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A breeder reactor is a nuclear reactor that produces more fissile material than it consumes through a sustained chain reaction.

Core Requirements
Fissile fuel starter: You need an initial fissile material (like uranium-235 or plutonium-239) that can sustain a chain reaction when neutrons cause it to fission.

Fertile material blanket: The reactor is surrounded by or mixed with fertile material (like uranium-238 or thorium-232) that can absorb neutrons and convert into fissile material through nuclear transmutation.

Neutron economy: The key is producing more than 2 neutrons per fission on average. One neutron sustains the chain reaction, and the excess neutrons convert fertile material into new fissile fuel.