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
Nuclear Installations Safety
Devoted specifically to the safety of nuclear installations and the health and safety of the public, this division seeks a better understanding of the role of safety in the design, construction and operation of nuclear installation facilities. The division also promotes engineering and scientific technology advancement associated with the safety of such facilities.
Meeting Spotlight
ANS Student Conference 2025
April 3–5, 2025
Albuquerque, NM|The University of New Mexico
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
Mar 2025
Jul 2024
Latest Journal Issues
Nuclear Science and Engineering
March 2025
Nuclear Technology
Fusion Science and Technology
April 2025
Latest News
Penn State and Westinghouse make eVinci microreactor plan official
Penn State and Westinghouse Electric Company are working together to site a new research reactor on Penn State’s University Park, Pa., campus: Westinghouse’s eVinci, a HALEU TRISO-fueled sodium heat-pipe reactor. Penn State has announced that it submitted a letter of intent to host and operate an eVinci reactor to the Nuclear Regulatory Commission on February 28 and plans to engage with the NRC on specific siting decisions. Penn State already boasts the Breazeale reactor, which began operating in 1955 as the first licensed research reactor at a university in the United States. At 70, the Breazeale reactor is still in operation.
T. J. Krieger, P. F. Zweifel
Nuclear Science and Engineering | Volume 5 | Number 1 | January 1959 | Pages 21-27
Technical Paper | doi.org/10.13182/NSE59-A27324
Articles are hosted by Taylor and Francis Online.
The spatial and temporal distribution of thermal neutrons in a multiplying assembly following the introduction of a short burst of fast neutrons is investigated by means of an extension of the so-called “asymptotic reactor theory” to the time-dependent case. It is shown that the solution for an nth mode fast neutron source can be reduced to that for an nth mode thermal neutron source, so that only the latter need be considered. A formal solution to the time-dependent thermal diffusion equation with an nth mode thermal source is found for an arbitrary slowing-down kernel. The asymptotic behavior of the flux in the long-time limit is shown to be exponential, with a decay constant satisfying a generalized material buckling equation The asymptotic behavior following a burst of fast neutrons is also found to be exponential with the same time constant. In a continuous slowing-down model, all neutrons slow down in the same time implying that the time-dependent part of the time-dependent slowing-down kernel is a Dirac delta-function. In this case, an explicit expression for the flux following a burst can be derived from which the approach to the asymptotic behavior is clearly seen. The mean slowing-down time (t) is used to find an approximate expression for the asymptotic decay constant. To evaluate (t) for hydrogenous media, it is noted that the Laplace transform of the Boltzmann equation is identical with the time-independent Boltzmann equation if, in the latter,Σa (E) is replaced by Σa(E) + η/υ(E), where υ(E) is the neutron velocity and η the Laplace transform variable The resulting equation can then be solved by standard methods. The infinite medium B2 = 0) result of 0.92 µsec for the slowing-down time to 1.4 ev is in good agreement with the value 0.85 µsec obtained from Monte Carlo calculations. The validity and application of the method are discussed.