Hand calculational methods for criticality safety - a primer

Before the advent of high-speed desktop computers, pioneers in the field of nuclear criticality safety, such as Joe Thomas, David Smith and Hugh Paxton, took the time to create various criticality safety hand methods for single fissile units or fissile units arranged into array configurations. These methods have been described in a variety of technical papers, manuals, and guides. To assemble this information in one document, a Primer has been developed for the most commonly used hand methods for criticality safety calculations: one group and modified onegroup diffusion theory, buckling conversions, core-density conversions, surface density method, density analog method, solid angle method and the limiting surface density method. The Primer discusses the applicability of the various hand methods, illustrates how they are used with numerous sample problems, and provides an interpretation of the computed results. Hand calculation methods can be used as a starting point for more advanced calculations and, in many circumstances, can be used as a simple tool to perform perturbation analyses for many fissile systems almost as efficiently as using a criticality safety code. The most widely used tools available to a criticality safety practitioner are the Monte Carlo or deterministic criticality safety codes (MCNP, KENO, DANTSYS, etc.). These codes can be used to model very complex systems, but, at times, it is possible for practitioners to treat these codes as "black boxes." The hand methods can be used to delve into the various criticality safety parameters that may affect the multiplication factor, the critical mass, the critical size or the material spacing in an array of a fissile system. Learning these hand methods can also be valuable to new criticality safety practitioners developing intuition, knowledge and experience in the field of criticality safety.