MAGIC MERV
Introduction
MAGIC MERV isn’t exactly what might pop in your head when you think of criticality safety, but soon it will be! MAGIC MERV is an acronym that is often used to help remember the different nuclear parameters that affect criticality. It’s not the only acronym that exists, there’s also MERMAIDS, but MAGIC MERV seems to be more widespread in use, and they all really talk about the same stuff anyway. MAGIC MERV stands for: Mass, Absorber, Geometry, Interaction, Concentration, Moderation, Enrichment, Reflection, and Volume. We’ll break down each one of those and discuss some related topics at a high level in further sections. We’ll even add links to posts related to the parameters as we write more on each topic, so be sure to check back here for new topics related to these parameters. If you’re completely new to criticality safety, then it’ll be helpful to learn a few concepts before moving forward.
Definitions
Fission
Fission is the term used to describe an event where the nucleus of an atom becomes excited (meaning that it has more energy than it can handle) by something depositing energy into it, like a neutron. The nucleus doesn’t want to be in this excited state, it wants to be stable, so to get rid of the energy, it might split into other isotopes, release some thermal energy (heat), and releases some gamma and neutron radiation. The neutrons released from a fission can then go on to cause other fissions, which is why it can be referred to as a “chain reaction”. It’s a common misconception that fission occurs from a neutron physically hitting the nucleus and causing it to split. What actually happens is that the neutron gets absorbed into the nucleus briefly, which is how the nucleus gets all that extra energy, then the fission might occur. It also might not occur, depending on the nucleus, the neutron might just stay absorbed for a longer period of time before energy is released some other way.
Criticality
Criticality is a term used to describe neutron multiplication in a system that is currently undergoing fission. As mentioned above in the fission definition, once a nucleus fissions, it will usually release several neutrons. Those neutrons can then go on to cause more fissions. If a system is releasing as many neutrons as it is using to generate fissions (meaning that, for every neutron that is used to cause a fission, the neutrons that were generated from that fission go on to cause at least one other fission), that is considered a neutron multiplication of 1. A neutron multiplication of 1 is called being “critical”, whereas anything less than 1 is considered “subcritical”, and anything above 1 is “super critical”. Nuclear reactors usually operate in the critical state (there’s some technicalities here about reactors actually operating in a super critical state, but this isn’t a site for reactors), which will maintain the chain reaction of generating a lot of fissions, which will in turn produce a lot of heat, but also a lot of radiation. When working closely with material that can fission, you always want to be in the subcritical state, which will not be producing any sustainable chain reaction, therefore not much heat or radiation will be produced. You may also see neutron multiplication defined as the variable keff. This variable is used to represent neutron multiplication in neutron transport calculations and diffusion theory, so you may see it both ways.
Fissile
Fissile is a term used to describe material that can readily fission. This is a little different that “fissionable” material, which is still material that can fission, but just not very readily or needs to be in really specific circumstances to happen. When discussing criticality safety, you’ll almost always be talking about fissile material, with the most common isotopes being ²³⁵U and ²³⁹Pu. You also may notice that fissile isotopes all have an odd atomic number, whereas fissionable isotopes (like ²³⁸U or ²⁴⁰Pu) have even atomic numbers.
Nuclear Parameter
A nuclear parameter in this context is an attribute of a system containing fissile material that can impact neutron multiplication. Each parameter in MAGIC MERV will impact neutron multiplication in some way. Most of the time, if you change on parameters, many of the others will change as will. Some will positively impact neutron multiplication, while others will have a negative impact. So trying to guess how neutron multiplication may change based on a change in a fissile system attribute is really a game of gains and losses.
With these initial definitions out of the way, you should be able to follow along the discussion in each parameter section. Each section will define what the parameter is, so don’t worry if you don’t know what something means right off the bat.
