# Prompt Neutron Lifetime – PNL

## Prompt Neutron Lifetime

Prompt neutron lifetime, l, is the average time from a prompt neutron emission to either its absorbtion (fission or radiative capture) or to its escape from the system. This parameter is defined in multiplying or also in nonmultiplying systems. In both systems the prompt neutron lifetimes depend strongly on:

• material composition of the system
• multiplying – nonmultiplying system
• system with or without thermalization
• isotopic composition of the system
• geometric configuration of the system
• homogeneous or heterogeneous system
• shape of entire system
• size of the system

In an infinite reactor (without escape) prompt neutron lifetime is the sum of the slowing down time and the diffusion time.

l=ts + td

In an infinite thermal reactor ts << td and therefore l ≈ td. The typical prompt neutron lifetime in thermal reactors is on the order of 10−4 second. Generally, the longer neutron lifetimes take place in systems in which the neutrons must be thermalized in order to be absorbed.

Systems in which most of the neutrons are absorbed at higher energies and the neutron thermalization is suppressed (e.g. in fast reactors), have much shorter prompt neutron lifetimes. The typical prompt neutron lifetime in fast reactors is on the order of 10−7 second.

Slowing Down and Diffision Times for Thermal Neutrons in an Infinite Medium

Source: Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.

Dependencies of asymptotic time period on the reactivity required for different reactor types with different prompt neutron lifetimes. Source: http://www.hindawi.com/journals/ijne/2014/373726/

## Example – Infinite Multiplying System Without Source and Delayed Neutrons

An equation governing the neutron kinetics of the system without source and with the absence of delayed neutrons is the point kinetics equation (in certain form). This equation states that the time change of the neutron population is equal to the excess of neutron production (by fission) minus neutron loss by absorption in one prompt neutron lifetime. The role of prompt neutron lifetime is evident. Shorter lifetimes give simply faster responses of multiplying systems.

If there are neutrons in the system at t=0, that is, if n(0) > 0, the solution of this equation gives the simplest form of point kinetics equation (without source and without delayed neutrons):Let us consider that the prompt neutron lifetime is ~2 x 10-5 and k (k – neutron multiplication factor) will be step increased by only 0.01% (i.e. 10pcm or ~1.5 cents), that is k=1.0000 will increase to k=1.0001.

It must be noted such reactivity insertion (10pcm) is very small in case of LWRs. The reactivity insertions of the order of one pcm are for LWRs practically unrealizable. In this case the reactor period will be:

T = l / (k∞ – 1) = 2 x 10-5 / (1.0001 – 1) = 0.2s

This is a very short period. In one second the neutron flux (and power) in the reactor would increase by a factor of e5 = 2.7185, in 10 seconds the reactor would pass through 50 periods and the power would increase by e50 = ……

Furthermore in case of fast reactors in which prompt neutron lifetimes are of the order of 10-7 second, the response of such a small reactivity insertion will be even more unimaginable. In case of 10-7 the period will be:

T = l / (k∞ – 1) = 10-7 / (1.0001 – 1) = 0.001s

Reactors with such a kinetics would be very difficult to control. Fortunately this behaviour is not observed in any multiplying system. Actual reactor periods are observed to be considerably longer than computed above and therefore the nuclear chain reaction can be controlled more easily. The longer periods are observed due to the presence of the delayed neutrons.

## Interactive chart – Infinite Multiplying System Without Source and Delayed Neutrons

Press the “clear and run” button and try to stabilize the power at 90%.

Look at the reactivity insertion you need to insert in order to stabilize the system (of the order to tenth of pcm).

Do you think that such a system is controlable?

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.

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:

Prompt Gamma Rays

Prompt Neutrons

## See next:

Prompt Generation Time