An Analytic Method for Analyzing Prompt-Critical Reactivity Transients

An analytic method for analyzing prompt-critical reactivity transients for a nonlinear energy feedback model is derived. The nonlinear point kinetics equation is replaced by a least-squares equivalent linear equation, and an approximate time-dependent reactivity is determined analytically. Assuming the power burst is infinitely sharp and symmetric about the peak, the transient peak energy, power, and pressure are expressed in terms of the inserted reactivity. The resulting expressions allow the definition of an equivalent step reactivity transient that preserves both the peak energy and power. The method is applied to the case where the feedback nonlinearity is small, and simplified expressions for the transient peak energy and power are determined and shown to approximate the known exact results in the case of a ramp reactivity insertion and a linear energy feedback model.