JAEA-Data/Code 2007-004 - Welcome to Research Group for ...

shown in Fig.7.1-7.
Information contained in a record;
W, L0, LLL, (T(k), k=1,2,...,LLL), (II(k), k=1,2,...,LLL)
The optical length
λ k is calculated by
λ k = T(k)× {Cross section of II(k)} for k=1,2,..,LLL
Loop of source region, repeated for k=1,2,...,L0
i = II(k)
; source region number
λ i = λ k ; optical thickness of source region
Set λ = 0 ; optical distance between source region and collision region
ij
Contribution to the diagonal element
Δ ( ρ , ϕ)
= F(0)
× λ − F(0)
+ F(
λ )
ii
{
i
i
} ΣiΣi
Δ ii = ∫ W × Δ ii ( ρ,
ϕ)
dρdϕ
Loop of collision region repeated for k'=k+1,...,LLL
j = II(k') ; collision region number
Set λ j ⇐ λij
; optical thickness of collision region
Contribution to the off-diagonal element
Δ ( ρ , ϕ)
= F(
λ ) − F(
λ + λ ) − F(
λ + λ ) + F(
λ + λ + λ )
ij
{
ij ij i ij j
ij i j
} ΣiΣ
j
Δ ij = ∫W
× Δ ij ( ρ,
ϕ)
dρdϕ
Prepare optical distance for the next k’
Set λ ij ⇐ λij
+ λ j
End loop for collision region k’
unless the mirror condition (LLL > L0), then
Contribution to the escape element
Δ ( ρ , ϕ)
= F(
λ ) − F(
λ + λ ) / Σ
is
{
ij ij i
}
i
Δ is = ∫ W × Δ is ( ρ,
ϕ)
dρdϕ
End loop for source region k
Fig.7.1-7 Computational flow-diagram for numerical integration by “Ray-Trace” method
The function F(λ) appearing in the integrands in Fig.7.1-7 is given by
F ( λ)
= E 3 ( λ)
for slab (7.1-75a)
i
F ( λ)
= exp( −λ)
for sphere (7.1-75b)
F ( λ)
= K 3 ( λ)
for one- and two-dimensional cylinder (7.1-75c)
i
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