Nuclear Power

Nuclear fusion and nuclear fission result in a mass change, Δm, between the starting and end products.
The loss of mass produces 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 burning 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 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 (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 (June 2018), there were 450 nuclear fission power plants in operation worldwide, 58 under construction, and 153 in the planning stages. America’s 99 nuclear power plants generated 20% percent of the nation’s electricity in 2017. For other countries it varies between 0%, e. g. in New Zealand, and 71.6% in France, worldwide in average meeting 10.6% 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 would be the complete reprocessing of all radioactive waste and nuclear transmutation of long-lived fission products. However, developments in that area have not progressed extensively.

The picture to the left is the power plant, Gundremmingen in Germany. The two blocks of the power plant account for about 30% of the electricity generated in Bavaria, and prevent annual emissions of 21 million tons of carbon dioxide that would be required by comparative fossil fuel power stations. However, several catastrophic 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 (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 of a disaster 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 advances 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 those for 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, generates dangerous radiation as well, 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. Thus 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 this 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, Tnτ, 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. This is shown in the image to the left, taken from a report of the Max Planck Institute for Plasma Physics. The ignition diagram shows the progress of fusion research since 1960. The fusion product  is given in the unit 1017 particles per cubic centimeter × seconds × degrees Celsius.






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. As early as 1988, the United States, Russia, Japan, China, South Korea, and the Euratom started the project ITER (International Thermo-nuclear Experimental Reactor) and, in 2005, began building the project 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 have increased above 10 billion Euros.







ITER expects to produce plasma in 2020, and operation with deuterium and tritium fuels is scheduled for 2027. The figure to the right 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 for at least another 20 years. But all energy from our sun is produced by nuclear fusion. Humanity is making progress toward mastery of this source of energy on Earth.




In addition to the Tokamak, another energy project, the Stellarator is under development. It was called the “Stellarator” to emphasize its similarity to the fusion processes in a star (latin stella). This type of a fusion machine was introduced in 1951 at the Princeton Laboratory for Plasma Physics, and would operate on a different principle than the tokamaks. 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 stellarator-type reactors 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 has been in construction since 2005 in the Institute of Plasma Physics of the Max Planck Society at Greifswald and the first plasma could be produced at the end of 2015. Wendelstein uses an optimized magnetic field that overcomes the difficulties of earlier stellarator concepts. The experiment aims to demonstrate that a power plant can work on the basis of a continuously operating stellarator. The figure to the left 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 a nuclear fusion with a 500-terawatt-flash of ligh. 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 initiates higher energy production via nuclear fusion in the pellet. The progress of this project is regularly reported on a NIF page.

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 et aux énergies alternatives. The project began in 2002 and performed a first series of experiments on October 23, 2014. Information about the efficiency of the inertial confinement fusion for energy production is expected from NIF and LMJ in the near future.