# Neutron Generation – Neutron Population

## Neutron Generation – Neutron Population

Both terms, the neutron generation and the neutron population are closely associated with the multiplication of neutrons in the reactor core. The infinite multiplication factor is the ratio of the neutrons produced by fissionin one neutron generation to the number of neutrons lost through absorption in the preceding neutron generation. This can be expressed mathematically as shown below.

## Example:

The difference may be well expressed by following example:

Example:

The number of neutrons (the neutron population) in the core at time zero is 1000 and k = 1.001 (~100 pcm).

Calculate the number of neutrons after 100 generations. Let say, the mean generation time is ~0.1s.

Solution:
To calculate the neutron population after 100 neutron generations, we use following equation:

Nn=N0. (k)n
N1=N0.1.001 = 1001 neutrons after one generation
N2=N0.1.001.1.001 = 1002 neutrons after two generations
N3=N0.1.001.1.001.1.001 = 1003 neutrons after three generations
.
.

N50=N0. (k)50 = 1051 neutrons after fifty generations.

.

.

N100=N0. (k)100 = 1105 neutrons after hundred generations.

If we consider the mean generation time to be ~0.1s, so the increase from 1000 neutrons the 1105 neutrons occurs within 10 seconds.

It is obvious the infinite multiplication factor in a multiplying system is a measure of the change in the fission neutron population from one neutron generation to the subsequent generation.

• k < 1. If the multiplication factor for a multiplying system is less than 1.0, then the number of neutrons is decreasing in time (with the mean generation time) and the chain reaction will never be self-sustaining. This condition is known as the subcritical state.
• k = 1. If the multiplication factor for a multiplying system is equal to 1.0, then there is no change in neutron population in time and the chain reaction will be self-sustaining. This condition is known as the critical state.
• k > 1. If the multiplication factor for a multiplying system is greater than 1.0, then the multiplying system produces more neutrons than are needed to be self-sustaining. The number of neutrons is exponentially increasing in time (with the mean generation time). This condition is known as the supercritical state.

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

Press the “clear and run” button and try to increase the power of the reactor.

Compare the response of the reactor with the case of Infinite Multiplying System Without Source and without Delayed Neutrons (or set the β = 0).

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.