Nuclear Energy

Nuclear fusion and nuclear fission result in a mass change, Δm, between the starting product and the end product. The loss of mass produces an energy E = Δm c2, where c equals the speed of light. As a consequence of this Einstein relation, the mass of 1 kg can be converted into an energy of about 9 × 1016 J or 25 × 109 kWh. This is equivalent to the combustion of 3 million tons of coal. The production of electrical energy by nuclear fission is widespread, while nuclear fusion is still under development.

Nuclear Fission

Uranium fission starts with the absorption of a slow-moving neutron by the non-stable isotope U-235. The obtained U-236 splits into Ba-139 and Kr-94 and releases three free neutrons. The mass defect of about 0.2 atomic mass units is converted into an energy of 210 MeV, see figure at right. For an atomic mass unit, u, we have u ≈ 1.66 × 10−27 kg, and the atomic energy unit electron volt, eV, is about 1.60 × 10−19J.

According to the World Nuclear Association (1 December 2014), there were 437 nuclear fission power plants in operation worldwide, 70 under construction, and 179 in the planning stages. America’s 100 nuclear power plants generated 19.4% percent of the nation’s electricity in 2013. For other countries it varies between 0%, e. g. in New Zealand, and 73.3% in France, worldwide in average meeting 11% of the world's electricity demand.

There are two main concerns about nuclear power plants: waste storage and possible meltdown. Nuclear power plants also produce radioactive waste; for example, a 1-GW nuclear power plant produces 300 kg of the α-emitter plutonium, which has a half-life of about 24,000 years, see Environmental Risks. The present ways for disposing such waste are not satisfying. One acceptable solution is the complete reprocessing of all radioactive waste and nuclear transmutation of long-lived fission products. However, developments in that area are not progressed considerably.

The picture to the left is the power plant Gundremmingen. The two blocks of the power plant account for about 30% of the electricity generated in Bavaria, and prevent every year the emission of 21 million tons of carbon dioxide by corresponding fossil fuel power stations. However, several scenarios could take place in this and other nuclear power plants. One scenario is if the boiling water reactor fails at removing the residual heat, causing the fuel to heat and core structures to melt, see Environmental Risks. In the worst case, the hydrogen can ignite, resulting in an explosion that could destroy the foundation and cause groundwater contamination. The possibility of terrorist threats and disasters such as earthquake, tsunami and hurricane increase such fears. The last example was the Fukushima Daiichi nuclear disaster following the Tōhoku earthquake and tsunami on 11 March 2011.

Nuclear power plants of the next generation have made no progress on waste disposal, but there have been advancements to prevent meltdowns. By 2020, very high temperature reactors (VHTR), also called pebble bed reactors (PBR), should be in use. A 13-MW experimental reactor AVR was operated in Jülich from 1967−1988, and a nuclear power plant with a 300-MW-reactor was operated from 1983−1989 in Hamm-Uentrop. These experimental reactors provided important insights into the remaining risks. New developments are occurring in the USA, in South Africa, Japan and China, with China planning to build 30 of these reactors.

The pebble bed reactor is characterized by a low uranium consumption, low heat generation, and the potential for district heating. Using helium gas as a coolant and graphite as a moderator allows for temperatures of 300−950 °C. The enriched fuel cores with 8% fissile material have a diameter of only 0.5−0.7 mm. They are coated with three layers of silicon carbide and pyrolytic graphite that have an extremely high efficiency for fission products at high temperatures (1600 °C). As shown in the figure to the right, the small spheres are pressed in a fuel element-graphite matrix with a diameter of 6 cm. If the permeation of oxygen is prevented, the fuel does not melt after the loss of cooling. Steam with a temperature of 530 °C and 200 bar pressure can be generated in an additional generator. Using a gas turbine and helium at 900 °C can create efficiencies up to 45%.

Nuclear Fusion

Unlike with nuclear fission plants, there are no expected problems procuring or disposing of fuels for future fusion power plants. Waste from nuclear fusion, such as the reactor materials after disassembling, also generates radiation, but 99% of the waste has a half life of less than 10 years. In the 1960s, it was believed that at the end of the 21 century much of the energy generated would come from nuclear fusion. However, at the end of the last century it was found that turbulent processes in plasma give rise to energy and particle losses and reduce the energy confinement time in which plasma can be kept stable. And now, the first nuclear fusion plant is not expected before 2030.

The fusion of a deuterium and a tritium nucleus creates an alpha particle, a neutron and 17.6 MeV energy. The latter should sustain the plasma to reaction temperature, so that escaping neutrons, which absorb 80% of the fusion energy, heat the water which drives the stream turbines. The figure to the left shows the fusion reaction

The main problem with fusion on earth is the extreme reaction temperature. The reaction plasma must remain at more than a hundred million degrees on a stable position away from any material.

