stray neutron that happens to be present in the core (for example from spontaneous fission of the fuel, from radioactive decay of fission products, or from a neutron source) will trigger an exponentially decaying chain reaction. Although the chain reaction is not self-sustaining, it acts as a multiplier that increases the equilibrium number of neutrons in the core. This subcritical multiplication effect can be used in two ways: as a probe of how close a core is to criticality, and as a way to generate fission power without the risks associated with a critical mass. If is the neutron multiplication factor of a subcritical core and is the number of neutrons coming per generation in the reactor from an external source, then at the instant when the neutron source is switched on, number of neutrons in the core will be . After 1 generation, this neutrons will produce neutrons in the reactor and reactor will have a totality of neutrons considering the newly entered neutrons in the reactor. Similarly after 2 generation, number of neutrons produced in the reactor will be and so on. This process will continue and after a long enough time, the number of neutrons in the reactor will be, This series will converge because for the subcritical core, . So the number of neutrons in the reactor will be simply, The fraction is called subcritical multiplication factor. Since power in a reactor is proportional to the number of neutrons present in the nuclear fuel material (material in which fission can occur), the power produced by such a subcritical core will also be proportional to the subcritical multiplication factor and the external source strength. As a measurement technique, subcritical multiplication was used during the Manhattan Project in early experiments to determine the minimum critical masses of 235U and of 239Pu. It is still used today to calibrate the controls for nuclear reactors during startup, as many effects (discussed in the following sections) can change the required control settings to achieve criticality in a reactor. As a power-generating technique, subcritical multiplication allows generation of nuclear power for fission where a critical assembly is undesirable for safety or other reasons. A subcritical assembly together with a neutron source can serve as a steady source of heat to generate power from fission. Including the effect of an external neutron source ("external" to the fission process, not physically external to the