Page 263 - Dynamics and Control of Nuclear Reactors

264 APPENDIX C Basic reactor physics

For example, for a moderator temperature of 300 °C, the effective fission cross sec-
tion of U-235 is 348 b (compared to σ f (20 °C) of 549 b).
The result is

P=m f ¼ 2:948 10 10 σ f 293Þ xT 0:5 =M f xϕ
ð
For a fuel enrichment of ε, the specific power is usually expressed as power/mass of
total uranium

P=m U ¼ 2:948 x10 10 x ε x σ f 293Þ xT 0:5 =M f x ϕ
ð
or
10 0:5
ϕ ¼ P=m U Þ= 2:948 x 10 xε x σ f 293Þ xT =M f
ð
ð
where
m U ¼mass of total uranium in the reactor.
For example, for fuel with an enrichment of 3% and a specific power of 30 kw/kg
2
of U, the flux is 3.47 10 13 neutrons/(cm s).

C.7 Neutron lifetime and generation time
The total neutron lifetime, l, is given by
(C.12)
l ¼ l s + l th

l s ¼slowing down time ( 10 7 s).
4
l th ¼ thermal lifetime ( 10 s).
Slowing down time is the time a neutron spends in slowing from fission to thermal
energies. Thermal lifetime is the time a neutron spends diffusing at thermal energies
before absorption by a fissile nucleus.
A quantity called the neutron generation time is also used in the reactor kinetics
equations. Neutron lifetime and generation time are equal in a critical reactor. The
two quantities have slightly different (but inconsequential) definitions for an
unsteady state reactor. The only significant impact is in determining the form of
the kinetics equations (see Chapter 3). The neutron lifetime (or generation time)
4
is around 10 –10 5 s for light water reactors (PWRs, BWRs).

C.8 Multiplication factor and reactivity
In a nuclear power reactor, the fission reaction is maintained (regulated) to give
a desired power level. In a steady-state reactor, the number of neutrons from one
generation to the next generation (an interval of one generation time) remains
constant.