the UK, the US's NSTX
National Spherical Torus Experiment
The National Spherical Torus Experiment is an innovative magnetic fusion device based on the spherical tokamak concept that was constructed by the Princeton Plasma Physics Laboratory in collaboration with the Oak Ridge National Laboratory, Columbia University, and the University of Washington at...
, and numerous others.
Further theoretical work has cast some doubt on the use of spherical tokamaks as a route to lower cost power producing reactors. Further research is needed to better understand the "scaling laws" associated with this design. Even in the event that spherical tokamaks do not lead to lower cost approaches to generation, they are still lower cost in general; this makes them attractive devices for general plasma physics uses, or as concentrated high-energy neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
sources.
Aspect ratio
Fusion reactor efficiency is based on the amount of power released from fusion reactions compared with the power needed to keep the plasma hot. This can be calculated from three key measures; the temperature of the plasma, its density, and the length of time the reaction is maintained. The product of these three measures is the "fusion triple product", and in order to be economic it must reach the Lawson criterionLawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the...
, ≥3 • 1021 keV • seconds / m³.
Tokamak
Tokamak
A tokamak is a device using a magnetic field to confine a plasma in the shape of a torus . Achieving a stable plasma equilibrium requires magnetic field lines that move around the torus in a helical shape...
s are the leading approach within the larger group of magnetic fusion energy (MFE) designs, all of which attempt to confine a plasma using powerful magnetic fields. In the MFE approach, it is the time axis that is considered most important for ongoing development. 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 increasing times on the order of seconds to minutes.
A key measure of MFE reactor economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
is "beta
Beta (plasma physics)
The beta of a plasma, symbolized by β, is the ratio of the plasma pressure to the magnetic pressure...
", β, the ratio of magnetic pressure to plasma 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. Tokamaks operate at relatively low betas, a few %, and generally require superconducting magnets in order to have enough field strength to reach useful densities.
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
Aspect ratio
The aspect ratio of a shape is the ratio of its longer dimension to its shorter dimension. It may be applied to two characteristic dimensions of a three-dimensional shape, such as the ratio of the longest and shortest axis, or for symmetrical objects that are described by just two measurements,...
, 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.
Reducing A
During the 1980s, researchers at Oak Ridge National LaboratoryOak Ridge National Laboratory
Oak Ridge National Laboratory is a multiprogram science and technology national laboratory managed for the United States Department of Energy by UT-Battelle. ORNL is the DOE's largest science and energy laboratory. ORNL is located in Oak Ridge, Tennessee, near Knoxville...
(ORNL), led by Ben Carreras and Tim Hender, were studying the operations of tokamaks as A was reduced. They noticed, based on magnetohydrodynamic considerations, that tokamaks were inherently more stable at low aspect ratios. In particular, the classic "kink instability" was strongly suppressed. Other groups expanded on this body of theory, and found that the same was true for the high-order ballooning instability
Ballooning instability
The ballooning instability, or ballooning mode, is a form of plasma instability seen in tokamak fusion power reactors. The name refers to the shape and action of the instability, which acts like the elongations formed in a balloon when it is squeezed....
as well. This suggested that a low-A machine would not only be less expensive to build, but have better performance as well.
One way to reduce the size of the magnets is to re-arrange them around the confinement area. This was the idea behind the "compact tokamak" designs, typified by the Alcator C-Mod
Alcator C-Mod
Alcator C-Mod is a tokamak, a magnetically confined nuclear fusion device, at the MIT Plasma Science and Fusion Center. It is the tokamak with the highest magnetic field and highest plasma pressure in the world...
, Riggatron
Riggatron
A Riggatron is a magnetic confinement fusion reactor design created by Robert W. Bussard in the late 1970s. It is tokamak on the basis of its magnetic geometry, but some unconventional engineering choices were made, in particular the use of copper magnets positioned inside the blanket, which was...
and IGNITOR
IGNITOR
IGNITOR is the Italian name for a nuclear research project of magnetic confinement fusion, developed by ENEA Laboratories in Frascati.The project theory is based on ignited plasma in tokamak. Started in 1977 by Prof...
. The later two of these designs place the magnets inside the confinement area, so 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, is that it places the magnets directly in the high-energy neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
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" designs, which include ITER
ITER
ITER is an international nuclear fusion research and engineering project, which is currently building the world's largest and most advanced experimental tokamak nuclear fusion reactor at Cadarache in the south of France...
.
Spherical tokamaks
In 1984, Martin Peng of ORNL 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 ST's can reach the same operational triple product 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.
