Department of Physics and Measurement Technology224429/FULLTEXT01.pdf · Department of Physics and Measurement Technology Master’s Thesis Determination of representative spectra

Department of Physics and Measurement Technology

Master’s Thesis

Determination of representative spectra for the

characterization of waste from a 450 GeV protonaccelerator (SPS, CERN)

Lisa Bläckberg

LITH-IFM-EX--09/2064--SE

Department of Physics and Measurement TechnologyLinköpings universitet

SE-581 83 Linköping, Sweden

Master’s ThesisLITH-IFM-EX--09/2064--SE

Determination of representative spectra for the

characterization of waste from a 450 GeV protonaccelerator (SPS, CERN)

Lisa Bläckberg

Supervisor: Peter Müngerifm, Linköpings universitet

Luisa UlriciCERN

Examiner: Peter Müngerifm, Linköpings universitet

Linköping, 2 April, 2009

Avdelning, Institution

Division, Department

Department of Physics and Measurement TechnologyDepartment of Physics and Measurement TechnologyLinköpings universitetSE-581 83 Linköping, Sweden

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Date

2009-04-02

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Language

� Svenska/Swedish

� Engelska/English

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Report category

� Licentiatavhandling

� Examensarbete

� C-uppsats

� D-uppsats

� Övrig rapport

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URL för elektronisk version

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-19037

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ISRN

LITH-IFM-EX--09/2064--SE

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Titel

TitleDeterminering av representativa spektrum för karaktärisering av avfall från en 450GeV protonaccelerator (SPS, CERN)

Determination of representative spectra for the characterization of waste from a450 GeV proton accelerator (SPS, CERN)

Författare

AuthorLisa Bläckberg

Sammanfattning

Abstract

Radioactive waste has been accumulated at CERN as unavoidable consequence ofthe use of particle accelerators. The elimination of this waste towards the finalrepositories in France and Switzerland requires the determination of the radionu-clide inventory. In order to calculate the residual induced radioactivity in thewaste, it is necessary to determine the spectra of secondary particles which are re-sponsible for the material activation. In complex irradiation environments like inan accelerator tunnel it is expected that the secondary particle spectra vary withthe characteristics of the machine components in a given section of tunnel. Inorder to obtain the production rates of the radionuclides of interest the spectra ofsecondary particles are to be folded with the appropriate cross sections. Thoughtechnically feasible, it would be impractical to calculate the particle spectra inevery area of any machine and for all possible beam loss mechanisms. Moreover, afraction of the waste has unknown radiological history, which makes it impossibleto associate an item of waste to a precise area of the machine. Therefore it is use-ful to try to calculate “representative spectra”, which shall apply to a relativelylarge part of the accelerator complex at CERN. This thesis is dedicated to the cal-culation of representative spectra in the arcs of the 450 GeV proton synchrotron,SPS, at CERN. The calculations have been performed using the Monte Carlo codeFLUKA. Extensive simulations have been done to assess the dependence of proton,neutron and pion spectra on beam energy, size of the nearby machine componentand position with respect to the beam-loss point. The results obtained suggestthat it is possible to define one single set of representative spectra for all the arcsof the SPS accelerator, with a minor error associated with the use of these.

Nyckelord

Keywords induced radioactivity, radioactive waste, CERN, characterization, particle spectra

Abstract

Radioactive waste has been accumulated at CERN as unavoidable consequence ofthe use of particle accelerators. The elimination of this waste towards the finalrepositories in France and Switzerland requires the determination of the radionu-clide inventory. In order to calculate the residual induced radioactivity in thewaste, it is necessary to determine the spectra of secondary particles which areresponsible for the material activation. In complex irradiation environments likein an accelerator tunnel it is expected that the secondary particle spectra varywith the characteristics of the machine components in a given section of tunnel.In order to obtain the production rates of the radionuclides of interest the spectraof secondary particles are to be folded with the appropriate cross sections. Thoughtechnically feasible, it would be impractical to calculate the particle spectra in ev-ery area of any machine and for all possible beam loss mechanisms. Moreover, afraction of the waste has unknown radiological history, which makes it impossibleto associate an item of waste to a precise area of the machine. Therefore it is usefulto try to calculate “representative spectra”, which shall apply to a relatively largepart of the accelerator complex at CERN. This thesis is dedicated to the calcu-lation of representative spectra in the arcs of the 450 GeV proton synchrotron,SPS, at CERN. The calculations have been performed using the Monte Carlo codeFLUKA. Extensive simulations have been done to assess the dependence of proton,neutron and pion spectra on beam energy, size of the nearby machine componentand position with respect to the beam-loss point. The results obtained suggestthat it is possible to define one single set of representative spectra for all the arcsof the SPS accelerator, with a minor error associated with the use of these.

Sammanfattning

Radioaktivt avfall har ackumulerats på CERN som en oundviklig konsekvens avanvändandet av partikelacceleratorer. Elimineringen av detta avfall mot de slut-giltiga förvaringsplatserna i Frankrike och Schweiz kräver att inventariet av radi-onuklider är känt. För att räkna ut den residuala inducerade radioaktiviteten iavfallet är det nödvändigt att bestämma de spektrum av sekundärpartiklar somär ansvariga för aktiveringen av materialet. I komplexa strålningsmiljöer, såsomen accelerator tunnel, är det väntat att spektrumen av sekundär partiklar varierarmed karaktäristiken hos de närvarande maskinkomponenterna i en given tunnel-sektion. För att erhålla produktionshastigheten av de intressanta radionukleidernaska dessa spektrum av sekundärpartiklar korsas med lämpliga reaktionstvärsnitt.Trots att det är tekniskt möjligt, är det opraktiskt att räkna ut partikelspektrum

v

vi

i varje del av alla maskiner och för alla möjliga strålförlustmekanismer. Dess-utom har en stor del av de existerande avfallet okänd strålningshistorik, vilketgör det omöjligt att associera ett avfallsföremål till ett precist område i en ma-skin. På grund av detta är det användbart att försöka beräkna “representati-va” spektrum som kan användas för en relativt stor del av acceleratorkomplexetpå CERN. Den här rapporten är dedikerad till beräkningen av representativaspektrum i bågarna på proton synchrotronen, SPS, på CERN. Beräkningarna harutförts med Monte Carlo koden FLUKA. Utförliga simuleringar har gjorts för attfastställa hur proton, neutron och pi-meson spektrum beror av energin på denprimära protonstrålen, strorleken på närliggande maskinkomponenter, och posi-tion i förhållande till strålförlustpunkten. De erhållna resultaten antyder att detär möjligt att använda representativa spektrum för at karaktärisera avfall somkommer från alla bågarna i SPS-acceleratorn, utan att införa ett för stort fel.

Acknowledgments

First of all I would like to thank my supervisors at CERN, Matteo Magistris andLuisa Ulrici, for all their encouragement and support during the work with thisthesis. Especially Matteo’s patience and interest has been invaluable. I would alsolike to thank my supervisor in Linköping, Peter Münger for his feedback on thereport. A thank you also goes to my office mates, flat mates and other friends inGeneva who have been making my year in Switzerland a memorable experience.To my family and my boyfriend Petter, thank you for all your love and support.

Stockholm, april 2009.

vii

Contents

1 Introduction 31.1 CERN and its accelerators . . . . . . . . . . . . . . . . . . . . . . . 31.2 Production of waste . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Beam Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 51.2.2 Waste at CERN . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 The activation process . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.1 Elastic interactions . . . . . . . . . . . . . . . . . . . . . . . 71.3.2 Inelastic interactions . . . . . . . . . . . . . . . . . . . . . . 71.3.3 Reaction cross sections . . . . . . . . . . . . . . . . . . . . . 91.3.4 Radioactive decay . . . . . . . . . . . . . . . . . . . . . . . 101.3.5 Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.6 Induced radioactivity in high energy proton accelerators . . 121.3.7 The activation formula . . . . . . . . . . . . . . . . . . . . . 13

1.4 The matrix method . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.5 FLUKA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.6 Lethargy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.7 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Method and Monte Carlo simulations 212.1 Characteristics of the SPS . . . . . . . . . . . . . . . . . . . . . . . 212.2 Waste from the SPS . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.1 Naming convention . . . . . . . . . . . . . . . . . . . . . . . 242.3.2 From point losses to uniform losses . . . . . . . . . . . . . . 25

2.4 The FLUKA input . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.2 Beam properties . . . . . . . . . . . . . . . . . . . . . . . . 302.4.3 Physics Settings . . . . . . . . . . . . . . . . . . . . . . . . 302.4.4 Scoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3 Analysis of the results 333.1 Position relative to beam loss point . . . . . . . . . . . . . . . . . . 33

3.1.1 Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1.2 Fractions of LE . . . . . . . . . . . . . . . . . . . . . . . . . 35

ix

x Contents

3.1.3 Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.2.1 Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.2.2 Fractions of LE . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.3 Dipole / Quadrupole . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3.1 Neutron moderation . . . . . . . . . . . . . . . . . . . . . . 443.3.2 Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.3.3 Fractions of LE . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.4 Propagation of the statistical error . . . . . . . . . . . . . . . . . . 463.4.1 Numerical estimation of the statistical error . . . . . . . . . 48

4 Conclusions 51

5 Future work 535.1 Characterization of waste from the straight sections of the SPS . . 535.2 Characterization of massive objects . . . . . . . . . . . . . . . . . . 535.3 Characterization of waste from the Proton Synchrotron . . . . . . 53

Bibliography 55

A The track length estimator 57

Nomenclature

Here follows a list of the symbols and abbreviations used in the thesis. Units aregiven where applicable.

Symbols

α Alpha particleβ Beta particlee Electronη Eta mesonv Neutrinov Antineutrinon Neutronπ Pionγ Photonp Protonσ Reaction cross section [1 b (barn) = 10−24 cm2]Rb Production rate of nuclide b [s−1 cm−2]E Particle energy [eV]λ Decay constant [s−1]t1/2 Half-life [s]τ Mean lifetime [s]A Activity [Bq]A Specific activity [Bq/kg]tirr Irradiation time [s]twait Waiting time [s]NAv Avogadros number [6.02 × 1023 nuclei/mole]Lb Reference limit of specific activity of nuclide b [Bq/kg]u Lethargyϕ Normalized particle spectraΦ Particle spectrad Dipole magnetq Quadrupole magnet

1

2 Contents

Abbreviations

CERN Conseil Européen pour la Recherche NuclèaireCNGS CERN Neutrinos to Gran SassoCOMPASS Common Muon and Proton Apparatus for Structure and SpectroscopyFLUKA FLUktuierende KAskadeLE Limite d’ExemptionLHC Large Hadron Collidern_TOF neutron Time-Of-Flight facilityPS Proton SynchrotronPSI Paul Scherrer InstitutSPS Super Proton Synchrotron

Chapter 1

Introduction

1.1 CERN and its accelerators

CERN, the European Organization for Nuclear Research, is the world’s largestparticle-physics research facility. The laboratory was founded in 1954 and is lo-cated outside Geneva on the Franco-Swiss border. There are currently 20 Europeanmember states collaborating to keep the facility running.

At CERN scientists are studying the basic constituents of matter and theforces that act between them. For this purpose the laboratory provides variousparticle accelerators which are used for a wide range of experiments. With thesemachines, particles, such as protons, electrons and ions, are accelerated to highenergies, using strong electrical and magnetic fields. The accelerated particles caneither collide against each other or be sent onto a fixed target, depending on whichtype of experiment they are used for.

