Shielding Studies for the CERN Super-Proton-Synchrotron at Experimental Point 5

Home , Proton Synchrotron, Super Proton Synchrotron, UA1 experiment

Dissertation

ausgeführt zum Zwecke der Erlangung des akademischen Grades Doktor der technischen Wissenschaften unter der Leitung von

Univ. Prof. Dr. Ewald Schachinger Institut für Theoretische Physik – TU Graz

und

CERN-THESIS-2004-038 21/08/2004 Dr. Graham R. Stevenson CERN, Schweiz

Eingereicht an der Technischen Universität Graz Technisch-Naturwissenschaftliche Fakultät

von

Dipl. Ing. Mario J. Mueller

Matrikelnummer 9030360 Sackstrasse 19/1/4 A-8010 Graz

Genéve, August 2004

Meinem Grossvater / To my grandfather

Johann Konrad

30.10.1923 - 27.02.2003

Acknowledgements

As one can assume it needs many people for the successful completion of a doctoral thesis – it is time to thank:

First of all I would like to thank Dr. Graham R. Stevenson for giving me the opportunity to carry out this thesis at CERN. This work would not have been possible without his assistance and continuous support.

I am indebted to my supervisor and mentor Prof. Dr. Ewald Schachinger who supported and supervised my work far beyond the supervisor's duties.

Special thanks to Dr. Doris Forkel-Wirth and Dr. Hans-Georg Menzel, for all the motivating support they had given me.

I would also like to thank Dr. Waldemar Ninaus for supporting me during my work periods in Graz/Austria.

Special thanks to all my colleagues and friends, for all the discussions and fun we had. – Thank you : Angela Malina-Mitaroff, Evangelia Dimovasilis, Sabine Mayer, Chris Theis, Helmut Vincke, Heinz Vincke, Markus Brugger, Stefan Roesler.

Thank you to my family – the roots one needs for growing.

Thank you Manuela – thank you for being on my side.

THIS RESEARCH WAS PERFORMED UNDER THE AUSPICES OF THE AUSTRIAN FEDERAL MINISTRY OF EDUCATION, SCIENCE AND CULTURE AS PART OF THE AUSTRIAN DOCTORAL THESIS PROGRAM AT CERN. ii Contents

Kurzfassung xiii

Abstract xv

1Introduction 1 1.1 History of Accelerators...... 1 1.1.1 Electrostatic accelerator ...... 1 1.1.2 LINAC...... 1 1.1.3 Cyclotron...... 2 1.1.4 Betatron...... 3 1.1.5 Synchrotron ...... 3 1.1.6 StorageRingColliderAccelerators...... 4 1.2CERN...... 4 1.2.1 History...... 4 1.2.2 AcceleratorsatCERN...... 5 1.2.3 Super-Proton-Synchrotron(SPS)...... 7 1.2.4 UA1...... 7 1.3 Structure of Thesis...... 8

2 Principles of Physics 11 2.1 The Standard Model ...... 11 2.2 Particle Transport...... 19 2.2.1 HighEnergyHadronInteractions...... 19 2.2.2 Mesondecay...... 20 2.2.3 ChargedParticleScattering...... 20 2.2.4 IntermediateEnergyRegimeandEnergyLoss...... 21 2.2.5 Detailed Description of Intermediate Energy Processes ...... 21 2.2.6 Low energy neutron processes ...... 22 2.2.7 NuclearRecoils-ElasticScatteringandModeration...... 23 2.2.8 Thermalneutrons...... 23 2.3MonteCarloSimulation...... 23 2.3.1 MonteCarloBasics...... 24 2.3.2 IntegrationwithMC...... 24

iii iv CONTENTS

2.3.3 ParticletransportwithMC...... 27 2.3.4 RandomtrackingtreatmentwithinMCtransport...... 31 2.3.5 Markovprocess-Variancereduction...... 32

3 Radiation Protection foundations 35 3.1RadiationHealthPhysics...... 35 3.1.1 Somatic Effects...... 35 3.1.2 Genetic Effects...... 35 3.2 Dosimetry basics ...... 39 3.2.1 Physicalquantities...... 39 3.2.2 Protectionquantities...... 42 3.2.3 Operationalquantities...... 44 3.2.4 Conversion coefficients...... 44 3.3GeneralPrinciplesofRadiationProtection...... 46 3.4 Working area classificationsatCERN(ECA5)...... 47

4 ComparisonofFLUKAandMCNPX 49 4.1FLUKA...... 49 4.1.1 PhysicsimplementedinFLUKA...... 50 4.1.2 GEOMETRYpackage...... 53 4.1.3 TRANSPORT ...... 53 4.1.4 BIASING...... 54 4.1.5 SCORING...... 54 4.2MCNPX...... 55 4.2.1 PhysicsimplementedinMCNPX...... 56 4.3 DifferencesbetweenFLUKAandMCNPX...... 56 4.3.1 Geometry ...... 56 4.3.2 Physics...... 57 4.3.3 Tallies, scoring...... 57 4.3.4 Biasing...... 57 4.4 Geometry conversion FLUKA MCNPX...... 60 4.5 SimplifiedGeometry.....⇒...... 62 4.6 Results for the simplifiedGeometry...... 62

5 Dose-rates for Experimental Point 5 of the SPS 65 5.1 Design-Re-Assessment ...... 65 5.2 Geometry overview...... 66 5.3Materials...... 68 5.4 Simulation Setup ...... 68 5.4.1 FLUKA...... 68 5.4.2 Coordinatesystem...... 68 5.4.3 DetailedGeometry...... 70 5.4.4 Loss-Setuporthesourceterm...... 75 CONTENTS v

5.4.5 BeamandParticletransportproperties...... 76 5.4.6 Dose-equivalent...... 78 5.5Results...... 80 5.5.1 General...... 80 5.5.2 Main-shielding...... 82 5.5.3 VerticalShafts...... 82 5.5.4 Cross-galleriesintheshieldbridge...... 83 5.5.5 Surface Levels ...... 83 5.5.6 Doseratecontours...... 86

6 Particle Fluences for SPS5 91 6.1Chicane,Spiral-StaircaseandElevatorshaft...... 91 6.2FLUKA-DetectorSettings...... 91 6.2.1 Upwards streaming particles inside the spiral-staircase and the ele- vatorshaft...... 92 6.2.2 Particles inside each level — ECA, ECX entries and MID-position . 95 6.2.3 Volume-detectorsforspiral-staircaseandelevator-shaft...... 96 6.3Resultsofthesimulation...... 96 6.3.1 Boundary-crossing energy particle spectra for upwards streaming particlesinsidetheelevatorshaft...... 98 6.3.2 Boundary-crossing energy particle spectra for upwards streaming particlesinsidethespiral-staircase...... 101 6.3.3 Volume passing energy particle spectra for particles inside the elevator- shaft...... 104 6.3.4 Volume passing energy particle spectra for particles inside the spiral- staircase...... 108 6.3.5 Volume passing energy particle spectra for particles inside the ECA sidesgallerycrossings...... 112

7 Conclusion 113 7.1ComparisonofFLUKAwithMCNPX...... 113 7.2 SPS5-simulations ...... 114

A Tables of Dose Rates in Critical Volumes 127

B Visualization in 3D for FLUKA MC Simulation of SPS5 135 B.1Introductiontovisualization-statebeforethesis...... 136 B.2 How to visualize ? ...... 137 B.3Theresultswithnewvisualization...... 139

C Particle spectra for the SPS5 liaison area 141 C.1Boundary-crossingparticlespectraforLevel9...... 142 C.2Boundary-crossingparticlespectraforLevel7...... 144 vi CONTENTS

C.3Boundary-crossingparticlespectraforLevel6...... 146 C.4Boundary-crossingparticlespectraforLevel5...... 148 C.5Boundary-crossingparticlespectraforLevel4...... 150 C.6Boundary-crossingparticlespectraforLevel3...... 152 C.7Boundary-crossingparticlespectraforLevel1...... 154 List of Figures

1.1Schematicsofacyclotron...... 2 1.2Schematicviewofasynchrotron...... 3 1.3AcceleratorsatCERN...... 6 1.4 SPS-Accelerator ...... 7 1.5 Look into the ECX5 area with the UA1-Detector experiment during as- sembly1981...... 8

2.1 The four classical elements after Aristotle - a 1st try of bringing symmetry intophysics...... 11 2.2 A "periodic table" of the proton and the neutron and some of their relatives: The Eightfold Way - with hypercharge Y as a combination of S + B, StrangenessandBaryon-number...... 13 2.3 The latest knowledge about the fundamental constituents of matter: six diﬀerent quarks and six diﬀerent leptons divided into three families. . . . . 14 2.4 Deuterium: The strong interaction binds quarks together in protons and neutronsandresidualstronginteractionbuildsupthenuclei...... 15 2.5 Charging of particles...... 15 2.6 Properties of the four interactions and their messenger particles ...... 16 2.7Feynman-diagramsforelectron-positronreactions...... 17 2.8 The ultimate theory would describe the single primitive interaction out of whichtheUniversewasborn...... 18 2.9 Hadronic Interactions...... 19 56 2.10 Total Neutron cross-section for 26Fe...... 22 2.11Totalamountofsolidangelforanimpingingparticle...... 28 2.12 Schematic illustration of the geometrical cross-section...... 29 2.13BasictrackingmethodusingMonteCarlotechniques...... 31

3.1 DNA-molcule - visible two strang architecture ...... 36 3.2 Purine and pyrimidine bases - one of the foundation parts of DNA . . . . . 37 3.3 Scaling proporties from cell to DNA dimension - compared with ionizing densityofanimpingingalpha-particle...... 38 3.4DNAdamagescausedbyimpingingparticle/radiation...... 38 3.5 Timedependance of Radiation eﬀects...... 39

vii viii LIST OF FIGURES

3.6Relationshipofquantitiesforradiationprotection...... 40 3.7Irradiationgeometriesofhumanphantom...... 45 3.8 EﬀectivedoseconversioncoeﬃcientsforneutronsfromICRP74...... 46

4.1MCNPXAcceptanceofLibraryand/orModelTransport...... 55 4.2SurfacesplittingBiasingtechnique...... 59 4.3RussionRouletteasBiasingTechnique...... 59 4.4 Data-flow to convert FLUKA-geometry data into MCNPX data-format and how to visualize Geometry together with simulation results.(Black-framed parts - FLUKA; Red-framed parts - MCNPX; Green-framed parts - Com- bined Visualization)...... 61 4.5 Simplified Geometry for testing importance factors and to compare results between FLUKA and MCNPX. The red blocks indicate the mesh- tallies/userbinsusedforthedose-ratecalculations...... 62 4.6 FLUKA ambient dose-rates in [Sv/h] for neutrons for the simplified geom- etryincludingbiasingtechniques...... 63 4.7 MCNPX ambient dose-rates in [Sv/h] for neutrons for the simplified geom- etryincludingbiasingtechniques...... 63 4.8 MCNPX ambient dose-rates in [Sv/h] for neutrons for the simplified geom- etrywithoutbiasingtechniques...... 64

5.1 SPS-Ring with six sextant subdivisions and indicated experimental points along the beamline...... 66 5.2SubsurfaceconstructionofSPSexperimentalpoint5 ...... 67 5.3Openconstruction-siteoftheECX5-areain1978...... 67 5.4VerticalcutthroughtheaxesofECA/ECXarea...... 68 5.5 Horizontal cut at beam height through the ECA and ECX areas. All dimensions are in cm...... 69 5.6 Biasing slices for the liaison area (these pictures were generated with MC- NPvised)...... 72 5.7Levelsubdivisionstoorganizetheliasionarea...... 73 5.8 Detailed wall arangements for each level of the sub-surface construction of theSPS5...... 74 5.9Beamlineelementsalongthevacuum-pipe...... 75 5.10 Cross-sections of quadrupoles: 1st row quadrupoles: left side QF518, Right sideQD519;2ndrowWiggler:MDHW.Alldimensionsareincm...... 76 5.11 Horizontal section through the main shield indicating the positions of the Critical Volumes ...... 81 5.12 Hadron dose rates as a function of Entry Point of the proton loss for different Levels, showing data for Critical Volume 1 on the ECX side of the mainshield...... 82 LIST OF FIGURES ix

5.13 Hadron dose rates as a function of Entry Point of the proton loss for different Level, showing data for Critical Volume 2 on the ECA side of the mainshield...... 83 5.14 Hadron dose rates as a function of Level Number for the accessible shafts in the liaison areas, showing data for the lift-shaft, Critical Volume 8, in theupstreamliaisonareaontheECAsideofthemainshield...... 84 5.15 Hadron dose rates as a function of Level Number for the accessible shafts in the liaison areas, showing data for shaft containing the spiral staircase, Critical Volume 7, in the downstream liaison area on the ECA side of the mainshield...... 84 5.16 Hadron dose rates as a function of the Entry Point of the proton loss for different Levels in the cross-galleries inside the shield bridge on the ECA side(CriticalVolume9)...... 85 5.17 Hadron dose rates at the Critical Volumes in Level—0 for different proton EntryPoints...... 85 5.18 Hadron dose rates at the Critical Volumes in Level—1 for different proton EntryPoints...... 86 5.19 a) Surface Level—0: b) First underground Level—1. All dimensions are in cm. 87 5.20a)Level—2:b)Level—3.Alldimensionsareincm...... 87 5.21 Contour Plots of Dose Rates due to proton losses on the second wiggler magnet (EP4). a) Level—4: b) Level—5. All dimensions are in cm...... 88 5.22 Contour Plots of Dose Rates due to proton losses on the second wiggler magnet (EP4). a) Level—6: b) Level—6. All dimensions are in cm...... 88 5.23 Contour Plots of Dose Rates due to proton losses on the second wiggler magnet (EP4). a) Level—8: b) Level—9. All dimensions are in cm...... 89

6.1Cut-throughtheSPS5-subsurfaceconstructionatbeam-height...... 92 6.2 Region identiﬁers and spatial detector settings (green rectangulars) inside thespiral-staircaseandtheelevatorshaftoftheSPS5subsurfaceconstruction93 6.3 left) Vertical separation concept of the SPS5 liaison geometry in ECA, MID and ECA parts and the horizontal level organisation. right) Arrangement of the boundary detectors (red/blue ﬁlled rectangulars) on each liaison-level - one can see three detectors on the upstream area (red-elliptical bordered) and three on the downstream area (blue-elliptical bordered) — from left to righttheECA,MID,ECXorderisgiven...... 95 6.4 Volume detectors for estimating the energy-particle spectra in the spiral- staircaseandtheelevator-shaft...... 97

B.1 Before thesis situation, a PAW - 2D contour plot of FLUKA dose-rate results136 B.2GeometryofSPS5visualizedwithParaview...... 137 B.3Window-captureoftheVolVistool...... 138 B.4 3D plots of the dose-rate situation along the beamline in SPS5 housing - generatedcorrespondingtocontourplotofFigureB.1...... 139 x LIST OF FIGURES List of Tables

3.1 Radiation exposure eﬀectsonhumanbody...... 36 3.2Radiationweightingfactors...... 42 3.3CompositionbyweightoftheICRUtissuereferencesphere...... 43 3.4Tissueweightingfactors...... 44 3.5DesignConstraintsforDosesandDose-ratesoutsideShielding...... 48

4.1FLUKA’senergyrangesforparticletransport...... 54 4.2GeometryandSimulationconversiontools...... 60

5.1CompositionofMaterials...... 69 5.2EntrypointsforprimaryprotonsintheFLUKAsimulations...... 77 5.3 Biasing factors ...... 78 5.4BinStructures...... 79 5.5 Vertical extent of Critical Volumes for the ECX/ECA5 zones. simulations . 80 5.6 Horizontal extent of Critical Volumes for the ECX/ECA5 zones. simulations 80

6.1 Boundary-Detector areas for normalizing the particle-fluences...... 94 6.2 Boundary-Detector areas for normalizing the particle-fluences...... 96 6.3 Volume-Detector volumes for normalizing the particle-fluences...... 97

xi xii KURZFASSUNG Kurzfassung

Das europäische Forschungszentrum für Teilchenforschung - CERN - betreibt das Super Proton Synchrotron (SPS) seit mehr als 30 Jahren basierend auf Erfahrungen über Ab- schirmungsanlagen aus den frühen 1970er Jahren. Zu dieser Zeit waren Teilchen Transport Programme weder verfügbar noch konnte man für komplexe, dreidimensionale Geometrien Abschirmungs-Berechnungen durchführen. Heute sind für den SPS-Beschleuniger, als Vorbeschleuniger des zukünftigen LHC Beschleunigers, erhöhte Strahlintensitäten konzipiert bei gleichzeitiger Reduktion der Grenzwerte für die Strahlungsexposition von Menschen. Diese Bedingung, gemeinsam mit dem Faktum, das eine steigende Nicht-Akzeptanz für ungeprüfte und unoptimierte Strahlenbelastungen gegeben war, motivierte zu einer Wiederaufnahme der unterirdischen Abschirmungen der Experimentieranlage am Punkt 5 des SPS Beschleuniger zwischen der ECA und der ECX Kaverne. In dieser ECX Kaverne war vor 20 Jahren das UA1 Experi- ment untergebracht - Carlos Rubbia und seinem Team gelang es die Existenz von W und Z Bosonen erstmals nachzuweisen, wofür sie 1984 den Nobelpreis erhielten. Diese Doktorarbeit beschreibt eine solche Wiederaufnahme basierend auf Simulations- rechnungen mit FLUKA - ein für verschiedene Teilchen-Transport-Anwendungen einset- zbares Programm. Um die FLUKA-Transportrechnungen zu optimieren wurde ein zweites Programm (MCNPX) hinzugezogen. MCNPX diente vorallem zum Entwerfen der Geome- trie und den Entwurfs-Modifikationen aber auch um Methoden der Varianz-Reduktion in beiden Programmen zu vergleichen. Die so gefundenen Synergien bildeten die Basis- Routinen um das riesige und komplexe SPS5 Areal zu behandeln. An verschiedenen Orten entlang des Strahlrohres wurden Strahlverluste angenommen, die gemeinsam mit Flussraten-zu-Dosis Konversions-Rechnungen verwendet wurden um den schlimmsten Fall bzgl. Strahlenschutzauslegung herauszufinden. Dosisraten, für alle Ebenen der unterirdischen Konstruktion - genauso wie energieabhängige Teilchenspektren für die Zutrittsbereiche des Lift-Schachtes und der Wendeltreppe werden aufgezeigt um eine Einsicht in die resultierenden Simulationsdaten zu erreichen. Schlussbetrachtungen der Doktorarbeit zeigen auf, dass die Hauptabschirmung am SPS5 einst stark genug dimensioniert wurde, sodass die momentan gültigen Dosis-Grenz- werte nicht einmal bei den am höchsten geplanten Strahlintensitäten erreicht werden. Berechnete Dosisraten in den Verbindungsbereichen auf beiden Seiten der Hauptabschir- mung überschreiten hingegen signifikant die Grenzwerte bereits unter normalen Umstän- den.

xiii xiv ABSTRACT

Diese Doktorarbeit als Diskussions-Basis führte zu Modiﬁkationen in den Sicherheits- behandlungen der SPS5 Areale - im speziellen wurden die geltenden Zutrittsberechtigun- gen um jeweils eine Stufe angehoben. Abstract

The European Laboratory for Particle Research - CERN - has been operated the Super Proton Sychrotron (SPS) for more than 30 years with the shielding design knowledge of theearly1970’s.Atthattimeparticletransportcascadecodeswereneitheravailablenor capable of dealing with deep lateral shielding calculations. But time goes by - and for the future LHC accelerator increasing projected values of the circulating beam intensity in the SPS and decreasing limits to radiation exposure, taken with the increasing non- acceptance of unjustified and unoptimized radiation exposures, have led to the need to re-assess the shielding between the ECX and ECA underground experimental areas at point 5 of the SPS. 20 years ago, these experimental areas housed the UA1 experiment, where Carlos Rubbia and his team verified the existence of W and Z bosons and received the nobel-price in 1984. The thesis reported here describes such a re-assessment based on simulations using the multi-purpose radiation transport code FLUKA. In order to optimize FLUKA simulation performance a second code, MCNPX was utilized for geometry design and modifications on one hand and to compare some variance reduction methods of both codes on the other hand. These revealed synergies founded the basis of tools for treating the huge and complex geometry of the SPS5 area. Different beam-loss points along the beam-line together with particle fluence-to-doserate conversions were calculated to find the worst case of the radiation protection point of view. Dose-rates, as one kind of results are quoted for every level of the subsurface construction as well as particle-energy spectra inside the accessible elevator-shaft and the spiral-staircase to accomplish the insight to resulting simulation data. Finally the thesis concludes that whereas the main shield, which is made of concrete blocks and is 4.8 m thick satisfactorily meets the current design limits even at the highest intensities presently planned for the SPS, dose rates calculated for liaison areas on both sides of the main shield significantly exceed the design limits under normal circumstances. This thesis were used as discussion foundation, which had led to modifications in the safety treatment for the SPS5 area - in particular, access restrictions were upgraded by one step.

xv xvi ABSTRACT Chapter 1 Introduction

The ancient greek philosopher Thucydides1 once mentioned: "First of all you have to know a lot about the past, to be able to inﬂuence the future, because similar events to those of the past will certainly recur in the future because human nature is unchanging"

1.1 History of Accelerators

1.1.1 Electrostatic accelerator Charged particles can be accelerated by an electrostatic field - e.g. by placing electrodes with a large potential difference at each end of an evacuated tube; based on that principle John D. Cockcroft2 and Ernest Walton3 were able to accelerate protons to 250 keV . Another electrostatic accelerator is the Van de Graaff accelerator, which was developed in the early 1930s by the American physicist Robert Jemison Van de Graaff4.This accelerator uses the same principles as the Van de Graaff Generator. The Van de Graaff accelerator builds up a potential between two electrodes by transporting charges on a moving belt. Modern Van de Graaff accelerators can accelerate particles to energies as high as 15 MeV.

1.1.2 LINAC Another machine, ﬁrstconceivedinthelate1920s,istheLINearACcelerator,which uses alternating voltages of high magnitude to push particles along in a straight line. Particles pass through a line of hollow metal tubes enclosed in an evacuated cylinder. An alternating voltage is timed so that a particle is pushed forward each time it goes through a gap between two of the metal tubes. Theoretically, a linac of any energy can be

1 THUCYDIDES.( 471 B.C.— 400 B.C.), athenian historian, philosopher 2 Cockcroft, Sir John∼ Douglas (1897-1967),∼ British physicist and Nobel laureate 1951 3 Ernest Walton (1903 - 1995), british Physicist and Nobel Laureate 1951. 4 Robert Jemison Van de Graaﬀ (1901- 1967), American physicist and inventor of the Van de Graaﬀ generator.

