How is the number of neutrons in an assembly involved in creating a sustained nuclear chain reaction?

Answer 1

This answer can not be accurately answered without first knowing what type of nuclear reactor it is. A pressurized-water nuclear reactor is probably the most common so I'll briefly talk about some factors that affect the number of chain reactions in that type of nuclear reactor. First of all, the temperature of the water entering the reactor core will affect the number of chain reactions. The colder the water, the greater the number of reactions. This is primarily because the colder water is more dense and thus releases more neutrons which speeds up the chain reaction rate. Of course, reactor operators, wishing to control the number of chain reactions in order to make the reactor stable may raise or lower "rods" which will be made of a material that tends to absorb neutrons and thus lowering the chain reaction rate. These are the two most common factors affecting chain reaction rate. Would delve further into this question but it gets rather complicated at this point.

Answer 2

If the chain reaction is sustained at a steady power level, this means a steady rate of number of fissions per second, and so a steady number of total free neutrons in the reactor assembly, or at any place within it. The actual density of neutrons (the neutron flux) will vary from place to place, being less at the core boundaries due to leakage out of the active core.