The accelerators at CERN form an extensive accelerator complex (see figure1.1). Particles are accelerated up to a certain energy in one accelerator and arethen injected into the next one in order to achieve an even higher energy. Thisprocess continues until the particle beam has attained the energy required by theexperiment in which it is to be used. There are both linear and circular acceleratorsat CERN.

The last part of the accelerator chain is the Large Hadron Collider (LHC). Inthis circular accelerator with a circumference of 27 km, protons can be acceleratedup to an energy of 7 TeV, which corresponds to a velocity very close to the speedof light. The beam has circulated for the first time in the LHC in September 2008.

In order to deal with all the experimental data CERN has also been leading inthe development of computing tools. In 1990 the World Wide Web was inventedat CERN to facilitate the communication between particle physicists from all overthe world.

3

4 Introduction

Figure 1.1. Schematic layout of the CERN accelerator complex.

1.2 Production of waste

As a consequence of the operation of the accelerators, machine components canbecome radioactive. Induced radioactivity in the components of the machine andits surrounding structures is a consequence of the interaction of radiation withmatter. This is possible, for example, in case of beam losses. When high-energyparticles hit a material this can be activated. Secondary particles are generatedin the collisions, which also have the ability of inducing radioactivity.

In this section the mechanisms responsible for the beam losses in the accelera-tors are discussed. A brief description of the radioactive waste generated at CERNis also included.

1.2 Production of waste 5

1.2.1 Beam Dynamics

In any type of accelerator there is an ideal orbit, the so-called design orbit, onwhich all the particles with zero transversal momentum move. If the design orbitis curved, which is the case in most of CERN’s accelerators, there is a need forbending forces in order to keep the particles on the circular track.

Most of the particles slightly deviate in the transversal plane from the designorbit. To keep these deviations in track there is a need also for focusing forces.Both the bending and the focusing forces are created by means of magnetic fields.The bending forces are created by dipole magnets which constrain the particlesto the circular orbit. The focusing forces are created by means of quadrupolemagnets. There are two kinds of quadrupole magnets, those which keep the beamfocused in the horizontal plane, and those which keep the beam focused in thevertical plane. These are called focusing and defocusing magnets, because when themagnet focuses in one direction it defocuses in the other. A succession of focusingand defocusing magnets is needed in order to keep both kinds of deviations undercontrol. When a particle drifts away from the central orbit, it gets pushed back bythe focusing force. The resulting beam will contain particles which oscillate aroundthe central orbit both vertically and horizontally. These oscillations are called theBetatron oscillations and they are described by the so-called Hill’s equation, [1]:

d2x

ds2+K(s) · x = 0 (1.1)

where x is the displacement from the design orbit, s is the longitudinal positionin the accelerator and K is the restoring force which varies with s.Hills equation is a second order differential equation and its solution is:

{

x =√ǫβ cosφ

x = −α√

ǫβ cosφ−

√

ǫβ sinφ

(1.2)

where α and β are parameters which depend on the design of the machine and ǫ isthe transverse emittance whose value is determined by the initial beam conditions.A plot of x versus x as φ goes from 0 to 2π results in the so-called phase spaceellipse, [1].

The variable β depends on the position s and will change under the influence ofthe magnets and in turn affect the shape of the ellipse along the machine. Howeverit is only the shape of the ellipse that will change, its area will remain constantthroughout the accelerator1. The projection of the ellipse on the x-axis shows howthe transverse beam size will vary along the longitudinal position. A large value ofβ(s) will give the phase space ellipse a large projection on the x-axis, and thereforea large transverse beam size.

There are two concepts regarding the phase space ellipse that need to be men-tioned. The first one is the emittance, which equals the area of the ellipse thatcontains 95% of the primary particles. The second concept is the acceptance which

1In a real machine, the area of the ellipse actually increases because of non-linearities anderrors in the machine components.

6 Introduction

is the maximum area of the ellipse which the emittance can attain without loosingany particles. In those parts of the accelerator where the emittance is close to orlarger than the acceptance there are significant beam losses. These beam losseslead to the interaction of particles with matter, which in turn leads to inducedradioactivity. [1]

Another source of beam losses are beam-gas interactions. These occur whenparticles from the beam hit residual gas molecules which are present in the beampipe. This causes the primary particle to scatter away from the design orbit or toundergo nuclear reactions and generate secondary particles.

1.2.2 Waste at CERN

Due to the beam losses the operation of the CERN accelerators unavoidably leadsto the activation of materials. Both the components on the beam line (such asmagnets) and the objects further out from the beam line (such as cables and othersmaller objects) might be activated. The level of activation depends on the energyof the primary beam, the number of primary particles that are accelerated and onthe magnitude of the beam losses. The level of activity in a certain item dependson its proximity to the beam losses, its chemical material composition, the time ithas been placed in the tunnel and the time which has passed since the activation.During maintenance, dismantling and decommissioning of the accelerators theactivated material is removed from the tunnel and is disposed of as radioactivewaste, unless it can be reused elsewhere in the machine. In general, smaller objectsare removed and exchanged during short-time periods of maintenance while largerobjects are removed only during longer periods of shutdown. However, the largestamount of waste comes from the dismantling of the machines.

The radioactive waste is temporarily stored in dedicated buildings or in oldaccelerator tunnels at CERN. At this moment CERN stores about 200 m3 ofradioactive waste per year. Most of the waste has very low radioactivity (specificactivity < 100 Bq/g), but there is also a small fraction which has low to mediumlevel of radioactivity. The interim storage facilities of radioactive waste at CERNare currently close to saturation.

The waste needs to be eliminated towards final repositories in France andSwitzerland. According to the CERN safety policy waste which has been activatedon the french part of the CERN site has to be disposed of in France, and the wasteactivated on the swiss part in Switzerland. The treatment of the waste must followthe legislation valid in each of the Host Countries. [5]

1.3 The activation process

When a particle collides with a nucleus in such a way that this nucleus gainsinternal energy there is a nuclear reaction. The result of the reaction can be adifferent isotope of the same atom, an isotope of another chemical element or thesame atom elevated to an excited state. The resulting nucleus can be found either

1.3 The activation process 7

in a stable or an unstable state. When the nucleus is unstable it can decay and isreferred to as radioactive.

These kinds of collisions are called inelastic interactions. Collisions which donot lead to the production of radioactive nuclides are called elastic interactions.

1.3.1 Elastic interactions

A collision in which the sum of the kinetic energy of the incoming particle andthe nucleus is conserved is called elastic scattering. In this type of reaction theonly things that change are the direction and kinetic energy of the particles. Thenucleus is preserved in its original state and no radioactivity is induced. Theincident particle however looses some of its energy to the nucleus. Elastic scatteringoccurs for all incident particle types and for all particle energies.

The forces which are responsible for the change in direction are the electro-static Coulomb force and the nuclear forces. Charged particles are influenced byboth forces while uncharged particles are affected only by the nuclear ones. Thenuclear forces are the forces which hold the nucleons together in the nucleus, andthey do not depend considerably on charge. These forces act on a much shorterdistance than the Coulomb force. [4]

1.3.2 Inelastic interactions

In inelastic interactions the composition of the nucleus can be changed, and henceradioactive nuclei can be created. The kind of reaction which takes place when aparticle collides with a nucleus depends on the kinetic energy, charge and mass ofthe incoming particle and of the target nucleus. Here follows a description of thereactions of interest for this study. The reactions are grouped according to theenergy of the incident particle.

Low energy inelastic reactions

Low energy interactions take place only when the incident particle is a neutron.This is because the neutron is uncharged and can traverse the Coulomb barriereven with almost zero kinetic energy. Charged particles on the contrary will needa certain amount of energy in order to traverse this barrier and enter the nucleus.

When a low energy neutron collides with a nucleus it can get absorbed bythe latter. The resulting nucleus will be heavier by one neutron, and thus a newisotope is created. This new nucleus can be either stable or unstable. This kind ofreaction is called neutron capture and is written as (n,γ), since the incident particleis a neutron and one or more γ-rays are emitted in the reaction. This reaction ispossible with neutrons with down to zero velocity, the so-called thermal neutrons.Thermal neutrons are created when neutrons with higher energies travel through amaterial and gradually loose their energy by elastic scattering with nuclei which are

8 Introduction

at rest (apart from their thermal motions). The energy of such thermal neutronsis typically around 0.025 eV.

Thermal neutrons can also make the nucleus unstable, so that it breaks intotwo or more fragments. This reaction is called fission and can occur when thenucleus is a heavy element containing a large number of nucleons which are notstrongly grouped together.

Also (n,p) and (n,α) reactions, where the neutron enters the nucleus and knocksout a proton or an α-particle, are possible at low energies. [4]

Evaporation

Particles with an intermediate energy can knock out one or more nucleons whilecolliding with a nucleus. The intermediate energy range needed for this to happenis a few MeV up to about 50 MeV for protons. For neutrons the energy neededis the same or lower, since the neutrons are not affected by the Coulomb barrierand thus need less energy in order to enter the nucleus. The process of an incidentparticle knocking out one or more nucleons can be described by a sequence ofevents. Firstly the incoming particle enters, and gets absorbed by, the nucleus.In the physical model which is used to describe this process it is assumed thatthe energy of the incoming particle is randomly distributed among the nucleons.When the energy of the incoming particle is not too great none of the nucleonsachieve enough energy to escape immediately from the nucleus. This process leavesthe nucleus in an excited state. The nucleus in this state is called a “compoundnucleus”. However, statistical fluctuations in the energy distribution will eventuallyconcentrate enough energy to one nucleon so that it can escape. This can happenmore than once, leading to a sequential emission of nucleons. Each emitted particlehas a relatively low kinetic energy. This kind of emission of particles from anexcited nucleus is called evaporation. [4]

High energy inelastic interactions

When the incoming particles have even higher kinetic energies the situation getsmore complicated. When nucleons are struck by high energy particles they canobtain enough energy to move and hit another nucleon within the same nucleus.The hit nucleon can in turn hit another nucleon, and so on. This sequence ofevents is called an intranuclear cascade of fast nucleons. When a nucleon is hit itcan either escape from the nucleus or it can be captured and give away its energyto the nucleus leaving this in an excited state. The excited residual nucleus cande-excite in various ways:

• Evaporation can occur in a way similar to that described in the previousparagraph. The evaporated nucleons or groups of nucleons are called spalla-tion products.

• The nucleus can be divided into two or more pieces, undergoing so-calledhigh energy fission.


The occurrence of intranuclear cascades dramatically increases the number ofpossible residual nuclei.

Apart from intranuclear cascades there are also other reactions which are pos-sible when a high energy particle collides with a nucleus:

• Fragmentation reactions, which is a direct ejection of high energy ions orlight nuclei from the nucleus.

• Production of new particles which themselves can move within the nucleusand hit other nucleons. Pions, nucleons and antinucleons are particles whichcan develop intranuclear cascades of their own. The energy threshold forpion production is of about 290 MeV, [8], and for production of nucleonsand antinucleons the threshold is around 4.5 GeV. [4]

Photonuclear reactions

In addition to the previously described interactions, where the incident particle isa hadron (proton, neutron or pion), also photons can interact with the nucleus.These high-energy photons are generally γ-rays, X-rays or synchrotron radiation.The reactions can either be of the type where the nucleus gets excited, or photo-spallation. In photospallation nucleons or fragments of the nucleus can get knockedout by the incident photon. [4]

Particle showers

When the energy of the primary hadron is above a few tens of MeV, the secondaryparticles emitted in the reactions can themselves trigger further interactions, cre-ating a hadronic shower.

