Dollar (reactivity)

Last updated

A dollar is a unit of reactivity for a nuclear reactor, calibrated to the interval between the conditions of criticality and prompt criticality. Prompt criticality will result in an extremely rapid power rise, with the resultant destruction of the reactor, unless it is specifically designed to tolerate the condition. A cent is 1⁄100 of a dollar. In nuclear reactor physics discussions, the symbols are often appended to the end of the numerical value of reactivity, such as 3.48$ or 21 ¢. [1] [2]

Contents

Reactivity (denoted ρ or ΔK/K) is related to the effective neutron multiplication factor (keff), the average number of all neutrons from one fission that cause another fission. [2]

ρ = ⁠keff - 1/keff⁠

But in nuclear physics, it useful to talk about the reactivity contributed by just the prompt neutrons. This is the reactivity in dollars or cents.

In general, reactivity is not in dollars or cents, because keff measures its total value, a summation of the reactivity of both the prompt and delayed neutrons. Reactivity in dollars is dependent on the delayed neutron fraction (βeff). [2]


Reactivity in dollars = ⁠ρ/βeff⁠

Reactivity in cents = 100 x (⁠ρ/βeff⁠)

When certain components or parameters change the reactivity of a nuclear reactor, the changes may be calculated as their reactivity worth. A control rod and a chemical reactor poison both have negative reactivity worth, while the addition of a neutron moderator would generally have a positive reactivity worth. Reactivity worth can be measured in dollars or cents. During the design and testing of a nuclear reactor, each component will be scrutinized to determine its reactivity worth, often at different temperatures, pressures, and control rod heights. For example, the burning of reactor poisons are important to the lifespan of the reactor core, since their reactivity worth decreases as the core ages.

Reactivity in general

Reactivity (ρ) is dimensionless, but may be modified to make it less cumbersome. Since reactivity is often a small number, it may be denoted in percent, i.e. %ΔK/K. [2] Thus, a reactivity of 0.02 ΔK/K would be reported as 2 %ΔK/K. A nuclear reactor with a 2% reactivity is supercritical. A negative sign would indicate that it is subcritical.

The per cent mille (pcm) is used for even finer-grained measurements of reactivity, amounting to one-thousanth of a percent. [2] Likewise, an InHour (inverse hour) is another small measurement of reactivity that takes into account the time of multiplication.

The unitless, pcm, percent, and inverse-time-based versions of reactivity can all be converted to dollars with the formula above and the InHour equation. From there, the startup rate (SUR), reactor period and doubling time of the reactor can be calculated. [3]

Meaning and use

Each nuclear fission produces several neutrons that can be absorbed, escape from the reactor, or go on to cause more fissions in a nuclear chain reaction. When an average of one neutron from each fission goes on to cause another fission, the reactor is "critical", and the chain reaction proceeds at a constant power level. Adding reactivity at this point will make the reactor supercritical, while subtracting reactivity will make it subcritical.

Most neutrons produced in fission are "prompt", i.e., created with the fission products in less than about 10 nanoseconds (a "shake" of time), but certain fission products produce additional neutrons when they decay up to several minutes after their creation by fission. These delayed-release neutrons, a tiny fraction of the total, are key to stable nuclear reactor control. Without delayed neutrons, a reactor that was just barely supercritical would present a significant control problem, as reactor power would increases exponentially on millisecond or even microsecond timescales – much too fast to be controlled with current or near-future technology.

Such a rapid power increase can also happen in a real reactor when the chain reaction is sustained without the help of the delayed neutrons. Suppose that the delayed neutron fraction for a particular reactor is 0.00700, or 0.700%. Suppose also that the reactor is highly supercritical and ΔK/K is 0.00700.

Reactivity in dollars = ⁠ρ/βeff⁠ = ⁠0.007/0.007⁠ = 1$

If the excess reactivity of a reactor is 1 dollar (1$) or more, the reactor is prompt critical. Prompt neutrons are so numerous that the production of delayed neutrons is no longer needed to sustain the reaction. At or above 1$, the chain reaction proceeds without them, and reactor power increases so fast that no conventional controlling mechanism can stop it. A reactor in such a state will produce a reactor excursion and could have a reactor accident.

An extreme example of a prompt critical reaction is an exploding nuclear weapon, where considerable design effort goes into keeping the core constrained in a prompt critical state for as long as possible until the greatest attainable percentage of material has fissioned. [4]

The SPERT Reactors studied reactors close to the point of prompt critical to answer questions about the reactor physics of pressurized water and boiling water reactors during supercritical operation. [1] At the SPERT reactors, reactivity could be added by a programmed gradual insertion (ramp addition of reactivity) or by ejecting a transient control rod out the bottom of the core (step addition of reactivity). [1]

