SUBCRITICAL MULTIPLICATION DOE-HDBK-1019/2-93 Reactor Theory (Reactor Operations) Because the reactor is subcritical, neutrons introduced in the reactor will have a decreasing effect on  each  subsequent  generation.    The  addition  of  source  neutrons  to  the  reactor  containing fissionable material has the effect of maintaining a much higher stable neutron level due to the fissions occurring than the neutron level that would result from the source neutrons alone.  The effects of adding source neutrons at a rate of 100 neutrons per generation to a reactor with a k_eff of 0.6 are shown below. Generation 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 100 60 36 22 13 8 5 3 2 1 0 0 100 60 36 22 13 8 5 3 2 1 0 100 60 36 22 13 8 5 3 2 1 100 60 36 22 13 8 5 3 2 100 60 36 22 13 8 5 3 100 60 36 22 13 8 5 100 60 36 22 13 8 100 60 36 22 13 100 60 36 22 100 60 36 100 60 100 Total n 100 160 196 218 231 239 244 247 249 250 250 ... A  neutron  source  strength  of  100  neutrons  per  generation  will  result  in  250  neutrons  per generation being produced from a combination of sources and fission in a shutdown reactor with a  k_eff  of  0.6.    If  the  value  of  k_eff  were  higher,  the  source  neutrons  would  produce  a  greater number  of fission  neutrons  and  their  effects  would  be felt  for  a larger  number of  subsequent generations after their addition to the reactor. The effect of fissions in the fuel increasing the effective source strength of a reactor with a k_eff of less than one is subcritical multiplication.   For a given value of k_eff there exists a subcritical multiplication  factor  (M)  that  relates  the  source  level  to  the  steady-state  neutron  level  of  the core.  If the value of k_eff is known, the amount that the neutron source strength will be multiplied (M) can easily be determined by Equation (4-1). (4-1) M   1 1      k_eff NP-04 Rev. 0 Page 2