(Transcript of the lesson commentary.)
Role of nucleons, nuclear forces and binding energy in fusion theory
Nuclear fusion, in which atomic nuclei of light elements combine is a synonym to a clean source of energy. A resource with virtually inexhaustible fuel reserves, operating without the production of hazardous waste and with minimal impact on the environment. The basis of the fusion theory is protons and neutrons, which are bound together by strong nuclear forces in a small atomic nucleus. If we would like to split the nucleus into individual nucleons, we must supply it with a certain amount of energy, which is directly proportional to the mass deficit, i.e. the difference between the total mass of all nucleons in the nucleus and the actual mass of the nucleus at rest.
The strength of the binding of nucleons in the nucleus is described even more vividly by the binding energy per nucleon. The light elements at the beginning of the periodic table and the heavy elements at the end have a lower binding energy per nucleon value than the nuclei of the stable elements in the middle of the table. By synthesizing light elements into heavier ones or by the fission of heavy elements into lighter ones. In both cases, we move into the middle region of more stable nuclei. The binding energy per nucleon increases and the result of these nuclear reactions is, apart from a new nuclei, the release of energy related to the increase in the stability of nuclei. And this can be used energetically if certain conditions are met.
So that two nuclei can be joined during fusion, it is necessary to get over the electrostatic repulsive forces between the positively charged nuclei and bring them closer to a distance where nuclear forces begin to act. This can be done dynamically, where the nuclei are energized, increasing their speed until they come within fusion distance of each other by inertia. The second possibility of nuclear proximity is static, when an external force acts on the nuclei that gets over the Coulomb repulsion and the nuclei are so close that they fuse. The speed of particles is related to their temperature. A high temperature at the level of several tens to hundreds of millions of kelvin means a sufficiently high speed of the particles. And an external force getting over the repulsive forces of the nuclei can be thought of as compressing them into a very small volume.
Fuel for thermonuclear fusion reactors
So far, the only functioning fusion reactor in our solar system is the Sun. Every second, at a temperature of about 15.7 million Kelvin, it burns approximately 500 million tons of fuel, which are protons or nuclei of ordinary hydrogen, in its core. Under Earth conditions, this relatively inefficient proton-proton chain cannot be used energetically, as both the probability of the nuclear reactions of which it is composed of and the energy gains are very low.
The most promising thermonuclear fusion reaction that humankind would like to ignite and use is the fusion of deuterium and tritium cores into a helium nucleus and a free neutron, taking place at a temperature of 160 million Kelvin. At such high temperatures, any fuel, in a state of ionized gas, is known as plasma.
But the suitable fuel can be other light elements and their isotopes. Choosing the right combination for a fusion reaction depends only on the achievement of the required fusion temperature, the willingness of the nuclei to fuse and the energy gain of the given reaction. The more energy released during the reaction, the more energetically advantageous the reaction is, of course.
Deuterium is a naturally occurring stable isotope of hydrogen containing one proton and one neutron. Although there are about six and a half thousand atoms of ordinary hydrogen per atom of deuterium in nature, deuterium can be obtained relatively easily from seawater using a proven industrial technique.
The second fuel isotope is slightly radioactive tritium, which is also an isotope of hydrogen that contains two neutrons in its nucleus. Tritium has a half-life of approximately 12 years and is naturally very rare on Earth. A certain amount of tritium is produced artificially as a by-product in existing nuclear reactors.
During the fusion reaction of deuterium and tritium nuclei, apart from the helium nucleus, one more high-energy neutron is produced. This fact will be reflected in the fusion reactor equipment, where the reaction will take place, by the embrittlement of the materials of the reaction chamber as a result of the high flow of neutrons and the associated activation.
Formulation, parameters and results of the Lawson criterion
The production of electricity in fusion power plants will only be possible if we get significantly more energy from the fusion reaction than we use to ignite and sustain it. The ratio of the energy produced to the energy required to sustain the fusion reaction is called the gain factor. The conditions necessary for a fusion reactor to achieve the required output were already formulated in the middle of the last century by British physicist and engineer John David Lawson.
The first parameter of Lawson’s criterion is temperature. The higher the temperature, the more energy the particles gain and the more likely they are to collide and fuse. The second parameter is the density of the fuel. In a denser fuel, the particles are more likely to meet and fusion will occur. The third and last parameter of Lawson’s criterion is time or the confinement time of particles with the desired temperature and density in the reaction space.
Mathematically, the Lawson criterion could be defined as the product of density and time, which is a function of residual temperature. In the original formulation, the criterion indicated the minimum value of this product that leads to a net energy output. Further analysis showed that the triple product of density, confinement time and plasma temperature is also a very useful data referred to by Lawson’s criterion.
From the formulation and results of Lawson’s criteria, there are essentially two options for achieving an economically viable fusion. The first possibility is to maintain a relatively low-density plasma for a longer period of time, which is the basic principle of magnetic confinement. The second option is the opposite and consists in keeping the plasma for a shorter time but with a significantly higher density. This is used in inertial confinement.
Two routes to controlled fusion — magnetic and inertial plasma containment
The conditions for the successful course of fusion reactions include the achievement of the necessary plasma density and corresponding confinement time, and the achievement of a specific fusion temperature at which the given reaction can take place. In principle, two basic types of confinement arise from these conditions: magnetic and inertial.
In magnetic confinement, the plasma is in a closed reaction space that is formed by a magnetic field. Charged particles move in it along closed magnetic field lines and heat up to the fusion temperature. The closed space created by the magnetic field is chosen because no other material could withstand such high temperatures. Relatively lower plasma density is characteristic for magnetic confinement. On the other hand, the confinement time ranges from tens to hundreds of seconds.
Tokamaks and stellarators are based on the principle of magnetic confinement. Tokamaks create an additional toroidal magnetic field induced by an electric current flowing directly through the plasma. The most famous tokamak is the international thermonuclear experimental reactor ITER, which is being built in Cadarache, France.
Stellarators, unlike tokamaks, create a suitably shaped magnetic field by adding external helical magnetic coils, usually of a very specific shape. Stellarators could theoretically work continuously in the future whereas tokamaks are more pulse facilities.
In inertial confinement, it is about achieving short-term high plasma density by compressing a small grain of frozen thermonuclear fuel using symmetrical beams of radiation, most often generated by powerful lasers. After evenly compressing the fuel from all sides, the density and temperature of nuclear fusion is reached in its centre. But the compression and heating is so rapid that the fusion ignition occurs before the fuel is dispersed. The very high density of the fuel allows a significantly shorter confinement time according to the Lawson criterion, which can be in the order of nanoseconds.
