An analytically solvable, axially non-homogeneous reactor model: I. General solutions

In conceptual and model studies of neutron noise and diagnostics, and even in most practical applications, simple homogeneous reactor models have been used so far, in which closed form analytical solutions are possible. In this paper a less trivial, axially non-homogeneous reactor model is used. In this model both the static flux and the noise equations can still be solved by analytical methods. The model consists of a 2-D homogeneous rectangular core in which a 0- function (Feinberg-Galanin) control rod is inserted partially. Solution of both the static flux and the dynamic equations (the latter corresponding to a rod manoeuvring experiment in which the rod is moved up and down periodically) can be given by two different analytical methodologies. Both are calculated and discussed in the paper. This model will be used later in concrete diagnostic applications as well as in studies of reactor kinetic approximations