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This division promotes the development and timely introduction of fusion energy as a sustainable energy source with favorable economic, environmental, and safety attributes. The division cooperates with other organizations on common issues of multidisciplinary fusion science and technology, conducts professional meetings, and disseminates technical information in support of these goals. Members focus on the assessment and resolution of critical developmental issues for practical fusion energy applications.
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April 3–5, 2025
Albuquerque, NM|The University of New Mexico
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Nuclear News 40 Under 40 discuss the future of nuclear
Seven members of the inaugural Nuclear News 40 Under 40 came together on March 4 to discuss the current state of nuclear energy and what the future might hold for science, industry, and the public in terms of nuclear development.
To hear more insights from this talented group of young professionals, watch the “40 Under 40 Roundtable: Perspectives from Nuclear’s Rising Stars” on the ANS website.
George I. Bell
Nuclear Science and Engineering | Volume 21 | Number 3 | March 1965 | Pages 390-401
Technical Paper | doi.org/10.13182/NSE65-1
Articles are hosted by Taylor and Francis Online.
We consider the probability, pn(R,t∫; ,,t), that in a multiplying system, a neutron with position velocity , at time t leads to exactly n neutrons in region R of , space at time t∫. By formulating pn in terms of first collision probabilities we derive a non-linear (Boltzmann-like) integro-differential equation for the probability generating function, G. The linearized equation for = 1 - G is shown to be adjoint to the usual Boltzmann equation for the average neutron flux. The behavior of for subcritical and supercritical systems is analyzed. For large t∫-t, it is shown that for subcritical systems approaches zero exponentially, while for supercritical systems → which is a solution of the time-independent non-linear equation for and equals the probability of getting a divergent chain reaction from the initial neutron. In section B, one-velocity theory with isotropic scattering is described in some detail while in section C are outlined the extensions to 1) energy-dependent problems with anisotropic scattering 2) multiple final states, 3) random sources, 4) counting problems, and 5) delayed neutron precursors. In section D methods for solution of equations for G are briefly discussed, and it is shown that the asymptotic behavior may be found from solutions of linear time-independent ‘adjoint α’ and ‘adjoint k’ calculations. Derivation of a point model independent of space and velocity is carried out by an expansion in adjoint α eigenfunctions and the model parameters are shown to differ from those usually assumed in point models.