Abstract
The generalized perturbation method is described relevant to ratios of bi-linear functionals of the real and adjoint neutron fluxes of critical multiplying systems. Simple linear analysis for optimization and sensitivity studies are then feasible relative to spectrum and space-dependent quantities, such as Doppler and coolant void reactivity effects in fast reactors.
Highlights
This heuristic methodology, initially limited to the neutron domain, was successively further extended to the nuclide field [6,7] enabling, in particular, sensitivity studies relevant to fuel depletion evolution
We limit to note that, whereas with the variational approach one makes use of the mathematical concept of adjoint function and of its properties, and realizes that it may be associated with the importance, with the HGPT approach one starts with defining this latter quantity and heuristically, via conservation principles, arrives at the equation governing it and, at the sensitivity/perturbation expressions
A quite similar reasoning applies in relation to the diverging of importance r*(t) at tF, considering that its physical meaning corresponds to the contribution to the response [defined as r(tF)] due to a unit energy insertion at tF or, which is the same, to an overall power pulse d
Summary
The interest in perturbation/sensitivity methodologies for reactor physics studies started during the stage of Augusto Gandini as an associate researcher by the Reactor Physics Division of the Argonne National Laboratory in years 1961–62 [1]. In further developments the heuristically based GPT methodology has been applied: – to nonlinear problems [11], in particular, to the coupled neutron/nuclide field for reactor cycle analysis; – in the estimation of spatial shifts of power peak points following a perturbation [12]; – to reactor design optimization [13]; – to the development of the EGPT methodology [14], by which, for the analysis of reactivity coefficients, the calculation of the importance functions, implying the solution of inhomogeneous equations, is replaced by the calculation of functions, solution of simpler homogeneous ones governed by a properly modified operator; – to the analysis of subcritical (ADS) reactors [15] This led to the definition of ‘generalized reactivity’, properly taking into account the intensive control variable required (for instance, the neutron source strength) for maintaining the established power level.
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