Soliton-like waves of nuclear burning in the neutron multiplicating media : (theory and computational approach) (2009)

The research project has dealt with a conceptual design of a model of an innovative inherently safe nuclear soliton-like fast reactor of Feoktistov type. The main findings are summarized below.\nThe kinetics of self-stabilising fast uranium-plutonium reactor, which generates self-propagating neutron-fission nuclear burning wave, that satisfies all conditions of inherent safety, was considered for the Feoktistov uranium-plutonium fuel cycle. For simplicity the neutron spectrum was assumed the same as the fission spectrum. A case with little or no moderator was considered - the neutron spectrum is the same as the initial neutron spectrum.\nThe auto-wave solution for the transmutation chain with necessary condition n_crit < ñ_Pu was obtained and analyzing this solution it was shown that the soliton-like propagation of neutron-fission nuclear burning wave is possible in U_238 medium only under the condition of a certain ratio between equilibrium and critical plutonium concentration (ñ_Pu > n_crit), which is characterized by Bohr-Sommerfeld quantization condition.\nA preliminary model of nuclear fast reactor of Feoktistov type is proposed. The obtained model satisfied the requirement of inherent safety. The numerical experiments of nuclear reactor with uranium-plutonium fuel cycle are made and the solution in the form of soliton-like progressive burning wave is obtained.\nThe physical conditions of Feoktistov wave mode are generalized and the necessary and sufficient condition of the soliton-like wave origin and propagation are first obtained. The soliton-like wave propagation velocity in the neutron-multiplicating medium is generally defined by two conditions, one of them the necessary one is predetermined by ratio of equilibrium plutonium concentration and critical plutonium concentration n_Pu /n_crit > 1, or, to be more precise, Bohr-Sommerfeld quantization condition, and the other the sufficient one is determined by the Gaussian simplectic ensemble (GSE) statistics with respect to parameter a, which characterizes the concentration wavefront width of the active component of nuclear fuel.\nThe heuristic description of the slow burning process propagation in the reactor core is given.\nThe simplified one-dimentional model of Pu accumulation and U burnup kinetics was proposed. Taking into account delayed neutrons three-dimensional model for one-group diffusion approximation is offered.\nThe numerical solution for the obtained physical model of the reactor is provided. In oder to verify theoretical model the computational experiment is performed. The simulations were done for the different initial and boundary condition, with and without initial fuel enrichment. The calculated wave velocity was in good agreement with the necessary and sufficient conditions obtained.\nThe numerical solution using the method of mesh points in the implicit form is obtained and the simulation results and its verification were given.\nOn the basis of proposed reactor model the hypothesis of slow nuclear burning on the boundary of the liquid and solid phases of the Earth's core was offered.\nOn the basis of the analysis of the temporal evolution of radiogenic heat emission power of the Earth in the framework of the geochemical model of the mantle differentiation and the Earth's crust growth complemented by a nuclear energy source on the boundary of the solid and liquid phases of the Earth's core, altentative estimation of the geoantineutrino intensity and the geoantineutrino spectrum on the Earth surface from different radioactive sources (238U , 232Th, 40K and 239Pu) is obtained.\nIt's also shown that natural nuclear reactors may exist on the boundary of the solid and liquid phases of the Earth's core as spontaneous reactor-like processes based on Feoktistov U - Pu fuel cycle and/or Teller-Ishikawa-Wood Th - U fuel cycle. Note that, as compared to 238U-medium, the wave velocity in the 232Th-medium has the value of about L/[tau] [approx.] 0.1 cm/day (where L [approx.] 5 cm is the diffusion length of the neutron absorption in thorium, [tau] = 39.5/ln257 days is the time of 233U generation due to the [beta]-decay of 233Pa). It means that the speed of the neutron-fission wave propagation in the 232Th-medium (Teller-Ishikawa-Wood fuel cycle) is by an order of magnitude less than the similar speed of Feoktistov burning wave.\nFinally, concerning the 3He/4He distribution in the Earth's interior and the geoneutrino spectrum on of the Earth's surface (KamLAND-experiment) the possibility of the existence of soliton-like nuclear reactor with U - Pu or/and Th - U fuel cycle on the boundary of the liquid and solid phases of the Earth's core is shown.