Nuclear fusion

File:Nuclear fusion dt reaction.gif

In physics, nuclear fusion is a process where two small nuclei join together to form a larger nucleus. Nuclear fusion is the energy source that causes stars to shine, and is one of the processes in the hydrogen bomb.

Any two nuclei can be forced to fuse with enough effort. 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. One is not so lucky 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 1000 times greater.

Requirements for Fusion

A substantial energy barrier opposes the fusion reaction. The long range Coulomb repulsion between the nuclei is offset by the 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=nσν

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 pτ where p=nT.

Releasing a 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 10 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.

We are not so lucky here on Earth, however, where fusion fuel is expensive and we don't have an entire star-full to allow to "simmer". In order to be useful, the rate of fusion must be considerably greater, and thus the temperatures much higher. However the gas law notes that the pressure of a gas, in this case the fuel plasma, varies inversely with the temperature. Thus, raising the temperature of the fuel to increase the rate makes it much harder to contain for any length of time. Thus earth-bound fusion is based on a catch-22 that has so far proven difficult to master.

One way to do so is to explosively compress the fuel to enormous temperatures and pressures. 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.

Such means are not very useful as a civilian power generator, although there have been ideas based on it. For any particular fuel there is a particular value of nTτ that will result in more energy being released than is required to start the reaction, this is known as the Lawson Criterion after it was first pointed out by Lawson in 1957. For the easiest reaction in D-T fuel, nTτ is about 10^14 sec/cm^3, a figure that has proven extremely difficult to achieve even after 50 years of trying.

Fusion Reactions

(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 star 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. 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.

Some other fusion reactions which are interesting for building a terrestrial reactor are:

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)

D-T reaction (good for reactors because cross section peaks at lower temperature ~50 keV)

D + T --> He⁴ (3.5 MeV) + n (14.1 MeV)

D-He³ reaction

D + He³ -_51%-> He⁴ + n + p + 12.1 MeV

D + He³> -_43%-> He⁴ (4.8 MeV) + D (9.5 MeV)

D + He³ -_6%-> He⁵ (2.4 MeV) + p (11.9 MeV)

Fuel confinement

Gravitational confinement is how stars work. However, there are engineering difficulties in building reactors. No-one knows how to create the necessary confinement field without using impractically large masses, or unavailably dense materials.

Inertial confinement is basically squeezing the plasma with external photons (huge lasers or in the case of a thermonuclear weapon the intense x-rays emitted from a nuclear fission explosion) or particles (usually heavy ions). Inertial confinement schemes are inherently not steady state and a reactor design would require repetitions of inertial reactions (small explosions)

Electrostatic confinement uses grids, usually spherical in a sort of large vacuum tube, to concentrically accelerate ions to a focus. Since one electron volt equals 11,604 degrees, this approach can achieve fusion with practical voltages. This is the approach taken by the Farnsworth-Hirsch Fusor. Fusors are accelerators, not heated bottles. They therefore achieve consistent high-energy collisions, which makes them far more efficient. Also, unlike linear accelerators, they recycle ions which do not fuse, because the ions scatter elastically and are refocused by the field.

Fusors are attractive for many reasons. They theoretically should be able to use fusion reactions that are impractically energetic for a thermal reactor, such as the proton - Boron 11 reaction, which generates only high energy alpha particles with no gamma or neutrons. Some designs could electrostatically decelerate ionized reaction products, achieving direct conversion of nuclear power to electricity, at efficiencies above 90%. Fusors are mostly vacuum, so they should have a mass low enough to be a practical power source for vehicles, including aircraft and spacecraft. Fusors might even be portable: operating fusors have been built with vacuum chambers as small as 30cm. Finally, fusor research uses relatively small amounts of equipment. It should therefore be inexpensive compared to the other forms of fusion.

However, reseearchers believe that fusors do not achieve break-even because the ions collide with the grids, which wastes energy. Some people, attracted by the advantages and the low research costs, believe that this problem might be both more valuable and more easily solved than the problems that have surfaced in inertial and magnetic confinement thermal fusion rectors.

Magnetic confinement of a thermally accelerated plasma is the most highly-developed form of fusion reactor. It uses the electromagnetic properties of a plasma to confine the particles with a magnetic field. A magnetic field confines a particle in two dimensions, rather than three, so magnetic confinement devices (for example tokamaks and stellarators) are toroidal, so that the particles can be confined for long periods of time.

