Military science

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Military_science 

Military science is the study of military processes, institutions, and behavior, along with the study of warfare, and the theory and application of organized coercive force. It is mainly focused on theory, method, and practice of producing military capability in a manner consistent with national defense policy. Military science serves to identify the strategic, political, economic, psychological, social, operational, technological, and tactical elements necessary to sustain relative advantage of military force; and to increase the likelihood and favorable outcomes of victory in peace or during a war. Military scientists include theorists, researchers, experimental scientists, applied scientists, designers, engineers, test technicians, and other military personnel.

Military personnel obtain weapons, equipment, and training to achieve specific strategic goals. Military science is also used to establish enemy capability as part of technical intelligence.

In military history, military science had been used during the period of Industrial Revolution as a general term to refer to all matters of military theory and technology application as a single academic discipline, including that of the deployment and employment of troops in peacetime or in battle.

In military education, military science is often the name of the department in the education institution that administers officer candidate education. However, this education usually focuses on the officer leadership training and basic information about employment of military theories, concepts, methods and systems, and graduates are not military scientists on completion of studies, but rather junior military officers.

History

Main articles: History of military science and Military history

 

Class in telephony: enlisted men, U. S. Army. The telephone in modern warfare has robbed battle of much of its picturesqueness, romance, and glamor; as the dashing dispatch rider on his foam-flecked steed is antiquated. A message sent by telephone annihilates space and time, whereas the dispatch rider would, in most cases, be annihilated by shrapnel. Published 1917.

Even until the Second World War, military science was written in English starting with capital letters, and was thought of as an academic discipline alongside physics, philosophy and the medical sciences. In part this was due to the general mystique that accompanied education in a world where, as late as the 1880s, 75% of the European population was illiterate. The ability by the officers to make complex calculations required for the equally complex "evolutions" of the troop movements in linear warfare that increasingly dominated the Renaissance and later history, and the introduction of the gunpowder weapons into the equation of warfare only added to the veritable arcana of building fortifications as it seemed to the average individual.

Until the early 19th century, one observer, a British veteran of the Napoleonic Wars, Major John Mitchell, thought that it seemed nothing much had changed from the application of force on a battlefield since the days of the Greeks. He suggested that this was primarily so because as Clausewitz suggested, "unlike in any other science or art, in war the object reacts".

Until this time, and even after the Franco-Prussian War, military science continued to be divided between the formal thinking of officers brought up in the "shadow" of the Napoleonic Wars and younger officers like Ardant du Picq who tended to view fighting performance as rooted in the individual's and group psychology and suggested detailed analysis of this. This set in motion the eventual fascination of the military organisations with application of quantitative and qualitative research to their theories of combat; the attempt to translate military thinking as philosophic concepts into concrete methods of combat.

Military implements, the supply of an army, its organization, tactics, and discipline, have constituted the elements of military science in all ages; but improvement in weapons and accoutrements appears to lead and control all the rest.

The breakthrough of sorts made by Clausewitz in suggesting eight principles on which such methods can be based, in Europe, for the first time presented an opportunity to largely remove the element of chance and error from command decision making process. At this time emphasis was made on the topography (including trigonometry), military art (military science), military history, organisation of the army in the field, artillery and the science of projectiles, field fortifications and permanent fortifications, military legislation, military administration and manoeuvres.

The military science on which the model of German combat operations was built for the First World War remained largely unaltered from the Napoleonic model, but took into the consideration the vast improvements in the firepower and the ability to conduct "great battles of annihilation" through rapid concentration of force, strategic mobility, and the maintenance of the strategic offensive better known as the Cult of the offensive. The key to this, and other modes of thinking about war, remained analysis of military history and attempts to derive tangible lessons that could be replicated again with equal success on another battlefield as a sort of bloody laboratory of military science. Few were bloodier than the fields of the Western Front between 1914 and 1918. The person who probably understood Clausewitz better than most, Marshal Foch, initially participated in events that nearly destroyed the French Army.

It is not, however, true to say that military theorists and commanders were suffering from some collective case of stupidity. Their analysis of military history convinced them that decisive and aggressive strategic offensive was the only doctrine of victory, and feared that overemphasis of firepower, and the resultant dependence on entrenchment would make this all but impossible, and leading to the battlefield stagnant in advantages of the defensive position, destroying troop morale and willingness to fight. Because only the offensive could bring victory, lack of it, and not the firepower, was blamed for the defeat of the Imperial Russian Army in the Russo-Japanese War. Foch thought that "In strategy as well as in tactics one attacks".

In many ways military science was born as a result of the experiences of the Great War. "Military implements" had changed armies beyond recognition with cavalry to virtually disappear in the next 20 years. The "supply of an army" would become a science of logistics in the wake of massive armies, operations and troops that could fire ammunition faster than it could be produced, for the first time using vehicles that used the combustion engine, a watershed of change. Military "organisation" would no longer be that of the linear warfare, but assault teams, and battalions that were becoming multi-skilled with the introduction of machine guns and mortars and, for the first time, forcing military commanders to think not only in terms of rank and file, but force structure.