1 2 CHAPTER 1. INTRODUCTION built. The largest linac in the world, at SLAC (Stanford university Linear ACcelerator), is 3.2 km long. It is capable of accelerating electrons to an energy of 50 GeV .SLAC’s linac is designed to collide two beams of particles accelerated on diﬀerent tracks of the accelerator.

1.1.3 Cyclotron The American physicist Ernest O. Lawrence5 developed the cyclotron, the ﬁrst circular accelerator in the early 1930s. A cyclotron is somewhat like a LINAC wrapped into a tight spiral. Instead of many tubes, the machine has only two hollow vacuum chambers, called dees, that are shaped like capital letter D’s back to back (thus: ;seeFigure 1.1).

Figure 1.1: Schematics of a cyclotron

Amagneticﬁeld, produced by a powerful electromagnet, keeps the particles moving in a circle. Each time the charged particles pass through the gap between the dees, they are accelerated. As the particles gain energy, they spiral out toward the edge of the accelerator until they gain enough energy to exit the accelerator. The world’s most powerful cyclotron, the K1200, began operating in 1988 at the National Superconducting Cyclotron Laboratory at Michigan State University. The machine is capable of accelerating nuclei to an energy approaching 8 GeV . When nuclear particles in a cyclotron gain an energy of 20 MeV or more, they become appreciably more massive according to the theory of relativity. This tends to slow them down and throws the acceleration pulses at the gaps between the dees out of phase. A solution to this problem was suggested in 1945 by the Soviet physicist Vladimir I. Veksler6 and the American physicist Edwin M. McMillan7. The solution, the synchrocyclotron, is sometimes called the frequency modulated cyclotron. In this instrument, the oscillator (radio-frequency generator) that accelerates the particles around the dees is automatically

5 Lawrence, Ernest Orlando (1901-58), American physicist and Nobel laureate in 1939. 6 Vladimir I. Veksler (1907-1966), Russian Physicist. 7 McMillan, Edwin Mattison (1907-91), American physicist and Nobel laureate. 1.1. HISTORY OF ACCELERATORS 3 adjusted to stay in step with the accelerated particles; as the particles gain mass, the frequency of accelerations is lowered slightly to keep in step with them. As the maximum energy of a synchrocyclotron increases, so must its size, for the particles must have more space in which to spiral. The largest synchrocyclotron is the 6mphasotron at the Dubna Joint Institute for Nuclear Research in Russia; it accelerates protons to more than 700 MeV and has magnets weighing 7200 metric tons.

1.1.4 Betatron When electrons are accelerated, they undergo a large increase in mass at a relatively low energy. At 1 MeV energy, an electron weighs two and one-half times as much as an electron at rest. Synchrocyclotrons cannot be adapted to make allowance for such large increases in mass. Therefore, another type of cyclic accelerator, the betatron, is employed to accelerate electrons. The betatron consists of a doughnut-shaped evacuated chamber placed between the poles of an electromagnet. The electrons are kept in a circular path by a magnetic fieldcalledaguidefield. By applying an alternating current to the electromagnet, the electromotive force induced by the changing magnetic flux through the circular orbit accelerates the electrons. During operation, both the guide field and the magnetic flux are varied to keep the radius of the orbit of the electrons constant.

1.1.5 Synchrotron The synchrotron is the most recent and most powerful member of the accelerator family. A synchrotron consists of a tube in the shape of a large ring through which the particles travel; the tube is surrounded by magnets that keep the particles moving through the center of the tube (see Figure 1.2).

Figure 1.2: Schematic view of a synchrotron.

The particles enter the tube, coming from the ion-source, after already having been accelerated to several MeV’s. Particles are accelerated at one or more points on the ring each time the particles make a complete circle around the accelerator. To keep the particles 4 CHAPTER 1. INTRODUCTION in a rigid orbit, the strengths of the magnets in the ring are increased as the particles gain energy. In a few seconds, the particles reach energies greater than 1 GeV and are ejected, either directly into experiments or toward targets that produce a variety of elementary particles when struck by the accelerated particles. The synchrotron principle can be applied to either protons or electrons, although most of the large machines are proton-synchrotrons. The ﬁrst accelerator to exceed the 1 GeV mark was the cosmotron, a proton-synchrotron at Brookhaven National Laboratory, in Brookhaven, New York. The cosmotron was operated at 2.3 GeV in 1952 and later increased to 3 GeV . In the mid-1960s, two operating synchrotrons were regularly accelerating protons to energies of about 30 GeV .Thesewere the Alternating Gradient Synchrotron at Brookhaven National Laboratory, and a similar machine near Geneva, Switzerland, operated by CERN (more details in the next chapter). By the early 1980s, the two largest proton-synchrotrons were a 400 GeV device at CERN and a similar one at the Fermi National Accelerator Laboratory (Fermilab) near Batavia, Illinois. The capacity of the latter, called Tevatron, was increased to 1 TeV in 1983 by installing superconducting magnets, making it the most powerful accelerator in the world.

1.1.6 Storage Ring Collider Accelerators A storage ring collider accelerator is a synchrotron that produces more energetic collisions between particles than a conventional synchrotron, which slams accelerated particles into a stationary target. A storage ring collider accelerates two sets of particles that rotate in opposite directions in the ring, then collides the two sets of particles. CERN’s LEP (Large- Electron-Positron) Collider was a storage ring collider. In 1987, Fermilab converted the Tevatron into a storage ring collider and installed a three-story-high detector that observed and measured the products of the head-on particle collisions. As powerful as today’s storage ring colliders are, more powerful devices to test today’s theories are necessary. CERN is building the Large Hadron Collider (LHC) in the existing 27 km tunnel that had housed the LEP Collider. Therefore the beam intensities for the second largest ring the SPS (super proton synchrotron), which will act as injector accelerator for the LHC, will increase - one of the reasons for carrying out this thesis.

1.2 CERN

1.2.1 History To redress the balance and restore European science to its former prestige, at the European Cultural Conference at Lausanne, the French physicist and Nobel prize-winner Louis de Broglie8 proposes 1949 the creation of a European science laboratory. At the 5th General

8 Louis de Broglie - French physicist (born Aug. 15, 1892, died Mar. 19, 1987) - received the 1929 Nobel Prize for physics. 1.2. CERN 5

Conference of UNESCO9 in Florence, the American physicist and Nobel prize-winner Isidore Rabi10 puts forward a resolution, unanimously adopted, authorizing UNESCO, "to assist and encourage the formation and organization of regional centres and laboratories in order to increase and make more fruitful the international collaboration of scientists ...". This marks the beginning of CERN "Conseil Européen pour la Recherche Nucléaire" in 1950 as the European Organization for Nuclear Research. Today it is also known as the "European Laboratory for Particle Physics", although CERN retained as handy acronym. Its business - fundamental physics - ﬁnding out what makes our Universe work, where it came from and where it is going. At CERN, some of the world’s biggest and most complex machines are used to study nature’s tiniest building blocks, the fundamental particles (see subsection 2.1). From the original 12 signatories of the CERN convention membership in 1954 it has grown to 20 Member States. Austria joins in 1959 with a contribution of approximately 2.8% to the total budget of CERN, which is about 1 billion swiss-francs a year. The Laboratory sits astride the Franco-Swiss border west of Geneva at the foot of the Jura mountains.

1.2.2 Accelerators at CERN

CERN’s accelerator complex (see Figure 1.3) is built around three principal inter-dependent accelerators. The oldest, the Proton Synchrotron (PS), was built in the 1950s and was briefly the world’s highest energy accelerator. The Super Proton Synchrotron (SPS), built in the 1970s, was the scene of CERN’s first Nobel prize in the 1980s - more details will be shown in the following sub-section. The Large Electron-Positron collider (LEP) came on stream in 1989. It was the Laboratory’s flagship research machine until 2000. LEP was an enormous machine. Built in a circular underground tunnel, it was 27 kilometers around and weighed over 23000 tones. In December 1994 CERN’s governing body, the Council, officially approved the construction of CERN’s Large Hadron Collider (LHC) - a technologically challenging super conducting ring, which will be installed in the existing former LEP tunnel (LEP was completely dismantled before) - to provide proton-proton collisions after machine startup in 2008 at energies 10 times greater than any previous machine. One of the fundamental questions it will address is that of the mechanism which gives matter its mass. The LHC will bring protons and ions into head-on collisions at higher energies than ever achieved before, allowing to recreate conditions prevailing just after the "Big-Bang" - at least, that’s the idea.

9 UNESCO - the United Nations Educational, Scientiﬁc and Cultural Organization was born on No- vember 16, 1945. 10Isidore Isaac Rabi (29. July 1898 Raymanov, Austria - 1988), Nobel prizewinning physicist 1944 6 CHAPTER 1. INTRODUCTION

Figure 1.3: Accelerators at CERN 1.2. CERN 7

1.2.3 Super-Proton-Synchrotron (SPS) The 400 GeV Super Proton Synchrotron is a circular accelerator (see Figure 1.4 and 5.1), approximately 7 km in circumference, buried underground. A first design was put forward to Council in 1964 and, in a considerably modified form, the project was finally approved in February 1971. It was built originally to accelerate protons - and continued to do so - but it has since also operated as a proton-antiproton collider, a heavy-ion accelerator, and an electron/positron injector for LEP (the Large Electron Positron collider). The SPS can also accelerate lead ions to an energy of 170 GeV per nucleon, with 208 nucleons in the lead nucleus. In 2000, this was the highest energy obtained in the world, and it served for the study of the quark-gluon plasma which may have occurred shortly after the big bang. The SPS will be the final pre-injector for the LHC (Large Hadron Collider), accelerating GeV GeV 26 c protons from the PS to 450 c before extraction to LHC. Many changes to the existing SPS are necessary before it can deliver the high brightness proton beams required by the LHC. These changes were among other things one of the main reasons to re-assess the shielding conditions of the experimental area in point 5.

Figure 1.4: SPS-Accelerator

1.2.4 UA1 From 1978 to 1990 the UA1 (see Figure 1.5) experiment at CERN serves as detector for proton-antiproton collisions. This idea of a big detector to provide informations on all emerging particles was an integral part of Carlo Rubbia’s 1976 antiproton proposal. The experiment code-name UA for "Underground Area" was formally approved by the Research Board on 29 June 1978, and work got underway in earnest for the mighty 2000 tonne detector to be installed and checked out in its Long-Straight-Section 5 (LSS5) pit, ready to intercept the ﬁrst proton-antiproton collisions in summer of 1981. 8 CHAPTER 1. INTRODUCTION

Figure 1.5: Look into the ECX5 area with the UA1-Detector experiment during assembly 1981.

Initial collisions rates were low, and spirits sank when an accident in 1982 delayed the start of serious data-taking. But with the collider benefiting from its enforced rest, performance exceeded expectations and the first W-boson’s were intercepted late that year. The 1983 spring run provided the rarer Z-boson’s and the champagne flowed. In 1984 came the Nobel Prize for Carlos Rubbia11 and for Simon van der Meer12,whoseinventionof stochastic cooling had made the whole antiproton project possible. Rarely had a Nobel Prize been awarded so promptly. Subsequently UA1 went through a major refitand consolidated the knowledge of this physics. The experiment had a long list of distinguished and able collaborators, many of whom have gone on to take up important positions elsewhere. Although not as big as the LEP experiments which came later, UA1 blazed a trail for major collaborations and for collider physics in particular.

1.3 Structure of Thesis

Chapter 1: Historical points of view from the beginning of particle accelerators up to nowadays available highly advanced CERN machine build the introduction to this thesis. Basic descriptions emphasizing the meaning of accelerators for human society and pointing out the complexity and interconnections of making theoretical physics and

11Rubbia, Carlo (1935-), italian physicist, Nobel Laureat 1984. 12van der Meer, Simon (1925- ), dutch physicist, Nobel Laureat 1984. 1.3. STRUCTURE OF THESIS 9 proving the results afterwards experimentally were shown. Chapter 2:WhatarethePrinciples of Physics used throughout this thesis? Starting with the standard model (SM) and its origins - followed by basic reflections of the particle transport, including high energy hadrons interactions down to low energy neutron processes will be shown systematically.. How is Monte Carlo (MC) simulation carried out? - What are the foundations of MC simulation? - and how can they be utilized for particle transport will be treated in part 3ofchapter2. Chapter 3: As the interconnection between primarily occurring energy deposition of particles in matter and finally stated cell damage in human bodies - Radiation Protection Physics will be characterized for further utilization. Chapter 4: Due to the reasons that both FLUKA and MCNPX were used in a syn- ergetic way - the basics of both codes are described in this chapter. The differences of FLUKA and MCNPX will be emphasized and for a simplified geometry (simplified regarding the complex geometry of chapter 5) the neutron dose-rates convoluted with ICRP74 fluence-to-doserate conversion coefficients will be compared. These results, based on deep penetration optimization for particles transported through thick shielding, have also revealed the appropriate variance reduction factors for the further calculations. Chapter 5:TheDose-rate calculations for Experimental Point 5 of the SPS as the main chapter of the thesis treats the re-assessment of the shielding arrangements of the SPS5. The geometry designed and re-developed for FLUKA purposes will be described extensively, followed by FLUKA simulation setup’s and calculation approaches. The results shown here have revealed the weak points of the SPS5 area. Chapter 6: In order to support further investigations with more detailed data - particle energy spectra for all levels with special care to the elevator shaft and the spiral staircase as the most radiation exposed regions are quoted. Which methods were used are described - results are placed here and in appendix C. Chapter 7: Conclusions will finally end this thesis - some outlooks should open up the mind. 10 CHAPTER 1. INTRODUCTION Chapter 2 Principles of Physics

2.1 The Standard Model

SincetimeimmemorialpeoplehavebeentryingtounderstandwhattheUniverseismade of. One of the earliest theories made by Empedocles of Agrigentum1 said that everything could be built from just four elements, Earth, Air, Fire and Water (see Figure 2.1).

Figure 2.1: The four classical elements after Aristotle - a 1st try of bringing symmetry into physics

This was a great scientiﬁc theory because it was simple, had already shown the nowadays basic concept of symmetry to simplify descriptions of nature, but it had one big drawback: it was wrong. Another major drawback with this theory was that it was no use because it could not predict anything. In modern science, it is not enough simply to describe

1 Empedocles (490 BC - 430 BC) was a Greek philosopher and a citizen of Agrigentum in Sicily.

11 12 CHAPTER 2. PRINCIPLES OF PHYSICS what is going on, a theory must also be able to predict what will happen in a given set of circumstances. It is this that allows experiments to differentiate between different theories. A theory’s power of prediction is a measure of its quality. The Greek philosopher Leucippus of Miletus2 and his follower Democritus3 set the scene for modern physics in 5th century B.C. in Athens when they considered what would happen if one chopped up matter into ever smaller pieces. There would be a limit, beyond which one could not go. And they called their fundamental particles atoms4. Testing the theory was not easy with ancient Greek technology and it was not until the 17th century, that what today is called elements were found. There were all kinds of them and, for a while, the ideas people had for describing them were far more complex than the Earth, Air, Fire and Water model. But people started to notice patterns in the masses of the elements and eventually Dmitri Ivanovich Mendeleev5, professor of chemistry at St. Petersburg, arranged them into his famous periodic table of the elements, first published in 1869. The patterns Mendeleev documented are called a symmetry and whenever there is symmetry in nature, it means that there’s a simpler way of describing things. With the elements, the patterns in the masses were a clue that all the elements are made up of smaller particles and their differing masses are simply determined by how many of those particles they have inside them. Mendeleev’s idea of the periodic table is a perfect example of a good scientifictheory. First, it simplified things enormously, and second it allowed Mendeleev to correctly predict new elements. Element 101, mendelevium, is named in his honour. The observation that elements contained different combinations of the same building blocks eventually brought the number of fundamental particles down from all the elements to just three particles: protons, neutrons and electrons. With these three particles one could explain all known matter. Protons and neutrons are about 2000 times heavier than electrons, so it’s the number of them that determines an atom’s mass. The number of protons, which are positively electrically charged, matches the number of electrons in an atom and determines its chemical properties. In the early 20th century, however, another explosion of complexity was recognized. By studying particles coming from space, other particles beside protons, neutrons, and electrons were found - but how will they fitintoamodel? Symmetry again provided the answer. By looking at the properties of all the particles and organizing them in another "periodic table", two men found symmetries that betrayed the presence of smaller particles inside protons, neutrons, and the new particles. This periodic table goes by the name of "The Eightfold Way"[58]. It was so-named in 1964 by Murray Gell-Mann6 and Yuval Ne’eman7. Earlier, Gell-Mann had noted a new property

2 Leucippus or Leukippos of Miletus (5th century BCE) was the originator of atomism 3 Democritus of Abdera in the north of Greece (460 B.C. - 370 B.C.) 4 The word is derived from the Greek atomos, indivisible, from a-,not,andtomos,acut. 5 Dmitri Ivanovich Mendeleev (February 7, 1834 - January 20, 1907) - Russian chemist 6 Murray Gell-Mann (born September 15, 1929) - American physicist. - received the 1969 Nobel Prize in physics for his work on the theory of elementary particles 7 Yuval Neéman (born 14.5.1925) - israelischer Physiker 2.1. THE STANDARD MODEL 13 in some of the new particles that had been discovered. Since these new particles were strange, he called this property strangeness. In their book "The Eightfold Way", Gell- Mann and Ne’eman suggested that protons and neutrons could be made up of two types of smaller particles. In their theory, a third kind gave rise to the property of strangeness observed in the more exotic particles. Borrowing from James Joyce’s8 novel Finnigan’s Wake [41], which bears the line "three quarks for muster mark", Gell-Mann called these three types of particle quarks - named up-, down- and strange-quark. Unlike down- and 1 2 strange-quark with an electric charge of 3 the up-quark has + 3 . That means that two ups and one down result in a particle with− charge +1: a proton. Two downs and one up result in a particle with charge 0: a neutron. When Gell-Mann and Ne’eman classified particles according to quantities like charge and strangeness, for example, they found that they fit into tidy patterns called multiplets. In the multiplet containing protons and neutrons, there are eight particles, hence "The Eightfold Way" (see Figure 2.2)

Figure 2.2: A "periodic table" of the proton and the neutron and some of their relatives: The Eightfold Way - with hypercharge Y as a combination of S + B, Strangeness and Baryon-number.

History had just repeated itself. Gell-Mann and Ne’eman had described observation per- fectly, and they had provided a way to predict a new particle called the omega-minus, a negatively charged particle with three units of strangeness, corresponding to a missing particle in one of the multiplets. Sure enough, in due course the omega-minus was discovered. Its three units of strangeness simply mean that it is made up of three strange 1 quarks, each of which has charge −3 , leading to a total charge of 1. Today there are six kinds of quarks, charm-quark, bottom-quark and top-quark have− joined the initial three.

8 James Augustine Aloysius Joyce (February 2, 1882 - January 13, 1941) - an expatriate Irish writer and poet 14 CHAPTER 2. PRINCIPLES OF PHYSICS

The six quarks are arranged into three generations, up and down are the lightest, then come strange and charm, and heaviest of all are bottom and top. Each generation has associated with it two light particles called leptons - from the Greek for light. The electron is one of the leptons in the lightest generation, the other is called the electron- neutrino. All of ordinary matter can be made from up-quarks, down-quarks, and electrons. The electron-neutrinos play no role in making up atoms, but they are very important nevertheless, as can be seen further down. Particles of the other generations are identical in every way to the lighter ones, except they are heavier. That is why they don’t appear in ordinary matter, they tend to shed their excess mass as energy and transform themselves into the lightest particles - up-quarks, down-quarks, and electrons.

Figure 2.3: The latest knowledge about the fundamental constituents of matter: six diﬀerent quarks and six diﬀerent leptons divided into three families.

The "periodic table" of the quarks and leptons looks like that in Figure 2.3. As far as known, these particles have nothing inside them - to all intents and purposes, they are the "atoms" dreamed of by Leucippus 2500 years ago. So far all the particles are defined for using them as fundamental bricks of matter, but what about the adhesive that glues them together to organize more complex structures? There are four interactions known, they are called gravity, electromagnetism, weak and strong. These interactions often manifest themselves as forces between particles. The gravitational interaction, for example, is responsible for the attractive force between masses. The electromagnetic interaction is responsible for the attractive or re- pulsive forces between charges. Interactions are referred to as forces when an amount of strength can be quoted as a measure of the interaction. In fact force is just a special case of an interaction. As one will see the interactions can do much more than just act as forces! Gravity is the most familiar interaction, but it is by far the weakest of them all. The weak and strong interactions differ from the other two in one very important way: they only act over very short distances and are confined to the scale of atomic nuclei. The weak interaction is responsible for radioactive beta decay, and it plays a vital role in the energy generating processes of stars. The weak interaction acts on a kind of "weak charge". 2.1. THE STANDARD MODEL 15

The strong interaction holds quarks together to make protons and neutrons (see Figure 2.4), and a residual strong interaction holds protons and neutrons together to form nuclei - rather like the van der Waal’s9 interaction does for molecules. The charge of the strong interaction is called color. It comes in three varieties - red, blue, and green - and is carried by quarks. However, all the particles made of quarks are colorless. Protons and neutrons, for example, contain three quarks, one of each color, and just as with real colors, adding them together gives white. Other particles, called mesons, are made of a quark and an antiquark. Here, the antiquark carries the "complementary" color, or anticolor, to that ofthequark,onceagaingivingwhite.

Figure 2.4: Deuterium: The strong interaction binds quarks together in protons and neutrons and residual strong interaction builds up the nuclei.

Not all particles carry all kinds of charge. This means that not all particles "feel" all interactions. Figure 2.5 shows which particles belonging to the lightest generation possess which properties.

Figure 2.5: Charging of particles

According to current theories, interactions are communicated or carried by messenger particles that are diﬀerent from matter particles. The messengers of the strong interaction

9 Johannes Diderik van der Waals (1837-1923), Dutch Physicist - Nobel Prize in Physics 1910 16 CHAPTER 2. PRINCIPLES OF PHYSICS are called gluons because they "glue" the quarks together into particles like protons and neutrons and in turn glue protons and neutrons together into atomic nuclei. Photons are the messengers of the electromagnetic interaction and particles called W and Z bosons carry the weak interaction (see Figure 2.6). Gravitons are believed to carry gravity, but they have so far not been found. One of the things that determines the range of an interaction is the mass of the messenger particles....heavier messengers have a shorter range.

