The Concept of Multiple-Input Zero Power Describing Functions in Nuclear Reactors

The concept of multiple-input zero power describing functions is introduced in terms of the nonlinear response of a zero power reactor to a large periodic reactivity input, and the dual-input zero power describing function is calculated explicitly. The effect of amplitude and phase of the second input on the describing function is investigated numerically. The zero power describing function is used to construct the describing function at high power using closed loop feedback circuit theory. This approach allows nonlinear effects and feedback effects to be discussed separately. The nonlinear stability of a two-temperature reactor is investigated using the high power describing function and Nyquist stability criterion with particular attention to the existence and stability of limit cycles. In addition, the discrepancies between various definitions of the describing function are discussed and clarified.