How does a fission chain reaction grow so rapidly in an atomic bomb?

In an atomic bomb, a fission chain reaction grows rapidly because the device is designed to be highly supercritical, meaning the multiplication factor, k, is significantly greater than unity.1

The multiplication factor k represents the ratio of fissions in one generation to those in the preceding one. When k > 1, the number of fissions increases exponentially at each step. To maximize the speed and intensity of this growth, the bomb is engineered to keep the time between successive neutron generations as short as possible.1

This rapid, divergent reaction is achieved by ensuring that more than one neutron from each fission event successfully induces fission in another nucleus. By utilizing a supercritical mass of fissile material—often shaped into a sphere to minimize neutron escape—and potentially compressing the core to increase density, the device ensures that emitted neutrons are highly likely to strike other nuclei before escaping. This process releases a massive amount of energy within a fraction of a second, resulting in a devastating nuclear explosion.123