Nuclear reactor safety: Multiplicity Distribution of Prompt Neutron Fission, Frehaut and Terrel Comparison
Fabrice Pelestor Université de Toulon Ingénieur atomicien (diplômé de l’INSTN) Ingénieur mécanicien énergéticien (diplômé de l’ENSIMEV) Mathématiques spéciales (Lycée Dumont D’Urville)
ABSTRACT : multiplicity of neutrons when a fission occur has probability laws given by two authors,Terrel and Frehaut. This intrinsic random phenomena can have important implications on nuclear safety (when a reactor start, there is, then, for example, a certain probability that the reactor may go beyond prompt critical before any neutron signal is detected (Bell & Glasstone, Nuclear Reactor Theory, ed Van Nostrand, 1970,Reinhold, page 36). Its study is so important. I show this study must becompleted.
I) Introduction : fluctuations and Boltzmann equation
Man use currently chemical energy since many years, 500 000 for fire, without any bigs problems. Even if sometimes this dragon escape from its hands, the damages aren’t too excessive. Nuclear energy is only in use since an instant, opposite to the fire. But its power is more strong, many order of scale. So, an accident caninjure millions peoples. If we want to use safety for thousands years this splendid energy, it is necessary to study it very carefully in all its aspects, without taboos. The simulation of start of a nuclear engine turns aside from the beaten track. I want to say there is not only the classical Boltzmann equation. Of course it’s a very important equation, but it must not mask underlyingphenomenas, radio active behaviour of fission, which are of greatest important, particularly in this phase. Indeed, the radio actives phenomenas have intrinsics uncertains (for don’t say random) behaviours. This behaviour is taking into account by probabilities laws. The determinist Boltzmann equation use, in classical neutronic (in classical statistic mechanic too), cross sections as a traduction of this «random » behaviour, and it gives only the mean value of the number of neutrons. But there is another spring of uncertainty we don’t see with this equation. It’s the probability (US says multiplicities) that a fission give 0, 1, 2 …, 7, etc… neutrons. This involve intrinsics fluctuations of the number of neutrons in an engine, Theses fluctuations are not dues to imperfects technologies, but toradio actives naturals process that man cannot master. Can theses fluctuations be dangerous ? Of course this phenomena is known since many times, and a pioneer of its study was the Nobel price Feynman . However quantification of these probabilities emission of neutrons by fission was made at the end of the fifties , then in 1988 by J. Frehaut of CEA/Division des Applications Militaires  whooffer a probability law of events with an anomaly : sum of probability of all events not to equal to one. The more deep equation managing the neutronic is the backwards Kolmogorov equations. Theses equations was established first by Hungarian engineer L. PàL . Pàl, in his pioneering work, use a point reactor model. It is George Bell, of Los Alamos, who take more clearly, in 1963, account ofspace and energy dependence of neutrons . Fundamentals data for use theses works are the probability of number of neutrons emitted by fission. I will present comparison of Terrell and Frehaut distribution law, with some consequences.
« There is then, for example, a certain probability that the reactor may go beyond prompt critical before any neutron signal is detected » ; Bell & Glasstone(Nuclear Reactor Theory, ed Van Nostrand, 1970,Reinhold, page 36)
II) The mathematical formulation of the distributions of the number of neutrons emitted by fission
I will not comment how, and what hypothesis was taken by the authors to establish their distributions laws. I will only present their formulation. I note P the probability to have ν neutrons. P depend of the energy ν ν of the...
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