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. Such a helical field can be generated by adding a toroidal field (traveling around the torus in circles) and a poloidal field (traveling in circles orthogonal to the toroidal field). In a tokamak, the toroidal field is produced by electromagnets that surround the torus, and the poloidal field is the result of a toroidal electric current that flows inside the plasma. This current is induced inside the plasma with a second set of electromagnets.

The tokamak is one of several types of magnetic confinement devices, and is one of the most-researched candidates for producing controlled thermonuclear fusion power. Magnetic fields are used for confinement since no solid material could withstand the extremely high temperature of the plasma. An alternative to the tokamak is the stellarator.

Tokamaks were invented in the 1950s by Soviet physicists Igor Tamm and Andrei Sakharov, inspired by an original idea of Oleg Lavrentiev.^[1]

The word tokamak is a transliteration of the Russian word токамак, an acronym of either "тороидальная камера с магнитными катушками" (toroidal'naya kamera s magnitnymi katushkami)—toroidal chamber with magnetic coils, or "тороидальная камера с аксиальным магнитным полем" (toroidal'naya kamera s aksial'nym magnitnym polem)—toroidal chamber with axial magnetic field.^[2]

History[link]

Although nuclear fusion research began soon after World War II, the programs in various countries were each initially classified as secret. It was not until after the 1955 United Nations International Conference on the Peaceful Uses of Atomic Energy in Geneva that programs were declassified and international scientific collaboration could take place.

Experimental research of tokamak systems started in 1956 in Kurchatov Institute, Moscow by a group of Soviet scientists led by Lev Artsimovich. The group constructed the first tokamaks, the most successful being T-3 and its larger version T-4. T-4 was tested in 1968 in Novosibirsk, conducting the first ever quasistationary thermonuclear fusion reaction.^[3]

In 1968, at the third IAEA International Conference on Plasma Physics and Controlled Nuclear Fusion Research at Novosibirsk, Soviet scientists announced that they had achieved electron temperatures of over 1000 eV in a tokamak device. British and American scientists met this news with skepticism, since they were far from reaching that benchmark; they remained suspicious until laser scattering tests confirmed the findings a few years later.

Toroidal design[link]

Tokamak magnetic field and current. Shown is the toroidal field and the coils (blue) that produce it, the plasma current (red) and the poloidal field produced by it, and the resulting twisted field when these are overlaid.

Positively and negatively charged ions and negatively charged electrons in a fusion plasma are at very high temperatures, and have correspondingly large velocities. In order to maintain the fusion process, particles from the hot plasma must be confined in the central region, or the plasma will rapidly cool. Magnetic confinement fusion devices exploit the fact that charged particles in a magnetic field feel a Lorentz force and follow helical paths along the field lines.

Early fusion research devices were variants on the Z-pinch and used electrical current to generate a poloidal magnetic field to contain the plasma along a linear axis between two points. Researchers discovered that a simple toroidal field, in which the magnetic field lines run in circles around an axis of symmetry, confines a plasma hardly better than no field at all. This can be understood by looking at the orbits of individual particles. The particles not only spiral around the field lines, they also drift across the field. Since a toroidal field is curved and decreases in strength moving away from the axis of rotation, the ions and the electrons move parallel to the axis, but in opposite directions. The charge separation leads to an electric field and an additional drift, in this case outward (away from the axis of rotation) for both ions and electrons. Alternatively, the plasma can be viewed as a torus of fluid with a magnetic field frozen in. The plasma pressure results in a force that tends to expand the torus. The magnetic field outside the plasma cannot prevent this expansion. The plasma simply slips between the field lines.

