An Overview and Basic Design Principles of Tokamak Nuclear Fusion Reactors

Fedja Kadribasic
March 27, 2013

Submitted as coursework for PH241, Stanford University, Winter 2013

Fig. 1: Schematics showing the toroidal, poloidal, and combined magnetic fields inside a tokamak. The resultant field ends up surrounding and stabilizing the plasma. Source: Wikimedia Commons)

Nuclear fusion is a process that can be used to make electrical energy by combining light atomic nuclei to form heavier ones. The most commonly used fuel sources are deuterium and tritium, which are isotopes of hydrogen with one and two extra neutrons, respectively. Combining these two nuclei at very high temperatures and pressures produces a neutron, a helium nucleus, and a lot energy that heats the surrounding plasma. [1] The neutrons and the heat from the plasma can be collected and used to heat water surrounding the reaction, which turns to steam to drive turbines that produce electricity. Deuterium can be directly extracted from seawater where it exists in a relatively high concentration naturally, and tritium can be made when lithium combines with a neutron in a nuclear reactor. [2] Additionally, the helium that is produced as a waste product in a fusion reaction does not pose environmental risks because it is not radioactive and, when it is released into the air, it floats to the top of the atmosphere and disappears into space.

Despite all these benefits, nuclear fusion also has many disadvantages that include the fact that there are still no commercial fusion plants in the world and that the capital investments, so far, have been very high with very little short-term gain. One of the main reasons for this is that, compared to more standard nuclear fission reactors, where uranium and other heavy elements are broken up to release energy, nuclear fusion reactors are much more difficult to build and operate. This is because there is an extremely high Coulomb repulsion due to the positive charges of the nuclei that needs to be overcome to get deuterium and tritium to fuse, which can in practice only be accomplished by making the gases extremely dense and hot. The temperature required is so high that all that remains of the hydrogen gas is the bare nuclei, forming hot, dense plasma, and to get the nuclei to fuse the temperature needs to be comparable to that of the Sun's core. The temperature of this plasma when fusion is taking place is on the order of hundreds of millions of Kelvin, which means one needs very nonstandard methods to contain the plasma. [1]

The two most common methods for doing so are inertial and magnetic confinement. Inertial confinement uses very powerful lasers to heat and pressurize a tiny amount of fussionable material. Magnetic confinement uses magnets to confine the plasma into a toroid where the nuclear reactions take place. The first commercially-viable nuclear fusion reactor, the International Thermonuclear Experimental Reactor or ITER, is an international collaboration and is currently being constructed in France. [3] It uses magnetic fields to confine the plasma, which means that such a design could become more relevant of the two in the near future. Consequently, this paper will concentrate on some of the design considerations for these types of reactors.

Fusion reactors such as the International Thermonuclear Experimental Reactor ITER use a tokamak, which is a combination of magnets that make a toroidal field and poloidal field. The toroidal field has the shape of a torus that surrounds the plasma, and the poloidal field moves in circles around the plasma. The result is a magnetic field that has a similar shape to the toroidal plasma it is trying to confine and surrounds it on all sides, thereby trapping it. [1] The reason it works in the first place is that the plasma is a gas of ionized atoms and electrons, so, like any collection of charged particles, can be deflected and confined by a magnetic field. Despite the fact that the magnetic field does a very good job of confining the plasma, it cannot do so for much longer than a few seconds because instabilities in the plasma accumulate that eventually make fusion impossible and containment very difficult. [1] Consequently, a fusion reaction in such a device only lasts for a very short time, so the containment chamber does not need to be exposed to the extreme conditions for very long.

This still does not eliminate some of the problems that need to be taken into account when designing this chamber. Probably the most commonsense consideration is that the plasma- facing materials need to be able to withstand the extremely high temperatures produced by the fusion reaction. If the walls of the reaction chamber should melt, one has a hundred-million Kelvin plasma that has just been exposed to the outside world to worry about. Consequently, safety is a very important feature that needs to be taken into account. However, the bar needs to be set much higher than that for the structural materials because the plasma needs to be maintained at relatively high purity for the reaction to work. Thus, not only can the material not melt, it needs to have a low enough vapor pressure at high temperatures to avoid contaminating the plasma. [3] It may seem a bit counterintuitive that a solid could have a vapor pressure, but a very simple example of this is that even solid materials sometimes have a distinct smell, which indicates that a small fraction of the molecules of the material are evaporating from the surface and reaching one's nose. This effect can be especially detrimental when one is dealing with an event so delicate yet extreme as nuclear fusion.

Examples of some materials that are used include tungsten, carbon, and beryllium. [4] Tungsten and carbon seem very logical choices because of their extremely high heat tolerances; tungsten has a melting point above 3600 Kelvin and carbon in the form of diamond sublimes at close to 4000 Kelvin. [4] To put these numbers in perspective, iron boils at a little over 3000 Kelvin, so these are very extreme materials by any standard. [4] Beryllium, on the other hand, may seem a little less obvious. Beryllium only has a melting point of around 1500 Kelvin, which is not nearly as high the other two materials considered. [4] However, beryllium nuclei do not have a very detrimental effect on the operation of the fusion reaction, at least compared to some of these other materials, which means that it can be useful in some circumstances. [3]

The intense conditions inside tokamak nuclear reactors call for complicated means of addressing potential problems. These include using materials that have extremely high heat tolerances and have as little negative impact on the plasma as possible. The difficulties of designing nuclear fusion devices is not only limited to takamak reactors, but covers the entire range of nuclear fusion systems. These complexities pose a great hindrance that needs to be overcome if nuclear fusion is to become a feasible energy source in the near future.

© Fedja Kadribasic. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] L. C. Woods, Theory of Tokamak Transport, (Wiley-VCH, 2006).

[2] A. Earnshaw and N. Greenwood, Chemistry of the Elements, 2nd Ed. (Butterworth-Heinemann, 1997), pp. 39-41.

[3] R. J. Hawryluk et al., "Principal Physics Developments Evaluated in the ITER Design Review." Nucl. Fusion 49, 065012 (2009).

[4] W. M. Haynes, CRC Handbook of Chemistry and Physics, 93rd Ed. (CRC Press, 2013), pp. 121-123.