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A tokamak is a machine producing a toroidal magnetic field for confining a plasma which is characterized by azimuthal symmetry and the use of a plasma-borne electric current to generate the helical component of the magnetic field necessary for stable equilibrium. It is one of several types of magnetic confinement devices, and is one of the most-researched candidates for producing controlled thermonuclear fusion power.

It was invented in the 1950s by Sovietmarker physicists Igor Yevgenyevich Tamm and Andrei Sakharov, inspired by an original idea of Oleg Lavrentyev).

The tokamak is accompanied by the stellarator design, another toroidal magnetic confinement device which has a discrete, often fivefold rotational symmetry . This form takes into acount the plasmahydrodynamics so that all confining magnetic fields are produced by external coils which avoids the need to induce a high current in the plasma to keep it in the desired shape. It is on the other hand more challenging in the construction.

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)—to'roidal chamber with magnetic coils, or (toroidal'naya kamera s aksial'nym magnitnym polem)—toroidal 'chamber with axial magnetic field.

Toroidal design

Tokamak magnetic field and current

Ions and electrons in the centre of 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 tube 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 dirft, 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.

The figure illustrates the toroidal field, the poloidal field, and the twisted field when these are overlaid.

Plasma heating

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

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 current. 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

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

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.

Radio-frequency heating

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.

Tokamak cooling

A tokamak contains reacting plasma which spirals around the reactor. Since a high number of reactions per second is required to sustain the reaction in a tokamak, high energy neutrons are released quickly in large amounts. These neutrons 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 are very high energy neutrons; the freed neutrons provide a simple way to extract heat from the plasma stream. The inside wall of the tokamak must be cooled because these neutrons are at a high enough temperature to melt the walls of the reactor. A cryogenic system is used to cool the magnets and inside wall of the reactor. Mostly liquid helium and liquid nitrogen are used as refrigerants. Ceramic plates specifically designed to withstand hot temperatures are also placed on the inside reactor wall to protect the magnets and reactor.

Experimental tokamaks

Currently in operation

(in chronological order of start of operations)

Previously operated

  • LT-1, Australia National University's plasma physics group built the first tokamak outside of Russia circa 1963
  • T-3, in Kurchatov Institutemarker, Moscow, Russia (formerly Soviet Union);
  • T-4, in Kurchatov Institutemarker, Moscow, Russia (formerly Soviet Union); in operation in 1968
  • Texas Turbulent Tokamak, University of Texasmarker, USA; in operation from 1971 to 1980.
  • Alcator A and Alcator C, MIT, USA; in operation from 1975 until 1982 and from 1982 until 1988, respectively.
  • TFTR, Princeton Universitymarker, USA; in operation from 1982 until 1997
  • CASTOR, in Prague, Czech Republic; in operation from 1983 after reconstruction from Soviet TM-1-MH until 2006
  • T-15, in Kurchatov Institutemarker, Moscow, Russia (formerly Soviet Union); 10 MW; in operation from 1988 until 2005
  • UCLA Electric Tokamak, in Los Angelesmarker, United Statesmarker; in operation from 1999 to 2005
  • Tokamak de Varennes; Varennesmarker, Canadamarker; 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


See also


  1. Bondarenko B D "Role played by O A Lavrent'ev in the formulation of the problem and the initiation of research into controlled nuclear fusion in the USSR" Phys. Usp. 44 844 (2001) available online
  2. Merriam-Webster Online
  3. Tokamak Cryogenics reference
  4. Ramos J., Meléndez L. et al., Diseño del Tokamak Novillo, Rev. Mex. Fís. 29 (4), 551, 1983
  5. Tore Supra
  6. DIII-D (video)
  8. Alcator C-Mod
  10. ITER press release June 2008
  11. The SST-1 Tokamak Page


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