The ST concept appeared to represent an enormous advance in tokamak design. However, it was being proposed during a period when US fusion research budgets were being dramatically scaled back. ORNL was provided with funds to develop a suitable central column built out of a high-strength copper alloy called "Glidcop
Glidcop
Glidcop is the registered trademark name of SCM Metal Products, Inc. that refers to a family of copper-based metal matrix composite alloys mixed primarily with aluminum oxide ceramic particles...
". However, they were unable to secure funding to build a demonstration machine, "STX".
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 spheromakSpheromak
A spheromak is an arrangement of plasma formed into a toroidal shape similar to a smoke ring. The spheromak contains large internal electrical currents and their associated magnetic fields arranged so the magnetohydrodynamic forces within the spheromak are nearly balanced, resulting in long-lived ...
machine to the ST layout.
Spheromaks are essentially "smoke ring
Smoke ring
A smoke ring is a visible vortex ring formed by sudden release of smoke. It can be created by blowing smoke from the mouth, quickly lighting a cigarette lighter and putting it out or holding a burning incense stick or a cigarette vertically, pushing it with the burning side up and suddenly pulling...
s" of plasma that are internally self-stable. They can, however, drift about within their confinement area. 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.
Machines 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 in the early 1980s, HSE was quickly converted to a ST in 1987 by adding new magnets to the outside of the confinement area and attaching them to its 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
Australian Nuclear Science and Technology Organisation
The Australian Nuclear Science and Technology Organisation 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 outskirts of Sydney at Lucas Heights, in the Sutherland Shire...
and the SPHEX 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 RobinsonDerek Robinson (physicist)
Derek Charles Robinson FRS was a physicist who worked in the UK fusion power program for most of his professional career. Studying turbulence in the UK's ZETA reactor, he helped develop the reversed field pinch concept, an area of study to this day...
, of the United Kingdom Atomic Energy Authority
United Kingdom Atomic Energy Authority
The United Kingdom Atomic Energy Authority is a UK government research organisation responsible for the development of nuclear fusion power. It is an executive non-departmental public body of the Department for Business, Innovation and Skills and was formerly chaired by Lady Barbara Judge CBE...
(UKAEA) fusion center at Culham
Culham
Culham is a village and civil parish on the north bank of the River Thames, just over south of Abingdon in Oxfordshire.-Manor:The toponym comes from the Old English Cula's hamm, referring to the village's position in a bend of the Thames...
. What is today known as the Culham Centre for Fusion Energy
Culham Centre for Fusion Energy
The Culham Centre for Fusion Energy , located at the Culham Science Centre, near Culham, Oxfordshire, is the site of the Joint European Torus , Mega Ampere Spherical Tokamak and the now closed Small Tight Aspect Ratio Tokamak .Since September 2008 the director has been Professor Steven Cowley, and...
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
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. The experiment began at the Culham Science Centre in the United Kingdom in 1991 and was retired in 1998. It was built as a low cost design, largely using parts already...
, 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 (fusion reactor)
DIII-D is the name of a tokamak machine developed in the 1980s by General Atomics in San Diego, USA, as part of the ongoing effort to achieve magnetically confined fusion. DIII-D pioneered new technology including the use of beams of neutral particles to penetrate the confinement field of the...
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
Ballooning instability
The ballooning instability, or ballooning mode, is a form of plasma instability seen in tokamak fusion power reactors. The name refers to the shape and action of the instability, which acts like the elongations formed in a balloon when it is squeezed....
destabilizes the plasma. This so-called "Troyon limit" 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 magnitudeOrder of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
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
National Spherical Torus Experiment
The National Spherical Torus Experiment is an innovative magnetic fusion device based on the spherical tokamak concept that was constructed by the Princeton Plasma Physics Laboratory in collaboration with the Oak Ridge National Laboratory, Columbia University, and the University of Washington at...
(NSTX) and Pegasus experiments in the US, Globus-M in Russia, and the UK's follow-on to START, MAST
Mega Ampere Spherical Tokamak
The Mega Ampere Spherical Tokamak, or MAST experiment is a nuclear fusion experiment in operation at Culham, Oxfordshire, England since December 1999. It follows the highly successful START experiment...
. START itself found new life as part of the Proto-Sphera project in Italy, where experimenters are attempting to eliminate the central column by passing the current through a secondary plasma.
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 solenoidSolenoid
A solenoid is a coil wound into a tightly packed helix. In physics, the term solenoid refers to a long, thin loop of wire, often wrapped around a metallic core, which produces a magnetic field when an electric current is passed through it. Solenoids are important because they can create...
