MATHEMATICAL LOGIC: Nuclear Fusing with Lasers

Wednesday, October 18, 2023

Nuclear Fusing with Lasers

 Fusion is a process in which atoms of two elements are compressed to such an extent that their nuclei fuse together and a new element is produced, whose mass is less than the sum of the masses of the two elements. The difference in mass is converted into energy in accordance with Einstein's equation E = mc2.

For example, if one gram of mass is converted into energy, 9×1011 Joules of energy will be released, which is equal to the energy generated by 1000 MW power station run continuously for 25 hours. The enormous amount of energy released from the sun is due to fusion of hydrogen brought about by gravitational forces. The sun produces energy of the order of 3×1026 Joules/sec.

Fusion also is a source of energy in stars. The potential of controlled thermonuclear fusion, as an inexhaustible source of energy, is now well established.

For the nuclei to fuse together a way must be found to overcome the mutual electrostatic repulsion or Coulomb repulsive barrier between the proton clouds of the two nuclei. This could be done by heating the matter to such a high temperature (~10 K) that the thermal velocity imparted to the nuclei is sufficient to overcome the mutual electrostatic repulsion. Matter at such high temperature comprises a mixture of electrons and ions (i.e.,) a plasma.

The fusion power released at such a high temperature is much greater than the energy lost by radiation. However, for the release of a sufficient amount of thermonuclear energy and to sustain fusion reaction, it is necessary to confine the hot plasma, so that the fusion reaction continues for a long time. The laser has the potential to generate very high temperature and pressure required to initiate a fusion reaction and to concentrate large amount of energy in a small volume and hence, can be an extremely useful tool in bringing about a fusion reaction.





In a typical scheme, a pea-sized target pellet, a fraction of a millimetre in diameter containing fusion fuel - usually a deuterium-tritium mixture- is projected into a reaction chamber, where it is suddenly irradiated with intense, high-energy laser beam. A pulse of 1ns duration develops a power density of ~1016 cm2 at the pellet surface. As the surface of the target blasts away, the rocket like reaction forces implode the target's interior to densities (~1,000 times liquid density) and temperature (~100,000,000°C) sufficient to cause the nuclei to fuse, releasing a large amount of thermonuclear energy in accordance with the equation

D + T ⟶ 4He + n + 17.6 MeV

, where n represents a neutron.

For both inertial and magnetic fusion, burn efficiency (i.e.,) the percentage of nuclei that fuse is proportional to the product of density and confinement time. In magnetic fusion, the fuel density is limited by material properties, so the efficiency of the burn is increased by extending the duration of confinement. In inertial fusion, Newton's laws and thermal velocity limit the confinement time, so the fuel is compressed to higher densities.


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