the Molten Salt Energy Technologies Web Site

and
The assumed boundary conditions are
q,(O, 7) = n q,(O, 7) , (5)
3q2(0, 7) +,(O, 7)
= m
ax ax
(6)
The solution in the half space
x > 0 is then
A =
n
1--
4i
n
1t-
sm
\
J
(8)
The image source is thus always weaker
than the given source. It is positive
or negative depending on whether
is smaller or greater than 1.
The solution in the reflector is
given by
47 I ”
that is, the neutrons seem to come
from a “refracted” source of strength
B =
L
- 2n
r-
dm
n
1+-
4i
PERIOD ENDING DECEWIBER 10, 1952
located at
y=-
X
7
Jm
(11)
with the whole space filled with
material that has the same properties
as the reflector. The refracted
source is always positive.
That the solutions satisfy, for
their respective regions, the di f-
ferential equations 3 and 4 and that
they also satisfy the boundary con-
ditions 5 and 6 can be shown by direct
substi tu tion.
The constancy of m and n is not a
bad assumption in many cases, because
the scattering cross section and,
hence, < and are usually constant
over a wide lethargy range. The
constancy of the scattering cross section
is not a necessary condition for the
constancy of m and n. For instance,
if the 5’s and p’s are constant and
the scatt,ering cross sections in both
media vary in such a way that their
ratio remains constant, m and n would
still remain unchanged. However, there
are few practical examples in which m
and n are constant and the scattering
cross sections vary, The most im-
portant, but somewhat trival, example
is the case in which the two media are
of the same material and differ only
in density. Then the “image source”
w i l l have strength zero. The refracted
source has the strength 1, and there
is the same amount of material between
the refracted source and the boundary
x = 0 as there is between the actual
source and the boundary.
If the macroscopic absorption cross
section Ca is not zero, then the image
method can be applied only in the
somewhat trivial and not very realistic
case in which
If there are several sources, or a
continuum of source, the solutions for
45