Neutron Energy
Neutron energy is exactly as it sounds, it’s the amount of energy a neutron has. The neutron energy also corresponds to the speed at which a neutron is moving. A neutron with more energy will be traveling faster than a slower energy neutron. Neutron energy is important to know about because the energy often determines how likely a neutron is to interact with a nucleus (more info on this in the nuclear cross section definition), and these nuclear interactions are what ultimately determine neutron multiplication. There are several different terms you might see that all describe neutron energy. High energy neutrons can sometimes be referred to as “fast” neutrons since high energy also means high speed. The opposite is also true, low energy neutrons can be called “slow” neutrons since they’ll be lower in speed. Some low energy neutrons might also be called “thermal” neutrons, which are neutrons that have the same energy (or move at the same speed) as the environment they are in (usually considered to be 2200 m/s). When discussing a spectrum of energies, meaning the range of different neutron energies that you might see in a system, you can also see terms like “hard” and “soft” spectrums. In this case, a hard spectrum is one that has mostly higher energy/fast neutrons, while soft spectrums will have lower energy/slower neutrons. Neutron energy is measured in units of electron volts (eV) and usually ranges all the way from 10⁶ eV (1 MeV), representing the energy of a neutron coming right of a fission, down to 10⁻² eV, with about 0.0254 eV generally being considered “thermal”. With such a wide range of magnitude being covered by neutron energies (108 difference between high energy and low energy), you’ll often see neutron energy plotted logarithmically, instead of linearly, that way you can see the data across all the energies better.
Nuclear Cross-Section
Nuclear cross-sections, or just cross-sections for short, describe the likelihood of a certain type of nuclear interaction occurring. Generally, the larger the value of the cross-section, the higher the likelihood of a certain interaction happening. It does get a little more complicated than that, but there’ll be more on that later in the discussion. There are many different types of events that cross-sections can describe and it all depends on the exact nucleus of an atom (so different isotopes will have different cross-sections), the particle type that the nucleus is interacting with (alpha, beta, gamma, neutron), and the energy of the incoming particle. For the sake of staying on topic with things that are more relevant to criticality safety, we’ll focus more on cross-sections that impact criticality. These would be cross-sections for interactions occurring with neutrons, since those are the particles that cause fission, and can usually be boiled down to three main types of interactions: scattering, absorption, and fission. Neutron scattering occurs when an incoming neutron scatters off a nucleus, usually losing some (or a lot) of energy and continuing on to cause another interaction. Neutron absorption is where a nucleus accepts (i.e., absorbs) an incoming neutron as one of its own, and the neutron becomes part of the nucleus. Since the nucleus has to also deal with all the energy the neutron brought with it, you can sometimes see a “release” of this energy by some means, like sending out a gamma ray. We’ve already discussed fission, so all you need to know here is that there is a cross-section for incoming neutrons that cause a fission.
There are two different flavors of cross-sections: microscopic cross-sections (σ) and macroscopic cross-sections (Σ). Microscopic cross-sections are measured in units of area, typically cm², and represent the likelihood of a certain particle interaction happening with a specific nucleus. For example, Uranium – 235 (U-235) has a microscopic fission cross-section of roughly 585x10⁻²⁴ cm² specifically at a neutron energy of ~0.025 eV (thermal). This value is only useful for a single atom of U-235 though, because the microscopic cross-section is a measurement on a single nucleus. This means that if you want to compare the likelihood of a fission occurring between two materials (say a uranium metal and plutonium metal), you can’t use the microscopic cross-section to do this. Because materials are made up of sextillions (that’s 10²¹) of atoms, and the exact number of those atoms that you can fit in a defined space depends on how well those atoms can be packed together (which depends on a lot of things we won’t get into here). So, to compare the likelihood of fission between two materials, you have to take into account 1) what the likelihood of fission is for a single nucleus and 2) how many of those nuclei you can cram together in a given volume/how tightly can those nuclei be packed together. This is where the macroscopic cross-section comes into play. We won’t go over the exact equation here for the basic definition, but the macroscopic cross-section is a value that takes into account both the likelihood of an interaction happening to a single nucleus (microscopic cross-section) AND how tightly those nuclei can be packed together (also known as a number density or atom density). The macroscopic cross-section is given in units of inverse length, usually in units like cm⁻¹, and can be used to compare nuclear interactions between different materials. The macroscopic cross-section for fission, caused by a neutron with an energy of ~0.025 eV, occurring in uranium metal (assuming a density of 19 g/cm3), would be roughly 28.5 cm⁻¹.
