Magnetic Nuclear Fusion

Julian Kates-Harbeck
November 28, 2010

Submitted as coursework for Physics 240, Stanford University, Fall 2010


Nuclear fusion is the energy source that powers our sun. It has long been a dream of many scientists and engineers to replicate this means of energy production here on earth. Unfortunately, it has proven to be exceptionally difficult to make fusion possible terrestrially. This is partly because of the enormous requirements for temperature and pressure to make fusion possible. Two approaches for achieving these criteria prevail: inertial confinement and magnetic confinement. This report will outline the science of magnetic fusion, the advantages of the technology and the current status of research.

Basic Principles

Both nuclear fission - which is today used widely in nuclear reactors around the world as a source of energy and nuclear fusion take advantage of the same principle of nuclear physics. Atomic nuclei are held together by the residual strong force, which only acts between adjacent nucleons. On the other hand, the positively charged protons in the nucleus repel each other electromagnetically. This electromagnetic force follows an inverse square law with distance, which means that it acts on all protons in the nucleus. As a consequence of these two counteracting forces, the atomic stability, which can be expressed as a binding energy per nucleon, reaches a maximum at atomic nuclei the size of iron. [1] This means that when nuclei smaller than iron are fused together as well as when nuclei larger than iron are split, energy is released. An especially stable though light nucleus is the helium nucleus (also called alpha particle). Therefore, the fusion of hydrogen nuclei to form an alpha particle releases exceptional amounts of energy. This is the reaction that takes place in our sun. A special type of this reaction is the deuterium-tritium reaction. These isotopes of hydrogen are fused together and produce a helium nucleus as well as a neutron. Compared to other fusion reaction, the deuterium-tritium reaction is one of the easiest to achieve and has been the center of attention in fusion research so far.

The Lawson Criterion

In order for a sustained fusion reaction to occur, several criteria need to be met. First, since atomic nuclei repel each other at distance, large kinetic energies have to be provided to bring them close enough together to fuse. On a macroscopic scale this means that the temperature of the fusion plasma has to be high. Second, in order for reactions to occur reasonably often in a reactor, the density of particles also needs to be high. Third, the energy lost from the system per unit time must be relatively small for the reaction to be sustainable. Empirically, the so called triple product of the temperature T, the density n and the confinement time &tauE (which is a measure of energy loss per unit time) n T τE has proven a good figure of merit for evaluating fusion plasmas. For a magnetic confinement fusion reactor, a burning deuterium-tritium fusion reaction requires the triple product to reach about n T τE = 3.5 × 1028 °K s/m3 (3 × 1021 keV s/m3). This figure is named the Lawson criterion. No current fusion experiment has achieved this value yet but there have been improvements over many orders of magnitude. The ITER machine currently under construction in Southern France aims to fulfill it. [2]

Magnetic Fusion

Most magnetic fusion devices today make use of a toroidally shaped magnetic field to confine the plasma. Such a toroidal device with magnetic field coils is called a tokamak, after a Russian acronym. The device was first developed by Andrei Sakharov, a famous physicist in the Soviet Union of mid 20th century. He not only is credited for many important contributions to nuclear physics and its applications, but he also received the Nobel Peace Prize in 1975. Despite his many achievements and even his important role in the development of the Soviet hydrogen bomb, he was harassed by the Soviet authorities due to his dissident views. [2]

In a tokamak, fusion plasmas will need to have temperatures of over 100 million C°, which makes proper confinement a crucial point. Any contact of the plasma with the walls of the reactor would immediately release impurities, cool the plasma down and stop the reaction. In order to achieve this, very strong magnetic fields are required in the torus, which is achieved by using large, superconducting coils.

