The Physics of Energy, page 74
Delayed Neutrons
A small fraction – less than 1% – of all neutrons emitted in fission are delayed by times ranging from ~1 second to ~1 minute. This small fraction d of delayed neutrons allows a reactor to be controlled over those time scales as long as the reactivity ρ does not exceed d.
Thus, the existence of delayed neutrons is absolutely essential to the control of thermal fission power reactors. As long as a reactor has a thermal-neutron multiplication factor that exceeds unity by less than d, the reactor time scale is set by the delayed neutrons and is long enough for control with modern engineering methods. If, however, the k-factor in a reactor exceeds , the reactor is prompt critical, and is in danger of getting out of control. The Chernobyl disaster was initiated when, through a series of mishaps, a poorly designed reactor was allowed to go prompt critical (see Box 19.2). One aim of novel reactor designs is to include intrinsic safeguards, described below, so that the heat generated by an inadequately controlled reactor would itself automatically reduce k to the point that the fission reaction would cease.
Box 19.2 The Chernobyl Accident
The most serious reactor accident, in terms of loss of life and contamination of property, took place at the Chernobyl reactor complex, near Pripyat in the Ukraine in 1986. It occurred when operators were testing an unusual proposal to power the backup cooling system: in the event of loss of electric power, energy stored in the reactor's turbines, functioning like flywheels, was to be used to run the primary coolant pumps until diesel generators could kick in. The idea had been tested several times previously, but it had failed. The new test, which required powering down the 3 GWth reactor to about 700 MWth, was scheduled for the day shift on April 25, 1986, but was postponed until late evening because of power demands on the grid to which the reactor was connected. The night-shift operators were not as experienced with the reactor or the planned test as the day-shift operators.
There is still controversy about the relative importance of design flaws and operator errors in the Chernobyl event [95]. Some of the flaws in the RBMK-1000 reactor are generally agreed upon:
The graphite-moderated, water-cooled reactor had such a large core – diameter 11 meters and height 7 meters – that an external containment structure was deemed impractical and not constructed. Instead the reactor was capped with a 2000 ton plate to which the entire reactor was connected. The size of the core also meant that local conditions were not well controlled by global responses – it has been said that different parts of the reactor responded essentially independently.
The reactor was operating in a mode where it had a large, positive coefficient of void (see §19.2.1), so boiling of the water coolant would increase reactivity, potentially leading to a dangerous positive feedback loop.
The reactor control rods were to be lowered into channels in the graphite core that were normally filled with coolant water. The bottom third of the control rods, known as displacers, were made of graphite, which were intended to remain within the reactor core during normal operation. If the rods were totally withdrawn, then reinserting them would displace water (an effective neutron absorber) with graphite, causing an initial increase in reactivity, before the B4C in the main part of the rods decreased ρ.
Before the test, the reactor's output was reduced below 700 MWth, leading to a build up of fission poison, which caused the power to decrease still further to ~500 MWth. At this point, it appears that control rods were mistakenly inserted, and the reactor reached a near shutdown state of ~30 MWth, which led to a much larger increase in the burden. Attempting to bring the reactor back up to a level where the test could be performed, and apparently not understanding the inhibiting role of the , the operators disabled safety constraints, allowing them to withdraw many control rods (including the graphite displacers) completely. This put the reactor in a very unstable mode, and when the test was performed, the sudden drop in cooling initiated a dramatic increase in reactivity. Reinserting the control rods initially displaced neutron-absorbing water with graphite moderator and increased the reactivity still further. It is estimated that the reactor output spiked to 30 GWth seconds after the test began. Such a high reactor output could only have occurred if at least sections of the reactor core went prompt critical. The subsequent explosions and fires released tons of the reactor core material to the atmosphere. Although no more have been built, other RBMK-reactors remain in service in the states of the former Soviet Union. Safety systems and procedures at these reactors have been improved in light of the Chernobyl experience.
19.1.7 Fission Poisons and Reactor Operation
The notion of a fission poison was introduced in §18.3.5. In the context of a fission reactor, a fission poison is any nuclide with an anomalously large neutron-absorption cross section. Any material that absorbs neutrons inhibits the fission chain reaction by reducing the thermal neutron utilization factor f. Naturally occurring, stable fission poisons (e.g. ) are useful components of control rods, but must be avoided in other reactor materials. Early in World War II, for example, German scientists concluded that graphite would not work as a moderator because their graphite was contaminated with boron that was used in its preparation.
Some fission poisons occur as fission fragments and build up during the course of reactor operation, requiring operators to take compensating measures to keep the chain reaction going. Some decay radioactively or convert to non-fission-poison isotopes when they absorb a neutron, in which case they build up to an equilibrium value during the operation of a reactor. The left-hand side of Figure 19.5, labeled “before shutdown” shows the negative contribution to the k-factor from the build up of a fission poison. Other fission poisons, hafnium isotopes for example, form a sequence of isotopes, all of which have large neutron-absorption cross sections, so they effectively build up continuously during reactor burning.