By definition, reactivity of zero dollars is just barely on the edge of criticality using both prompt and delayed neutrons. A reactivity less than zero dollars is subcritical; the power level will decrease exponentially and a sustained chain reaction will not occur. One dollar is defined as the threshold between delayed and prompt criticality. At prompt criticality, on average each fission will cause exactly one additional fission via prompt neutrons, and the delayed neutrons will then increase power. Any reactivity above 0$ is supercritical and power will increase exponentially, but between 0$ and 1$ the power rise will be slow enough to be safely controlled with mechanical and intrinsic material properties (control rod movements, density of coolant, moderator properties, steam formation) because the chain reaction partly depends on the delayed neutrons. A power reactor operating at steady state (constant power) will therefore have an average reactivity of 0$, with small fluctuations above and below this value. [2]

Reactivity can also be expressed in relative terms, such as "5 cents above prompt critical". [5]

While power reactors are carefully designed and operated to avoid prompt criticality under all circumstances, many small research or "zero power" reactors are designed to be intentionally placed into prompt criticality (greater than 1$) with complete safety by rapidly withdrawing their control rods. Their fuel elements are designed so that as they heat up, reactivity is automatically and quickly reduced through effects such as doppler broadening and thermal expansion. Such reactors can be "pulsed" to very high power levels (e.g., several GW) for a few milliseconds, after which reactivity automatically drops to 0$ and a relatively low and constant power level (e.g. several hundred kW) is maintained until shut down manually by reinserting the control rods. [6]

Subcritical reactors, which thus far have only been built at laboratory scale, would constantly run in "negative dollars" (most likely a few cents below [delayed] critical) with the "missing" neutrons provided by an external neutron source, e.g. spallation driven by a particle accelerator in an accelerator-driven subcritical reactor.

History

According to Alvin Weinberg and Eugene Wigner, Louis Slotin was the first to propose the name "dollar" for the interval of reactivity between barely critical and prompt criticality, and "cents" for the decimal fraction of the dollar. [7]

Related Research Articles

<span class="mw-page-title-main">Nuclear fission</span> Nuclear reaction splitting an atom into multiple parts

Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay.

<span class="mw-page-title-main">Nuclear chain reaction</span> When one nuclear reaction causes more

In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series or "positive feedback loop" of these reactions. The specific nuclear reaction may be the fission of heavy isotopes. A nuclear chain reaction releases several million times more energy per reaction than any chemical reaction.

<span class="mw-page-title-main">Nuclear reactor</span> Device for controlled nuclear reactions

A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. When a fissile nucleus like uranium-235 or plutonium-239 absorbs a neutron, it splits into lighter nuclei, releasing energy, gamma radiation, and free neutrons, which can induce further fission in a self-sustaining chain reaction. The process is carefully controlled using control rods and neutron moderators to regulate the number of neutrons that continue the reaction, ensuring the reactor operates safely, although inherent control by means of delayed neutrons also plays an important role in reactor output control. The efficiency of nuclear fuel is much higher than fossil fuels; the 5% enriched uranium used in the newest reactors has an energy density 120,000 times higher than coal.

<span class="mw-page-title-main">Critical mass</span> Smallest amount of fissile material needed to sustain a nuclear reaction

In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties, density, shape, enrichment, purity, temperature, and surroundings. The concept is important in nuclear weapon design.

<span class="mw-page-title-main">Scram</span> Emergency shutdown of a nuclear reactor

A scram or SCRAM is an emergency shutdown of a nuclear reactor effected by immediately terminating the fission reaction. It is also the name that is given to the manually operated kill switch that initiates the shutdown. In commercial reactor operations, this type of shutdown is often referred to as a "scram" at boiling water reactors, a "reactor trip" at pressurized water reactors and "EPIS" at a CANDU reactor. In many cases, a scram is part of the routine shutdown procedure which serves to test the emergency shutdown system.

<span class="mw-page-title-main">Neutron transport</span> Study of motions and interactions of neutrons

Neutron transport is the study of the motions and interactions of neutrons with materials. Nuclear scientists and engineers often need to know where neutrons are in an apparatus, in what direction they are going, and how quickly they are moving. It is commonly used to determine the behavior of nuclear reactor cores and experimental or industrial neutron beams. Neutron transport is a type of radiative transport.

A neutron reflector is any material that reflects neutrons. This refers to elastic scattering rather than to a specular reflection. The material may be graphite, beryllium, steel, tungsten carbide, gold, or other materials. A neutron reflector can make an otherwise subcritical mass of fissile material critical, or increase the amount of nuclear fission that a critical or supercritical mass will undergo. Such an effect was exhibited twice in accidents involving the Demon Core, a subcritical plutonium pit that went critical in two separate fatal incidents when the pit's surface was momentarily surrounded by too much neutron reflective material.

A criticality accident is an accidental uncontrolled nuclear fission chain reaction. It is sometimes referred to as a critical excursion, critical power excursion, divergent chain reaction, or simply critical. Any such event involves the unintended accumulation or arrangement of a critical mass of fissile material, for example enriched uranium or plutonium. Criticality accidents can release potentially fatal radiation doses if they occur in an unprotected environment.

