Chapter 47. Fundamentals of Nuclear Energy

Transcription

1 Chapter 47 Fundamentals of Nuclear Energy Fundamental particles and structure of the atom 1 In the fifth century B.C. Greek philosophers postulated that all matter is composed of indivisible particles called atoms. Over the next 24 centuries there were many speculations on the basic structure of matter but all theories lacked any experimental basis. It was not until late in the nineteenth and early twentieth centuries that the existence of fundamental particles, the proton, neutron and electron, was confirmed. The discovery of nuclear fission, credited to Otto Hahn, Lise Meitner and Fritz Strassman, was made possible through an accumulation of knowledge on the structure of matter beginning with Becquerel s 1896 detection of radioactivity. As shown in Fig. 1, the structure of an atom is pictured as a dense, positively charged nucleus surrounded by an array of negatively charged electrons. Each proton, the equivalent of a hydrogen atom nucleus, carries an elemental positive charge of electricity. The number of protons determines the type of chemical element of the atom. Each neutron is an electrically neutral particle with a mass slightly greater than the proton. Because of their association with the nucleus of the atom, protons and neutrons are also referred to as nucleons. Each electron shown orbiting around the nucleus has an elemental negative charge and a mass about 1/2000 that of a proton. The nucleus of an atom with a characteristic number of neutrons and protons is called a nuclide. Despite the minute size of the atom, there is a relatively great distance between the nucleus and the orbiting electrons. This distance, approximately 10 5 times the dimension of the nucleus, accounts for the ability of various radiations to pass through apparently dense materials. Fig. 1 also indicates the relationship of the positively charged protons in the nucleus and the negatively charged electrons. In the un-ionized state, the number of protons is balanced by an equal number of electrons. An atom becomes ionized by gaining or losing one or more electrons. A gain of electrons yields negative ions and a loss results in positive ions. An atom in an ionized state can interact with other elements to form various compounds. When an atom has more than two electrons, their orbits are located in a series of separate and distinct groupings of energy levels or shells. Each shell is capable of containing a specific number of electrons. In general, an inner shell fills to its maximum number of electrons before electrons begin to form in the next shell. An x-ray is a quantum of electromagnetic energy that is emitted when an electron transitions from an outer shell to an inner shell or between energy levels within the same shell. The number of electrons in the outermost shell determines certain chemical properties of the elements. The properties are similar for elements which have similar electron distributions in the outer shell regardless of the number of inner shells. This accounts for the repetition of chemical properties in the Periodic Table of the Elements. (See Appendix 1.) Nuclides and isotopes A nuclide is characterized by its atomic number Z (number of protons in the nucleus) and the mass number A (total number of protons plus neutrons). When nuclides are described by chemical symbol, the atomic Fig. 1 Structure of the atom (Z = atomic number; A = mass number). Steam 41 / Fundamentals of Nuclear Energy 47-1

2 number is the left hand subscript and the mass number the right hand superscript. For example, the α particle can be represented as α, 2α 4, or 2He 4. With most chemical elements there are several types of atoms having different mass numbers, i.e., different numbers of neutrons in the nucleus but the same number of protons. An isotope is one of two or more nuclides of the same chemical element having different mass numbers. Two isotopes of hydrogen and two isotopes of oxygen are depicted in Fig. 1. An ordinary hydrogen atom 1H 1, contains one proton and no neutrons. Its atomic number Z and mass number A are 1. It combines with oxygen to form H 2 O or regular or light water. The deuterium atom, 1 H 2 or 1 D 2, has one proton and one neutron; Z is 1 and A is 2. It combines with oxygen to form D 2 O or heavy water. A third isotope of hydrogen, tritium, 1 H 3 or 1 T 3, has one proton and two neutrons. Heavier nuclides are also identified by chemical name and mass number. Oxygen-16 and oxygen-17 (Fig. 1) have 16 and 17 nucleons respectively, although each has eight protons. For example, symbols for the two isotopes of oxygen described above are 8 O 16 and 8 O 17. Although either the atomic number or the chemical symbol could identify the chemical element, subscripts sometimes are useful in accounting for the total number of charges in an equation. Mass It is customary to list the mass of atoms and fundamental particles in atomic mass units (AMU). This is a relative scale in which the nuclide 6 C 12 (carbon-12) is assigned the exact mass of 12 AMU by agreement at the 1962 International Union of Chemists and Physicists. One AMU is the equivalent of approximately grams, or the reciprocal of the presently accepted Avogadro number, atoms per gram-atom. A gram-atom of an element is a quantity having a mass in grams numerically equal to the atomic weight of the element. Table 1 lists the masses of the fundamental particles and the atoms of hydrogen, deuterium and helium in atomic mass units. Mass defect The mass of the hydrogen atom 1H 1 listed in Table 1 is almost but not quite equal to the sum of the masses of its individual particles, one proton and one electron. However, the mass of a deuterium atom 1H 2 is noticeably less than the sum of its constituents a proton, neutron and electron. Measurements show that the mass of a nuclide is always less than the sum of the masses of its protons, neutrons and electrons. This difference, the mass defect (MD), is customarily calculated as: ( ) (1) MD = Zm + A Z m m h n e where MD = mass defect, AMU Z = number of protons in the nucleus of the nuclide m h = mass of the hydrogen atom, AMU A Z = number of neutrons in the nucleus m n m e Table 1 Masses of Particles and Light Atoms Isotope or Particle Mass, AMU Electron Proton, 1 p Neutron, 0 n Hydrogen, 1 H Deuterium, 1 H Helium, 2 He = mass of neutron, AMU = mass of the nuclide including its Z electrons, AMU Binding energy Although most nuclei contain a plurality of protons with mutually repulsive positive charges, the nucleus remains tightly bound together, and it takes considerable energy to cause disintegration. This energy, called binding energy, is equivalent to the mass defect. From the equivalence of mass and energy, as defined by Einstein s equation E = mc 2, one AMU equals 931 million electron volts (MeV ). An electron volt is the energy gained by a unit electrical charge when it passes, without resistance, through a potential difference of 1 volt. Therefore, Binding energy ( MeV) { ( ) } = Zm + A Z m m h n e 931 (2) This represents the amount of radiant or heat energy released when an atom is formed from neutrons and hydrogen atoms. It also represents the energy which must be added to fission an atom into its basic nucleons, i.e., neutrons and protons. Dividing Equation 2 by A, the number of nucleons in the nucleus, yields the binding energy per nucleon. This in turn can be plotted as a function of A, the mass number as shown in Fig. 2. The result shows that the binding energy per nucleon rapidly increases for low mass numbers, reaches a maximum for mass numbers in the range of 40 to 80, and then drops off with an increasing slope. On the rising portion of this curve, fusion or joining of nucleons to atoms of higher mass number means that there is an increased binding energy per nucleon and consequently a release of energy. On the falling portion of this curve, the fission process or splitting of an atom results in nuclides of lesser mass numbers and greater binding energy per nucleon. Again, energy is released because of the increased mass defect. Radioactivity and decay Nuclear radiations Nuclides that occur in nature are stable in most cases. However, a few are unstable, especially those of atomic number 84 and above. The unstable nuclides 47-2 Steam 41 / Fundamentals of Nuclear Energy