Tactics changed, too, with infantry for the first time segregated from the horse-mounted troops, and required to cooperate with tanks, aircraft and new artillery tactics. Perception of military discipline, too, had changed. Morale, despite strict disciplinarian attitudes, had cracked in all armies during the war, but the best-performing troops were found to be those where emphasis on discipline had been replaced with display of personal initiative and group cohesiveness such as that found in the Australian Corps during the Hundred Days Offensive. The military sciences' analysis of military history that had failed European commanders was about to give way to a new military science, less conspicuous in appearance, but more aligned to the processes of science of testing and experimentation, the scientific method, and forever "wed" to the idea of the superiority of technology on the battlefield.

Currently military science still means many things to different organisations. In the United Kingdom and much of the European Union the approach is to relate it closely to the civilian application and understanding. For example, in Belgium's Royal Military Academy, military science remains an academic discipline, and is studied alongside social sciences, including such subjects as humanitarian law. The United States Department of Defense defines military science in terms of specific systems and operational requirements, and include among other areas civil defense and force structure.

Employment of military skills

In the first instance military science is concerned with who will participate in military operations, and what sets of skills and knowledge they will require to do so effectively and somewhat ingeniously.

Military organization

Main article: Military organization

Develops optimal methods for the administration and organization of military units, as well as the military as a whole. In addition, this area studies other associated aspects as mobilization/demobilization, and military government for areas recently conquered (or liberated) from enemy control.

Force structuring

Force structuring is the method by which personnel and the weapons and equipment they use are organized and trained for military operations, including combat. Development of force structure in any country is based on strategic, operational, and tactical needs of the national defense policy, the identified threats to the country, and the technological capabilities of the threats and the armed forces.

Force structure development is guided by doctrinal considerations of strategic, operational and tactical deployment and employment of formations and units to territories, areas and zones where they are expected to perform their missions and tasks. Force structuring applies to all Armed Services, but not to their supporting organisations such as those used for defense science research activities.

In the United States force structure is guided by the table of organization and equipment (TOE or TO&E). The TOE is a document published by the U.S. Department of Defense which prescribes the organization, manning, and equipage of units from divisional size and down, but also including the headquarters of Corps and Armies.

Force structuring also provides information on the mission and capabilities of specific units, as well as the unit's current status in terms of posture and readiness. A general TOE is applicable to a type of unit (for instance, infantry) rather than a specific unit (the 3rd Infantry Division). In this way, all units of the same branch (such as Infantry) follow the same structural guidelines which allows for more efficient financing, training, and employment of like units operationally.

Military education and training

Main article: Military education and training

Studies the methodology and practices involved in training soldiers, NCOs (non-commissioned officers, i.e. sergeants and corporals), and officers. It also extends this to training small and large units, both individually and in concert with one another for both the regular and reserve organizations. Military training, especially for officers, also concerns itself with general education and political indoctrination of the armed forces.

Military concepts and methods

Much of capability development depends on the concepts which guide use of the armed forces and their weapons and equipment, and the methods employed in any given theatre of war or combat environment.

Military history

Main article: Military history

Military activity has been a constant process over thousands of years, and the essential tactics, strategy, and goals of military operations have been unchanging throughout history. As an example, one notable maneuver is the double envelopment, considered to be the consummate military maneuver, notably executed by Hannibal at the Battle of Cannae in 216 BCE, and later by Khalid ibn al-Walid at the Battle of Walaja in 633 CE.

Via the study of history, the military seeks to avoid past mistakes, and improve upon its current performance by instilling an ability in commanders to perceive historical parallels during battle, so as to capitalize on the lessons learned. The main areas military history includes are the history of wars, battles, and combats, history of the military art, and history of each specific military service.

Military strategy and doctrines

Main articles: Military strategy and Military doctrine

Military strategy is in many ways the centerpiece of military science. It studies the specifics of planning for, and engaging in combat, and attempts to reduce the many factors to a set of principles that govern all interactions of the field of battle. In Europe these principles were first defined by Clausewitz in his Principles of War. As such, it directs the planning and execution of battles, operations, and wars as a whole. Two major systems prevail on the planet today. Broadly speaking, these may be described as the "Western" system, and the "Russian" system. Each system reflects and supports strengths and weakness in the underlying society.

Modern Western military art is composed primarily of an amalgam of French, German, British, and American systems. The Russian system borrows from these systems as well, either through study, or personal observation in the form of invasion (Napoleon's War of 1812, and The Great Patriotic War), and form a unique product suited for the conditions practitioners of this system will encounter. The system that is produced by the analysis provided by Military Art is known as doctrine.

Western military doctrine relies heavily on technology, the use of a well-trained and empowered NCO cadre, and superior information processing and dissemination to provide a level of battlefield awareness that opponents cannot match. Its advantages are extreme flexibility, extreme lethality, and a focus on removing an opponent's C3I (command, communications, control, and intelligence) to paralyze and incapacitate rather than destroying their combat power directly (hopefully saving lives in the process). Its drawbacks are high expense, a reliance on difficult-to-replace personnel, an enormous logistic train, and a difficulty in operating without high technology assets if depleted or destroyed.

