Mod-01 Lec-38 Nuclear fusion Contd..

So, in the last lecture we talked about thermonuclear fusion and we discussed that the most important parameter is reaction rate. That is how many fusion reactions take place per unit volume per unit time? If a particular plasma concentration is confined in a certain volume at certain temperature and I gave you an expression and promised that I will justify it in this lecture.

And the expression was that reaction rate would be something like the concentration of the 2 interacting species and then average value of sigma v. So, this is reaction rate n x n y x and y are the 2 nuclear species which are fusing which are doing that fusion reaction. So, x plus y is going to z and possibly some other particle gamma particle or a small

nucleon or something. So, this x and y and this n x n y are the concentrations that means number of nuclei, number of x nuclei per unit volume and similarly, this n y is number of y nuclei per unit volume sigma is the cross section

for that particular reaction. Roughly speaking sigma you can take as an area presented by x nucleus. And if this y nucleus hits that area the fusion reaction takes place that is how we define cross section? We remember cross section is in units of centimeter square. It is an area unit. So, if you have nucleus

x and another nucleus y here and if they are coming towards each other you can take x relative to x y is coming and then this x mentally you think that this is an area. This area surrounding this x nucleus and if this y hits somewhere in this area the reaction will take place so that, is how the cross section is geometrically conceived so that,