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# Nuclear fusion

In physics, nuclear fusion (a thermonuclear reaction) is a process in which two nuclei join to form a larger nucleus, thereby giving off energy. Nuclear fusion is the energy source which causes stars to "shine", and hydrogen bombs to explode.

Any two nuclei can be forced to fuse with enough energy. When lighter nuclei fuse, the resulting nucleon has too many neutrons to be stable, and the neutron is ejected with high energy. Most lighter nuclei will return more energy that it requires to cause them to fuse, making the reaction exothermic, generating net power.

The opposite case, heavy nuclei with too few neutrons, is also unstable and leads to nuclear fission. Unlike fusion however, fission reactions require so little extra energy for very heavy nuclei that they occur all the time on their own. This is not the case with fusion, where the lowest mass nucleon, hydrogen, still requires considerable energy to fuse.

The total energy contained in a nucleus, the so-called binding energy, is considerably greater than the energy that binds the electrons to the nucleus. Thus the energy released in most nuclear reactions is much larger than that for chemical reaction. For example, the ionization energy gained by adding an electron to hydrogen is 13.6 eV. Compare that to the energy being released in the D-T reaction shown to the right, which at 17 MeV is over 1,000,000 times greater.

A substantial energy barrier opposes the fusion reaction. The long range Coulomb repulsion between the nuclei is offset by the stronger but short range attractive strong nuclear force. The problem becomes one of bringing the nuclei sufficiently close for the strong nuclear force to overcome the Coulomb barrier[?].

The magnitude of the repulsion of the nuclei depends on their total electrical charge, and thus the total number of protons they contain. The magnitude of strong force depends on the total number of nucleons, which means that larger nuclei have a greater strong force. The combination of these two factors results in the fusion threshold energy being lowest for heavy isotopes of hydrogen, which have only one proton keeping them apart, but several additional neutrons pulling them together.

The simplest way to provide such energies is to heat the nuclei. Temperature is a measure of the average kinetic energy of a substance, meaning that some of the atoms within will have higher energies, and some lower. For any particular temperature, a certain percentage of the nuclei will have enough energy to fuse.

The reaction cross section combines the effects of the potential barrier and thermal velocity distribution of the nuclei into an "effective area" for fusion collisions. The cross section forms an equation

$f = n \sigma \nu$

where n is the density of nuclei, σ is the cross section, ν is the thermal velocity, and f is the frequency of fusion producing collisions.

Increasing any of these three quantities will increase the fusion-causing collision frequency, and thus the overall rate of fusion. The cross section is also itself a function of thermal energy in the nuclei. Cross section increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of 10 - 100 keV. At these temperatures, well above typical ionization energies, the fusion reactants exist in a plasma state.

For any given amount of fuel in a particular state, the rate of fusion in the fuel, f, is constant. Thus the measure of the actual net energy being released is a function of f (and in turn, the temperature), the number of particles in a particular area (its density), and the amount of time they remain together (the confinement time). This can be quantified by what is commonly called the fusion triple product, nTτ or where p=nT.

Releasing useful energy from a fuel can thus take place at a low value of f. For instance, the conditions inside the sun are actually quite "poor", and the nuclei only undergo fusion once in every 1029 seconds. However, the fact that the sun contains 1059 nuclei means that the net reaction rate is actually quite high, and since the sun is around for billions of years, eventually the fuel is used up and the total energy released is huge.

On Earth, where fusion fuel is expensive and we have significantly less than a solar mass of available fuel, the rate of fusion must be considerably greater, and thus the temperatures much higher. The higher the temperature, the higher the pressure and the more difficult it is to confine the fuel plasma.

For any particular fuel there is a particular value of nTτ that will result in more energy being released than is required to heat the fuel to start the reaction, this is known as the Lawson Criterion[?]. For the easiest reaction in D-T fuel, nTτ is about 1014 sec/cm³, a figure that has proven extremely difficult to achieve even after 50 years of trying.

The Lawson Criterion essentially defines a minimum lower bound where net power will be produced from the fusion reaction, often referred to as break even. Another important energy is the ignition point, where the heat generated in the reactions is enough to heat the fuel to fuse. This might sound like it would be the same number, but in fact it tends to be considerably higher because much of the energy generated will tend to "escape" any reasonably sized machine. This is not a concern in a star, where the particles will eventually react with other parts of the star, but in a Earth-bound machine keeping all of the energy in the system is much more difficult. A reactor does not have to reach the ignition point in order to be a useful power generator. However, ignition remains one of the main goals of most research systems.