Soviet military doctrine (and its descendants, in CIS countries) relies heavily on masses of machinery and troops, a highly educated (albeit very small) officer corps, and pre-planned missions. Its advantages are that it does not require well educated troops, does not require a large logistic train, is under tight central control, and does not rely on a sophisticated C3I system after the initiation of a course of action. Its disadvantages are inflexibility, a reliance on the shock effect of mass (with a resulting high cost in lives and material), and overall inability to exploit unexpected success or respond to unexpected loss.

Chinese military doctrine is currently in a state of flux as the People's Liberation Army is evaluating military trends of relevance to China. Chinese military doctrine is influenced by a number of sources including an indigenous classical military tradition characterized by strategists such as Sun Tzu, Western and Soviet influences, as well as indigenous modern strategists such as Mao Zedong. One distinctive characteristic of Chinese military science is that it places emphasis on the relationship between the military and society as well as viewing military force as merely one part of an overarching grand strategy.

Each system trains its officer corps in its philosophy regarding military art. The differences in content and emphasis are illustrative. The United States Army principles of war are defined in the U.S. Army Field Manual FM 100–5. The Canadian Forces principles of war/military science are defined by Land Forces Doctrine and Training System (LFDTS) to focus on principles of command, principles of war, operational art and campaign planning, and scientific principles.

Russian Federation armed forces derive their principles of war predominantly from those developed during the existence of the Soviet Union. These, although based significantly on the Second World War experience in conventional war fighting, have been substantially modified since the introduction of the nuclear arms into strategic considerations. The Soviet–Afghan War and the First and Second Chechen Wars further modified the principles that Soviet theorists had divided into the operational art and tactics. The very scientific approach to military science thinking in the Soviet union had been perceived as overly rigid at the tactical level, and had affected the training in the Russian Federation's much reduced forces to instil greater professionalism and initiative in the forces.

The military principles of war of the People's Liberation Army were loosely based on those of the Soviet Union until the 1980s when a significant shift begun to be seen in a more regionally-aware, and geographically-specific strategic, operational and tactical thinking in all services. The PLA is currently influenced by three doctrinal schools which both conflict and complement each other: the People's war, the Regional war, and the Revolution in military affairs that led to substantial increase in the defense spending and rate of technological modernisation of the forces.

The differences in the specifics of Military art notwithstanding, Military science strives to provide an integrated picture of the chaos of battle, and illuminate basic insights that apply to all combatants, not just those who agree with your formulation of the principles.

Military geography

Main article: Military geography

Military geography encompasses much more than simple protestations to take the high ground. Military geography studies the obvious, the geography of theatres of war, but also the additional characteristics of politics, economics, and other natural features of locations of likely conflict (the political "landscape", for example). As an example, the Soviet–Afghan War was predicated on the ability of the Soviet Union to not only successfully invade Afghanistan, but also to militarily and politically flank the Islamic Republic of Iran simultaneously.

Military systems

How effectively and efficiently militaries accomplish their operations, missions and tasks is closely related not only to the methods they use, but the equipment and weapons they use.

Military intelligence

Main article: Military intelligence

Military intelligence supports the combat commanders' decision making process by providing intelligence analysis of available data from a wide range of sources. To provide that informed analysis the commanders information requirements are identified and input to a process of gathering, analysis, protection, and dissemination of information about the operational environment, hostile, friendly and neutral forces and the civilian population in an area of combat operations, and broader area of interest. Intelligence activities are conducted at all levels from tactical to strategic, in peacetime, the period of transition to war, and during the war.

Most militaries maintain a military intelligence capability to provide analytical and information collection personnel in both specialist units and from other arms and services. Personnel selected for intelligence duties, whether specialist intelligence officers and enlisted soldiers or non-specialist assigned to intelligence may be selected for their analytical abilities and intelligence before receiving formal training.

Military intelligence serves to identify the threat, and provide information on understanding best methods and weapons to use in deterring or defeating it.

Military logistics

Main article: Military logistics

The art and science of planning and carrying out the movement and maintenance of military forces. In its most comprehensive sense, it is those aspects or military operations that deal with the design, development, acquisition, storage, distribution, maintenance, evacuation, and disposition of material; the movement, evacuation, and hospitalization of personnel; the acquisition or construction, maintenance, operation, and disposition of facilities; and the acquisition or furnishing of services.

Military technology and equipment

Main article: Military technology

Military technology is not just the study of various technologies and applicable physical sciences used to increase military power. It may also extend to the study of production methods of military equipment, and ways to improve performance and reduce material and/or technological requirements for its production. An example is the effort expended by Nazi Germany to produce artificial rubbers and fuels to reduce or eliminate their dependence on imported POL (petroleum, oil, and lubricants) and rubber supplies.

Military technology is unique only in its application, not in its use of basic scientific and technological achievements. Because of the uniqueness of use, military technological studies strive to incorporate evolutionary, as well as the rare revolutionary technologies, into their proper place of military application.

