Lawson's criterion

A fusion reactor is designed to produce energy from nuclear fusion in a controlled way.we wish to investigate the conditions under which this is possible.

1)A proposed fusion reactor is based on deuterium-tritium fusion (D-T reaction).

It's quite apparent that such a reaction generally needs very high temperatures.

Under such temperature s,the atoms are fully ionized and the fuel assembly is plasma. The hot plasma will lose energy by striking against the wall of the container and melt it, so a major technological challenge is to confine the plasma to the interior of the container.Suppose by some technique the plasma is confined for a short time. Then the energy released per unit volume from fusion is $(1/k){n}^{2}zvQt$ , Where $n$ is the electron no. density(densities of D-T ions are assumed to be equal), $z$ is the cross section for the fusion reaction, $v$ is the speed of the ions and t the confinement time.(to elaborate, $z$ means probability of fusion reaction per unit time per unit flux of incident beam on a single target nucleus.

Flux is the number of particles crossing a unit area in a unit time. $Q$ denotes the energy released from a single D-T reaction.

Note that a D-T reaction gives helium and neutron.

Find $k^2$ .

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Source: Inpho-2000.