<span class="mw-page-title-main">Light-water reactor</span> Type of nuclear reactor that uses normal water

The light-water reactor (LWR) is a type of thermal-neutron reactor that uses normal water, as opposed to heavy water, as both its coolant and neutron moderator; furthermore a solid form of fissile elements is used as fuel. Thermal-neutron reactors are the most common type of nuclear reactor, and light-water reactors are the most common type of thermal-neutron reactor.

In nuclear engineering, prompt criticality describes a nuclear fission event in which criticality is achieved with prompt neutrons alone and does not rely on delayed neutrons. As a result, prompt supercriticality causes a much more rapid growth in the rate of energy release than other forms of criticality. Nuclear weapons are based on prompt criticality, while nuclear reactors rely on delayed neutrons or external neutrons to achieve criticality.

A subcritical reactor is a nuclear fission reactor concept that produces fission without achieving criticality. Instead of sustaining a chain reaction, a subcritical reactor uses additional neutrons from an outside source. There are two general classes of such devices. One uses neutrons provided by a nuclear fusion machine, a concept known as a fusion–fission hybrid. The other uses neutrons created through spallation of heavy nuclei by charged particles such as protons accelerated by a particle accelerator, a concept known as an accelerator-driven system (ADS) or accelerator-driven sub-critical reactor.

In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron decay which can occur within the same context, emitted after beta decay of one of the fission products anytime from a few milliseconds to a few minutes later.

In nuclear engineering, a delayed neutron is a neutron emitted after a nuclear fission event, by one of the fission products, any time from a few milliseconds to a few minutes after the fission event. Neutrons born within 10−14 seconds of the fission are termed "prompt neutrons".

Neutron economy is defined as the ratio of excess neutron production divided by the rate of fission. The numbers are a weighted average based primarily on the energies of the neutrons.

<span class="mw-page-title-main">Nuclear reactor physics</span> Field of physics dealing with nuclear reactors

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.

In applications such as nuclear reactors, a neutron poison is a substance with a large neutron absorption cross-section. In such applications, absorbing neutrons is normally an undesirable effect. However, neutron-absorbing materials, also called poisons, are intentionally inserted into some types of reactors in order to lower the high reactivity of their initial fresh fuel load. Some of these poisons deplete as they absorb neutrons during reactor operation, while others remain relatively constant.

The Clean and Environmentally Safe Advanced Reactor (CAESAR) is a nuclear reactor concept created by Claudio Filippone, the Director of the Center for Advanced Energy Concepts at the University of Maryland, College Park and head of the ongoing CAESAR Project. The concept's key element is the use of steam as a moderator, making it a type of reduced moderation water reactor. Because the density of steam may be controlled very precisely, Filippone claims it can be used to fine-tune neutron fluxes to ensure that neutrons are moving with an optimal energy profile to split 238
92U
 nuclei – in other words, cause fission.

Shutdown is the state of a nuclear reactor when the fission reaction is slowed significantly or halted completely. Different nuclear reactor designs have different definitions for what "shutdown" means, but it typically means that the reactor is not producing a measurable amount of electricity or heat and is in a stable condition with very low reactivity.

A startup neutron source is a neutron source used for stable and reliable initiation of nuclear chain reaction in nuclear reactors, when they are loaded with fresh nuclear fuel, whose neutron flux from spontaneous fission is insufficient for a reliable startup, or after prolonged shutdown periods. Neutron sources ensure a constant minimal population of neutrons in the reactor core, sufficient for a smooth startup. Without them, the reactor could suffer fast power excursions during startup from state with too few self-generated neutrons.

The Inhour equation used in nuclear reactor kinetics to relate reactivity and the reactor period. Inhour is short for "inverse hour" and is defined as the reactivity which will make the stable reactor period equal to 1 hour. Reactivity is more commonly expressed as per cent millie (pcm) of Δk/k or dollars.

References

  1. 1 2 3 J. Dugone (November 1965). "SPERT III Reactor Facility: E-Core Revision".
  2. 1 2 3 4 5 6 "Reactivity". nuclear-power.net. n.d. Archived from the original on 14 December 2017. Retrieved 7 July 2021.
  3. ↑ Reactor Period Nuclear-power.com
  4. ↑ Hugh C. Paxton: A History of Critical Experiments at Pajarito Site. Los Alamos Document LA-9685-H Archived 2014-10-14 at the Wayback Machine , 1983.
  5. ↑ McLaughlin, Thomas P.; et al. (2000). A Review of Criticality Accidents (PDF). Los Alamos: Los Alamos National Laboratory. p. 75. LA-13638. Archived (PDF) from the original on 27 September 2007. Retrieved 5 November 2012.
  6. ↑ "WSU Reactor Pulsing to 1.2 GW (January 2007)". YouTube. 20 February 2012. Retrieved 7 July 2021.
  7. ↑ Weinberg, Alvin M.; Wigner, Eugene P. (1958). The Physical Theory of Neutron Chain Reactors. Chicago: University of Chicago Press. p. 595.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.