Suppose that a fuel pellet in a laser fusion device is made of a liquid deuterium-tritium mixture containing equal numbers of deuterium and tritium atoms. The density of the uncompressed pellet is and the uncompressed radius of the fuel pellet is . Suppose that the compressed fuel pellet “burns” with an efficiency of 10%. That is, only 10% of the deuterons and 10% of the tritons participate in the fusion reaction

We have to calculate (a) the amount of energy is that would be released when the pellet is compressed with lasers so that fusion takes place. (b) We have to express this energy in equivalent of TNT. The heat of combustion of TNT is . (c) If a fusion reactor is constructed on the basis of 100 micro-explosions per second of pellets, we have to calculate the power of the reactor. (Note that part of this power must be used to operate the lasers.)

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(a)

Let the number of deuterium or the equal number of tritium atoms per 1 be n. The density of the uncompressed deuterium-tritium mixture containing equal numbers of deuterium and tritium atoms is . Let mass of a deuterium atom be and mass of a tritium atom be . We thus have

The radius of a fuel pellet is . Therefore, the total number of atoms (or equal number of atoms) contained in the pellet will be

We assume that deuterons and tritons fuse with each other as per the process

.

The Q value for this process is 17.59 MeV. Assuming that the compressed fuel pellet “burns” with an efficiency of 10%, the energy released due to fusion in each pellet will therefore be

(b)

The amount of fusion energy per pellet in unit of TNT will be

(c)

If the fusion reactor is constructed on the basis of 100 micro-explosions per second of pellets, the power generated in the reactor will be