Magnetically-confined plasmas have to be heated. Only a small fraction of the most energetic ions actually achieve the temperatures necessary to fuse.

Fusion as a power source

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.

Some argue that fusion is the best option for a truly sustainable or long term energy source because the fuel is virtually inexhaustible and readily available throughout the world. Deuterium can be taken from water, and a thimble full of deuterium is equivalent to 20 tons of coal in energy production – a medium size lake contains enough deuterium to supply a nation with energy for centuries using fusion.

Like fission, fusion will be environmentally sound without atmospheric pollutants or contribution to global warming (compared to fossil fuels where 64 lbs of CO₂ is produced per American per day from fossil fuel usage).

In addition fusion power is considerably more attractive than existing fission systems as a nuclear power source. Much less radioactive waste results from fusion than from fission plants. During the D-T reaction, neutrons are released which cause the reactor vessel to become radioactive, but this radioactivity can be greatly reduced by using "low activation" materials. Such materials would have half-lives of tens of years, rather than the tens of thousands of years for radioactive waste produced from fission.

However, critics point out that it is far from clear that nuclear fusion will indeed be economically competitive with other forms of power. It is possible that fusion advocates are making some of the same mistakes in creating unrealistic economic projections that fission advocates have made in the past. When the cost of the plant is factored in, it is not clear that fusion will be cheaper than traditional forms of power, and although there are many economic estimates of the cost of fusion power, these estimates can give wildly different answers as to the economic viability of fusion power, depending on what the input assumptions of the models are. Fusion advocates would counter that it is very dificult to predict these future costs, especially as they depend upon political climates which would set regulatory standards, and was a large source of the rising price of fission power, for instance. It has also been argued, although most economists would disagree, that it is dificult to weigh an increased economic cost with the environmental advantages of fusion.

Fusion does also have potential safety concerns. Although there intrinsically would be no danger of a runaway fusion reaction (a meltdown) and any malfunction would result in a rapid shutdown of the plant, there are possible scenarios which are safety concerns. In 1973 the American Association for the Advancement of Science (AAAS) pointed out several concerns for a fusion power plant, including the possibility of a tritium leak, lithium fire or the accidental release of magnetic energy. These concerns would need to be addressed as part of any reactor design.

Unfortunately, there are still significant barriers standing between current scientific understanding and technological capabilities and the practical realization of fusion as an energy source, and it is far from clear that an economically viable fusion plant is even possible. It is an extremely difficult task to harness a 100 million degree plasma in an economically efficient way, so a working reactor is still many years down the road and is an active part of plasma physics research.

Plasma Heating

In an operating fusion reactor, part of the energy generated will serve to maintain the plasma temperature as fresh deuterium and tritium are introduced. However, in the startup of a reactor, either initially or after a temporary shutdown, the plasma will have to be heated to 100 million degrees Celsius. In current tokamak (and other) magnetic fusion experiments, insufficient fusion energy is produced to maintain the plasma temperature. Consequently, the devices operate in short pulses and the plasma must be heated afresh in every pulse.

• Ohmic Heating: Since the plasma is an electrical conductor, it is possible to heat the plasma by passing a current through it; in fact, the current that generates the poloidal field also heats the plasma. This is called ohmic (or resistive) heating; it is the same kind of heating that occurs in an electric light bulb or in an electric heater. The heat generated depends on the resistance of the plasma and the current. But as the temperature of heated plasma rises, the resistance decreases and the ohmic heating becomes less effective. It appears that the maximum plasma temperature attainable by ohmic heating in a tokamak is 20-30 million degrees Celsius. To obtain still higher temperatures, additional heating methods must be used.

• Neutral-Beam Injection involves the introduction of high-energy (neutral) atoms into the ohmically -- heated, magnetically -- confined plasma. The atoms are immediately ionized and are trapped by the magnetic field. The high-energy ions then transfer part of their energy to the plasma particles in repeated collisions, thus increasing the plasma temperature.

• Magnetic Compression: A gas can be heated by sudden compression. In the same way, the temperature of a plasma is increased if it is compressed rapidly by increasing the confining magnetic field. In a tokamak system this compression is achieved simply by moving the plasma into a region of higher magnetic field (i.e., radially inward). Since plasma compression brings the ions closer together, the process has an additional benefit of facilitating attainment of the required density for a fusion reactor.