3 undergo spontaneous change at specific rates by radioactive disintegration or decay. Many nuclides decay into other unstable nuclides, resulting in a decay chain that continues until a stable isotope is formed. There are generally three types of radiation commonly arising out of the decay of specific nuclides: alpha (α) particles, beta (β) particles and gamma (γ) rays. Alpha particle The α particle is equivalent to the nucleus of a helium atom comprising two neutrons and two protons. It results from radioactive decay of an unstable nuclide and, with very few exceptions, is observed only in the decay of heavy nuclides. Beta particle The β particle results from radioactive decay and has the same mass and charge as an electron. It is believed that the nucleus of an atom does not contain electrons and, in radioactive β decay, the β radiation arises from conversion of a neutron into a proton and β particle; therefore: neutron proton + β + energy In some instances a positive β particle (called a positron) is produced from the conversion of a proton to a neutron. Gamma ray Gamma rays are electromagnetic radiation resulting from a nuclear reaction. They can be treated like particles in many nuclear reactions and are included among the fundamental particles. Although γ rays have physical characteristics similar to x- rays, their energy is greater and wave length shorter. The only other difference between the two rays is that γ rays originate from within the nucleus while x-rays originate from within the shell structure of the atom. Biological effects of radiation The organs of the human body are composed of tissue which is composed of atoms. When electrons are knocked out of or added to atoms (ionized), the chemical bonds which bind atoms together to make molecules are broken. This process is called ionization. The recombination of these broken molecules can result in changes in the molecular structure of a cell which may affect the way the cell functions, its growth characteristics and its interaction with other cells. In cases Fig. 2 Binding energy per nucleon versus mass number. of high radiation exposure, cancer may result. The term used to describe the effects of radiation on humans is biological damage. Ionization is a direct result of alpha and beta particles interacting with human tissue. These particles produce a continuous path of ionization as they travel throughout the body. Gamma radiation produces ionization indirectly in matter by the photoelectric effect, the Compton effect and pair production. All three processes yield electrons which in turn produce most of the ionization which occurs within the body. 2 In the photoelectric effect, the γ ray transfers all its energy to the electron that it strikes. The electron then causes ionization in the medium. In the Compton effect, only part of the γ ray s energy is transferred to the electron as kinetic energy. The remaining energy gives rise to a lower energy γ ray. Pair production occurs when the γ ray has an energy greater than 1.02 MeV. All of its energy is given up and two particles, an electron and a positron, are produced. (All three processes produce electrons which then ionize the absorbing matter.) Although ionization causes biological damage, the seriousness of the damage is determined by many factors such as the types of cells effected (how radiosensitive they are), the age of the person receiving the exposure (young cells are more radiosensitive) and whether the dose is received over a short (acute exposure) or long (chronic exposure) period of time. Acute exposure is more detrimental because a large amount of damage is incurred rapidly and the cells do not have an adequate amount of time to repair themselves. Under chronic exposure, cells are very effective in repairing injury. The effects of chronic exposure and the amount required to produce damage have been extrapolated primarily from known cases of acute radiation exposure. More recent radiobiology laboratory and other studies have developed data which assess the effects of chronic exposure. As the nuclear industry continues, the database for low level occupational exposure grows and it becomes more evident that the associated risks are low. The data available suggest that the body can tolerate low doses of radiation received over long periods of time with little risk. This is supported by the exposure and health history of x-ray technicians, physicians and radiation workers. In many laboratory and historic exposure studies, beneficial effects of low level radiation are demonstrated. These studies certainly counter the argument that no level is low enough and that allowable levels must be endlessly reduced in the pursuit of safety. Radiation protection Alpha particles, due to their large mass and double positive charge, travel very short distances. Their range in air is only a few centimeters. Fig. 3 illustrates the penetration ranges of various types of radiation. Alpha particles are seldom harmful when the source is located outside the human body because an α particle of the highest energy will barely penetrate the outer layer of skin. If emitted inside the body, however, α radiation can be serious. It is important, there- Steam 41 / Fundamentals of Nuclear Energy 47-3

4 fore, to prevent the ingestion or inhalation of α emitting nuclides. Particular care is required to keep the air in working spaces free of dust containing α emitters. Fabrication of α emitters such as plutonium normally takes place inside gloveboxes that remain under a slight negative pressure. The boxes discharge air effluent through a filter designed to prevent α bearing dust from entering the working spaces and the atmosphere in general. The air is continuously monitored and analyzed. Beta particles penetrate up to an inch of wood or plastic material and travel several yards in air. The skin and the lenses of the eye are most vulnerable to external β radiation. However, clothing and safety glasses provide adequate protection for external exposure to β radiation. The β particle is not as great an internal hazard as the α particle. The β particle, due to its smaller mass and lower charge, will travel farther than the α particle through tissue and will deposit less energy in a localized area. Gamma rays penetrate deeply and deposit their energy throughout the entire body. They have great ranges in air and may present a hazard at large distances from the source; however, they do not present as large an internal hazard as α particles. Neutrons, like gamma radiation, are an external hazard and their damage extends throughout the body. In addition, the effectiveness of neutrons to produce biological damage is 2.5 to 10 times greater than γ rays. The concrete and water shielding provide the primary protection against neutrons and gamma rays. Decay rate The rate at which a radioactive nuclide emits radiation is a characteristic of the nuclide and is unaffected by temperature, pressure or the presence of other elements that may dilute the radioactive substance. Each nucleus of a specific radioactive nuclide has the same probability of decaying in a definite period of time at a rate characterized by its radioactive decay constant. The rate of decay at any time, t, always remains proportional to the number of radioactive atoms existing at that particular instant. The decay is calculated by: Fig. 3 Ranges of various types of radiation in materials. N t N 0 e ()= ( ) where N(t) = the number of atoms per cm 3 at time t N(0) = the number of atoms per cm 3 at time zero λ = radioactive decay constant λt (3) Half life Decay is usually expressed in terms of a unit of time called radioactive half life, T 1/2. This represents a measurable period of time, the period it takes for a quantity of radioactive material to decay to one half of its original amount. The relationship between half life and decay constant can be determined by substituting (T 1/2) for t and N(0)/2 for N(t) in Equation 3 and solving for λ. The result is: λ = T 1 / 2 (4) Decay constants for radioactivity isotopes are easily obtainable with a listing of measured half lives. 3 If N(t) represents the number of radioactive atoms present at time t, then λn(t) becomes the number of radioactive nuclei that decay per unit of time at time t. This is referred to as the radioactivity, or more simply the activity, of the atoms and is expressed in curies. A curie is disintegrations per second. N(t) can be converted directly to curies by the relation N(t)/( ). Fig. 4 shows on a relative scale how the activity decreases during several half lives. This curve applies to all radioactive substances. It is sometimes difficult to distinguish between stable and radioactive nuclides. All nuclides heavier than bismuth-209 (Bi-209) are unstable. However, the specific nuclides thorium-232 (Th-232), uranium-235 (U-235) and U-238 have half lives of 10 8 to years and can be considered stable. In fact, they are generally referred to as the stable isotopes of the heavier chemical elements. Table 2 shows half lives of some nuclides of high atomic number. Induced nuclear reactions By providing sufficient energy, all of the fundamental particles can be made to react with various nuclei. In this procedure, the particle strikes or enters an atomic nucleus causing a transfiguration or change in structure of the nucleus and the release of a quantity of energy. Particles which activate these reactions include neutrons, deuterons, α, β, protons, electrons and γ. Many reactions produce artificial radioactive nuclides. Charged particles such as alphas, betas and protons do not have great penetration power in matter because the interaction with the existing electrical field within the atoms either slows or stops them. Collisions between like charged particles require exceedingly high kinetic energy. Electrical fields, however, can not deflect electrically neutral neutrons; therefore, they collide with nuclei of the material on a statistical basis. The neutron is therefore the most effective particle for inducing nuclear reactions including fission. Reactions of principal interest in the design of nuclear reactors are those that involve neutrons and those that involve the interaction of the particles pro Steam 41 / Fundamentals of Nuclear Energy