(D is a shorthand notation for deuterium, H², and T is short for tritium, H³)

Fusion powers the Sun and other stars, where the fuel is contained by the gravity of the fuel itself. In stars the size of the sun or smaller, the proton-proton chain predominates; in larger stars, the CNO cycle is the dominant reaction. Both of these cycles have considerably higher threshold temperatures than reactions being studied on Earth, and the corresponding reaction rates are therefore much lower.

For Earth-bound fusion reactors the primary concern is a low threashold energy. This implies a lower Lawson Criterion, and therefore less startup effort. Another concern is the production of neutrons, which are difficult to use and control. Reactions that release no neutrons are referred to as the aneutronic reactions and are of considerable interest, but those that release lower-energy neutrons are equally interesting.

Low threshold energy reactions:

D-T reaction (lowest threshold energy, ~50 keV)

D + T → He4 (3.5 MeV) + n (14.1 MeV)

D-D reaction (both reactions are equally likely to occur)

D + D → T (1.01 MeV) + p (3.02 MeV)
D + D → T (0.82 MeV) + n (2.45 MeV)

T-T reaction

T + T -> He4 + 2 n (11.3 MeV)

Other interesting reactions, mostly aneutronic:

He³ reactions

He³ + He³-> He4 + 2 p

D + He³ → He4 (3.6 MeV) + p (14.7 MeV)

T + He³ → He4 (0.5 MeV) + n (1.9 MeV) + p (11.9 MeV) (51%)
T + He³ → He4 (4.8 MeV) + D (9.5 MeV) (43%)
T + He³ → He5 (2.4 MeV) + p (11.9 MeV) (6%)

Li6 reactions

p + Li6 → He4 (1.7 MeV) + He4 (2.3 MeV)
D + Li6 → 2 He4 (22.4 MeV)
He³ + Li6 → 2 He4 + p (16.9 MeV)

Tritium "breeder" reactions used in "dry" fusion bombs and some proposed fusion reactors:

n + Li6 → T + He4
n + Li7 → T + He4 + n

B11 reaction

p + B11 → 3 He4 (8.7 MeV)

Note that many of the reactions form chains. For instance, a reactor fueled with T and He³ will create some D, which is then possible to use in the D + He³ reaction if the energies are "right". The two most studied aneutronic reactions are the T + He³ and D + Li6, the later forms the basis for thermonuclear bombs. However all of these, even the aneutronic ones, do not operate "cleanly" and a number of less interesting reactions will occur at the same time, some of those producing neutrons.

Gravitational confinement All mass, and energy in general, creates a gravitational force. One way to hold the fuel together long enough to undergo fusion is to put enough of it in one place that the gravity created by the fuel is enough to hold it together, as in stars. Stars are self-regulating, the force holding the star out against its own gravity is the heat being generated by the fusion inside. Thus if the rate of fusion rises, the star expands and the rate slows. Some simple math can demonstrate that the mass of fuel needed to make a star using the D-D reaction is about the size of the Moon.

Inertial confinement The fuel can be explosively compressed with external photons or other particles. Of course with an explosive, this implies that the containment time will tend to be quite small. However if the compression is high enough this is of little concern, as the fuel will still undergo significant fusion. This is the process used in the hydrogen bomb, where a huge explosion, provided by a nuclear fission bomb, compresses a small cylinder of fusion fuel.

In a thermonuclear weapon the x-rays generated by a fission device "boils" a plastic foam, creating a shock wave that is focused onto a "trigger" cylinder containing a liquid D-T mix. Other forms of inertial confinement have been attempted for fusion power, including using large lasers focused on a small pellet of fuel, or using ions of the fuel itself accelerated into a central region as in the Farnsworth-Hirsch Fusor.

Magnetic confinement A plasma consists of charged particles which can then be confined with appropriate magnetic fields. A variety of magnetic fields can be used to confine and insulate a fusion plasma. However, the confined plasma interacts with different confining magnetic fields in ways that affect the heating and confinement efficiency of the system. The nature of the fusion reactor will also be profoundly affected by the particular magnetic configuration. There are only two basic magnetic structures which have been shown to confine plasmas of fusion interest: the magnetic mirror and the magnetic torus. However, each of these magnetic confinement systems has several variations. These confinement systems differ in practice by emphasizing particular principles of fusion science to improve plasma confinement or to simplify the technical requirements for producing the magnetic fields. Historically, the tokamak, a toroidal confinement concept, embodied a set of principles which was comparatively easy to implement in the laboratory. As a result, most of the scientific progress has been made with this concept.

For many years, considerable theoretical and experimental effort has gone into tapping fusion power, initially for electricity generation and possibly as an extremely efficient spacecraft propulsion system. See fusion power for an extensive discussion.

• ITER (http://www.iter.org)
• FIRE (http://fire.pppl.gov)
• FUSION FAQ (http://fusedweb.pppl.gov/FAQ/fusion-faq)

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