Sunday, December 27, 2009

Nuclear Fusion / Fission and Fusion / Nuclear power

b) Nuclear Fusion

The curve of binding energy, that is shown before, indicates that nuclear energy can be released either by fission of heavy nuclei or by fusion of light nuclei. The binding-energy curve is steepest near its left end, showing that the most energy per nucleon is released by fusing the very lightest element-hydrogen. Indeed, the fusion reactions powering the Sun and many other stars begin with the fusion of hydrogen to form deuterium:

11H +11H ------------> 21H + e+ + (0.42 MeV) (1)

a positron (e+) and neutrino (ע) are also released, and the total energy liberated in the reaction is 0.42 Mev. Deuterium then fuses with hydrogen to form the. helium isotope 32He:

11H + 21H ------------> 32He + γ (5.49 MeV). (2)

Here γ represents a gamma ray, and the quantity in parentheses is the total energy released. Helium-3 nuclei from two such reactions then react to give a single 4He nucleus and a pair of protons; this event liberates 12.86 MeV:

32He +32He ------------> 42He + 211H (12.86 MeV). (3)

There is one additional energy-producing reaction associated with these events: the positron from reaction (1) annihilates with an electron, forming two gamma rays with a total energy of 2mc2 or 1.022 MeV as follows:

e+ + e- ------------> 2γ (1.022 MeV). (4)

The reactions (1 to 3) constitute the proton-proton cycle. In the full cycle, reactions (1) and (2) occur twice for each occurrence of reaction (3). The net effect, including two occurrences of the annihilation reaction (4), is to con­vert four protons and two electrons into a single helium-4 nucleus; a total of 26.7 MeV is released in the process. In massive stars,42He is then the building block for the formation of still heavier nuclei by additional fusion reactions .

Although ordinary hydrogen (11H) is abundant, the reaction (1) has a low cross section and so does not occur readily. Terrestrial fusion research has therefore focused on reactions involving the heavier hydrogen isotopes. of most immediate interest are deuterium-deuterium (D-D) and deuterium-tritium (D-T) reactions, listed below along with the energy released in each:

411H + 2e- ------------> 42He + 26.7 Me V

The two possible outcomes of the D-D reaction have nearly equal probability.

21H + 21H ------------> 32He + 10n (3.27 Me V) (5)

21H + 21H ------------> 31H + 11H (4.03 Me V) (6)

21H + 31H ------------> 42He + 10n (17.6 Me V). (7)

The electrical repulsion between nuclei makes it difficult to bring them close enough to fuse. In potential-energy terms, nuclei must overcome the potential barrier associated with the electrostatic force before they can drop into the deep potential well of the stronger but shorter-range nuclear force .

Potential-energy diagram for two nuclei, showing electro­static potential barrier and deep well as­sociated with attractive nuclear force is shown.

Nuclei can quantum-mechanically tunnel through the potential barrier when they lack sufficient energy to overcome it. Although the possibility of tunneling lowers the energy needed to initiate fusion, that energy still remains high. In the Sun's core, for example, fusing nuclei approach one another with energies of the order of 1 Kev, corresponding to a temperature of 15 MK.

In terrestrial applications, the high temperatures required for fusion pose two problems: first, how to achieve those temperatures and, second, how to contain the fusing material. The stars solve both problems with their immense gravitational fields. A star is born as interstellar material-mostly hydrogen and helium-collapses under its own gravity; the resulting compression heats the material to fusion temperatures. Once fusion has begun, the star settles into an equilibrium in which the high pressure of the fusing material is balanced by the gravitational force.

Gravitational confinement is not possible in terrestrial fusion applications, and we must find another means of confining the fusing material. For net fusion energy production, confinement must last long enough for the energy produced by fusion to exceed the energy needed to heat the material. The heat input required is proportional to the number of nuclei being heated, or, to the density, n. However, the rate of fusion energy production per unit volume is proportional to the square of the density. You can see this by considering half the nuclei as targets to be struck by the other half. If you double the number of target nuclei alone, you double the fusion rate. Doubling the density doubles the number of targets and the number of projectiles hitting them, and therefore quadruples the fusion rate.

