Magnetic Fusion Machines

Melis Tekant
March 21, 2013

Submitted as coursework for PH241, Stanford University, Winter 2013


Fig. 1: The interior of the JET tokamak. (Courtesy of the European Fusion Development Agreement).

Nuclear fusion is a process through which light elements fuse into each other, creating energy. The first usage of this process was through weapons of mass destruction, but now scientists are seeking ways to use fusion for commercial energy production. Because particles fuse only under extreme conditions such as high temperatures and pressures, nuclear fusion is very hard to achieve. Thus, it has not yet become a commercial energy source. Yet, as scientists learn more about the properties of plasmas and technical equipments are developed, we will be closer to a new energy source that is foreseen to be clean, safe, abundant and cheap.

Due to the requirement of extreme conditions in the core, scientists have been seeking ways to confine plasmas without coming in contact with the walls. So far, there have been two main approaches to this problem: magnetic and inertial confinement. Magnetic confinement works by exerting a magnetic force on the charged plasma particles and thus keeping them in helical or circular orbit. There are seven types of magnetic fusion machines: tokamak, stellarator, spherical torus, reversed-field pinch, spheromak, field-reversed configuration, and tandem mirror. [1]


The most successful fusion device so far, the tokamak confines the plasma particles in a toroidal region using magnetic fields. These particles are held in small gyrating orbits by the field. Though the principal magnetic field is toroidal, the confinement of the plasma is achieved through a poloidal magnetic field. Current in the plasma itself, flowing in the toroidal direction, mainly produces these fieds. [2]

Since its discovery in 1954 in Russia, various research facilities have attained promising results using tokamaks: The Tokamak Fusion Test Reactor (TFTR) in Princeton was the first to reach 100 million degrees Celsius in 1985, the minimum required temperature to attain nuclear fusion. Later, TFTR broke another record by reaching 520 million degrees Celsius, the highest temperature ever produced in a laboratory. [3] The Joint European Torus (JET) attained the highest plasma current with 7 MA and greatest power output with 16.1 MW. Furthermore, an output power of more than sixty percent of the input has been achieved. Even though the required temperature for fusion, density, and confinement time have all been obtained in tokamaks, it has been for different plasmas, making tokamaks close, but not yet ready for commercial use. [2]

A new large-scale project is on its way to change this fact. The International Thermonuclear Experimental Reactor (ITER) aims to demonstrate the possibility of producing commercial energy from fusion. Expected to be completed by 2018, it aims to produce ten times the input energy with an output of 500 MW. [4]

Fig. 2: Schematic of a stellarator. (Courtesy of Wikimedia Commons).


A stellarator is a helically symmetric system bent into a torus with a large axisymmetric toroidal field, a moderately sized helical field with lθ-nφ symmetry, and a small axisymmetric vertical field. [5] All toroidal current in a stellarator is due to the bootstrap effect and no externally driven current exists. [6]

Stellarators are very similar to tokamaks, but the stellarator has two major improvements over the tokamak: it is inherently in steady state, and the likelihood of exciting major disruptions is much lower. The only major disadvantage of the stellarator is that the coil system needed to generate the magnetic field is much more complicated compared to that of the tokamak. [6] With the advancement of 3D imaging and construction techniques, interest in stellarators have increased, making this machine the major competitor for success in nuclear fusion energy after the tokamak.

Spherical Torus

This fusion machine is radially thin and tall, and contains a central hole to accommodate the inner legs of the TF coils and their shielding. The toroidal magnetic field is two to three times less compared to tokamaks, which result in much less shielding requirements. Yet, the resistive energy losses in the normal magnets could be significant and require large recirculating power. [1]

The Spherical Torus design has received considerable interest since the late 1980s, when it was introduced, due to its advantages over the tokamak design. Recently though, further theoretical computations have cast doubt on the use of this design as a lower cost power producing reactor. Currently, there are about twenty operational spherical torus experiments, with the largest ones being NSTX in the United States and MAST in the United Kingdom. [1]

Reversed-Field Pinch

This configuration is very similar to a tokamak, but with magnetic fields ten times weaker than that of a tokamak. Also the toroidal field reverses direction in the radial axis. The weak magnetic field leads to many positive features of this concept, such as high mass power density, compactness, favorable economics, less shielding, and a single piece maintenance system. [1] The disadvantage of this design is the resistive wall instability. This occurs when pulse lengths are longer than magnetic diffusion time. [5]

There are several reversed-field pinch experiments in the world, with the largest one in Reversed-Field eXperiment (RFX) in Paradua, Italy. [7]


A spheromak is a compact, asxisymmetric, toroidal configuration which could theoretically attain high pressures. Due to the absence of toroidal field coils and an ohmic transformer, the vacuum chamber has a spherical topology. The magnetic fields are produced by driving steady state currents coupled with an externally applied polodial magnetic field. [6]

The advantages of a spheromak lies in its simplicity: steady state operation on this machine is possible using only three, low-technology, DC power supplies. [6] On the other hand, the plasma dynamo has fluctuations and turbulence, and thus its behavior is difficult to predict. [1]

Field-Reversed Configuration

Linear, open ended, and cylindrical, this is a much different design than the tokamak. Though this system permits easy construction and maintenance, plasma stability and energy confinement are still unresolved issues. Yet, field-reversed machines have been helpful in investigating the advantages and disadvantages of the D-3He fuel cycle. [1]

Tandem Mirror

Like the field-reversed configuration, tandem mirrors are also linear in nature. In addition, they are terminated by mirror cells. Maintenance is easy and requires relatively low-technology magnets. This configuration is currently used as an educational device, rather than energy research, as in GAMMA 10 in Japan. [1]


Currently, fusion research is being done on all seven kinds of magnetic fusion machines, with each design having its own advantages and disadvantages. Still, the most successful magnetic confinement system seems to be the tokamak. With ITER, we are taking large steps in the direction of using nuclear fusion as a commercial energy source, and might be seeing some exciting results in just a couple of years.

© Melis Tekant. 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] S. B. Krivit, T. B. Kingery and J. H. Lehr, eds., Nuclear Energy Encyclopedia: Science, Technology, and Applications (Wiley, 2011).

[2] J. Wesson, Tokamaks, 4th Ed. (Oxford U. Press, 2011).

[3] J. Wood, Nuclear Power (Institution of Engineering and Technology, 2007).

[4] L. Parker, "A Future for Fusion?" Wall Street Journal, 22 Feb 10.

[5] D. C. Robinson, "Alternative Approaches: Concept Improvements in Magnetic Fusion Research," Phil. Trans. Roy. Soc. A 357, 515 (1999).

[6] J. P. Freidberg, Plasma Physics and Fusion Energy, 1st Ed. (Cambridge U. Press, 2008).

[7] R. Albanese et al., "Linearized Models for RFX Configurations," Fusion Eng. Design 56-57, 733 (2001).