Solution of the neutron transport equation in cyclindrical geometry with spectral green's function method

Neutron transport equation is one of the current topics of reactor physics. The solutions to the transport equation till now have been done in slab geometry and it is solved for very idealized systems. In this PhD study, the solutions to the transport equation is presented in details. This equation is written in cylindrical geometry and then a new analytical solution is produced by the separation of variables for isotropic scattering and one- group case. After that, it is conversed to the discrete-ordinates equation system by using orthogonal polynomials. Spectral Green's Function method is devoloped to provide more accurate solutions to the transport equation in cylindrical geometry. Discrete-ordinates equations is solved by Spectral Green's Function (SGF) and Diamond Difference (DD) methods. The methods that have been used in the solution of transport equation in slab geometry are taken to be the base for our cylindrical transport solutions. The results we obtained for scaler neutron flux are consistent with the results by earlier studies and numerical calculations. Key Words: Neutron transport equation, cylindrical geometry, Spectral Green's Function, Diamond Difference.