The total energy produced by fusion is, in turn, given by the fusion rate multiplied by the time τ during which fusion is occurring. Requiring that the fusion energy, proportional to n2τ, exceed the heating energy, proportional to n, gives a minimum value for the quantity nτ- the product of density and confinement time-that must be met in an energy-producing fusion device. This condition on nτ is called the Lawson criterion. For the D-D and D-T reactions the Lawson criteria are approximately

> 1022 s/m3 (D-D)

> 1020 s/m3 (D-T).

The factor-of-l00 difference between these two Lawson criteria shows that D-T fusion is much more readily achieved.

The Lawson criterion offers a choice in the design of a fusion device: Strive for a high plasma density with a short confinement time or a lower density with a longer time. Two distinct approaches emphasize these two possibilities. Iner­tial confinement relies on the inertia of the reacting particles-that is, on their inability to be accelerated instantaneously away from the reaction site to provide confinement; very short confinement times are required in this scheme. Inertial confinement occurs in fusion weapons and in particle-beam and laser ­fusion devices. In magnetic confinement, the more traditional approach to controlled fusion, complicated magnetic field configurations confine the fusion plasma at lower densities but for longer times. However the Lawson criterion is met, it is of course also necessary to surpass the critical ignition temperature.

1- Fusion Reactors

In order to produce useful power from the fusion of nuclei several conditions are re­quired. In particular the particle density and confinement time must satisfy Lawson's criterion. There are two basic approaches to confining a plasma to achieve Lawson's criterion. In the magnetic confinement tech­nique, a Iow particle density is compensated for by a rela­tively long (1s) confinement time. In a system based on inertial confinement, the particle density is high but only for a short (1 ns) time.

Magnetic Confinement

Controlled fusion research began in the 1950s with magnetic confinement of the fusion plasma.

The Tokamak is a magnetic confinement device invented in the USSR.

The plasma in a Tokamak is confined by the combination of magnetic fields. The toroidal field Bt and the poloidal field Bp produce a net field whose lines are helical as shown in the figure.

A strong toroidal field, Bt , is produced by about 20 coils wrapped around the perimeter of a torus. A weaker poloidal field, Bp, is pro­duced by a large current (106 A) that is induced in the plasma by a different, time-varying field generated by coils in the same plane as the torus. The resultant magnetic field lines are helical and serve to confine the plasma. If the plasma were to come into contact with the walls of the containment chamber, the plasma would lose energy and cool down. Furthermore, impurities would be released into the chamber and would severely curtail the operation of the reactor.

The first job of any magnetic confinement scheme is to create a magnetic configuration that keeps plasma away from the relatively cool walls of the device. Plasma particles can reach the walls in three general ways: (1) If mag­netic field lines penetrate the walls, particles spiraling along those field lines may hit the walls. This mechanism is known as end loss. (2) Collisions among particles, and inhomogeneities in the magnetic field, result in particles drifting across the field lines toward the walls of the fusion device. (3) Plasmas are notoriously unstable. A wide variety of waves can propagate in plasma, and some of these waves can grow exponentially at the expense of particle energy, resulting in gross distortion of the plasma and field configuration that lets plasma hit the walls.

The following figure shows the plasma loss in magnetic confinement.

(a) End losses occur when field lines intersect the device walls.

(b) Curvature of the field lines results in cross-field drifts.

(c) Large-scale instabilities distort the plasma and magnetic field. Here the so-called sausage ,instability causes alternate narrowing and bulging of the plasma column.

The most promising magnetic confinement devices eliminate end loss alto­gether, using a toroidal magnetic field whose field lines do not penetrate the device walls : A toroidal fusion device has no end losses, since its mag­netic field lines don't penetrate the device walls. The toroidal shape of the Tokamak Fusion Test Reactor at Prince­ton University shows clearly in this photo taken inside the device during its assembly.

The initial heating of the plasma is accomplished by the induced current mentioned above. Then, beams of high­ energy neutral particles (accelerated as ions and then neu­tralized) are injected into the plasma to deliver about 20 MW, thereby further raising its temperature. Radio fre­quency coils are also used to heat the plasma.

The 14.1 MeV neutrons from the D-T reaction (7) are absorbed by a molten lithium "blanket" surrounding the containment chamber. The thermal energy deposited in this blanket can than be used to produce steam for a conven­tional electrical generator. The tritium produced in the reac­tions

n + 7Li ------------> 3H + 4He + n

n + 6Li ------------> 3H + 4He

can be extracted and reused.

