With constantly rising global energy needs, the uncertainty of long term fossil fuel supplies and their negative effect on the climate, there is a growing demand for environmentally clean energy sources. For decades, nuclear fission power has been a cheap and reliable source of energy for many countries. In such fission reactors, the actual fuel for the fission reaction is the uranium isotope U-235.
A fission reactor generates electricity by fissioning materials such as U-235 by impacting them with thermal neutrons, which creates great amounts of energy (around 200 MeV per reaction). Each such fission reaction produces another 2-3 neutrons, which can then again be used to fission other atoms and so on. Some neutrons are lost in the reactor through several processes without ever causing a further fission reaction, such that the average number of neutrons that can cause further fissioning produced after one reaction is somewhat lower. The average number of fission neutrons produced for each given fission neutron is called the neutron multiplication factor, κ. In a nuclear power plant, it is desirable to keep κ close to 1, such that the number of reactions per unit time (and thus the power output) stays constant. This has as a consequence that a reactor is always operated close to criticality, i.e. close to the point where the fission reaction would run away if left to itself. The fact that fission reactors have to produce their own neutron flux is the central issue leading to this weakness. In other words, free neutrons are a valuable good in the nuclear power industry.
One of the other main disadvantages of the current use of nuclear fission power is the fact that the current reserves of uranium will only be able to support the current energy equirements for about a century, if we assume U-235 to be the only fuel.  Of the uranium that occurs naturally, this isotope makes up only 0.7 percent of the total mass, the rest of the uranium is made up by the isotope U-238. U-238 by itself cannot be used as fuel for a fission reactor, since it is not "fissile." Nonetheless, U-238 is a "fertile" isotope, which means that a fissile element (in this case plutonium-239) can be bred from it. It is therefore very desirable to find a means to breed the rest of the uranium resources such that they too can be used as fuel for nuclear power plants, since this would vastly increase the timescale over which nuclear fission could provide power. This breeding process can take place when U-238 is being hit by thermal neutrons, which again illustrates the great value of free neutrons for this industry. This is the central function of a fusion-fission hybrid reactor.
The basic idea of the fusion-fission hybrid reactor is to use the high intensity neutron flux produced by a fusion reactor to drive a nuclear fission reaction and at the same time breed fissile fuel from fertile materials.
A hybrid reactor will have as a core a nuclear fusion reactor, in which deuterium and tritium nuclei will be fused together to form helium and a fast neutron. Each such reaction releases about 17 MeV, which is substantially less than the 200 MeV released during the fissioning of U-235, but still remarkable. For the purpose of this paper I will focus on magnetic confinement fusion reactors. The most advanced and most promising such reactor design is the tokamak reactor. A tokamak is a toroidal chamber with magnetic coils around it such that they produce a toroidal field inside the chamber and prevents any charged particle from leaving the chamber. Since the fusion takes place with all materials in the plasma state, all nuclei are charged and will therefore be confined by this toroidal "magnetic bottle."
The charged helium nucleus produced in each fusion reaction remains in the plasma and keeps it heated. In addition, auxiliary heating is required to keep the plasma at sufficient temperature for fusion to occur. The ratio of input heating power to output fusion power is denoted by the dimensionless factor Q. Currently, fusion machines are at the verge of reaching a Q-value of 1, while a commercial pure fusion reactor would require a Q of about 10 to be viable.
The neutron produced in each reaction carries away about 14.5 of the total 17 MeV and is therefore the prime energy carrier of the reaction products. Since it is neutral, it is not charged and will escape from the magnetic confinement. The total outward neutron flux produced by a fusion reactor is substantial in relation to its power output, and poses a great engineering and materials science hurdle for the blanketing of the reactor core.
In a hybrid reactor, there will be a blanket of fertile materials surrounding the fusion reactor core. This blanket will fulfill several purposes. First, the outgoing neutrons will be decelerated and their kinetic energy will be absorbed. Second, in the collision-rich deceleration process and in other atomic processes related to the neutron impacts in the blanket, a number of secondary neutrons is produced. Third, each free neutron can now either lead to a breeding reaction, thereby transforming a fertile nucleus into a fissile one, and fourth, the neutrons can hit fissile materials, producing great amounts of energy and further neutrons.
The hybrid reactor design poses many great features. First, the fusion power required for the hybrid reactor to be viable is substantially less than that required for a pure fusion reactor. This is because the main purpose of the fusion core is not the production of energy, but rather the production of neutrons. The fissile materials in the blanket that are targeted by these neutrons produce substantially more energy per reaction and therefore can make up for weak power output performance of the fusion machine itself. In fact, a hybrid reactor would be viable with a fusion Q factor of only 2, which is much lower than the value of 10 required for a pure fusion machine.  Second, a hybrid reactor would produce enough fissile fuel through breeding to fuel several other traditional fission reactors, which would lead to an even better overall power output performance. As a fertile blanketing material, either U-238 or thorium-232 are desirable, since they would breed the useful fissile isotopes Pu-239 and U-233, respectively. Third, the experience gained from commercially operating a fusion reactor in a hybrid design would be very useful in working towards the long term goal of sustainable pure fusion energy (which basically has unlimited fuel supply) without the strict requirements for performance as for a standalone fusion reactor. Fourth, the hybrid reactor doesn't increase the risk of nuclear proliferation, granted that hybrid reactors are run only in the politically stable countries that possess nuclear weapon technology today. In this case, the fissile fuel could be exported to other countries in a far subcritical concentration (mixed with fertile U-238 for example), such that very advanced enrichment technologies would be required to produce nuclear fuel suitable for weapons. The spent fuel can then be brought to the hybrid reactor "fuel production plants" again for additional breeding and so on. This overall situation would be similar to the present day situation in which a few uranium rich countries export fissile fuels in low, subcritical concentrations (the natural U-235 concentration of 0.7%) around the world. Fifth, the blanket subject to neutron flux could be used to transmute long-lived radioactive waste from conventional fission reactors into less harmful, short lived waste which is easier to dispose of. 
A hybrid reactor essentially combines the respective advantages of both nuclear fission and fusion, while mitigating their respective weaknesses. The hybrid reactor design produces useful fissile fuel from otherwise radioactive waste. This fuel can then be used in existing, conventional nuclear power plants. A hybrid reactor uses a nuclear fusion reactor core, which only requires a Q factor of 2 for the entire hybrid system to be viable, since most of the energy produced by the reactor will be generated by fission reactions in the blanketing. The engineering, construction and maintenance of the core fusion reactor will be helpful in achieving the future goal of pure fusion power. Finally, nuclear proliferation is not increased with the fuel producing hybrid reactor design, spent fuel which would otherwise be radioactive waste can be used to produce useful new fissile fuel and long-lived radioactive waste can be transmuted into less dangerous, shorter-lived waste.
© Julian Kates-Harbeck. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 H. A. Bethe, "The Fusion Hybrid," Physics Today 32, No. 5 (May 1979).
 J. P. Freidberg and A. C. Kadak, "Fusion-Fission Hybrids Revisited," Nature Phys. 5, 370 (2009).