• Radio-frequency Heating: High-frequency waves are generated by oscillators outside the torus. If the waves have a particular frequency (or wavelength), their energy can be transferred to the charged particles in the plasma, which in turn collide with other plasma particles, thus increasing the temperature of the bulk plasma.

See fusion power

Historical Development of Fusion

• 1929 - Atkinson and Huetermans used the measured masses of light elements and applied Einstein's discovery that E=mc² to predict that large amounts of energy could be released by fusing small nuclei together.
• 1939 - Hans Bethe won the Nobel Prize in physics (awarded 1968) for quantitative theory explaining fusion
• shortly after World War II and the success of the Manhattan Project the hydrogen bomb was built, which released large amounts of fusion energy from a reaction ignited by a fission trigger
• 1951 - Argentina publicly claimed that they had harnessed controlled nuclear fusion (these claims were false), sparking a responsive research effort in the U.S.
  • Lyman Spitzer started the Princeton Plasma Physics Laboratory (or PPPL) which was originally codenamed Project Matterhorn - most early work was done on a type of magnetic confinement device called a stellarator.
  • James Tuck, an English physicist, began research at Los Alamos National Laboratory (LANL) under the codename of project Sherwood, working on pinch magnetic confinement devices. (Some people claimed that the project was named Sherwood based on Friar Tuck)
  • 1952 Edward Teller expanded hydrogen bomb research at Lawrence Livermore National Laboratory (LLNL) and began studying inertial confinement using high powered lasers.
• 1952 - Cousins and Ware build a small toroidal pinch device in England, and demonstrate that instabilities in the plasma make pinch devices inherently unstable.
• 1953 - pinch devices in the US and USSR attempt to take the reactions to fusion levels without worrying about stability. Both report detections of neutrons, which are later explained as non-fusion in nature.
• 1954 - ZETA stabilized toroidal pinch device starts operation in England.
• 1958 - American, English and Soviet scientists began to share previously classified fusion research, as their countries declassified controlled fusion work as part of the Atoms for Peace conference in Geneva (an amazing development considering the Cold War political climate of the time)
• 1958 - ZETA experiments end. Several firings produce neutron spikes that the researchers initially attribute to fusion, but later realize are due to other effects. Last few firings show an odd "quiet period" of long stability in a system that otherwise appeared to prove itself unstable. Research on pinch machines generally dies off as ZETA appears to be the best that can be done.
• 1967 - Demonstration of Farnsworth-Hirsch Fusor appears to generate neutrons in a nuclear reaction.
• 1968 - Results from the T-3 Soviet magnetic confinment device, called a tokamak, which Igor Yevgenyevich Tamm and Andrei Sakharov had been working on - showed the temperatures in their machine to be over an order of magnitude higher than what was expected by the rest of the community. The western scientists visited the experiment and varified the high temperatures and confinement, sparking a wave of optimism for the prospects of the tokamak as well as construction of new experiments. which is still the dominant magnetic confinement device today.
• 1974 - Taylor re-visits ZETA results of 1958 and explains that the quiet-period is in fact very interesting. This leads to the development of "reversed field pinch", now generalized as "self-organizing plasmas", an ongoing line of research.
• 1978 - The European Community (with Sweden and Switzerland) launched the JET (tokamak) project in the UK
• 1988 - The Japanese tokamak, JT-60 came online
• March 1989 - some scientists announced that they achieved cold fusion - causing fusion to occur at room temperatures. However, they made their announcements before any peer review of their work was performed, and no subsequent experiments by other researchers revealed any evidence of fusion.
• 1993 - The TFTR tokamak at Princeton (PPPL) does experiments with 50% deuterium, 50% tritium, which eventually produces as much as 10 MegaWatts of power from a controlled fusion reaction.
• 1997 - The JET tokamak in the UK produces 16 MW of fusion power. This is roughly their break even point — producing as much fusion power as they were using to heat the plasma and sustain the reaction.
• 1997 - combining a field-reversed pinch with an imploding magnetic cylinder results in the new Magnetized Target Fusion concept. In this system a "normal" lower density plasma device is explosively squeezed using techniques developed for high-speed gun research.
• 2002 - Claims and counter-claims are published regarding bubble fusion, in which a table-top apparatus is reported as producing small-scale fusion in a liquid undergoing acoustic cavitation.