There is another kind of nuclear energy that has been powering the Sun and stars since their formation. It is nuclear fusion—a process in which two lighter nuclei, typically isotopes of hydrogen, combine together under conditions of extreme pressure and temperature to form a heavier nucleus.
In this chapter, harnessing the energy produced in nuclear fusion reaction in a laboratory environment is discussed. Various research programs dedicated to building fusion reactors are also discussed. The s were heady times for nuclear physics. The means of unlocking enormous amount of energy stored inside a nucleus seemed at hand. Finally, the discovery of nuclear fission in ushered in a new era in the history of mankind—the nuclear age [ 1 ].
There are two nuclear processes in which enormous amount of energy is released from nuclear bonds between the particles within the nucleus. They are nuclear fission and nuclear fusion. The importance of nuclear fission for the production of energy is obvious. In fission reactions, a heavy nucleus is split into two lighter fragments and two or three neutrons. About MeV of energy is produced in the fission of an actinide to one of its most probable daughter pairs.
This means that 1 kg of uranium U is capable of producing enough energy to keep a Watt light bulb running for about 25, years [ 2 ]. All nuclear power plants in operation today rely on controlled fission of the isotopes of uranium and plutonium [ 3 ].
The reactor functions primarily as an exotic heat source to turn water into pressurized steam. Only the source of heat energy differs—nuclear power plants use fissile radioactive nucleus, while nonnuclear power plants use fossil fuel. The rest of the power train is the same. The steam turns the turbine blades, the blades generate mechanical energy, the energy runs the generator, and the generator produces electricity.
The major improvement is the elimination of the combustion products of fossil fuels—the greenhouse gases, which have destroyed our environment beyond repair. Because of its abundance in nature, most nuclear reactors use uranium as fuel. Natural uranium contains 0. When U is bombarded with a slow neutron, it captures the neutron to form U , which undergoes fission producing two lighter fragments and releases energy together with two or three neutrons.
The neutrons produced in the reaction cause more fission resulting in a self-sustaining chain reaction. A reactor is considered safe when a self-sustained chain reaction is maintained with exactly one neutron from each fission inducing yet another fission reaction.
Although fission-based nuclear reactors generate huge amounts of electricity with zero greenhouse gas emissions, and thus was hailed as a solution not only to global warming but also to global energy needs, nuclear energy is now seen by many, and with good reasons, as the misbegotten stepchild of nuclear weapons programs. Another area of great concern is the hazards associated with the disposal of highly radioactive waste products.
What has raised our fear in regard to nuclear power more than anything else are the accidents at Chernobyl in and Fukushima in They were a sobering reminder of what we can expect from an accident due to catastrophic reactor failure or human errors. The Fukushima disaster in particular has shattered the zero risk myth of power reactors and heightened our concern about the invisibility of the added lethal component, nuclear radiation. Consequently, they have spurred our interest in the other source of nuclear energy—fusion.
Nuclear fusion is the process in which two lighter nuclei, typically isotopes of hydrogen, combine together under conditions of extreme pressure and temperature to form a heavier nucleus, resulting in the release of enormous amount of energy.
The fusion of four protons to form the helium nucleus 4 He , two positrons, and two neutrinos, for example, generates about 27 MeV of energy. In the s, scientists, particularly Hans Bethe, discovered that it is fusion that has been powering the Sun and stars since their formation [ 4 ].
Beginning in the s, researchers began to look for ways to initiate and control fusion reactions to produce useful energy on Earth. We now have a very good understanding of how and under what conditions two nuclei can fuse together. The fusion of hydrogen into helium in the Sun and other stars occurs in three stages. First, two ordinary hydrogen nuclei 1 H , which are actually just single protons, fuse to form an isotope of hydrogen called deuterium 2 H , which contains one proton and one neutron.
The positron is very quickly annihilated in the collision with an electron, and the neutrino travels right out of the Sun:. Once created, the deuterium fuses with yet another hydrogen nucleus to produce 3 He —an isotope of 4 He. The reaction is. The final step in the reaction chain, which is called the proton-proton cycle, takes place when a second 3 He nucleus, created in the same way as the first, collides and fuses with another 3 He , forming 4 He and two protons.
In symbols,. The net result of the proton-proton cycle is that four hydrogen nuclei combine to create one helium nucleus. The mass of the end product is 0. This mass difference, known as mass defect in the parlance of nuclear physics, is converted into The proton-proton cycle is particularly slow—only one collision in about 10 26 for the cycle to start.
Despite the slowness of the proton-proton cycle, it is the main source of energy for the Sun and for stars less massive than the Sun. The amount of energy released is enough to keep the Sun shining for billions of years. Besides the proton-proton cycle, there is another important set of hydrogen-burning reactions called the carbon-nitrogen-oxygen CNO cycle that occurs at higher temperatures. A star like Sirius with somewhat more than twice the mass of the Sun derives almost all of its energy from the CNO cycle.
An obstacle called the Coulomb barrier caused by the strongly repulsive electrostatic forces between the positively charged nuclei prevents them from fusing under normal circumstances.
However, fusion can occur under conditions of extreme pressure and temperature. That is why fusion reaction is often termed as thermonuclear reaction. Nuclei, which have positive charges, must collide at extremely high speeds to overcome the Coulomb barrier.
