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Description of Delayed Neutrons

Delayed Neutrons

Parameters of Delayed Neutrons
Delayed neutrons are traditionally represented by six delayed neutron groups, whose yields and decay constants (λ) are obtained from nonlinear least-squares fits to experimental measurements.

Delayed neutrons are emitted by neutron-rich fission fragments that are called delayed neutron precursors. These precursors usually undergo beta decay, but a small fraction of them are excited enough to undergo neutron emission. The neutron is produced via this type of decay, and this happens orders of magnitude later than the emission of the prompt neutrons, which plays an extremely important role in the control of the reactor.

While most of the neutrons produced in fission are prompt neutrons, the delayed neutrons are important in reactor control. The presence of delayed neutrons is perhaps the most important aspect of the fission process from reactor control. In this context, the term “delayed” means that the neutron is emitted with half-lives, ranging from few milliseconds up to 55 s for the longest-lived precursor 87Br. These neutrons have to be distinguished from the prompt neutrons, which are emitted immediately (on the order of 10-14 s) after a fission event from a neutron-rich nucleus. Although the amount of delayed neutrons is only on the order of tenths of a percent of the total amount, the timescale in seconds plays an extremely important role.

 
Key Characteristics of Delayed Neutrons
  • The presence of delayed neutrons is perhaps the most important aspect of the fission process from reactor control.
  • Delayed neutrons are emitted by neutron-rich fission fragments that are called delayed neutron precursors.
  • These precursors usually undergo beta decay, but a small fraction of them are excited enough to undergo neutron emission.
  • The emission of neutrons happens orders of magnitude later compared to the emission of the prompt neutrons.
  • About 240 n-emitters are known between 8He and 210Tl. About 75 of them are in the non-fission region.
  • It is suggested to group together the precursors based on their half-lives to simplify reactor kinetic calculations.
  • Therefore delayed six delayed neutron groups traditionally represent neutrons.
  • Neutrons can also be produced in (γ, n) reactions (especially in reactors with heavy water moderators), and therefore, they are usually referred to as photoneutrons. Photoneutrons are usually treated no differently than regularly delayed neutrons in the kinetic calculations.
  • The total yield of delayed neutrons per fission, vd, depends on:
    • An isotope that is fissioned.
    • The energy of a neutron induces fission.
  • Variation among individual group yields is much greater than variation among group periods.
  • In reactor kinetic calculations, it is convenient to use relative units as delayed neutron fraction (DNF).
  • At the steady-state condition of criticality, with keff = 1, the delayed neutron fraction is equal to the precursor yield fraction β.
  • In LWRs, the β decreases with fuel burnup. This is due to isotopic changes in the fuel.
  • Delayed neutrons have initial energy between 0.3 and 0.9 MeV with an average energy of 0.4 MeV.
  • Depending on the type of the reactor, and their spectrum, the delayed neutrons may be more (in thermal reactors) or less effective than prompt neutrons (in fast reactors). The effectively delayed neutron fraction – βeff must be defined to include this effect in the reactor kinetic calculations.
  • The effectively delayed neutron fraction is the product of the average delayed neutron fraction and the importance factor βeff = β . I.
  • The weighted delayed generation time is given by τ = ∑iτi . βi / β = 13.05 s, therefore the weighted decay constant λ = 1 / τ ≈ 0.08 s-1.
  • The mean generation time with delayed neutrons is about ~0.1 s, rather than ~10-5 as in section Prompt Neutron Lifetime, where the delayed neutrons were omitted.
  • Their presence completely changes the dynamic time response to some reactivity change, making it controllable by control systems such as the control rods.
Delayed Neutron Production - MT-455
Delayed Neutron Production
This chart shows the energy dependency of delayed neutrons production. The delayed neutrons production remains constant to 4 MeV, then a linear decrease is observed. Source: JANIS (Java-based Nuclear Data Information Software); ENDF/B-VII.1
 
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Delayed Neutrons

See next:

Characteristics of Delayed Neutrons