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 developed to produce controlled thermonuclear fusion power. , it was the leading candidate for a practical fusion reactor.

Tokamaks were initially conceptualized in the 1950s by Soviet physicists Igor Tamm and Andrei Sakharov, inspired by a letter by Oleg Lavrentiev. The first working tokamak was attributed to the work of Natan Yavlinsky on the T-1 in 1958. It had been demonstrated that a stable plasma equilibrium requires magnetic field lines that wind around the torus in a helix. Devices like the z-pinch and stellarator had attempted this, but demonstrated serious instabilities. It was the development of the concept now known as the safety factor (labelled ''q'' in mathematical notation) that guided tokamak development; by arranging the reactor so this critical factor ''q'' was always greater than 1, the tokamaks strongly suppressed the instabilities which plagued earlier designs.

By the mid-1960s, the tokamak designs began to show greatly improved performance. The initial results were released in 1965, but were ignored; Lyman Spitzer dismissed them out of hand after noting potential problems in their system for measuring temperatures. A second set of results was published in 1968, this time claiming performance far in advance of any other machine. When these were also met skeptically, the Soviets invited a delegation from the United Kingdom to make their own measurements. These confirmed the Soviet results, and their 1969 publication resulted in a stampede of tokamak construction.

By the mid-1970s, dozens of tokamaks were in use around the world. By the late 1970s, these machines had reached all of the conditions needed for practical fusion, although not at the same time nor in a single reactor. With the goal of breakeven (a fusion energy gain factor equal to 1) now in sight, a new series of machines were designed that would run on a fusion fuel of deuterium and tritium. These machines, notably the Joint European Torus (JET), Tokamak Fusion Test Reactor (TFTR), had the explicit goal of reaching breakeven.

Instead, these machines demonstrated new problems that limited their performance. Solving these would require a much larger and more expensive machine, beyond the abilities of any one country. After an initial agreement between Ronald Reagan and Mikhail Gorbachev in November 1985, the International Thermonuclear Experimental Reactor (ITER) effort emerged and remains the primary international effort to develop practical fusion power. Many smaller designs, and offshoots like the spherical tokamak, continue to be used to investigate performance parameters and other issues. , JET remains the record holder for fusion output, reaching 16 MW of output for 24 MW of input heating power.

Etymology

The word ''tokamak'' is a transliteration of the Russian word , an acronym of either:

:
:
: toroidal chamber with magnetic coils;

or

:
:
: toroidal chamber with axial magnetic field.

The term was created in 1957 by Igor Golovin, the vice-director of the Laboratory of Measuring Apparatus of Academy of Science, today's Kurchatov Institute. A similar term, ''tokomag'', was also proposed for a time.

Also considering the existence of many Turkic nations living in the Russian region, it can be thought that the etymological analogy is the origin of the word Turkish tokmak. Old Turkish
toḳımaḳ
ref name=toḳımaḳ> Dīwān Lughāt al-Turk 1073br>Turkish Etimology
/ref> (the beater used by the beaters)

In addition, since it is used for forging iron in blacksmithing, it is technically reasonable to conside
this Turkish word
as appropriate. It is known that the oldest usage of the word Tokamak/Tokmak is in Göktürk Khanate

History

First steps

In 1934, Mark Oliphant, Paul Harteck and Ernest Rutherford were the first to achieve fusion on Earth, using a particle accelerator to shoot deuterium nuclei into metal foil containing deuterium or other atoms. This allowed them to measure the nuclear cross section of various fusion reactions, and determined that the deuterium–deuterium reaction occurred at a lower energy than other reactions, peaking at about 100,000 electronvolts (100 keV).

Accelerator-based fusion is not practical because the reactor cross section is tiny; most of the particles in the accelerator will scatter off the fuel, not fuse with it. These scatterings cause the particles to lose energy to the point where they can no longer undergo fusion. The energy put into these particles is thus lost, and it is easy to demonstrate this is much more energy than the resulting fusion reactions can release.

