A Comparative Analysis of Fission Moderators

Christopher Barry
November 30, 2017

Submitted as coursework for PH241, Stanford University, Winter 2017

Introduction and Importance

Fig. 1: The Genoa Generating Station and La Crosse Boiling Water Reactor (LACBWR) is a retired nuclear power plant that once contained a reactor with a water moderator. (Source: Wikimedia Commons).

In thermal nuclear reactors, moderators are the substances that interact directly with reacting nuclear material in order to slow down the neutrons that are ejected in the reaction to a thermal speed. After the neutrons pass through a moderator, they move through a coolant that transfers their heat through a turbine to generate electricity.

There exists a wide array of options for what moderators can be used in a reactor, and the choice can in large part determine the safety, efficiency, and enrichment requirements for the system as a whole. As a result, there has been extensive study into the advantages and disadvantages that each type of moderator brings to the table, as well as considerable exploration into possibilities for new moderators or ways to eliminate them entirely.

An ideal moderator has three characteristics. It must have a "large neutron scattering cross-section, meaning it should have a relatively large area that neutrons can hit to facilitate as many collisions as possible. It should also have a "low neutron absorption cross-section" so that neutrons ejected during the fission process pass through the moderator into the coolant. Finally, it should have a "large neutron energy loss per collision," so that neutrons slow down as much as possible when they collide with the atoms in the moderator. [1]


Water is by far the most commonly used moderator, especially in the United States. [2] The reactors that use water as a moderator, Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs), generally have relatively large enrichment requirements of U-235 (3.2% in the case of PWRs), and substantially increased safety relative to other types of reactors. [2] Nuclear fuel in light water reactors also becomes compromised with large amounts of fission product waste such as Krypton and Xenon, which absorb the rods' neutron population. As a result, the systems can be inefficient with their use of fuel: some forms of light water reactors use only 5% of available fuel before discarding it. [3]

Using water as a moderator contributes to the need for enriched nuclear fuel because of two additional factors: water's requirement to be "under-moderated," and its relatively high absorption cross-section. Water-moderated reactors must maintain a low moderator-to-fuel ratio, meaning that for the amount of uranium in the chamber, a smaller amount of water than is maximally efficient can be safely used. This is because having too much water would result in a higher level of absorption of neutrons, causing the water to heat and expand. This reduction in density would cause an increase in kinetic activity and radioactivity in the reactor, causing a dangerous cycle that could lead to a meltdown. That being said, if the reactor is already under-moderated, an increase in heat would result in the addition of negative reactivity, as water has a negative "moderator temperature coefficient" when it is at an under-moderated temperature. The second disadvantage comes from its high absorption cross-section, especially compared to heavy water, which features deuterium and has a very low cross-section. [1,3] These factors together decrease water reactors' ability to "go critical" and sustain a nuclear reaction with unenriched uranium. [1]

The most important safety feature of light water reactors is that, since they use one substance for both their moderator and coolant, the system shuts down if the coolant drains out. As a result, the core can't have a nuclear explosion if it looses coolant: nothing would serve as a moderator for such a disaster. Additionally, part of the reason that water is an intrinsically safe moderator is its negative "fuel temperature coefficient," also known as a "Doppler reactivity coefficient." This signifies that an increase in fuel power causes an opposite effect in fuel temperature because it becomes easier to absorb a neutron that the nucleus is moving toward. As a result, an increase in temperature also widens the range of neutrons that can be absorbed inside the fuel. Although this is a minor effect on overall safety of the system, it is an incremental improvement. [1] Furthermore, water reactors have low "void coefficients," which indicate how much steam is forming within moderators. An increase in steam allows neutrons to exit with increased speed, but they also decrease the moderator-to-fuel ratio, which lowers reactivity and counters the effect of a higher-energy system. [1]

Heavy Water

Heavy water moderators provide more efficiency and a lower requirement for uranium enrichment compared to water moderators, but these advances come with some sacrifices to safety. As mentioned above, the deuterium in heavy water causes its neutron absorption cross-section to be extremely low. [2] As a result, the CANDU nuclear reactor, which is the only nuclear reactor that uses this method, uses unenriched (.72% U-235) uranium dioxide held in zirconium alloy cans as fuel. [2,3]

Part of the drop in safety of this system relates to its Doppler reactivity coefficient, which is much less negative than that of a light water reactor. That being said, scientists from the CANDU Owners Group defend this potential danger because neutrons do not get absorbed nearly as quickly (in fact, neutron absorption happens approximately 40 times slower than it does in a light water reactor), so the power of the system increases much more slowly in CANDU reactors than in other types of reactors. As a result, a CANDU reactor's other features can control increases in temperature or reactivity. Furthermore, extensive safety meetings about the reactor have been needed because of its positive void coefficient. Increased steam actually increases the reactivity of the system, which creates more steam and could lead to a dangerous cycle. The "long neutron lifetime," or the long timeframe at which neutrons are absorbed, could also help keep this danger in control; operators of CANDU reactors believe they could insert control rods quickly enough to respond to any real danger. [4]