5 Fig. 4 Exponential decay of radioactive nuclides. duced by fission and other nuclear processes within the reactor and surrounding materials. The expression: ( ) (5) X A1 P P X A2 Z1 1 2 Z 2 is generally used to denote a nuclear reaction and is the short form for: X A1 P X A* X A2 P Z1 + 1 Z Z The X* notation indicates formation of a compound nucleus which is generally unstable. Terms P 1 and P 2 represent incident and resultant particles respectively. The individual sum of the Zs (atomic numbers) and the sum of the As (mass numbers) on the left side of the equation always equals, respectively, the sum of the Zs and the sum of the As on the right side of the equation. (See Table 3). Nuclear reactions always conserve total mass-energy on the two sides of the equation in accordance with Einstein s equation for the equivalence of mass and energy. However, there is usually an energy difference and Table 2 Half Lives of Heavy Elements Decay Mode Half Life Naturally occurring nuclides: Thorium-232 α 1.39 x yr Uranium-238 α 4.51 x 10 9 yr Uranium-235 α 7.13 x 10 8 yr Artificial nuclides: Thorium-233 β 22.1 min Protactinium-233 β 27.4 d Uranium-233 α 1.62 x 10 5 yr Uranium-239 β 23.5 min Neptunium-239 β 2.35 d Plutonium-239 α 2.44 x 10 4 yr a mass difference. A good statistical probability for the reaction to occur exists when energy is released as a result of reaction. The more probable reactions generally can be initiated by lower energy particles. The less probable ones, those that require significant energy addition, can be initiated only by high energy particles. Table 3 gives some typical induced nuclear reactions. In a nuclear reactor, many heavy nuclides with mass numbers greater than 238 are produced by a series of neutron captures accompanied by β and/or α decay. These artificially produced nuclides have many uses some are readily fissionable, some are fertile because they absorb a neutron and then transmute to a fissionable nuclide, some have high energy α decay modes that can be used in neutron sources, and some are used as sources in medical procedures. Probability of nuclear reactions cross-sections The probability of a nuclear reaction between a neutron, or other fundamental particle, and a particular nuclide is expressed as the cross-section for that reaction. The probability is dependent on the energy of the interacting particle. Because neutron interactions are most important in a nuclear reactor, the following discussion is directed toward neutron cross-sections; however, the concepts can be directly applied to all particle interactions. Two types of nuclear cross-sections are defined: 1. The microscopic cross-section or interaction probability is an intrinsic characteristic of the nuclei of the material. It has dimensions of an area and is normally expressed in barns where one barn equals cm 2. Short Form Table 3 Typical Induced Nuclear Reactions Long Form Alpha: 4Be 9 (α,n) 6C 12 4Be α 4 6C n 1 7N 14 (α,p) 8 O 17 7N α 4 9 F 18 * 8 O p 1 Deuteron: 15P 31 (d,p) 15 P 32 15P d 2 16 S 33 * 15 P p 1 4Be 9 (d,n) 5 B 10 4Be d 2 5 B 11 * 5 B n 1 Gamma: 4Be 9 (γ,n) 4 Be 8 4Be γ 0 4 Be n 1 1H 2 (γ,n) 1 H 1 1H γ 0 1 H 2 * 1 H n Neutron: 5B 10 (n,α) 3 Li 7 5B n 1 5 B 11 * 3 Li α 4 48Cd 113 (n,γ) 48 Cd Cd n 1 48 Cd 114 * 48 Cd γ 0 1H 1 (n,γ) 1 H 2 1H n 1 1 H 2 * 1 H γ 0 8O 16 (n,p) 7 N 16 8O n 1 8 O 17 * 7 N p 1 Proton: 6C 12 (p,γ) 7 N 13 6C p 1 7 N 13 * 7 N γ 0 4Be 9 (p,d) 4 Be 8 4Be p 1 5 B 10 * 4 Be d 2 * Indicates formation of a compound nucleus which is generally unstable. Steam 41 / Fundamentals of Nuclear Energy 47-5

