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Division Spotlight
Operations & Power
Members focus on the dissemination of knowledge and information in the area of power reactors with particular application to the production of electric power and process heat. The division sponsors meetings on the coverage of applied nuclear science and engineering as related to power plants, non-power reactors, and other nuclear facilities. It encourages and assists with the dissemination of knowledge pertinent to the safe and efficient operation of nuclear facilities through professional staff development, information exchange, and supporting the generation of viable solutions to current issues.
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!
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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.
Dan G. Cacuci
Nuclear Science and Engineering | Volume 128 | Number 1 | January 1998 | Pages 1-16
Technical Paper | doi.org/10.13182/NSE98-A1941
Articles are hosted by Taylor and Francis Online.
A novel analysis of the neutron multigroup diffusion equation is presented for two-dimensional piecewise homogeneous domains with interior corners that arise at the intersections between regions with distinct material properties. Using polar coordinates centered at a typical interior corner, the solution of the multigroup flux is obtained as an infinite series of products of pairs of functions such that, for every pair, one of the functions depends solely on the angular variable and a single energy group while the other function depends on the radial variable and on all energy groups. The angular functions are shown to be the eigenfunctions of a Sturm-Liouville system that admits an infinite set of discrete and, in general, noninteger eigenvalues. On the other hand, the radial functions are the solutions of an infinite system of second-order ordinary linear differential equations. Exact explicit solutions for the multigroup diffusion equation (MGDE) for two-dimensional disk-like homogeneous domains are also derived and shown to yield analytic expressions for the group fluxes. This analyticity is shown to stem from the fact that the relevant eigenvalues are positive integers, independent of material properties and/or group structure. The exact expressions for the angular eigenvalues and corresponding eigenfunctions for two-region domains are then derived and shown to depend crucially on the specific angle between the two regions. This fact is underscored by deriving the exact expressions for the complete sets of eigenvalues and eigenfunctions for two geometries of particular importance to nuclear reactors, namely the hexagonal and rectangular geometries, respectively, and by showing that they are fundamentally distinct from one another. Of course, these expressions reduce to one and the same form for both geometries when the respective two-region domains are reduced to a single-region domain. Finally, the multigroup fluxes are shown to be bounded but nonanalytic at the respective interior corners; the reason underlying this behavior is traced back to the noninteger character of the relevant eigenvalues. This nonanalyticity is shown to be the fundamental reason for the failure of conventional (e.g., finite difference, finite element) numerical methods for solving the MGDE at and around such corners.