Solution of two-point kinetics equations for reflected reactors using Analytical Inversion Method (AIM)

The development of sophisticated kinetics theory model of a reflected reactors which comprising core and reflector regions has been considered. Within each region, the theory is space-independent and assumes one energy group. A detailed investigation of both mathematical and numerical solutions has been conducted and applied to the two-point kinetics for reflected reactors using the Analytical Inversion Method (AIM), which permits a fast inversion of polynomials by going temporarily to the complex plane. This method has been tested using two types of reflected reactor systems: the experimental zero-power reactor (PROTEUS) and a large tightly coupled system with a small homogeneous core surrounded by a series of non-multiplying reactors (AGN-201). In addition, an economical general approximate expression to the exponential function for the two-point kinetics matrix is derived and Padé rational approximations of different types are applied. In order to ensure the validity and stability of this method, the numerical results obtained with this algorithm are tested on a set of four kinetic problems, step, ramp, zigzag and oscillatory of reflected reactors reactivity change under considerations.