ABSTRACT
This chapter applies the neutron diffusion equation to several reactor geometries that are idealizations or simplifications to real reactors. These reactor geometries include rectangles, cylinders, and spheres. Time dependent reactors behave differently than steady state reactors do. In military reactors, physical space is at a premium and reactors can only be refueled once every thirty or forty years. By increasing the initial enrichment of the fuel inside the core to about 95%, the core of a military reactor can be made to be extremely small. A three-dimensional rectangular reactor is similar to the infinite slab reactor, except that the same procedure must be applied to the y and z directions. In this reactor, the neutron flux is a function of x, y, and z. A spherical reactor is similar to a rectangular reactor when the core is spatially homogeneous. For a completely symmetrical core without a reflector, the neutron flux is a function of the radius only.
