P
th
fV
3.12 x 1010
fissions
watt sec
Reactor Theory (Neutron Characteristics)
DOE-HDBK-1019/1-93
REACTION RATES
Rev. 0
Page 21
NP-02
The power released in a reactor can be calculated based on Equation (2-6). Multiplying the
reaction rate by the volume of the reactor results in the total fission rate for the entire reactor.
Dividing by the number of fissions per watt-sec results in the power released by fission in the
reactor in units of watts. This relationship is shown mathematically in Equation (2-7) below.
(2-7)
where:
P
= power (watts)
= thermal neutron flux (neutrons/cm -sec)
th
2
= macroscopic cross section for fission (cm )
f
-1
V
= volume of core (cm )3
Relationship Between Neutron Flux and Reactor Power
In an operating reactor the volume of the reactor is constant. Over a relatively short period of
time (days or weeks), the number density of the fuel atoms is also relatively constant. Since the
atom density and microscopic cross section are constant, the macroscopic cross section must also
be constant. Examining Equation (2-7), it is apparent that if the reactor volume and macroscopic
cross section are constant, then the reactor power and the neutron flux are directly proportional.
This is true for day-to-day operation. The neutron flux for a given power level will increase very
slowly over a period of months due to the burnup of the fuel and resulting decrease in atom
density and macroscopic cross section.