For energies above 290 MeV, pions are produced. These particles can trans-fer energy to the electromagnetic sector. This happens due to the production ofmesons (such as π0 and η). The mesons quickly decay into electromagnetic par-ticles (e± and γ). When the production of pions is significant, it gives rise toelectromagnetic showers.

High energy hadronic showers will always create also electromagnetic ones, butthe electromagnetic showers however proceed without significant hadronic particleproduction, due to the small probability of electro and photonuclear interactions.[8]

1.3.3 Reaction cross sections

The reactions described in 1.3.2 will not occur every time a particle hits an atom.The probability of a reaction is proportional to a cross sectional target area pre-sented by the nucleus. The number of reactions that will take place per secondand per unit volume of the target can be described by:

N = ϕiσiNT (1.3)

where ϕi is the flux of the particle type i per unit time and per cm2, σi is thecross section and NT is the total number of atoms per cm3 in the target.

10 Introduction

The cross section for a certain reaction depends on the type of incident particle,the type of atom and on the energy of the incident particle. [4]

In the case of a flux of particles of different energy, one has to fold the spectrawith the appropriate cross sections in order to calculate the production rate2 of acertain radionuclide from a certain element. This is done according to:

Rb =

[

∑

i

∫

σi,e,b(E)ϕi(E)dE

]

·NT (1.4)

where σi,e,b(E) is the cross section for the production of the radioisotope b fromthe element e by the particle type i, and ϕi(E) is the spectrum of the particle typei.

1.3.4 Radioactive decay

Radioactive nuclei which are created in the nuclear reactions are unstable, and willeventually decay into stable nuclei. The decay occurs by means of the emission ofparticles from the nucleus. The most common type of decays are α-decay, β-decay,γ-decay, spontaneous fission and nucleon emission.

α-decay

In α-decay an α-particle is emitted from the nucleus. Such particle is composedof 2 protons and 2 neutrons which are bound together like in a helium nucleus. Inthis process an element which is lighter by 4 nucleons (2p and 2n) is created. Thedecay process can be written as:

AZXN → A−4

Z−2X′

N−2 + 42He2 (1.5)

[10]

β-decay

In β-decay a proton is converted to a neutron, or a neutron to a proton withinthe nucleus. There are three possible basic decay processes. In each of them aneutrino (v) or an antineutrino (v) is emitted.

• In β−-decay a neutron is converted to a proton, and an electron in additionto a v is emitted in order to conserve electric charge.

• In β+-decay a proton is converted to a neutron, and a positron in additionto a v is emitted in order to conserve electric charge.

• In electron capture an atomic electron is swallowed by the nucleus and aneutron is created from a proton. In addition a v is emitted. [10]

2The production rate is here defined as the number of radioactive nuclei produced per secondand per cubic centimeter.


γ-decay

γ-decay occurs with the emission of a γ-ray. In this reaction the number of protonsand neutrons in the nucleus (the chemical element) is not changed. Instead it istransformed from one excited state into a lower one, or into the ground state. Theenergy of the emitted photon equals the energy difference between the nuclearstates. γ-decay can occur by itself, or subsequent to α and β decay, since theseprocesses often leave the daughter nucleus in an excited state. [10]

Spontaneous fission

Spontaneous fission is similar to the neutron induced fission described in section1.3.2, but without a previous neutron capture. In this process a heavy nucleus withan excess of neutrons splits into two lighter nuclei. The types of possible daughternuclei are statistically distributed over the entire range of medium weight nuclei.[10]

Nucleon emission

This type of decay occurs, as the name suggests, with the emission of a nucleon.The reaction is most common in fission products which have a large neutron excess.[10]

1.3.5 Activity

The rate at which the previously described decays occur and the nuclei return totheir stable state is different depending on the kind of radioactive nuclei. Thedecay process is of statistical nature and it is not possible to predict when a givennucleus will decay. One can only make predictions about the number of radionucleiin the sample as a whole.

If a sample contains only one kind of radioactive nuclei, and at the time t itcontainsN nuclei and no new radioactive nuclei are created, then the disintegrationcan be described by:

λ = − (dN/dt)

N(1.6)

where λ is the so-called decay constant and represents the probability per unittime that an atom will decay. This constant is independent of the age of the atom,and specific for every kind of radionuclei.

Integrating equation 1.6 leads to the exponential law of radioactive decay, whichdescribes how the number of radioactive nuclei changes in time:

N(t) = N0e−λt (1.7)

where N0 is the number of radioactive nuclei present in the sample at the an initialtime.

Another concept which is often used while talking about radioactivity is thehalf-life, t1/2. The half-life is the time necessary for half of the radioactive nuclei

12 Introduction

in a sample to decay. This constant is also specific for each radionucleus and isrelated to the decay constant according to:

t1/2 =ln(2)

λ(1.8)

This expression is obtained from equation 1.7 by setting N = N0/2.

The inverse of the decay constant is called the mean lifetime, and is the averagetime that a nucleus is likely to survive before it disintegrates:

τ = 1/λ (1.9)

With equation 1.7 it is possible to predict the number of nuclei present in asample at a certain time, assuming that the number of nuclei at an initial timeis known. However, this is not a very practical way to determine how radioactivea certain item is, since the number of nuclei is a property which is very diffi-cult to measure. Much easier is to measure the number of decays during a certainperiod of time. This can be done by observing the radiation emitted from the item.

Activity, A, is a quantity defined as the number of decays per unit time. Theactivity can be predicted, by measuring this quantity at an initial time, accordingto the equation:

A(t) ≡ λN(t) = A0e−λt (1.10)

where A0 is the activity at the initial time. The SI unit for activity is Becquerel[Bq]. One Bq equals one decay per second. [10]

In practice it is more common to talk about the specific activity, A, of a sample.The specific activity is the activity per unit mass:

A =Am

(1.11)

where m is the mass of the sample. Specific activity is normally expressed inBq/kg. [9]

1.3.6 Induced radioactivity in high energy proton accelera-tors

The machines which are of interest in this study are high energy proton accelera-tors. The amount of radioactivity which will be induced in these depends on thebeam losses (number of particles lost, their charge and their energy), the compo-sition of the materials in the accelerator, the spectra of secondary particles, andthe production cross sections for the radionuclides of interest. The amount ofactivity present in an item at a certain time will depend on the half lives of theradionuclides, the time during which the item was irradiated, and the time whichhas passed since the irradiation stopped.


Since the incident particles in these kinds of accelerators have very high en-ergies, a large variety of radioisotopes is produced in the reactions. Furthermorethe materials present in the machine are of various different compositions, whichfurther increase the number of different isotopes.

The radioisotopes created in high energy accelerators commonly decay by emis-sion of electrons or positrons, or by neutron capture (β-decay). The daughternuclei also commonly emits γ-rays. [15] The production of α-emitters is not verycommon in proton accelerators.

Components on the beam line

Items which are placed along the beam line in the accelerator can be activated bothby the primary particles lost from the beam as well as by the secondary particlesgenerated in the nuclear reactions. The activation is mostly due to spallationreactions.

Components off the beam line

In hadron accelerators, the activation of items which are placed far from the beamline occurs by means of secondary hadrons (p,n and π±). The activation process israther complex due to the large energy span of the secondary particles, and theirnon uniform spectral distribution. The activation mechanisms can be divided intotwo parts:

• Activation due to spallation reactions by high energy secondary hadrons.

• Activation due to evaporation and capture reactions involving low-energyneutrons.

The activation from low-energy neutrons depends critically on the chemicalcompositions of the irradiated item, including trace elements. [15]

The ratio between the thermal and high energy particle fluences depends onthe layout of the specific machine, and on the beam energy. The ratio can alsovary considerably between different positions in the accelerator.

Massive objects

If the objects are massive, regardless of whether they are placed along or far fromthe beam line, the induced radioactivity will not be homogeneous, since the spectraof activating particles will change with depth inside the material.

1.3.7 The activation formula

The activity of a certain item of waste depends, as already mentioned, on manyfactors. The irradiation time, the waiting time, the spectra of activating particles,the material composition of the item and the reaction cross sections all affect theamount of activity of the item.

14 Introduction

The number of radioactive nuclei of isotope b per gram of target element eproduced per unit time by I primary particles per second is:

nb = INAvMe

∑

i=p,n,π,pho

∫

Φi(E)σi,e,b(E)dE (1.12)

where NAv is Avogadro’s number (NAv = 6.02 × 1023 nuclei/mole), Me is theatomic weight of the target element e, Φi(E) is the spectrum of particle i (proton,neutron, pion or photon) generated by one primary particle and σi,e,b(E) is thecross section for the production of isotope b from target element e by the particlei.

This equation can be extended to express the specific activity Ab of the ra-dionuclide b per gram of material after an irradiation time tirr and a waiting timetwait:

Ab = I∑

e

NAvMexe

∑

i=p,n,π,pho

∫

Φi(E)σi,e,b(E)dE(1 − e−λbtirr )e−λbtwait (1.13)

where xe is the weight fraction of element e in the item and λb is the decay constantof the isotope b. The term (1 − e−λbtirr )e−λbtwait represents the time build-up.During the irradiation the number of radioactive nuclei will increase with theproduction rate Rb. At the same time they will decay due to the radioactivedecay. The amount of activity in a sample after an irradiation time tirr can bedescribed by:

Ab = Rb(1− e−λbtirr ) (1.14)

When the irradiation stops the activity will only decrease. After a waiting timetwait the activity in the sample will be reduced to (using equation 1.10):

Ab = Rb(1− e−λbtirr )e−λbtwait (1.15)

[10]

1.4 The matrix method

In order to eliminate the radioactive waste generated at CERN it is necessary todetermine the radionuclide inventory for all the items. This can be done in a num-ber of ways, of which one is simulations. The Monte Carlo code FLUKA (whichwill be described in section 1.5) can estimate the residual nuclei in an item, fora given irradiation cycle (tirr and twait). This requires a full implementation ofthe accelerator components and knowledge of the radiological history of the item.This method also requires one separate set of simulations for each of the itemsof waste with their exact material composition and geometry. Because of this itis not a very practical way of characterizing all the items of waste since it wouldrequire too much time in terms of geometry implementation and CPU time.

1.4 The matrix method 15

In the matrix method, [12], only the spectra of secondary particles in thetunnel are determined by Monte Carlo simulations. The radionuclide inventory isafterwards calculated offline for each of the items of waste.

The method is based on the activation formula, equation 1.13. The idea isto calculate the production rates of all possible residual nuclei, produced from allpossible target elements. These production rates are then stored in a matrix andthe final activities are calculated a-posteriori using the material composition andirradiation cycle of each item.

The matrix method can be used to characterize waste which fulfills the followingcriteria:

• The physical processes responsible for the activation are continuous in time.

• Known irradiation cycle, with a minimal uncertainty.

• Uniform particle spectra inside the item.