Military and society

This speciality examines the ways that military and society interact and shape each other. The dynamic intersection where military and society meet is influenced by trends in society and the security environment. This field of study can be linked to works by Clausewitz ("War is the continuation of politics by other means") and Sun Tzu ("If not in the interest of the state, do not act"). The contemporary multi and interdisciplinary field traces its origin to World War II and works by sociologists and political scientists. This field of study includes "all aspects of relations between armed forces, as a political, social and economic institution, and the society, state or political ethnic movement of which they are a part". Topics often included within the purview of military and society include: veterans, women in the military, military families, enlistment and retention, reserve forces, military and religion, military privatization, Civil-military relations, civil-military cooperation, military and popular culture, military and the media, military and disaster assistance, military and the environment and the blurring of military and police functions.

Recruitment and retention

In an all volunteer military, the armed forces relies on market forces and careful recruiting to fill its ranks. It is thus, very important to understand factors that motivate enlistment and reenlistment. Service members must have the mental and physical ability to meet the challenges of military service and adapt to the military's values and culture. Studies show that enlistment motivation generally incorporates both self-interest (pay) and non-market values like adventure, patriotism, and comradeship.

Veterans

The study veterans or members of the military who leave and return to the society is one of the most important subfields of the military and society field of study. Veterans and their issues represent a microcosm of the field. Military recruits represent inputs that flow from the community into the armed forces, veterans are outputs that leave the military and reenter society changed by their time as soldiers, sailors, marines and airmen. Both society and veteran face multiple layers of adaptation and adjustment upon their reentry.

The definition of veteran is surprisingly fluid across countries. In the US veteran's status is established after a service member has completed a minimum period of service. Australia requires deployment to a combat zone. In the UK "Everyone who has performed military service for at least one day and drawn a day's pay is termed a veteran." The study of veterans focuses much attention on their, sometimes, uneasy transition back to civilian society. "Veterans must navigate a complex cultural transition when moving between environments," and they can expect positive and negative transition outcomes. Finding a good job and reestablishing a fulfilling family life is high on their resettlement agenda.

Military life is often violent and dangerous. The trauma of combat often results in post-traumatic stress disorder as well as painful physical health challenges which often lead to homelessness, suicide, substance, and excessive alcohol use, and family dysfunction. Society recognizes its responsibilities to veterans by offering programs and policies designed to redress these problems. Veterans also exert an influence on society often through the political process. For example, how do veterans vote and establish party affiliation? During the 2004 presidential election veterans were basically bipartisan. Veterans who fought in Croatia's war of independence voted for the nationalist parties in greater numbers.

Reserve forces

Reserve forces are service members who serve the armed forces on a part-time basis. These men and women constitute a "reserve" force that countries rely on for their defense, disaster support, and some day-to-day operations etc. In the United States an active reservist spends a weekend a month and two weeks a year in training. The size of a county's reserve force often depends on the type of recruitment method. Nations with a volunteer force tend to have a lower reserve percentage.

Recently the role of the reserves has changed. In many countries it [has] gone from a strategic force, largely static, to an operational force, largely dynamic. After WWII, relatively large standing forces took care of most operational needs. Reserves were held back strategically and deployed in times of emergency for example during the Cuban missile crisis. Subsequently, the strategic and budget situation changed and as a result the active duty military began to rely on reserve force, particularly for combat support and combat service support. Further large-scale military operation, routinely mobilize and deploy reservists 

Lomsky-Feder et al (2008p. 594) introduced the metaphor of reserve forces as Transmigrants who live "betwixt and between the civilian and military worlds". This metaphor captures "their structural duality" and suggests dynamic nature of reservist experience as they navigate commitments to their often conflicting civilian and military worlds. Given their greater likelihood of lengthy deployment, reservists face many of the same stresses as active duty but often with fewer support services.

Nuclear reactor physics

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Nuclear_reactor_physics 

 

Pressurized water reactor: Projective representation of the thermal neutron flux of a fuel assembly of the 18×18 array with 300 fuel rods and 24 inserted control rods

Nuclear reactor physics is the field of physics that studies and deals with the applied study and engineering applications of chain reaction to induce a controlled rate of fission in a nuclear reactor for the production of energy. Most nuclear reactors use a chain reaction to induce a controlled rate of nuclear fission in fissile material, releasing both energy and free neutrons. A reactor consists of an assembly of nuclear fuel (a reactor core), usually surrounded by a neutron moderator such as regular water, heavy water, graphite, or zirconium hydride, and fitted with mechanisms such as control rods which control the rate of the reaction.

The physics of nuclear fission has several quirks that affect the design and behavior of nuclear reactors. This article presents a general overview of the physics of nuclear reactors and their behavior.

Criticality

In a nuclear reactor, the neutron population at any instant is a function of the rate of neutron production (due to fission processes) and the rate of neutron losses (due to non-fission absorption mechanisms and leakage from the system). When a reactor’s neutron population remains steady from one generation to the next (creating as many new neutrons as are lost), the fission chain reaction is self-sustaining and the reactor's condition is referred to as "critical". When the reactor’s neutron production exceeds losses, characterized by increasing power level, it is considered "supercritical", and when losses dominate, it is considered "subcritical" and exhibits decreasing power.

