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%ΔK/K – percent – unit of reactivity

Units of Reactivity

Mathematically, reactivity is a dimensionless number, but various units can express it. The most common units for research reactors are units normalized to the delayed neutron fraction (e.g.,, cents and dollars) because they exactly express a departure from prompt criticality conditions.

The most common units for power reactors are units of pcm or %ΔK/K. The reason is simple. Units of dollars are difficult to use because the normalization factor, the effectively delayed neutron fraction, significantly changes with the fuel burnup. In LWRs, the delayed neutron fraction decreases with fuel burnup (e.g.,, from βeff = 0.007 at the beginning of the cycle up to βeff = 0.005 at the end of the cycle). This is due to isotopic changes in the fuel. It is simple. Fresh uranium fuel contains only 235U as the fissile material. Meanwhile, during fuel burnup, the importance of fission of 239Pu increases (in some cases up to 50%). Since 239Pu produces significantly fewer delayed neutrons (0.0021 for thermal fission), the resultant core delayed neutron fraction of a multiplying system decreases (the weighted average of the constituent delayed neutron fractions).

βcore= ∑ Pii


The unit of reactivity in percent of the effective multiplication factor. For example, the subcriticality of keff = 0,98 equals -2% in units of %ΔK/K. Since this is a very large amount of reactivity, these units are usually used to express significant reactivity like power defects, xenon worth, the integral worth of control rods, or shutdown margin. This unit is inappropriate for operational changes that affect the effective multiplication factor because these changes are of the lower order.

keff = 0.99     ρ = (keff – 1) / keff = -0.01     ρ = -0.01 * 100% = -1 %

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: