SUBCRITICAL MULTIPLICATION DOE-HDBK-1019/2-93 Reactor Theory (Reactor Operations) If the term M in Equation (4-2) is replaced by the expression 1/1-k_eff from Equation (4-1), the following expression results. (4-3) N      S              1 1      k_eff Example: A  reactor  contains  a  neutron  source  that  produces  110,000  neutrons  per  second.   The reactor  has  a  k_eff  of  0.986.    Calculate  the  stable  total  neutron  production  rate  in  the reactor. Solution: The neutron production rate is calculated using Equation (4-3). N      S              1 1      k_eff 110,000               neutrons second                  1 1      0.986 7.86  x  10⁶                        neutrons second To this point it has been necessary to know the neutron source strength of the reactor in order to  use  the  concept  of  subcritical  multiplication.    In  most  reactors  the  actual  strength  of  the neutron  sources  is  difficult,  if  not  impossible,  to  determine.    Even  though  the  actual  source strength may not be known, it is still possible to relate the change in reactivity to a change in neutron level. Consider  a  reactor  at  two  different  times  when  k_eff  is  two  different  values,  k₁  and  k₂.    The neutron  level  at  each  time  can  be  determined  based  on  the  neutron  source  strength  and  the subcritical multiplication factor using Equation (4-3). N₁        S            1 1      k₁ N₂        S            1 1      k₂ NP-04 Rev. 0 Page 4