REACTOR STARTUP WITH STATISTICAL FLUCTUATIONS
Technical Report
·
OSTI ID:4120515
In the early stage of the start-up of a reactor with a small source, statistical fluctuations may be important. The influence of these fluctuations will persist in the subsequent stage of the start-up when the power level is high in the sense that the early fluctuations provide a statistical distribution of initial conditions to be applied in the treatment of the high-level stage. In almost all cases of practical interest, the statistical stage will have terminated before the reactivity greatly exceeds delayed critical. Hence, it is possible to carry out the statistical analysis on the basis of the approximation that the prompt generation time is zero. From this viewpoint the elementary statistical event is the chain of prompt fissions caused when a single source neutron or delayed neutron is introduced into the assembly. The distribution function of delayed neutron progenitors from a single prompt neutron chain depends on the prompt reactivity at the time that the chain occurs. The calculation of this distribution function in terms of the distribution function for the emission of prompt neutrons is described. The method is based on the evaluation of the generating function by a Laplace transform procedure. The statistical distribution of progenitor population as a function of time during the start-up may be calculated in terms of the single prompt chain distribution function by generating function techniques, taking into account the dependence of reactivity on time. A formula is developed for the probability as a function of time that the delayed neutron progenitor population will be smaller than a specified number. A method for solving the generating function equation which is suitable for calculating this probability is suggested. This method leads to equations similar to but more powerful than the equations for the expectation value and second moment of the progenitor population. (auth)
- Research Organization:
- General Electric Co. Research Lab., Schenectady, N.Y.
- NSA Number:
- NSA-15-006988
- OSTI ID:
- 4120515
- Report Number(s):
- 60RL-(2405E)
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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