Chapter 3 Basic Instrumentation for Nuclear Technology 1

Chapter 3. Basic Instrumentation for Nuclear Technology 1. Accelerators 2. Detectors 3. Reactors Outline of experiment: • �� get particles (e. g. protons, …) • �� accelerate them • �� throw them against each other • �� observe and record what happens • �� analyse and interpret the data

1. Accelerators • • • History-Why Particle Sources Acceleration stage Space charge Diagnostics Application

2. Detectors Gas-Filled Radiation Detectors ionization chambers proportional counters Geiger-Muller counters Scintillation Detectors Photomultiplier tube Semiconductor Detectors Personal Dosimeters Others Particle identification Measurement theory Detection Equipment photographic films photographic emulsion plates Cloud and Bubble Chambers E-ΔE, TOF

3. Reactors Reactions Involving Neutrons Sustained, moderation Thermal-Neutron Properties of Fuels General features The Neutron Life Cycle in a Thermal Reactor Homogeneous and Heterogeneous Cores Reflectors Reactor Kinetics Reactivity Effects (feedback)

n + 235 U X + Y+ n + γ + E 200 Me. V “The energy produced by the breaking down of the atom is a very poor kind of thing. Anyone who expects a source of power from the transformations of these atoms is talking moonshine. ” Lord Ernest Rutherford, 1933.

Self-sustaining Chain reaction Dec. 2, 1942, Fermi achieved sustained chain reaction, and the first fission reactor provided data for future design of nuclear reactors.

The Vision • “It is not too much to expect that our children will enjoy in their homes [nuclear generated] electrical energy too cheap to meter. ” – Lewis Strauss, Chairman of the U. S. Atomic Energy Commission (1954)

The total and fission cross section for 235 U based on NJOYprocessed ENDF/B (version V) data.

Why neutron moderation is needed? Fission neutron energy spectrum The average energy of prompt fission neutrons is about 2 Me. V

Reactions Involving Neutrons

Neutron Scattering The elastic scattering is the main mechanism in moderating neutrons in thermal nuclear reactors.

The corresponding neutron energy loss Average Logarithmic Energy Loss on a logarithmic energy scale a neutron loses the same amount of logarithmic energy per elastic scatter, regardless of its initial energy average number of scatters required to bring a neutron of initial energy E 1 to a lower energy E 2

Slowing of neutron (moderation) by various materials. Here n is the number of elastic scatters to slow, on the average, a neutron from 2 Me. V to 0. 025 e. V Is H 2 O a good moderator (慢化剂)

Thermal Neutrons Cross Sections Thermal neutron capture cross sections ( c) Thermal neutron cross section for fission ( f) c /b 1 H 0. 33 2 H 12 C 0. 00052 0. 0034 1. 82 14 N 16 O 0. 0002 113 Cd 19, 820 Moderators: H 2 O vs. D 2 O vs. C Fermi’s used Cd for emergency Nuclear Fission 15

Neutron Capture Reactions Neutron leakage Safety consideration

Spontaneous fission: The fission produced in these cases is insignificant for energy production However the phenomenon is important since represents an uncontrollable source of neutrons in a reactor and it is, furthermore, possible to make use of it in the start-up stage. An example of the use of this fission is the neutron source of 252 californium.

Induced fission: Certain heavy nuclei can be induced to fission, as result of one neutron capture. Consequently, several high-energy neutrons are produced, which permit to maintain the chain reaction process. The nuclei 235 U, 233 U, 239 Pu and 241 Pu experience fission with low-energy thermal neutrons and they are called fissile materials. The nuclei 238 U and 232 Th fission with fast neutrons. The radiative capture of neutrons by 238 U and 232 Th leads to the formation of the fissionable materials 239 Pu and 233 U, so they are called fertile materials.