To maintain fusion and produce net energy output, the bulk of the fuel must be raised to high temperatures so its atoms are constantly colliding at high speed; this gives rise to the name ''thermonuclear'' due to the high temperatures needed to bring it about. In 1944, Enrico Fermi calculated the reaction would be self-sustaining at about 50,000,000 K; at that temperature, the rate that energy is given off by the reactions is high enough that they heat the surrounding fuel rapidly enough to maintain the temperature against losses to the environment, continuing the reaction.

During the Manhattan Project, the first practical way to reach these temperatures was created, using an atomic bomb. In 1944, Fermi gave a talk on the physics of fusion in the context of a then-hypothetical hydrogen bomb. However, some thought had already been given to a ''controlled'' fusion device, and James L. Tuck and Stanislaw Ulam had attempted such using shaped charges driving a metal foil infused with deuterium, although without success.

The first attempts to build a practical fusion machine took place in the United Kingdom, where George Paget Thomson had selected the pinch effect as a promising technique in 1945. After several failed attempts to gain funding, he gave up and asked two graduate students, Stanley (Stan) W. Cousins and Alan Alfred Ware (1924–2010), to build a device out of surplus radar equipment. This was successfully operated in 1948, but showed no clear evidence of fusion and failed to gain the interest of the Atomic Energy Research Establishment.

Lavrentiev's letter

In 1950, Oleg Lavrentiev, then a Red Army sergeant stationed on Sakhalin, wrote a letter to the Central Committee of the Communist Party of the Soviet Union. The letter outlined the idea of using an atomic bomb to ignite a fusion fuel, and then went on to describe a system that used electrostatic fields to contain a hot plasma in a steady state for energy production.

The letter was sent to Andrei Sakharov for comment. Sakharov noted that "the author formulates a very important and not necessarily hopeless problem", and found his main concern in the arrangement was that the plasma would hit the electrode wires, and that "wide meshes and a thin current-carrying part which will have to reflect almost all incident nuclei back into the reactor. In all likelihood, this requirement is incompatible with the mechanical strength of the device."

Some indication of the importance given to Lavrentiev's letter can be seen in the speed with which it was processed; the letter was received by the Central Committee on 29 July, Sakharov sent his review in on 18 August, by October, Sakharov and Igor Tamm had completed the first detailed study of a fusion reactor, and they had asked for funding to build it in January 1951.

Magnetic confinement

When heated to fusion temperatures, the electrons in atoms dissociate, resulting in a fluid of nuclei and electrons known as plasma. Unlike electrically neutral atoms, a plasma is electrically conductive, and can, therefore, be manipulated by electrical or magnetic fields.

Sakharov's concern about the electrodes led him to consider using magnetic confinement instead of electrostatic. In the case of a magnetic field, the particles will circle around the lines of force. As the particles are moving at high speed, their resulting paths look like a helix. If one arranges a magnetic field so lines of force are parallel and close together, the particles orbiting adjacent lines may collide, and fuse.

Such a field can be created in a solenoid, a cylinder with magnets wrapped around the outside. The combined fields of the magnets create a set of parallel magnetic lines running down the length of the cylinder. This arrangement prevents the particles from moving sideways to the wall of the cylinder, but it does not prevent them from running out the end. The obvious solution to this problem is to bend the cylinder around into a donut shape, or torus, so that the lines form a series of continual rings. In this arrangement, the particles circle endlessly.

Sakharov discussed the concept with Igor Tamm, and by the end of October 1950 the two had written a proposal and sent it to Igor Kurchatov, the director of the atomic bomb project within the USSR, and his deputy, Igor Golovin. However, this initial proposal ignored a fundamental problem; when arranged along a straight solenoid, the external magnets are evenly spaced, but when bent around into a torus, they are closer together on the inside of the ring than the outside. This leads to uneven forces that cause the particles to drift away from their magnetic lines.

During visits to the Laboratory of Measuring Instruments of the USSR Academy of Sciences (LIPAN), the Soviet nuclear research centre, Sakharov suggested two possible solutions to this problem. One was to suspend a current-carrying ring in the centre of the torus. The current in the ring would produce a magnetic field that would mix with the one from the magnets on the outside. The resulting field would be twisted into a helix, so that any given particle would find itself repeatedly on the outside, then inside, of the torus. The drifts caused by the uneven fields are in opposite directions on the inside and outside, so over the course of multiple orbits around the long axis of the torus, the opposite drifts would cancel out. Alternately, he suggested using an external magnet to induce a current in the plasma itself, instead of a separate metal ring, which would have the same effect.

