NUKEFACT #2

NON-FISSION NEUTRONS ARE NOT THE PRINCIPAL NEUTRON SOURCE

last update March 9, 1997

Traditionally, neutrons in reactors have been categorized by the reaction that produces them. Thus, all neutrons from neutron induced fission are called "fission" neutrons, with two subsets, prompt fission neutrons and delayed fission neutrons. Neutrons produced by reactions other than neutron induced fission are called "non-fission" neutrons. Typical reactions in this category are (alpha,n) reactions, (gamma,n) reactions, and spontaneous fission. An alternate, and perhaps more informative, method of categorizing neutrons is by the function served in the chain reaction.

The chain reaction is a series of fission events in time, where each fission, other than the first, is produced by a fission neutron from an immediately preceding fission event. The first fission, which initiates the chain is produced by a source neutron. The chain can be modeled by dividing time into a series of increments equal to the prompt neutron lifetime, which is extremely short, being of the order of 1x10^-4 seconds. Then, if all prompt neutrons appearing within a given increment are placed at the beginning of the interval, these fast neutrons will, on average, proceed through a neutron life cycle as a group, starting as fast neutrons, slowing down, until finally a fraction of the group produces fissions at the end of the prompt lifetime increment. New prompt neutrons appear at the start of the next prompt life time increment and the process repeats. The neutron balance equation, as shown below, is based on this model.

Solving for n/l in the steady state condition, and dividing both sides of the equation by 3.1x10¹⁰ (fissions/second)/watt gives:

This expression defines the core power for all steady state conditions from shutdown to full power (more on this in a later NUKEFACT). The numerator on the right-hand-side is the sum of neutron production from the non-fission source, S-bar, and from precursor decay, C-bar. This is not an inadvertent addition of apples and oranges. The equation states, explicitly, that delayed neutrons function in the same manner as the non-fission neutrons. Both act as source neutrons that initiate chain reactions. Considering that both non-fission neutrons and delayed neutrons are produced by radioactive decay, perhaps this revelation is not all that surprising.

The denominator of this equation, which forms a multipling factor of 1/(beta - rho), represents the source multiplication factor, as described in NUKEFACT #3. Note that this multiplication factor is not limited to negative reactivities, but rather, is applicable up to near prompt criticality.

The precursor balance equation for the one-delay group model is:

When far subcritical, at reactivity = -0.0300, the non-fission source is nearly a factor-of-ten stronger than the delayed neutron source. With criticality imminent, at reactivity = -0.0001, the situation is reversed. The delayed neutron strength is more than a factor-of-10 greater than the non-fission source strength. And while it is common knowledge that at a positive reactivity value of +beta the reactor condition is one of "prompt criticality", observe that at a negative reactivity value of -beta the delayed neutron source strength exactly equals the non-fission source strength, i.e. lambda-effective x C = S.

From this brief description of the chain reaction and from the neutron balance equation, itself, it is possible to summarize the function of neutrons in the reactor as follows:

• Non-fission neutrons - are always classed as "source" neutrons, because the non-fission reactions provide a source of neutrons for initiating chain reactions. The non-fission neutron source is relatively weak, typically of the order of 1x10⁸ neutrons/second for the entire core, and can be considered constant during short term reactor transients. The lifetime of the source neutron is of the same order as the prompt neutron.

• Prompt neutrons - exist for one prompt neutron lifetime and are the propagators of the chain reaction. Prompt neutrons, which always make up the majority of the neutron population in a multiplying medium, are always a multiple of the neutron source strength. Operationally, this multiple rarely exceeds a factor-of-200, as determined from 1/(beta - rho).
• Delayed neutrons - result from fission reactions but by function in the chain are source neutrons. Delayed neutrons provide a weak source at reactor shutdown, typically of the order of 1x10⁶ neutrons/second, but an enormous source at high power, for example 1x10¹⁸ neutrons/second at 2500 mwt. From the attainment of criticality to full power, delayed neutrons are the prinicipal neutron source in the reactor. Once emitted, the lifetime of the delayed neutron is of the same order as the prompt neutron.