The sun does not have the temperature problem. The main process in the sun is the proton-proton chain reaction. First two hydrogen nuclei 1H+ (protons) fuse into a deuterium nucleus 2H+, releasing a positron e+ and an electron neutrino νe as one proton changes into a neutron:

The resulting deuterium nucleus reacts with another proton, resulting in the light helium isotope 3He2+ and a gamma ray photon γ:


In the reaction of the pp I branch helium-4 comes from fusing two of the helium-3 nuclei produced:


In order to hold the reaction plasma in a stable position far from any material on Earth, three fields are superimposed in a Tokamak (russ. тороидальная камера в магнитных катушках). The picture on the right, from EFDA-JET shows the super-conducting magnetic coils and the three fields of the rose plasma current, of the blue toroidal field coils, and the green transformer circuit.

The fusion product consists of the temperature T, particle density n, and energy inclusion time τ. Since 1983, the Tokamak experiment JET (Joint European Torus) from the European Fusion Program has been in operation in Culham, England. The fusion product of the JET is only a factor of 5 under the goal value for a power plant, as is shown in the image below, taken from a report of the Planck Institute for Plasma Physics

The fusion energy gain factor, usually expressed with the symbol Q, is the ratio of fusion power produced in a nuclear fusion reactor to the power required to maintain the plasma in steady state. At the end of the last century, a value for Q of 0.5 was reached, meaning that twice as much energy is consumed than is obtained. Already in 1988 the United States, Russia, Japan, China, South Korea, and the Euratom started the project ITER (International Thermo-nuclear Experimental Reactor) and 2005 began the building work in Cadarache, France. Now the giant Tokamak reactor for 0.5 GW, 500 s pulse length, and Q = 10 is under construction. The estimated costs increased above 10 billion Euros. ITER expects the production of plasma in 2020, and the operation with Deuterium and Tritium fuels is scheduled for 2027.

The figure above shows a section of the plasma ring. The superconducting coils must be cooled to 4 K in a cryostat containing liquid helium. Considering milestones and costs of the ITER project, it is clear that nuclear fusion will not provide a significant amount of energy within the next 20 years. But energy from the sun is nuclear fusion energy, and humanity makes progress to master this source of energy also on the earth.


In addition to the Tokamak the different principle of the Stellarator is under development. This type of a fusion machine was introduced in 1951 at the Princeton Laboratory for Plasma Physics, and the name stellarator was given, in order to emphasize the similarity to the fusion processes in a star (latin stella). Tokamaks create a part of the magnetic field (for enclosing the plasma) by means of the strong electric current flowing in the plasma, as shown above. But stellarators use only external fields for the plasma inclusion. It makes the construction more difficult since the magnetic cage is produced with a single coil system without a transformer. But it also makes stellarators suitable for continuous operation, whereas tokamaks without auxiliary facilities operate in pulsed mode.

The stellarator Wendelstein 7-X is in construction since 2005 in the Institute of Plasma Physics of the Max Planck Society in Greifswald and was tested in 2014. It consists of an optimized magnetic field that overcomes the difficulties of earlier stellarator concepts. It aims to demonstrate that a power plant can work on the basis of a continuously operating stellarator. The figure above shows the sophisticatedly shaped coils (blue) and the plasma.

Inertial confinement fusion is a process where nuclear fusion reactions are initiated by heating and compressing a fuel target in the form of a pellet. In contrast to the magnetic confinement of the fusion plasma in the tokamak or stellarator, the inertial confinement of deuterium-tritium fuel holds only for a few nanoseconds. During this short time the mass inertia ensures the cohesion of the plasma. The hydrogen bomb functions on this principle. Research in the field of inertial fusion, therefore, can be used for military purposes, and research institutions are supported by the national military budget.

The National Ignition Facility (NIF) was built from 1997-2009 at the Lawrence Livermore National Laboratory in Livermore, California. The 192-beam NIF laser system can fire 1 megajoule of laser energy at a peppercorn-size target located at the center of the 10-meter-diameter target chamber and trigger by the 500-terawatt-flash of light the nuclear fusion. The plasma collapses at a rate of 1.5 million km/h and can reach a temperature of 100 million degrees Celsius. A total energy of 2 MJ shall initiate an higher energy production by nuclear fusion in the pellet. For the progress of the project see NIF update.

Laser Mégajoule (LMJ) is another large research project for inertial confinement fusion. The laser facility is located in Le Barp near Bordeaux, France, and belongs to the Commissariat à l'énergie atomique (CEA). The project began in 2002 and should be completed after ten years. Information about the efficiency of the inertial confinement fusion for energy production is expected from NIF and LMJ in the next future.