3. Reactors Reactions Involving Neutrons Thermal-Neutron Properties of Fuels General features The Neutron Life Cycle in a Thermal Reactor Homogeneous and Heterogeneous Cores Reflectors Reactor Kinetics Reactivity Effects

Thermal-Neutron Properties of Fuels σf and σγ are the cross-sections for fission and capture v is the average number of emitted neutrons per nuclear fission The number of neutrons emitted when one neutron is absorbed in the nucleus expressed as η

1. 233 U has the largest value of η, the number of fission neutrons produced per thermal neutron absorbed, and hence is the best prospect for a thermal breeder reactor ( 增值反应堆）. A breeder reactor needs an η of at least two since one neutron is needed to sustain the chain reaction and one neutron must be absorbed in the fertile material （增值材料） to breed a new fissile fuel atom. Fertile materials are those such as 232 Th and 238 U that, upon thermal neutron absorption, may yield fissile materials

2. Although the plutonium isotopes produce almost 3 fission neutrons per thermal fission, their relatively high radiative capture (n, γ) cross sections result in low values of η. E> ~100 ke. V, 239 Pu and 241 Pu, η >3. Thus fast reactors using plutonium as fuel are attractive as breeder reactors.

3. The fertile isotopes 232 Th and 238 U have absorption cross sections of about 1% or less than those of their conversion fissile isotopes 4. The fertile isotope 240 Pu has a large capture cross section for the production of the fissile isotope 241 Pu. η-values for important fissile nuclides

3. Reactors Reactions Involving Neutrons Sustained, moderation Thermal-Neutron Properties of Fuels General features The Neutron Life Cycle in a Thermal Reactor Homogeneous and Heterogeneous Cores Reflectors Reactor Kinetics Reactivity Effects

general features Active core: (1) fissile fuel which through its fissioning is the main source of neutrons, (2) moderator material if the fission neutrons are to slow down, (3) coolant if the heat generated by the fissions is to be removed from the core, and (4) structural material which maintains the physical integrity of the core. Reflector: scatter neutrons back towards the core Blanket region: captures neutrons leaking from the core to produce useful isotopes such as 60 Co Shield Control: allow the chain reaction to be started up, maintained at some desired level, and safely shutdown

Reactors are broadly classified according to the energy of the neutrons : fast reactor, the fast fission neutrons do not slow down very much before they are absorbed by the fuel and cause the production of a new generation of fission neutrons. thermal reactor, almost all fissions are caused by neutrons that have slowed down and are moving with speeds comparable to those of the atoms of the core material, i. e. , the neutrons are in thermal equilibrium with the surrounding material.

The fast fission cross section for three fissionable uranium isotopes based on NJOY processed ENDF/B (version V) data

3. Reactors Reactions Involving Neutrons Thermal-Neutron Properties of Fuels General features The Neutron Life Cycle in a Thermal Reactor Homogeneous and Heterogeneous Cores Reflectors Reactor Kinetics Reactivity Feedback

The Neutron Life Cycle in a Thermal Reactor The neutron life cycle in a thermal reactor showing the major mechanisms for the loss and gain of neutrons. The n fast neutrons beginning the cycle produce n‘ second-generation fast neutrons which, in turn, begin their life cycle

critical state neutrons generated by nuclear fission + neutrons increased by (n, 2 n), etc. = absorbed neutrons + leaked neutrons supercritical state subcritical state right side > left side

Quantification of the Neutron Cycle 1. fast fission factor ε （快中子增殖因数）: the ratio of the total number of fast neutrons produced by both thermal and fast fission to the number produced by thermal fission alone. ε -> 1 238 U 2. resonance escape probability p （逃脱共振俘获概率）: the probability that a fast fission neutron slows to thermal energies without being absorbed p -> 1 235 U This is the measure of how many neutrons can go through resonances without being absorbed:

3. thermal utilization f （热中子利用系数）: probability that, when a thermal neutron is absorbed, it is absorbed by the "fuel" (F) and not by the "nonfuel" (NF) Σ is called the macroscopic cross section for a homogeneous(均匀的） core =0 ->1

Example 10. 1 what is thermal utilization factor in a mixture of graphite and natural uranium with a carbon-to-uranium atom-ratio / of 450?