For a toroidal plasma to be effectively confined by a magnetic field, there must be a twist to the field lines. There are then no longer flux tubes that simply encircle the axis, but, if there is sufficient symmetry in the twist, flux surfaces. Some of the plasma in a flux surface will be on the outside (larger major radius, or "low-field side") of the torus and will drift to other flux surfaces farther from the circular axis of the torus. Other portions of the plasma in the flux surface will be on the inside (smaller major radius, or "high-field side"). Since some of the outward drift is compensated by an inward drift on the same flux surface, there is a macroscopic equilibrium with much improved confinement. Another way to look at the effect of twisting the field lines is that the electric field between the top and the bottom of the torus, which tends to cause the outward drift, is shorted out because there are now field lines connecting the top to the bottom.

When the problem is considered even more closely, the need for a vertical (parallel to the axis of rotation) component of the magnetic field arises. The Lorentz force of the toroidal plasma current in the vertical field provides the inward force that holds the plasma torus in equilibrium.

This device where a large toroidal current is established (15 Mega-amps in ITER) suffers from a fundamental problem of stability. The nonlinear evolution of magnetohydrodynamical instabilities leads to a dramatic quench of the plasma current on a very short time scale, of the order of the millisecond. Very energetic electrons are created (runaway electrons) and a global loss of confinement is finally obtained. A very high energy is deposited on small areas. This phenomenon is called a major disruption ^[4]. The occurrence of major disruptions in running tokamaks has always been rather high, of the order of a few percent of the total numbers of the shots. In currently operated tokamaks, the damage is often large but rarely dramatic. In the ITER tokamak, it is expected that the occurrence of a limited number of major disruptions will definitively damage the chamber with no possibility to restore the device ^{[5] [6] [7]}. This critical issue is rarely debated by the promoters of the project.^{[citation needed][neutrality is disputed]} In fact, the very large diameter of the next generation tokamak implies that it will be very difficult to mitigate the disruptions that pose a significant challenge in future tokamaks where the increased stored energy can lead to unacceptably large transient heat loads on plasma facing components.^{[citation needed]}

Plasma heating[link]

In an operating fusion reactor, part of the energy generated will serve to maintain the plasma temperature as fresh deuterium and tritium are introduced. However, in the startup of a reactor, either initially or after a temporary shutdown, the plasma will have to be heated to its operating temperature of greater than 10 keV (over 100 million degrees Celsius). In current tokamak (and other) magnetic fusion experiments, insufficient fusion energy is produced to maintain the plasma temperature.

Ohmic heating[link]

Since the plasma is an electrical conductor, it is possible to heat the plasma by inducing a current through it; in fact, the induced current that heats the plasma usually provides most of the poloidal field. The current is induced by slowly increasing the current through an electromagnetic winding linked with the plasma torus: the plasma can be viewed as the secondary winding of a transformer. This is inherently a pulsed process because there is a limit to the current through the primary (there are also other limitations on long pulses). Tokamaks must therefore either operate for short periods or rely on other means of heating and current drive. The heating caused by the induced current is called ohmic (or resistive) heating; it is the same kind of heating that occurs in an electric light bulb or in an electric heater. The heat generated depends on the resistance of the plasma and the amount of electric current running through it. But as the temperature of heated plasma rises, the resistance decreases and ohmic heating becomes less effective. It appears that the maximum plasma temperature attainable by ohmic heating in a tokamak is 20-30 million degrees Celsius. To obtain still higher temperatures, additional heating methods must be used.

Neutral-beam injection[link]

Neutral-beam injection involves the introduction of high-energy (rapidly moving) atoms into the ohmically heated, magnetically confined plasma. The atoms are ionized as they pass through the plasma and are trapped by the magnetic field. The high-energy ions then transfer part of their energy to the plasma particles in repeated collisions, increasing the plasma temperature.

Magnetic compression[link]

A gas can be heated by sudden compression. In the same way, the temperature of a plasma is increased if it is compressed rapidly by increasing the confining magnetic field. In a tokamak system this compression is achieved simply by moving the plasma into a region of higher magnetic field (i.e., radially inward). Since plasma compression brings the ions closer together, the process has the additional benefit of facilitating attainment of the required density for a fusion reactor.