You may have noticed that the values for cross-sections can be quite small. Considering that U-235 has a pretty large thermal fission cross-section and still is in the range of 10⁻²⁴, these values are tiny. To make these numbers a little easier to read and/or write, there was a new unit introduced in the WWII timeframe called a “barn” (b). A barn is simply defined as 10⁻²⁴ cm². The story goes that scientists during this time considered a nuclear cross-section the size of 10⁻²⁴ cm² to be like “hitting the broad side of a barn” when considering all the cross-sections they were measuring at the time, and so the barn was born as a unit! To give an example, the thermal fission cross-section for U-235 given above at 585x10⁻²⁴ cm² could also be written as 585 b (read 585 barns).
Make sure to include a discussion on how they represent the likelihood of certain events happening, but that by themselves they are not a probability and that you have to take the ratio of each individually event happening to the total likelihood that movement would happen to get an actual probability.
Mass
Mass refers to the amount of fissile mass in the system. The more fissile mass you have in a system, the more fissile atoms there will be to be able to fission. The more fissions you have, the more neutrons you’ll be able to produce! Mass is usually controlled as a maximum value, and is represented in a few different ways: by fissile mass, by element mass, or by net weight/total weight.
Controlling by Fissile Mass
Using uranium as an example, controlling by fissile mass would be to set a max mass, say 350g, of the fissile isotope ²³⁵U. So the requirement might look something like “The canister shall contain less than 350g ²³⁵U”. This typically would mean that the container can be loaded with other materials that aren’t ²³⁵U that don’t count against the mass limit. The tricky part about this requirement is that the mass of ²³⁵U specifically has to be known for the material you’re loading in the can and there are a lot of materials that have a bunch of other elements in them that aren’t ²³⁵U, so simply taking a weight wouldn’t get you there. The most accurate way to meet this type of fissile mass requirement is by knowing the fissile mass from the origination of the material (by way of knowing the material composition/enrichment). The fissile mass can then be kept track of throughout the material’s life cycle. This makes more sense with whole items, like metal ingots. The elemental composition or enrichment of a material form like metal ingots is not going change unintentionally. Making metal ingots would also most likely follow a formulaic approach each time to reach the desired composition, which can be confirmed by lab samples. Controlling by fissile mass is still feasible however, even when the fissile mass of the original material is unknown. Probably a more commonly used method is through non-destructive assay (NDA), where the gamma radiation coming of the material is captured with a detector, and the unique gamma (185.7 keV) to ²³⁵U is used to estimate the mass of ²³⁵U in the material. This method would be used for things that are difficult to track from the source, like for material that’s been building up in systems over long periods of time that have multiple different sources and the exact distribution of those sources isn’t easy to figure out.
Controlling by Elemental Mass
Controlling by elemental mass is similar to controlling by the fissile mass, except instead of only controlling the mass of the fissile isotope, you would control the mass of the entire element that contains the fissile isotope. Again, using uranium as an example, a control might look like “The canister shall contain less than 350g U”. In this case, you would only need to keep track of the total amount of uranium that you put in the container and not specifically how much of that uranium is ²³⁵U. This has some advantages, like being easier to measure with certain types of material, but also might be preferred in some situations where the enrichment of the material might change a lot, but you also don’t want operators to pack containers full of material if they’re working with a really low enrichment.
Controlling by net weight or total weight
Controlling by net weight or total weight/mass is potentially the most intuitive version of mass control, at least for the operator handling the material. In this case, the requirement is placed on the total mass of material that you load into a container and not a specific isotope or element. An example of this type of requirement is “The canister shall weigh less than 5kg net weight”. This is much more intuitive for an operator because the net weight of material can be measured directly with a scale and you don’t need to keep track of a fissile isotope from the source material or perform an NDA to confirm it was loaded correctly. This type of requirement has benefits over the other control types when you need to limit both the amount of fissile material in the canister and the amount of moderator or reflector present in the canister. Since the net weight includes everything in the container, you can have a max expected amount of both fissile mass and moderator for the evaluation.