The speed of particles in a gas is governed by the temperature. At the very center of the Sun and other stars, it is extremely hot and density is very high. For the Sun, the temperature is around 15 million degrees Celsius, and the central density is about times that of water. The plasma as a mixture of positive ions nuclei and negative electrons is overall electrically neutral. Without the high pressure of the overlying layers, the hot plasma at the solar core would simply explode into space, shutting off the nuclear reactions.
At this distance, the attractive strong nuclear force that binds protons and neutrons together in the nucleus becomes dominant and pulls the incoming particles together, causing them to fuse.
Additionally, massive gravitational force causes nuclei to be crowded together very densely. This means collisions occur very frequently, another requirement if a high fusion rate is to occur.
A quick and crude calculation suggests that we need about 10 38 collisions per second to keep the Sun going, while within the core we get about 10 64 collisions per interactions per second, implying only one in 10 26 collisions needs to be a successful fusion event. We can estimate the minimum temperature required to initiate fusion by calculating the Coulomb barrier which opposes two protons approaching each other to fuse.
The kinetic energy of the nuclei moving with a speed v is related to the temperature T by. By equating the average thermal energy to the Coulomb barrier height and solving for T gives a value for the temperature of around 10 billion Kelvin K.
The probability P of such an event happening is. If the trend for current fusion devices held true for ITER, its much stronger poloidal magnetic field would result in a heat-flux width on the divertor of less than 1 cm. The turbulence may spread heat across a larger area of the divertor surface and significantly increase the heat-flux width to over 5 cm—much wider than current smaller-scale fusion devices.
Yet turbulence at the plasma edge has not been the focus of first-principles-based, heat-flux width predictions until recently because it requires a significant amount of computing power to simulate.
Because electrons move much faster than heavier ions, electron calculations for the plasma edge required 60 times more time steps and were rapidly crunched on GPUs, whereas the larger, slower ions were modeled using CPUs. A wider heat load on the divertor reduces risk of rapid or unexpected damage to the divertor, and plasma edge simulations can help guide planning for ITER experiments, ultimately reducing cost through more accurate predictions. The single largest supporter of basic research in the physical sciences in the United States, the Office of Science is working to address some of the most pressing challenges of our time.
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The missing mass times c 2 equals the binding energy of the nucleus—the greater the binding energy, the greater the missing mass. This means that if two low-mass nuclei can be fused together to form a larger nucleus, energy can be released. The larger nucleus has a greater binding energy and less mass per nucleon than the two that combined.
Thus mass is destroyed in the fusion reaction, and energy is released see Figure 2. On average, fusion of low-mass nuclei releases energy, but the details depend on the actual nuclides involved. Figure 2. The major obstruction to fusion is the Coulomb repulsion between nuclei. Since the attractive nuclear force that can fuse nuclei together is short ranged, the repulsion of like positive charges must be overcome to get nuclei close enough to induce fusion.
Figure 3 shows an approximate graph of the potential energy between two nuclei as a function of the distance between their centers. The graph is analogous to a hill with a well in its center. A ball rolled from the right must have enough kinetic energy to get over the hump before it falls into the deeper well with a net gain in energy. So it is with fusion. If the nuclei are given enough kinetic energy to overcome the electric potential energy due to repulsion, then they can combine, release energy, and fall into a deep well.
One way to accomplish this is to heat fusion fuel to high temperatures so that the kinetic energy of thermal motion is sufficient to get the nuclei together. Figure 3. Potential energy between two light nuclei graphed as a function of distance between them. If the nuclei have enough kinetic energy to get over the Coulomb repulsion hump, they combine, release energy, and drop into a deep attractive well.
Tunneling through the barrier is important in practice. The greater the kinetic energy and the higher the particles get up the barrier or the lower the barrier , the more likely the tunneling. You might think that, in the core of our Sun, nuclei are coming into contact and fusing. However, in fact, temperatures on the order of 10 8 K are needed to actually get the nuclei in contact, exceeding the core temperature of the Sun.
Quantum mechanical tunneling is what makes fusion in the Sun possible, and tunneling is an important process in most other practical applications of fusion, too. Since the probability of tunneling is extremely sensitive to barrier height and width, increasing the temperature greatly increases the rate of fusion. The closer reactants get to one another, the more likely they are to fuse see Figure 4.
Thus most fusion in the Sun and other stars takes place at their centers, where temperatures are highest. Moreover, high temperature is needed for thermonuclear power to be a practical source of energy.
Figure 4. The probability of tunneling increases as they approach, but they do not have to touch for the reaction to occur. The principal sequence of fusion reactions forms what is called the proton-proton cycle :. The energy in parentheses is released by the reaction. Note that the first two reactions must occur twice for the third to be possible, so that the cycle consumes six protons 1 H but gives back two.
The overall effect of the cycle is thus. The solar interior is dense, and the reactions occur deep in the Sun where temperatures are highest. It takes about 32, years for the energy to diffuse to the surface and radiate away. However, the neutrinos escape the Sun in less than two seconds, carrying their energy with them, because they interact so weakly that the Sun is transparent to them.
Negative feedback in the Sun acts as a thermostat to regulate the overall energy output. For instance, if the interior of the Sun becomes hotter than normal, the reaction rate increases, producing energy that expands the interior.
This cools it and lowers the reaction rate.
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