Figure 2.6: Properties of the four interactions and their messenger particles

In order to handle all that interactions via messenger particles between matter a big simpliﬁcation tool in understanding is in use. Feynman diagrams named after American physicist Richard Feynman10. They help to visualize how matter particles exchange messenger particles. Feynman diagrams are much more than simple drawings, however, they are also a way of writing complex equations. Each element of a Feynman diagram (see Figure 2.7) is equivalent to a piece of an equation, so Feynman diagrams also help to simplify mathematical equations. In Figure 2.7-a) an electron and a positron bounce oﬀ each other - by exchanging a photon, labelled gamma. This is an example of an interaction manifesting itself as a force. In example b) the interaction is not manifesting itself as a force. Instead, an electron and a positron destroy each other, or annihilate, creating a photon, which later materializes into a new electron and positron. A closer look at the annihilation in Figure 2.7-b): Starting on the left, the negatively chargedelectronandpositivelychargedpositroncometogetherandmeet.Whentheydo, they disappear and give rise to a photon, which has no charge; the positive and negative have cancelled each other out. A bit later, the photon materializes into a new positive

10Richard Phillips Feynman (May 11, 1918 - February 15, 1988) (surname pronounced "ﬁne-man") - American physicists - For his work on quantum electrodynamics, Feynman was one of the recipients of the Nobel Prize in Physics for 1965. 2.1. THE STANDARD MODEL 17

Figure 2.7: Feynman-diagrams for electron-positron reactions and a new negative particle. If the initial electron-positron collision has the right amount of energy, these particles could be pairs of muons, taus, or quarks - as long as their combined charge adds up to zero. Conservation of electric charge in particle interactions is a fundamental law of nature. The interaction in Figure 2.7-c) looks very similar, but one of the messengers of the weak interaction has been exchanged, a Z particle. In Figure 2.7-d), something different is going on, the weak messenger particle is carrying electric charge. In this case, the messenger is a W particle. Unlike photons and Z particles, W particles are electrically charged, and there are both positive and negatively charged ones. This process could not happen electromagnetically, because charge would not be conserved with an electrically neutral messenger. It should be considered that some processes such as electron-positron scattering proceed via photon and Z particle exchange: they have contributions from both the electromagnetic(like in Figure 2.7-a) and the weak interaction (like Figure 2.7-e). The last aspects of weak and electromagnetic interaction reveals that there is a lot in common between those two forces. Generally in considering patterns, finding symmetries in order to simplifies the picture of particles and interactions leads to a general framework - one of the basic ideas of physics - Unification (see Figure 2.8). The first step to unifying the forces was made by Scottish mathematician James Clerk Maxwell11 in the latter half of the 19th century. He realized that electricity and mag- netism had a lot in common and wrote down a theory to describe them both. Then in the 1960s three scientists, Sheldon Glashow12 and Abdus Salam13 along with Stephen Wein-

11James Clerk Maxwell (June 13, 1831 - November 5, 1879) - Scottish physicist 12Sheldon Lee Glashow (born 1932) - American physicist. In 1979, Glashow shared the Nobel Prize in Physics with Abdus Salam and Steven Weinberg.

13Abdus Salam (January 29, 1926 - November 21, 1996) - Pakistani physicist - Nobel Laureate in Physics in 1979 for his work in electroweak theory - The validity of the theory was ascertained in the 18 CHAPTER 2. PRINCIPLES OF PHYSICS

Figure 2.8: The ultimate theory would describe the single primitive interaction out of which the Universe was born berg14 worked out how to unify electromagnetism and the weak interaction into a single electroweak theory. The unification had to account for the different ranges of the two interactions, which turned out to be due the masses of the messenger particles. Photons have no mass, which gives them infinite range. The hypothesized carriers of the weak interaction had to be very massive to confine their range to the scale of nuclei. Confirming the electroweak theory rested upon finding the W and Z particles and CERN soon entered the hunt with the UA1 detector, which was housed inside the ECX5 cavern of the SPS accelerator. In 1983, the Laboratory’s efforts were successful, bringing the Nobel prize to CERN for the first time the following year. Two CERN physicists were honoured, Carlo Rubbia15 andSimonvanderMeer16.

To honor these two physicists and the discovery of W±,Z bosons, a museum is meant to be installed at the bottom of the ECA5 cavern, the former installation hall of the UA1 experiment at the experimental point 5 of the Super-Proton-Synchrotron. Therefore it was thus considered that it was eminently opportune to re-assess the shielding around ECX5 using the best available modern techniques (see next chapter and the following).

following years through experiments carried out at the Super Proton Synchrotron facility at CERN in Geneva which led to the discovery of the W and Z bosons. 14Steven Weinberg (b. 1933) - American physicist - Nobel Prize in Physics in 1979 together with Sheldon Glashow and Abdus Salam

15Carlo Rubbia (born in the small town of Gorizia, Italy, in 1934) - Italian physcist - together with Simon van der Meer, the Nobel prize for physics 1984 16Simon van der Meer (b. 1925) - Dutch physcist - together with Carlos Rubbia, the Nobel prize for physics 1984 2.2. PARTICLE TRANSPORT 19 2.2 Particle Transport

Throughout a particle life-time different interactions may be occur. In the flow-chart of Figure 2.9 most of these currently known interaction-processes are combined and inter- linked as they are utilized on the particles. Corresponding to the kind of particle and its initial energy three possible entry-scenarios are given - indicated as blue-filled circles.:

Particle starts at the upper-left circle: complete particle cascade has to be consid- • ered, Particle starts at the mid-circle: no INC (Intra Nuclear Cascade) processes have to • be treated, Particle starts at the bottom-right circle: only EM processes will take place. •

Figure 2.9: Hadronic Interactions

2.2.1 High Energy Hadron Interactions The energy regime above about 5 GeV is considered as the “high energy” regime in particle production calculations, where hadrons interact with target nuclei treated as ensembles of 20 CHAPTER 2. PRINCIPLES OF PHYSICS independent nucleons. The incoming hadron and target nucleons are described at parton level as collections of valence quarks, valence diquarks, and sea quark pairs. In simulation codes like FLUKA or MCNPX (which uses an old FLUKA high-energy event-generator), this is handled via the Dual Parton Model (DPM), where the exchange particles, instead of being gluons, are Pomerons or Reggeons (quasi-particles) modelling the whole Quant- Chromo-Dynamics (QCD) interaction. Each hadron splits into two colored partons, which combine to form back-to-back jets. The model tracks the color flow from the original collision through recombination to the production of color-neutral “chains” that constitute the final state hadrons. In effect, the parton level description conserves quantum numbers, such as color, while the exchanged quasi-particles provide the dynamics.

2.2.2 Meson decay Through a variety of hadronic and nuclear processes the incident hadron will produce + 0 secondaries that are predominantly pions (π , π−, π ), strange mesons and baryons (k±, λ0,...), and photons. The π0 component is noteworthy, and will appear throughout the shower cascade where hadron energies are above the single pion production threshold. The π0’s decay “immediately” into two photons, producing imbedded electromagnetic showers, and irreversibly shifting shower energy from the hadronic to the electromagnetic sector (arrow from meson decay to EM interactions in Figure 2.9). The electromagnetic fraction of total shower energy increases with incident energy because there are more generations of shower cascades, giving more opportunities for π0 production. Some muons will be produced in the shower due to charged pion decay, and will most often exit the area where they are produced.

2.2.3 Charged Particle Scattering Most energy loss for high energy charged particles is due to the atomic processes included dE in the Bethe-Bloch formula for dX , often referred to as "ionizing energy loss". The cross dE sections for these atomic processes are so large that dX energy loss accounts for "all" of 2 the energy deposited in EM showers, and roughly 3 of the energy deposited in hadronic showers. (This fraction has large ﬂuctuations from shower to shower, and is lower for low energy hadronic showers because of the smaller electromagnetic fraction, discussed above.) dE These large dX cross sections imply that hadronic shower shape is determined primar- dE ily by the sequence of hadronic interactions, coupled to dX loss of charged particles as they propagate in materials. In the transport codes, these corresponds to "high energy sector" interactions (modeled via the dual parton model in FLUKA and hence MCNPX), dE accompanied by dX loss simulation while tracking charged particles. dE 1 This section has been focussing on dX loss by charged particles. But since roughly 3 of hadronic shower energy is lost by other means, much of it by neutrons, these are an dE important component of showers. Lacking dX loss, neutrons propagate "decoupled" from the rest of the shower, subject to elastic scattering and low energy nuclear interactions, 2.2. PARTICLE TRANSPORT 21 and in most situations, considerably more penetrating than the charged component. Much of the complexity of FLUKA and MCNPX is associated with neutron transport, and focus will be given here and on the upcoming sections.

2.2.4 Intermediate Energy Regime and Energy Loss Hadrons above approximately 100 MeV can undergo nuclear reactions that lead ulti- mately to the creation of more neutrons. The most violent of these are called “spallation”, which may break the nucleus into a number of small or large fragments, accompanied by the direct release of neutrons and the possibility of additional neutrons “evaporating” from the fragments. Since these fragments are ionized by the collision, and have large dE Z, they will stop quickly in dense materials by dX energy loss, and may deposit sizeable quantities of ionization in very small regions. The local ionization densities from these typesofeventsmaybehundredsoftimeslargerthanthosetypicalofminimumioniz- ing particles. When calculating the “total ionizing dose” (TID) in a given region, one dE must add these contributions to the usual dose calculated from the dX loss of individual particles.

2.2.5 Detailed Description of Intermediate Energy Processes The above discussion of spallation greatly understates the complexity of nuclear processes in the intermediate energy regime. Neutron transport codes must treat this energy range in much more detail to get the correct yields for neutrons and photons. Between approximately 100 MeV and several GeV , there is the region where the characteristic momentum transfer and the incident hadron wavelength are comparable to the size of individual nucleons smaller than a nuclei, larger than the partonic level used in the DPM. For this reason, most neutron transport codes treat the ﬁrst stage of the hadron-nucleus reaction as an intranuclear cascade (INC), where the incoming hadron collides with one or more individual nucleons, which in turn collide with other nucleons in the same nucleus, creating a cascade. This description is essentially classical, and relies on having accurate nucleon-nucleon and pion-nucleon cross sections as input. The original INC code was written by Bertini [65], and there are more recent versions such a ISABEL, by Yariv (used in LAHET as part of MCNPX). After the nucleus has been excited by the INC, the standard approach is to let the nucleus undergo “evaporation” (EVAP), to shed neutrons, protons, and light nuclei. This evaporation process assumes that the nucleus has attained thermal equilibrium at an energy scale less than the nuclear potential depth of about 40 MeV.Unfortunately there is an energy gap between this scale and the INC scale, which some codes, such as standalone FLUKA, ﬁll in with a “pre-equilibrium” stage, to cover energies below about 100 150 MeV. The pre-equilibrium stage is clearly a quantum mechanical model (following− a classical INC stage), and this whole sequence of INC/pre-equilibrium/evaporation should probably be seen as a “brave attempt” at modeling nuclear processes in this energy 22 CHAPTER 2. PRINCIPLES OF PHYSICS range. More realistically, it is a complex parameterization that can be tuned reasonably well to experimental data.

2.2.6 Low energy neutron processes

To complicate the neutron phenomenology further, the total cross section in some materials exhibits a rich resonance structure in the domain where incident neutrons are of the right energy to excite nuclear energy levels. A classic example of this in an often used shielding material - iron, whose cross section exhibits a rich resonance structure beginning at around 1 keV and ending around 5 MeV, as shown in Figure 2.10. This region creates a problem because neutrons at the cross section peaks will be absorbed. But for neutrons with energies in the minima, the material will appear much more transparent, and these neutrons may escape the shield. In many cases, cast iron can solve this problem because its carbon content causes a small moderation eﬀect. Even this small eﬀect helps, because it shifts neutrons at the minima into the peaks, where they interact.

56 Figure 2.10: Total Neutron cross-section for 26Fe. 2.3. MONTE CARLO SIMULATION 23

2.2.7 Nuclear Recoils - Elastic Scattering and Moderation The neutronelastic scattering cross section on nuclei is large at all energies and leads to a useful tactic that is often employed in shielding applications to reduce neutron back- grounds. Kinematics dictates that the scattered neutron will give up energy on each elastic collision, especially if target nucleus is light, and carries away a large fraction of the energy as it recoils. So hydrogen and light elements are most eﬀective at reducing neutron kinetic energy. This process is called “moderation” and materials introduced to cause it are called “moderators”. Hydrogen and carbon are the two most practical and commonly used moderators. What is gained by moderating neutrons if their numbers are not changed? There are two advantages: In most cases, high energy neutrons are a more serious radiation background than • low energy neutrons because they can do more damage or cause electronic disruption. Moderation can drop their energies below certain thresholds (Personal Radiation Protection tresholds or Damage thresholds for electronic devices). At low energies, neutrons can be stopped by materials with large capture cross • sections.

2.2.8 Thermal neutrons Note that by the process of repeated elastic scatters, neutrons can moderate to the point where they reach equilibrium with the thermal velocity distributions of the materials in their environment. At this point they are termed “thermal neutrons”, with energies 5 typically as low as 10− eV . Materials such as lithium, boron, and cadmium have large neutron capture cross sections, and may be used ‘as is’ in some convenient compound (Heavy concrete), or added as dopants to moderators such as epoxy or polyethylene. This latter form is particularly eﬃcient since the neutrons will be captured in the mixed material as soon as they moderate to low energies. The disadvantage of enhancing neutron capture with dopants is that capture gammas are radiated during the process, and if these are of suﬃciently high energy, they must be attenuated.

2.3 Monte Carlo Simulation

The name "Monte Carlo" was coined in the 1940s by scientists working on the nuclear weapon project in Los Alamos to designate a class of numerical methods based on the use of random numbers. Nowadays, Monte Carlo methods are widely used to solve complex physical and mathematical problems [[78],[20],[64]], particularly those involving multiple independent variables where more conventional numerical methods would demand formi- dable amounts of memory and computer time. In the early publication of Herman Kahn [29] a readable survey of Monte Carlo - further on just MC -techniques, including simple applications in radiation transport, statistical physics is given. 24 CHAPTER 2. PRINCIPLES OF PHYSICS

2.3.1 Monte Carlo Basics One short description of MC methods was defined by Hermann Kahn in [29]: "The expected score of a player in any reasonable game of chance, however complicated, can in principle be estimated by averaging the results of a large number of plays of the game. Such estimation can be rendered more efficient by various devices which replaces the original game with another known to have the same expected score. The new game may lead to a more efficient estimate by being less erratic, that is, having a score of lower variance or by being cheaper to play with the equipment on hand". The MC simulation of particle transport of a given experimental arrangement consists of the numerical generation of random histories (more details in 2.3.3). To simulate these histories an "interaction model" is needed, i.e. a set of differential cross sections (DCS) for the relevant interaction mechanism. The DCSs determine the probability distribution functions (PDF) of the random variables that characterize a track:

1) free path between successive interaction events 2) kind of interaction taking place 3) energy loss and angular deﬂection in a particular event (if any secondaries - their initial states)

Once these PDFs are known, random histories can be generated by using appropriate sampling methods. If the number of generated histories is large enough, quantitative information on the transport process may be obtained by simply averaging over the simulated histories. Basically the MC-method yields the same information as the solution of the Boltzmann transport equation with the same interaction model (see [37] chapter 3.3 and following), but is easier to implement (see [65]). In particular, the simulation of radiation transport in finite samples is straightforward, while even the simplest geometries (e.g. thin foils) are very difficult to be dealt with by the transport equation. The main drawback of the MC-method lies in its random nature, all the results are affected by statistical uncertainties, which can be reduced at the expense of increasing the sampled population and, hence the computation time. Under special circumstances, the statistical uncertainties may be lowered by using variance-reduction techniques , mainly described in [[78], [67], [37]] and partially in chapter 4.3.4.

2.3.2 Integration with MC One of the basic concepts of MC simulation was pointed out by James [20], at least in a formal sense: all MC calculations are equivalent to integrations. This equivalence permits a formal theoretical foundation for MC techniques. An important aspect of simulation is the evaluation of the statistical uncertainties of the calculated quantities. By considering the simplest MC calculation, namely, the evaluation of a unidimensional integral, the fundamental principles can be shown. This facts are evidently extendable to multidimensional integrals. The integral : 2.3. MONTE CARLO SIMULATION 25

b I = F (x)dx (2.1) Za which could be rewritten for expectation values:

b I = f(x)p(x)dx f (2.2) ≡ h i Za b by introducing an arbitrary Probability Density Function (PDF) p(x) [with a p(x)dx =1; p(x) > 0 in (a, b) and p(x)=0outside this interval] and setting f(x)= F (x) .TheMC Rp(x) evaluation of the integral I is done by generating a large number N of random points xi from the PDF p(x) and accumulate the sum of values f(xi) in a counter. At the end of the calculation the expected value is estimated as

1 N f = f(x ). (2.3) N i i=1 X The law of large numbers says that, as N becomes very large,

f I (in probability). (2.4) → In statistical terminology, this means that f, the Monte Carlo result, is a consistent estimator of integral 2.1. This is valid for any function f(x) that is ﬁnite and piecewise continuous, i.e. with a ﬁnite number of discontinuities. The law of large numbers 2.4 can be restated as

1 N f =lim f(xi). (2.5) N N h i →∞ i=1 X By applying this law to the integral that deﬁnes the variance of f(x),whichis

var f(x) f 2(x) f(x) 2 (2.6) { } ≡ − h i with ® var f(x) = f 2(x)p(x)dx f 2 (2.7) { } − h i Z one obtains N N 2 1 2 1 var f(x) = lim [f(xi)] f(xi) . (2.8) N N N  { } →∞ i=1 − " i=1 #  X X  The expression in the curly brackets of equation 2.8 is a consistent estimator of the   variance of f(x). It is clear that different MC runs (with different, independent sequences of N random numbers of xi from a PDF p(x)) will yield different estimates f. This implies that the outcome of any MC code is affected by statistical uncertainties, similar to those found in 26 CHAPTER 2. PRINCIPLES OF PHYSICS laboratory experiments, which need to be properly evaluated to determine the "accuracy" of the MC result. For this purpose, f could be considered as random variable, the PDF of which is, in principle, unknown. Its mean and variance are given by 1 N 1 N f = f(x ) = f = f (2.9) N i N * i=1 + i=1 h i h i X X and ® 1 N 1 N 1 var(f)=var f(x ) = var f(x ) = var f(x) , (2.10) N i N 2 i N " i=1 # i=1 { } { } X X where use has been made of properties of the expectation and variance operators. The standard deviation (or standard error) of f, var f(x) σf = var(f)= { }, (2.11) N q r gives a measure of the statistical uncertainty of the MC estimate f. The result 2.11 has an important practical implication: in order to reduce statistical uncertainty by factor of 10, one has to increase the sample size N by a factor of 100. Evidently, this sets a limit to the accuracy that can be attained with the available computer power. Using the central limit theorem, which establishes that, in the limit N ,thePDF →∞ of f is a (Gaussian) distribution with mean f and standard deviation σf , h i (f f )2 −h i 1 2σ2 p(f)= eÃ− f ! (2.12) σf √2π It follows that, for sufficiently large values of N, for which the theorem is applicable, the interval f n.σf contains the exact value f with the probability of 68.3% if n =1, 95.4% if n±=2and 99.7% if n =3. The validationh i of the central limit theorem is a very powerful tool, since it predicts that the generated values of f follow a specific distribution, but it applies only asymptotically. The minimum number N of sampled values needed to apply the theorem with confidence depends on the problem under consideration. In order to evaluate the effectiveness of a MC algorithm, it is common to use the efficiency (also most widely known as Figure of merit FOM), which is defined by 1 = ,(2.13) σf T · where T is the computing time (or any other measure of the calculation effort) needed 2 1 to get the simulation result. Since σf and T are roughly proportional to N and N, respectively, is a constant (i.e. it is independent of N), on average. The so-called variance-reduction methods are techniques that aim to optimize the efficiency of the simulation through an adequate choice of the PDF p(x).Improvingtheefficiency of the algorithms is an important, and delicate, part of the art of MC simulation (see chapter 2.3.5, 4.1.4, 4.3.4). Although of common use, the term "variance reduction" is somewhat misleading, since a reduction in variance does not necessarily lead to improved efficiency. 2.3. MONTE CARLO SIMULATION 27

2.3.3 Particle transport with MC In MC-simulations of radiation transport, the history (track) of a particle is viewed as a random sequence of free flight that ends with an interaction event where the particle changes its direction of movement, loses energy and, occasionally, produces secondary particles. For the sake of simplicity in explanation the following consideration are limited to the detailed simulation method, where all the interaction events experienced by a particle are simulated in chronological succession, and the production of secondary particles is disregarded - so that only one kind of particle is transported. A particle starts its history with an energy E and moves by random scattering in a given medium, that could be a homogeneous gas, liquid or amorphous solid. The atoms of each media are distributed at random with uniform density. The composition of the medium is specified by its atomic number Zi and the mass number Ai of all the materials present. This is almost the same for both MCNPX and FLUKA code - only one difference in handling exists. For the material definition of electromagnetic particle transport (photon, electrons, positrons) in media within FLUKA - it is necessary to specify all parameters for the desired physics in so-called PEG-files explicitly - this is given due to the fact, that the EM-transport definitionsofFLUKAarestillintheEGS4codeformat. In case of alloys, e.g., they may be set equal to the percentage in number of each element and then a "molecule" is a group 100 atoms with the appropriate proportion of each element. The "molecular weight" is AM = i niAi where Ai istheatomicweightofthe i-th element. The number of molecules per unit volume is given by P ρ N˜ = n0 ,(2.14) AM where n0 is Loschmidt’s number and ρ is the mass density of the material used. In each interaction, the particle may lose an energy E0 and/or change its direction of movement. The angular deflection is determined by the polar scattering angle Θ, i.e. the angle between the direction of the particle before and after the interaction (see Figure 2.13), and the azimutal angle Φ. Assuming that the particle can interact with the medium through two independent mechanism, denoted as "A" and "B" (e.g., elastic and inelastic scattering - basically there are more than just two - see Appendix E of [66]). The scattering model is completely specified by the differential cross section (DCS)