The "Six-factor formula" is the neutron life-cycle balance equation, which includes six separate factors, the product of which is equal to the ratio of the number of neutrons in any generation to that of the previous one; this parameter is called the effective multiplication factor k, also denoted by K_eff, where k = Є L_f ρ L_th f η, where Є = "fast-fission factor", L_f = "fast non-leakage factor", ρ = "resonance escape probability", L_th = "thermal non-leakage factor", f = "thermal fuel utilization factor", and η = "reproduction factor". This equation's factors are roughly in order of potential occurrence for a fission born neutron during critical operation. As already mentioned before, k = (Neutrons produced in one generation)/(Neutrons produced in the previous generation). In other words, when the reactor is critical, k = 1; when the reactor is subcritical, k < 1; and when the reactor is supercritical, k > 1.

Reactivity is an expression of the departure from criticality. δk = (k − 1)/k. When the reactor is critical, δk = 0. When the reactor is subcritical, δk < 0. When the reactor is supercritical, δk > 0. Reactivity is also represented by the lowercase Greek letter rho (ρ). Reactivity is commonly expressed in decimals or percentages or pcm (per cent mille) of Δk/k. When reactivity ρ is expressed in units of delayed neutron fraction β, the unit is called the dollar.

If we write 'N' for the number of free neutrons in a reactor core and ${\displaystyle \tau }$ for the average lifetime of each neutron (before it either escapes from the core or is absorbed by a nucleus), then the reactor will follow the differential equation (evolution equation)

${\displaystyle \frac{dN}{dt}=\frac{\alpha N}{\tau }}$

where ${\displaystyle \alpha }$ is a constant of proportionality, and ${\displaystyle dN/dt}$ is the rate of change of the neutron count in the core. This type of differential equation describes exponential growth or exponential decay, depending on the sign of the constant ${\displaystyle \alpha }$, which is just the expected number of neutrons after one average neutron lifetime has elapsed:

${\displaystyle \alpha =P_{impact}{P}_{fission}{n}_{avg}-P_{absorb}-P_{escape}}$

Here, ${\displaystyle P_{impact}}$ is the probability that a particular neutron will strike a fuel nucleus, ${\displaystyle P_{fission}}$ is the probability that the neutron, having struck the fuel, will cause that nucleus to undergo fission, ${\displaystyle P_{absorb}}$ is the probability that it will be absorbed by something other than fuel, and ${\displaystyle P_{escape}}$ is the probability that it will "escape" by leaving the core altogether. ${\displaystyle n_{avg}}$ is the number of neutrons produced, on average, by a fission event—it is between 2 and 3 for both ²³⁵U and ²³⁹Pu.

If ${\displaystyle \alpha }$ is positive, then the core is supercritical and the rate of neutron production will grow exponentially until some other effect stops the growth. If ${\displaystyle \alpha }$ is negative, then the core is "subcritical" and the number of free neutrons in the core will shrink exponentially until it reaches an equilibrium at zero (or the background level from spontaneous fission). If ${\displaystyle \alpha }$ is exactly zero, then the reactor is critical and its output does not vary in time (${\displaystyle dN/dt=0}$, from above).

Nuclear reactors are engineered to reduce ${\displaystyle P_{escape}}$ and ${\displaystyle P_{absorb}}$. Small, compact structures reduce the probability of direct escape by minimizing the surface area of the core, and some materials (such as graphite) can reflect some neutrons back into the core, further reducing ${\displaystyle P_{escape}}$.

The probability of fission, ${\displaystyle P_{fission}}$, depends on the nuclear physics of the fuel, and is often expressed as a cross section. Reactors are usually controlled by adjusting ${\displaystyle P_{absorb}}$. Control rods made of a strongly neutron-absorbent material such as cadmium or boron can be inserted into the core: any neutron that happens to impact the control rod is lost from the chain reaction, reducing ${\displaystyle \alpha }$. ${\displaystyle P_{absorb}}$ is also controlled by the recent history of the reactor core itself (see below).

Starter sources

Main article: Startup neutron source

See also: Zero power critical

The mere fact that an assembly is supercritical does not guarantee that it contains any free neutrons at all. At least one neutron is required to "strike" a chain reaction, and if the spontaneous fission rate is sufficiently low it may take a long time (in ²³⁵U reactors, as long as many minutes) before a chance neutron encounter starts a chain reaction even if the reactor is supercritical. Most nuclear reactors include a "starter" neutron source that ensures there are always a few free neutrons in the reactor core, so that a chain reaction will begin immediately when the core is made critical. A common type of startup neutron source is a mixture of an alpha particle emitter such as ²⁴¹Am (americium-241) with a lightweight isotope such as ⁹Be (beryllium-9).

The primary sources described above have to be used with fresh reactor cores. For operational reactors, secondary sources are used; most often a combination of antimony with beryllium. Antimony becomes activated in the reactor and produces high-energy gamma photons, which produce photoneutrons from beryllium.