6 2. The macroscopic cross-section is a probability of interaction per centimeter of neutron path and takes into account the density of the material. It has the dimensions cm -1. The symbol σ represents the microscopic cross-section. In the case of a neutron approaching a fissionable atom it becomes possible to consider a total crosssection σ T in which: σt = σc + σs + σf = σa + σs (6) where σ c = the capture cross-section, a measure of the probability for absorption without fission σ s = the scattering cross-section, the probability that the nucleus will scatter the neutron σ f = the fission cross-section (present in only a few of the many nuclei), the probability for a neutron to strike and cause a fission to occur σ a = the absorption cross-section, the sum of the probabilities for capture and fission The macroscopic cross-section can be obtained from: Σ=N0ρσ/ M (7) where Σ = macroscopic cross-section, cm -1 N 0 = Avogadro s number, atoms/ gram-atom ρ = density of the material, grams/cm 3 σ = microscopic cross-section, cm 2 /atom M = atomic weight, grams/gram-atom Experimental measurements determine microscopic cross-sections for each element. Total cross-section measurements are generally made by transmission techniques. For example, placing a material of known density and thickness in front of a neutron source permits measuring the intensity of neutrons at a particular energy on each side of the material. The difference represents the loss or attenuation of neutrons by the material. The cross-section required to obtain this attenuation is derived by calculation. Isotopes of the same element can have very different cross-sections. For example, the isotope xenon-134 (Xe-134) has a microscopic cross-section for neutron absorption of about 0.2 barn, yet Xe-135 has a microscopic cross-section of barns. U-235 is fissionable at any energy, and U-238 only at high energy. Cross-sections of some nuclides also contain abrupt peaks called resonances at certain energy bands (Fig. 5). Because a cross-section is really a function of relative energy of the neutron and the nucleus, an effective change in the cross-section results when the energies of the neutron and the nucleus increase or decrease as a result of temperature changes. Where the curve of cross-section versus energy is fairly smooth, the effect of a temperature change of the target nucleus is relatively small. However, the effect of a temperature change is large and important in the vicinity of a resonance. An increase in temperature results in increased vibration of the nucleus with a corresponding increase in the number of probable collisions between the nucleus and neutron occurring at energies in the vicinity of the resonance. Therefore, an increase in the temperature of the nucleus results in an apparent broadening of the energy width of the resonance. This in turn results in a very effective increase in resonance neutron absorption, i.e., capture and fission. Conversely, a decrease in temperature of the nucleus results in narrowing the resonance width and decreasing resonance absorption. The change in resonance energy width with temperature, known as the Doppler effect, is important in reactor control. Fig. 5 illustrates a typical cross-section curve showing the neutron capture cross-section of U-238 as a function of neutron energy. Below 10 2 ev the height of the resonance peaks is about 10 3 barns. Between 10 2 and ev the great number of resonances makes it impractical to show the cross-section as a curve, although the resonance parameter data are available for use on a computer. Between and 10 5 ev the curve represents a statistical average of the measurements which have been made. The fission process Nuclear fission is the splitting of a nucleus into two or more separate nuclei accompanied by release of a large amount of energy. In the fission of an atom due to a neutron, the mass of the neutron plus its energy must be equal to or greater than the mass defect associated with the two fission products. U-235 is the only naturally occurring nuclide that is capable of undergoing fission by interaction with low energy or slow neutrons. Some of the artificially produced heavy nuclides are also fissionable with slow neutrons, including plutonium-239 (Pu-239) and U-233. Other nuclides such as U-238 and Pu-242 require higher energy neutrons to cause fission. This difference in fission capability occurs because the binding energy of a nucleus is not only determined by its mass number but also by whether the number of protons and neutrons is even or odd. A nuclide with an even number of neutrons and protons, such as U- 238, has the highest binding energy per nucleon and requires the most added energy to fission. Fission only occurs with high energy or fast neutrons (> 1MeV). A nuclide with an odd number of protons and an even number of neutrons or an even number of protons and an odd number of neutrons, such as U-235, Pu-239 and U-233, has a lower binding energy per nucleon. Nucleons with both an odd number of protons and neutrons have the lowest binding energy per nucleon for essentially equivalent mass numbers. U-235 and Pu-239 are fissionable with slow or thermal neutrons (~0.025 ev). The term thermal neutron refers to a neutron energy distribution that is in thermal equilibrium with the temperature of the surrounding materials. Fission occurs when the fissionable nucleus absorbs a neutron. In the case of U-235 the reaction is: * 92U + 0n 92U Energy 236* A1 A2 1 92U Z1X Z 2Y 243 0n 47-6 Steam 41 / Fundamentals of Nuclear Energy

7 Fig. 5 Capture cross-section of uranium-238. As previously noted, the asterisk in 92 U 236* indicates an unstable nuclide. The value 2.43 applies to U-235 fission by a thermal neutron and is the statistical average of the number of neutrons produced per reaction. X and Y represent the fission products which are distributed as shown in Fig. 6. Energy from fission Fission also produces γ rays, neutrons, β particles and other particles. The energy release per fission amounts to about 204 MeV for U-235 and is distributed as shown in Table 4. Release of approximately this amount of energy per fission can be predicted by examination of Fig. 2 for binding energy, considering that two fission products are formed as shown in Fig. 6. Table 4 also includes data for Pu-239. Neutrons from fission The fact that additional neutrons are born or generated by a fission event makes it possible to establish a chain reaction, as depicted in Fig. 7, that can sustain itself as long as sufficient fissionable material and neutrons are present. The neutrons produced per fission event, υ, and the average number of neutrons produced per neutron absorbed in the fuel, η, vary with the different fissionable isotopes and with the energy of the neutron producing the fission. Statistical averages for these quantities are given in Table 5. There are individual fission reactions that produce only one neutron, possibly none, or as many as five. Because some of the neutrons are absorbed without producing fission, η becomes a more meaningful quantity in reactor design than υ. The values in the table are for fission by low energy or thermal neutrons at room temperature [0.025 ev neutron energy or 7218 ft/s (220 m/s) neutron velocity]. To maintain a chain reaction, the average number of neutrons per absorption must be significantly greater than 1 because some of the neutrons will be lost to absorption in the moderator and structural materials, to absorption in control materials, and to leakage from the core. Control materials such as boron and silver-indium-cadmium are used to maintain a steady-state chain reaction by absorbing any additional neutrons over that needed for steady-state operation. Fission neutron energy distribution Neutrons released from fission vary in initial energy over a wide range up to 15 MeV and above. The distribution of neutrons produced by fission as a function of energy has been determined from several experimental measurements, and typical results for U-235 and Pu-239 are shown in Fig. 8. Based on these measurements, the average energy of fission neutrons is about 2 MeV; the peak of the energy distribution occurs at about 0.8 MeV. Fig. 6 Mass distribution of fission products from fission of U-235. Steam 41 / Fundamentals of Nuclear Energy 47-7

8 Table 4 Energy Produced in Fission (MeV/fission) U-235 Pu-239 Instantaneous Kinetic energy of fission products γ ray energy 8 8 Kinetic energy of fission neutrons Delayed β particles from fission products 8 8 γ rays from fission products 7 6 Neutron-capture γs* Total * Energy produced depends on reactor composition. Burnup As a mass of uranium undergoes fission it produces energy. The term burnup is used to represent the amount of energy produced per unit mass of the material. The units of burnup are megawatt days per metric ton (MWd/t m ) of initial heavy metal, i.e., uranium. One megawatt day represents about fissions. A nuclear fuel assembly is typically discharged from the reactor when it has achieved a burnup of about 50,000 MWd/t m. In commercial power reactors that are fueled with uranium comprising mainly the isotope U-238, with 4% or less U-235, most of the energy produced comes from the fissioning of U-235. At burnups of 50,000 MWd/t m only about 5% of the initial uranium content of the fuel assembly has fissioned. Even when the other nuclear reactions that cause loss of the original uranium atoms are considered, there is still more than 90% of the initial uranium remaining in the fuel assembly when it is discharged. Fission products When a nucleus undergoes fission, experimental measurements have shown that predominantly two fission products or fragments are generated. The distribution of these fission products for U-235 fissions has also been measured and is shown in Fig. 6. In fission, as in any nuclear reaction, there is always conservation of Fig. 7 Chain reaction. total mass-energy so that one of the two fission products will come from each hump of the distribution. Examination of Fig. 6 reveals that mass number of the fission products ranges from about 70 to 170 with two plateaus at approximately 95 and 135. Curves are shown for fission caused by thermal energy neutrons and by 14 MeV neutrons. The higher the neutron energy causing fission the more uniform the fission product distribution. Many fission products interact with neutrons, absorbing them so that they are not available to the chain reaction. As these fission products build up (see Fig. 9), they act as absorbers to retard the chain reaction. All long lived fission products except samarium build up as the core is operated, reaching a maximum effect at the end of core life. Table 5 Neutrons from Fission Avg. Neutrons per Avg. Neutrons per Fuel Fission, υ Absorption in Fuel, η Uranium Uranium Natural uranium Plutonium Plutonium Fig. 8 Fission neutron energy distribution Steam 41 / Fundamentals of Nuclear Energy