2 2 d σA d σB (E; E0,θ) and (E; E0,θ) (2.15) dE0dΩ dE0dΩ where dΩ is a solid angle element in the direction (Θ, Φ). These DCSs are tabulated in worldwide available ENDF format (see Appendix B of [66]), which have to be converted before getting used in FLUKA (limited amount of libraries, only FLUKA developers have access to the implementation) or MCNPX (in ACE format, free access and users have the possibility to create their own libraries with NJOY (see [66]) supported by NEA(Nuclear Energy Agency in Paris) or PREPRO2000 supported by IAEA (International Atomic Energy Agency in Vienna)). 28 CHAPTER 2. PRINCIPLES OF PHYSICS

Thetotalcrosssectionsare

E π d2σ σ (E)= dW 2π sin θdθ A,B (E; E ,θ). (2.16) A,B dE dΩ 0 Z0 Z0 0 The PDFs of the energy loss and the polar scattering angle in individual scattering events are 2 2π sin θ d σA,B pA,B(E; E0,θ)= (E; E0,θ). (2.17) σA,B(E) dE0dΩ

Notice that pA(E; E0,θ).dE0dθ gives the (normalized) probability that, in a scattering event of type A, the particle loses energy in the interval (E0,E0 + dEˆ0) and is deﬂected into directions with polar angle (relative to the initial direction) in the interval (θ, θ+dθ). The azimuthal scattering angle in each collision is uniformly distributed in the interval (0, 2π), i.e. 1 p(Φ)= . (2.18) 2π The total interaction cross section is

σT (E)=σA(E)+σB(E). (2.19)

When the particle interacts with the medium, the kind of interaction that occurs is a discrete random variable (has to be sampled - "probability mixing" technique), that takes the value "A" or "B" with the probability σ σ p(A)= A or p(B)= B . (2.20) σT σT To get an intuitive picture of the scattering process the cross section σ gives the probability for a scattering to occur (see Figure 2.11). Brieﬂy described - the unit of cross section is

Figure 2.11: Total amount of solid angel for an impinging particle 2.3. MONTE CARLO SIMULATION 29

24 2 dσ area [barn =10− cm ];thedifferential cross section is defined as dΩ ;agivenamountof solid angle is dΩ = dΦ.d cos θ (2.21) which leads via +1 2π +1 2π dΩ = d cos θ dΦ =4π (2.22) 1 0 1 0 Z− Z Z− Z to the total amount of solid angle Ω. One can imagine each molecule as a sphere of radius R (see Figure 2.12), which is impinged by a particle of radius r ≪ R. The scattering describing parameter is b defined by

b = R sin(α) or b =sin(θ ) db = 1 R sin( θ )dθ (2.23) 2 − 2 2 together with the cross-section

θ 1 θ R2 dσ = b.db.dΦ = R cos( ) R sin( )dθ dΦ = sin θ.dθ.dΦ (2.24) | | 2 2 2 4 · ¸· ¸ the diﬀerential cross-section is determined as

2 dσ b.db.dΦ R sin θ.dθ.dΦ R2 = = 4 = (2.25) dΩ sin θ.dθ.dΦ sin θ.dθ.dΦ 4

Figure 2.12: Schematic illustration of the geometrical cross-section. such that the cross-sectional area equals the total cross section (see [66] equation 2.5)

dσ R2 2πR2 π σ = dΩ = sin θ.dθ.dΦ = sin θdθ = πR2. T dΩ 4 4 ZZ ZZ Z0 30 CHAPTER 2. PRINCIPLES OF PHYSICS

Assuming that a particle impinges normally on a very thin material foil of thickness ds,it will see a uniform distribution of Nds˜ spheres per unit surface. An interaction takes place when the particle strikes one of these spheres. Therefore, the probability of an interaction within the foil equals the fractional area covered the spheres, Nσ˜ T ds. In other words, Nσ˜ T is the interaction probability per unit path length. Its inverse 1 λT = (2.26) Nσ˜ T is the (total) mean free path length between interactions in a speciﬁcmedia. Considering a particle that moves within an unbound medium, the corresponding PDF p(s) of the path length s of the particle from its current position to the site of the next interaction can be obtained in the following way. The probability that the particle travels a path length s without interacting is

∞ F(s)= p(s0)ds0 (2.27) Zs The probability p(s)ds of having the next interaction when the travelled length is in the interval (s, s + ds) equals the product of F(s) (which is the probability of arrival at s without interacting) and 1 ds (the probability of interacting within ds). It then follows λT that 1 p(s)= ∞ p(s )ds . (2.28) λ 0 0 T Zs The solution of this integral equation, with the boundary condition p( )=0,isthe familiar exponential distribution ∞

1 s p(s)= e− λT . (2.29) λT

Notice that the mean free path λT coincides with the average path length between collisions: ∞ s = s.p(s)ds = λT (2.30) h i Z0 The diﬀerential inverse mean free path for the interaction process "A" is deﬁned as

2 1 d 2 λA d σA (E; E0,θ)=N˜ (E; E0,θ). (2.31) dE³0dΩ´ dE0dΩ Evidently, the integral of the diﬀerential inverse mean free path gives the inverse mean free path for the process,

d2 1 1 λA = dE 2π sin θdθ (E; E ,θ)=Nσ˜ . (2.32) λ 0 dE³ dΩ´ 0 A A Z Z 0 2.3. MONTE CARLO SIMULATION 31

In the literature, the product of Nσ˜ A is frequently called the macroscopic cross section (see chapter 2 of [66]), although this name is not appropriate for a quantity that has the dimension of inverse length - it could be considered as the probability of an interaction per unit length. Notice that the total inverse mean free path is the sum of the inverse mean free paths of the different active interaction mechanism, as assumed the sum of two, 1 1 1 = + . (2.33) λT λA λB 2.3.4 Random tracking treatment within MC transport Each particle track starts off at given position, with initial direction and energy in accordance with the characteristics of the source. The "state" of a particle immediately after an interaction is defined in phase space by its position coordinates r =(x, y, z), the energy E and direction cosines of the direction of flight, i.e. the components of the unit vector d =(u, v, w), as seen from the laboratory reference frame. Each simulated track is thus characterized by a series of states rn, En, dn,wherern is the position of the n-th interaction and En and dn are the energy and the direction cosines of the direction of movement just after that interaction. Assuming that a particle track has already simulated up to the state rn, En, dn (see Figure 2.13).

Figure 2.13: Basic tracking method using Monte Carlo techniques

The length s of the free path to the next collision, the involved scattering mechanism, the change of direction and the energy loss in that collision are random variables that are sampled from the corresponding PDFs, that represents the physical interaction process. Hereafter, ξ stands for a random number uniformly distributed in the interval (0, 1). Random values of s are generated by using

s = λT ln ξ (2.34) − 32 CHAPTER 2. PRINCIPLES OF PHYSICS which leads to the following position of an interaction at

rn+1 = rn + s.dn.(2.35)

Which type of interaction (reduced assumption "A" or "B") from the point of probability (see equation 2.20) is selected will be determined by using e.g. the inverse transform method for sampling (see [37]). The energy loss E0 and the polar scattering angular θ are sampled from the distribution pA,B(E; E0,θ) of equation 2.17 by using a suitable sampling technique. The azimutal scattering angle is generated, according to the uniform distribution in (0, 2π),asΦ =2πξ. After sampling the values of E0, θ and Φ, the energy of the particle is reduced, En+1 = En E0, and the direction of movement after the interaction dn+1 =(u0,v0,w0) is obtained − by performing a rotation of dn =(u, v, w). The simulation of the track then proceeds by repeating these steps. A track (particle history) is finished either when it leaves the material system (which is specified by the external void in FLUKA or the universe in MCNPX respectively) or when the energy becomes smaller than a given energy - that could be the energy Eabs, where particles are assumed to be absorbed in the medium - or being effectively stopped at energy Ecutoff , which could be specified separately for each kind of particles (that method is also known as simulation-time-limiting variance reduction method by killing particles crossing a certain energy-threshold).

2.3.5 Markov process - Variance reduction All the basic concepts, definitions of the previous chapters regarding the MC simulations rest on the assumption that particle transport can be modelled as a Markov process17, i.e. "future values of a random variable (interaction) are statistically determined by present events and depend only on the events immediately preceding". Owing to the Markovian character of the particle transport the generation of a particle history can be stopped at an arbitrary state at any point of the track and resumed from this state without introducing any bias in the results. Throughout the last chapters the transport mechanism was only considered in a single homogeneous medium. In practical application - as realized for the SPS5 project in chapter 5 & 6 - the material structure where particles are transported consists of various regions with different compositions. The interfaces between contiguous media are sharp, i.e. there is no diffusion of chemical species across them. In simulation codes like FLUKA or MCNPX, when a particle arrives at an interface, it is stopped there and the simulation is resumed with interaction properties of the new medium. Obviously, this procedure is consistent with the Markovian property of the transport process. A great number of the previously mentioned interfaces are inserted into geometries of deep penetration problems, in order to transport particles utilizing a special kind of

17Andrei Andrejevitch Markov (1856-1922), Russian mathematician, known for his work in probability theory 2.3. MONTE CARLO SIMULATION 33 variance-reduction-technique (VRT). Unfortunately, VRTs are basically extremely problem- dependent, and general recipes to minimize the variance do not exist. In many cases, ana- logue simulation does the work in a reasonable time. Spending man-hours by complicating theinput,togetamodestreductionincomputingtimemaynotbeagoodinvestment. It is also important to realize that an efficient VRT usually lowers the statistical error of a given quantity at the expense of increasing the uncertainties of other quantities. Thus, VRTs have to be used rather carefully - in this thesis mainly the VRT of importance biasing had been used, therefore just this technique will be exemplified. The VRT called "Importance biasing" or "Geometry Biasing" consists of two single techniques, which are normally used in conjunction - "Geometry- or Surface-Splitting" and "Russian Roulette". These two are effective in problems where interest is focused on a localized spatial region. Typical examples are the calculation of dose functions in deep regions of irradiated objects and, in the case of collimated radiation beams, the evaluation of radial doses far from the beam axis. The basic idea of Surface-Splitting and Russian- Roulette methods is to favour the flux of particles towards region of interest (ROI) and inhibit particles that leaves ROI. Importance Biasing is accomplished by modifying the weight of the particles when passing from one region to the next, corresponding the ratio S of importances, which are associated to each region. It is assumed that primary particles start moving with unit weight and each secondary particle produced by a primary one is assigned an initial weight equal to that of the primary. Geometry Splitting consists of transforming a particle, with weight ω0, into a number S>1 of identical particles ω0 with weights ω = S . Splitting should be applied when the particle "approaches" the ROI. Russian Roulette technique is, in a way, the reverse process: when a particle tends 1 to move away from ROI it is "killed" with a certain probability, K = S < 1,and,ifit 1 survives, its weight is increased by a factor 1 K . Here, killing means that the particle is just discarded (and does not contribute to− the scores anymore). Evidently, splitting and killing leave the simulation unbiased. The effectiveness of these methods relies on the adopted values of the parameters S and K, and on the strategy used to decide when splitting and killing are to be applied. A more specified description of the two techniques inside FLUKA and MCNPX is given in the chapter 4. 34 CHAPTER 2. PRINCIPLES OF PHYSICS Chapter 3 Radiation Protection foundations

3.1 Radiation Health Physics

Manhattan project workers in Los Alamos, Oak Ridge, Hanford, and atomic workers in the former U.S.S.R. suffered various degrees of anorexia (loss of appetite), fatigue, headache, nausea, vomiting, and diarrhea. Their physical states provide information on the delayed effects of ionizing radiation. Basically radiation effects are divided into somatic effects and genetic effects. The former affects the function of cells and organs, whereas the latter affects the future generations.

3.1.1 Somatic Effects Somatic effects are cell damages that pass on to succeeding cell generations. Radiation affects rates of cell division. Hastening and slowing down cell division affects embryonic tissues. Damages to cell membranes, mitochondria and cell nuclei result in abnormal cell functions, affecting their division, growth and finally death. Exposure to radiation strongly affects the rapidly dividing tissues and cells. Effects on some of these tissues are listed together with corresponding dose in Table 3.1.

3.1.2 Genetic Effects Genetic effects are damages to genes and chromosomes that affect future generations. Genetic information for the production and function of a new organ is contained in the chromosomes of germ cells - sperm and ovum. In reality, genetic effects are due to the damages to DNA molecules. Normal human somatic cells contain 46 chromosomes. Each chromosome contains a deoxyribonucleic acid (DNA) molecule, which is a complex macro- molecule (gigantic polymer). Each DNA consists of two complementary strands (see Fig- ure 3.1), each of which consists of a backbone made up of phosphoric acid and sugar.

35 36 CHAPTER 3. RADIATION PROTECTION FOUNDATIONS

System eﬀected Symptoms Dose / Sv

Skin, Erythema Burning / infection, sloughing of skin, hair loss 10 G.I. system, lining G.I. hinders digestion and absorption 10 Gastrointestinal Syndrome Nausea, vomiting, diarrhea, dehydration Bone marrow / Blood cells Chills, fatigue, hemorrhage, ulceration 3 8 Hematopoietic Syndrome infections, anemia (lack of blood cells) ÷ embryonic developments mature to have disproportionate parts Nervous system Shock, severe, nausea, disorientation, 100 CNS or Cerebrovascular Syndrome seizures, coma Gonad systems - Ovaries 0.6 0.8 Sterility Testes 2.5 ÷ 6.0 ÷ Table 3.1: Radiation exposure eﬀects on human body

Figure 3.1: DNA-molcule - visible two strang architecture 3.1. RADIATION HEALTH PHYSICS 37

Figure 3.2: Purine and pyrimidine bases - one of the foundation parts of DNA

Attached to each sugar molecule are two types of bases: purine bases (adenine and guanine), and pyrimidine bases (cytosine and thymine) - see Figure 3.2. Adenine (A) always pair up by thymine (T), and guanine (G) by cytosine (C) via hydrogen bonds. The A-T and G-C pairs stack on top of each other, but the two strands spiral around each other. Two successive turns have a distance of 3.4 nm, and 10 pairs of bases pack in this distance. The diameter of the double helix is about 2 nm, but its length reaches several centimeters to meters in some mammalian species (see also the illustration of cell lengths in Figure 3.3). DNA molecules carry out two functions: replication and transcription. Replication gives a copy of the DNA molecules to the daughter cells so that all the genetic information is preserved. Transcription synthesizes messenger ribonucleic acid (mRNA) using DNA molecules as templates. The mRNA molecules specify the amino acid sequence in the formation of polypeptide and proteins. Thus, the sequences of base pairs in DNA molecules are accountable for the biochemistry of the subject as well as for the genetic information of future generations. Thus, damages to DNA molecules by radiation result in delayed somatic and genetic effects. When two or more DNA molecules in the same nucleus are broken by radiation (see Figure 3.4), the broken ends recombine, perhaps not in the previous order. This phenom- enon is called translocation - the consequence is acute deformation and mutation of the bioinformatic content. Starting with translocations inside the DNA-strand a subsequent chain of processes is started - the timeline in Figure 3.5 shows the different levels of affects from physical interactions, via chemical and molecular reactions, passing biochemical levels - up to cell metabolism - until the timescale ends up with cell death or the origin of tumor-cells. Further on, beyond cell dimensions there is the genetical component, which transports the physical influences of radiation in the nm-area into the macroscopic world of human- generations. 38 CHAPTER 3. RADIATION PROTECTION FOUNDATIONS

Figure 3.3: Scaling proporties from cell to DNA dimension - compared with ionizing density of an impinging alpha-particle

Figure 3.4: DNA damages caused by impinging particle/radiation 3.2. DOSIMETRY BASICS 39

Figure 3.5: Timedependance of Radiation eﬀects

3.2 Dosimetry basics

There are two types of quantities speciﬁcally deﬁned for use in radiological protection - see [72] and [38]:

Protection quantities,deﬁned by the International Commission for Radiation • Protection (ICRP) and used for assessing the limits,

Operational quantities,deﬁned by the International Commission for Radiation • Units (ICRU) and intended to provide a reasonable estimate of the protection quantities.

These radiation protection parameters have led to a system of correlated quantities, which areillustratedbytheschemeinFigure3.6.

3.2.1 Physical quantities Flux, fluence, current and flow are used as a basis throughout the field of radiation protection. Basically it is interesting to note that the rate terms, flux alias "fluence rate" and current alias "flow rate" are the terms that most often conflict. This conflict is based on the fact that transport theory was first used in a reactor theory context. There it was power what one cared about, so the "Rate"-terms (like power) were the ones that got a 40 CHAPTER 3. RADIATION PROTECTION FOUNDATIONS

Figure 3.6: Relationship of quantities for radiation protection word defined, which was in constant use. The contrary is given for radiological studies - there the cumulative effects are important, so the time-integrated terms, fluence and flow, have linguistic preference. But old habits die hard, so it is best to be familiar with both sets of terms.

Differences of flux and current One of the most discussed disagreements [1] are given for those two quantities, not at least 1 Hz because both of them have the units of cm2.s or cm2 means rate of particles crossing unit area per unit time. Basically the flux can be defined as £ ¤

ϕ(r,E, Ω,t)=v n(r,E, Ω,t) × m v speed of particles s n particle density 1 (3.1) cm£ 3 ¤ r position vector £ ¤ E energy Ω solid angle t time

In order to get fluence, the time integral of fluence-rate or flux (both terms are used 3.2. DOSIMETRY BASICS 41 interchangably thoughout literature) - equation 3.1 has to be integrated:

Φ(r,E, Ω)= dt.ϕ(r,E, Ω,t)= v.dt.n(r,E, Ω,t) (3.2) Z Z This fluence can be seen as the number of particles crossing a hypothetical sphere of unit cross section area, or and more useful, but still an equivalent definition as tracklength per unit volume. The big advantage of the latter definition is given due to easier numerical implementation as an estimator into Monte Carlo Simulation codes - e.g. as fluence- estimator built in MCNPX

Φ(r,E, Ω) W .v.∆t = W λ ≈ V V (3.3) W statisticalP weight of particlesP V Volume of tracklengths λ tracklength On the contrary, whereas fluence "counts" the particles irrespective of their direction, current is a measure of the net number of particles crossing a surface with a well defined orientation. In a directed radiation field, fluence and current are the same only for normal 1 incidence to the surface. At all other angles the fluence is higher by a factor of cos(θ) ,with θ as angle of incidence in relation to the surface.

Absorbed dose, [70] is the radiation energy absorbed per unit mass of the target material. Formally given in equation 3.4,

dE D = (3.4) dm where dE is the mean energy imparted by ionizing radiation to matter of mass dm. Like temperature, absorbed dose is a point, or intensive function. The SI unit of absorbed dose J is joule per kilogram ( kg ). The special unit is gray (Gy).

KERMA [75] The kerma, K, is the quotient of dE K = , (3.5) dm where dE is the sum of the initial kinetic energies of all the charged particles liberated by indirectly ionizing particles in a volume element of the speciﬁed material, and dm is the mass of the matter in that volume element. 42 CHAPTER 3. RADIATION PROTECTION FOUNDATIONS

Radiation weighting Type of Radiation Energy Range factor, wR Photons all energies 1 Electrons and Muons all energies 1 Neutrons < 10 keV 5 10 keV to 100 keV 10 >100 keV to 2 MeV 20 > 2 MeV to 20 MeV 10 > 20 MeV 5 Protons, other than recoil protons > 2 MeV 5 Alphas, ﬁssion fragments, heavy nuclei 20 Table 3.2: Radiation weighting factors

Kerma has the same dimension as absorbed dose and both quantities have the same special unit, the rad. The unit in the International System of Units (SI) is the gray, J symbol Gy; 1 Gy =1kg =100rad. The quantity kerma has the advantage that it is independent of the complexities of the energy transport by charged secondaries. A further advantage is that kerma has a defined value for a material sample of vanishing sizewhichisembeddedinsomeothermaterialorwhichispositionedinfreespace.Thisis not the case for absorbed dose. It is therefore often convenient to refer to a value of kerma or kerma rate for a specified material in free space or at a point in a different material. This is the value which would be obtained if a small mass of the specified material were placed at the point of interest. The size of this mass is usually not critical as long as the condition is fulfilled that the presence of the sample does not appreciably disturb the field of the indirectly ionizing particles. It is permissible to make a statement such as "the tissuekermaatthepointPinsideawaterphantomis...."

3.2.2 Protection quantities

The equivalent dose,HT ,inatissueororgan,T,isgivenby:

HT = R wR.DT,R P DT,R average absorbed dose from radiation R (3.6) R radiation source T Tissue or Organ wR radiation weighting factor of radiation R The radiation weighting factors of equation 3.6 are standardized in the ICRP recommendations and shown in Table 3.2. When calculation of radiation weighting factors for neutrons requires a continuous 3.2. DOSIMETRY BASICS 43

Element Weight [%] H 10.1 C 11.1 N 2.6 O 76.2 Table 3.3: Composition by weight of the ICRU tissue reference sphere function, following approximation is in use:

2 (ln(2En)) [ − ] wR=5+17e 6 (3.7)

En NeutronenergyinMeV

For radiation types and energy that are not included in the table, an approximation of wR can be obtained by calculation of Q,asdeﬁnedinequation3.8,atadepthof10 mm in the ICRU sphere, which is deﬁned as a 30 cm diameter sphere of unit density tissue and composition by weight as quoted in Table 3.3. by equation

1 Q= D Q(L).D(L).dL ZL (3.8) Absorbed dose in 10 mm D(L).dL between linear energy transfer L and L+dL Q(L) Quality factor at 10 mm

The eﬀective dose, E, is the sum of the weighted equivalent doses, HT , in the tissues and organs of the body:

E = wT .HT (3.9) T X These tissue weighting factors arestandardizedasitisgivenfor the radiation weighting factors and shown in Table 3.4. The remainder, mentioned as last entry in Table 3.4, is composed of the following additional tissues and organs: adrenals, brain, thoracic airways, small intestine, kidney, muscle, pancreas, spleen, thymus and uterus. In those exceptional cases in which a single one of the remainder tissues or organs receives an equivalent dose in excess of the highest dose in any of the twelve organs for which a weighting factor is speciﬁed, a weighting factor of 0.025 should be applied to that tissue or organ and a weighting factor of 0.025 to average dose in the rest of the remainder as deﬁned above. 44 CHAPTER 3. RADIATION PROTECTION FOUNDATIONS

Tissue weighting Tissue or organ factors, wT Gonads 0.2 Bone marrow, Colon, Lung, Stomach 0.12 Bladder, Breast, Liver, Oesophagus, Thyroid 0.05 Skin, Bone surface 0.01 Remainder 0.05 Table 3.4: Tissue weighting factors

3.2.3 Operational quantities From the operational quantities just the ambient dose equivalent should be emphasized - it was used for the MCNPX comparison calculations (see chapter 4). The ambient dose equivalent, H*(d),atapointinaradiationfield,isthedoseequivalentthatwouldbe produced by the corresponding expanded and aligned field, in the ICRU sphere at a depth, d, on the radius opposing the direction of the aligned field. The special name for the unit J of the ambient dose equivalent is Sievert (Sv), which corresponds to [ Kg]. For strongly penetrating radiation, a depth of 10 mm is currently recommended. The ambient dose equivalent for this depth is then denoted by H*(10). The operational quantities used in measurements were designed to provide a reasonable estimate of the appropriate protection quantity under normal working conditions. This may be simply expressed by the goal that the ratio of the value of the appropriate protection quantity to the measurement of the operational quantity is less than unity:

Hprotection 5 1(3.10) Hoperational Since neither of the protection quantities and operational quantities can be measured directly, it is extremely important to relate these quantities to basic physical quantities (such as particle ﬂuence), which is done with conversion coeﬃcients.