Figure 19.5 Percentage change in k due to xenon poisoning as a function of time before and just after shutdown of a typical reactor. The horizontal dashed line at –5% indicates the maximum decrease in that typically can be compensated by removal of control rods. After Lilley [77].
The most important, and perhaps most insidious fission poison is an isotope of xenon, , which was mentioned in §18.3.5. The production and decay paths for are summarized in Figure 19.6. As a reactor runs, begins to build up, mostly via β-decay of , which is a common fission fragment. A nucleus either β-decays or absorbs a thermal neutron. While a reactor is operating, neutron absorption converts to , which is stable and has a relatively small neutron-absorption cross section. β-decay of yields , which is long-lived and has a small neutron-absorption cross section. In equilibrium, the rate of production of is exactly balanced by the rate that is eliminated by neutron absorption or β-decay. So a reactor that has been running for a few days has built up an equilibrium concentration of . This would cause the neutron multiplication factor k to decrease from its original value at startup. For a reactor burning natural uranium with , , and a neutron flux of cm–2 s–1, for example, k would be reduced by about 3% when is in equilibrium [77]. This reduction in k is compensated by partially removing control rods. If the build up of becomes too great for the control rods to compensate, or if other considerations require running with the control rods further engaged, then the reactor must be shut down to let the xenon decay away.
Figure 19.6 Data on the production, decay, and lifetimes of the fission poison and its precursor, . Production in fission and half-lives for β-decay are shown. After Lilley [77].
It is after a reactor is shut down that has its greatest impact, because when a reactor is powered down, the amount of actually grows dramatically. Shutting down the reactor eliminates the neutron flux that is deactivating most of the , while , the source of most , continues to decay with a ~7 h lifetime. The amount of increases and, as shown in Figure 19.5, the reactivity drops dramatically and only recovers over several days after a typical reactor is shut down.
The reactor characterized by Figure 19.5 cannot be restarted for a period of about 30 hours after it is shut down. To be effective at eliminating the , the shutdown should last significantly longer than this. Modern light-water reactors (see §19.4.1) can be designed to reduce the constraints imposed by the generation of fission poisons following a reduction in power output. Nevertheless, nuclear reactors are most efficient when run at constant power, and have difficulty responding to short-term fluctuations in load demands on a complex power grid.
For another example of the role of fission poisons, see the discussion of the Chernobyl accident in Box 19.2.
19.2Physics Issues Affecting Fission Reactor Operation and Safety
Before describing specific nuclear reactor designs, we summarize some of the physics principles that underlie questions about the safety of nuclear power. For no other energy source, perhaps, do social, political, and ethical questions more completely dominate public perception and discussion. Nevertheless, the difficulties with nuclear fission power and their possible resolution are highly constrained by the laws of physics.
There are three basic categories of concern regarding the safety and security of nuclear power:
Reactor control and cooling The reactor itself must be controlled, the heat it generates must be carried away, and the structure that contains it must be able to contain radioactive and poisonous materials even under a “worst case” scenario.
Nuclear waste Spent reactor fuel and other reactor components contain many species of radioactive nuclei with a wide variety of lifetimes, decay chains, and types of radiation. The spent fuel, in particular, must be sequestered safely away for a long time, though reprocessing can reduce its activity and volume.
Nuclear proliferation can be fashioned into a nuclear device of great destructive power, as can , which is produced copiously in a thermal reactor. These materials, as well as nuclear waste that can be used to produce “dirty bombs,” must be kept out of the hands of irresponsible people whatever their political affiliation.
Each is a complex issue with grave consequences if the safety or security goals are not achieved.
The second two issues primarily involve physics that takes place outside of the nuclear reactor itself. Discussion of the nuclear fuel cycle and nuclear proliferation require some knowledge of the types and properties of radiation, and is postponed until §20 (Radiation). The first of the above categories, reactor control and safety, is discussed here along with some aspects of the second two categories that are internal to the reactor itself. We introduce here only the basic physical concepts underlying the issues of reactor safety and control. For a more extensive non-technical discussion of nuclear fission energy safety, see [81].
19.2.1 Inherent Safety
The nomenclature of nuclear reactor safety analysis requires explanation. A reactor design may have active safety systems such as control rods or coolant pumps that must be activated by an operator or automatic control system in order to function. It may also have passive safety systems such as pressure release valves or gravity-driven coolant circulation, which function automatically to reduce reactivity in the event of other system failures, independent of human intervention. Finally, features of a reactor may be designed to be inherently safe, meaning that the safety features are physical features of the materials themselves. We describe two examples of inherent safety features here, first negative void coefficient of reactivity (or negative coefficient of void as it is often known), meaning that ρ drops if a void develops in the coolant, and negative temperature coefficient of reactivity, i.e. , meaning that the reactivity drops if the reactor heats up.