9 After discharge from the reactor and sitting in storage for a few years, most of the fission products will have decayed due to their relative short half lives. However, some of the long half life fission products will contribute significantly to the γ ray source that must be shielded against in handling the fuel during its ultimate disposal. These isotopes include strontium-90 (Sr-90), ruthenium-106 (Ru-106), cesium-134 (Cs- 134) and 137 (Cs-137), cerium-144 (Ce-144) and europium-154 (Eu-154). These isotopes will either be bound in the fuel pellets or on the inside surface of the cladding. Other isotopes important to fuel handling are the artificially produced nuclides in the fuel pellet that decay by spontaneously fissioning. These isotopes include Pu-238, americium-241 (Am-241), and curium-242 (Cm-242) and 244 (Cm-244). In addition, the γ emitting isotope cobalt-60 (Co-60) is produced in the structural steels and Inconel through neutron activation and must be shielded against. Fission product behavior with time Certain fission products, specifically Xe-135 and samarium-149 (Sm-149), both of which have very high cross-sections for absorption of thermal neutrons, are not only produced directly from fission but also are the decay products of other fission products. Essentially all initial products of fission are highly radioactive and decay rapidly to less active isotopes with somewhat longer half lives. There are usually several isotopes in the chain before a stable end product is reached. The most significant such decay chain is the following: β β β β Te 53I 54Xe 55Cs 56Ba < 10. min. 67. h 92. h yr In this chain, tellurium-135 (Te-135) with a one minute half life decays to iodine-135 (I-135) with a 6.7 hour half life and then to Xe-135. This xenon isotope, which fortunately has only a 9.2 hour half life, has a macroscopic cross-section for thermal neutron absorption approximately 100,000 cm -1, as great as all the long lived fission products together. Unfortunately, the nuclides of this chain occur abundantly as fission products a predictable happening, because the mass number 135 occurs at a peak in the fission product distribution (Fig. 6). The Xe-135 absorbs an appreciable Fig. 9 Fission product chain. fraction of available neutrons as long as the reactor is operating. This changes some of the Xe-135 to Xe-136 (which has negligible neutron absorption). As a result, when a water reactor operates at constant power level, the Xe-135 builds up to its equilibrium value in 36 to 48 hours. When reactor power lessens and, particularly, when the reactor is shut down, the I-135 formed at the original power level continues for a time to generate Xe- 135 at a rate corresponding to the original power level. Therefore, the Xe-135 builds up rapidly after shutdown because fewer neutrons are available for conversion to Xe-136. The buildup reaches a peak 4 to 12 hours after shutdown and then slowly decays. The time behavior of Xe-135 must be addressed in reactor control. Sm-149, the second important fission product in the reactor core during operation, is generated as follows: Nd 61Pm 62 Sm (stable) In the chain, neodymium-149 (Nd-149) decays (1.7 hour half life) into promethium-149 (Pm-149), which in turn decays (47 hour half life) into Sm-149. Although Sm-149 is a stable isotope it is destroyed so rapidly by neutron absorption that it reaches an equilibrium value when the reactor operates at constant power. Typically, Sm-149 reaches equilibrium in a pressurized water reactor after 50 to 100 days. Buildup after shutdown is slower and less extensive than for Xe-135. Decay after shutdown has little consequence for all other fission fragments because of their long lives and comparable capture cross-sections between parent and daughter nuclide. Nuclear reactor composition A reactor core is composed of fuel, structural and control materials, and a moderator and/or coolant. Typical pressurized water reactor (PWR) fuel assembly and control component designs are shown in Fig. 10. A depiction of the interactions that take place within a fuel assembly is shown in Fig. 11. Neutrons react not only with uranium, but also with the nuclei of most other elements present. Therefore, many materials which have high neutron absorption properties should not be used for structural purposes. Fortunately, a few materials such as aluminum and zirconium have low neutron absorption cross-sections. Inconel, steel and stainless steel also can be used to a limited extent. The choice of coolants includes water, helium and liquid sodium. Thermal reactor design, where the neutron energy distribution is essentially in thermal equilibrium with its surroundings, requires a moderator (a material containing atoms of a light element such as hydrogen, deuterium or carbon) in the core to reduce the kinetic energy of the neutrons. Hydrogen is the ideal moderator because its nucleus is as light as a neutron and, therefore, it can absorb the energy of the neutron in a single direct collision. Hydrogen is normally present in the form of water. The heavier the Steam 41 / Fundamentals of Nuclear Energy 47-9

10 Fig. 11 PWR neutron moderator/coolant-fuel interactions. atom the less energy it absorbs per collision, and the less slowing effect on the neutron. Carbon, in the form of graphite, is about the heaviest atom that can be used practically as a moderator. Carbon has the additional advantage of absorbing very few neutrons, even less than hydrogen. Other low weight atoms can be used, but they are less practical because of excess neutron absorption or high material cost. Because the helium nucleus absorbs essentially no neutrons, it would be an ideal moderator except that helium is a gas at reactor operating temperatures. In this state it would be impossible to provide the core with a sufficient number of atoms to be an effective moderator. All thermal reactors contain some fast (high energy) neutrons because only fast neutrons result from fission. The amount of moderator provided determines the degree of thermalization (energy reduction) or the percentage of thermal neutrons present in the reactor. Perhaps the greatest advantage of the thermal reactor is its compatibility with the water coolant. Water has proven to be the most practical and economical coolant. The low neutrons per fission available with natural uranium makes it difficult to design a natural uranium (0.71% U-235) reactor. However, it can be accomplished if all materials are of especially high purity and if discrete sections of fuel are placed in a heterogeneous array such that the neutrons can slow down in the moderator and then re-enter the fuel material as slow neutrons. Under these conditions, there is a relative high probability of causing fission. The normal moderators used in natural uranium reactors are either graphite or deuterium oxide (heavy water). The absorption cross-section of normal hydrogen makes it less desirable than the other moderators. Also, minute quantities of any high neutron absorbers can prevent a chain reaction. Nevertheless, all early reactors used natural uranium and many still operate, notably the large plutonium producing reactors and the Canadian CANDU pressurized heavy water reactors. (See Chapter 46.) Physical description of nuclear chain reactions 4-7 To use fission as a continuous process for power production, it is necessary to initiate and maintain a fission chain reaction at a controlled rate or level which can be varied with power demand. Obtaining a steadystate chain reaction requires the availability of more than one neutron for each fission produced because non-fission reactions absorb some neutrons and others leak from the reactor. For a reactor as a whole, the neutrons born in each instant of time constitute one generation of neutrons. The term effective multiplication factor, k eff, is defined as the ratio of the number of neutrons in one generation to that in the previous generation. With a multiplication factor of less than one, the system is a decaying one and will never be self-sustaining. With a multiplication factor greater than one, a nuclear system produces more neutrons than it uses, and power increases. For a steady-state chain reaction, k eff = 1. The steady-state equation for neutron balance in a chain reaction can also be written as: Production = Absorption + Leakage (8) Fig. 10 Typical PWR fuel assembly and control components. When this condition is obtained, the reactor has gone critical meaning that the necessary amount of neutron production has been achieved to balance the leakage and the absorption of neutrons. The mass of fissionable material required to achieve this condition is called the critical mass. Production, absorption and leakage all depend heavily on interactions of neutrons with nuclei of the various materials in the reactor. Production depends Steam 41 / Fundamentals of Nuclear Energy

