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Effective Precursor Decay Constant – Lambda-Effective

Effective Precursor Decay Constant – Lambda-Effective

The effectively delayed neutron precursor decay constant (pronounced lambda effective) is a new term, which has to be introduced in the reactor period equation in the case of a single precursor group model. Creating a simple kinetic model conducive to understanding reactor behavior is useful to reduce the precursors to a single group further. But if we do this, the convention is to employ a constant precursor yield fraction and a variable precursor decay rate, as defined by lambda effective (λeff). In the single precursor group model, the lambda effect is not a constant but rather a dynamic property that depends on the mix of precursor atoms resulting from the reactivity.

The reason the constant decay constant cannot be used is as follows. There is a difference in the decay and the creation of short-lived and long-lived precursors during power transients.

During a power increase (positive reactivity), the short-lived precursors decaying at any given instant were born at a higher power level than the longer-lived precursors decaying at the same instant. The short-lived precursors become more significant. As the magnitude of the positive reactivity increases, the value of lambda effective increases closer to that of the short-lived precursors (let say 0.1 s-1 for +100pcm).

During a power decrease (negative reactivity), the long-lived precursors decaying at a given instant were born at a higher power level than the short-lived precursors decaying at that instant. The long-lived precursors become more significant. As the magnitude of the negative reactivity increases, the value of lambda effective decreases closer to that of the long-lived precursors (let say 0.05 s-1 for -100pcm).

If the reactor is operating at steady-state operation, all the precursor groups reach an equilibrium value and the λeff value is approximately 0.08 s-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 previous:

Example – Point Kinetics

See above:

Delayed Neutrons

See next:

Effect on Reactor Control