"A mechanism based on implosion provided the solution to this problem. In this design, the fissile material is shaped into a single sphere with a mass slightly less than critical. Layers of carefully shaped high explosives surround the sphere. When the explosives are detonated, the force of the shock wave compresses the fissile material into a smaller volume, forming a supercritical mass. This method of assembly is much faster than the gun-type mechanism and thus eliminates the problems resulting from spontaneous neutron emission of Pu-240. The spherical mass resulted in a pumpkin-shaped weapon called "Fat Man".
"To assure that a chain reaction occurs, an initiator is placed at the center of the sphere of fissile materials. It consists of a source of alpha particles, radioactive polonium, surrounded with thin aluminum foil. The foil-wrapped source is then surrounded with beryllium powder. When the initial explosion squeezes the fissile material into a supercritical mass, the foil breaks, allowing the alpha particles to reach the beryllium and produce the initial neutrons."
Source: http://www.chemcases.com/nuclear/nc-09.htm
It greatly increases the yield of a nuclear weapon.
You are correct. A neutron generator is essential to the design of smaller nuclear (fission) bombs.
>>>"neutron generator"
What was that thing that a scientist had buried under his rose bed at his home again? (Iraq)