11 primarily on those interactions with U-235 nuclei which result in fission. Absorption depends on interactions of neutrons with any nuclei in the core that result in absorption of neutrons with or without fission. Leakage depends on the scattering effect of collisions between neutrons, nuclei and other particles, which results in transport of neutrons toward the boundaries of the chain reacting system and ultimate escape from the system. Table 5 indicates that each fission of a U-235 atom by a thermal neutron makes available an average of 2.43 neutrons. However, only 2.07 neutrons are produced per thermal neutron absorbed in U-235 as also indicated in Table 5. The other 0.36 neutrons are absorbed in non-fission reactions. If natural uranium is used, the number of neutrons produced per thermal neutron absorbed is reduced to 1.34 because of the neutron absorption in U-238. Most of this absorption results in the ultimate production of fissionable Pu However, neutrons used in this manner are no longer available to help maintain the chain reaction. A neutron chain reaction is possible because each fission event on the average produces more than one neutron. If the process is controlled such that just one of the neutrons produced from fission causes another fission reaction then a steady state process is maintained and a constant power level is achieved. To best understand the process, a general description of the lifetime of a neutron follows. It must be realized that for a power reactor the number of neutrons crossing a 1 cm 2 surface (neutron flux) near the center of the reactor is on the order of neutrons/cm 2 /s. The lifetime of a neutron is on the order of 10-9 seconds. Therefore, this description is only representative of what happens in an instant of time. As described previously, a neutron produced by the fission process has an average energy of about 2 MeV and is termed a fast neutron. At this energy, elastic or inelastic scattering reaction with the moderator, the fuel or with the structural materials are most probable. However, about 2% of the fast neutrons cause a fission in U-238 and produce an even higher number of neutrons than produced from thermal fission. In an elastic scattering reaction some of the neutron energy is transferred to the nucleus with which it collides in the form of kinetic energy; this can cause the nucleus to be displaced from its normal lattice position in the material. In an inelastic collision a compound nucleus is formed in an excited state and it reduces its energy by releasing a lower energy neutron and a γ ray. Some of the original neutron s energy is also deposited as the kinetic energy on the nucleus. The net impact of the scattering reactions is to cause the neutron to lose energy or slow down into the energy range where resonance interactions with various materials (especially U-238) can take place. In the resonance range, neutrons will have a high probability of being captured if their energy coincides with any of the resonances associated with the uranium fuel or the fission products and will not be available to react with the U-235 to help sustain the chain reaction. The resonance escape probability is the fraction of neutrons that escape capture while slowing down to the thermal energy range. The term resonance escape refers particularly to U-238 because in the intermediate range of neutron energy there are several resonance peaks of absorption cross-section for this isotope. These resonances are useful in the production of plutonium; however, to maintain criticality in a thermal reactor, sufficient neutrons must escape absorption in the resonance region. In contrast, collisions with hydrogen atoms in the moderator can slow down the neutron very rapidly, and therefore the resonance escape probability is high for water moderated systems. Once past the resonance range the neutron is said to become thermalized and becomes part of a Maxwellian energy distribution with an average energy of about 0.2 ev. As the fission crosssections for U-235 and Pu-239 are the highest in the thermal energy range, most fission reactions take place in this range. The probability of having a fission reaction is referred to as the thermal utilization and is the ratio of the fission cross-section to the absorption cross-section (capture plus fission) averaged over the moderator plus the fuel and structural materials. The other mechanism for loss of neutrons is leakage from the system. This is dependent on the size of the system and the length of the path neutrons travel between source and capture. For a thermal reactor this length is approximately 2.95 in. (75 mm). Today s power reactors are on the order of 13.1 ft (4 m) in diameter and therefore only neutrons born in the fuel assemblies on the periphery of the core have a significant probability of being lost from the system. Control of the chain reaction More than 99% of neutrons produced in fission are prompt neutrons; that is, they are produced almost instantaneously. About 0.73%, in the case of U-235, are released by the decay of fission products rather than directly from fission. The average half life for these delayed neutrons from fissioning of U-235 is about 13 seconds. This provides time for the reactor operator to respond to small changes in either power demand by the system or reactor system parameters. The chain reaction can be regulated by placing materials with high neutron absorption capability in the reactor and providing a means of varying their amounts. These materials tend to stop the chain reaction and include boron, cadmium-silver-indium, hafnium and gadolinium. One or more of these materials usually goes into the reactor in the form of control rods that can be withdrawn to start up the reactor or to increase power level and reinserted to reduce power or to shut down the unit. To assure accurate control of power, at least some of the rods must be capable of fine regulation. Reactivity The first step in establishing a chain reaction is to bring the reactor to critical condition at essentially no thermal power or zero power level. The reactor power is gradually increased up to the desired level by the removal of a control material and maintained there. The objective in each step of this procedure is to obtain and hold a constant value of k eff = 1.0. In view of Steam 41 / Fundamentals of Nuclear Energy 47-11