In January 1951, Kurchatov arranged a meeting at LIPAN to consider Sakharov's concepts. They found widespread interest and support, and in February a report on the topic was forwarded to Lavrentiy Beria, who oversaw the atomic efforts in the USSR. For a time, nothing was heard back.

Richter and the birth of fusion research

On 25 March 1951, Argentine President Juan Perón announced that a former German scientist, Ronald Richter, had succeeded in producing fusion at a laboratory scale as part of what is now known as the Huemul Project. Scientists around the world were excited by the announcement, but soon concluded it was not true; simple calculations showed that his experimental setup could not produce enough energy to heat the fusion fuel to the needed temperatures.

Although dismissed by nuclear researchers, the widespread news coverage meant politicians were suddenly aware of, and receptive to, fusion research. In the UK, Thomson was suddenly granted considerable funding. Over the next months, two projects based on the pinch system were up and running. In the US, Lyman Spitzer read the Huemul story, realized it was false, and set about designing a machine that would work. In May he was awarded $50,000 to begin research on his stellarator concept. Jim Tuck had returned to the UK briefly and saw Thomson's pinch machines. When he returned to Los Alamos he also received $50,000 directly from the Los Alamos budget.

Similar events occurred in the USSR. In mid-April, Dmitri Efremov of the Scientific Research Institute of Electrophysical Apparatus stormed into Kurchatov's study with a magazine containing a story about Richter's work, demanding to know why they were beaten by the Argentines. Kurchatov immediately contacted Beria with a proposal to set up a separate fusion research laboratory with Lev Artsimovich as director. Only days later, on 5 May, the proposal had been signed by Joseph Stalin.

New ideas

By October, Sakharov and Tamm had completed a much more detailed consideration of their original proposal, calling for a device with a major radius (of the torus as a whole) of and a minor radius (the interior of the cylinder) of . The proposal suggested the system could produce of tritium a day, or breed of U233 a day.

As the idea was further developed, it was realized that a current in the plasma could create a field that was strong enough to confine the plasma as well, removing the need for the external magnets. At this point, the Soviet researchers had re-invented the pinch system being developed in the UK, although they had come to this design from a very different starting point.

Once the idea of using the pinch effect for confinement had been proposed, a much simpler solution became evident. Instead of a large toroid, one could simply induce the current into a linear tube, which could cause the plasma within to collapse down into a filament. This had a huge advantage; the current in the plasma would heat it through normal resistive heating, but this would not heat the plasma to fusion temperatures. However, as the plasma collapsed, the adiabatic process would result in the temperature rising dramatically, more than enough for fusion. With this development, only Golovin and Natan Yavlinsky continued considering the more static toroidal arrangement.

Instability

On 4 July 1952, Nikolai Filippov's group measured neutrons being released from a linear pinch machine. Lev Artsimovich demanded that they check everything before concluding fusion had occurred, and during these checks, they found that the neutrons were not from fusion at all. This same linear arrangement had also occurred to researchers in the UK and US, and their machines showed the same behaviour. But the great secrecy surrounding the type of research meant that none of the groups were aware that others were also working on it, let alone having the identical problem.

After much study, it was found that some of the released neutrons were produced by instabilities in the plasma. There were two common types of instability, the ''sausage'' that was seen primarily in linear machines, and the ''kink'' which was most common in the toroidal machines. Groups in all three countries began studying the formation of these instabilities and potential ways to address them. Important contributions to the field were made by Martin David Kruskal and Martin Schwarzschild in the US, and Shafranov in the USSR.

One idea that came from these studies became known as the "stabilized pinch". This concept added additional magnets to the outside of the chamber, which created a field that would be present in the plasma before the pinch discharge. In most concepts, the external field was relatively weak, and because a plasma is diamagnetic, it penetrated only the outer areas of the plasma. When the pinch discharge occurred and the plasma quickly contracted, this field became "frozen in" to the resulting filament, creating a strong field in its outer layers. In the US, this was known as "giving the plasma a backbone."

