I don't know enough about this. Are you familiar with the "gun method"?
The other type, the "implosion" device, uses a sphere of explosive lenses to compress a chunk of plutonium to achieve critical mass.
Both methods work. The sphere method has a more efficient yield, but the gun is simpler to design and build.
Hiroshima was a uranium gun weapon (Little Boy) and Nagasaki was a plutonium implosion weapon (Fat Man). The Trinity test explosion in New Mexico was identical to the device used over Nagasaki.