• The particle spectra responsible for the activation should be known andnormalized to one secondary particle per unit surface per unit time, accordingto:

ϕi =Φi(E)

∑

l

∫

Φl(E)dE(1.16)

where Φi is the absolute fluence of the particle i obtained by FLUKA andϕi is the same fluence normalized to one secondary particle. The sum isperformed over all the secondary particles of interest (neutrons, protons, π+

and π−) and the integral is calculated in the energy range from 10−5 eV to1 TeV for neutrons, and from 1 MeV to 1 TeV for the other particles.

• Uniform material composition of the item.

• Known material composition of the item.

• Absence of heavy elements.

• No contamination.

• Possibility of measuring a dose rate which is representative for the wholeitem.

Apart from the material composition, it is the specific activities which are ofinterest in order to decide how to eliminate a particular item of waste. Each ofthe radionuclides emits radiation which can be more or less harmful. Because ofthis, for a given elimination pathway, there are nuclide-specific limits. The specificactivities of the nuclei in the item are to be compared to a set of reference limitsin order to choose the appropriate elimination pathway.

16 Introduction

The final number of interest is the so-called absolute level of radioactivity:

RAD =∑

b

AbLb

(1.17)

where Ab is the specific activity of radionuclide b and Lb is its correspondingreference limit.

A combination of equations 1.13 and 1.17 gives:

RAD =∑

b

1

Lb

∑

e

xeINAvMe

∑

i=p,n,π,pho

∫

Φi(E)σi,e,b(E)dE(1 − e−λbtirr )e−λbtwait

(1.18)This equation can be rewritten in matrix form. The components of the resultingexpression are:

• The material composition vector−−−−−−−−−→W (material). This vector contains the

value we =∑

xeNAv/Me for each of the elements in the item. we equals thenumber of atoms of target element e per gram of material.

• The reference limits Lb are coupled with the time dependent function:

gb(tirr, twait) =(1− e−λbtirr )e−λbtwait

tirr(1.19)

These components are forming the vector−−−−−−−−→D(irr.cycle) containing one ele-

ment Db(tirr, twait) = gb(tirr, twait)/Lb for each of the radionuclides b.

• For all elements e and all radionuclides b the productions rates are calculatedfrom the coefficients:

fb,e(ϕ) =∑

i

∫

σi,e,b(E)ϕi(E)dE (1.20)

where σi,e,b(E) is the cross section for production of radionuclide b fromtarget element e by incident particle i and ϕi(E) is the unitary spectrum ofparticle type i. The sum is calculated over all particle types (p,n, π±) andthe integral over all possible particle energies. These production rates aregrouped in a matrix M(spectra). The matrix contains one column for everytarget element e and one row for every radionuclide b. The appearance ofthe matrix is:

M(spectra) =

fb1,e1(ϕ) · · · · · · · · · fb1,enϕ

· · · . . . · · ·

· · · . . . · · ·

· · · . . . · · ·fbn,e1

(ϕ) · · · · · · · · · fbn,en(ϕ)

(1.21)

1.5 FLUKA 17

• A normalization factor is finally defined as:

K = Itot∑

i

∫

Φi(E)dE (1.22)

where Itot is the total number of primary particles lost near the item of wasteduring the time tirr, the sum is calculated over all particle types and theintegral over all possible energies. The sum represents the total radiationintensity as a result of one lost primary particle. K can be estimated bymeasuring the dose rate near the radioactive item.

The resulting expression of the RAD value is:

RAD = K[

gb1 (tirr ,twait)Lb1

· · · · · · · · · gbn (tirr ,twait)Lbn

]

×

×

fb1,e1(ϕ) · · · · · · · · · fb1,enϕ

· · · . . . · · ·

· · · . . . · · ·

· · · . . . · · ·fbn,e1

(ϕ) · · · · · · · · · fbn,en(ϕ)

we1

...

...

...wen

(1.23)

= K−−−−−−−−→D(irr.cycle)[M(spectra)]

−−−−−−−−−→W (material) (1.24)

It should be noted that the calculation of the RAD-value can only be performedif there exists a set of reference limits. Otherwise the matrix method is limited tothe estimation of the specific activities of each single radioactive nuclide.

1.5 FLUKA

FLUKA is a Monte Carlo code which is used for calculations involving transport ofparticles and their interactions with matter.[7], [6] The code is used for a numberof applications such as shielding calculations, activation studies, detector design,radiotherapy, etc. The code can simulate the interactions and propagation inmatter of about 60 different particles. Photons and electrons can be simulatedfrom 1 keV to thousands of TeV, neutrinos and muons for any energy and hadronsup to 20 TeV. Time evolution and tracking of emitted radiation from unstablenuclei can be performed online.

The code is based on nuclear models, except for interactions of neutrons withenergies below 19.6 MeV. The transport and interactions of these particles aretreated by a tabulated cross section library. This library contains 72 energygroups.3

3This is valid for the FLUKA version 2006.3(b) which was the version used for the simulationsfor this study. However there has recently been a new release, and the FLUKA version 2008.3has 20 MeV as the transition limit between model and group treatment instead of 19.6 MeV. Thenew version also contains 260 energy groups instead of 72 for the low energy neutrons.

18 Introduction

The code can handle complex geometries implemented with combinatorial ge-ometry. The geometries are formed by a number of regions which are each assigneda material.

To do the simulations one has to provide an input file to the code. The inputfile is written with special commands, called cards, where the physics settings,problem geometry, beam properties and output options are specified.

1.6 Lethargy

All the particle spectra in this thesis will be presented in fluence per unit lethargyas a function of particle energy. Lethargy, u, is defined as, [16]:

u = lnE0

E(1.25)

where E0 is an arbitrary reference energy. Differentiation of equation 1.25 leadsto:

du = − 1

EdE (1.26)

FLUKA generates spectra in the format of differential distribution of fluence inenergy:

dΦ(E)

dE(1.27)

The fluence per unit lethargy is obtained using equation 1.26 according to:

dΦ

du=

dΦ

dE· dE

du= −dΦ

dEE (1.28)

In all the graphs of particle spectra presented in this thesis dΦ(E)dE E is plotted

against the particle energy E. E is the average energy over the logarithmic energybin and calculated as E =

√

Ei ·Ei+1, where Ei and Ei+1 are the limits of energybin i.

The concept of lethargy was invented for nuclear reactor physics, where theneutron spectra are of great importance. When a neutron collide elastically withan atom in a material it can loose part of its energy to the atom. How much energyit looses depends on the scattering angle and on the weight of the atom. Themaximum energy loss (leading to the minimum final energy of the neutron) occursafter a head-on collision. The difference between the initial and the minimum finalenergy of the neutron can be described by the equation:

EminE′

= 1− 4A

(A+ 1)2= 1− α (1.29)

where A is the mass number of the struck atom, E′ is the initial energy of theneutron, Emin the minimal final energy and α = 4A

(A+1)2 [16].This expression is obtained using the momentum and energy conservation prin-

ciples for collisions, in a non relativistic frame. Since neutrons are not charged

1.7 Problem description 19

they will not be affected by the electrons of the atom, and the interaction cantherefore be described as a simple elastic collision between the neutron and thenucleus. The non relativistic frame can be used since the neutrons participatingin these kind of collisions generally have a relatively low energy, and because thenucleus is assumed to be at rest before the collision. After the collision the neutronwill have any of the energies between the minimum final energy, Emin, and theinitial energy, E′, with equal probability. The average energy loss in a collisionis αE

′

2 . For hydrogen A = 1, which leads to α = 1 and which in turn gives an

average energy loss of E′

2 . The energy loss in elastic collisions is a percentage ofthe initial energy E′ rather than a fixed value. This is the result which leads tothe convenience of a new scale where the loss is independent of the initial energy:the lethargy scale.

For hydrogen where A = 1 the use of the lethargy scale gives a uniform spec-trum if no neutrons are absorbed by the material, since in hydrogen the neutronsloose on average half of their energy in each collision.

Plotting the fluence per unit lethargy gives the opportunity to deduce physicalprocesses from the shape of the spectrum. It is possible to see for which energiesneutrons are absorbed and for wich energies many reactions take place.

The other particles (protons and pions) have a different behavior in the colli-sions since they are charged and will interact with the electrons before reachingthe nucleus of the atom. However in this thesis the lethargy scale is adopted alsofor these particles simply for reasons of readability.

1.7 Problem description

Over the years machine components have become radioactive as a consequenceof the operation of the accelerators at CERN. The storage facilities at CERN areclose to saturation, and the waste needs to be eliminated towards final repositoriesin France and Switzerland. In order to do this the radionuclide inventory of thewaste needs to be determined.

In the matrix method, described in section 1.4, the radionuclide inventory isexplicitly calculated from the spectra of secondary particles responsible for theactivation. In complex irradiation environments like an accelerator tunnel it is ex-pected that these spectra vary with the characteristics of the machine componentspresent in a given section of tunnel.

Though technically feasible it would be impractical to calculate the particlespectra for every area of any machine and for all possible beam loss mechanisms.Moreover, a fraction of the waste currently stored at CERN has unknown radio-logical history, which makes it impossible to associate an item of waste to a precisearea of the machine.

The number of spectra to be calculated is a compromise between simplicityand accuracy. Only the spectra which differ considerably in terms of productionrates shall be implemented in the method.

The aim of this thesis is to investigate the possibility of finding one single set

20 Introduction

of representative spectra of secondary particles, which can be applied to all of thearcs of the Super Proton Synchrothron (SPS) at CERN. Such “representative”spectra would be used to calculate the production rates of long lived radionuclidesin small accelerator components located in the arcs.

From the material composition of the item of waste, the production rates andthe radiological history, and by normalization with a dose-rate measurement onecan obtain the activity of the radionuclides in the item. The dependence of thesecondary particle spectra on distance from loss point, beam energy and thicknessof the nearby accelerator component is investigated.

Chapter 3 concludes with the choice of the representative spectra and thecalculation of the associated statistical error.

Chapter 2

Method and Monte Carlosimulations

2.1 Characteristics of the SPS

The Super Proton Synchrotron (SPS) which was switched on in 1976 is the secondlargest particle accelerator at CERN, after the LHC. It is a circular acceleratorwith a circumference of 6.9 km and it is used to accelerate protons and, to a minorextent, ions. The particles are injected to the SPS from the Proton Synchrotron(PS) with an energy of 25 GeV. They are then accelerated to 400 or 450 GeVdepending on where they are to be used. The SPS provides proton beams for theLHC, the CNGS experiment and the COMPASS experiment.

The SPS ring is composed of straight sections and arcs. The straight sectionsare all different from each other and contain an irregular pattern of acceleratorcomponents. In the arcs however one can find a repetitive pattern of magnets.Because of these characteristics it was decided to study the arcs first, due to therelatively simple implementation for simulations.

In total the SPS contains 1317 electromagnets, of which 744 are bendingdipoles. [13]

2.2 Waste from the SPS

The secondary particles produced during the operation of the SPS may induceradioactivity in items located in the accelerator tunnel. The highest levels of in-duced radioactivity are located around the injection and extraction points as wellas beam dump regions. However beam losses can occur anywhere in the acceler-ator which makes it necessary to study the induced radioactivity also in the arcsand straight sections of the ring. Among all radioactive waste from the SPS only asmall fraction comes from the so called hot spots (injection, extraction and dumpregions). The rest comes from the remaining parts of the tunnel.