Coefficient of Void The basic ingredients in the core of a thermal-neutron reactor are fuel, moderator, and coolant. The moderator slows the neutrons and the coolant transfers the heat generated by nuclear fission to power generating equipment. We distinguish two situations: first, where the same fluid serves as both moderator and coolant, and second, where the moderation and cooling are performed by different materials. Most commercial reactors in the world today are of the first type. They use regular (light) liquid water as both a coolant and a moderator. Water is a good moderator (§18.3.6) and, with high heat capacity and very effective heat transfer in boiling, also makes an excellent coolant. If, due to some system failure, water vaporizes, a void is created where the coolant and moderator density is much lower than it had been. When water is the principal moderator and it boils off, the resonance escape probability p drops sharply, sending the reactivity negative and shutting off the fission chain reaction. The reactor remains hot, but the possibility of a runaway chain reaction is averted. Thus a water-cooled, water-moderated reactor has a negative coefficient of void. This is a desirable inherent safety feature of these reactor designs. Note, however, that this is not the end of the story. Although the fission chain reaction may have been shut down, the reactor continues to generate heat from the decay of fission fragments (see §19.2.2). Cooling must be maintained for a long time after shutdown to avert structural damage and release of radioactivity. Thus, for example, the reactors at Fukushima Daiichi were destroyed in the 2011 accident not by the reactors going prompt critical, but rather by heat from residual radioactivity due to failure of the backup core cooling systems after the reactors had been shut down.
The opposite situation can arise in water-cooled reactors that use either graphite or heavy water for moderation. Such reactors can have a positive coefficient of void, allowing their reactivity to increase if a void develops in the coolant. How could this happen? Consider a reactor in which the fuel is embedded in a fixed matrix of solid moderator, like graphite, and where the cooling is supplied by pressurized water flowing through channels in the fuel/graphite array. If the cooling water vaporizes, the graphite is unaffected. It continues to moderate the neutrons and the fission chain reaction continues. Since the hydrogen in the cooling water also functions as a neutron absorber (see Table 19.2), vaporizing the cooling water reduces neutron absorption and therefore increases the thermal utilization factor and the reactivity. In short, a void leads to an increase in reactivity and perhaps to a runaway chain reaction. A certain class of electric power reactors of this design (known as RBMK reactors), including one in Chernobyl in the Ukraine, were built in the Soviet Union. The positive coefficient of void was a contributing factor to the catastrophic failure of the Chernobyl reactor in 1986 (see Box 19.2). Heavy-water-moderated reactors also have a positive coefficient of void, since the heavy water used as coolant is physically separated from the moderator. Although positive, the coefficient of void is small enough in this case to allow ample margin for control.
Doppler Broadening Another inherent safety factor, which manifests as a negative contribution to the temperature coefficient of reactivity, is known as Doppler broadening. This term refers to the fact that as reactor fuel heats up, the width in energy of the peaks in the neutron-absorption cross section in increases. Remember that as a neutron slows down through collisions with the moderator, it must avoid capture into one of the “forest” of narrow absorption resonances in , shown in Figure 18.4(c) and (d). If the neutron's energy coincides with the location of a peak, then it has a high probability of being absorbed in a collision. The peaks are very narrow at normal operating temperatures, so if the neutron's energy differs slightly from the location of the resonance, it evades capture. As the fuel heats up, however, all of the neutron-absorption peaks get wider. This increases the chance that, when a neutron hits a series of nuclei, its energy overlaps an absorption resonance for one of the nuclei, so the radiative capture probability goes up and the resonance escape probability p goes down.
Doppler broadening can be understood quite simply as a consequence of classical kinematics. Thermal energy causes the uranium nuclei to vibrate about their equilibrium positions in the solid fuel: the higher the temperature, the more vigorous the vibrations, and the greater the range of possible velocities of the uranium nuclei. This, in turn, gives rise to a spread in the center of mass energy of the neutron-uranium system, increasing the possibility of overlap with an absorption resonance.
Thus, heating leads to decreased reactivity. Doppler broadening is used as a key inherent safety component in a novel reactor design, the very high temperature reactor, one of the Generation IV reactors discussed in §19.4.2. Doppler broadening also appears in the context of absorption of electromagnetic radiation in §23.4.
Inherent Safety
Physical features of fission reactor fuel, coolant, and moderator can be exploited to improve the inherent safety of a nuclear reactor.
Inherent safety features include the negative void coefficient of reactivity of water-cooled and moderated reactors, and the negative temperature coefficient of reactivity of uranium fuel caused by Doppler broadening of the peaks in the radiative capture cross section.