Sakharov revisited his original toroidal concepts and came to a slightly different conclusion about how to stabilize the plasma. The layout would be the same as the stabilized pinch concept, but the role of the two fields would be reversed. Instead of weak external fields providing stabilization and a strong pinch current responsible for confinement, in the new layout, the external magnets would be much more powerful in order to provide the majority of confinement, while the current would be much smaller and responsible for the stabilizing effect.

Steps toward declassification

In 1955, with the linear approaches still subject to instability, the first toroidal device was built in the USSR. TMP was a classic pinch machine, similar to models in the UK and US of the same era. The vacuum chamber was made of ceramic, and the spectra of the discharges showed silica, meaning the plasma was not perfectly confined by magnetic field and hitting the walls of the chamber. Two smaller machines followed, using copper shells. The conductive shells were intended to help stabilize the plasma, but were not completely successful in any of the machines that tried it.

With progress apparently stalled, in 1955, Kurchatov called an All Union conference of Soviet researchers with the ultimate aim of opening up fusion research within the USSR. In April 1956, Kurchatov travelled to the UK as part of a widely publicized visit by Nikita Khrushchev and Nikolai Bulganin. He offered to give a talk at Atomic Energy Research Establishment, at the former RAF Harwell, where he shocked the hosts by presenting a detailed historical overview of the Soviet fusion efforts. He took time to note, in particular, the neutrons seen in early machines and warned that neutrons did not mean fusion.

Unknown to Kurchatov, the British ZETA stabilized pinch machine was being built at the far end of the former runway. ZETA was, by far, the largest and most powerful fusion machine to date. Supported by experiments on earlier designs that had been modified to include stabilization, ZETA intended to produce low levels of fusion reactions. This was apparently a great success, and in January 1958, they announced the fusion had been achieved in ZETA based on the release of neutrons and measurements of the plasma temperature.

Vitaly Shafranov and Stanislav Braginskii examined the news reports and attempted to figure out how it worked. One possibility they considered was the use of weak "frozen in" fields, but rejected this, believing the fields would not last long enough. They then concluded ZETA was essentially identical to the devices they had been studying, with strong external fields.

First tokamaks

By this time, Soviet researchers had decided to build a larger toroidal machine along the lines suggested by Sakharov. In particular, their design considered one important point found in Kruskal's and Shafranov's works; if the helical path of the particles made them circulate around the plasma's circumference more rapidly than they circulated the long axis of the torus, the kink instability would be strongly suppressed.

Today this basic concept is known as the ''safety factor''. The ratio of the number of times the particle orbits the major axis compared to the minor axis is denoted ''q'', and the ''Kruskal-Shafranov Limit'' stated that the kink will be suppressed as long as ''q'' > 1. This path is controlled by the relative strengths of the external magnets compared to the field created by the internal current. To have ''q'' > 1, the external magnets must be much more powerful, or alternatively, the internal current has to be reduced.

Following this criterion, design began on a new reactor, T-1, which today is known as the first real tokamak. T-1 used both stronger external magnets and a reduced current compared to stabilized pinch machines like ZETA. The success of the T-1 resulted in its recognition as the first working tokamak.
For his work on "powerful impulse discharges in a gas, to obtain unusually high temperatures needed for thermonuclear processes", Yavlinskii was awarded the Lenin Prize and the Stalin Prize in 1958. Yavlinskii was already preparing the design of an even larger model, later built as T-3. With the apparently successful ZETA announcement, Yavlinskii's concept was viewed very favourably.

Details of ZETA became public in a series of articles in ''Nature'' later in January. To Shafranov's surprise, the system did use the "frozen in" field concept. He remained sceptical, but a team at the Ioffe Institute in St. Petersberg began plans to build a similar machine known as Alpha. Only a few months later, in May, the ZETA team issued a release stating they had not achieved fusion, and that they had been misled by erroneous measures of the plasma temperature.

T-1 began operation at the end of 1958. It demonstrated very high energy losses through radiation. This was traced to impurities in the plasma due to the vacuum system causing outgassing from the container materials. In order to explore solutions to this problem, another small device was constructed, T-2. This used an internal liner of corrugated metal that was baked at to cook off trapped gasses.

