Abstract
It is well known that the enormous energy released from the sun and the stars is due to thermonuclear fusion reactions, and scientists have been working for over 40 years to devise methods to generate fusion energy in a controlled manner. Once this is achieved, one will have an almost inexhaustible supply of relatively pollution-free energy. A thermonuclear reactor based on laser-induced fusion offers great promise for the future. With the tremendous effort being expended on fabrication of extremely high-power lasers, the goal appears to be not too far away, and once it is practically achieved, it would lead to the most important application of the laser.
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Notes
- 1.
Beyond the range of this short-range force, the forces are of Coulomb type.
- 2.
The binding energy is calculated using the famous Einstein mass–energy relation: \(E = mc^2\) where \(c\,\left( {\approx 3 \times 10^{10}{\textrm{cm}}/\textrm{s}}\right)\) is the speed of light in free space. If Z and N represent the number of protons and of neutrons, respectively, inside the nucleus, then the total binding energy Δ will be given as
$$\Delta = \left( {Zm_{\textrm{p}} + Nm_{\textrm{n}} - M_{\textrm{A}} } \right)c^2$$where m n, m p, and M A represent the masses of the neutron, the proton, and the atomic nucleus, respectively. For example, the nucleus of the deuterium atom (which is known as the deuteron) has a mass of 2.01356 amu (1 amu ≈ 1.661 × 10–24 g, which is equivalent to 931.5 MeV). Since deuteron consists of one proton and one neutron, one obtains
$$\begin{array}{ll}\Delta &= \left( {1.00728 + 1.00866 - 2.01356} \right) \times 1.661 \times 10^{- 24} \times \left( {3 \times 10^{10} } \right)^2 {\textrm{erg}} \\ & = {3}{.56} \times {10}^{- 6} \times \left( {1.6 \times 10^{- 12} } \right)^{- 1} \times {10}^{- 6}\,{\textrm{MeV}} \\ & \approx {2}{.23}\,{\textrm{MeV}} \\ \end{array}$$which represents the binding energy of the deuteron. In the above equation, we have used 1.00728 and 1.00866 amu to represent the masses of proton and neutron, respectively.
- 3.
On the other hand, in a fission process, a loosely bound heavy nucleus splits into two tightly bound lighter nuclei, again resulting in the liberation of energy. For example, when a neutron is absorbed by a \({}_{92}{\textrm{U}}^{235}\) nucleus, the \({}_{92}{\textrm{U}}^{236}\) nucleus is formed in an excited state (the excitation energy is supplied by the binding energy of the absorbed neutron). This \({}_{92}{\textrm{U}}^{236}\) nucleus may undergo fission to form nuclei of intermediate mass numbers (like \({}_{56}{\textrm{B}}^{140}\) and \({}_{36}{\textrm{Kr}}^{93}\) along with three neutrons). The energy released in a typical fission reaction is about 200Â MeV.
- 4.
The nuclei are identified by symbols like \({}_{11}{\textrm{Na}}^{23}\); the subscript (which is usually omitted) represents the number of protons in the nucleus and the superscript represents the total number of nucleons in the nucleus. Thus \({}_{11}{\textrm{Na}}^{23}\) represents the sodium nucleus having 11 protons and 12 neutrons. Similarly \({}_1{\textrm{H}}^3\) represents the tritium nucleus having 1 proton and 2 neutrons.
- 5.
Equation (16.3) can also be written in the form
$${}_1{\textrm{H}}^2 + {}_1{\textrm{H}}^3 \to {}_2{\textrm{He}}^4 + {}_0{\textrm{n}}^1$$ - 6.
Temperatures of the order of 100 million K are required in fusion reactors; see Section 16.3.
- 7.
See, e.g., Booth et al. (1976).
- 8.
