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
Human Factors, Instrumentation & Controls
Improving task performance, system reliability, system and personnel safety, efficiency, and effectiveness are the division's main objectives. Its major areas of interest include task design, procedures, training, instrument and control layout and placement, stress control, anthropometrics, psychological input, and motivation.
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.
Masaoki Komata
Nuclear Science and Engineering | Volume 38 | Number 3 | December 1969 | Pages 193-204
Technical Paper | doi.org/10.13182/NSE69-A21154
Articles are hosted by Taylor and Francis Online.
The purpose of this paper is to present the mechanics of the derivation of Avery's coupled reactor kinetics equations, which have been given by his physical consideration. Firstly, the diffusion equation and its adjoint equation are expressed in the matrix form. Then the partial flux and the partial adjoint flux are defined explicitly. The neutron flux, introduced by Henry, is represented as an amplitude T(t) times a shape function ψ(r, t). The adiabatic approximation is adopted in the neutron-flux shape function. Using the commutation law (given in the Appendix) between the diffusion operator and its adjoint operator, Avery's equations are derived from the time-dependent diffusion equations for the partial adjoint flux. The assumptions introduced are; (a) the delayed-neutron fission spectrum is the same as the prompt-neutron fission spectrum, (b) the neutron-flux shape function is approximated by the adiabatic method, (c) the time constant of the amplitude T(t) is much smaller than the minimum time constant of the shape function ψ(r, t) at that instant. As the result of these assumptions, the delay time associated with the transfer of neutron does not appear explicitly in Avery's equations.