Reactivity estimation for source-driven systems using first-order perturbation theory. Page: 3 of 11
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PHYSOR 2002, Seoul, Korea, October 7-10, 2002
(Mo-11oFo*)V*4 = 0, (4)
where F* and M* are the adjoint operators ofF (=Fp + Fdk ) and M, respectively, and subscript
0 means the initial state.
Inserting the factorization in Eq. (2) into Eq. (1), integrating over space and energy with the weighting
function * , and dividing the resulting expression by
F'a(t) = ((D , FT), (5)
the point kinetics equations for an initially subcritical system can be obtained as:
dp _ p(t) - 8(t) 1 s(t) (6a)
dt A(t) A0 A(t)
dt - -Akk (t) + /t k (t)p(t), (6b)
p(t) = (Q*, ,[F - M]T)/lF, (t), (6c)
Ck (t)- (CD,dkCk)/F o, (6d)
s(t) = ((* ,S)/Fl(t). (6e)
and the other notations are standard. In Eq. (6), the precursors and independent source are
represented in the "reduced" form rather than in simple adjoint-weighted integrals employed in more
conventional point kinetics equations. These reduced quantities represent the relative values of these
integrals to the adjoint-weighted quasi-stationary fission source, and provide a simpler and more
direct physical interpretation than the conventional ones.
The reactivity defined in Eq. (6c) is called "dynamic reactivity," and it is formed with the time-
dependent flux as it physically appears during a transient. It is noteworthy that the dynamic reactivity
at t = 0 is numerically equal to the static reactivity of the initial stationary state:
P(O) =1I- 10 =1I-1/ Ik"o = po . (7)
This is because the dynamic reactivity is defined in the same form as the static one and the initial
source-free X-mode adjoint function is used as the weighting function.
III. PERTURBATION THEORY EXPRESSIONS OF REACTIVITY
The parameters of the exact point kinetics equations can be determined only when the exact solution
of the space-energy-dependent problem is known. Thus, some approximations need to be introduced
to derive a practical point reactor model. For the practical estimation of reactivity changes,
perturbation theory expressions are generally employed. In this section, the exact perturbation theory
(EPT) expression is first derived from the dynamic reactivity defined in Eq. (6c). Then, the FOP
reactivity expression is approximately obtained from the exact one. The EPT expression based on the
adiabatic approximation is also derived for comparison purposes.
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Kim, Y.; Yang, W. S.; Taiwo, T. A. & Hill, R. N. Reactivity estimation for source-driven systems using first-order perturbation theory., article, July 2, 2002; Illinois. (digital.library.unt.edu/ark:/67531/metadc734030/m1/3/: accessed October 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.