Absorption of neutrons and the

The time between neutron generations is the time between a neutron being produced and the time it is absorbed, into either a fissile or non-fissile nucleus. In reality this time interval will vary between individual neutrons, but we will make the simplifying assumption that the lifetime of all neutrons may be characterized by the average neutron lifetime, /, which is typically 1 millisecond in a commercial thermal reactor. Neutrons are being bom continuously in a reactor, and we may assume that at any instant of time the neutrons have a uniform spread of all ages between 0 and I seconds. Let us divide the neutron lifetime. /, into a large number, M, of time intervals. Si, where 

considering a typical region of the reactor core of volume Im, we divide the n neutrons (prompt and delayed) it contains at the start of the current generation into M groups, each of which contains ttc neutrons that are within Si of eachother in age, where 

Substituting this back into equation (21.13) gives  

Making M very large (which presents no problem, as has been noted) means that Si - 0, allowing equation (21.15) to be replaced by the differential equation for the rate of loss of neutrons in the reactor by absorption  

Turning now to the prompt neutrons formed, let us name the increase in prompt neutrons immediately following an absorption event Snp, so that we have 

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