12 the changes that continually occur in a nuclear system, it is never possible to keep k eff = 1.0 for more than a short period of time without adjustments to compensate for variations. Operating a reactor at any constant power level at an effective multiplication factor of unity corresponds to steering a ship on a compass course. It takes a continual effort, either automatic or manual, to hold the ship on the exact course. If a reactor operates at a specific power level with k eff = 1.0, and if anything changes to increase or decrease the multiplication factor, a reactivity change is said to have occurred. It may be of positive or negative change depending upon the direction of change in k eff. Reactivity, represented by the symbol ρ, is defined as the ratio: ρ = ( keff 1 ) / keff (9) Reactivity has been given units of dollars ($) and cents ( ) or inhours. It is usually expressed in the units of pcm (per cent milli) which corresponds to a ρ of As will be shown, most processes in the reactor, except for control rod insertion, generate reactivities of 1 to 10 pcm which constitute a very small change from a k eff of 1. Calculation of reactor physics parameters 4-7 The calculation of a chain reaction (or the design of a nuclear reactor) requires solution of the steadystate equation: Production = Absorption + Leakage or its counterpart for nonsteady-state (transient) conditions: Production Absorption Leakage = dn / dt (10) where dn/dt is the variation of the neutron density with time. The production rate is evaluated as: Production = υ Σ f nv (11) where υ = neutrons per fission Σ f = macroscopic fission cross-sections, cm -1 n = neutron density, neutrons/cm 3 v = neutron velocity, cm/s If the neutron flux is defined as the product of the neutron density and neutron velocity, then the production rate can be defined as: Production = υσ f φ (12) where φ = nv = neutron flux Similarly, the absorption rate is defined as: Absorption =Σ a φ (13) where Σ a = macroscopic absorption cross-section, cm -1 Leakage is a complicated function of the gradients in the neutron flux at boundaries of the region under consideration. In performing reactor calculations, the core is divided into discrete spatial regions or nodes, and the continuous neutron energy range is divided into a number of groups. The above equations then become a coupled set of partial differential equations that are solved in both the space and energy domains to find the neutron flux and reaction rates in each node. In the design of the early reactors, most calculations of reactor physics parameters were done by hand using homogeneous models of the core components. Neutron cross-sections were obtained from experimental plots of total, absorption, scattering and fission crosssections. Critical experiments were performed mocking up the fuel designs and modeling both the fuel and control rods. From these experiments, modeling adjustments were developed to ensure high accuracy predictions of reactor performance parameters. As with most other disciplines, the advent of more powerful computers has permitted the designer to perform detailed calculations in both space and energy. The following sections describe some techniques that have been used in calculations for commercial PWR fuel cycle design and licensing. Cross-sections Basic neutron and gamma cross-sections are compiled and verified as part of the industry effort to maintain the cross-section libraries. These libraries provide the basic data needed to calculate the cross-section of each isotope as a function of incident neutron energy. Typically two major energy groups, each containing subgroups, are used by the designer. The first, the fast and epithermal group, spans energies from 1.85 ev to 20 MeV and is composed of 40 or more subgroups. The second, the thermal energy group, covers energies from ev to 1.85 ev and is composed of 50 or more subgroups. In the fast and epithermal energy range, only scattering reactions that decrease neutron energy are used in the calculations. In the thermal energy range, the neutron energies are in thermal equilibrium with the moderator, and energy can be imparted to the neutron during scattering collisions. Therefore, scattering reactions, which can increase or decrease neutron energy, are permitted in the calculations for this group. When designing a reactor core, specific cross-sections are calculated using the total multigroup crosssection set (40 epithermal plus 50 thermal groups) for each material present. Each cell type in the fuel assembly can then be modeled (Fig. 12). This calculation determines the neutron flux distribution in each energy group and cell. The resulting neutron flux is then used to average the cross-sections over the two major energy groups and over various regions of the fuel assembly. A full core representation, indicating the position of fuel assemblies and control components, is shown in Fig Steam 41 / Fundamentals of Nuclear Energy

13 The important quantities that describe the reactor core and its performance include critical boron concentration, core power generation distribution, control rod reactivity worths, and the reactivity coefficients associated with changes in reactor conditions. Critical boron concentration There is sufficient U-235 in a commercial power reactor to power the unit for 12 to 24 months before refueling. Without additional absorbers present in the system, the k eff would be greater than 1. It is impractical to provide the absorption using control rods. Therefore, for long-term control k eff = 1 is maintained by soluble boron in the moderator (boron dissolved in water) and/or burnable absorbers. Burnable absorbers contain a limited concentration of absorber atoms such that, as neutrons are absorbed, the effectiveness of absorption decreases and essentially burns out with time. Burnable absorbers may be in the fuel rods or in fixed absorber rods that are placed in fuel assembly guide tubes. The boron concentration in the coolant can be near 1800 ppm at the beginning of a fuel cycle. This concentration can decrease to near zero at the end of the cycle, when a significant portion of the Fig. 12 Cross-sectional view of fuel assembly. Fig. 13 Cross-sectional computer modeling of PWR core. uranium is depleted and fission products have built up. The critical boron concentration is the boron level required to maintain steady-state reactor power levels. The burnable absorber limits the amount of soluble boron that is used at the beginning of the cycle. Power distribution The primary factor governing acceptable reactor operation is the energy production rate at every point in each fuel rod. If the rate is too high, the fuel can melt and cause rod failure. Excessive energy rates can also cause coolant steaming, which results in poor heat transfer and can lead to cladding burnout. The energy production rate, or power, at each fuel rod location is referred to as the core power distribution. This has typically been calculated by forming a three-dimensional model of the reactor and representing each fuel assembly as a homogenized region over an axial interval. A more recent method for power calculations involves reconstructing the power production in each fuel rod based on detailed fuel assembly calculations. This method is more accurate because it provides a better fuel assembly model that can include water, burnable absorbers or guide tube control rods. With proper fuel assembly placement, the core power distribution can be optimized to limit power peaks in fuel rod segments. As part of this primary analysis, initial enrichments of the fuel and burnable absorbers can be determined, as well as the necessary soluble boron concentration in the coolant over the cycle. Control rod worths Control rods are used in a pressurized water reactor to change power levels and to shut down the reactor. Approximately 48 rods, divided into banks of 8, are commonly used and core reactivity is changed by sequentially moving the banks. The control rod banks are grouped into shutdown and control (or regulating) banks. The shutdown banks provide negative reactivity to bring the reactor from hot to cold conditions. During a shutdown, the core temperature decreases Steam 41 / Fundamentals of Nuclear Energy 47-13