4. thermal fission factor η （热裂变中子数）: number of fast fission neutrons produced per thermal neutron absorbed by the "fuel. " Equivalently, η is the average number of neutrons per thermal fission (v) times the probability a fission occurs when a thermal neutron is absorbed by the fuel, η > 1, sustaining chain reaction is a property of the fuel material alone and is unaffected by the type and amount of nonfuel material in the core.

5. thermal non-leakage probability （热中子在扩散过程 中不泄漏概率） : probability a thermal neutron does not leak from the core before it is absorbed. R: spherical core of radius there is no leakage 临界屈曲 for a homogeneous mixture of fuel (F) and moderator (M) D is thermal diffusion coefficient

Moderator properties for thermal (0. 00253 e. V) neutrons. L is thermal diffusion length.

（快中子在慢化过程中不泄漏概率） the probability a fast neutron does not leak from the core as it slows to thermal energies. Г is the Fermi age from fission to thermal energies Г ：one-sixth the mean squared distance between the point at which a fast fission neutron is born and begins to slow down and the point at which it reaches thermal energies.

thermal utilization

fastabso rp.

Effective Multiplication Factor （有效增殖因数） For an infinite medium, there is no neutron leakage. "four-factor formula" is a property of only the core material and is independent of the size and shape of the core.

Variation of Keff and its factors with the fuel-to-moderator ratio. This example is for a homogeneous mixture of water and 2%-enriched uranium. Here NF /NM = atom density of uranium to molecular density of water.

subcritical supercritical self-sustaining

What is of a homogeneous mixture of 235 U and graphite with an atomic uranium to carbon ratio of 1 to 40, 000? For such a dilute mixture of fully enriched uranium and carbon, so that

What is the radius R of a critical bare sphere composed of a homogeneous mixture of 235 U and graphite with a uranium to carbon atom ratio of 1 to 40, 000? For criticality, R = 125 cm

fastabso rp.

3. Reactors General features Reactions Involving Neutrons Thermal-Neutron Properties of Fuels The Neutron Life Cycle in a Thermal Reactor Homogeneous and Heterogeneous Cores Reflectors Reactor Kinetics Reactivity Effects Fission Product Poisons

Homogeneous and Heterogeneous Cores The least expensive fuel to use in a reactor assembly is natural uranium (0. 72 atom-% 235 U). But a fast fission neutron would lose so little energy in each scatter from a uranium nucleus that over 2000 scatters would be required to slow the neutron to thermal energies 238 U has large absorption cross sections, for a pure natural uranium core, the resonance escape probability p would be very small so that <<1

The simplest assembly is a homogeneous mixture of natural uranium and a moderator material Small, too little moderation, p is very small Large, thermal neutrons are not absorbed easily by the fuel, f is small Optimum moderator-fuel ratios for a homogeneous mixture of natural uranium and moderator Conclusion? Ways for improvement?

heterogeneous core the fast neutrons are thermalized in the moderator away from the 238 U and hence they can slow through the energy ranges of the 238 U resonances with little likelihood of being captured increase p Fast neutrons born in the fuel lumps have a greater probability of causing fast fissions in 238 U if they are surrounded by only uranium atoms. In a homogeneous system, a fast fission neutron may first encounter a moderator atom, scatter, and lose so much energy that it is no longer capable of causing fast fission. Increase fast fission factor ε

Cross-section of a heterogeneous core. Each unit cell of pitch a contains a 1. 25 -cm radius fuel rod (black circles) of natural uranium metal. The remainder of each lattice cell is graphite.