Atoms for Peace and the doldrums

As part of the second Atoms for Peace meeting in Geneva in September 1958, the Soviet delegation released many papers covering their fusion research. Among them was a set of initial results on their toroidal machines, which at that point had shown nothing of note.

The "star" of the show was a large model of Spitzer's stellarator, which immediately caught the attention of the Soviets. In contrast to their designs, the stellarator produced the required twisted paths in the plasma without driving a current through it, using a series of magnets that could operate in the steady state rather than the pulses of the induction system. Kurchatov began asking Yavlinskii to change their T-3 design to a stellarator, but they convinced him that the current provided a useful second role in heating, something the stellarator lacked.

At the time of the show, the stellarator had suffered a long string of minor problems that were just being solved. Solving these revealed that the diffusion rate of the plasma was much faster than theory predicted. Similar problems were seen in all the contemporary designs, for one reason or another. The stellarator, various pinch concepts and the magnetic mirror machines in both the US and USSR all demonstrated problems that limited their confinement times.

From the first studies of controlled fusion, there was a problem lurking in the background. During the Manhattan Project, David Bohm had been part of the team working on isotopic separation of uranium. In the post-war era he continued working with plasmas in magnetic fields. Using basic theory, one would expect the plasma to diffuse across the lines of force at a rate inversely proportional to the square of the strength of the field, meaning that small increases in force would greatly improve confinement. But based on their experiments, Bohm developed an empirical formula, now known as Bohm diffusion, that suggested the rate was linear with the magnetic force, not its square.

If Bohm's formula was correct, there was no hope one could build a fusion reactor based on magnetic confinement. To confine the plasma at the temperatures needed for fusion, the magnetic field would have to be orders of magnitude greater than any known magnet. Spitzer ascribed the difference between the Bohm and classical diffusion rates to turbulence in the plasma, and believed the steady fields of the stellarator would not suffer from this problem. Various experiments at that time suggested the Bohm rate did not apply, and that the classical formula was correct.

But by the early 1960s, with all of the various designs leaking plasma at a prodigious rate, Spitzer himself concluded that the Bohm scaling was an inherent quality of plasmas, and that magnetic confinement would not work. The entire field descended into what became known as "the doldrums", a period of intense pessimism.

Progress in the 1960s

In contrast to the other designs, the experimental tokamaks appeared to be progressing well, so well that a minor theoretical problem was now a real concern. In the presence of gravity, there is a small pressure gradient in the plasma, formerly small enough to ignore but now becoming something that had to be addressed. This led to the addition of yet another set of magnets in 1962, which produced a vertical field that offset these effects. These were a success, and by the mid-1960s the machines began to show signs that they were beating the Bohm limit.

At the 1965 Second International Atomic Energy Agency Conference on fusion at the UK's newly opened Culham Centre for Fusion Energy, Artsimovich reported that their systems were surpassing the Bohm limit by 10 times. Spitzer, reviewing the presentations, suggested that the Bohm limit may still apply; the results were within the range of experimental error of results seen on the stellarators, and the temperature measurements, based on the magnetic fields, were simply not trustworthy.

The next major international fusion meeting was held in August 1968 in Novosibirsk. By this time two additional tokamak designs had been completed, TM-2 in 1965, and T-4 in 1968. Results from T-3 had continued to improve, and similar results were coming from early tests of the new reactors. At the meeting, the Soviet delegation announced that T-3 was producing electron temperatures of 1000 eV (equivalent to 10 million degrees Celsius) and that confinement time was at least 50 times the Bohm limit.

These results were at least 10 times that of any other machine. If correct, they represented an enormous leap for the fusion community. Spitzer remained sceptical, noting that the temperature measurements were still based on the indirect calculations from the magnetic properties of the plasma. Many concluded they were due to an effect known as runaway electrons, and that the Soviets were measuring only those extremely energetic electrons and not the bulk temperature. The Soviets countered with several arguments suggesting the temperature they were measuring was Maxwellian, and the debate raged.