3.2.4 Conversion coefficients [[72], [76]] A ’conversion coefficient’ links the protection and operational quantities to physical quantities characterizing the radiation field,asshowninFigure3.6.Inpractice,thephysical quantities that are usually calculated or used are the tissue-absorbed dose (DT ), air kerma free-in-air (Ka), and particle fluence (Φ) as utilized for the SPS5-calculations. Because the number of conceivable geometries in which the human body might be irradiated is virtually limitless, it has become conventional to limit, somewhat arbitrarily, the number of irradiation geometries for which calculations are performed. In general, calculations are carried out assuming whole-body irradiation by broad unidirectional or plane-parallelbeamsasitisgiveninFigure3.7. 3.2. DOSIMETRY BASICS 45

Figure 3.7: Irradiation geometries of human phantom

Typical irradiation geometries are:

Anterior-posterior (AP): The ionizing radiation is incident on the front of the body • in a direction orthogonal to the long axis of the body.

Posterior-anterior (PA): The ionizing radiation is incident on the back of the body • in a direction orthogonal to the long axis of the body.

Lateral geometry (LAT): The ionizing radiation is incident on either side of the • body in a direction orthogonal to the long axis of the body. When it is necessary to be more speciﬁc the direction could also be distinguished - RLAT lateral irradiation fromtherightsidetotheleftsideofthebody-orLLATlateralirradiationfrom the left side to the right side. Basically there are just small diﬀerences in absorbed dose between RLAT and LLAT geometries, because of the well-nigh symmetry of the human body.

Rotational geometry (ROT): Human body irradiation by a parallel beam of ionizing • radiation, from a direction orthogonal to the long axis of the body, which rotates at a uniform rate around the long axis, while irradiating the body by a broad beam of ionizing radiation from a stationary source located on an axis at right angles to the long axis of the body. 46 CHAPTER 3. RADIATION PROTECTION FOUNDATIONS

Isotropic geometry (ISO): Defined by a radiation fieldinwhichtheparticlefluence • per unit of solid angle is independent of direction.

Basically fluence-to-dose conversion are post-processed by convoluting the particle- and energy-dependent fluence spectra with the fluence-to-dose-conversion-coefficients (e.g. ICRP74 fluence-to-dose conversion factors for neutrons are shown in Figure 3.8).

Figure 3.8: Eﬀective dose conversion coeﬃcients for neutrons from ICRP 74.

During the simulation with FLUKA this was carried out by a just in time conversion for every kind of particle at its specific energy to receive the corresponding dose (ambient dose and effective dose). Therefore the concept of the WORST geometry irradiation was considered - means for a given energy of a particle the highest value of Conversion Coefficient for any of the geometries AP, PA, LAT is chosen. This is useful for instantaneous losses at colliders where one has not a clue in which orientation the victim will find himself. - It cannot be worse than this !

3.3 General Principles of Radiation Protection

Exposure of persons to ionizing radiation shall be controlled as speciﬁed in Recommen- dation 60 of the International Commission for Radiological Protection (ICRP) which is based on the principle of justifying the need for, optimizing, and limiting exposure to ionizing radiation [38]: 3.4. WORKING AREA CLASSIFICATIONS AT CERN (ECA5) 47

No practice which exposes persons to radiation may be adopted unless its intro- • duction is essential to the laboratory’s work and the results cannot be achieved by other methods which avoid such exposure.

ALARA ... these ﬁve simple letters as acronym for "As Low As Reasonably • Achievable" is the foundation for all radiation protection considerations - means, there should be no practice which exposes persons to radiation may be adopted until it has been ensured that such exposure is kept to the minimum reasonably achievable, taking into account the social and economic factors.

By applying the following rules of conduct - exposure to ionizing radiation can be • reduced:

— reduce the intensity of the radiation source used; — increase the distance between the exposed person and the source; — reduce the time of exposure to ionizing radiation; — reduce radiation levels by the use of suitable shielding; — avoid inhaling or ingesting any radioactive substances.

3.4 Working area classiﬁcations at CERN (ECA5)

Dose and dose-rate design constraints result from the CERN laboratory’s policy on radiation area classiﬁcation. Table 3.5 gives the current constraints based on the policy stated in [60] and in the CERN Radiation Safety Manual [25]. The ECA5 area is presently classiﬁed as a Simple Controlled Radiation Area, which means a dose-rate constraint of µSv 10 h . One would like to maintain the areas above ground level as Supervised Radiation µSv Areas, which means a dose-rate constraint of 1 h . As a design limit for such areas one µSv would like to have a safety factor of about three, giving limits of 3 and 0.3 h for Simple Controlled and Supervised Radiation Areas respectively for beam losses during normal SPS operation. 48 CHAPTER 3. RADIATION PROTECTION FOUNDATIONS

Area Max.-Loss Norm.-Loss Max. Dose-rate Regulation

Classification Dose Dose-rate RP...Radiation Protection µSv µSv mSv h h RSO ... Radiation Safety Offi cer No fi lm badge required Non-designated 0.3 0.1 0.5 • 5 Public exposure < 1mSv/year • No fi lm badge required Supervised 2.5 1 7.5 • 5 Employees exposure < 1mSv/year • Film badge required • Simple Controlled 50 10 100 Employees exposure 5 • can not exceed 15 mSv/year

mSv Film badge and personal dosimeter required Limited Stay 2 • 5 h Work needs Authorization from RP and RSO mSv • > 2 Film badge and personal dosimeter required h • High radiation but Strict Access control enforced mSv • < 100 Access needs Authorization from RP and RSO h • Access protected by machine interlocks • mSv Access needs authorization of department Prohibited — > 100 • h leader, medical service and RP group

Access monitored by RP group • Table 3.5: Design Constraints for Doses and Dose-rates outside Shielding Chapter 4

Comparison of FLUKA and MCNPX

Both, FLUKA and MCNPX are well established codes in the nuclear Monte Carlo Simula- tion world, used in a wide ﬁeld of applications - but there are almost no direct comparisons available between those two codes. Among that fact, also the necessity to determine the right biasing factors for optimizing the calculations of the complex SPS5-geometry was given. So why not killing two birds with one stone.

4.1 FLUKA

FLUKA is a general purpose tool for calculations of particle transport and interactions with matter, covering an extended range of applications spanning from proton and electron accelerator shielding, target design with deep penetration calculation for neutrons, calorimetry, activation, dosimetry, detector design, Accelerator Driven Systems, cosmic rays, neutrino physics, radiotherapy, etc. etc. The code started being developed in 1962 by J. Ranft and H. Geibel, who initiated the code for hadron beams. The name FLUKA (from the german origin: "FLUktuierende KAscade") came eight years later, since at that time the code was mainly used for applications concerning event-to-event fluctuations in calorimetry. Between 1970 and 1987 the development of the code was carried out in the framework of a collaboration between CERN and the groups of Leipzig and Helsinki. That version was essentially for shielding calculations. Since 1989 FLUKA is being developed within INFN (National Institute of Nuclear Physics) with the personal collaboration of A. Fasso (CERN) and J. Ranft (Leipzig). One of the main aims is developing an all-purpose, general code with new physics models. Presently very little was left of the 1987 version. In 1990 MCNPX officially started using FLUKA for its high energy part, which was not updated since then. In 1993 FLUKA was interfaced with GEANT3 (for the hadronic part only). This interface did not follow the subsequent FLUKA developments and it is therefore now obsolete. Since 2002 FLUKA is an INFN project, with the main aim of providing a better diffusion of the code and stimulating all those studies that can be of interest for applied

49 50 CHAPTER 4. COMPARISON OF FLUKA AND MCNPX research, with focus on dosimetry, medical physics and, more generally, radiobiology. Nowadays FLUKA is able to simulate with high accuracy the interaction and propagation in matter of about 60 different particles, including photons and electrons starting at an energy of 1 keV up to thousands of TeV (see also Table 4.1), neutrinos, muons of any energy, hadrons of energies up to 20 TeV (could be extended up to 10 PeV by linking FLUKA with the newest version of DPMJET code) and all the corresponding an- tiparticles, neutrons down to thermal energies and heavy ions. The library transport for neutrons in FLUKA is restricted both to an upper energy of 20 MeV and to the fixed implemented materials (about 140), there is no way for extending the volume of libraries like it is given in MCNPX - see next subsection. For neutron energy deposition FLUKA uses kerma factors; recoil protons and protons from (n,p)-reactions are transported explicitly. FLUKA can handle very complex geometries - using an improved version of the well- known Combinatorial Geometry (CG) package. The tracking treatment even works correctly in the presence of magnetic and electric field. Hadron-nucleon interactions model are based on resonance production (see also 4.1.1) and decay below a few GeV and on the Dual Parton model above. For the hadron- GeV nucleus interactions two models are in use - below momenta of 3 5 c the PEANUT (Pre-Equilibrium Approach to NUclear Thermalization) package,− which includes a very detail Generalized Intra-Nuclear Cascade (GINC) and a pre-equilibrium stage (see section 4.2.1 and Figure 2.9), while at higher energies the Gribov-Glauber multiple collision mechanism is included in a less refined GINC. As can be seen in Figure 2.9 these two models are followed by equilibrium processes: evaporation, fission, Fermi break-up, gamma de-excitation. Photonuclear reaction could be simulated and FLUKA can fully integrate photon-neutron coupled calculations. Multiple Coulomb scattering and ionization fluctuations treatment allows to handle accurately problems such as electron backscattering and energy deposition in thin layers even in the few keV -energy-range. Due to the reasons of computational time this feature was not utilized throughout the whole thesis-work, but the possibly and interesting aspect should be posted here.

4.1.1 Physics implemented in FLUKA Hadron physics of inelastic nuclear interactions Energy between 4 GeV and 20 TeV: • Dual Parton Model (original version by Ranft & coll., present version by A. Ferrari and P.R. Sala, description and examples in [11])

Energy between 2.5 GeV and 4 GeV : • Resonance production and decay model (Hänßgen et al.[[48], [49], [44], [47], [50], [45], [46]]), modiﬁed to take into account correlations among cascade particles and nuclear eﬀects (Ferrari-Sala) 4.1. FLUKA 51

Between 0.02 GeV and 2.5 GeV : • Pre-equilibrium-cascade model PEANUT (Ferrari-Sala) [[10], [3]] All three models include evaporation and gamma de-excitation of the residual nucleus [[8], [9]]. Light residual nuclei are not evaporated but fragmented into a maximum of 6 bodies, according to a Fermi break-up model.

Treatment of antiparticle capture: • antinucleons according to resonance model, π− by the pre-equilibrium-cascade model.

Hadron physics of Elastic Scattering Parameterized nucleon-nucleon cross sections. Tabulated nucleon-nucleus cross sections [[73], [74]]. Tabulated phase shift data for π-p and phase-shift analysis for k-p scattering. Detailed kinematics of elastic scattering on H-nuclei and transport of proton recoils (Ferrari-Sala).

Transport of charged hadrons and muons Energy loss: Bethe-Bloch theory [[32], [33], [35], [19], [18]], optional δ-ray production and transport with account for spin effects or Landau fluctuations [51]. The FLUKA 2002 version includes a treatment [4] which combines δ-ray production with properly restricted + "Landau/Vavilov" fluctuations with corrections for particle spin and e−/e and "distant collision" straggling corrections (similar to Blunck-Leisegang ones). Shell and other low- energy corrections derived from Ziegler [43], density effect according to Sternheimer [77]. Special transport algorithm, based on Molière’s theory of multiple Coulomb scattering improved by Bethe [[27], [28], [34]], with account of several correlations: between lateral and longitudinal displacement and the deflection angle, between projected angles, and between projected step length and total deflection. Accurate treatment of boundaries andcurvedtrajectoriesinmagneticandelectricfields, automatic control of the step, path length correction, spin-relativistic effects at the level of the second Born approximation [12]. Nuclear size effects (scattering suppression) on option (simple nuclear charge form factors are implemented, more sophisticated ones can be supplied by the user). Correction for cross-section variation with energy over the step. Bremsstrahlung and electron pair production at high energy by heavy charged particles, treated as a continuous energy loss and deposition or as discrete processes depending on user choice. Muon photonuclear interactions, with or without transport of the produced secondaries.

Low-energy neutrons physics below 0.02 GeV : ENEA multigroup P5 cross-sections [17], with gamma-ray generation and diﬀerent temperatures available. Doppler broadening for temperatures above 0 K. Transport: standard multigroup transport with photon and ﬁssion neutron generation. 52 CHAPTER 4. COMPARISON OF FLUKA AND MCNPX

Detailed kinematics of elastic scattering on hydrogen nuclei and transport of proton recoils and protons from N(n,p) reaction. Capture photons are generated but not transported according to the multigroup treatment, except with the more accurate EMF package which performs continuous transport in energy and allows for secondary electron generation. For nuclei other than hydrogen, kerma factors are used to calculate energy deposition (including from low-energy ﬁssion). For details about the available materials, group structure etc. see the description in the FLUKA manual [6].

Electrons physics Special transport algorithm [12], including complete multiple Coulomb scattering treatment (see hadron and muon transport above). Correct lateral displacement even near a boundary. Accurate treatment of the variations with energy of the discrete event + cross-sections and of the continuous energy loss. e /e−-differences in stopping power considered. Bremsstrahlung differential cross-sections from Seltzer and Berger [[81], [82]], with tip finite value; differences between positron and electron bremsstrahlung are taken into account [52]. Detailed angular distribution of bremsstrahlung photons. Landau- Pomeranchuk-Migdal suppression effect [[53], [54], [14], [15]], Ter-Mikaelyan polarization effect in the soft part of the bremsstrahlung spectrum [69]. Electrohadron production (only above rho mass energy 770 MeV) via virtual photon spectrum and Vector Meson Dominance Model [31]. (The treatment of the latter effect has not been checked with the latest versions, however). e+-annihilation, δ-ray production via Bhabha and Möller scattering. Note: the present lowest transport limit for e− is 1 keV. However, it must be kept in mind that in high-Z materials the Molière multiple scattering model becomes unreliable below 20-30 keV . The minimum recommended energy for PRIMARY electrons is about 50-100 keV for low-Z materials and 100-200 keV for heavy materials. A single scattering algorithm allows to overcome most of the limitations at low energy for the heaviest materials at the price of some CPU increase.

Photons physics Pair production with actual angular distribution of electrons and positrons. Compton effect with account for atomic bonds through use of inelastic Hartree-Fock form factors. Photoelectric effect with actual photoelectron angular distribution [21], detailed interaction on six K and L single sub-shells, optional emission of fluorescence photons and approximate treatment of Auger electrons. Rayleigh effect as in EGS4 [84]. Photon polarization taken into account for Compton, Rayleigh and Photoelectric. Photohadron production: Vector Meson Dominance Model (Ranft [42]), modified and improved (Ferrari-Sala) using PEANUT below 770 MeV [3]. Giant Resonance and Quasideuteron interactions. Note: the present lowest transport limit for photons is 1 keV. However, fluorescence emission may be underestimated at energies lower than the K-edge in high-Z materials, because of lack of Coster-Kronig effect. The minimum recommended energy for PRIMARY photons is about 5 to 10 keV . 4.1. FLUKA 53

Optical photon physics Generation and transport (on user’s request) of Cerenkov and Transition Radiation (not yet implemented). Transport of light of given wavelength in materials with user-deﬁned optical properties.

Neutrino physics Electron and muon (anti)neutrinos are produced and tracked on option, without interactions. Neutrino interactions however are implemented, but independently from tracking.

4.1.2 GEOMETRY package Combinatorial Geometry from MORSE [61], with additional bodies (infinite circular and elliptical cylinder parallel to X,Y,Z axis, generic plane, planes perpendicular to the axes). Distance to nearest boundary taken into account for improved performance. Accurate treatment of boundary crossing with multiple scattering and magnetic or electric fields. The maximum number of regions (without recompiling the code) is 5000. The tracking strategy has been substantially changed with respect to the original CG package. Speed has been improved and interplay with charged particle transport (multiple scattering, magnetic and electric field transport) has been properly set. A limited repetition capability (lattice capability) is available, but hardly utilized. This allows to avoid describing repetitive structures in all details. Only one single module has to be described and then can be repeated as many times as needed. This repetition does not occur at input stage but is hard-wired into the geometry package, namely repeated regions are not set up in memory, but the given symmetry is exploited at tracking time using the minimum amount of bodies/regions required. This allows in principle to describe geometries with even tens of thousands regions (e.g. spaghetti calorimeters) with a reasonable number of region and body definitions. For debugging the FLUKA geometry the PLOTGEOM built-in card is used for plotting of selected sections. The more practically ALIFE geometry editor and parser, written in Tcl/Tk programming language, simplifies the preparation and maintenance of FLUKA input cards both for geometry and materials as well as tracking and scoring options. It supports a modular structure for the geometry definitionprovidingaveryefficient way for several users to work on the same geometry. Further options for visualization of both the geometry and the 3D-volume results are described in section B.

4.1.3 TRANSPORT Condensed history tracking for charged particles, with single scattering option. Time cut- oﬀ. Legendre angular expansion for low-energy neutron scattering. Transport of charged particles in magnetic and electric ﬁelds. Transport limits of all particles is shown in Table 4.1 54 CHAPTER 4. COMPARISON OF FLUKA AND MCNPX

Secondary particles Primary particles charged hadrons 1 keV - 20 TeV 100 keV - 20 TeV neutrons thermal - 20 TeV thermal - 20 TeV antineutrons 50 MeV - 20 TeV 100 MeV - 20 TeV muons 1 keV - 1000 TeV 100 keV - 1000 TeV electrons in low-Z materials 1 keV - 1000 TeV 70 keV - 1000 TeV electrons in high-Z materials 150 keV - 1000 TeV photons 1 keV - 1000 TeV 7 keV - 1000 TeV Table 4.1: FLUKA’s energy ranges for particle transport

4.1.4 BIASING

Leading particle biasing for electrons and photons: region dependent, below user-deﬁned energy threshold and for selected physical eﬀects. Russian Roulette and splitting at boundary crossing based on region relative importance. Region-dependent multiplicity tuning in high energy nuclear interactions. Region-dependent biased down-scattering and non-analog absorption of low-energy neutrons. Biased decay length for increased daughter production; biased inelastic nuclear interaction length; biased interaction lengths for electron and photon electromagnetic interactions; biased angular distribution of decay secondary particles. Region-dependent weight window in three energy ranges (and energy group dependent for low energy neutrons). A more detailed description of the biasing techniques utilized for this thesis is explained in chapter 4.3.4.

4.1.5 SCORING

Star density by producing particles in regions. Energy density by region, total or from electrons/photons only. Star and energy density in a geometry-independent binning structure (Cartesian or cylindrical), averaged over the run or event by event. Energy deposition weighted by a quenching factor (Birks law [40]). Step size independent of bin size. Time window. Coincidences and anticoincidences. Fluence and current scoring as a function of energy and angle, via boundary-crossing, collision and track-length estimators coincident with regions or region boundaries. Track- length fluence in a binning structure (Cartesian or cylindrical) independent of geometry. Particle yield from a target or differential cross section with respect to several different kinematic variables. Residual nuclei. Fission density. Neutron balance. No limit to the number of estimators and binnings within the total memory available (but a maximum number must be fixed at compilation time). Energy deposition can be scored on option disregarding the particle weights (useful for studying computer performance, etc.) 4.2. MCNPX 55 4.2 MCNPX

[55], [63], [30], [80] MCNPX is a Los Alamos 3-D Monte Carlo radiation transport code, written in Fortran90 capable of tracking 34 particle types (including 4 light ions) at all energies. The code uses standard evaluated data libraries (proton, neutron, photonuclear, many extended to 150 MeV, see [62]), along with physics models where libraries are not available (see Figure 4.1).

Figure 4.1: MCNPX Acceptance of Library and/or Model Transport

MCNPX is supported on all UNIX, Linux and PC platforms, and can be multi-processed with PVM or MPI. It is a superset of MCNP4C3, LAHET 2.8 and CEM and can generally be expected to track MCNP4C3. The MCNPX program began in 1994 in support of the Accelerator Production of Tritium Project (APT). The work involved a formal extension of MCNP to all particles and energies, improvements of physics simulation models, extension of neutron, proton and photonuclear libraries to 150 MeV, and the formulation of new variance reduction and data analysis techniques. Since the initial release of Version 2.1 on October 23, 1997, MCNPX has an extensive amount of beta-testers, that helps improving the code on feed- back base. The ﬁeld of application is at least as big as it is for FLUKA - with some additions, like

Medical physics, especially proton and neutron therapy. • 56 CHAPTER 4. COMPARISON OF FLUKA AND MCNPX

Comparison of physics-based and table-based data. • Single-event upset (SEU) in semiconductors, from cosmic rays in spacecraft of from • the neutron component on the earth’s surface.

