When a fissile atom is hit with a neutron with the right amount of energy, the atom will go into an excited state where it oscillates and wobbles, eventually wobbling too much (kind of like resonating), and stretch into a dumbbell shape far enough apart that the “strong” nuclear force can no longer hold it together and it splits apart.
The first neutron can come from spontaneous fission (the atom randomly splits). However spontaneous fast fission doesn’t make enough neutrons for us to safely monitor and control the reactor during startup. For the first startup of a fresh core we insert a neutron source like californium -252 to help boost the neutron count high enough so that we can monitor the startup and control it.
After the first startup, the fuel is irradiated and the nuclear waste products produce enough neutrons as they break down. The nuclear waste byproducts in the irradiated fuel supply the neutrons. We can take the sources out and we only need to put them back in if the core is shut down for many years or if the core is replaced with entirely fresh fuel
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