21

22 Method and Monte Carlo simulations

The items of waste from the SPS differ considerably both in size and materialcomposition. Typical examples of waste are:

• cables;

• massive magnets;

• supports;

• pumps and other elements from the vacuum system.

This variety makes the task of characterizing the waste even more difficult. Thisthesis is dedicated to the study of the spectra of secondary particles responsiblefor the activation of small items exposed to secondary radiation in the SPS arcs.Figures 2.1 and 2.2 shows typical waste. Only the induced radioactivity caused bybeam losses during acceleration of protons will be considered, since only a limitedamount of ions are accelerated, and therefore they do not affect significantly thefinal activities.

Figure 2.1. Activated magnets. Figure 2.2. Activated cables.

2.3 Strategy

The arcs of the SPS house magnets arranged in a repetitive pattern of one quadrupolefollowed by four dipoles, which will be referred to as a “magnetic pattern”.

The spectra in one location in the accelerator is assumed not to be affectedby beam losses in components more than one magnetic pattern upstream. Thisassumption is based on a previous study of hadronic cascades in high energy protonaccelerators [14]. In this study it is shown that when a 1 TeV proton beam hits avirtually infinite iron target, all the high energy (>50 MeV) interactions take placewithin the first 2.25 m layer of material. This distance, which is an indicator ofthe dimension of the geometry to be included in the simulations, is considerablyshorter than the length of one magnetic pattern in the SPS, which is 29.5 m.

2.3 Strategy 23

Furthermore such distance decreases with decreasing beam energy, which impliesthat for a 400 GeV proton beam the length to be considered should be even shorter.

The spectra in every magnetic pattern are also expected to be similar in shape.Following these considerations only one magnetic pattern was implemented in theFLUKA simulations.

The beam losses in the SPS can be divided into three main kinds:

• Losses due to beam-gas interactions.

• Losses due to betatron oscillations.

• Point losses in the septum magnets located at the injection and extractionpoints.

The last kind is beyond the scope of this study since these points are not located inthe arcs, and anyway only a very small fraction of the waste from the SPS comesfrom regions close to these points.

Beam-gas interactions occur when beam particles interact with residual gasmolecules in the beam pipe. The intensity of the beam losses depends on the pres-sure in the beam pipe. This pressure changes along the accelerator and thereforeso will also the intensities of the losses. In this study they are however assumedto be uniformly distributed along a magnetic pattern.

The losses due to betatron oscillations are not uniform. The longitudinal posi-tion of these losses are determined by the variations of the beam pipe aperture Aand the β(s)-function, which is described in section 1.2.1. In the position s wherethe ratio A√

βhas a minimum it is expected that the loss is high.

The β(s)-function depends on the operation mode of the accelerator and onthe energy of the beam. Depending on these factors the beam losses occur indifferent longitudinal positions. During its 30 years of operation the SPS has beenrunning with different operation modes and with different beam energies, leadingto different losses in various positions. For a particular item of waste it is almostimpossible to know where, with respect to the beam losses, it was located dur-ing irradiation. There is therefore no choice but to consider also the losses frombetatron oscillations as uniform, rather than point losses, and estimate the errorintroduced by this approximation.

In order to estimate the error introduced by assuming uniform losses, the lossesare simulated as point losses. The spectra in a given point of the tunnel is thenobtained by summing the contributions from each loss point. Because of the as-sumption of uniformity, every loss is assigned the same intensity. This strategyallows comparing the spectra from the point losses with the spectra from theuniform losses. By doing this it is possible to calculate the error introduced byassuming that an item has been exposed to uniform losses if in reality it has been


exposed only to secondaries from a point loss.

The study focuses on the losses in the quadrupole and the losses in a dipole,assuming that the irradiation environment produced by a loss in either of the fourdipoles would be equivalent. Under this hypothesis two sets of simulations wereperformed: one with losses in the quadrupole and one with losses in the down-stream dipole. (See figures 2.3 and 2.4. The origin of the arrows corresponds tothe beam loss.) The point losses are positioned after 1/3 of the respective magnetslength in order to ensure that most of the hadronic cascade is contained inside themagnet. Moreover, it is at the beginning of the magnet that most of the lossesdue to betatron oscillations actually take place.

The SPS accelerates protons from 25 GeV up to an energy of 450 GeV. Inorder to study the dependence of the spectra on primary beam energy, three setsof simulations were performed. One with a beam energy of 26 GeV, one with 400GeV and one with the intermediate energy of 200 GeV. The value of 400 GeVwas chosen because a large fraction of the historic waste from the SPS-tunnel wasgenerated during machine operation with such beam energy.

In total, six different scenarios have been studied in order to cover the threebeam energies (26, 200 and 400 GeV) and the two loss points (quadrupole anddipole).

It should be noted that the main difference between quadrupoles and dipoles,for the purposes of the present study, lays in the lateral thickness.

Lateral thickness is here defined as the amount of material in the magnet,between the beam pipe and the location of the irradiated item.

This parameter affects both the intensity of the radiation outside the magnet(self-absorption) and the energy dependence of the particle spectra (moderation).

2.3.1 Naming convention

The particle spectra resulting from the FLUKA simulations are normalized to oneprimary particle. The absolute values of these spectra are of interest only whencalculating the spectra from uniform beam losses. Here the absolute values of thecontributing spectra reflect how much each of the point losses contributes to thefinal spectra.

However once these calculations are performed the absolute values of the spec-tra are of minor interest since the intensity of the beam losses, responsible for theactivation of a particular item, is not known. The spectra are therefore normalizedto one secondary particle, according to the formula 1.16.

In order to distinguish between spectra of different beam energy, type of sec-ondary particle and loss point, subscripts are used, like Φi,j,k,l where

• i is the secondary particle type (ln for low energy neutrons, hn for highenergy neutrons, p for protons, π+ or π− for positive or negative pions).

• j is the beam energy (26, 200 or 400 GeV).

• k is the loss point (q for quadrupole and d for dipole).

2.3 Strategy 25

• l is the relative position with respect to the loss point.

Φp,200,d,1 is for example the absolute fluence of protons resulting from a point lossof a 200 GeV primary beam in the dipole, estimated in the air outside the magnetdirectly downstream of the loss. The notations are illustrated in figures 2.3 and 2.4.

Figure 2.3. Naming convention for spectra of protons resulting from a beam loss of 200GeV in a quadrupole.

Figure 2.4. Naming convention for spectra of protons resulting from a beam loss of 200GeV in a dipole.

2.3.2 From point losses to uniform losses

In order to obtain the spectra in a certain point all the relevant contributingspectra are summed. Two different sums are calculated for each energy, in order to


compare the spectra outside accelerator components of different thicknesses. Thefirst sum concerns the spectra expected outside the quadrupole and the second thespectra outside a dipole.

The contributing spectra in a given point are the ones produced by the lossesin the upstream magnets, the losses in the magnet at 90◦ from the point and thebackscattering from losses in the first downstream magnet. This is illustrated infigure 2.5.

Figure 2.5. Contributing spectra assuming uniform beam losses.

For items located outside a quadrupole, the resulting spectra of protons for abeam energy of 200 GeV, is given by:

Φp,200,q = Φp,200,d,3 + Φp,200,d,2 + Φp,200,d,1 + Φp,200,q,0 + Φp,200,d,−1 (2.1)

Similarly the spectra for items located near a dipole is given by:

Φp,200,d = Φp,200,d,3 + Φp,200,d,2 + Φp,200,q,1 + Φp,200,d,0 + Φp,200,d,−1 (2.2)

The third subscript in Φp,200,q and Φp,200,d here indicates that the spectra areeither outside the quadrupole (q) or outside the dipole (d).

One should note that the spectra in these sums are numerically the same as theones illustrated in figure 2.3 and 2.4, but conceptually they have another meaning.For example Φp,200,d,1 in equation 2.1 refers to the spectrum near the quadrupoleresulting from a point loss in the dipole directly upstream of this. On the otherhand in figure 2.4, Φp,200,d,1 refers to the spectrum estimated near the seconddipole downstream of the quadrupole, resulting from a loss in the first dipole. Inother words, the spectra from a point loss in a given position is assumed to dependon the kind of magnet where the loss has taken place but not on the kind of magnetnearby the position of interest.

2.4 The FLUKA input 27

2.4 The FLUKA input

Each of the six scenarios presented in section 2.3 was addressed with a separateset of simulations. The sets share the same geometry and physics settings. Thedifferences are the energy of the primary beam and the location of the beam loss.The beam energies are 26, 200 and 400 GeV, and the locations of the point lossesare inside the quadrupole and inside the first dipole. In the following subsectionsthe common content of the input files is explained.

2.4.1 Geometry

The outer part of the geometry consists of a 36 m long section of the acceleratortunnel. Its walls are 20 cm thick and made of concrete (52.9% O, 33.7% Si, 4.4%Ca, 3.4% Al, 1.6% Al, 1.4% Fe, 1.3% K, 1% H, 0.2% Mg, 0.1% C). The tunnelis represented by a straight cylinder in the geometry, thus neglecting the slightcurvature of a real SPS arc.1 The tunnel section houses one magnetic patternwhich has a total length of 29.5 m. The center of the beam line is located 123cm from the floor of the tunnel, and at 136 and 264 cm distance from each of thetunnel walls. The magnetic pattern is surrounded by air (76% N, 23% O, 1% Ar).Figure 2.6 shows the geometry of the tunnel and the magnetic pattern. Figure 2.7shows a photography of a section of the SPS arc.

Figure 2.6. Section of the SPS tunnel as implemented in the simulations.

The implemented magnets are one quadrupole and four dipoles, each separatedby approximately 40 cm. Both magnets are composed of an iron yoke surroundingcopper coils. The density of the iron is 7.874 g/cm3 and the density of the copper

1The SPS ring has a radius of 1098 m. The piece of the tunnel which is implemented inthe geometry has a length of 36 m. Calculations using the laws of sines and cosines show thatthe end of a straight tunnel is deviated of about 60 cm from the end of a curved tunnel. Thisdeviation can be considered negligible in comparison with the size of the tunnel section.


Figure 2.7. Photography of a section of the SPS arc, containing one magnetic pattern.

8.96 g/cm3. No trace elements are included in these materials since they give aminor contribution to the characteristics of the spectra of secondary particles.

The length of the quadrupole is 305 cm and the total cross section of its yokeis 75.4×75.4 cm2. The details of the cross section can be seen in figure 2.8.

[cm]

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Cross section of the quadrupole.

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Figure 2.8. Cross sectional view of the quadrupole

The total length of a dipole is 626 cm. The yoke has a cross section of 84.0×48.1cm2. The coils of the dipole have a more complicated structure than the ones ofthe quadrupole, with one part of the coil sticking out of the yoke, as can be seen


in figure 2.10. The cross section of a dipole is shown in figure 2.9.

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Figure 2.9. Cross sectional view of a dipole

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Figure 2.10. Side view of the beginning of a dipole

The beam pipe connects and goes through all the magnets. It has an ellipticalcross section inside the quadrupole and a rectangular one in the rest of the tunnelsection. The pipe is made of steel (61.195% Fe, 18.5 % Cr, 14 % Ni, 3% Mo, 2%Mn, 1% Si, 0.2% N, 0.045% P, 0.03% S, 0.03% C) and filled with the FLUKAmaterial “vacuum”. The cross section of the rectangular pipe has an inner size of14.24×2.97 cm2 and an outer one of 14.64×3.85 cm2.

