Reactor Theory (Nuclear Parameters) DOE-HDBK-1019/2-93 NEUTRON LIFE CYCLE When  the  multiplication  factor  of  a  reactor  is  not  equal  to  exactly  one,  the  neutron  flux  will change and cause a change in the power level.   Therefore, it is  essential to know more about how this factor depends upon the contents and construction of the reactor.  The balance between production of neutrons and their absorption in the core and leakage out of the core determines the  value  of  the  multiplication  factor.    If  the  leakage  is  small  enough  to  be  neglected,  the multiplication factor depends upon only the balance between production and absorption, and is called the infinite multiplication factor (k ) since an infinitely large core can have no leakage. When the leakage is included, the factor is called the effective multiplication factor (k_eff). The effective multiplication factor (k_eff) for a finite reactor may be expressed mathematically in terms of the infinite multiplication factor and two additional factors which account for neutron leakage as shown below. k_eff   =   k f t Fast  Non-Leakage  Probability  ( _f) In a realistic reactor of finite size, some of the fast neutrons leak out of the boundaries of the reactor core before they begin the slowing down process.  The fast non-leakage probability ( _f) is defined as the ratio of the number of fast neutrons that do not leak from the reactor core to the number of fast neutrons produced by all fissions.   This ratio is stated as follows. f    number  of  fast  neutrons  that  do  not  leak  from  reactor number  of  fast  neutrons  produced  by  all  fissions Thermal  Non-Leakage  Probability  ( _t) Neutrons  can  also  leak  out  of  a  finite  reactor  core  after  they  reach  thermal  energies.    The thermal non-leakage  probability ( _t) is defined as the ratio of the number of thermal neutrons that do not leak from the reactor core to the number of neutrons that reach thermal energies.  The thermal non-leakage probability is represented by the following. t    number  of  thermal  neutrons  that  do  not  leak  from  reactor number  of  neutrons  that  reach  thermal  energies The  fast  non-leakage  probability  ( _f)  and  the  thermal  non-leakage  probability  ( _t)  may  be combined into one term that gives the fraction of all neutrons that do not leak out of the reactor core.   This term is called the total non-leakage  probability and is given the symbol _T, where T = f    t .    _f and _t are both effected by a change in coolant temperature in a heterogeneous water-cooled, water-moderated reactor.  As coolant temperature rises, the coolant expands.  The density of the moderator is lower; therefore, neutrons must travel farther while slowing down. This effect increases the probability of leakage and thus decreases the non-leakage probability. Consequently,  the  temperature  coefficient  (defined  later)  for  the  non-leakage  probabilities  is negative, because as temperature rises, _f and _t decrease. Rev. 0 NP-03 Page 9