Analytical estimations of pulse parameters in the modified integral neutron kinetics model for pulsed reactor and subcritical block

AbstractApplication of modified integral neutron kinetic model to calculate principal characteristics of pulsed coupled reactor system consisting of pulsed reactor and subcritical block is discussed. The model is based on the use of respective time-dependent kernels of integral equation for reactor power and space-time Green's function for the subcritical block. It is possible to reduce the set of integral equations to the set of elementary algebraic and first-order differential equations by using exponential approximation of the kernels and Green's function.Approximations of «inertialess» reactivity dumping and jump reactivity boost on prompt neutrons are used as the «reactivity-power» feedback in order to close the mathematical model. This allows integrating corresponding kinetic equations in analytical form notwithstanding the fact that the kinetic equation for reactor is nonlinear.Analytical relations allowing estimating basic characteristics of the system such as energy and maximum pulse power in the reactor and in the subcritical block with accuracy sufficient in engineering practices were obtained.The performed calculations showed applicability of the analytical dependences of energy characteristics of the system on the impact coefficient of subcritical block on the reactor, on the lifetime of neutrons in the reactor and on the «time» constant of the block for fixed value of pulse energy in the reactor. The obtained ratio is valid for the reactor within the whole range of variation of system parameters while for the subcritical block it is correct only for the system operated with fast neutron spectrum in the reactor and with thermal neutron spectrum in the subcritical block when the so-called “delta” approximation of the reactor pulse is realized. In the case when such approximation is not valid the “Gaussian” approximation to the shape of the reactor pulse is applied for which more accurate analytical formulas were also obtained for estimation of maximum pulse energy in the block. These formulas depend on the ratio of duration of start-up period of the pulsed coupled reactor system to the value of “time” constant of the subcritical block and are correct for the systems with similar neutron spectra.The obtained analytical relations can be applied for optimization of parameters of coupled reactor-laser systems

On feasibility of optimizing the neutronic parameters of a laser system pumped by a pulsed reactor

The paper examines the calculated feasibility of improving the energy characteristics of power pulses in a system consisting of a reactor and a subcritical block. A BARS-type fast neutron reactor is used as a self-quenching pulsed reactor. The subcritical block is a cylindrical structure comprising laser-active elements, moderator components and two reflectors (internal and external). The internal reflector material is zirconium hydride, and the external reflector material is beryllium. The pumping area containing the laser-active elements consists of zirconium hydride moderator, aluminum and uranium–molybdenum fuel (95% enriched uranium). The system operates in a pulsed mode. Fast neutrons are generated in the nuclear reactor at the pulse moment, many of which are leakage neutrons entering the subcritical block, slowing down there and inducing fissions of uranium nuclei in the laser-active elements. After the pulse terminates, the reactor changes to a deeply subcritical state, and the laser pulse generation stops. The neutron kinetics in the system under consideration is modeled based on a modified integral model. The pulse maximum power and energy in the system's subcritical block, as well as its weight and energy-to-weight ratio are selected as functionals for the optimization. The fissile material and moderator weight and the thickness of the subcritical block's internal and external reflectors are adopted as variables. The calculations have shown that it is possible to improve the energy characteristics of a reactor-laser system by increasing the amount of the fissile material in the block, not using the moderator in the block and fixing the thickness of the internal zirconium hydride reflector at a level of 3.1cm. It has been shown that a change in the external beryllium reflector thickness leads to a highly multidirectional behavior of the functionals (energy and maximum power, as well as the block weight and energy-to-weight ratio)

Assessment of the critical condition for the operation of an IBR reactor with a subcritical unit in an equilibrium mode

There considered a system consisting of a fast neutron batch pulsed IBR type reactor and a subcritical unit (neutronically thermal). The reactor is fitted with a reactivity modulator, which provides short-term “transfer” of the system from a deep subcritical to a prompt supercritical state and back. The system is in a deep subcritical state in the intervals between pulses. Such a system is capable to operate in an equilibrium (static) mode only when a critical condition is fulfilled for the kinetic parameters describing its operation. The neutron kinetics is described as part of a two-point approximation. It is assumed that the change in the reactor reactivity at the pulse generation time takes place periodically according to a parabolic law and the reactor is deeply subcritical in the intervals between pulses. Numerical simulation of the critical condition is extremely time-consuming, and analytical representation is almost impossible due to the need for solving ordinary differential equations with variable coefficients. There proposed a methodology for approximate estimating of parameters of a coupled “batch pulsed reactor–subcritical unit” system operating in an equilibrium mode. Analytical relations have been obtained in a quadrature form to calculate the “critical” condition of such a system in the approximation of “frequently recurring” pulses, when the decay of the delayed neutron precursors in the interval between pulses can be ignored. Calculations of the “critical condition” are illustrated by an example of a laser system consisting of an IBR-type batch pulsed reactor and a subcritical neutron multiplication unit, in which fission energy is converted into laser emission energy. Critical parameters of the system were estimated using analytical relations, as well as direct numerical calculations based on the STIK program that models the neutron kinetics in the considered system in a two-point approximation. It has been shown that the results of direct calculations and the estimates based on analytical relations matched good