Blackness coefficients, effective diffusion parameters, and control rod worths for thermal reactors - Methods

Simple diffusion theory cannot be used to evaluate control rod worths in thermal neutron reactors because of the strongly absorbing character of the control material. However, reliable control rod worths can be obtained within the framework of diffusion theory if the control material is characterized by a set of mesh-dependent effective diffusion parameters. For thin slab absorbers the effective diffusion parameters can be expressed as functions of a suitably-defined pair of 'blackness coefficients'. Methods for calculating these blackness coefficients in the P1, P3, and P5 approximations, with and without scattering, are presented. For control elements whose geometry does not permit a thin slab treatment, other methods are needed for determining the effective diffusion parameters. One such method, based on reaction rate ratios, is discussed. (author)