Detection technology using charged particles (e.g., abandoned landmine) • Nuclear Safeguards •

4.2.1 Physics implemented in MCNPX In the thesis of Igor Koprivnikar [37] a description of the basic physics implemented in MCNPX (version <2.1.5) is well described, thus here only the improvements and adaptation since then should be emphasized. The INC-Model as described in "The physics of High Energy Reactions" [11] and in the originally work of Hugo Bertini [36] is modernized with the current state of the art INCL4/ABLA physic models. INCL4, based on the work of Joseph Cugnon at the University of Liege, Belgium and ABLA, principally developed by Karl-Heinz Schmidt at GSI-Darmstadt, Germany - improve physics in the energy range of 150 MeV to 3 GeV for targets with A > 25 [2]. In former MCNPX versions (< 2.5d) a conglomerate of models (Bertini-Dresner-Atchison) were built-in the LAHET module, which is the high energy part of MCNPX up to 3.5 GeV - this is now replaced by the INCL4/ABLA model in LAHET3. This package oﬀers the opportunity to switch to Single-Bertini model for low- energy particles; together with the ABLA part (the new treatment of ﬁssion evaporation), the overall performance both in precision and calculation speed increases.

4.3 Diﬀerences between FLUKA and MCNPX

4.3.1 Geometry Surfaces like "plane", "sphere", "cylinder", "cone" .... encloses regions of space called "cells" in MCNPX. Each cell has a importance for each particle type being transported. An importance of 0 means the cell is a sink for any particle entering the cell. Every geometry must be completely surrounded by 0 importance space (for all particles) to avoid going "forever". FLUKA geometry deﬁnition is similar - only the sign of a "MCNPX-cell" is opposite to the "FLUKA-region". There are "FLUKA-bodies" instead of "MCNPX- surfaces" and MCNPX knows a few more basic bodies/surfaces like torus and special spheres than FLUKA. MCNPX’s geometry is more advanced regarding unifying cells and the creation of complementary cells which is not part of FLUKA. The concept of a universe outside the outermost cells in MCNPX is not implemented in FLUKA - thus an outermost body has to be deﬁned. 4.3. DIFFERENCES BETWEEN FLUKA AND MCNPX 57

4.3.2 Physics While FLUKA has every interaction activated on default - and one has to define which particles or physics should not take place MCNPX uses the bottom-up method - there is no physics without definition. At high energies, MCNPX shows a harder spectrum than what FLUKA is predicting. The difference in the high energy (larger than 100 MeV) part between FLUKA and MCNPX spectra can be attributed to the use of an old version of the FLUKA high energy interaction generator in MCNPX. The present version of FLUKA has undergone several major improvements/reworking along the years which has vastly improved its performance when compared with available experimental data. The discrepancies in between 20 and 100MeV could be still a consequence of the different high energy generator physics, or a genuine difference arising from low and intermediate energy hadronic modelling in the two codes which are completely independent.

4.3.3 Tallies, scoring Due to the reason that FLUKA is able to tally fluences of all kind of particles at once, which is not possible in MCNPX - a restriction in tallying had to be found, in order to compare dose-rates calculated with FLUKA and MCNPX inside the SPS5 geometry. Thus only neutron ambient dose-rates convoluted with the ICRP-74 neutron fluence- to-ambient-dose-rate conversion coefficients were considered. Due to the fact, that the ambient dose-rate in deep penetration problems is dominated by neutrons, this restriction is acceptable.

4.3.4 Biasing For low energies is Monte Carlo a technique to integrate the Boltzmann equation: what matters is the expectation value of a finite number of quantities of interest, which is obtained by integration over phase space, due to the ergodic theorem - integration takes place over the individual particle paths in phase space - i.e. the histories (see also chapter 2.3.3). The statistical weighting techniques used in biased Monte Carlo are mathemat- ically rigorous. Means for N , all calculated averages tend to the corresponding physical expectation values, although→∞ it could happen, that the speed of convergence may be very different in different regions of phase space (this was one of the major problems in the SPS5 geometry, because of the three-dimensional extension up to ground level - see chapter 5). Importance biasing which is the most widely used Variance Reduction Technique combines two methods:

Surface Splitting (also called Geometry Splitting) which reduces the uncertainty σ • but increases the computational time t. 58 CHAPTER 4. COMPARISON OF FLUKA AND MCNPX

Russian Roulette - which reduces the computational time t but increases the uncer- • tainty σ. Basically the user assigns during geometry developing a relative importance to each geometry region/cell (the actual absolute value doesn’t matter), based on: expected ﬂuence attenuation with respect to other regions/cells. • probability of contribution to score by a particle entering that region/cell. • FLUKA-Surface Splitting

If a particle crosses a region boundary, coming from region of importance I1 (see Figure 4.2) and entering a region of higher importance I2 >I1: The particle is replaced on average by n = I2 identical particles with the same I1 • characteristics

The statistical weight of each daughter-particle is multiplied by I1 . • I2 An internal limit in FLUKA prevents excessive splitting if I1 is too large. I2

FLUKA-Russian Roulette Russian Roulette acts in the opposite direction: if a particle crosses a boundary from a region of importance I1 to one of lower importance I2

MCNPX-Surface Splitting Each cell is assigned with an importance, which is deﬁned utilizing an IMP card. A particle coming from a cell with low importance I1, as illustrated in Figure 4.2, passing the surface border into a high importance I cell will be splitted into n = I2 particles 2 I1 in case n is an integer. If n is not an integer but bigger than 1 the splitting is done probabilisticly, means the importance ratio n =integer I2 is kept, means with the I1 probability p = I2 1 , n +1particles are used and withh probabilityi 1 p, n particles. I1 − − E.g. if the ratio I2 =2.75 = n = integer I2 =2; p =2.75 2=0.75;1 p = 0.25 I1 ⇒ I1 − − = 75% of the cases splitting will take placeh withi the ration of 1:3 and to 25% with the ratio⇒ of 1:2. 4.3. DIFFERENCES BETWEEN FLUKA AND MCNPX 59

Figure 4.2: Surface splitting Biasing technique

MCNPX-Russian Roulette

On the contrary to the surface splitting technique when a particle passes from the higher important cell to the lower important cell - so that I2 < 1 - Russian Roulette is played and I1 the particle will be killed with the probability of 1 I2 or could survive with probability − I1 I2 . I1

Figure 4.3: Russion Roulette as Biasing Technique

The major diﬀerence between importance biasing in FLUKA and MCNPX is given due to 4 4 the fact, that FLUKA limits the importance factors to the range of (10− 10 ),which causes problems for deep penetration geometries. MCNPX on the other hand÷ limits the ratio of splitting - if the ratio I2 > 4 a warning is written to the output-ﬁle (PRINT table I1 120). 60 CHAPTER 4. COMPARISON OF FLUKA AND MCNPX

Tool Created by Functionality

FLUKA A. Ferrari et al. MC multi purpose code for particle transport

ALIFE A. Morsch Improves FLUKA input generation

ACAD Autodesk Construction/Design for mechanical constructions

Alifenumnew H.Vincke Recreation of implemented Region numbers to the ALIFE-FLUKA input

FLUKACAD H.Vincke Script creation of an FLUKA formatted input for ACAD script read-in

PLOTGEOM.store G.R.Stevenson creates a 2-dim slice of the FLUKA input

MIM2L1 M.J.Mueller Corrects FLUKA geometry inputs with more than 1000 regions

f2m V.Vlachoudis, M.J.Mueller Conversion of FLUKA-geometry into MCNPX geometry

MCNPX L. Water et al. MC multi purpose code for particle transport

MCNP-VISED4C2 Visual Editor Consultants Visual Editor for creation and modifying MCNP—ﬁ les

m2p M.J. Mueller Conversion of MCNPX mesh tally results into FLUKA-PAW comparable format

prepxyz S. Roesler Conversion of FLUKA - USRBIN results into PAW format

PAW CERN Physical Analysis Workstation - Fortran Lib to analyze data

VolVIS Chris Theis Visualization of Geometry and Volume data in 3D

BIN2XYZ M.J.Mueller ConverterofFLUKA-USRBINdatatovoxel-datarepresentation

XYZ2STL M.J.Mueller Converter of voxel- data to STL-data representation (readable in ParView)

ParaView Kitware - LANL Visualization of STL formatted data

Table 4.2: Geometry and Simulation conversion tools

4.4 Geometry conversion FLUKA MCNPX ⇒ In the standard FLUKA input the bodies are numbered and are referred to in the region definitions by these numbers. Many studies require the geometry to be definedingreat detail. The geometry for the SPS5 calculations described in that thesis consists of more then 500 bodies and 4500 regions. Developing and modifying geometries of this complexity in conventional way is a very time-consuming task. For example, if a body is added to the list at a certain position or is removed from the list all the bodies following the modified body-entry have to be renumbered, which means that also the numbers in the region definitions have to be changed correspondingly. Similarly if a region is split and the regions are renumbered sequentially then all subsequent assignments to the regions have to be altered. If one wants to use the same geometry created with FLUKA in combination with ALIFE for simulations with MCNPX a recreation is one way to handle it, but quite sumptuous - so the conversion of FLUKA-geometry-data into MCNPX-geometry-data is more adequate. In Figure 4.4 all data-flow, starting with geometry construction using FLUKA-ALIFE, via multiple conversions of both geometry and volume-results to the finally visualization is shown. A brief description of the used tools is quoted in Table 4.2. By using FLUKA & ALIFE and MCNPX & MCNP-Vised, both during basic-creation of the geometry and the post-creation-processes (like beamline adaptation or shielding upgrades), synergies were revealed that accelerate the process of geometry-development 4.4. GEOMETRY CONVERSION FLUKA MCNPX 61 ⇒

Figure 4.4: Data-flow to convert FLUKA-geometry data into MCNPX data-format and how to visualize Geometry together with simulation results.(Black-framed parts - FLUKA; Red-framed parts - MCNPX; Green-framed parts - Combined Visualization). 62 CHAPTER 4. COMPARISON OF FLUKA AND MCNPX and helps to find e.g. regions to modify, in a minimum on time and effort.

4.5 Simpliﬁed Geometry

One of the main problem in deep penetration transport of particles is given due to time- consuming calculations. Therefore biasing as described in the former section was utilized. By using importance biasing, appropriate biasing factors for each considered region/cell were necessary. These factors were investigated both for FLUKA and MCNPX with a simpliﬁed geometry (see Figure 4.5), due to the fact, that it was not possible to get any result with the original SPS5-geometry in a reasonable amount of time.

Figure 4.5: Simpliﬁed Geometry for testing importance factors and to compare results between FLUKA and MCNPX. The red blocks indicate the mesh-tallies/userbins used for the dose-rate calculations.

The simpliﬁed geometry consists of a simple beam-line (narrow green line) and sliced molasse and earth cylinders (cycle colored slices) above the proton loss point. For the FLUKA/MCNPX simulations the same loss-scenario setup as for the complex SPS5 geom- GeV etry were used - means 450 c protons get lost at a single point inside the beam-pipe wall, exact at the intersection point of beam-pipe with the superﬁcies surface of the parallel to the X-axes oriented cylinder-slices. Finally these tests leads to biasing factors, which were optimized on two points of view - on the fact that FLUKA limits the impor- 4 4 tance biasing factor to (10− 10 ), which is not a desired restriction - by simultaneously perpetuation of particle numbers,÷ which was the actual goal.

4.6 Results for the simpliﬁed Geometry

After renormalization to the given beam intensity of 1.2 1013 protons per second the ambient dose-rates for neutrons calculated with FLUKA (including· biasing) were visualized in Figure 4.6 - corresponding MCNPX ambient dose-rate are shown in Figure 4.7. 4.6. RESULTS FOR THE SIMPLIFIED GEOMETRY 63

Figure 4.6: FLUKA ambient dose-rates in [Sv/h] for neutrons for the simpliﬁed geometry including biasing techniques.

Figure 4.7: MCNPX ambient dose-rates in [Sv/h] for neutrons for the simpliﬁed geometry including biasing techniques.. 64 CHAPTER 4. COMPARISON OF FLUKA AND MCNPX

In comparison to the biased calculations for particle transport through 61 slices (deep penetration transport through 12m of earth) the unbiased ambient dose-rates are given in Figure 4.8.

Figure 4.8: MCNPX ambient dose-rates in [Sv/h] for neutrons for the simpliﬁed geometry without biasing techniques..

Deep penetration transport with importance biasing techniques both with FLUKA and MCNPX leads to comparable ambient dose-rates for neutrons inside the biasing zones. Major diﬀerences were revealed for areas close to the biasing zones - it seems, that the Russian roulette method, which should be the vice versa method to geometry splitting works diﬀerent in MCNPX compared with FLUKA (see also chapter 4.3.4). Chapter 5

Dose-rates for Experimental Point 5 of the SPS

5.1 Design-Re-Assessment

The ECX5 experimental area and ECA5 assembly area were constructed in the late 70s to house the UA1 experiment designed to study p p collisions. At that time there was a considerable body of knowledge concerning shield− design available from studies at proton accelerators with energies up to 30 GeV , but none had yet been performed at the Fermilab and SPS accelerators to confirm their design bases. Particle transport cascade codes were not capable of dealing with deep lateral shielding calculations at that time. However they were capable of determining the development of the high-energy (several hundred GeV ) cascades in their early stages and thus could give the extended source term that could be used with the lower energy experimental studies to form the basis of the ECX/ECA5 design. This design proved sufficient for many years of SPS operation with only one major incident, when a very small beam-pipe was left installed after a collider machine study, thus provoking large unexpected losses in ECX5. The shielding around the ECA5 area was designed for an SPS intensity of about 3 1012 protons per second. Future plans for the SPS now involve intensities of 1.2 1013 protons× per second, a factor of 4 higher than the original design intensity. In the late× seventies, the annual limit for the exposure of radiation workers was 50 mSv. At present the annual limit is 20 mSv,a factor of 2.5 lower. This has led to more strict limits to exposure at all levels and this has also to be seen in the light of increasing non-acceptance of unjustified and unoptimized radiation exposure. At the present time, particle transport cascade codes such as FLUKA, MCNPX and MARS are now capable of following cascades to large depths in shielding, and have been used for shield design purposes in all recent accelerator projects. It was thus considered that it was eminently opportune to re-assess the shielding around ECX5 using the best available modern techniques.

65 66 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS 5.2 Geometry overview

[68] The SPS (Super Proton Synchrotron) is one of the particle accelerator systems at CERN (see also chapter 1.2.2), the second largest in circumference. It is housed up to 100 m below surface (see Figure 1.4) between both CERN sites at Meyrin and at Prevessin.

Figure 5.1: SPS-Ring with six sextant subdivisions and indicated experimental points along the beamline.

A schematic plan of all SPS installations is shown in Figure 5.1. The straight section at point 5 is indicated as “Sextant 5” in the bottom right-hand corner of the plan. The complete SPS construction of experimental area is built below surface. A schematic representation of the underground areas is given in Figure 5.2. ECA5 is a cylindrical structure open at the ground level; the ECX5 cylinder is covered by a dome of approximately 5 m of earth, which was excavated during construction phase in 1978 (see Figure 5.3) and reﬁlled with earth afterwards. The two cylinders are linked by a complex liaison zone. A vertical section through these areas is indicated in Figure ??. The earth shielding berm (used for additional shielding above ground ﬂoor) is also indicated, as is the concrete shield between the ECX and ECA areas. A horizontal section through these areas at the 5.2. GEOMETRY OVERVIEW 67

Figure 5.2: Subsurface construction of SPS experimental point 5

Figure 5.3: Open construction-site of the ECX5-area in 1978 68 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS height of the SPS beam is given in Figure 5.5.

Figure 5.4: Vertical cut through the axes of ECA/ECX area

5.3 Materials

The chemical compositions of the concrete of the tunnel structures, that of the molasse rock surrounding the tunnels and that of the earth over the dome of ECX5 are given in table 5.1. The tunnels were ﬁlled with air at STP (Standard Temperature and Pressure).

5.4 Simulation Setup

5.4.1 FLUKA The calculations were carried out using the 2002 version of the Monte-Carlo cascade simulation program FLUKA, see references [[7], [5]] and the references they contain. In the present study only the hadron components of the particle cascade were simulated since they contribute to over 80% of the dose [24].

5.4.2 Coordinate system The geometry for the simulations was described in a right-handed orthogonal system with the origin of the vertical X-axis at beam height. The Z-axis was horizontal, aligned with the proton beam but pointing in the upstream direction. Its origin was in the median 5.4. SIMULATION SETUP 69

Figure 5.5: Horizontal cut at beam height through the ECA and ECX areas. All dimensions are in cm. Element Concrete Earth Molasse g g g ρ =2.35 cm3 ρ =2.16 cm3 ρ =2.38 cm3 Hydrogen 0.6 1.56 0.65 Carbon 3 3.14 4.94 Oxygen 50 55.78 49.175 Sodium 1 0.67 0.47 Magnesium 0.5 0.8 3.195 Aluminium 3 3.33 6.34 Silicon 20 20.39 19.67 Phosphorus 0.03 Potassium 1 0.78 1.745 Calcium 19.5 16.93 9.635 Titanium 0.07 Vanadium 0.01 Chromium 0.015 Manganese 0.095 Iron 1.4 1.32 3.895 Cobalt 0.005 Nickel 0.01 Zinc 0.01 Strontium 0.03 Barium 0.005 Table 5.1: Composition of Materials 70 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS plane of the ECX/ECA cylinders. The Y-axis was also horizontal, pointing away from the ECA area with its origin at the beam-line.

5.4.3 Detailed Geometry The geometry of the ECA and ECX areas of SPS Point 5 used for the simulations consisted of four main parts.

The firstpartwastheSPSTunnel.Acylinderof2.07 m radius represented this • with the floor at a distance of 1.08 m below the axis of the tunnel. The SPS beam was 1.2 m above the floor of the tunnel and 58 cm from the tunnel axis towards the outside of the SPS ring (positive Y-direction). There were enlargements to the tunnel on either side of the ECX5 experimental area. These enlargements were again cylindrical with a 3 m radius and the floor was 1.6 m below the beam and the axis centered on the beam in the vertical and Y-directions. The walls and floor of the SPS tunnel and the enlargements were assumed to be 30 cm thick.

The second main part is the ECX experimental area, which consists of a vertical • cylinder of 10 m inner radius. The vertical axis of the cylinder is 1 m from the beam axis in the negative Y-direction. The floor of the area is 5.3 m below beam height. The roof of the ECX area is a spherical dome of radius 12.4 m centered at a height of 8.48 m above the floor, giving a cylindrical wall height of 15.78 m. The thickness of the wall of the cylinder, the roof and the floor was taken to be 50 cm.Thereis a 5 m thick earth cover above the dome.

The third part of the geometry is the ECA assembly area, which consists of a second • verticalcylinderofinnerradius10 m, with its axis situated at a distance of 26.6 m fromtheECXaxis.Thiscylinderisopenatgroundlevelanditsﬂoor is 5.3 m below beam height and 26.6 m below ground level. The thickness of the wall of the cylinder and the ﬂoor was taken to be 50 cm.

The last part contains the liaison area between the ECA and ECX areas. At the • sides of the liaison area there are two pillars, separated by a distance of 13 m.Each pillar contains three vertical shafts of approximately square cross-section, leading from ground level to the floor of the ECA/ECX areas. There is a lift in the shaft on the ECA side of the upstream pillar for personnel access and a spiral staircase in the shaft on the ECA side of the downstream pillar. The other shafts are used to bring electrical, signal and water services from the surface to the underground areas. At a height of 12.6 m above the floor the two pillars are linked by two series of cross-galleries, separated by 5 m in the Y-direction, with the wall of the shaft between the two series of cross-galleries at a distance of 10.8 m from the ECX axis. This shaft and the open gap between the pillars are filled with shield blocks during SPS operation. The central part of fig (blue hatched) represents this shield. The substructure of the shielding is also indicated in Figure 5.6 which shows the biasing 5.4. SIMULATION SETUP 71

regions (narrow vertical slices) used for the calculations and which will be explained in a later section. The three main shielding layers of the wall each have a different height: the closer they get to the ECX area, the higher the shield, which gives a more uniform shielding layer as a function of azimuthal angle from the beam-line. The central shafts also contain an additional 1.6 1.6 m2 pillars of concrete blocks to just above beam height in order to provide extra× shielding. There are openings linking the vertical shafts in the side-pillars at several levels, and there are links between the side-pillars and the ECA/ECX areas at the floor level of the experimental areas and at 6.5m above the floor. The geometry extended from 10000 cm to +10000 cm in the and Y -directions and from 11000 cm to +11000− cm in the Z-direction. Within this, the concrete structures− were included in the volume from 680 cm to +2130 cm in X, 3820 cm to +960 cm in Y and 11000 cm to +11000− cm in Z. TheECX/ECAvolumeshavebeendividedinto9levelsasanaidtounderstanding− − the geometry of the different volumes, especially of the liaison areas. These are indicated in a transverse section through the liaison area in Figure 5.7 and Figure 5.8, also shown are the Horizontal sections through the different levels of the liaison.

These levels are described in more detail: Level — 1 The horizontal cut is taken at a depth of 2 m below ground level. There are cross-galleries on both the ECX and ECA side and it is possible to walk round the vertical shaft. The main shield does not extend up to this level but the top of the shaft is covered with an 80 cm thick layer of concrete blocks. Levels — 2, 3 and 4 The horizontal cuts are taken at depths of 3, 5 and 10 m below ground level. The cross-gallery on the ECA side covers all three levels whereas the cross- gallery on the ECX side covers only levels 2 and 3. There is only one layer of the main shield at level 2, but two layers at levels 3 and 4. Level — 5 The horizontal cut is taken at a depth of 12.5 m below ground level. There is a cross-gallery on the ECA side: now the ECX area encloses the volume where the other cross-gallery would have been. The upstream service shaft is linked with the ECX area via a square opening to allow access to the crane rails at the top of the ECX cylinder. Now the main shield has its full 3-layer thickness. Level — 6 The horizontal cut is taken just below the top of the opening between the ECA and ECX areas at a height of 11 m above the floor. Level — 7 The horizontal cut is taken at a height of 7 m above the floor. The service shafts have large openings towards the ECX and ECA areas to allow the passage of signal cables for the experiment. Level — 8 The horizontal cut is taken at a height of 4 m above the floor. It is identical to level 6 except for the presence of the extra shielding columns in the central service shafts. Level — 9 The horizontal cut is taken just above the floor. There are large openings towards the ECX and ECA areas to allow the passage of personnel and signal cables. 72 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Figure 5.6: Biasing slices for the liaison area (these pictures were generated with MCN- Pvised) 5.4. SIMULATION SETUP 73

Figure 5.7: Level subdivisions to organize the liasion area. 74 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Figure 5.8: Detailed wall arangements for each level of the sub-surface construction of the SPS5. 5.4. SIMULATION SETUP 75

5.4.4 Loss-Setup or the source term The proton beam-line in the ECX5 area is given in Figure 5.9 . In this Figure the • protons pass from left to right: to ease visualization the line has been cut into 4 parts. As can be seen in Figure 5.5 left side, the centers of the two quadrupoles QF51810 and QD51910 coincide with the junctions between the enlargements on either side of ECX5 and the SPS tunnel. After QF51810 there are four wiggler magnets (MDHW51832, MDHW51834, MDHW51835 and MDHW51837). The sim- pliﬁed cross-sections of these magnets used in the simulations can be seen in Figure 5.10. All coils have been assumed to be part of the steel yoke. However the pole faces and vacuum chambers inside the magnets have a shape and dimensions very close to the originals.

