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A nuclear chain reaction occurs when neutron amounts are multiplied by fission. A neutron triggers a fission, which causes the fissioned atom to release multiple neutrons. If of those multiple neutrons, one on average causes another fission, we have a controlled nuclear chain reaction such as in a nuclear reactor, whereas nuclear explosives have an exponential multiplication due to more than one of the released neutrons causing other fissions.

However, what I have always wondered about nuclear chain reactions is: how does the chain reaction start? There has to be a neutron somewhere starting the chain reaction.

According to Wikipedia article about free neutron decay if there happens to be a free neutron somewhere, it has a half-life of only 10 minutes and after that time decays to proton and electron (and a neutrino). So, based on this, free neutrons should be really rare -- after all, the universe is over 13 billion years old so any remaining free neutrons should have had about 0.7*1015 half-lives to decay.

There are obviously some processes that release new neutrons. For example, some atoms can spontaneously fission. In plutonium-239 bombs, there is always some amount of plutonium-240 present that releases neutrons due to spontaneous fission. Thus, any nuclear explosive made of plutonium needs to be assembled to above critical mass extremely rapidly and the percentage of plutonium-240 must be kept low, or else the chain reaction starts too early, when the mass is not yet above the critical mass by a sufficiently large margin.

However, uranium-235 bombs and nuclear reactors that today mostly burn enriched uranium-235 should not initially have any plutonium-240 when loaded with the fuel. Obviously plutonium-240 is later formed due to two neutron captures by uranium-238, but initially it should not be present. Also fission products may emit delayed neutrons but when the reactor is initially loaded with fuel, there should be no fission products nearby.

So, how does a nuclear chain reaction start? How does the first neutron reach the critical mass of a fissionable material?

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    $\begingroup$ Btw, free neutrons are created all the time by cosmic radiation, but they are quickly captured on other nuclei after a couple of milliseconds. The half-life of neutrons is only relevant in vacuum $\endgroup$ – Sentry Mar 27 at 15:59
  • $\begingroup$ @Sentry I didn't know that. I mainly thought about free neutrons being a part of cosmic radiation (which they can't be as they would quickly decay). Is there some source that would tell more about the creation of free neutrons by cosmic radiation? $\endgroup$ – juhist Mar 27 at 16:12
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    $\begingroup$ Free neutrons can be produced by a process called "nuclear spallation", I'd start there. The process happens in the atmosphere when high-energy protons collide with nuclei (cosmic ray spallation) and is also used to artificially produce neutrons (spallation neutron source), where beams from a particle accelerator are shot onto a heavy target material. $\endgroup$ – Sentry Mar 27 at 16:41
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However, uranium-235 bombs and nuclear reactors that today mostly burn enriched uranium-235 should not initially have any plutonium-240 when loaded with the fuel.

Spontaneous fission is not exclusive to plutonium-240. Uranium, thorium and the transuranium elements (including all plutonium isotopes) also have a small chance of undergoing spontaneous fission. So there is always a chance that somewhere in your assembly the first neutron is created and a chain reaction is started.

In practice, however, fission chain reactions in nuclear reactors are often started by inserting a neutron source into the core.

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In an atomic bomb, the fissionable bomb material is always spontaneously fissioning and thereby generating neutrons- but the shape of the uranium or plutonium material is such that most of the neutrons escape without causing more fissions. For example, you can split the critical mass of uranium into two hemispheres and set them far enough apart that the neutrons emitted by one will not trigger fissions in the other.

To set off the bomb, you trigger conventional explosives that squeeze the pieces together and once the chunk of material is nearly spherical, the neutrons have to trigger more fissions before they can escape. Since one fission generates (on average) slightly more than two free neutrons, the fission process then "runs away" and within a microsecond or so, the whole bomb explodes.

You can also manufacture the fissionable material shaped like a oblong egg-shape and then use explosives to press it into a spherical shape, or shape the material into a hollow sphere and surround it with explosives to crush it into a spherical shape.

To guarantee that the bomb explodes as intended, it is also common to place inside it a neutron source which when activated produces a quick and intense flash of neutrons right in the center of the bomb at the moment that the explosives crush the fissionable material.

Early bomb designs used a neutron source consisting of beryllium and polonium which were mixed together by the crushing of the surrounding fissionable material by the explosives. The alpha particles spontaneously emitted by the polonium then struck the beryllium nuclei, causing them to emit neutrons. Those neutrons then guaranteed the prompt criticality of the fissionable mass.

The activity of the polonium decays significantly with time, meaning that its effectiveness diminishes during storage of the weapon, and so it had to be replentished. Later bomb designs used neutron generators external to the fissionable core mass which shot neutrons into it upon being triggered, which were more easily disassembled for replentishment.

The most modern designs use miniature particle accelerators which shoot protons at targets which yield high-energy neutrons, which are then piped into the core. These pulsed neutron sources do not require periodic replentishment since they contain no polonium.

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