Set of hyperfrequency tubes (84 GHz and 118 GHz) for plasma heating by electron cyclotron waves on the Tokamak à Configuration Variable (TCV). Courtesy of CRPP-EPFL, Association Suisse-Euratom.

Radio-frequency heating[link]

High-frequency electromagnetic waves are generated by oscillators (often by gyrotrons or klystrons) outside the torus. If the waves have the correct frequency (or wavelength) and polarization, their energy can be transferred to the charged particles in the plasma, which in turn collide with other plasma particles, thus increasing the temperature of the bulk plasma. Various techniques exist including electron cyclotron resonance heating (ECRH) and ion cyclotron resonance heating. This energy is usually transferred by microwaves.

Tokamak cooling[link]

The fusion reactions in the plasma spiraling around a tokamak reactor produce large amounts of high energy neutrons. These neutrons, being electrically neutral, are no longer held in the stream of plasma by the toroidal magnets and continue until stopped by the inside wall of the tokamak. This is a large advantage of tokamak reactors since these freed neutrons provide a simple way to extract heat from the plasma stream; this is how the fusion reactor generates usable energy. The inside wall of the tokamak must be cooled because these neutrons yield enough energy to melt the walls of the reactor. A cryogenic system is used to prevent heat loss from the superconducting magnets. Mostly liquid helium and liquid nitrogen are used as refrigerants.^[8] Ceramic plates specifically designed to withstand high temperatures are also placed on the inside reactor wall to protect the magnets and reactor.

Experimental tokamaks[link]

Currently in operation[link]

(in chronological order of start of operations)

Alcator C-Mod

• TM1-MH (since 1977 Castor, since 2007 Golem^[9]) in Prague, Czech Republic; in operation in Kurchatov Institute since early 1960s; 1977 renamed to Castor and moved to IPP CAS,^[10] Prague; 2007 moved to FNSPE, Czech Technical University in Prague, and renamed to Golem
• T-10, in Kurchatov Institute, Moscow, Russia (formerly Soviet Union); 2 MW; in operation since 1975
• TEXTOR, in Jülich, Germany; in operation since 1978
• Joint European Torus (JET), in Culham, United Kingdom; 16 MW; in operation since 1983
• Novillo Tokamak,^[11] at the Instituto Nacional de Investigaciones Nucleares,in Mexico City, Mexico; in operation since 1983
• JT-60, in Naka, Ibaraki Prefecture, Japan; in operation since 1985
• STOR-M, University of Saskatchewan; Canada in operation since 1987; first demonstration of alternating current in a tokamak.
• Tore Supra,^[12] at the CEA, Cadarache, France; in operation since 1988
• Aditya, at Institute for Plasma Research (IPR) in Gujarat, India; in operation since 1989
• DIII-D,^[13] in San Diego, USA; operated by General Atomics since the late 1980s
• COMPASS,^[10] in Prague, Czech Republic; in operation since 2008, previously operated from 1989 to 1999 in Culham, United Kingdom
• FTU, in Frascati, Italy; in operation since 1990
• Tokamak ISTTOK,^[14] at the Instituto de Plasmas e Fusão Nuclear, Lisbon, Portugal; in operation since 1991
  

  

  Outside view of the NSTX reactor
• ASDEX Upgrade, in Garching, Germany; in operation since 1991
• Alcator C-Mod,^[15] MIT, Cambridge, USA; in operation since 1992
• Tokamak à configuration variable (TCV), at the EPFL, Switzerland; in operation since 1992
• TCABR, at the University of São Paulo, São Paulo, Brazil; this tokamak was transferred from Centre des Recherches en Physique des Plasmas in Switzerland; in operation since 1994.
• HT-7, in Hefei, China; in operation since 1995
• HL-2A, in Chengdu, China; in operation since 2002
• MAST, in Culham, United Kingdom; in operation since 1999
• NSTX in Princeton, New Jersey; in operation since 1999
• EAST (HT-7U), in Hefei, China; in operation since 2006
• KSTAR, in Daejon, South Korea; in operation since 2008
• SST-1, in Institute for Plasma Research Gandhinagar, India; 1000 seconds operation.^[16]
• IR-T1, Islamic Azad University, Science and Research Branch, Tehran, Iran ^[17]

Previously operated[link]

The control room of the Alcator C tokamak at the MIT Plasma Science and Fusion Center, in about 1982–1983.

