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In the theory of power oscillations
in a circulating-fuel reactor, it is
now possible todemonstrate the damping
influence of the fuel circulation, even
if some of the previous assumptions
are replaced by considerably more
gene r a1 c ond i ti ons Spec i f i c a 11 y ,
it is no longer necessary to assume
that all particles of the fuel spend
the same time in the reactor and that
the fuel and power distributions are
constant over the reactor. The more
general condition (Eq. 11, which
replaces the old assumptions, covers,
among other things, the case in which
the power distribution is constant
only in the direction of flow, but not
necessarily in the direction perpen-
dicular to it, and in which there are
a number of alternate fuel paths, each
with a different fuel transit time.
In the field of reactor calcu-
lations, it was found that the slowing
down of neutfrons in parallel slabs of
ma te r i a 1 s w i t, h (1 i f f c ren t pro pe r t i e s
can be described, under some not too
unrealistic conditions, by a set of
images of the original neutron sourcee
The images are somewhat similar to
those which would be obtained if the
neutron source were replaced by a
light source and the interfaces between
the slabs were replaced by mirrors or
refracting surf aces e
For some time, attempts have been
made to obtain a better understanding
of the nuclear physics involved in the
temperature coefficient of reactivity.
These attempts have now resulted in an
explicit expression for the tempera-
ture dependence of a macroscopic
absorption cross section. The tempera-
ture dependence is caused by the
thermal motion of the atoms.
CalculaLions specifically carried
out for the ARE and Fireball Critical
Experiments are reported in connection
with these experiments (Sec. 5).
4. REACTOR PHYSICS
W. K. Ergen, ANP Division
PERIOD ENDING DECEMBER 10, 1952
OSCILLATIONS IN THE CIRCULATING
FUEL REACTOR
W. K. Ergen, ANP Division
It was shown previously' ') that ,
under certain conditions, the circu-
lation of the fuel introduces a damping
of power oscillations of a reactor.
These previous considerations have
since been generalized, and the
damping can still be demonstrated,
even if one drops the assumptions that
all particles of the fuel spend the
same time in the reactor and that the
flux and power distributions are
constant over the reactor.
The delayed neutrons are still
neglected, and it is still assumed
that a change AT of the average fuel
temperature T causes an instantaneous
change -dT in the reactivity and that
the inlet temperature is constant.
The old assumptions of constant fuel-
transit t i m e and constant flux and
power distribution are replaced by the
much more general condition that
* i
T = E P(t)
m
1
- J do- K b b P(t - 9) , (1)
0
where E is a positive constant associ-
ated with the reciprocal heat capacity
and P is the reactor power. The
kernel K(G) has the property dK/dcr $ 0,
and, for CT greater than some fixed
value A, K ( D ) = 0. The t e r m EP
cor re s ponds to the ins tan t aneous
increase in reactor temperature due to
the power generation. The integral
("W. K. Ergen, ANP Quar. Yrog. Kep. March 10,
1952, ORNL-1227, p. 41; S. Tamor, ANP Quar. Prog.
Rep. June 10. 1952. ORNL-1294, p. 31; S. Tamor.
Note on the Nan-Lincrrr Kinctics of Circulating-
Fuel Reactors. Y-F10-109 (Aug. 15, 1952).
41