Magnetic Confinement Fusion as Applied to Future Energy

Isaac Ramos
December 12, 2012

Submitted as coursework for PH240, Stanford University, Fall 2012


Fig. 1: A Familiar Ignited Plasma Undergoing Fusion. Source: Spitzer Space Telescope archive. (Courtesy of NASA/JPL- Caltech.)

Since the 1930s it has been understood that the energy of the sun and other stars is created by means of thermonuclear fusion occurring within the extraordinarily hot plasmas of which they are made. [1] The aim of this paper is to explain the principals of magnetic confinement fusion given a basic understanding of the nuclear fusion process briefly summarized below, explore the possibilities of fusion as an energy source, and review current and future prospects in the development and commercialization of magnetically confined fusion technology as an energy source of the future.

Within the environment of an exceedingly hot plasma, two light positively charged nuclei may gain enough energy to penetrate the Coulomb barrier and approach one another close enough to initiate a fusion reaction, losing mass in the process but expelling vast amounts of energy. Deuterium and tritium, both isotopes of hydrogen, have the highest probability of collision in a plasma and are therefore primarily considered as a basis for confined fusion. [2]

Ignition and Q-Factor of the Magnetic Fusion System

Ignition of a plasma occurs when the heat generated by a chain fusion reaction is high enough such that the temperature of the plasma is maintained for fusion to continue without external power input. Typically, the temperatures necessary to ignite the plasma are higher than 106 °C. These temperatures are much higher than any physical containment vessel could withstand; enter magnetic confinement. In magnetically confined fusion, high temperatures can theoretically be achieved via a variety of methods from basic plasma physics such as ohmic heating, neutral beam heating, radio frequency heating, and self heating. [2]

In a magnetically confined plasma system, the charged plasma particles spiral along the magnetic field lines according to a plasma parameter called the gyro-frequency. Currently, the most promising magnetic confinement systems are toroidal, and of these the most advanced is the Tokamak. [3] The fusion energy factor Q of a given system is the ratio of power generated to power consumed by the reactor. Once Q becomes infinite the reaction becomes self sustaining and no energy input is required for the reaction to continue. In the case of a practical power plant using a Tokamak for magnetic confinement, a Q between 20 and 40 would likely correspond to normal operation. [2]

Confinement Fusion as an Energy Source

The energy collection process in a confinement fusion reaction is not nearly as difficult as sustaining fusion itself. In the Deuterium-Tritium fusion reaction, neutrons are the main carriers of energy. Once ejected from the plasma, they are stopped by "blankets" containing lithium which serves the dual purpose of collecting the deposited kinetic energy of the neutrons as heat and creating more tritium to continue the reaction. In this process helium is also created, this lone byproduct can be extracted from the system via a diverter.

The materials required for nuclear fusion via magnetic confinement are abundant in the Earth. Deuterium can be extracted from all forms of water and the Tritium breeding Lithium is abundant both in the Earth's crust and in seawater. Estimates suggest that if all the world's electricity were provided by fusion, known lithium reserves would last us at least a thousand years. [4]

Nuclear fusion is an inherently safe energy source due to the fact that the amount of material available for fusing in the reactor at any time is quite small (grams) and the high temperatures mean any instabilities or deviations from normal operation would lead to cooling and an inability to react, thus suggesting an impossibility of the uncontrolled or critical conditions which remain possible in fission based reactors.

Fig. 2: Triple Product Achieved On Different Fusion Facilities. [4] (Public use release on p. 207 of [4].)

Recent Progress and Future Prospects

Although magnetic nuclear fusion may sound promising, there are reasons it has yet to be achieved which suggest its impossibility. The most compelling argument involves the state of a very hot plasma and its nearness to the ignition condition. This can be characterized by the product of temperature (T), density (n), and confinement time (τ). [2] This is known as the triple product and is derived from the so-called Lawson Criterion to obtain a value of approximately

T n τ ≈ 5.0 × × 1021 keV s/ m3

thought to be a good estimate of a requirement for sustained fusion. [4,5] No fusion reactor has been able to achieve the extremely high requirements of the triple (also known as "fusion") product. The International Thermonuclear Experimental Reactor (ITER) is a Tokamak based fusion reactor in South France currently under construction which hopes to be the first to satisfy the triple product requirements, thus proving the feasibility of a nuclear reactor with reasonable Q, although the first plasma is not expected to be produced from the system for several years. [6]


Based on the current state it is reasonable to estimate that no commercial nuclear fusion power plants could be operational before at least the middle of this century and only under the assumption that the ITER is successful. It is worth noting that other technologies do exist such as inertial confinement, muonic, and laser fusion. With respect to the realization of a power plant, however, magnetically confined fusion is the most developed technology.

Though it is not yet known if fusion is a possibility, it is quite clear that should fusion one day become possible with a moderate Q, nuclear fusion by means of magnetic confinement has the means to power Earth with an efficiency six orders of magnitude higher than a conventional carbon combustion process. [2] Finally, numerous studies suggest that the cost of electricity produced via a magnetic nuclear reactor could be close to the current price of electricity from fossil fuel based power plants of about thirteen cents per kWh. [4]

© Isaac Ramos. 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] J. A. Phillips, "Magnetic Fusion," Los Alamos Science, No. 7, Winter/Spring 1983. p. 64.

[2] Plasma Science: From Fundamental Research to Technological Applications (National Academy Press, 1995).

[3] F. J. Chen, Introduction to Plasma Physics and Controlled Fusion (Springer, 2010)

[4] J. Mlynar, "Focus On: JET," European Centre of Fusion Research, EFD-R(07)01, March 2007.

[5] J. Kates-Harbeck, "Magnetic Nuclear Fusion," Physics 240, Stanford University, Fall 2010.

[6] "Summary of the ITER Final Design Report," Intl. Atomic Energy Agency, IAEA/ITER EDA/DS/22, July 2001