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

3/28/2016 2016 - #02 Physics and technology of nuclear reactors

Gulevich A.V. Kukharchuk O.F. Brezhnev A.I.

https://doi.org/10.26583/npe.2016.2.09

### UDC: 621.039.5

Application 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 the 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.

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neutron kinetics laser system pumped by nuclear reactor pulse energy and maximum power