Reactivity Coefficients

Today I'm going to talk about one of the natural safety features of a nuclear reactor, the reactivity coefficient. First, lets define reactivity:

Reactivity is the change that a reactor sees away from it's normal state. For example, if a reactor is operating and you insert control rod banks to shut it down, you are subtracting reactivity (or adding negative reactivity). If you are familiar with the "k" value, this is expressed as:


(k_eff - 1)/k_eff


So you could see this as the deviation of "k" away from 1 (critical).

There are several different reactivity coefficients, which are basically just measures of how the reactor responds to certain changes in the system. For example:

The moderator temperature coefficient is a measure of how much reactivity is gained or lost when the moderator (usually water) changes temperature. In a typical nuclear reactor this is a small negative number. What that means is that when the moderator temperature increases (a positive change) you multiply it by moderator temperature coefficient (a negative number) to see what the change in reactivity will be:

+ Change in moderator temperature * - change in reactivity/change in moderator temperature              = - change in reactivity


Thus an increase in moderator temperature would decrease the overall reactivity of the system. Similarly, the fuel temperature coefficient (also known as the Doppler coefficient) measures the change in reactivity based on the temperature of the fuel. This is also an inherently negative number, which is important because the fuel is the first area to see temperature changes.

Finally, the void coefficient is a measure of the reactivity change versus the change in voids (meaning areas of no moderator). This is best known as one of the causes of the Chernobyl incidents. The Cherynobyl RMBK reactor had a large positive void coefficient, which meant that when it began boiling (creating voids) the power began to go up. With more power comes more boiling, creating a feedback loop that ultimately melted the core.

Reassuringly, in the U.S.A all of the nuclear reactors in use have a negative void coefficient, meaning if boiling (or a loss of coolant) ever occurred, the natural tendency of the core would be to shut itself down.