Visualization of a changing dose field. Page: 4 of 7
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When the user places an object in the drawing, a
customized properties window appears that allows the user
to set key parameters such as shielding thicknesses or source
properties. The drawing in Figure 2 shows two gloveboxes,
two thin hydrogenous shields, three sources (circles inside
gloveboxes), and two detectors.
DOSE CALCULATIONS
For all situations of interest at Los Alamos, the primary
component of the dose is composed of neutrons and
photons. Neutrons are born through spontaneous fission and
(a,n) reactions, and can then be multiplied if the medium
through which they travel has a nonzero fission cross
section. Photons (gamma-rays) come from the natural decay
of radioactive isotopes. A description of the equations used
to calculate these quantities is provided below.
Neutron Dose Calculations
Calculating the neutron current density at the surface of
the source and then radially attenuating it to the detector
determines the flux at the detector. Assuming a
monoenergetic neutron spectrum (the source neutrons have
some minor energy dependence), the neutron current density
is governed by Fick's Law from diffusion theory, which is
stated as_ - R+d sinBr
B2D r sinB(R+d) J(3)
where R is the radius of the source and B2 is the material
buckling, given by2 v, -Z"
D(4)
To obtain the current at the surface (the number of neutrons
leaking from the sphere per unit area), we take the derivative
of the flux and multiply by the diffusion coefficient
according to Eq. (1). The results of the derivation and
multiplication areR S(R+d) sin BR-BR cos BR
B 2R 2 sinB(R+d)(5)
Finally, we calculate the neutron flux at the detector by
radially attenuating the current density to the detector
position. If a is the distance from the surface of the source
to the detector, the equation for the flux at the detector isR 2
(R + a)= J(R)
(R+a)2where
J = the neutron current density or the net number of
neutrons that pass per unit time through a unit area
In/cm2-s],
D = the diffusion coefficient [cm], and
0 = the neutron flux [n/cm2-s].
The generalized neutron diffusion equation that
approximates the transport of neutrons through media that
contain absorbing and fissionable materials is
DO20~X#+vjo+S =0, (2
where
E, = the macroscopic absorption cross section [cm I],
Ej = the macroscopic fission cross section [cm ], and
v = the average number of neutrons emitted per fission.
Assuming a solid spherical source and that the flux varies in
the radial direction only, we can apply the symmetry and
surface boundary conditions, where d is the extrapolation
distance [cm], to obtain the solution for the neutron flux in
the source sphere asNote that Eq. (6) does not take into account any shielding.
The presence of water can have a significant effect on the
neutron EDE. To account for neutron thermalization from
hydrogenous materials (e.g., polyethylene shields or
persons), we use a numerical fit for neutron thermalization
effects. The discrete-ordinates particle transport code
ONEDANT[5] is used to determine the effect of water.
Although the fast flux drops below the thermal flux in
increasingly thick water shields, the EDE from fast neutrons
comprises about 90% of the total EDE, even with very thick
water slabs. This is the result of the much larger dose
conversion factor for fast neutrons than for thermal neutrons
(the EDE from fifty 0.0253-eV neutron flux units ~ the EDE
from one 2-MeV neutron flux unit). To account for the
removal of neutrons from the fast groups. (with thermal
neutrons being discounted as contributing negligibly to the
total EDE), a macroscopic "removal cross section" of 0.15
cm1 is used per the transport analysis, and the neutron EDE
is therefore given byD = [S} hEa + S(an)hE(an) (R +a~e
, (7)
where
J = -DVO ,
(1)
(6)
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Helm, T. M (Terry M.) & Kornreich, D. E. (Drew E.). Visualization of a changing dose field., article, January 1, 2002; United States. (https://digital.library.unt.edu/ark:/67531/metadc933226/m1/4/: accessed April 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.