SUBCRITICAL MULTIPLICATION DOE-HDBK-1019/2-93 Reactor Theory (Reactor Operations) Solution: Step 1: Determine the initial value of k_eff for the core. k₁    1 1      r₁ 1 1      (  0.01000) 0.9901 Step 2: Determine the final value of k_eff for the core.  The final value of reactivity will be -500 pcm (-1000 + 500). k₂    1 1      r₂ 1 1      (  0.00500) 0.9950 Step 3: Use Equation (4-4) to determine the final count rate.        CR₁ CR₂ 1      k₂ 1      k₁ CR₂       CR₁ 1      k₁ 1      k₂ 42  cps                 1      0.9901 1      0.9950 83  cps Notice from this example that the count rate doubled as the reactivity was halved (e.g., reactivity was changed from -1000 pcm to -500 pcm). Use  of  1/M  Plots Because  the  subcritical  multiplication  factor  is  related  to  the  value  of  k_eff,  it  is  possible  to monitor the approach to criticality through the use of the subcritical multiplication factor.   As positive reactivity is added to a subcritical reactor, k_eff will get nearer to one.  As k_eff gets nearer to  one,  the  subcritical  multiplication  factor  (M)  gets  larger.    The  closer  the  reactor  is  to criticality, the faster M will increase for equal step insertions of positive reactivity.   When the reactor becomes critical, M will be infinitely large.   For this reason, monitoring and plotting M during  an  approach  to  criticality  is  impractical  because  there  is  no  value  of  M  at  which  the reactor clearly becomes critical. NP-04 Rev. 0 Page 6