Absorber
Absorber refers to neutron absorbers, which are sometimes called poisons. Neutron absorbers are specific elements or materials that do exactly as the name implies, they essentially absorb neutrons, which prevents them from being able to cause a fission. There are two general categories of absorbers: Strong absorbers and weak absorbers.
Strong Absorbers
Strong absorbers are usually what someone would be talking about when they refer to a neutron absorber. These elements have a much higher probability of capturing a neutron (larger neutron capture cross section) than most other elements, but they are not found in materials commonly used to build equipment. So they would have to be purposely placed into a system to help reduce the fission rate. Strong absorbers include materials like boron, cadmium, and gadolinium. If these materials are going to be used in a system to reduce reactivity, they will definitely be controlled with a lot of rigor. Strong absorbers usually have a significant impact to reactivity, so if they suddenly disappear from the system, reactivity can increase dramatically. As an NCS engineer, dramatic increases in reactivity is usually not what you’re shooting for!
Weak Absorbers
Weak absorbers are usually elements that do have a probability to capture neutrons (some level of neutron capture cross section), however the probability is not very high. These elements to still help reduce the number of fissions by preventing neutrons from causing fissions, but they won’t decrease the fission rate as dramatically as strong absorbers. Some examples of weak absorbers are iron, chlorine, and nitrogen. Weak absorbers also differ from strong absorbers in that they can be found in all types of standard building materials, like steel (which contains iron) and some plastics (which may contain chlorine). Weak absorbers can also be found in commonly found processing fluids like nitric acid, which contains nitrogen. Not all weak absorbing elements are created equal though, some of them have very small neutron capture cross sections, whereas others can have some fairly significant capture cross sections (like lithium). So it’s important to understand how the cross sections of these elements may impact your system before including them in any models. Something else to keep in mind with weak absorbers is that, if they are included in a system model, then their presence is being counted on the keep the reactivity down. This may require that they be controlled in some way depending on how sensitive the system is to the presence of these weak absorbers. Sometimes this requires chemical analysis, other times it may be as simple as requesting a material certificate from a supplier showing that the material meets a certain material composition standard and the weighing or measuring the equipment to make sure enough of the material is there to get you the right amount of absorber. Either way, weak absorbers can easily find their way into your analysis, so it’s important to know their impact to your system and if they need to be controlled or not.
Geometry
Geometry is really just the shape of the fissile material, or if it’s a liquid, the shape of the container that the material is going to be in since liquid will just take whatever shape you put it in. The geometry of fissile material matters because it helps determine how neutrons are used in the material. A general rule of thumb that can be used for determining the effectiveness of a geometry is the ratio of surface area to volume. Fissile geometries are generally broken down into three categories, listed from generally most reactive to generally least reactive: spheres, cylinders, and cubes/slabs.
Surface Area (SA) to Volume (V) Ratio Rule of Thumb
When trying to figure out why one geometry might be more effective at using neutrons to generate fissions than another geometry, it’s useful to think about the geometries in terms of their surface area and their volume. Surface area on a shape represents the amount of space that is available for neutrons to be able to escape (aka leak out of) the shape. If a neutrons leaves the material, it can’t interact and cause a fission, so this would cause a decrease in fission rate or reactivity. Volume is somewhat the opposite, a shape with a larger volume is going to have more space for a neutron to interact while staying within the geometry. Giving a neutron more opportunity to interact more will generally increase the likelihood of it causing a fission, therefore increasing reactivity.
The ratio of these two values can then be used to help determine, roughly, what type of geometry would be most reactive with surface area representing the losses of neutrons out of the system and volume representing the ability of the geometry to hold those neutrons in. This means that geometries with higher SA/V ratios would have more neutron leakage and generally be less reactive than shapes with lower SA/V ratios. This rule of thumb doesn’t apply in every case like, like with cylinders explained down below, and it definitely doesn’t apply in situations where there are more than one unit (see interaction).
A good way to actually do a comparison is by choosing a volume to use with multiple geometries, then calculating the surface area for each, taking the SA/V ratio, and comparing that value. Below is a table comparing a sphere, a cylinder with a height to diameter ratio of 1, and a cube (equal on all sides), each with a volume of 10L.
