First and higher order, heuristically based generalized perturbation theory (HGPT) with optional control reset variable

The heuristically based generalized perturbation theory (HGPT), to first and higher order, applied to the neutron field of a reactor system, is discussed in relation to the criticality reset procedure. This procedure is implicit within the GPT methodology, corresponding to the 8o called filtering of the importance function relevant to the neutron field from the fundamental mode contamination. It is common practice to use the so called A-mode filter. In order to account for any possible reset option, a general definition is introduced of an intensive control variable (p) entering into the governing equations, and correspondingly a fundamental p-mode filtering of the importance function is defined, relevant to the real criticality reset (control) mechanism adopted. A simple example illustrates the need in many circumstances of interest of taking into proper account the correct filtering so to avoid significant inaccuracies in the sensitivity calculation results. The extension of this filtering technique to other functions entering into the GPT perturbative formulations at first and higher order is also discussed.