Kojiro Nishina

Theoretical Analysis of Two-Detector Coherence Functions in Large Fast Reactor Assemblies

The general expression of noise coherence function including the energy dependence of neutron detection cross section and the higher harmonic contributions in multi-dimensional model is developed on the basis of the modal expansion technique. Applicability of the method is demonstrated by numerical calculations carried out for a two-dimensional model of large fast reactor assemblies ZPPR-9 and −13C. The agreement between the theory and the measurement is satisfactory, which indicates the validity of the theory and the calculational model employed. In the assemblies, the coherence for a detector pair in a specific location can be approximately described by including the fundamental and the first harmonic modes.

Interpretation of control rod interaction effect on the basis of modal approach

Abstract A theoretical expression of reactivity interaction between control rods is developed on the basis of the explicit higher-order perturbation method. The expression shows that the magnitude of the interaction is inversely proportional to the λ-mode eigenvalue separation and dependence on the rod patterns is governed by the higher-harmonic eigenfunctions and the adjoint ones. Application of the formula is illustrated by numerical calculations carried out for a 1-D model of a large fast reactor core. The results indicate that the first harmonics dominantly contribute to the interaction, consequently the first-harmonic eigenvalue separation can be employed as a quantitative indication of interaction effect.

The Derivation of Neutron Generation Time for Reflected Systems and Its Physical Interpretation

For single-core reflected neutronic systems, generalized neutron generation time is derived and given physical interpretations in terms of importance. A system kinetic equation containing the moderator region response function previously introduced is reduced by a slow-variation approximation to the form of a conventional one-point kinetic equation, in which a parameter can be identified as generalized neutron generation time by analogy with a bare system. In such a mathematical expression for the parameter, one can further identify the amount of increase due to reflection over the bare system generation time. This amount is found to be the reflection time multiplied by the number of migrations that neutrons undergo between reflector and core in one generation. The theoretical generation time of the SHE assembly, a thermal-energy, graphite-moderated critical assembly, calculated by such a formation with cylindrical geometry, agreed well with that from pulsed neutron experiments.

A two-group response function treatment of coupled-core kinetic equations and coupling coefficient

A two-group, one-dimensional formulation of a coupled-core system is proposed as a revision of the one-group response function method by Shinkawa et al. The coupling coefficient of the Kyoto University Critical Assembly symmetric coupled-core loading is revised.

Derivation of Pál-Bell equations for two-point reactors, and its application to correlation measurements

Abstract For the analysis of noise problems in zero-power coupled-core reactors, one-energy group multipoint Pal-Bell equations are derived and their applications are illustrated. The illustration is made for the neutron correlation experiments of loosely-coupled two-core systems. We first derive a two-point version of the Pal-Bell equations for the neutron detection probability generating functions, and then derive the formulae of Feynman-alpha and Rossi-alpha (Orndoff type) experiments for a coupled-core system, using the factorial moment and cumulant expansions. With these formulae the following coupled-core kinetic parameters can be evaluated from neutron correlation experiments: coupling delay time, coupling coefficient and neutron generation time. The simplicity in the present derivation of Pal-Bell equations is pointed out.

Computational Breakdown of the High Conversion Light Water Reactor Infinite Lattice Void Reactivity into Contributing Nuclides and Energy Groups

By cell calculation with the SRAC code system, void reactivity is evaluated for a high conversion light water reactor tight lattice, with an emphasis on the breakdown of the void effect into component nuclides, nuclear reactions, and energy groups. The analysis is restricted to infinite lattices and deals with the consequence of neutron energy spectrum shifts caused by void. In a preliminary parameter survey over various fissile plutonium enrichments, a 7.5% enrichment is found approximtely to border the negative and the positive coefficients, when the moderator channel volume to fuel volume V/sub m//V/sub f/ is fixed at a typical value of 0.53. With this combination of the enrichment of V/sub m//V/sub f/ values fixed, the reactivity effect for an incremental void increase is analyzed in detail at low-void conditions (0 to 10%) and at high-void conditions (95 to 100%).

Stability region for a prompt power variation of a coupled-core system with positive prompt feedback

A stability analysis using a one-group model is presented for a coupled-core system. Positive prompt feedback of a ..gamma..p /SUB j/ form is assumed, where p /SUB j/ is the fractional power variation of core j. Prompt power variations over a range of a few milliseconds after a disturbance are analyzed. The analysis combines Lapunovs method, prompt jump approximation, and the eigenfunction expansion of coupling region response flux. The last is treated as a pseudo-delayed neutron precursor. An asymptotic stability region is found for p /SUB j/. For an asymmetric flux variation over a system of two coupled cores, either p /SUB I/ or p /SUB II/ can slightly exceed, by virtue of the coupling effect, the critical value (..beta../..gamma..-1) of a single-core case. Such a stability region is increased by additional inclusion of the coupling region fundamental mode in the treatment. The coupling region contributes to stability through its delayed response and coupling. An optimum core separation distance for stability is found.

Two mathematical expressions for the pulse decay in a two-point reactor

Abstract The mathematical equivalence of two solutions, both expressing the pulse decay in a two-point reactor, is illustrated. The first is a series superposing time eigenfunctions of two-point kinetic equations, while the second is a series summing the effects of groups of neutrons, each group having undergone a specified number of trips between the two cores after the initial pulse. The two expressions are alternative representations of a single solution. Taking a symmetric coupled-core system, numerical examples are given, and the relevant time range for the truncated solution of each is examined. The possibility of damped oscillation is investigated using the second solution. The concept of equivalence applies to the propagation of a neutronic disturbance within a large reactor core, provided the nodal model is feasible.

The Verification of the Moderator Response Function via Watson Transform

With the aid of residue evaluation, the timedependent reflection response G /SUB gr/ (t) of Shinkawa et al., which was recently used in a coupled-core stability analysis, is verified. The expansion series of the G /SUB gr/ (t) is summed with the Watson method, and its consistency with neutron conservation is checked. The result justifies the previous addition of -delta(t) to a reflection term, which was made in the stability analysis. The meaning of the response flux eigenfunction expansion for a moderator region is discussed.