• LT-1, Australia National University's plasma physics group built the first tokamak outside of Soviet Union c. 1963
• T-3, in Kurchatov Institute, Moscow, Russia (formerly Soviet Union);
• T-4, in Kurchatov Institute, Moscow, Russia (formerly Soviet Union); in operation in 1968
• Texas Turbulent Tokamak, University of Texas, USA; in operation from 1971 to 1980.
• Tokamak de Fontenay aux Roses (TFR), near Paris, France
• Alcator A and Alcator C, MIT, USA; in operation from 1973 until 1979 and from 1978 until 1987, respectively.
• TFTR, Princeton University, USA; in operation from 1982 until 1997
• T-15, in Kurchatov Institute, Moscow, Russia (formerly Soviet Union); 10 MW; in operation from 1988 until 2005
• UCLA Electric Tokamak, in Los Angeles, United States; in operation from 1999 to 2005
• Tokamak de Varennes; Varennes, Canada; in operation from 1987 until 1999; operated by Hydro-Québec and used by researchers from Institut de recherche en électricité du Québec (IREQ) and the Institut national de la recherche scientifique (INRS)
• START in Culham, United Kingdom; in operation from 1991 until 1998
• COMPASS in Culham; in operation until 2001
• HL-1M Tokamak,Chengdu,China; in operation from 1994 to 2001

Planned[link]

• ITER, international project in Cadarache, France; 500 MW; construction began in 2008, first plasma expected in 2019^{[citation needed]}
• DEMO; 2000 MW, continuous operation, connected to power grid. Planned successor to ITER; construction to begin in 2024 according to preliminary timetable.

See also[link]

• The section on Dimensionless parameters in tokamaks in the article on Plasma scaling
• Edge-Localized Mode
• Stellarator
• Reversed-field pinch
• List of plasma (physics) articles

Notes[link]

References[link]

• Braams, C.M., Stott, P.E. (2002). Nuclear Fusion: Half a Century of Magnetic Confinement Research. Institute of Physics Publishing. ISBN 0-7503-0705-6. 
• Dolan, Thomas J. (1982). Fusion Research, Volume 1 - Principles. Pergamon Press. LCC QC791.D64. 
• Nishikawa, K., Wakatani, M. (2000). Plasma Physics. Springer-Verlag. ISBN 3-540-65285-X. 
• Raeder, J.; et al (1986). Controlled Nuclear Fusion. John Wiley & Sons. ISBN 0-471-10312-8. 
• Wesson, John (2000). The Science of JET. http://www.jet.efda.org/wp-content/uploads/the-science-of-jet-2000.pdf. 
• Wesson, John; et al (2004). Tokamaks. Oxford University Press. ISBN 0-19-850922-7. 

External links[link]

• CCFE - site from the UK fusion research centre CCFE.
• Plasma Science - site on tokamaks from the French CEA.
• Fusion Programs at General Atomics, including the DIII-D National Fusion Facility, an experimental tokamak.
• Fusion and Plasma Physics Seminar at MIT OCW
• Unofficial ITER fan club, Club for fans of the biggest tokamak planned to be built in near future.
• www.tokamak.info Extensive list of current and historic tokamaks from around the world.
• SSTC-1 Overview video of a small scale tokamak concept.
• SSTC-2 Section View Video of a small scale tokamak concept.
• SSTC-3 Fly Through Video of a small scale tokamak concept.
• [1] Information on conditions necessary for nuclear reaction in a tokamak reactor