The Tokamak fusion test reactor (TFTR) at Princeton as shown, has operated with a particle density n = 3 x 1019 m-3 at a temperature such that kT = 1.5 keV, and a confinement time τ = 300 ms. Therefore the product in Law­son's criterion is nτ ≈ 1019 s/m3. In order for such a reactor to produce a 1000-MW electrical output, it would require a plasma temperature such that kT = 15 keV and the Lawson product to be nτ > 1020 s/m3.

In a driven fusion reaction, energy is continuously sup­plied to the plasma. However, in a D-T reaction, 20% of the kinetic energy is carried away by the alpha particle. These parti­cles may also be used to heat the plasma. If the plasma reaches the ignition temperature, it becomes self-sustain­ing.

Inertial Confinement

In the inertial confinement approach the fuel is in the form of tiny pellets, of diameter less than 1 mm, that contain a mixture of deuterium and tritium. In the NOVA system at Livermore, California, 0.1 ns pulses from 10 neodymium-doped glass lasers (operating at 1.05 µm) deliver about 200 kJ in 1 ns to each pellet. (This corre­sponds to a power of 2 x 1014 W, which is greater than the generating capacity of all the stations in the US!) The sur­face of the pellet vaporizes. As it expands, it sends a shock wave inward, which increases the density of the core by a factor of 103 and raises its temperature to over 108 K. This occurs within 1.5 ns, before the particles are able to dis­perse. That is, they are confined by their own inertia. The density of the pellet reaches 103 g/cm3 and its pressure reaches 1012 atm (1017 Pa)-which is greater than the pres­sure in the interior of stars. In a sense these are tiny hydro­gen bombs. A continuous supply of power would be pro­duced by fusing about 20-50 pellets each second. Charged particles, ions or electrons, may also be used in­stead of laser beams.

2- Prospects for Fusion Energy

There are several desirable features of fusion power. Deuterium (D) is easily extracted from sea water, where its concentration is 1/6500 of normal hydrogen atoms. Al­though tritium (T) is scarce and costly ($20 per kg), it can be produced by the bombardment of Li by neutrons, as we noted earlier. A "runaway" reaction is not possible be­cause of the Iow quantity of fuel present at any time. If the magnets or other systems fail, the plasma simply disap­pears. Radioactive wastes are less of a problem than with fission reactors. Tritium is toxic, but it has a relatively short half-life of 12.3 y. If fusion reactors become viable, we will have tapped the energy source of the stars.

When work on fusion power began in the 1950s, researchers confidently pre­dicted that limitless energy sources would be available in a few decades. But plasma confinement and heating have proved more complex and subtle than expected, and the newer inertial confinement scheme has revealed its own technical problems. Nevertheless, the promise of nearly unlimited energy-a gallon of seawater equivalent to more than 300 gallons of gasoline remains, and progress toward controlled fusion continues. An important milestone was reached in 1991, when the Joint European Torus in England produced some 2 MW of fusion power for several seconds.

Once controlled fusion proves scientifically feasible, there will remain formidable engineering challenges in the design of a practical fusion power plant. The intense neutron fluxes from D-T fusion cause severe degradation of the materials comprising the reaction chamber walls.

Furthermore, neutron­capture reactions produce radioactive isotopes within the walls, greatly compli­cating maintenance procedures. Although fusion does not produce the problem of radioactive materials present in fission products, handling of radioactivity especially from D-T reactions-is still a formidable problem. Heat from D-T fusion would be extracted by a heat-transfer medium, then used to drive a conventional steam turbine and generator. The figure shows a possible design for a D-T fusion power plant.

The first practical fusion power plants are likely to use D-T fusion because its ignition temperature and Lawson criterion are much lower than for D-D fusion. But the D-D reaction promises cleaner and more efficient power product­ion. With D-D fusion there is no radioactive tritium fuel. And a look at the D-D reactions (Equations, 5&6) shows that one of the reactions produces protons instead of neutrons. Thus there is less neutron-induced radioactivity. Furthermore, high-energy protons can be extracted and passed through a mag­netohydrodynamic generator, a device that uses electromagnetic induction to convert charged-particle energy directly into electricity. Use of MHD generators would bypass the conventional steam cycle and greatly increase the thermody­namic efficiency of the power plant. Even as they strive to make D-T fusion a reality, many fusion researchers have their eyes on a more distant future where D-D fusion provides much of our energy.

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