Figure 5.9: Beamline elements along the vacuum-pipe

Inside the first quadrupole QF51810, the cross-section of the vacuum chamber is • an elliptical cylinder (major diameter 15.6 cm,minordiameter4.23 cm, specified as CERN-SPS vacuum chamber profile F) with a wall-thickness of 0.2 cm.This section extends up to the first vacuum flange VF1.

The second section passes through the wiggler magnets up to vacuum flange VF11. • Known as the MBA-profile for SPS main-ring bending magnets, this slightly convex rectangular profile was approximated by a simple rectangular profile, again with a 76 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Figure 5.10: Cross-sections of quadrupoles: 1st row quadrupoles: left side QF518, Right side QD519; 2nd row Wiggler: MDHW. All dimensions are in cm.

wall-thickness of 0.2 cm. The outer dimensions were 15.6 cm and 3.93 cm. Vacuum ﬂanges VF2 to VF10 separate the wiggler magnets and at one time allowed extra diagnostic equipment and vacuum pumps to be installed in the beam-line.

The third section, the longest, extends to vacuum flange VF18. The chamber has • the profile of that installed in the SPS main-ring MBB bending magnets. The outer dimensions are 13.2 cm 5.23 cm and the wall thickness is 0.15 cm.Againthere are several extra vacuum×flanges, which remain from previous installations.

The ﬁnal vacuum chamber proﬁle, which also passes through quadrupole QD51910, • is a simple circular cylinder with an inner diameter of 8.3 cm and a wall thickness of 0.15 cm.

The flanges connecting the different parts of the vacuum chamber are implemented • in the FLUKA geometry as simple cylinders with an outer diameter of 12 cm and an inner cutout appropriate to the larger of the two beam-pipes. The longitudinal dimension of each flange is taken to be 5 cm.

5.4.5 Beam and Particle transport properties The maximum number of protons per second circulating in the SPS is taken to be identical to that used in [23] for the intensity in the injection lines to CNGS and the LHC, which 5.4. SIMULATION SETUP 77

Position Coordinate Description Device-Name X [cm] Y [cm] Z [cm] 1 Upstream quadrupole QF5180 0 -7.7 1740 2 Vacuum flange VF2 0 -7.7 1403 3 First wiggler MDHW51832 0 -7.7 1340 4 Second wiggler MDHW51834 0 -7.7 1200 5 Third wiggler MDHW51835 0 -7.7 1120 6 Fourth wiggler MDHW51837 0 -7.7 980 7 Vacuum flange VF11 0 -6.5 895 8 Vacuum flange VF13 0 -6.5 567 9 Vacuum flange VF15 0 -6.5 53 10 Vacuum flange VF18 0 -4.2 -1175 11 Downstream quadrupole QD5190 0 -4.2 -1740 Table 5.2: Entry points for primary protons in the FLUKA simulations was based on the work reported in [59] and [16]. This maximum intensity is 1.2 1013 GeV × protons per second at 450 c . The lower thresholds for particle transport were set to 10 MeV for all hadrons except neutrons which were followed down to thermal energies.

Loss Points

GeV Separate simulations were performed with the 450 c protons starting at eleven diﬀerent positions (see table 5.2) along the beam-line. These starting points were chosen a priori to give maximum dose rates in critical areas. They were set at the entry of several beam-line elements and at certain vacuum ﬂanges, in the vacuum chamber walls on the negative Y -side (closer to ECA area). The elements chosen are listed in table .

4 Normal beam losses are assumed to be 10− of the maximum beam intensity.

Biasing

In order to enhance the statistical signiﬁcance of the results in regions of high attenuation, use was made of region-importance biasing (see [13]). As the depth in the shield increased, the region-importances were increased every given distance l by a factor Fcomp 78 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Material ρ λ l Fcomp g g cm3 cm2 [cm] — Concrete 2.35 96.115 20 1.6307 Molasse 2.4 96.216 20 1.6449 Earth 2.4 94.224 20 1.6643 Table 5.3: Biasing factors

1 Fcomp = l e− X0

Fcomp Compensation-factor — l length of shielding cm (5.1)

g λ λ nuclear interaction length cm2 X0 X0 = ρ g cm ρ density cm3

The values for the nuclear interaction length were taken from [26] pages 80-81 and from the FLUKA 2002 output-data. Using formula 5.1 leads to factors for the shield materials as given in table 5.3. These factors compensate approximately the attenuation in each material, keeping the particle-history population roughly constant throughout the diﬀerent regions. To reduce computing-time and to reduce ﬂuctuations also weight-windows biasing technique was implemented.

5.4.6 Dose-equivalent During the simulation, the track-length of neutrons, protons and pions was scored in a number of Cartesian bin structures. When divided by the volume of a scoring bin this gives the average fluence in that bin. The track-length was weighted during the scoring procedure by energy- and particle type-dependent conversion factors using the EWTMP option in FLUKA as implemented by Roesler [79] to give effective dose directly. These conversion factors are based on fits to the data of Pelliccioni et al. [[57], [71]] and the concept of the WORST value of effective dose for any body orientation as described in [22] and in chapter 3.2.4. Six bin structures were used to cover (1) the beam-line environment, (2) and (3) the shield, liaison and ECA areas (because of its size, this latter area was separated in two bin-structures), (4) and (5) the coarse situation above the ground-level (also two bin-structures) and (6) one structure which covers the surface situation inside the BHA5-hall. Details are given in table 5.4. 5.4. SIMULATION SETUP 79

Bin Structure Axis Min. Max. Number Binwidth

[cm] [cm] of bins [cm]

(1) Beam environment x -800 1200 80 25

y -500 1000 60 25

z -1500 1500 120 25

(2) Shield, liaison and ECA areas - lower part x -800 1200 100 20

y -2500 -500 100 20

z -1100 1100 110 20

(3) Shield, liaison and ECA areas - upper part x 1100 2900 90 20

y -2500 -500 100 20

z -1100 1100 110 20

(4) Above ground - level ECA x 2100 2900 16 50

y -3900 2100 120 50

z -11000 6500 350 50

(5) Above ground - level ECX x 2100 2900 16 50

y 2000 7200 104 50

z -11000 6500 350 50

(6) Surface (First two meters above ground - level) x 2130 2330 10 20

y -3900 1000 245 20

z -2000 2000 200 20

Table 5.4: Bin Structures 80 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Position Description Coordinates [cm] xmin xmax Level-0 Surface 2130 2330 Level-1 Upper galleries 1830 2080 Level-2 Second gallery level 1700 1820 Level-3 Third gallery level 1430 1680 Level-4 Fourth gallery level 1110 1420 Level-5 Crane-access gallery level 780 1100 Level-6 Upper most shield level 450 770 Level-7 Upper cable-duct level 130 440 Level-8 Middle shield level -270 120 Level-9 ECA ﬂoor level -630 -280

Table 5.5: Vertical extent of Critical Volumes for the ECX/ECA5 zones. simulations

Position Description Coordinates [cm] ymin ymax zmin zmax CV1 Centre-front of shield on ECX side -1170 -970 -100 100 CV2 Centre-backofshieldonECAside -1865 -1665 -100 100 CV3 Downstream entrance to liaison area, ECX side -1200 -950 -1000 -710 CV4 Upstream entrance to liaison area, ECX side -1200 -950 710 1000 CV5 Middle of downstream liaison area -1580 -1260 -1000 -865 CV6 Middle of upstream liaison area -1580 -1260 865 1000 CV7 Downstream entrance to liaison area, ECA side -1910 -1630 -1000 -705 CV8 Upstream entrance to liaison area, ECA side -1910 -1630 820 1000 CV9 Centre of bridge gallery on ECA side -1940 -1735 -100 100 CV10 Centre of bridge gallery on ECX side -1110 -940 -100 100

Table 5.6: Horizontal extent of Critical Volumes for the ECX/ECA5 zones. simulations

5.5 Results

5.5.1 General In order to assist in the interpretation of the large quantities of data contained in the USRBIN files, certain Critical Volumes (CV) were defined, corresponding to positions close to the shield where persons could have access during beam operation. These volumes were approximately 2 2 2 m3; the exact vertical and horizontal extents are listed in Tables 5.5 and 5.6. They× are× indicated schematically in Figure 5.11. Critical Volumes at the front and back of the shield (CV1 and CV2) and in the centre of the bridge galleries (CV9 and CV10) are defined at all levels. However it is evident that CV1andCV2applyonlytoLevels6to9,whileCV9andCV10applytoLevels0to5. The dose rates averaged over these volumes for each of the loss positions are listed in the 5.5. RESULTS 81

Figure 5.11: Horizontal section through the main shield indicating the positions of the Critical Volumes 82 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Appendix A. A summary for speciﬁc volumes is given in the rest of this section.

5.5.2 Main-shielding Hadron dose rates on the inside and outside of the main shield between the ECX and ECA areas are shown in Figure 5.12 and 5.13 as a function of the position of the Entry Point chosen for the proton loss. Data are given for each of Levels 6 to 9. Figure 5.12 shows that the dose rate on the ECX side of the shield is essentially independent of Entry Point and Level and approaches 1000 Sv/h. The situation is less clear in Figure 5.13 for the ECA side of the shield due to poor statistics, but one can conclude that the dose rate for Level—9 (which is accessible) is safely below the critical level of 100 mSv/h. The dose rate approaches this critical level at beam height for proton entry points at the ﬁrst and second wiggler magnets (EPs 3 and 4).

Figure 5.12: Hadron dose rates as a function of Entry Point of the proton loss for diﬀerent Levels, showing data for Critical Volume 1 on the ECX side of the main shield

5.5.3 Vertical Shafts The vertical shafts on the ECA side in the liaison areas are accessible at all times during beam operation. Figure 5.14 and 5.15 show hadron dose rates at the diﬀerent levels for the upstream shaft containing the lift (Critical Volume 8) and the downstream shaft containing the spiral staircase (Critical Volume 7). A selected number of proton entry points are shown. For the lift-shaft (Figure 5.14) ), the highest dose rate occurs at Levels 5 and 6 for Entry Points 3 to 7, and this maximum value is approximately a factor of three 5.5. RESULTS 83

Figure 5.13: Hadron dose rates as a function of Entry Point of the proton loss for diﬀerent Level, showing data for Critical Volume 2 on the ECA side of the main shield. higher than the critical value of 100 mSv/h. In the shaft containing the spiral staircase (Figure 5.15) ), dose rates exceed the critical value by about a factor of 3—5 for almost all proton entry points in the lower levels 6—9.

5.5.4 Cross-galleries in the shield bridge The cross-galleries in the ﬁxed shielding bridge on the ECA side are also accessible during beam operation. The hadron dose rates in some of these galleries in Critical Volume 9 is given in Figure 5.16 as a function the Entry Point of the proton loss. Dose rates are signiﬁcantly below the critical 100 mSv/h for all levels and loss positions.

5.5.5 Surface Levels Hadron dose rates at the Critical Volumes in the upper two levels for different proton Entry Points are shown in Figure 5.17 and 5.18 The data for the surface level (Level—0) in Figure 5.17 indicate that, apart from the top of the staircase, Critical Volume 7, dose rates are significantly below the 100 mSv/h value. This is not the case for Level—1 (Figure 5.18)) which is the first underground level, where dose rates exceed 100 mSv/h in many critical volumes and for many loss conditions. 84 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Figure 5.14: Hadron dose rates as a function of Level Number for the accessible shafts in the liaison areas, showing data for the lift-shaft, Critical Volume 8, in the upstream liaison area on the ECA side of the main shield.

Figure 5.15: Hadron dose rates as a function of Level Number for the accessible shafts in the liaison areas, showing data for shaft containing the spiral staircase, Critical Volume 7, in the downstream liaison area on the ECA side of the main shield. 5.5. RESULTS 85

Figure 5.16: Hadron dose rates as a function of the Entry Point of the proton loss for diﬀerent Levels in the cross-galleries inside the shield bridge on the ECA side (Critical Volume 9).

Figure 5.17: Hadron dose rates at the Critical Volumes in Level—0 for diﬀerent proton Entry Points. 86 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Figure 5.18: Hadron dose rates at the Critical Volumes in Level—1 for diﬀerent proton Entry Points.

5.5.6 Dose rate contours It is not possible in this paper to provide contour plots of dose rate for each of the 10 levels and for each of the eleven proton loss points. However, it was thought worth-while to provide such plots for the loss position where most of the highest dose rates were recorded in accessible areas. This position is EP4, the second wiggler magnet. Contour plots for Levels—0 to 9 are given in Figure 5.19 to Figure 17. Level—0,1: (Figure 5.19) This plots confirms that the main source of radiation reaching the surface is the hole in the concrete floor of the building provided for the spiral staircase. Level—2,3 : (Figure 5.20) No outstanding features. Level—4 : (Figure 5.21a) At this level, the plot shows that the main source of radiation in the accessible areas is not the component coming through the main shield but is that penetrating through the galleries of the liaison areas. Level—5 : (Figure 5.21b) A weak point in the shielding of ECA5 at the junction with the vertical shaft containing the staircase is clearly visible. Level—6 : (Figure 5.22a) There is a gradient of more than a factor of three in the value of the dose rate in the staircase shaft at this level. This comes from radiation streaming through the straight pathway in the liaison area. This is not so obvious in the lift shaft since for the position chosen for the loss point, the entry to the upstream liaison area is better shielded, Level—7 : (Figure 5.22b) Similar comments as for Level—6. Level—8 : (Figure 5.23a) The greater efficiency of the baffle walls in the upstream liaison 5.5. RESULTS 87

Figure 5.19: a) Surface Level—0: b) First underground Level—1. All dimensions are in cm.

Figure 5.20: a) Level—2: b) Level—3. All dimensions are in cm. 88 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS

Figure 5.21: Contour Plots of Dose Rates due to proton losses on the second wiggler magnet (EP4). a) Level—4: b) Level—5. All dimensions are in cm.

Figure 5.22: Contour Plots of Dose Rates due to proton losses on the second wiggler magnet (EP4). a) Level—6: b) Level—6. All dimensions are in cm. 5.5. RESULTS 89 area (which are positioned diﬀerently with respect to a column of concrete shielding in the two liaison areas) is evident.

Figure 5.23: Contour Plots of Dose Rates due to proton losses on the second wiggler magnet (EP4). a) Level—8: b) Level—9. All dimensions are in cm.

Level—9 : (Figure 5.23b) Similar comments as for Level—8. 90 CHAPTER 5. DOSE-RATES FOR EXPERIMENTAL POINT 5 OF THE SPS Chapter 6 Particle Fluences for SPS5

The Dose-rate, calculated in former chapter is just one radiation protection quantity, which helps to judge the radiation protection conditions at each level of the SPS5- construction. In order to get more insight it is of immense importance to know the specific particle-spectra, too. How big is the energy-resolved fraction of a certain kind of particle in a defined region of the geometry? These collected simulation results are a well founded basis, if one wants to measure anywhere inside the liaison-area. Therefore the particle-fluence-spectras promotes the selection of finding the right detection system (ionization chamber, response functions. . . .).

6.1 Chicane, Spiral-Staircase and Elevator shaft

Chicanes, spiral-staircase and elevator shaft are as described in former chapters partially accessible and located on each side of the main shielding blocks, which separate the ECX from the currently supervised accessible ECA area. In order to ﬁnd an orientation system inside the geometry the construction were separated in an upstream and a downstream part. In Figure 6.1 one can see a cut-through the geometry model at approximately beam height. The passage ways and the entry on the ECX-upstream side is shown. In accordance with the coordinate cross of Figure 6.1 the beam is anti-parallel to the Z-axes. Bottom-up direction is in alignment to the X-axes and the main-shielding is oriented perpendicular to the Y-axes.

6.2 FLUKA - Detector Settings

Due to the complex and three-dimensional geometry at SPS5 approximately 50 energy- dependant boundary crossing ﬂuence detectors (USRBDXs) for selected kinds of particles were implemented. These detectors both parallel to the Y-axes (from ECX to ECA) and the X-axes (from bottom-up to ground-level) were set to acquire how particles evolve throughout the SPS5 subsurface construction.

91 92 CHAPTER 6. PARTICLE FLUENCES FOR SPS5

Figure 6.1: Cut-through the SPS5-subsurface construction at beam-height

In order to get an estimation for the particle-ﬂuence-spectra conditions inside each accessible area, which is given for the ECA sided spiral-staircase and the elevator-shaft also 17 volume detectors (USRTRACKs) were installed.

6.2.1 Upwards streaming particles inside the spiral-staircase and the elevator shaft For the upwards streaming particles, boundary crossing detectors (USRBDX) were im- 14 plemented for two different energy ranges - one from 1.10− GeV (the lowest value for reasonable neutron library transport treatment) to 0.019 GeV (the uppermost limit of the built in library transport) and from 0.02 to 450 GeV the highest possibly given particle energy, which coincides with the primary proton-beam energy. These energy-ranges were used for protons [FLUKA ID=1], neutrons [FLUKA ID=8], pions [FLUKA ID=209], muons [FLUKA ID=212] and for all-transportable particles [FLUKA ID=201]. For better orientation inside the complex SPS5-FLUKA geometry the input was converted into MCNPX format (see chapter 4.4) to accelerate post-processing. As a result of those procedures the region numbers as shown in Figure 6.2 were reproduced. The positions of each detector inside the spiral-staircase and the elevator-shaft are indicated (green rectangulars between each levels). The 1st digit of the number besides each green rectangular indicates the “coming-from”-level, the 2nd one the “going-to”-level. The following excerpt of the FLUKA input-file reveals the boundary-detector (USRBDX) concept for the spiral-staircase — how particles pass from the floor of the 7th level into the air of the 7th level were scored. In order to renormalize the particle fluence the boundary- 6.2. FLUKA - DETECTOR SETTINGS 93

Figure 6.2: Region identiﬁers and spatial detector settings (green rectangulars) inside the spiral-staircase and the elevator shaft of the SPS5 subsurface construction 94 CHAPTER 6. PARTICLE FLUENCES FOR SPS5

Detector Spiral — Staircase Elevator-Shaft [cm2] [cm2] Detector-Level 87 57300 36600 Detector-Level 76 54800 41100 Detector-Level 65 48400 36600 Detector-Level 54 51900 46225 Detector-Level 43 57300 36600 Detector-Level 21 54800 36600 Table 6.1: Boundary-Detector areas for normalizing the particle-fluences crossing area in [cm2] has to be defined (see table 6.2) — in the excerpt it is the last but one value (WHAT(5) in FLUKA jargon) in the 1st line of each USRBDX card. ************************************************************** ********************** USRBDX ******************************** ************************************************************** * detectors showing the energy dependant particle fluences *** ********************************** ********** Spiral-Stairscase ***** ********************************** **** spiral-staircase 87 boundary-crossing **** USRBDX -1.0 1.0 50.0 2650.0 2652.0 5.730E+04prot2652 USRBDX 450.0 0.02 100.0 & USRBDX -1.0 1.0 50.0 2650.0 2652.0 5.730E+04prot2652 USRBDX 0.0196 1.0E-14 100.0 & USRBDX -1.0 8.0 50.0 2650.0 2652.0 5.730E+04neut2652 USRBDX 450.0 0.02 100.0 & USRBDX -1.0 8.0 50.0 2650.0 2652.0 5.730E+04neut2652 USRBDX 0.0196 1.0E-14 100.0 & USRBDX -1.0 209.0 50.0 2650.0 2652.0 5.730E+04pion2652 USRBDX 450.0 0.02 100.0 & USRBDX -1.0 209.0 50.0 2650.0 2652.0 5.730E+04pion2652 USRBDX 0.0196 1.0E-14 100.0 & USRBDX -1.0 212.0 50.0 2650.0 2652.0 5.730E+04muon2652 USRBDX 450.0 0.02 100.0 & USRBDX -1.0 212.0 50.0 2650.0 2652.0 5.730E+04muon2652 USRBDX 0.0196 1.0E-14 100.0 & USRBDX -1.0 201.0 50.0 2650.0 2652.0 5.730E+04ges2652 USRBDX 450.0 0.02 100.0 & USRBDX -1.0 201.0 50.0 2650.0 2652.0 5.730E+04ges2652 USRBDX 0.0196 1.0E-14 100.0 & 6.2. FLUKA - DETECTOR SETTINGS 95

It is appropriate to mention that the USRBDX-detector is a boundary crossing estimator — hence the results are double differential, distributed fluences in energy and solid angle. In order to obtain a fluence spectrum (integral binned results) with no angular distribution the result of each bin must be multiplied by the width of the bin, which is the energy- intervall and by 2π for the one-way binning as used for this study.

6.2.2 Particles inside each level — ECA, ECX entries and MID- position In order to detect particles passing horizontally in Y-direction through all the chichane levels, six selected boundary detectors each level were deﬁned. In Figure 6.3, a schematic view of these detector arrangements as installed in each level is shown. Up- and downstream sided, the detectors of each level are indicated as ECX-, MID- and ECA-detector, which corresponds to the general position description.

Figure 6.3: left) Vertical separation concept of the SPS5 liaison geometry in ECA, MID and ECA parts and the horizontal level organisation. right) Arrangement of the boundary detectors (red/blue ﬁlled rectangulars) on each liaison-level - one can see three detectors on the upstream area (red-elliptical bordered) and three on the downstream area (blue- elliptical bordered) — from left to right the ECA, MID, ECX order is given.

