Nuclear Fusion

If light nuclei are forced together, they will fuse with a yield of energy because the mass of the combination will be less than the sum of the masses of the individual nuclei. If the combined nuclear mass is less than that of iron at the peak of the binding energy curve, then the nuclear particles will be more tightly bound than they were in the lighter nuclei, and that decrease in mass comes off in the form of energy according to the Einstein relationship. For elements heavier than iron, fission will yield energy.

For potential nuclear energy sources for the Earth, the deuterium-tritium fusion reaction contained by some kind of magnetic confinement seems the most likely path. However, for the fueling of the stars, other fusion reactions will dominate.

Deuterium-Tritium Fusion

The most promising of the hydrogen fusion reactions which make up the deuterium cycle is the fusion of deuterium and tritium. The reaction yields 17.6 MeV of energy but to achieve fusion one must penetrate the coulomb barrier with the aid of tunneling, requiring very high temperatures . 80% of that energy yield is in the energy of the neutron, which is not as easily utilized as if it were carried by a charged particle. The deuterium fuel is abundant, but tritium must be either bred from lithium or gotten in the operation of the deuterium cycle. 在氘核循环中，最有可能的氢融合反应是氘核与氚核的融合。该反应产生17.6 MeV的能量，但要实现融合，必须借助隧道效应穿透库仑壁垒，这需要极高的温度。其中80%的能量以中子的形式释放，而中子的能量不如带电粒子容易利用。氘燃料很丰富，但氚必须通过锂生产或在氘循环运行中获得。 Compare with fission 与裂变相比 Conditions for fusion 核融合的条件

Hydrogen Fusion Reactions

Even though a lot of energy is required to overcome the Coulomb barrier and initiate hydrogen fusion, the energy yields are enough to encourage continued research. Hydrogen fusion on the earth could make use of the reactions:

These reactions are more promising than the proton-proton fusion of the stars for potential energy sources. Of these the deuterium-tritium fusion appears to be the most promising and has been the subject of most experiments. In a deuterium-deuterium reactor, another reaction could also occur, creating a deuterium cycle:

Deuterium Cycle of Fusion

The four fusion reactions which can occur with deuterium can be considered to form a deuterium cycle. The four reactions:

can be combined as

or, omitting those constituents whose concentrations do not change:

Tritium Breeding

Deuterium-Tritium fusion is the most promising of the hydrogen fusion reactions, but no tritium occurs in nature since it has a 10 year half-life. The most promising source of tritium seems to be the breeding of tritium from lithium-6 by neutron bombardment with the reaction

which can be achieved by slow neutrons. This would occur if lithium were used as the coolant and heat transfer medium around the reaction chamber of a fusion reactor. Lithium-6 makes up 7.4% of natural lithium. While this constitutes a sizable supply, it is the limiting resource for the D-T process since the supply of deuterium fuel is virtually unlimited. With fast neutrons, tritium can be bred from the more abundant Li-7:

The conceptual sketch below is grossly oversimplified since the engineering for handling liquid lithium is quite complex.

Deuterium Source

Since the most practical nuclear fusion reaction for power generation seems to be the deuterium-tritium reaction, the sources of these fuels are important. The deuterium part of the fuel does not pose a great problem because about 1 part in 5000 of the hydrogen in seawater is deuterium. This amounts to over 10¹⁵ tons of deuterium. Viewed as a potential fuel for a fusion reactor, a gallon of seawater could produce as much energy as 300 gallons of gasoline. The tritium part of the fuel is more problematic - there is no sizable natural source since tritium is radioactive with a halflife of about 10 years. It would have to be obtained by breeding the tritium from lithium.

Fusion Energy Release

A large amount of energy is released by nuclear fusion reactions. It seems that for power generation, the deuterium-tritium reaction is the most practical, but it provides most of the energy to the released neutron. That is problematic because it is harder to extract the energy from neutrons compared to charged particles. The deuterium-deuterium fusion divides its output energy between neutrons and protons. The proton fraction interacts by the electromagnetic force with the medium and converts its kinetic energy to thermal energy very quickly.

It is practical to examine the kinetic energies of the products of nuclear fusion in the center of mass frame of reference. This amounts to neglecting the kinetic energies of the reacting particles before the fusion, which is justified by the fact that those energies are usually in the 1-10 keV range, and the fusion yield is in the MeV range. In the CM frame the energies of constituents a and b in terms of the fusion energy release Q are:

The magnitudes of the momenta in that frame are equal:

Combining these two equations gives:

This allows us to determine the relative magnitudes of the energies of the two fusion products:

For D-D fusion, the smaller particle carries 75% of the energy. With m(He3) = 2.8084 GeV/c2, m(H3) = 2.8089 GeV/c2,m(n) = 0.9396GeV/c2, and m(p) = 0.9383GeV/c2, the product energies for deuterium-deuterium fusion are shown. With a total yield of 3.27 GeV for the neutron reaction, the neutron carries 74.93% of the yield. For the proton reaction with yield 4.03 MeV, the proton carries 74.96%. 当³He的质量为2.8084 GeV/c²，³H的质量为2.8089 GeV/c²，中子的质量为0.9396 GeV/c²，质子的质量为0.9383 GeV/c²时，氘-氘融合的产物能量如图所示。对于中子反应总产额为3.27 GeV，中子携带了74.93%的产额。对于产额为4.03 MeV的质子反应，质子携带了74.96%的产额。 在D-D聚变中，较小的粒子携带75%的能量。

For D-T fusion, the smaller particle carries 80% of the energy. With m(He4) = 3.7274 GeV/c2 and m(n) = 0.9396 GeV/c2, the product energies for deuterium-tritium fusion are shown. With a total yield of 17.59 MeV for this reaction, the neutron carries 79.87% of the yield. 当氦-4的质量为3.7274 GeV/c²，中子的质量为0.9396 GeV/c²时，氘-氚聚变的产物能量如图所示。该反应总产额为17.59 MeV，其中中子携带了79.87%的产额。 在D-T聚变中，较小的粒子携带80%的能量。