The dimensions of the elliptical pipe can be described by the length of the two


semi-axes of the ellipse. The inner axes are 7.6 and 1.92 cm long while the outerones are 7.8 and 2.12 cm. The cross sections of the beam pipe can be seen in figure2.8 and 2.9 respectively.

2.4.2 Beam properties

The beam is a proton beam which has the energy of 26, 200 or 400 GeV dependingon the scenario. It has its starting point either inside the quadrupole or inside thedipole located directly downstream of it. The position and the direction cosines ofthe beam were chosen so that the particles hit the magnet with an angle of about1 degree after approximately 1/3 of the magnet.

For each of the six simulations 600000 primary protons were transported inorder to reduce statistical fluctuations.

2.4.3 Physics Settings

In the simulations the transport threshold was 10 MeV for all particles exceptneutrons, which were transported down to thermal energies. The threshold formultiple scattering of charged particles was set to 20 MeV, and the threshold fordelta ray production was 1 MeV. These are the standard settings used by FLUKA.

Furthermore the most recent evaporation models with heavy fragment evapo-ration were used and the coalescence effect was included in the nuclear model. Theactivation of these effects are CPU-expensive but needed in order to get accurateresulting spectra.

The transport of electrons and photons was switched off. The reason for thisis that the main cause of activation in proton accelerators is hadrons. Indeedthe photo nuclear reactions have much lower cross sections than the hadronicinteractions. This, in combination with the CPU time necessary to transportphotons and electrons, makes it reasonable to switch off the transport of theseparticles.

2.4.4 Scoring

The spectra of secondary particles are scored using the USRTRACK card whichscores the particle track length in a volume. This value, divided by the volume, isan estimate of the fluence. (The complete theorem is explained in Appendix A.)The FLUKA simulations gives the particle spectra as differential distributions offluence in energy [cm−2 GeV−1 per primary particle].

For this purpose one region outside each of the magnets is defined. Thesedetector-regions start at 5 cm distance from the respective magnet border and are50 cm thick in both directions perpendicular to the beam line. The length of adetector is the same as the length of the nearby magnet. The particles scoredare neutrons, protons and charged pions. Positive and negative pions are scoredseparately, as well as low (<19.6 MeV) and high (>19.6 MeV) energy neutrons. Inthe case of the neutrons the separation is due to the different treatment of these


particles internally in FLUKA (see section 1.5).

The energy binning for the protons and charged pions is made on a logarithmicscale ranging from 1 MeV to 1 TeV with 10 bins per energy decade. The binning ofthe neutrons follows the standard 72 groups used by FLUKA, ranging from 10−5

eV to 19.6 MeV, and 10 bins per decade up to 1 TeV for the high energy tail.

Chapter 3

Analysis of the results

The various spectra generated in the simulations need to be compared in order toestimate the error introduced by adopting one set of representative spectra for allthe SPS arcs. The influence on the spectra by the position relative to the beamloss point (Section 3.1), beam energy (Section 3.2) and thickness of the nearbymagnet (Section 3.3) are investigated.

3.1 Position relative to beam loss point

In order to compare the spectra at different positions relative to a beam loss thespectra resulting from the point losses are studied.

For these comparisons, the spectra generated by a loss in the dipole is chosen,since most of the magnets are dipoles. As beam energy, 200 GeV is chosen sincethis is the intermediate energy.

The spectra are compared in terms of shape and production rates. A study ofhow the intensity of the spectra depends on the distance from the loss point is alsoperformed. The error associated with the assumption of uniform losses instead ofpoint losses is evaluated.

3.1.1 Shape

The shapes of the spectra at different positions relative to a point loss are shownin figures 3.1 to 3.4. (The spectra of π− are very similar to the ones of π+, andtherefore only the spectra of one of the particle types are shown in the graphs.) Allof the spectra are normalized to one secondary particle, according to equation 1.16.

The spectra show that upstream of the loss, the largest fraction of secondariesare neutrons with energy below 1 keV.

The spectrum of low energy neutrons at 90◦ from the loss point contains veryfew particles below 1 keV (figure 3.1). This spectrum also has a larger peak thanthe others at around 1 MeV which is due to the neutrons created from evaporation.

33

34 Analysis of the results

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ϕln, 200, d, -1ϕln, 200, d, 0ϕln, 200, d, 1ϕln, 200, d, 2ϕln, 200, d, 3

Figure 3.1. Spectra of low energy neutrons at different positions relative to a point loss.

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Spectra of high energy neutrons

ϕhn, 200, d, -1ϕhn, 200, d, 0ϕhn, 200, d, 1ϕhn, 200, d, 2ϕhn, 200, d, 3

Figure 3.2. Spectra of high energy neutrons at different positions relative to a pointloss.

The spectra 2 and 3 magnets downstream of the loss are very similar in terms ofshape.

Also for the high energy neutrons the spectrum at 90◦ contains more particlesthan at the other positions (figure 3.2). However for energies above 1 GeV all thespectra, apart from the one upstream of the loss, are fairly similar. The spectrumupstream of the loss contains significantly fewer particles than all the others. Thisis because at high energy, most of the secondary particles are produced in theforward direction.

The characteristics of the spectra of high energy neutrons are repeated for theprotons and charged pions (Figure 3.3 and 3.4).

3.1 Position relative to beam loss point 35

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Spectra of protons

ϕp, 200, d, -1ϕp, 200, d, 0ϕp, 200, d, 1ϕp, 200, d, 2ϕp, 200, d, 3

Figure 3.3. Spectra of protons at different positions relative to a point loss.

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Spectra of positively charged pions

ϕπ+, 200, d, -1ϕπ+, 200, d, 0ϕπ+, 200, d, 1ϕπ+, 200, d, 2ϕπ+, 200, d, 3

Figure 3.4. Spectra of π+ at different positions relative to a point loss.

In general the shapes of the spectra at the different positions relative to theloss point are very similar. The exceptions are the ones upstream of the loss andthe ones at 90◦.

3.1.2 Fractions of LE

From the point of view of radiological characterization, two spectra can be con-sidered equivalent if they lead to the same production rates of the radionuclidesof interest, even though they differ in terms of shape.

To compare the production rates resulting from the different spectra we hererefer to the LE values (exemption limits) as listed in [2]. Although the material


from the SPS will have to be disposed of in France, where no LE are foreseen inthe radiation protection regulation, this study requires to reduce the long list ofspecific activities to a single number. This number is a quantitative indicator ofthe impact of a change in the particle spectra on the inventory.

LE are defined in the Swiss Radiation Protection regulation as the exemptionlimits for clearance of material. According to this regulation, an item is no longersubject to regulatory control if, among other requirements, the sum of the specificactivities divided by their corresponding exemption limits is below 1:

A1

LE1+A2

LE2+ · · ·+ An

LEn< 1 (3.1)

where A1, A2, . . . , An are the specific activities of the nuclides 1, 2,..., n in Bq/kg,and LE1, LE2, . . . , LEn are the exemption limits for these nuclides in Bq/kg. Thesum is to be calculated over all the radionuclides present in the item. The specificactivities are calculated from the spectra as described in section 1.3.7.

In order to estimate the error introduced by assuming uniform beam losses thefractions of LE are here calculated for the spectra at different distances from apoint loss, and for the spectra from uniform losses. By assuming uniform beamlosses, one is disregarding the possibility of an item being exposed only to secon-daries produced by a point loss.

The calculations are performed for three different representative material com-positions: stainless steel, iron and aluminum. The material compositions used arelisted in table 3.1. Trace elements in the material compositions will vary amongdifferent items. At present there are no information available about the exactmaterial compositions, and there are no average material compositions measured,for objects in the SPS accelerator. The compositions used here are taken from astudy performed at PSI, [3].A representative irradiation cycle with an irradiation time of 20 years and a wait-ing time of 10 years is chosen.

The fractions of LE resulting from the five sets of spectra produced after apoint loss in a dipole are presented in table 3.2. The last row of the table presentsthe fractions of LE calculated for the summed spectra outside a dipole, which isthe spectra assuming uniform beam losses. It should be noted that the fractionof LE for the spectra from the uniorm losses is not the average of the fractionsof LE from the point losses shown in the table. ϕ200,d was calculated accordingto equation 2.2, where Φ200,q,1 is used and not Φ200,d,1. In the table however, thefractions of LE for ϕ200,d,1 is shown and not the ones for ϕ200,q,1.


Stainless Steel Iron AluminumC 350.2 2701.3N 450.2 100O 200.1Mg 22511Al 100 100 970705.6Si 5002.4 7503.7 1200.6P 230.2 345.2S 150.1 300.1Ti 280.1 130.1V 880.4 310.2Cr 172082 730.4Mn 15007.2 9704.8 2001Fe 683809.3 971531 2601.3Co 1600.8 150.1Ni 105050.1 1800.9Cu 3001.4 3701.8 300.1Zn 350.2As 250.1Mo 12005.7Sn 770.4

Table 3.1. Material compositions of the representative materials. [ppm]

The values are normalized to 1 Bq/g of the dominant gamma emitter, whichis Co-60 for stainless steel and iron, and Na-22 for aluminum. For stainless steeland iron all the values are above 1. Indeed, the exemption limit for Co-60 is 1Bq/g and the inventory contains exactly 1 Bq/g of Co-60 by construction. Theadditive rule in equation 3.1 shows that therefore the values have to be at least1. For aluminum all values are above 0.33 since the limit for Na-22 is 3 Bq/g andthere is exactly 1 Bq/g of Na-22 by construction. [2].

Stainless steel Iron Aluminumϕ200,d,−1 1.0207 1.2246 0.6547ϕ200,d,0 1.0227 1.2561 0.3733ϕ200,d,1 1.0211 1.2302 0.3986ϕ200,d,2 1.0216 1.2348 0.4174ϕ200,d,3 1.0217 1.2366 0.4070

ϕ200,d 1.0232 1.2626 0.3734

Table 3.2. Fractions of LE per Bq/g of the dominant gamma emitter, calculated for a200 GeV point loss in a dipole and for the summed spectra outside a dipole.


The errors are calculated as the difference in fraction of LE between a pointloss and uniform losses, normalized to the value for uniform losses. For stainlesssteel all the values in table 3.2 are rather similar. The error introduced in thefraction of LE, by using the spectra from uniform losses instead of the ones froma point loss, lies below one per cent regardless of the position of the item relativeto the point loss.

For iron the values differ slightly more. The maximum error of about 3% oc-curs when the spectra from uniform losses is used instead of the ones from a pointloss downstream of the item (ϕ200,d instead of ϕ200,d,−1 according to the notationin 3.2).

After a beam loss low energy neutrons are created mostly by moderation andevaporation, and the spectrum generated is almost isotropic around the loss point.This means that the spectra of low energy neutrons does not differ much upstreamand downstream of the loss. Particles of higher energies are however spread mostlyin the beam direction. [8] This explains why the largest error occurs when assum-ing uniform losses instead of a point loss downstream of the item.

For aluminum the errors are considerably larger and the maximum is of 75%,for the position upstream of the loss. At 90◦ relative to the point loss and onemagnet downstream the error is below one per cent, and two or three magnetsdownstream of the loss the error is around 10%.

