NEUTRON DIFFUSION THEORY
© M. Ragheb
11/18/2007
1. INTRODUCTION
The diffusion theory model of neutron transport plays a crucial role in reactor theory since it
is simple enough to allow scientific insight, and it is sufficiently realistic to study many
important design problems.
The neutrons are here characterized by a single energy or speed, and
the model allows preliminary design estimates.
The mathematical methods used to analyze such
a model are the same as those applied in more sophisticated methods such as multigroup
diffusion theory, and transport theory.
The derivation of the diffusion equation will depend on Fick’s law, even though a direct
derivation from the transport equation is also possible.
The Helmholtz equation is derived, and
the limitations on diffusion equation as well as the boundary conditions used in its application to
realistic problems are discussed.
2. TRANSPORT CROSS-SECTION
The effect of the scattering angular distribution on the motion of a neutron is taken into
account by use of the transport cross section.
Let us assume:
1.
An infinite medium.
2.
A purely scattering medium without absorption.
3.
The energy of the neutron does not change as a result of a collision with the nuclei of the
medium.
4.
After each collision the particle travels a scattering mean free path
λ
s
and is deflected by
an angle
θ
.
After injection to the system, the neutron moves a distance:
s
Z
λ
=
0
(1)
the projected distance traveled after the first collision along the z-axis is, as shown in Fig. 1:
)
cos(
1
1
θ
λ
s
Z
=
The average value of
is:
1
Z
µ
λ
θ
λ
s
s
Z
=
=
)
cos(
1
1
(2)

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