ANS is committed to advancing, fostering, and promoting the development and application of nuclear sciences and technologies to benefit society.
Explore the many uses for nuclear science and its impact on energy, the environment, healthcare, food, and more.
Division Spotlight
Radiation Protection & Shielding
The Radiation Protection and Shielding Division is developing and promoting radiation protection and shielding aspects of nuclear science and technology — including interaction of nuclear radiation with materials and biological systems, instruments and techniques for the measurement of nuclear radiation fields, and radiation shield design and evaluation.
Meeting Spotlight
2024 ANS Winter Conference and Expo
November 17–21, 2024
Orlando, FL|Renaissance Orlando at SeaWorld
Standards Program
The Standards Committee is responsible for the development and maintenance of voluntary consensus standards that address the design, analysis, and operation of components, systems, and facilities related to the application of nuclear science and technology. Find out What’s New, check out the Standards Store, or Get Involved today!
Latest Magazine Issues
Aug 2024
Jan 2024
Latest Journal Issues
Nuclear Science and Engineering
October 2024
Nuclear Technology
Fusion Science and Technology
August 2024
Latest News
New laws offer nuclear industry incentives for existing power plant uprates
This year, the U.S. nuclear industry received a much-needed economic boost that could help preserve operating nuclear power plants and incentivize upgrades that extend their lifespan and power output.
Signed into law in 2022, the Inflation Reduction Act offers production tax credits (PTCs) for existing nuclear power plants and either PTCs or investment tax credits (ITCs) for new carbon-free generation. These credits could make power uprates—increasing the maximum power level at which a commercial plant may operate—a much more appealing option for utilities.
H. Kschwendt
Nuclear Science and Engineering | Volume 44 | Number 3 | June 1971 | Pages 423-434
Technical Paper | doi.org/10.13182/NSE71-A20173
Articles are hosted by Taylor and Francis Online.
A synthesis and generalization of several recently developed methods for the numerical solution of the neutron transport equation in a homogeneous slab, assuming anisotropic scattering and energy dependence is presented. The generalization lies in the explicit inclusion of anisotropic scattering. After a Fourier transformation, a system of linear integral equations is obtained, the kernal of which is expanded in spherical Bessel functions. To process the final result in the direction of numerical evaluation, an approximation is proposed that results in the SPN - PL method where the flux is given by a double sum over spatial and angular Legendre polynomials. The expansion coefficients are determined from a system of linear integral equations. Treating the energy dependence by means of the multigroup concept, this system is reduced to a linear system of algebraic equations. Corresponding matrix elements depend on the optical thickness of the slab and can be computed from expansions available for arbitrary slab thicknesses. The SPN - PL method is of great practical importance since it is possible to obtain the solution of the transport equation with low computational effort. For example, assuming monoenergetic neutrons and isotropic scattering, the first and second eigenvalues of the transport equation can both be obtained with five exact digits from 3 × 3 or 4 × 4 matrices. The influence of the mean value of the linear anisotropy on the first and second eigenvalue and the decay constant is studied in detail. The validity of our approach is confirmed by comparing it with the SN and other methods. For certain mean values and optical thicknesses the second eigenvalue is found to be a complex number. Critical flux distribution is determined with great accuracy and shows perfect agreement with other published values. The flux due to a δ source, and a combination of a δ source with a flat one, is analyzed; it is confirmed that the SPN - PL method is not only applicable to small systems, but also (in most cases) to very large assemblies.