Uranium-235 undergoes a small rate of natural spontaneous fission, so there are always some neutrons being produced even in a fully shutdown reactor. When the control rods are withdrawn and criticality is approached the number increases because the absorption of neutrons is being progressively reduced, until at criticality the chain reaction becomes self-sustaining. Note that while a neutron source is provided in the reactor, this is not essential to start the chain reaction, its main purpose is to give a shutdown neutron population which is detectable by instruments and so make the approach to critical more observable. The reactor will go critical at the same control rod position whether a source is loaded or not.

Once the chain reaction is begun, the primary starter source may be removed from the core to prevent damage from the high neutron flux in the operating reactor core; the secondary sources usually remains in situ to provide a background reference level for control of criticality.

Subcritical multiplication

Even in a subcritical assembly such as a shut-down reactor core, any stray neutron that happens to be present in the core (for example from spontaneous fission of the fuel, from radioactive decay of fission products, or from a neutron source) will trigger an exponentially decaying chain reaction. Although the chain reaction is not self-sustaining, it acts as a multiplier that increases the equilibrium number of neutrons in the core. This subcritical multiplication effect can be used in two ways: as a probe of how close a core is to criticality, and as a way to generate fission power without the risks associated with a critical mass.

If ${\displaystyle k}$ is the neutron multiplication factor of a subcritical core and ${\displaystyle S_0}$ is the number of neutrons coming per generation in the reactor from an external source, then at the instant when the neutron source is switched on, number of neutrons in the core will be ${\displaystyle S_0}$. After 1 generation, this neutrons will produce ${\displaystyle k\times S_0}$ neutrons in the reactor and reactor will have a totality of ${\displaystyle k\times S_0+S_0}$ neutrons considering the newly entered neutrons in the reactor. Similarly after 2 generation, number of neutrons produced in the reactor will be ${\displaystyle k\times (k\times S_0+S_0)+S_0}$ and so on. This process will continue and after a long enough time, the number of neutrons in the reactor will be,

${\displaystyle S_0+k\times S_0+k\times k\times S_0+\dots }$

This series will converge because for the subcritical core, ${\displaystyle 0<k<1}$. So the number of neutrons in the reactor will be simply,

${\displaystyle \frac{S_0}{1-k}}$

The fraction ${\displaystyle \frac{1}{1-k}}$ is called subcritical multiplication factor.

Since power in a reactor is proportional to the number of neutrons present in the nuclear fuel material (material in which fission can occur), the power produced by such a subcritical core will also be proportional to the subcritical multiplication factor and the external source strength.

As a measurement technique, subcritical multiplication was used during the Manhattan Project in early experiments to determine the minimum critical masses of ²³⁵U and of ²³⁹Pu. It is still used today to calibrate the controls for nuclear reactors during startup, as many effects (discussed in the following sections) can change the required control settings to achieve criticality in a reactor. As a power-generating technique, subcritical multiplication allows generation of nuclear power for fission where a critical assembly is undesirable for safety or other reasons. A subcritical assembly together with a neutron source can serve as a steady source of heat to generate power from fission.

Including the effect of an external neutron source ("external" to the fission process, not physically external to the core), one can write a modified evolution equation:

${\displaystyle \frac{dN}{dt}=\frac{\alpha N}{\tau }+R_{ext}}$

where ${\displaystyle R_{ext}}$ is the rate at which the external source injects neutrons into the core. In equilibrium, the core is not changing and dN/dt is zero, so the equilibrium number of neutrons is given by:

${\displaystyle N=-\frac{\tau R_{ext}}{\alpha }}$

If the core is subcritical, then ${\displaystyle \alpha }$ is negative so there is an equilibrium with a positive number of neutrons. If the core is close to criticality, then ${\displaystyle \alpha }$ is very small and thus the final number of neutrons can be made arbitrarily large.

Neutron moderators

To improve ${\displaystyle P_{fission}}$ and enable a chain reaction, natural or low enrichment uranium-fueled reactors must include a neutron moderator that interacts with newly produced fast neutrons from fission events to reduce their kinetic energy from several MeV to thermal energies of less than one eV, making them more likely to induce fission. This is because ²³⁵U has a larger cross section for slow neutrons, and also because ²³⁸U is much less likely to absorb a thermal neutron than a freshly produced neutron from fission.

Neutron moderators are thus materials that slow down neutrons. Neutrons are most effectively slowed by colliding with the nucleus of a light atom, hydrogen being the lightest of all. To be effective, moderator materials must thus contain light elements with atomic nuclei that tend to scatter neutrons on impact rather than absorb them. In addition to hydrogen, beryllium and carbon atoms are also suited to the job of moderating or slowing down neutrons.

Hydrogen moderators include water (H₂O), heavy water (D₂O), and zirconium hydride (ZrH₂), all of which work because a hydrogen nucleus has nearly the same mass as a free neutron: neutron-H₂O or neutron-ZrH₂ impacts excite rotational modes of the molecules (spinning them around). Deuterium nuclei (in heavy water) absorb kinetic energy less well than do light hydrogen nuclei, but they are much less likely to absorb the impacting neutron. Water or heavy water have the advantage of being transparent liquids, so that, in addition to shielding and moderating a reactor core, they permit direct viewing of the core in operation and can also serve as a working fluid for heat transfer.

