Example 6.3
A fast reactor assembly consisting of a homogeneous mixture of ^(239)Pu and sodium is to be made in the form of a bare sphere. The atom densities of these constituents are N_(F)=0.00395 imes 10^(24) for the ^(239)Pu and N_(S)=0.0234 imes 10^(24) for the sodium. Estimate the critical radius R_(c) of the assembly.
Solution. Introducing B_(1)^(2)=((pi )/(w)idetilde(R))^(2) from Eq. (6.32) into Eq. (6.50) and solving for widetilde(R) gives widetilde(R)_(c), the critical radius to the extrapolated boundary:
tilde(R)_(c)=pi sqrt((L^(2))/(k_(infty )-1))
Therefore, it is necessary to compute k_(infty ) and L^(2) to find widetilde(R).
Using the cross-sections in Table 6.1 gives
Sigma _(aF)=0.00395 imes 2.11=0.00833cm^(-1),
Sigma _(aS)=0.0234 imes 0.0008=0.000019cm^(-1),
Sigma _(a)=Sigma _(aF)+Sigma _(aS)=0.00835
Then from Eq. (6.9)
f=(0.00833)/(0.00835)â1
and
k_(infty )=eta fâ2.61.
To compute L^(2)=(D)/(Sigma _(a)) requires the value of D. This in turn is given by (see Eq. [5.10])
D=(1)/(3Sigma _(tr))
where Sigma _(tr) is the macroscopic transport cross-section. From the values of sigma _(tr) given in Table 6.1, containing approximately 500g of natural boron. Estimate the total worth of the rods.
26. The core of a fast reactor is a square cylinder 77.5cm in diameter Th
Suppose the fast reactor described in Example 6.3 is controlled with 50 rods, each rod containing approximately 500g of natural boron. Estimate the total worth of the rods.
Example 6.3
L2 R=n 9 19V975 k-1o o
(6.55)
adf nroto Therefore, it is necessary to compute k.. and L2 to find R. This resu Using the cross-sections in Table 6.1 gives nwolle.odegmi aug
(010)
as =0.0234 0.0008=0.000019 cm-1 (e20) Da=DaF+Zas=0.00835. avothcaeao bas ba Then from Eq.6.9 booaobnu aijow 0.00833 loiispd1opra isaun oonosquog-nof= 0.00835 11511d6.56
1obinoogi lo daa rTomog yde To 10 k.o=nf~2.61. somnSafvwwoH To compute L2=D/Ea requires the value of D.This in turn is given by (see osrwKbaTT oEq.[5.10]in Vnb o D=32 Eampla631al
(red)
Table 6.1,
