Reactor Theory (Reactor Operations) DOE-HDBK-1019/2-93 SUBCRITICAL MULTIPLICATION SUBCRITICAL MULTIPLICATION Subcritical  multiplication  is  the  phenomenon  that  accounts  for  the  changes  in neutron flux  that takes  place in  a subcritical  reactor due  to reactivity  changes. It  is  important  to  understand  subcritical  multiplication  in  order  to  understand reactor response to changes in conditions. EO  1.1 DEFINE  the  following  terms: a. Subcritical  multiplication b. Subcritical  multiplication  factor EO  1.2 Given  a  neutron  source  strength  and  a  subcritical  system  of known  k_eff, CALCULATE  the  steady-state  neutron  level. EO  1.3 Given  an  initial  count  rate  and  k_eff,  CALCULATE  the  final count rate that will result from the addition of a known amount of  reactivity. EO  1.4 Given     count     rates     vs.     the     parameter     being     adjusted, ESTIMATE  the  value  of  the  parameter  at  which  the  reactor will  become  critical  through  the  use  of  a  1/M  plot. Subcritical  Multiplication  Factor When a reactor is  in a shutdown condition, neutrons are still present to interact with the fuel. These source neutrons are produced by a variety of methods that were discussed in   Module 2. If neutrons and fissionable material are present in the reactor, fission will take place.  Therefore, a reactor will always be producing a small number of fissions even when it is shutdown. Consider a reactor in which k_eff is 0.6.  If 100 neutrons are suddenly introduced into the reactor, these 100 neutrons that start the current generation will produce 60 neutrons (100 x 0.6) from fission  to  start  the  next  generation. The  60  neutrons  that  start  the  second  generation  will produce 36 neutrons (60 x 0.6) to start the third generation.   The number of neutrons produced by  fission  in  subsequent  generations  due  to  the  introduction  of  100  source  neutrons  into  the reactor is shown below. Generation 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th Neutrons 100 60 36 22 13 8 5 3 2 1 0 0 Rev. 0 NP-04 Page 1