This is in contrast to fission reactions which are induced by neutrons which carry no charge. As such, even at room temperatures, there is a considerable probability for fission reactions to occur and hence it is relatively easy to construct a fission reactor. It may be mentioned that in a hydrogen bomb (where the fusion reactions are responsible for the liberation of energy), a fission bomb is first exploded to create the high temperatures required for fusion reactions to occur.
- 9.
In the sun (the energy of which is due to thermonuclear reactions), the plasma has a temperature of ≥ 10 million K and it is believed that the confinement is due to the gravitational forces.
- 10.
Since the masses of D and T nuclei are in the ratio of 2:3, the number of D nuclei will be
$$ \frac{{2\,M}}{5}\frac{1}{{M_{\textrm{d}} }} = \frac{{2\,M}}{5}\frac{1}{{2 \times 1.66 \times 10^{- 24} }}$$where \(M_{\textrm{d}}\,\left( {\approx 2 \times 1.66 \times 10^{- 23}\,{\textrm{g}}} \right)\) represents the mass of the deuteron; we have assumed equal numbers of D and T nuclei in the pellet. The energy released in a D–T reaction is 17.6 MeV [see Eq. (16.3)] and an additional 4.8 MeV is released when the neutron is absorbed by the lithium atoms in the blanket [see Eq. (16.15)] resulting in a net energy release of about 22 MeV. Thus, the output energy would be
$$E_{{\textrm{output}}} \approx f \times \frac{{2\,M}}{5} \times \frac{{22 \times 1.6 \times 10^{- 6} }}{{2 \times 1.66 \times 10^{- 24} }} \simeq 4.2 \times 10^{11} fM\,\,(J)$$ - 11.
For the kinetic energies to be about 10 keV (≈ 100 million K), the energy imparted would be
$$2 \times \left( {\frac{{2\,M \times 10 \times 10^3 \times 1.6 \times 10^{- 19} }}{{5 \times 2 \times 1.66 \times 10^{- 24} }}} \right)\, \approx 4 \times 10^8\,M\,\left( {\textrm{J}} \right)$$where M is in grams; the quantity inside the parentheses is the energy imparted to the deuteron, and the factor of 2 outside the parentheses is due to the fact that an equal energy has also to be imparted to tritium nuclei.
- 12.
The radiation pressure corresponding to an intensity of \(10^{17} {{\textrm{W}}/{{\textrm{cm}}^{2} }}\) is only about 108 atm.
- 13.
A compression ratio of a few thousand puts the laser energy requirement in the 105 J range (see Section 16.3).
- 14.
The time variation of the incident laser pulse was assumed to be roughly of the form \(\left( {t_0 - t} \right)^{- 2}\); thus the power varied from about 1011W at 10Â ns to 1015 W at 15Â ns.
- 15.
See, e.g., Kidder (1973).
- 16.
For details of other kinds of lasers used in fusion, see, e.g., Booth et al., (1976).
- 17.
Lithium is quite abundant and has good heat transfer properties.
- 18.
In addition, neutron multiplication will occur in the blanket through (n, 2n) reactions; these neutrons would further produce more tritium.
References
Booth, L. A., Freiwald, D. A., Frank, T. G., and Finch, F. T. (1976), Prospects of generating power with laser driven fusion, Proc. IEEE 64, 1460.
Brueckner, K. A., and Jorna, S. (1974), Laser driven fusion, Rev.Mod. Phys. 46(2), 325.
Kidder, R. E. (1973), Some aspects of controlled fusion by use of lasers, in Fundamental and Applied Laser Physics (M. S. Feld, A. Javan, and N. A. Kurnit, eds.), Wiley, New York.
Post, R. F. (1973), Prospects for fusion power, Phys. Today 26(4), 30.
Ribe, F. L. (1975), Fusion reactor systems, Rev. Mod. Phys. 47, 7.
Stickley, C. M. (1978), Laser fusion, Phys. Today 31(5),50.
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Thyagarajan, K., Ghatak, A. (2011). Laser-Induced Fusion. In: Lasers. Graduate Texts in Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6442-7_16
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