Approximate Solution of One-Point Reactor Kinetic Equations for Arbitrary Reactivities

摘要

This paper describes a very simple formulation of the reactor kinetic equation for arbitrary reactivity variations which can be solved analytically. The method of matched asymptotic expan-sions, which is a generalization of methods used in boundary-layer analysis, is employed to estimate the neutron density and the reactor period for ramp and periodic inputs. The small amounts of error arising in individual cases are analyzed quantitatively by comparison with results obtained from difference approximation (Runge-Kutta-Merson method). The validity of the zero-prompt-lifetime approximation and the stability condition for periodic inputs are also discussed. It is confirmed that the results obtained by the present method are numerically in complete agreement with those by other methods, provided the magnitudes of bias reactivity |ρ0|, reactivity amplitude |ρ1| and ramp reactivity |γt| are all very small compared with β, that the angular frequency ωβ/l*, and that, in particular, l*10-3.