[1] We give an alternative description of the data produced in the KamLAND experiment. Assuming the existence of a natural nuclear reactor on the boundary of the liquid and solid phases of the Earth's core, a geoantineutrino spectrum is obtained. This assumption is based on the experimental results of V. Anisichkin and his collaborators on the interaction of uranium dioxide and uranium carbide with iron-nickel and silica-alumina melts at high pressure (5-10 GPa) and temperature (1600-2200°C), which led to the proposal of the existence of an actinide shell in the Earth's core. We describe the operating mechanism of this reactor as solitary waves of nuclear burning in 238 U and/or 232 Th medium, in particular, as neutron fission progressive waves of Feoktistov and/or Teller et al. type. Next, we propose a simplified model for the accumulation and burn-up kinetics in Feoktistov's U-Pu fuel cycle. We also apply this model for numerical simulations of neutron fission wave in a two-phase UO 2 /Fe medium on the surface of the Earth's solid core. The proposed georeactor model offers a mechanism for the generation of

Physical fundamentals of traveling wave reactor are considered. We show that the condition of existence of nuclear burning soliton-like wave in a neutron-multiplying medium is determined in general by two conditions. The first condition (necessary) is determined by relationship between the equilibrium concentration and critical concentration of active (fissionable) isotope that is a consequence of the Bohr-Sommerfeld quantization condition. The second condition (sufficient) is set by the so-called Wigner quantum statistics, or more accurately, by a statistics of the Gaussian simplectic ensembles with respect to the parameter that describes the squared width of burning wave front of nuclear fuel active component.

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On the basis of the condition for nuclear burning wave existence in the neutron-multiplicating media (U-Pu and Th-U cycles) we show the possibility of surmounting the so-called dpaparameter problem, and suggest an algorithm of the optimal nuclear burning wave mode adjustment, which is supposed to yield the wave parameters (fluence/neutron flux, width and speed of nuclear burning wave) that satisfy the dpa-condition associated with the tolerable level of the reactor materials radioactive stability, in particular that of the cladding materials.It is shown for the first time that the capture and fission cross-sections of 238 U and 239 Pu increase with temperature within 1000-3000 K range, which under certain conditions may lead to a global loss of the nuclear burning wave stability. Some variants of the possible stability loss due to the so-called blow-up modes (anomalous nuclear fuel temperature and neutron flow evolution) are discussed and are found to possibly become a reason for a trivial violation of the traveling wave reactor internal safety.