Scienists are working hard to develop inclear fusion reactor Nocies of heavy hydrogen, \(_{\left({1}\right)}^{{{2}}}{H}\) , known as deuteron and denoted by \({D}\), can be thought of as a candidate for fusion rector . The \({D}-{D}\) reaction is \(_{\left({1}\right)}^{{{2}}}{H}{+_{{{1}}}^{{{2}}}}{H}{\rightarrow_{{{2}}}^{{{1}}}}{H}{e}+{n}+{e}\ne{r}{g}{y}\) in the core of fasion reactor a gas of heavy hydrogen of \(_{\left({1}\right)}^{{{2}}}{H}\) nucles and electrons is know as plasma . The nuclei move randonity in the reactor to take place Unally , the temperature in the reactor core are too ligh and to natrual will can be used to confine the to pleama for a time l_(0) before the particles by away from the case if \({n}\) is the denasity (number volume ) of determines , the product\({n}{t}_{{{0}}}\)is called Lavson number in one of the criteria , a reactor is termed successful if Lawson number is greater then \({5}\times{10}^{{{14}}}{s}/{c}{m}^{{{2}}}\)
it may be helpfull to use the following botczmann constant
\(\lambda={8.6}\times{10}^{{-{5}}}{e}{V}/{k},\frac{{{e}^{{{2}}}}}{{{4}\pi{s}_{{{0}}}}}={1.44}\times{10}^{{-{9}}}{e}{V}{m}\)
Result of calulations for fopur different desine of a fasion reactor using \({D}-{D}\) reaction are given below which of these is most promising based on Lawson crierion ?
(A) deuteron density \(={2.0}\times{10}^{{{12}}}{c}{m}^{{-{3}}}\),
confinement time \(={5.0}\times{10}^{{-{3}}}{s}\)
(B) deuteron density \(={8.0}\times{10}^{{{14}}}{c}{m}^{{-{3}}}\),
confinement time \(={9.0}\times{10}^{{-{1}}}{s}\)
(C) deuteron density \(={4.0}\times{10}^{{{23}}}{c}{m}^{{-{3}}}\),
confinement time \(={1.0}\times{10}^{{-{11}}}{s}\)
(D) deuteron density \(={1.0}\times{10}^{{{24}}}{c}{m}^{{-{3}}}\)
confinement time \(={4.0}\times{10}^{{-{12}}}{s}\)