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7.8 One-Point Kinetics Parameters
The following one-point kinetics parameters can be obtained by CITATION of SRAC.
• Effective delayed neutron fraction
⎡ * d
BVF
∫ ∑φ
⎤
⎢
g ( r)
χ g,
i ( r)
∑ Σ i.
g'
( r)
φ
g'
( r)
dV
⎥
g
g'
β = ∑ = ∑ ⎢
⎥
eff β eff , i
(7.8-1)
i
i ⎢ * t
∫
⎥
⎢ ∑φ
g ( r)
χ g ( r)
∑νΣ
f . g'
( r)
φ
g'
( r)
dV
⎥
⎣ g
g'
⎦
• Effective decay constant for the i-th family of delayed neutron precursor.
∫ ∑
∫
∑
*
∑
φg
( r)
χ g,
i ( r)
Σi.
g'
( r)
φ
g'
( r)
dV
1 g
g'
=
λeff
, i
* d
BVF
φ ( r)
χ ( r)
Σ ( r)
φ ( r)
dV
g
g
d
g,
i
∑
g'
BVL
i.
g'
g'
(7.8-2)
• Effective delayed neutron life time
l =
∫
∑
g
∫ ∑
k
g
* 1
φ g ( r)
φ(
r)
dV
υ ( r)
t
g
χ ( r)
*
φ g ( r)
k
eff
∑
g'
g
νΣ
f . g'
( r)
φ ( r)
dV
g'
= k
eff
Λ
(7.8-3)
BVF
i
where, Σ ( ν N )
≡ ∑ β m g,
m f , g,
m m
(7.8-4)
i, g
σ
m
BVL
i
i
≡ ∑ ( β ν σ / )
Σi, g
m g,
m f , g,
m N m λm
(7.8-5)
m
1
1
Σ υ , g ≡ ≈
(7.8-6)
E ( eV ) ( E + E ) / 2
g
g,
Lower
g,
Upper
The averaged neutron velocity for the g-th group is given by
υ (m / sec) =
g
2 × 1.60219E
−19
m ( kg)
n
1
Σ
υ,
g
1
= 13831.68 ×
Σ
υ,
g
The macroscopic cross-sections defined by Eqs.(7.8-4), (7.8-5) and (7.8-6) are stored in the
MACRO file for the calculation of the one-point kinetics parameters. Theses cross-sections are
collapsed and/or homogenized in the same manner (cf. Sec.7.5) as other usual macroscopic
cross-sections ( Σ , , etc.).
a,g
Σ f , g
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