Carbon in the form of graphite has been widely used as a moderator. It was used in Chicago Pile-1, the world's first man-made critical assembly, and was commonplace in early reactor designs including the Soviet RBMK nuclear power plants such as the Chernobyl plant.

Moderators and reactor design

The amount and nature of neutron moderation affects reactor controllability and hence safety. Because moderators both slow and absorb neutrons, there is an optimum amount of moderator to include in a given geometry of reactor core. Less moderation reduces the effectiveness by reducing the ${\displaystyle P_{fission}}$ term in the evolution equation, and more moderation reduces the effectiveness by increasing the ${\displaystyle P_{escape}}$ term.

Most moderators become less effective with increasing temperature, so under-moderated reactors are stable against changes in temperature in the reactor core: if the core overheats, then the quality of the moderator is reduced and the reaction tends to slow down (there is a "negative temperature coefficient" in the reactivity of the core). Water is an extreme case: in extreme heat, it can boil, producing effective voids in the reactor core without destroying the physical structure of the core; this tends to shut down the reaction and reduce the possibility of a fuel meltdown. Over-moderated reactors are unstable against changes in temperature (there is a "positive temperature coefficient" in the reactivity of the core), and so are less inherently safe than under-moderated cores.

Some reactors use a combination of moderator materials. For example, TRIGA type research reactors use ZrH₂ moderator mixed with the ²³⁵U fuel, an H₂O-filled core, and C (graphite) moderator and reflector blocks around the periphery of the core.

Delayed neutrons and controllability

Main article: Delayed neutron

Fission reactions and subsequent neutron escape happen very quickly; this is important for nuclear weapons, where the objective is to make a nuclear pit release as much energy as possible before it physically explodes. Most neutrons emitted by fission events are prompt: they are emitted effectively instantaneously. Once emitted, the average neutron lifetime (${\displaystyle \tau }$) in a typical core is on the order of a millisecond, so if the exponential factor ${\displaystyle \alpha }$ is as small as 0.01, then in one second the reactor power will vary by a factor of (1 + 0.01)¹⁰⁰⁰, or more than ten thousand. Nuclear weapons are engineered to maximize the power growth rate, with lifetimes well under a millisecond and exponential factors close to 2; but such rapid variation would render it practically impossible to control the reaction rates in a nuclear reactor.

Fortunately, the effective neutron lifetime is much longer than the average lifetime of a single neutron in the core. About 0.65% of the neutrons produced by ²³⁵U fission, and about 0.20% of the neutrons produced by ²³⁹Pu fission, are not produced immediately, but rather are emitted from an excited nucleus after a further decay step. In this step, further radioactive decay of some of the fission products (almost always negative beta decay), is followed by immediate neutron emission from the excited daughter product, with an average life time of the beta decay (and thus the neutron emission) of about 15 seconds. These so-called delayed neutrons increase the effective average lifetime of neutrons in the core, to nearly 0.1 seconds, so that a core with ${\displaystyle \alpha }$ of 0.01 would increase in one second by only a factor of (1 + 0.01)¹⁰, or about 1.1: a 10% increase. This is a controllable rate of change.

Most nuclear reactors are hence operated in a prompt subcritical, delayed critical condition: the prompt neutrons alone are not sufficient to sustain a chain reaction, but the delayed neutrons make up the small difference required to keep the reaction going. This has effects on how reactors are controlled: when a small amount of control rod is slid into or out of the reactor core, the power level changes at first very rapidly due to prompt subcritical multiplication and then more gradually, following the exponential growth or decay curve of the delayed critical reaction. Furthermore, increases in reactor power can be performed at any desired rate simply by pulling out a sufficient length of control rod. However, without addition of a neutron poison or active neutron-absorber, decreases in fission rate are limited in speed, because even if the reactor is taken deeply subcritical to stop prompt fission neutron production, delayed neutrons are produced after ordinary beta decay of fission products already in place, and this decay-production of neutrons cannot be changed.

The rate of change of reactor power is determined by the reactor period ${\displaystyle T}$, which is related to the reactivity ${\displaystyle \rho }$ through the Inhour equation.

Kinetics

The kinetics of the reactor is described by the balance equations of neutrons and nuclei (fissile, fission products).

Reactor poisons

Main article: Nuclear poison

Any nuclide that strongly absorbs neutrons is called a reactor poison, because it tends to shut down (poison) an ongoing fission chain reaction. Some reactor poisons are deliberately inserted into fission reactor cores to control the reaction; boron or cadmium control rods are the best example. Many reactor poisons are produced by the fission process itself, and buildup of neutron-absorbing fission products affects both the fuel economics and the controllability of nuclear reactors.

Long-lived poisons and fuel reprocessing

In practice, buildup of reactor poisons in nuclear fuel is what determines the lifetime of nuclear fuel in a reactor: long before all possible fissions have taken place, buildup of long-lived neutron absorbing fission products damps out the chain reaction. This is the reason that nuclear reprocessing is a useful activity: spent nuclear fuel contains about 96% of the original fissionable material present in newly manufactured nuclear fuel. Chemical separation of the fission products restores the nuclear fuel so that it can be used again.

