A civil nuclear reaction remains on the principle that uranium fission drives to production of neutrons that then create another uranium fission and so on. The reaction is controlled by various mechanism (bore, temperature, etc.).
But then, in a civil nuclear reaction, how the very first nuclear fission or uranium starts : is it spontaneous, or is it induced by a given mechanism (which one ?)? Do we launch a neutron to start it ?
There are two ways commonly used to "start" the chain reaction in operating nuclear power plants.
The first way uses the fact that you have quite a bit of exposed/burned fuel that emit neutrons. These can come from a number of reaction including spontaneous fission, gamma/neutron reactions, etc. You can also get spontaneous fissions from higher actinides that have build up.
The second way is to use a neutron source. One common source is antimony-beryllium. The antimony is irradiated during the power cycle and decays emitting high energy gammas. The high energy gammas react with the beryllium to create neutrons. Note that you have to irradiate the antimony to "charge" the source.
A third option, which is usually only used in the first cycle when all the fuel is fresh, is a californium source that has a high spontaneous fission rate. The problem with the californium source is that it will "burn out" if left in the reactor during power operations.
Some utilities use a neutron source, others rely on spent fuel activity. Neutron sources have other uses also. When loading the fuel, the detectors provide an adequate signal to detectors so they can detect incorrect loading patterns.
It is spontaneous. All it takes is the spontaneous decay of one atom, and conditions that result in the neutrons from any decay to be absorbed by and cause the decay of more atoms, resulting in the release if more neutrons. As long as the net gain is greater than 1, a chain reaction will proceed.
This is similar to what happens in a laser. Lasing occurs when and if the net amplification (gain) exceeds 1.
In both cases, the reaction rate increases exponentially until other effects reduce the gain to precisely 1.
You need one initial neutron, and after that the number of neutrons in the chain reaction grows exponentially. Neutrons are not a common component of natural background radiation on the earth's surface, so the initial neutron has to come from spontaneous fission within the fuel. The main isotopes used as fuel in nuclear reactors decay almost entirely by alpha decay and have extremely small probabilities of spontaneous fission, but it's not a zero probability: https://en.wikipedia.org/wiki/Spontaneous_fission A reactor's fuel will have a mixture of uranium and plutonium isotopes, and although some may be present only in trace amounts, they may contribute disproportionately to the number of neutrons from spontaneous fission if their probability of spontaneous fission is high or if their half-life is short. The typical time between emission of neutrons from spontaneous fission in a critical mass is on the order of milliseconds. (In gun-type bombs, this is inconveniently short.)