Variation of core parameters with cell size for the natural uranium and graphite core

Reflectors Most reactor cores are surrounded by some material that has a high scattering to-absorption cross section ratio (typical of moderators). This material, called a reflector it reflects some of the neutrons which would escape or leak from a bare core back into the core, thereby increasing the nonleakage probabilities. raise thermal flux density near the core edges. For heattransfer purposes it is desirable to maintain as constant a thermal flux profile

general features Active core: (1) fissile fuel which through its fissioning is the main source of neutrons, (2) moderator material if the fission neutrons are to slow down, (3) coolant if the heat generated by the fissions is to be removed from the core, and (4) structural material which maintains the physical integrity of the core. Reflector: scatter neutrons back towards the core Blanket region: captures neutrons leaking from the core to produce useful isotopes such as 60 Co Shield Control: allow the chain reaction to be started up, maintained at some desired level, and safely shutdown

3. Reactors Reactions Involving Neutrons Sustained, moderation Thermal-Neutron Properties of Fuels General features The Neutron Life Cycle in a Thermal Reactor Homogeneous and Heterogeneous Cores Reflectors Reactor Kinetics Reactivity Effects

Reactor Kinetics A Simple Reactor Kinetics Model Consider a core in which the neutron cycle takes l' seconds to complete The change Δn in the total number of thermal neutrons in one cycle at time t n(t) is the number of neutrons at the beginning of the cycle or

the neutron population (and hence the reactor power) varies exponentially in time if keff≠ 1. =1. 001 Uncontrollable !

A small fraction β (0. 65% for 235 U) of fission neutrons are emitted, not during the fission event, but by the radioactive decay of daughters of certain fission products at times up to minutes after the fission event that created the fission products. The fission products, whose daughters decay by neutron emission, are called delayed neutron precursors and the emitted neutrons are called delayed neutrons. An example of a fission product whose decay leads to a delayed neutron.

Delayed-neutrons are grouped by the apparent half-lives of the observed emission rates β delayed-neutron fraction

proportion β of delayed neutrons is insignificant. For 235 U, it is 0. 65%, while the proportion of the prompt neutrons is 99. 35%. Though the proportion of delayed neutrons is small but they have a very important effect in the control of the reactor. Delayed neutrons, the average energy being about one-half of that for prompt fission neutrons. lengthening of the neutron cycle time , causes the neutron population and reactor power to vary sufficiently slowly that control of the chain reaction is possible.

Reactivity and Delta-k the degree of departure from criticality reactivity The factor that determines how subcritical or supercritical a reactor may be is They are all positive for a supercritical system, negative for a subcritical reactor, and zero at criticality

Revised Simplified Reactor Kinetics Models Consider a thermal reactor fueled with 235 U Delayed neutron average lifetime is A fraction β of the fission neutrons requires a cycle time of while a fraction (1 -β) is the prompt-neutron fraction and requires a cycle time of only The average or effective generation time required for all the neutrons produced in a single neutron cycle is thus =0. 083 s

-> 0. 083 s controllable !

3. Reactors General features Reactions Involving Neutrons Thermal-Neutron Properties of Fuels The Neutron Life Cycle in a Thermal Reactor Homogeneous and Heterogeneous Cores Reflectors Reactor Kinetics Reactivity Effects

REACTIVITY EFFECTS

Poisoning effect Fission product mass yield per fission induced by thermal neutrons for important fissile nuclides[2]. Total yield is 200%.

135 Xe has a large thermal neutron cross-section, and it greatly affects the reactivity control of the reactor Fission products decay chain including 135 Xe

Fission product yield and decay constant for 135 I and 135 Xe in the fission of 235 U will generally cause a divergent oscillation in the output power

Fuel burn-up

The reactivity when all control material is removed from the core is called the excess reactivity Excess reactivity change during burnup

The following conditions have to be satisfied for nuclear reactor ① Exoergic reaction n + 235 U X + Y+ ηn + E 200 Me. V ② Sustainable as a chain reaction ③ Moderator ④ Controllable Delayed neutron ⑤ Safety Neutron evolution in a nuclear reactor