Principles
As a simplistic analysis, a system will be exactly critical if the rate of neutron production from fission is exactly balanced by the rate at which neutrons are either absorbed or lost from the system due to leakage. Safely subcritical systems can be designed by ensuring that the potential combined rate of absorption and leakage always exceeds the potential rate of neutron production.
The parameters affecting the criticality of the system may be remembered using the mnemonic MAGICMERV. Some these parameters are not independent from one another; for example, changing mass will result in a change of volume among others.
Mass: The probability of fission increases as the total number of fissile nuclei increases. The relationship is not linear. If a fissile body has a given size and shape but varying density and mass, there is a threshold below which criticality can not occur. This threshold is called the critical mass.
Absorption: Absorption removes neutrons from the system. Large amounts of absorbers are used to control or reduce the probability of a criticality. Good absorbers are boron, cadmium, gadolinium, silver, and indium.
Geometry/shape: The shape of the fissile system affects how easily neutrons can escape (leak out) from it, in which case they are not available to cause fission events in the fissile material. Therefore, the shape of the fissile material affects the probability of occurrence of fission events. A shape with a large surface area, such as a thin slab, favors leakage and is safer than the same amount of fissile material in a small, compact shape such as a cube or sphere.
Interaction of units: Neutrons leaking from one unit can enter another. Two units, which by themselves are sub-critical, could interact with each other to form a critical system. The distance separating the units and any material between them influences the effect.
Concentration/Density: Neutron reactions leading to scattering, capture or fission reactions are more likely to occur in dense materials; conversely neutrons are more likely to escape (leak) from low density materials.
Moderation: Neutrons resulting from fission are typically fast (high energy). These fast neutrons do not cause fission as readily as slower (less energetic) ones. Neutrons are slowed down (moderated) by collision with atomic nuclei. The most effective moderating nuclei are hydrogen, deuterium, beryllium and carbon. Hence hydrogenous materials including oil, polyethylene, water, wood, paraffin, and the human body are good moderators. Note that moderation comes from collisions; therefore most moderators are also good reflectors.
Enrichment: The probability of a neutron reacting with a fissile nucleus is influenced by the relative numbers of fissile and non-fissile nuclei in a system. The process of increasing the relative number of fissile nuclei in a system is called enrichment. Typically, low enrichment means less likelihood of a criticality and high enrichment means a greater likelihood.
Reflection: When neutrons collide with other atomic particles (primarily nuclei) and are not absorbed, they are scattered (i.e. they change direction). If the change in direction is large enough, neutrons that have just escaped from a fissile body may be deflected back into it, increasing the likelihood of fission. This is called 'reflection'. Good reflectors include hydrogen, beryllium, carbon, lead, uranium, water, polyethylene, concrete, Tungsten carbide and steel.
Volume: For a body of fissile material in any given shape, increasing the size of the body increases the average distance that neutrons must travel before they can reach the surface and escape. Hence, increasing the size of the body increases the likelihood of fission and decreases the likelihood of leakage. Hence, for any given shape (and reflection conditions - see below) there will be a size that gives an exact balance between the rate of neutron production and the combined rate of absorption and leakage. This is the critical size.
Other parameters include:
Temperature: This particular parameter is less common for the criticality safety practitioner, as in a typical operating environment, where the variation in temperature is minimal, or where the increase in temperature does not adversely affect the criticality of the system, often, it is assumed that room temperate is bounding of the actual temperature of the system being analyzed. This is however only an assumption, it is important for the criticality safety practitioner to understand where this does not apply, such as high temperature reactors, or low temperature cryogenic experiments.
Heterogeneity: Blending fissile powders into solution, milling of powders or scraps, or other processes that effects the small-scale structure of fissile materials is important. While normally referred to as heterogeneity control, generally the concern is maintaining homogeneity because the homogeneous case is usually less reactive. Particularly, at lower enrichment a system may be more reactive in a heterogeneous configuration compared to a homogeneous configuration.[2]
Physicochemical Form: Consists of controlling the physical state (i.e., solid, liquid, or gas) and form (e.g., solution, powder, green or sintered pellets, or metal) and/or chemical composition (e.g., uranium hexafluoride, uranyl fluoride, plutonium nitrate, or mixed oxide) of a particular fissile material. The physicochemical form could indirectly affect other parameters, such as density, moderation, and neutron absorption.