Culham Five

In the aftermath of ZETA, the UK teams began the development of new plasma diagnostic tools to provide more accurate measurements. Among these was the use of a laser to directly measure the temperature of the bulk electrons using Thomson scattering. This technique was well known and respected in the fusion community; Artsimovich had publicly called it "brilliant". Artsimovich invited Bas Pease, the head of Culham, to use their devices on the Soviet reactors. At the height of the cold war, in what is still considered a major political manoeuvre on Artsimovich's part, British physicists were allowed to visit the Kurchatov Institute, the heart of the Soviet nuclear bomb effort.

The British team, nicknamed "The Culham Five", arrived late in 1968. After a lengthy installation and calibration process, the team measured the temperatures over a period of many experimental runs. Initial results were available by August 1969; the Soviets were correct, their results were accurate. The team phoned the results home to Culham, who then passed them along in a confidential phone call to Washington. The final results were published in ''Nature'' in November 1969. The results of this announcement have been described as a "veritable stampede" of tokamak construction around the world.

One serious problem remained. Because the electrical current in the plasma was much lower and produced much less compression than a pinch machine, this meant the temperature of the plasma was limited to the resistive heating rate of the current. First proposed in 1950, Spitzer resistivity stated that the electrical resistance of a plasma was reduced as the temperature increased, meaning the heating rate of the plasma would slow as the devices improved and temperatures were pressed higher. Calculations demonstrated that the resulting maximum temperatures while staying within ''q'' > 1 would be limited to the low millions of degrees. Artsimovich had been quick to point this out in Novosibirsk, stating that future progress would require new heating methods to be developed.

US turmoil

One of the people attending the Novosibirsk meeting in 1968 was Amasa Stone Bishop, one of the leaders of the US fusion program. One of the few other devices to show clear evidence of beating the Bohm limit at that time was the multipole concept. Both Lawrence Livermore and the Princeton Plasma Physics Laboratory (PPPL), home of Spitzer's stellarator, were building variations on the multipole design. While moderately successful on their own, T-3 greatly outperformed either machine. Bishop was concerned that the multipoles were redundant and thought the US should consider a tokamak of its own.

When he raised the issue at a December 1968 meeting, directors of the labs refused to consider it. Melvin B. Gottlieb of Princeton was exasperated, asking "Do you think that this committee can out-think the scientists?" With the major labs demanding they control their own research, one lab found itself left out. Oak Ridge had originally entered the fusion field with studies for reactor fueling systems, but branched out into a mirror program of their own. By the mid-1960s, their DCX designs were running out of ideas, offering nothing that the similar program at the more prestigious and politically powerful Livermore didn't. This made them highly receptive to new concepts.

After a considerable internal debate, Herman Postma formed a small group in early 1969 to consider the tokamak. They came up with a new design, later christened Ormak, that had several novel features. Primary among them was the way the external field was created in a single large copper block, fed power from a large transformer below the torus. This was as opposed to traditional designs that used magnet windings on the outside. They felt the single block would produce a much more uniform field. It would also have the advantage of allowing the torus to have a smaller major radius, lacking the need to route cables through the donut hole, leading to a lower '' aspect ratio'', which the Soviets had already suggested would produce better results.

Tokamak race in the US

In early 1969, Artsimovich visited MIT, where he was hounded by those interested in fusion. He finally agreed to give several lectures in April and then allowed lengthy question-and-answer sessions. As these went on, MIT itself grew interested in the tokamak, having previously stayed out of the fusion field for a variety of reasons. Bruno Coppi was at MIT at the time, and following the same concepts as Postma's team, came up with his own low-aspect-ratio concept, Alcator. Instead of Ormak's toroidal transformer, Alcator used traditional ring-shaped magnets but required them to be much smaller than existing designs. MIT's Francis Bitter Magnet Laboratory was the world leader in magnet design and they were confident they could build them.

During 1969, two additional groups entered the field. At General Atomics, Tihiro Ohkawa had been developing multipole reactors, and submitted a concept based on these ideas. This was a tokamak that would have a non-circular plasma cross-section; the same math that suggested a lower aspect-ratio would improve performance also suggested that a C or D-shaped plasma would do the same. He called the new design Doublet