In a fission reaction, a reactor has a neutron flux that’s between 10^10 and 10^13 neutrons per cm^2 passing through the cord every second. That’s an absolutely massive amount of neutrons.
The neutrons come from the fission reaction. Splitting an atom makes 1-7 neutrons (2.4 is the average) and in a steady state reactor those 2.4 neutrons bounce around and slow down and you lose 1.4 of them and the remaining 1 neutron causes another fission.
We are dealing with massive numbers of fissions and atoms though. Millions of billions per second in the entire core.
When you are shut down, the neutrons come from the nuclear waste products breaking down. If you have a brand new core or if the core was shutdown for years you usually will insert a neutron source like CF 252 which provides some starter neutrons to allow you to better control and monitor the reaction and essentially jump start the core.
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