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
Princeton Plasma Physics Laboratory is a United States Department of Energy national laboratory for plasma physics and nuclear fusion science located on Princeton University's Forrestal Campus in Plainsboro Township, New Jersey. Its primary mission is research into and development of fusion as an...
. This starts with a development of a useful beta for a highly asymmetric volume:
Where
is the volume averaged magnetic field (as opposed to Troyon's use of the field in the vacuum outside the plasma, ). Following Freidberg, this beta is then fed into a modified version of the safety factorSafety 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...
:
Where
is the vacuum magnetic field, a is the minor radius, the major radius, the plasma current, and the elongation. In this definition it should be clear that decreasing aspect ratio, leads to higher average safety factors. These definitions allowed the Princeton group to develop a more flexible version of Troyon's critical beta:Where
is the inverse aspect ratio and is a constant scaling factor that is about 0.03 for any greater than 2. Note that the critical beta scales with aspect ratio, although not directly, because also includes aspect ratio factors. Numerically, it can be shown that is maximized for:Using this in the critical beta formula above:
For a spherical tokamak with an elongation
of 2 and an aspect ratio of 1.25:Now compare this to a traditional tokamak with the same elongation and a major radius of 5 meters and minor radius of 2 meters:
The linearity of
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 densityPower density
Power density is the amount of power per unit volume....
, 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 electrical 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
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...
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
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...
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:
Now we consider the average plasma pressure that can be generated with this magnetic field. Following Freidberg:
In an ST, where were are attempting to maximize
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, is zero. Considering a central column made of copper, we can fix the maximum field generated in the coil, to about 7.5 T. Using the ideal numbers from the section above:Now consider the conventional design as above, using superconducting magnets with a
of 15 T, and a blanket of 1.2 meters thickness. First we calculate to be 1/(5/2) = 0.4 and to be 1.5/5 = 0.24, then: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 ST's, but this work needs to be replicated at higher powers to better understand the scaling.
Advantages
ST's 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
Plasma stability
An important field of plasma physics is the stability of the plasma. It usually only makes sense to analyze the stability of a plasma once it has been established that the plasma is in equilibrium. "Equilibrium" asks whether there are net forces that will accelerate any part of the plasma...
that only appeared as the operating conditions moved ever closer to useful ones for fusion power. In 1954 Edward Teller
Edward Teller
Edward Teller was a Hungarian-American theoretical physicist, known colloquially as "the father of the hydrogen bomb," even though he did not care for the title. Teller made numerous contributions to nuclear and molecular physics, spectroscopy , and surface physics...
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 become 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
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...
", 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,
This limit is theoretically the same in the ST and conventional designs, but as the ST has a much higher 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 fields 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
Z-pinch
In fusion power research, the Z-pinch, also known as zeta pinch or Bennett pinch , is a type of plasma confinement system that uses an electrical current in the plasma to generate a magnetic field that compresses it...
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. 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
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, an electrical current will naturally arise within the plasma. This bootstrap current, and is commonly found in the tokamak reactor design...
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 operational ST machines
- MAST, Culham Science Center, United KingdomUnited KingdomThe United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
- NSTX, Princeton Plasma Physics LaboratoryPrinceton Plasma Physics LaboratoryPrinceton Plasma Physics Laboratory is a United States Department of Energy national laboratory for plasma physics and nuclear fusion science located on Princeton University's Forrestal Campus in Plainsboro Township, New Jersey. Its primary mission is research into and development of fusion as an...
, United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district... - Globus-M, Ioffe Institute, RussiaRussiaRussia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
- Proto-Sphera (formerly START), ENEAENEA (Italy)The L'Agenzia nazionale per le nuove tecnologie, l'energia e lo sviluppo economico sostenibile is an Italian Government sponsored research and development agency...
, ItalyItalyItaly , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and... - TST-2, University of TokyoUniversity of Tokyo, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...
, JapanJapanJapan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south... - SUNIST, Tsinghua UniversityTsinghua UniversityTsinghua University , colloquially known in Chinese as Qinghua, is a university in Beijing, China. The school is one of the nine universities of the C9 League. It was established in 1911 under the name "Tsinghua Xuetang" or "Tsinghua College" and was renamed the "Tsinghua School" one year later...
, ChinaChinaChinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture... - PEGASUS, University of Wisconsin-Madison, United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
- ETE, National Space Research Institute, BrazilBrazilBrazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...
External links
- Spherical Tokamaks – list of ST experiments at tokamak.info
- Culham Centre for Fusion Energy – spherical tokamaks at Culham, UK, including details of the MAST and START experiments