For aluminum the large difference in fraction of LE between a downstreampoint loss and uniform beam losses is due to the activity of Fe-55. Fe-55 is mainlyproduced from Fe-54 by neutron capture. This reaction has a large cross sectionfor low energy neutrons, see figure 3.5.

While calculating the matrix (equation 1.21) containing the production ratesof the different radionuclides (using equation 1.20) it is possible to see the contri-bution from different particle types to the final production rates. The calculationsshow that the main contributors to the total production rate of Fe-55 are the lowenergy neutrons. Upstream of the loss these particles give 99% of the total pro-duction rate. For the uniform beam loss the low energy neutrons give 86%.

In figure 3.6 and 3.7 the spectra of neutrons for the relevant scenarios areshown. As expected the spectrum from uniform losses contains more high energyneutrons than the one caused by the point loss.

The spectra of low energy neutrons are however not the same. In figure 3.5there are three peaks in the cross sections: One for energies below 1 eV, one around10 keV and one around 10 MeV. In the spectra of low energy neutrons for the twoscenarios the spectrum upstream of the loss contains more neutrons correspondingto the first peak, and the spectrum from uniform losses contains more neutronswith energies corresponding to the third peak. For the energies of the second peakthe two spectra are very similar. So all in all the differences in the shapes com-pensate each other in terms of production rates.


Figure 3.5. Neutron cross-sections for production of Fe-55 from Fe-54.

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Figure 3.6. Spectra of low energy neutrons, upstream of a point loss in a dipole andthe summed spectra outside a dipole.

In table 3.2 the fractions of LE for aluminum are normalized to 1 Bq/g ofNa-22. This is a nuclide which is produced mainly by high energy particles.

A measurement of 1 Bq/g of Na-22 upstream of the point loss corresponds toa very high activity of Fe-55, since there are few high energy secondaries in thisposition. By applying the spectra from uniform losses when in reality there hasbeen a point loss downstream of the item, the activity of Fe-55 is underestimatedsince the spectra produced by uniform losses has a more even relation betweenlow and high energy particles. By normalizing to Co-60 instead the error will be


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Figure 3.7. Spectra of high energy neutrons, upstream of a point loss in a dipole andthe summed spectra outside a dipole.

smaller, since Co-60 is also produced by low energy neutrons.

3.1.3 Intensities

We here define the intensity of a spectrum as the total number of secondaries perprimary proton per unit area.

In order to know how much each of the spectra contributes to the sums inequations 2.1 and 2.2, the intensities of the spectra at different distances from thepoint losses have to be studied.

Table 3.3 shows the intensities normalized to the number of secondaries at 90◦

with respect to the loss point. The values indicate the number of secondaries foundat each position, assuming that there is one secondary particle at 90◦.

Position -1 0 1 2 3 426 GeV, loss in dipole 0.1307 1.0 0.1374 0.0192 0.004126 GeV, loss in quadrupole 1.0 0.8006 0.0598 0.0109 0.0027200 GeV, loss in dipole 0.1255 1.0 0.1481 0.0205 0.0043200 GeV, loss in quadrupole 1.0 1.1041 0.0777 0.0139 0.0034400 GeV, loss in dipole 0.1238 1.0 0.1490 0.0206 0.0043400 GeV, loss in quadrupole 1.0 1.2061 0.0830 0.0148 0.0036

Table 3.3. Normalized intensities as a function of distance from loss point. 0 refers eachtime to the position of the loss.

It can be seen that the intensities, as expected, decrease with the distance fromthe loss point. These results indicate that losses more than one magnetic patternupstream of the point of interest affect the spectrum intensity by less than 0.5%.This result justifies - a posteriori - the assumption made in section 2.3.

3.2 Energy 41

For losses in the dipole it is the spectra at 90◦ relative to the loss point thatcontains most secondary particles. For losses in the quadrupole it is the spectradirectly downstream of the loss which are the most significant.

One can also see that for all the energies the normalized intensity outside themagnet downstream of the loss is much larger after a loss in a quadrupole thanafter a loss in the dipole. This could be explained by the following considerations.

• The quadrupole is thicker than the dipole;

• The dipole is about twice as long as the quadrupole.

The spectra at 90◦ from a point loss will contain mostly low energy neutrons,since these particles spread almost isotropically around the loss point, while theparticles with higher energies will travel mostly in the forward direction. Theselow energy neutrons can be absorbed by the material in the magnet, and the extentof the absorption depends on the thickness of the material. Since the quadrupoleis thicker than the dipole the intensity of the spectra at 90◦ after a loss in aquadrupole will be lower than after a loss in a dipole, due to the fact that athicker material will absorb more particles than a thinner one. Since the normal-ization is done with the spectra at 90◦ this will affect the value of the normalizedintensity downstream of the loss.

The simple fact that the dipole is longer than the quadrupole is not enough topredict how the spectra in front of the magnets will be related. This is because inthe forward direction not only low energy particles will travel, but also high energyparticles. When high energy particles collide with a new nucleus more particleswill be created. This will increase the number of particles, until the secondaryparticles created in each collision are in equilibrium with those absorbed by thematerial. When this happens the number of particles will start to decrease again.So depending on the length of the magnet, the intensity can increase or decrease.Since the intensity one magnet downstream of a loss in a dipole is so much lowerthan the intensity one magnet downstream of a loss in a quadrupole, one canassume that the dipole is long enough for the secondaries to loose enough energyto be absorbed.

Since the dipole is longer than the quadrupole, the scoring near the downstreammagnet will take place further away from the actual loss point, when the loss isin a dipole with respect to when it is in a quadrupole. Further away from theloss point the high energy particles will have deviated further away from the beamline, which implies that fewer particles are expected at this distance. This can alsoexplain the large difference in intensity.

3.2 Energy

The second factor which can affect the spectra is the energy of the beam. The effecton the spectra by beam energy is evaluated in terms of the shape of the spectraand the fractions of LE. From now on the spectra resulting from uniform beam


losses are used for the analysis, since the error introduced by disregarding pointlosses has already been evaluated. Furthermore the spectra outside the dipole areused for the comparisons since most of the components in a magnetic pattern aredipoles. The beam energies compared are 26, 200 and 400 GeV.

3.2.1 Shape

The shapes of the spectra of each particle type for the different beam energies arepresented in figures 3.8 to 3.11. (For the same reason as in 3.1.1 only the spectraof π+, and not π−, are shown.)

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Figure 3.8. Spectra of low energy neutrons for different beam energies.

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Figure 3.9. Spectra of high energy neutrons for different beam energies.

3.2 Energy 43

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Figure 3.10. Spectra of protons for different beam energies.

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ϕπ+, 26, dϕπ+, 200, dϕπ+, 400, d

Figure 3.11. Spectra of π+ for different beam energies.

These spectra show that the energy of the primary beam does not affect sig-nificantly the shapes of the spectra of secondary particles. In general the spectraare very similar for the lower energies while for the higher energies the differenceis slightly larger.

The reason why the spectra are so similar can be explained by the fact that thenuclear models used in FLUKA predicts similar results for energies above 20 GeV.In addition, the values are normalized to unitary fluence. Consequently largerdifferences are expected for lower beam energies, as in the case of the PS machineat CERN.



The fractions of LE for the spectra are calculated with the same irradiation cycleand material compositions as in section 3.1.2. The results are presented in table3.4.

Stainless steel Iron Aluminumϕd,26 1.0233 1.2632 0.3740ϕd,200 1.0232 1.2626 0.3734ϕd,400 1.0232 1.2625 0.3733

ϕd 1.0232 1.2628 0.3736

Table 3.4. Fractions of LE calculated for spectra outside a dipole, with different beamenergies.

These values show that for a given material composition the fraction of LEdoes not depend much on the energy of the beam. This is the case for all therepresentative material compositions. In table 3.4 the fractions calculated foran averaged spectra are also presented. The average is calculated over all beamenergies giving them equal weight. The error associated with this average is smallfor all three material compositions.

3.3 Dipole / Quadrupole

A specific item of waste coming from the SPS arcs can have been placed eitheroutside a quadrupole or outside a dipole during the time of irradiation. Thedifference between the spectra at these positions is studied in terms of shape andfraction of LE.

3.3.1 Neutron moderation

When neutrons travel through a material their characteristics are changed. Theintensity of the fluence decreases due to absorption of the neutrons by the material.

The mean energy of the neutrons will also decrease due to the effect of neutronmoderation. When neutrons travel through a material they collide with the nucleiof the media. These collisions can be either elastic or inelastic, but the result isalways that the neutron looses some of its energy. This is why, traveling througha material, the mean energy of the neutron fluence decreases. A thick materialwill lead to neutrons with lower energies than a thin material.

For neutrons with energies below 0.5 eV elastic collisions are very probable,and a small amount of energy is transferred to the nucleus of the material in eachcollision. This increases the amount of thermal neutrons. [9]

This information implies that the spectra produced by a loss in a magnet withlarger lateral thickness should contain fewer high energy neutrons than the spectrafrom a loss in a thinner magnet, and vice versa for the low energy neutrons.

3.3 Dipole / Quadrupole 45

3.3.2 Shape

For the following comparisons the averaged spectra over energy are used. Resultingin one set of spectra outside the quadrupole, and one outside the dipole. In figure3.12 and 3.13 the spectra of neutrons outside a dipole and outside a quadrupoleare shown. The spectrum outside the dipole contains more neutrons with energiesabove 1 keV than the spectrum outside the quadrupole.

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Figure 3.12. Spectra of low energy neutrons outside a dipole and outside a quadrupole.

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Figure 3.13. Spectra of high energy neutrons outside a dipole and outside a quadrupole.

The most significant part of the spectra at a given point in the magnetic patterncomes from losses in the magnet closest to this point. The main difference betweenthe two magnet types is that the quadrupole is thicker than the dipole (the crosssection of a quadrupole is 75.4 × 75.4 cm2, and the cross section of a dipole 84 ×48.1 cm2). Because of this the neutrons outside the quadrupole have lost a larger


part of their energy due to moderation, which explains the difference in the shapesof the spectra.


The fractions of LE are calculated also for the spectra outside a dipole and outsidea quadrupole. These are listed in table 3.5. The fractions of LE for the average ofthese two sets of spectra are also calculated. In this averaging the spectra outsidethe dipole is given a weight of 0.9 and the spectra outside the dipole a weight of0.1, resulting in the expression ϕav = 0.9 ∗ ϕd + 0.1 ∗ ϕq.

The weighting factors are calculated considering the facts that one magneticpattern contains 4 dipoles and 1 quadrupole, and that the length of the quadrupoleis about half the length of a dipole. This makes it much more likely that an objectwas placed outside a dipole than outside a quadrupole during the time of irradia-tion.

Stainless steel Iron Aluminumϕd 1.0232 1.2612 0.3741ϕq 1.0209 1.2305 0.3810

ϕav 1.0229 1.2570 0.3744

Table 3.5. Fractions of LE calculated for spectra outside a dipole and outside aquadrupole, and the averaged spectra.

The averaged spectra are similar to the ones outside the dipole, due to theweighting factors. This is reflected in the fractions of LE, whose average is alsoclose to the value for the dipole. The errors introduced by this averaging arelarger when the averaged spectra are applied to an item which in reality has beenexposed to the spectra outside a quadrupole. This error is of 0.19% for stainlesssteel, 2.11% for iron and 1.77% for the aluminum.

3.4 Propagation of the statistical error

There are two kinds of errors which will be associated with the resulting represen-tative spectra in this study.