Nuclear reprocessing is useful economically because chemical separation is much simpler to accomplish than the difficult isotope separation required to prepare nuclear fuel from natural uranium ore, so that in principle chemical separation yields more generated energy for less effort than mining, purifying, and isotopically separating new uranium ore. In practice, both the difficulty of handling the highly radioactive fission products and other political concerns make fuel reprocessing a contentious subject. One such concern is the fact that spent uranium nuclear fuel contains significant quantities of ²³⁹Pu, a prime ingredient in nuclear weapons (see breeder reactor).

Short-lived poisons and controllability

Main article: Iodine pit

Short-lived reactor poisons in fission products strongly affect how nuclear reactors can operate. Unstable fission product nuclei transmute into many different elements (secondary fission products) as they undergo a decay chain to a stable isotope. The most important such element is xenon, because the isotope ¹³⁵Xe, a secondary fission product with a half-life of about 9 hours, is an extremely strong neutron absorber. In an operating reactor, each nucleus of ¹³⁵Xe becomes ¹³⁶Xe (which may later sustain beta decay) by neutron capture almost as soon as it is created, so that there is no buildup in the core. However, when a reactor shuts down, the level of ¹³⁵Xe builds up in the core for about 9 hours before beginning to decay. The result is that, about 6–8 hours after a reactor is shut down, it can become physically impossible to restart the chain reaction until the ¹³⁵Xe has had a chance to decay over the next several hours. This temporary state, which may last several days and prevent restart, is called the iodine pit or xenon-poisoning. It is one reason why nuclear power reactors are usually operated at an even power level around the clock.

¹³⁵Xe buildup in a reactor core makes it extremely dangerous to operate the reactor a few hours after it has been shut down. Because the ¹³⁵Xe absorbs neutrons strongly, starting a reactor in a high-Xe condition requires pulling the control rods out of the core much farther than normal. However, if the reactor does achieve criticality, then the neutron flux in the core becomes high and ¹³⁵Xe is destroyed rapidly—this has the same effect as very rapidly removing a great length of control rod from the core, and can cause the reaction to grow too rapidly or even become prompt critical.

¹³⁵Xe played a large part in the Chernobyl accident: about eight hours after a scheduled maintenance shutdown, workers tried to bring the reactor to a zero power critical condition to test a control circuit. Since the core was loaded with ¹³⁵Xe from the previous day's power generation, it was necessary to withdraw more control rods to achieve this. As a result, the overdriven reaction grew rapidly and uncontrollably, leading to steam explosion in the core, and violent destruction of the facility.

Uranium enrichment

While many fissionable isotopes exist in nature, the only usefully fissile isotope found in any quantity is ²³⁵U. About 0.7% of the uranium in most ores is the 235 isotope, and about 99.3% is the non-fissile 238 isotope. For most uses as a nuclear fuel, uranium must be enriched - purified so that it contains a higher percentage of ²³⁵U. Because ²³⁸U absorbs fast neutrons, the critical mass needed to sustain a chain reaction increases as the ²³⁸U content increases, reaching infinity at 94% ²³⁸U (6% ²³⁵U).

Concentrations lower than 6% ²³⁵U cannot go fast critical, though they are usable in a nuclear reactor with a neutron moderator. A nuclear weapon primary stage using uranium uses HEU enriched to ~90% ²³⁵U, though the secondary stage often uses lower enrichments. Nuclear reactors with water moderator require at least some enrichment of ²³⁵U. Nuclear reactors with heavy water or graphite moderation can operate with natural uranium, eliminating altogether the need for enrichment and preventing the fuel from being useful for nuclear weapons; the CANDU power reactors used in Canadian power plants are an example of this type.

The Uranium enrichment is difficult because the chemical properties of ²³⁵U and ²³⁸U are identical, so physical processes such as gaseous diffusion, gas centrifuge, laser, or the mass spectrometry must be used for isotopic separation based on small differences in mass. Because enrichment is the main technical hurdle to production of nuclear fuel and simple nuclear weapons, enrichment technology is politically sensitive.

Oklo: a natural nuclear reactor

Main article: Oklo Mine

Modern deposits of uranium contain only up to ~0.7% ²³⁵U (and ~99.3% ²³⁸U), which is not enough to sustain a chain reaction moderated by ordinary water. But ²³⁵U has a much shorter half-life (700 million years) than ²³⁸U (4.5 billion years), so in the distant past the percentage of ²³⁵U was much higher. About two billion years ago, a water-saturated uranium deposit (in what is now the Oklo mine in Gabon, West Africa) underwent a naturally occurring chain reaction that was moderated by groundwater and, presumably, controlled by the negative void coefficient as the water boiled from the heat of the reaction. Uranium from the Oklo mine is about 50% depleted compared to other locations: it is only about 0.3% to 0.7% ²³⁵U; and the ore contains traces of stable daughters of long-decayed fission products.