Reactor Theory (Nuclear Parameters)   DOE-HDBK-1019/2-93 REACTIVITY Reactivity  Coefficients  and  Reactivity  Defects The  amount  of  reactivity  (r)  in  a  reactor  core  determines  what  the  neutron  population,  and consequently the reactor power, are doing at any given time.   The reactivity can be effected by many factors (for example, fuel depletion, temperature, pressure, or poisons).   The next several chapters  discuss  the  factors  affecting  reactivity  and  how  they  are  used  to  control  or  predict reactor behavior. To quantify the effect that a variation in parameter (that is, increase in temperature, control rod insertion,  increase  in   neutron  poison)  will  have  on  the  reactivity   of  the  core,  reactivity coefficients are used.   Reactivity coefficients are the amount that the reactivity will change for a given change in the parameter.   For instance, an increase in moderator temperature will cause a decrease in the reactivity of the core.   The amount of reactivity change per degree change in the  moderator  temperature  is  the  moderator  temperature  coefficient.    Typical  units  for  the moderator temperature coefficient are pcm/^oF.   Reactivity coefficients are generally symbolized by a_x, where x represents some variable reactor parameter that affects reactivity.  The definition of a reactivity coefficient in equation format is shown below. ax   ^D r D x If the parameter x increases and positive reactivity is added, then a_x is positive.  If the parameter x increases and negative reactivity is added, then a_x is negative. Reactivity  defects  (Dr)  are  the  total  reactivity  change  caused  by  a  variation  in  a  parameter. Reactivity defects can be determined by multiplying the change in the parameter by the average value  of  the  reactivity  coefficient  for  that  parameter.   The  equation  below  shows  the  general method for relating reactivity coefficients to reactivity defects. Dr = ax Dx Example: The  moderator  temperature  coefficient  for  a  reactor  is  -8.2  pcm/^oF.     Calculate  the reactivity defect that results from a temperature decrease of 5^oF. Solution: D r    aT  D T 8.2        pcm °F 5  °F 41  pcm The  reactivity  addition  due  to  the  temperature  decrease  was  positive  because  of  the negative temperature coefficient. Rev. 0 NP-03 Page 21