• The error due to statistical fluctuations in the FLUKA results.

• Systematical errors which come from the use of the representative spectrafor the characterization of all items in the arcs, instead of the spectra whichthey are actually being exposed to.

The latter has already been evaluated in the previous sections. The propaga-tion of the statistical fluctuations to the final result will be evaluated in this section.

3.4 Propagation of the statistical error 47

The final result in this thesis is expressed as the fractions of LE, the so-calledRAD-value using the exemption limits for free release in Switzerland, LE. TheRAD-value is calculated according to formula 1.18. The formula is made up ofessentially three parts:

• the secondary particle spectra ϕ;

• the cross sections σ;

• and the time build-up (1− e−λbtirr )e−λbtwait

The time build-up factor contains the irradiation and waiting times, tirr and twait,and the decay constant, λb, of every nuclide b. The irradiation cycle is chosen asa representative one for this study and has no statistical error associated withit. The decay constants are well known properties of the nuclides and thus havenegligible statistical errors.

The reaction cross sections are calculated from nuclear models, and apart froma few exeptions, no experimental data exists to benchmark these. Because of thisit is not possible to determine the statistical error associated with these values.However, even if such errors existed, the estimate of their propagation wouldrequire complex calculations because of the large number of elements and nuclidesinvolved. Such calculations are beyond the scope of this study.

Because of this only the statistical error associated with the representativespectra will be propagated. This error will be used as an estimate of the error inthe fractions of LE.

The particle spectra from the FLUKA simulations have a percentage errorassociated with the fluence in each of the energy bins. To simplify an averageerror is estimated for an entire spectrum. This is here called σfluka. σfluka isassumed to be the same for all the generated spectra.

The first calculation which is performed in this study is the calculation of thespectra from uniform losses by summing the spectra from the point losses accordingto the equations 2.1 and 2.2.

For a function u of the quantities xi with the associated uncertainties σi, theresulting uncertainty σu is calculated according to:

σ2u =

(

∂u

∂x1

)2

σ2x1

+

(

∂u

∂x2

)2

σ2x2

+ · · ·+(

∂u

∂xn

)2

σ2xn (3.2)

[9] In the case of a simple sum this gives:

σu =√

σ2x1

+ σ2x2

+ · · ·+ σ2xn (3.3)

Assuming that all the spectra have the associated uncertainty σfluka the resultinguncertainty of the spectra of particle type i from uniform losses outside a dipole,for the beam energy 200 GeV, is:

σi,d,200 =√

5 ∗ σ2fluka =

√5 ∗ σfluka (3.4)


and correspondingly for the spectra outside the quadrupole and for the energies26 and 400 GeV.

After this the normalization of the spectra to one secondary particle is per-formed. This is done by simple division of the spectra by a normalization factorFnorm leading to:

σi,d,200,norm =σi,d,200

Fnorm=√

5 ∗ σflukaFnorm

(3.5)

The normalized spectra are then averaged over energy according to:

ϕi,d =ϕi,26,d + ϕi,200,d + ϕi,400,d

3(3.6)

This leads to an uncertainty σi,d which is again calculated using the equation 3.2.The resulting expression is:

σi,d =

√

(σi,26,d,norm

3

)2+(σi,200,d,norm

3

)2+(σi,400,d,norm

3

)2=

=

√

1

3

(√

5 ∗ σflukaFnorm

)2

=

√

5

3∗ σflukaFnorm

(3.7)

The last step of the calculations is the averaging over position which leads tothe final representative spectra. This averaging is performed according to ϕi,av =0.9 ∗ ϕi,d + 0.1 ∗ ϕi,q, leading to an uncertainty of:

σi,av =√

(0.9 ∗ σi,d)2 + (0.1 ∗ σi,q)2 =

√

(0.81 + 0.001) ∗ 5

3∗σ2fluka

F 2norm

=

=

√

0.82 ∗ 5

3∗ σflukaFnorm

(3.8)

This is the final expresson showing how the statistical error propagates throughthe calculations of the representative spectra. It is assumed that the uncertaintyσfluka is applicable to all the spectra generated by FLUKA, independently ofparticle type and beam energy.

3.4.1 Numerical estimation of the statistical error

In order to get a numerical value of the uncertainty the initial uncertainty σflukaneeds to be determined. By studying the output from the FLUKA simulationsone can see that for the energy bins where the particle fluences are significant theassociated uncertainty never exceeds 10%. In equation 3.8 however the uncertaintyσfluka is expressed as an absolute error, not a relative one as the 10% obtainedfrom FLUKA. Therefore it is useful to rewrite equation 3.8 involving relativeuncertainties instead of absolute ones. The resulting expression is:

3.4 Propagation of the statistical error 49

σi,av,rel =

√

0.82 ∗ 5

3σfluka,rel ≈ 1.17 ∗ σfluka,rel = 11.7% (3.9)

where σfluka,relÊis the relative error from the initial FLUKA simulations, set to10%. This final expression is obtained taking into account that all absolute spectrashould be of the same order of magnitude.

Chapter 4

Conclusions

Thanks to this study, a relatively large number of spectra could be effectively re-duced to one single set of representative ones. The error introduced by using therepresentative spectra is 75% in the worst case scenario and around 10% undernormal conditions. The worst case scenario consists in 20 years of continuous irra-diation of an aluminum item with point losses downstream of it, which constitutesa very limited amount of waste.

The uncertainties in the final radionuclide inventory of an item will also be dueto a number of other factors:

• Uncertainties in the material compositions of the irradiated items. It isdifficult to know the exact material composition (including all trace elements)of an item of waste.

• Items can be activated non homogeneously due to self-absorption.

• Uncertainties in the irradiation cycle used. For a large part of the waste it isnot known exactly for how long it was placed in the accelerator tunnel, andhow much time has passed since it was removed from there.

• Errors in the measurement of the specific activity of the dominant gammaemitter.

With respect to these sources of uncertainties the use of representative spectraintroduces a minor error in the radionuclide inventory obtained with the matrixmethod.

51

Chapter 5

Future work

5.1 Characterization of waste from the straight

sections of the SPS

In this initial study spectra for the characterization of the waste from the arcs of theSPS was calculated. A similar study needs to be performed for the waste comingfrom the straight sections. The straight section contains an irregular pattern ofvarious accelerator components. In this study of the arcs it shows that the errorintroduced by using the same spectra outside accelerator components of differentthicknesses is minor. This implies that it should be possible to find representativespectra without introducing too large errors, also for the straight sections of theSPS.

5.2 Characterization of massive objects

The representative spectra of secondary particles calculated in this study can onlybe used to characterize small items of waste which have been placed off the beamline in the SPS arcs during irradiation. When a massive object is being irradiated,the spectra of activating particles will change with depth within the object. Thechanging spectra leads to non-homogeneous activation. In order to characterizethese objects a study on how the spectra changes within the item needs to beperformed. Close to the beam line the particle spectra also changes dramaticallywith distance, which needs to be taken into account while characterizing objectslocated on the beam line.

5.3 Characterization of waste from the Proton

Synchrotron

The Proton Synchrotron (PS) is the accelerator preceding the SPS in the acceler-ator chain at CERN (see figure 1.1). Also the PS is a circular accelerator, and it

53

54 Future work

has a circumference of 628 m. It has been running since 1959 and operates up toan energy of 25 GeV. It is used to deliver protons to the SPS and to the n TOFfacilities. The operation of this accelerator also leads to creation of radioactivewaste which needs to be characterized. Therefore also a study of the spectra inthe PS tunnel needs to be performed. Larger errors are expected in the use ofrepresentative spectra for the characterization of waste from this machine, due tothe lower beam energy.

Bibliography

[1] CAS Cern accelerator school. Fifth general accelerator physics course, 1994.

[2] Ordonnance du 22 juin 1994 sur la radioprotection (ORaP), 1994.http://www.admin.ch.

[3] F. Atchison and S. Teichmann. Realiserung des verfahrens zur klassifizierungund characterisierung der radioaktiven abfalle des psi-west:reprasentative ma-terialien und bestrahlungsspektren 590-mev areal, 2001. Nagra AN 01-035.

[4] M. Barbier. Induced radioactivity. North-Holland Publishing Company, 1969.

[5] CERN. Safety code F, radiation protection, 2006.

[6] A. Fassò, A. Ferrari, J. Ranft, and P.R. Sala. FLUKA: a multi-particle trans-port code. Technical note CERN-2005-10, CERN, 2005.

[7] A. Fassò, A. Ferrari, S. Roesler, P.R. Sala, G. Battistoni, F. Cerutti, E. Ga-dioli, M.V. Garzelli, F. Ballarini, A. Ottolenghi, A. Empl, and J. Ranft. Thephysics models of FLUKA: status and recent developments. In Computingin High Energy and Nuclear Physics 2003 Conference (CHEP2003), La Jolla,CA, USA, march 2003.

[8] A. Ferrari and P. R. Sala. Physics of showers induced by accelerator beams. In”F. Joliot”, Summer School in Reactor Physics, volume 1, pages 1154–1159.CEA, August 1995.

[9] G. F. Knoll. Radiation Detection and Measurement. John Wiley & Sons,2000.

[10] K. S. Krane. Introductory nuclear physics. John Wiley & Sons, 1988.

[11] I. Lux and L. Koblinger. Monte Carlo Particle Transport Methods: Neutronand Photon Calculations. CRC Press, 1991.

[12] M. Magistris. The matrix method for radiological characterization of radioac-tive waste. Nuclear Instruments and Methods in Physics Research Section B,262(2):182–188, 2007.

[13] W. C. Middelkoop and B. de Raad. The european 400 gev proton synchrotron.Nederlands Tĳdschrift Natuurkunde A, 43(1):15–19, 1977.

55

56 Bibliography

[14] M. Silari and G. R. Stevenson. Radiation protection at high energy protonaccelerators. Radiation Protection Dosimetry, 96(4):311–321, 2001.

[15] A. H. Sullivan. A Guide to Radiation and Radioactivity Levels Near HighEnergy Particle Accelerators. Nuclear Technology Publishing, 1992.

[16] A.M. Weinberg and E.P. Wigner. The Physical Theory of Neutron ChainReactors. The University of Chicago Press, 1958.

Appendix A

The track length estimator

The USRTRACK card in FLUKA is scoring the fluence of secondary particlesusing a track length estimator.

The official definition of fluence, used by ICRU (International Comission onRadiation Units and Measurements), is:

Φ =dN

da(A.1)

where dN is the number of particles incident on a sphere with the cross sectionalarea da.

However this definition is slightly misleading since the physical meaning offluence is that of a density of particle track lengths in an infinitesimal volume.Therefore the fluence can be expressed as the sum of the track lengths per unitvolume. The new definition of fluence is then:

Φ = lim∆V→0

∑

i Li∆V

(A.2)

where Li are the track lengths of particle i in the volume ∆V .

An expression similar to this can be derived from the ICRU definition. In aconvex body the mean length of randomly oriented chords d is described by :

d =4V

A(A.3)

where V is the volume of the body and A its surface area. For a sphere the relationbetween the cross sectional area a and the surface area A is A = 4a. This leadsto the expression:

Φ =dN

da=dN · ddV

(A.4)

Thus by scoring the particle track lengths in a volume it is possible to obtainthe particle fluence. [11]

57

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