The plasma is heated to ignition temperature through several means. First, ohmic heating is used by inducing currents in the plasma through varying magnetic fields. Since the internal resistance of the plasma falls with rising temperature, this ohmic heating can only bring the plasma to about 50 million C°. In order to reach the required 100 million degrees and more, high power microwave heating and high energy neutral beam injection are used. Ideally, once the plasma reaches ignition, part of the reaction energy will remain in the plasma to keep the temperature high enough and make the reaction self-sustaining. The rest of the energy can be extracted and converted to electricity. Due to the relative masses of the neutron and the alpha particle produced in the reaction, about a fifth of the reaction energy remains with the charged alpha particle and therefore within the magnetically confined plasma. The rest is carried away by the uncharged neutron which can escape the magnetic field. The inner walls of a reactor will be coated with special materials that absorb the neutron flux and convert their energy into heat. This heat can then be absorbed by a cooling fluid that runs through the wall panels and transports the heat to a steam generator which produces the useful electricity.

The neutrons of the reaction are will also serve a second purpose. As opposed to deuterium which is abundantly available from seawater, tritium is extremely scarce due to its short half-life of about 12 years. Tritium fuel for the fusion reaction therefore needs to be produced artificially. This can be accomplished by hitting lithium nuclei with neutrons, which causes the lithium to split into an alpha particle and tritium. This process can be integrated into the fluid cycle in the blanketing modules of the inner tokamak wall. By using lithium alloys as a cooling fluid and by using neutron multiplier materials in the blanketing modules the above described tritium breeding cycle can be combined with the heat transport cycle. The tritium can then be extracted from the cooling fluid along with the helium and re-injected into the reactor as fuel.

Challenges and Prospects

Theoretically, nuclear fusion could be a great source of energy for future societies. First, due to the extremely high energy output of the fusion reaction, the fuel requirements for a fusion reactor are extremely low. For example, in order to sustain annual production of 1 GW of electricity, one would need 100 km2 of solar panels (assuming 10% efficiency in central Europe) or 2.7 Megatons of coal. A fusion reactor on the other hand would need 100 kg of Deuterium and 150 kg of Tritium. [3] Second, the fuel supplies are vast: deuterium can be easily extracted from seawater and the reserves in seawater are sufficient to power the world for many billions of years. The lithium supplies in the earth's crust and in seawater for tritium production would be able to sustain power production for the world for 150 million years. [3] By this time, technology will most likely be advanced enough to produce power from the deuterium-deuterium reaction, eliminating the use of tritium. Third, the fusion reaction produces absolutely no hazardous substances; the only product is useful helium. Due to the high neutron flux, structural materials in the reactor become radioactive. Unlike with fission waste though, these materials don't have high half-lives and are not nearly as hazardous. In fact, with proper choice of materials, the radioactivity can be mitigated such that the materials reach the radioactivity of coal ash in 50 years. [3] Lastly, nuclear fusion is an economically and politically simple source of energy: fusion reactors can produce energy at anytime of the day and the year, they are centralized facilities with low environmental footprint and the fuels are available everywhere and not concentrated in certain areas of our planet.

Unfortunately, there are several difficulties with magnetic fusion power. The two main issues are the plasma confinement and the proper materials. The fusion plasma is very difficult to confine with the magnetic fields. The hot plasma tends to form instabilities and tries to escape from the magnetic confinement which results in cooling of the plasma and termination of the reaction. The materials pose an issue due to the high heat flux and neutron flux that will act on the inner blanketing modules of the reactor. It poses a serious problem to find materials that can withstand these conditions for prolonged periods of time.

These issues are currently being tackled in research facilities such as JET in the UK or Alcator C-Mod at MIT in the United States. Currently under construction in Southern France is the ITER reactor, the largest magnetic fusion project yet. This reactor is planned to be the first to have a self-sustained burning plasma for several minutes. Should the ITER project be successful, the technological feasibility of fusion energy will be proven. The next step will be to construct a demonstrational fusion reactor that actually produces power for the grid. There are already plans for such a project, and this DEMO reactor is scheduled for completion in the early 2030s.

© Julian Kates-Harbeck. 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. G. Prussin, Nuclear Physics for Applications: A Model Approach (Wiley-VCH, 2007).

[2] G. McCracken and P. Stott, Fusion - The Energy of the Universe (Elsevier, 2005).

[3] J. Ongena and G. van Oost, "Energy for Future Centuries: Will fusion be an Inexhaustible Safe and Clean Energy Source?" Trans. Fusion Sci. Technol. 49, 2 (2006).