CANDU reactors have historically affected geopolitical safety and security, as well. In fact, in the 1950s, Canada and the United States offered to assist India with building a CANDU-style reactor, then named the Canadian-Indian Reactor, U.S. (CIRUS). This allowed India, which did not have nuclear enrichment capabilities at the time, to gradually convert unenriched uranium into weapons-grade plutonium (which was created as a byproduct of CIRUS's operations), and detonate a nuclear weapon in 1974. This occurrence happened despite India's promises earlier in the century to never create or use a nuclear weapon, and clearly demonstrated the nuclear proliferation risk that CANDU reactors pose. As a result, the use of this type of reactor is now heavily scrutinized. [5]


Reactors with graphite moderators are used extensively throughout the world, as well. The Advanced Gas-Cooled Reactor (AGR) is a descendant of the Magnox reactor, the RBMK Reactor (infamous for the Chernobyl disaster) is water-cooled, and the experimental Pebble Bed Modular Reactor is helium-cooled. [2,6]

These types of reactors don't quite match the low nuclear enrichment requirements of the CANDU, but maintain a lower bar than light water reactors. The RMBK burns uranium dioxide fuel with 1.8% U-235. [6] In the case of the AGR, uranium pellets enriched to between 2.2% and 2.7% U-235 content are required. [7] Many pebble-bed reactors are currently under development, so enrichment requirements for the design going forward could vary. [2] That being said, a test reactor called the HTR-10 successfully went critical using 27000 pebbles of uranium oxide at 17% enrichment. [8] This enrichment threshold could decrease as the design of pebble bed reactors improves.

Unfortunately, the RMBK is seen in the United States as one of the most dangerous thermal reactors in existence. [2] The combination of graphite moderator and water coolant can create huge void coefficient that causes the reactor to heat uncontrollably when steam starts to appear at low power levels. In the case of the Chernobyl reactor, heated neutrons were shooting through the steam so fast that they caused it to switch from operating at 20% its normal power to 100 times its normal power in a matter of seconds. [6] In any case, graphite is a relatively efficient moderator that causes problems when combined with certain substances in dangerous situations.


Although experimental moderators are not the focus of this paper, the scientific community is exploring two more relevant developments. A next-generation CANDU reactor is being researched that could potentially alleviate the safety concerns that are held about the system. The moderator in the next-generation CANDU could absorb excess heat that would otherwise enter the coolant. This could prevent the out-of-control spiral that causes most nuclear accidents. [2] Furthermore, "fast reactors" are nuclear reactors that have no moderator, and instead use high-conductivity coolant. Liquid sodium has been proposed as a feasible substance for this process. Unfortunately, these systems are in very early development and not currently feasible. They could, if developed, reduce consumption of uranium by up to 40% by creating Plutonium through the fission process and recycling it. [2]


There are plenty of options for moderators in nuclear reactors, most of which can help create a perfectly safe, relatively efficient system. That being said, common concerns about fuel temperature coefficients and void coefficients need to be addressed with extensive safety mechanisms in most power plants, especially those with CANDU or RBMK reactors.

© Christopher Barry. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] "DOE Fundamentals Handbook: Nuclear Physics and Reactor Theory, Vol 2 of 2," U.D. Department of Energy, DOE-HDBK-1010/2-93, January 1983, pp. 20-24.

[2] "Nuclear Reactor Types," Institution of Electrical Engineers, November 1993.

[3] J. Dodaro, "Heavy Water Breeding," Physics 241, Stanford University, Winter 2016.

[4] D. Meneley and A. Muzumdar, "Power Reactor Safety Comparison - A Limited Review," in Proc. of the CNS 30th Annual Conference, Vol. 1 (Curran Associates, 2009), p. 113.

[5] M. Donohue, "Pokhran-I: India's First Nuclear Bomb," Physics 241, Stanford University, Winter 2014.

[6] G. Choppin, J. Rydberg, and U.-O. Liljenzin, Radiochemistry and Nuclear Chemistry (Butterworth-Heinemann, 2001), pp. 20, 563-566.

[7] E. Nonbol, "Description of the Advanced Gas Cooled Type of Reactor," Risø National Laboratory, NKS/RAK2(96)TR-C2, November 1996.

[8] Z. Wu, D. Lin and D. Zhong, "The Design Features of the HTR-10," Nucl. Eng. Des. 218, 25 (2002).