14 and its reactivity increases. The shutdown control rod banks counteract this increase. The controlling banks are used in conjunction with variations in the soluble boron concentration to take the reactor from hot zero power to full power. These banks also provide the reactivity to handle rapid power changes. The negative reactivity caused by the buildup of xenon in the core following a shutdown is offset by a combination of control rod removal and decreases in the coolant boron concentration. The reactivity worth of a control rod is a measure of its ability to reduce core reactivity. Control rod worths are calculated by first calculating the core with the control rod inserted to determine its k eff. The core is then similarly calculated with the rod withdrawn. Control rod worth is defined as: k k k k eff ( i) eff ( w) eff ( w) eff ( i) (14) where k eff(w) = multiplication factor, control rod withdrawn k eff(i) = multiplication factor, control rod inserted Bank worths are similarly calculated. Reactivity coefficients Reactivity coefficients define the rate of core reactivity change associated with the rate of change in reactor conditions. These coefficients indicate the relative sensitivity of the core operation to changes in operating parameters. In determining a coefficient, the core is first modeled with a given power and/or temperature distribution, and k eff is calculated. The reactor is then similarly modeled at a different power or temperature distribution. The coefficient is defined as the reactivity change per unit of power or temperature. Fig. 14 shows the impact of various core parameter changes on core reactivity. There are three basic reactivity coefficients that are important to reactor operation: 1) the moderator temperature, 2) Doppler, and 3) power coefficients. The moderator temperature coefficient is defined as the change in reactivity associated with a change in moderator temperature. It includes the effects of moderator density changes and the changes in nuclear crosssections. The Doppler coefficient is defined as the change in reactivity associated with changes in fuel temperature that occurs primarily because of fuel nuclides with large resonances. The power coefficient is defined as the change in reactivity associated with a change in power level. It is a combination of the moderator and Doppler coefficients and is based on the change in temperature as power changes. When the coolant temperature increases, the associated density reduction normally decreases its moderating capability. A net decline in core reactivity, i.e., a negative moderator temperature coefficient, occurs. Similarly, when the fuel temperature increases, core reactivity decreases. Both mechanisms provide an inherent safety response for the system. However, if the soluble boron concentration is too high, a positive moderator temperature coefficient can occur, and core Fig. 14 Core reactivity as a function of operating parameters. reactivity could increase. For this reason boron concentration is limited to ensure a negative moderator coefficient at full power. Neutron detectors When operating a nuclear chain reaction system, neutron detectors are used to measure the intensity of the neutron radiation (flux). This radiation is a direct indication of nuclear reaction intensity. Neutron detectors can be counters or ionization chambers. Counters, which detect neutrons by sensing the individual ionizations they produce, are most useful when the neutron flux is low. Ionization chambers are more useful at high neutron fluxes. They measure the electrical current that flows when neutrons ionize gas in a chamber. These two types of detectors, placed on the exterior of the pressure vessel, only measure neutrons leaking from the reactor. Two other types of detectors, a self-powered neutron detector and a miniature fission chamber, can be used to measure the neutrons inside the instrument tube of operating fuel assemblies. Self-powered detectors are usually arranged in strings and are positioned to continuously measure the neutron reactions at up to seven axial locations in the fuel assembly. The miniature fission chamber contains uranium, and fission events are detected by the electronics. The fission chamber is moved into and out of the core on a periodic basis, normally monthly, and measures the neutron level along the entire length of the fuel assembly. Neutron source During the start of the chain reaction, it is essential that the operator monitor nuclear instrumentation that is counting neutrons and not gamma rays. The mass of fuel in the core is much greater than the critical mass required to sustain a chain reaction. Control rods and soluble boron dissolved in the reactor coolant keep the core subcritical when no power output is required. When the core is to be brought to criticality, control rods are withdrawn to initiate the chain reaction. However, if the control rods are withdrawn before a measurable neutron flux is available, a reaction could be initiated by a stray neutron and build up to a high power level before the control rods could be reinserted to maintain the desired core output Steam 41 / Fundamentals of Nuclear Energy

15 To control the rate of buildup of the reaction, it is necessary to have a neutron source present in the core for startup. With a neutron source available, it is possible to measure neutron flux before moving control rods and help ensure a safe reactor startup. Several types of neutron sources are available. One is an americium-beryllium-curium source rod. The radioactive isotopes americium and curium emit α particles which react with the beryllium to produce neutrons. Fast reactors It is possible to design for a chain reaction to occur predominantly with either fast (high energy) neutrons or slow (thermal energy) neutrons. In fast reactors the chain reaction is maintained primarily by fast neutrons. Thermal reactors are those in which the chain reaction occurs primarily from thermal neutrons. Today s commercial water reactors are thermal reactors. Fertile material such as U-238 can be used as a fuel by first converting it to plutonium in a reactor. Fast reactors and particularly fast breeder reactors accomplish this conversion most effectively. Liquid sodium, which has essentially no moderating effect, is the coolant most often considered for fast breeders. Helium is used as a coolant in high temperature gas-cooled reactor designs. Conversion and breeding Most important of the conversion reactions is the capture of a neutron by a U-238 nucleus, resulting in a nucleus of fissionable Pu-239: U 0n 92U + + β β U 93Np 94Pu 23 min. 2.3 d 0 γ 0 The U-238 nucleus absorbs a neutron and becomes U-239, which decays with a half life of 23 minutes, into neptunium-239 (Np-239). Again this nuclide, with a half life of 2.3 days, is transmuted to Pu-239 by β decay. This is the nuclear process by which the most useful isotope of plutonium is formed. There are other reactions during operation which form different isotopes of plutonium. Some of these isotopes, including Pu-241, are fissionable, and others, including Pu-240, are converted to fissionable isotopes by neutron absorption. These isotopes can not be separated economically from Pu-239, and therefore must be taken into account when plutonium is used in a reactor. The large commercial PWRs in the United States operate on slightly enriched uranium fuel. These reactors convert U-238 to plutonium and produce about 50% as much plutonium as the U-235 consumed. A reactor is considered to be a converter when the amount of fissionable material produced, e.g., plutonium, is less than the amount of fissionable material consumed, e.g., U-235. A breeder reactor is one in which more fissionable material is produced than consumed. By definition, a breeder reactor must have the value of η (neutrons produced per neutron absorbed in fissionable fuel, Table 5) greater than 2.0. One neutron is required to maintain the chain reaction, one or more for the breeding, and an additional fraction for absorption in nonfuel materials and leakage. It is not possible to make a breeder reactor with natural uranium fuel, because η is less than 2.0. Table 5 shows that η does not greatly exceed 2.0 with any common fissionable isotopes for fissions produced by thermal neutrons. Consequently, it becomes difficult and impractical to make a breeder with a thermal reactor. Fortunately, at high neutron energies, η has a greater value than at thermal energies, particularly with Pu-239. For this reason, and because the absorption cross-sections of most materials are less than at thermal energy, fast reactors breed plutonium more effectively than thermal reactors. In addition, fast reactors operate best with plutonium fuel. 1. Evans, R.D., The Atomic Nucleus, R.E. Krieger Publishing Company, New York, New York, Moe, H.J., et al., Radiation Safety Training Technician Training Course, ANL-7291, Rev. 1, Argonne National Laboratory, Argonne, Illinois, Firestone, R.B., and Shirley, V.S., Eds., Table of Isotopes, Sixth Ed., Wiley-Interscience, Hobocan, New Jersey, Lamarsh, J.R., Introduction to Nuclear Reactor Theory, American Nuclear Society, LaGrange Park, Illinois, References 5. Lamarsh, J.R. and Baratta, A., Introduction to Nuclear Engineering, Third Ed., Prentice-Hall, Reading, Massachusetts, Duderstadt, J., and Hamilton, L., Nuclear Reactor Analysis, Wiley Publishers, Hobocan, New Jersey, Bell, G., Nuclear Reactor Theory, R.E. Krieger Publishing Company, New York, New York, Inconel is a trademark of the Special Metals Corporation group of companies. Steam 41 / Fundamentals of Nuclear Energy 47-15

16 Spent fuel storage at a nuclear power plant Steam 41 / Fundamentals of Nuclear Energy