Basically, boundaries are inﬁnitesimally narrow — to visualize them, as it is given in Figure 96 CHAPTER 6. PARTICLE FLUENCES FOR SPS5

Detector Upstream Downstream ECX MID ECA ECX MID ECA [cm2] [cm2] [cm2] [cm2] [cm2] [cm2] Level 9 5.112 104 3.096 104 1.062 105 5.112 104 3.096 104 1.062 105 × × × × × × Level 7 4.402 104 3.565 104 2.790 104 4.402 104 2.666 104 9.145 104 × × × × × × Level 6 4.544 104 3.680 104 9.440 104 4.544 104 2.752 104 9.440 104 × × × × × × Level 5 4.544 104 3.680 104 9.440 104 4.544 104 2.752 104 9.440 104 × × × × × × Level 4 4.402 104 3.565 104 9.145 104 4.402 104 2.666 104 9.145 104 × × × × × × Level 3 3.550 104 4.485 104 7.375 104 3.550 104 2.150 104 7.375 104 × × × × × × Level 1 3.550 104 2.875 104 7.375 104 3.550 104 2.150 104 7.375 104 × × × × × × Table 6.2: Boundary-Detector areas for normalizing the particle-ﬂuences

6.3, boundaries are widened up to a suitable size of a rectangular, which each represents one detector. The areas for renormalization are given in Table 6.2.

6.2.3 Volume-detectors for spiral-staircase and elevator-shaft The boundary crossing spectras for the spiral-staircase and the elevator shaft, as estimated with the USRBDX-detector only score the particles coming up through the floor of each level, which is enough for the physical point of view. With respect to areas, where people may have access not only upcoming particles are of interest, the more practical point of view needs a kind of estimation for the spectra in realistic volumes, where people are moving. Therefore volume-detectors were used to estimate the fluence. These FLUKA supported USRTRACKs sum up the track-lengths of the selected particles in the specified regions. Dividing this obtained value by the volume (WHAT(5) in USRTRACK) of the region leads to the estimated fluence in the region. Utilized volumes are shown in Figure 6.4 (dark-blue rectangulars together with the volume indication) and are defined in Table 6.3 with the same purpose as before for the boundary-crossing-detectors - to renormalize the fluence to the correspondent volume.

6.3 Results of the simulation

Both, the boundary-crossing-USRBDX and the volume-USRTRACK results are quoted with error bars only for the all-particle spectra. All calculated particle-spectra are shown at once for one region or volume respectively. In the following subsections the before mentioned spectras will be shown. Starting with spectra results for the elevator-shaft and the spiral-staircase — on the one hand boundary-crossing-spectra in chapter 6.3.1 and 6.3.2 for the upwards streaming particles andontheotherhandvolume-detectorresults in chapter 6.3.3 and 6.3.4. Chapter 6.3.5 shows the spectra for the crossing galleries in the 5th an the 1st level respectively. Finally the boundary-crossing-spectra for each level are shown in Appendix C. 6.3. RESULTS OF THE SIMULATION 97

Figure 6.4: Volume detectors for estimating the energy-particle spectra in the spiral- staircase and the elevator-shaft

Detector Spiral — Staircase Elevator — Shaft [cm3] [cm3] Level 9 53.100 106 18.036 106 Level 8 × 14.274 × 106 × Level 7 21.948 106 12.741 106 × × Level 6 22.656 106 11.712 106 × × Level 5 22.656 106 14.920 106 × × Level 4 21.948 106 11.346 106 × × Level 3 27.612 106 9.150 106 × × Level 1 21.240 106 5.142 106 × × Crossing — Level 5 61.750 106 × Crossing — Level 1 72.800 106 × Table 6.3: Volume-Detector volumes for normalizing the particle-ﬂuences 98 CHAPTER 6. PARTICLE FLUENCES FOR SPS5

6.3.1 Boundary-crossing energy particle spectra for upwards streaming particles inside the elevator shaft 6.3. RESULTS OF THE SIMULATION 99 100 CHAPTER 6. PARTICLE FLUENCES FOR SPS5 6.3. RESULTS OF THE SIMULATION 101

6.3.2 Boundary-crossing energy particle spectra for upwards streaming particles inside the spiral-staircase 102 CHAPTER 6. PARTICLE FLUENCES FOR SPS5 6.3. RESULTS OF THE SIMULATION 103 104 CHAPTER 6. PARTICLE FLUENCES FOR SPS5

6.3.3 Volume passing energy particle spectra for particles inside the elevator-shaft 6.3. RESULTS OF THE SIMULATION 105 106 CHAPTER 6. PARTICLE FLUENCES FOR SPS5 6.3. RESULTS OF THE SIMULATION 107 108 CHAPTER 6. PARTICLE FLUENCES FOR SPS5

6.3.4 Volume passing energy particle spectra for particles inside the spiral-staircase 6.3. RESULTS OF THE SIMULATION 109 110 CHAPTER 6. PARTICLE FLUENCES FOR SPS5 6.3. RESULTS OF THE SIMULATION 111 112 CHAPTER 6. PARTICLE FLUENCES FOR SPS5

6.3.5 Volume passing energy particle spectra for particles inside the ECA sides gallery crossings Chapter 7

Conclusion

7.1 Comparison of FLUKA with MCNPX

In order to compare FLUKA with MCNPX and to optimize importance biasing factors for the SPS5 geometry - pre-studies with a simplifiedgeometry(seeFigure4.5)werecarried out. The deep penetrating particle propagation in different materials (see equation 5.1) was 13 1 GeV investigated by using the original SPS5 beam setup (1.2 10 s protons with 450 c each, lost in a single point along the beamline). These investigations,× primarily calculated with FLUKA had revealed the most appropriate importance biasing factors (see Table 5.3) to compensate the attenuation of particles in order to keep the particle-history population roughly constant. Due to incompatibilites of using the FLUKA geometry directly as MCNPX geometry a couple of tools (illustrated in 4.4) developed to automize the geometry conversion from FLUKA to MCNPX, opened the possibility to compare doserate calculations of both codes.Provided that the corresponding physics and biasing setup was given, two superposed restrictions have to be assumed: 1. MCNPX is only able to handle scoring of particle track lengths into a mesh-grid for one kind of particle at a time. Considering that fact and due to the reason that neutrons are the most commanding particles in deep penetration applications, the particle track length scoring was reduced just for neutrons. 2. The neutron-fluences (total particle track length per unit volume) were only convoluted with ICRP74 fluence-to-doserate conversion factors, which was given by fact, tht the ICRP74 conversion factors were available for both codes. Using these two restrictions for the investigations lead finally to the resulting contour plots (4.6, 4.7 and 4.8). As one can see, the dose-rates calculated with biased-FLUKA and biased-MCNPX respectively, do correlate quite well as long as the point of interest is inside the biased zones. This correlation vanishes completely for the MCNPX non-biased zone situated far distant to the beamline around the multiple sliced biased zones (see Figure 4.5). The reason for that? - MCNPX limitates the ratios of importance biasing

113 114 CHAPTER 7. CONCLUSION factors in order to avoid an enormous growing of particle population, when particles pass from a much higher importance biased zone to an e.g. unity importance biased zone as it is obviously given for the upper cylinder part of the simpliﬁed geometry.

7.2 SPS5-simulations

1. The main shield which is made of concrete blocks and is 4.8 m thick satisfactorily meets the current design limits even at the highest intensities presently planned for the SPS. 2. Dose rates calculated for the lift-shaft and the shaft for the spiral staircase on the ECA side exceed the design limits by more than a factor of three and in certain cases by afactorofthirty. 3. Dose-rates in the first underground galleries (Level—1) can, under certain circumstances exceed the design limits. Even at the design stage of the ECX/ECA5 areas certain measures were envisaged to improve the shielding efficiency of the liaison areas, if needed. These included increasing the height of the columns of concrete blocks in the central shafts of the liaison areas and installing columns of concrete blocks on the ECX side alongside the main shield and liaison areas. This measure was in fact implemented on the upstream side at the start of operations but was abandoned due to the time necessary for mounting and dismounting during the frequent changes from p p to fixed-target operation of the SPS. Further measures could be envisaged, such as− installing shielding in front of the openings to the liaison areas on the ECX side. Further studies are required to study these various options. Until improvements are mSv implemented it is recommended that in order to meet the design guideline of 100 h for a maximum credible loss, beam intensities in the SPS should not exceed 1% of the maximum intensity considered here of 1.2 1013 protons per second. This gives 1.2 1011 protons per second or 2 1012 protons per× 16 second cycle. If this cannot be done× then access to the whole of the× underground ECA area should be forbidden. mSv 4 The maximum loss criterion implies dose rates of 10 h for fractional losses of 10− . This is the operational design limit for a Simple Controlled Radiation Area. To meet the design limit for a Supervised Area, which is an order of magnitude lower, losses must also mSv be correspondingly lower. Since on the surface level (Level—0) the 100 h level condition for a full loss is barely met under certain circumstances, this means that there could be problems in classifying the surface hall BB5 as a Supervised Area unless shielding is improved. No excessive dose rates have been seen in ECA5 in the recent past, but is must also be admitted that regular monitoring of radiation levels is not ensured in the most critical region of the staircase. In order to maintain a safe condition and ensure that levels stay within the appropriate limits, it would be advisable for abnormal operation of the SPS to be detected and prevented by a beam-loss monitor system. Bibliography

[1] A., Fasso. Personal Discussions, Units of Dose Function Card of MCNPX . LANL, New Mexico / USA: [email protected], 2003. [2] A. Boudard, J.C. David, L. Donadille S. Leray C. Volant J. Cugnon. Compar- isonofINCL4withExperiments. 91191 Gif-sur-Yvette Cedex / France, B-4000 Start Tilman, Liège 1 / Belgium: DAPNIA/SPhN, CEA/Saclay, University of Liège, Physics Department B5. [3] A. Fasso, A. Ferrari, J. Ranft and P.R. Sala. FLUKA: performances and applications in the intermediate energy range. Paris / France: Proc. (p. 287) of an AEN/NEA Specialists’ Meeting on Shielding Aspects of Accelerators, Targets and Irradiation Facilities, Arlington, Texas, 28-29 April 1994,OECD Documents, 1995. [4]A.Fasso,A.Ferrari,J.RanftandP.R.Sala.New developments in FLUKA modelling hadronic and EM interactions. KEK, Tsukuba / Japan: Proc. 3rd Workshop on Simulating Accelerator Radiation Environments, 7-9 May 1997 Ed. H. Hirayama, KEK Proceedings 97-5, p. 32-43, 1997. [5]A.Fasso,A.Ferrari,J.RanftandP.R.Sala. FLUKA: Status and Prospective for Hadronic Applications, invited talk in the Proceedings of the Monte Carlo 2000 Con- ference - October 23-26 2000, p955-960 . Portugal / Lisbon: A. Kling, F. Barao, M. Nakagawa, L. Tavora, P. Vaz eds., Springer-Verlag Berlin, 2001. [6]A.Fasso,A.Ferrari,J.RanftandP.R.Sala. FLUKA Manual. INFN - Milano / Italy: A. Fasso, A. Ferrari, J. Ranft and P.R. Sala, 2002. [7] A. Fasso, A. Ferrari, P.R. Sala. Electron-photon transport in FLUKA: status, invited talk in the Proceedings of the Monte Carlo 2000 Conference - October 23-26 2000, p159-164 . Portugal / Lisbon: A. Kling, F. Barao, M. Nakagawa, L. Tavora, P. Vaz eds., Springer-Verlag Berlin, 2001. [8] A. Ferrari, P.R. Sala, J. Ranft and S. Roesler. Cascade particles, nuclear evaporation, and residual nuclei in high energy hadron-nucleus interactions. Z. Phys. C70, p413, 1996. [9] A. Ferrari, P.R. Sala, J. Ranft and S. Roesler. The production of residual nuclei in peripheral high energy nucleus—nucleus interactions. Z. Phys. C71, p.75, 1996.

115 116 BIBLIOGRAPHY

[10] A. Ferrari, P.R. Sala. A new model for hadronic interactions at intermediate energies for the FLUKA code. Ed. by P. Dragovitsch, S.L. Linn, M. Burbank, World Scientific, Singapore: Proc. of the MC93 (p. 277-288) International Conference (22-26 February 1993) in Tallahassee, Florida on Monte Carlo Simulation in High Energy and Nuclear Physics, 1994. [11] A. Ferrari, P.R. Sala. The Physics of High Energy Reactions, in Proceedings of the Workshop on Nuclear Reaction Data and Nuclear Reactors Physics, Design and Safety, 15 April-17 May 1996, , p. 424 . International Centre for Theoretical Physics, Miramare-Trieste / Italy: edited by A. Gandini, G. Reffo-WorldScientific, 1998. [12] A. Ferrari, P.R. Sala, R. Guaraldi and F. Padoani. An improved multiple scattering model for charged particle transport. Int. Conf. on Radiation Physics, Dubrovnik / Slovenia: Nucl. Instr. Meth. in Phys. Res. B71,(1992) p.412-426, 1991. [13] A. Ferrari, M. Huhtinen, S. Rollet and G.R. Stevenson. Procedures used during the verification of shielding and access-ways at CERNŠs Large Hadron Collider (LHC) using the FLUKA code,in Proceedings of the American Nuclear SocietyŠs 1997 Win- ter Meeting on Nuclear Applications of Accelerator Technology, 1997 p. 463 .USA/ Albuquerque, New Mexico: CERN Preprint CERN/TIS-RP/97-14/CF, 1997. [14] A.B., Migdal. Bremsstrahlung and pair production in condensed media at high energies. Phys. Rev. 103, 1811, 1956. [15] A.B., Migdal. Bremsstrahlung and pair production at high energies in condensed media. Zh. Exp. Teor. Fiz. SSSR 32, 633 (1957) Sov. Phys. JETP 5, 527, 1957. [16] E., Weisse. Minutes of the 50th PLC meeting held on 21st April 1999 . Switzerland / CERN-Geneva: CERN, 1999. [17] E. Cuccoli, A. Ferrari, G.C. Panini. A group library from JEF 1.1 for flux calculations in the LHC machine detectors. JEF-DOC-340 (91), 1991. [18] F., Bloch. Bremsvermögen von Atomen mit mehreren Elektronen.Zeitschr.Phys. 81, 363, 1933. [19] F., Bloch. Zur Bremsung rasch bewegter Teilchen beim Durchgang durch die Materie. Ann. Phys. 16, 287, 1933. [20] F., James. Monte Carlo theory and practice. Rep.Prog.Phys 43, 1145-1189, 1980. [21] F., Von-Sauter. Ueber den atomaren Photoeffekt bei grosser Härte der anregenden Strahlung. Ann. der Phys. 9, 217-247 (1931) Ann. der Phys. 9, 454 (1931), 1931. [22] G.R., Stevenson. The implications of ICRP Publication 74 for the design of the LHC shielding. Switzerland / CERN-Geneva: CERN Divisional Report CERN/TIS- RP/97-15, 1997. BIBLIOGRAPHY 117

[23] G.R., Stevenson. Shielding studies for the access shafts to the LHC injection lines. Switzerland / CERN-Geneva: CERN Internal Report CERN/TIS-RP/IR/99-23, 1999.

[24] G.R. Stevenson, M. Huhtinen. A lateral shielding study for the LHC main ring. Switzerland / CERN-Geneva: CERN Internal Report CERN/TIS-RP/IR/94-33, 1994.

[25] Group, CERN Radiation Protection. Radiation Safety Manual. 1996: Switzerland / CERN-Geneva.

[26] Group, Particle Data. Review of Particle Physics. Eur. Phys. J. C15, 2000.

[27] G.Z., Molière. Theorie der Streuung schneller geladener Teilchen II - Mehrfach und Vielfachstreuung. Z. Naturforsch. 3a, 78, 1948.

[28] G.Z., Molière. Theorie der Streuung schneller geladener Teilchen III - Die Vielfach- streuung von Bahnspuren unter Berücksichtigung der statistischen Kopplung.Z. Naturforsch. 10a, 177, 1955.

[29] H., Kahn. Applications of Monte Carlo. Santa Monica / USA-California: United States Atomic Energy Commision / RAND Corporation, April 19, 1954.

[30] H. G. Hughes, et. al. MCNPX for Neutron-Proton Transport. Madrid / Spain: Inter- national Conference on Mathematics Computation, Reactor Physics Environmental. Analysis in Nuclear Applications, American Nuclear Society, September 27-30, 1999.

[31] H.-J., Möhring. On the contribution of electroproduction oﬀ nuclei to the generation of energetic hadrons in electromagnetic showers. DESY 89-150, 1989.

[32] H.A., Bethe. Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Ma- terie.Ann.Physik5,325,1930.

[33] H.A., Bethe. Bremsformel für Elektronen relativistischer Geschwindigkeit.Zeitschr. Phys. 76, 293, 1932.

[34] H.A., Bethe. Moliere’s theory of multiple scattering. Phys. Rev. 89, 1256, 1953.

[35] H.A. Bethe, W. Heitler. On the stopping of fast particles and on the creation of positive electrons. Proc. Roy. Soc. A146, 83, 1934.

[36] H.W., Bertini. Intranuclear-Cascade Calculation of the Secondary Nucleon Spectra from Nucleon-Nucleus Interactions in the EnergyRange 340 to 2900 MeV and Com- parisons with Experiment . Oak Ridge National Laboratory, Oak Ridge, Tennessee / USA: Physical Review, Vol 188,Nr.4, 20.December 1969, 1969. 118 BIBLIOGRAPHY

[37] I., Koprivnikar. The biological Shield of High Intensity Spallation Sources: A Monte Carlo Design Study. Graz / Austria: Institut für Theoretische Physik / TU-Graz, 2001.

[38] ICRP. Recommendations of the International Commission on Radiological Protec- tion. Publication No.60, Annals of the ICRP 21,1, 1991.

[39] inhouse production, CERN. PAW - A Physical Analysis Workstation.Geneva/ Switzerland: CERN.

[40] J., Birks. Theory and Practice of Scintillation Counting. Pergamon Press, 1964.

[41] J., Joyce. Finnegans Wake. ISBN 0-586-09150-9, 77-85 Fulham Palace Road, Ham- mersmith, London W6 8JB: HarperCollins.

[42] J. Ranft, W.R. Nelson. Hadron cascades induced by electron and photon beams in the GeV energy range. Nucl. Instr. Meth. A257, (1987) 177 , also SLAC-PUB-3959, 1986.

[43] J.F. Ziegler, H.H. Andersen. The stopping and ranges of ions in matter Vol. 1-4 . Pergamon Press, New York-Toronto-Oxford-Sydney- Frankfurt-Paris, 1977.

[44] K. Hänssgen, J. Ranft. Hadronic event generation for hadron cascade calculations and detector simulation I. Inelastic hadron nucleon collisions at energies below 5 GeV . Nucl. Sci. Eng. 88, 537, 1984.

[45] K. Hänssgen, J. Ranft. The Monte Carlo code HADRIN to simulate inelastic hadron- nucleon interactions at laboratory energies below 5 GeV . Comp. Phys. Comm. 39, 37, 1986.

[46] K. Hänssgen, J. Ranft. The Monte Carlo code NUCRIN to simulate inelastic hadron- nucleus interactions at laboratory energies below 5 GeV . Comp. Phys. Comm. 39, 53, 1986.

[47] K. Hänssgen, H-J. Möhring, J. Ranft. Hadronic event generation for hadron cascade calculations and detector simulation II. Inelastic hadron-nucleus collisions at energies below 5 GeV . Nucl. Sci. Eng. 88, 551, 1984.

[48] K. Hänssgen, R. Kirschner, J. Ranft and H. Wetzig. Monte Carlo simulation of inelastic hadron-hadron reactions in the medium energy range (sqrt(s) < 3 GeV). Description of the model used and of the Monte Carlo code HADRIN . KMU-HEP- 79-07, 1979.

[49] K. Hänssgen, R. Kirschner, J. Ranft and H. Wetzig. Monte-Carlo simulation of inelastic hadron nucleus reactions. Description of the Model and Computer Code NUCRIN . KMU-HEP-80-07, 1980. BIBLIOGRAPHY 119

[50] K. Hänssgen, S. Ritter. TheMonteCarlocodeDECAYtosimulatethedecayof baryon and meson resonances. Comp. Phys. Comm. 31, 411: KMU-HEP-79-14 (1979), 1984.

[51] L., Landau. On the energy loss of fast particles by ionisation.J.Phys.U.S.S.R.,8, 201, 1944.

[52] L. Kim, R.H. Pratt, S.M. Seltzer M.J. Berger. Ratio of positron to electron bremsstrahlung energy loss: An approximate scaling law. Phys. Rev. A33, 3002, 1986.

[53] L. Landau, I. Pomeranchuk. Electron-cascade processes at ultra-high energies Dokl. Akad. Nauk SSSR 92, 735 . Collected papers of L.D. Landau, Pergamon Press, Oxford,p.589,1952.

[54] L. Landau, I. Pomeranchuk. The limits of applicability of the theory of bremsstrahlung by electrons and of creation of pairs at large energies Dokl. Akad. Nauk SSSR 92, 535 . Collected papers of L.D. Landau, Pergamon Press, Oxford, p. 586, 1953.

[55] L. S. Waters, ed. MCNPX User’s Manual, Version 2.4.0 . LANL / USA: LA-CP-02- 408, September 2002.

[56] Lab, Kitware Los Alamos National. Paraview. http://www.kitware.com, 2003.

[57] M., Pelliccioni. Radiation weighting factors and high-energy radiation. Great Britain / Cambridge: Radiation Protection Dosimetry 80, 1998.

[58] M. Gell-Mann, Y. Ne’eman. The Eightfold Way. Library of Congress / USA: Perseus Publishing, 1964, 2000.

[59] M. Höfert, G.R. Stevenson. Design limits for doses and dose rates for beam operation at the LHC . Switzerland / CERN-Geneva: CERN Internal Report TIS-RP/IR/95- 04, 1995.

[60] M. Höfert, K. Potter, G.R. Stevenson. Summary of design values, dose limits, interaction rates etc. for use in estimating adiological quantities associated with LHC- operation. Switzerland / CERN-Geneva: CERN Internal Report TIS-RP/IR/95-19.1, 1995.

[61] M.B., Emmett. The MORSE Monte Carlo radiation transport system.OakRidge National Laboratory report ORNL-4972, 1975.

[62] M.B. Chadwick, P.G. Young, R.E. MacFarlane P. Moller G.M. Hale R.C. Little A.J. Koning S. Chiba. LA150 Documentation of Cross Sections, Heating, and Damage: Part A (Incident Neutrons) and Part B (Incident Protons). LANL / USA: LA-UR- 99-1222, 1999. 120 BIBLIOGRAPHY

[63] M.B. Chadwick, P.G. Young, S. Chiba S.C. Frankle G.M. Hale H.G. Hughes A.J. Koning R.C. Little R.E. MacFarlane R.E. Prael L.S. Waters. Cross Section Evalua- tions to 150 MeV for Accelerator-Driven Systems and Implementation in MCNPX . Nuclear Science and Engineering 131, Number 3,293, March 1999.

[64] M.H. Kalos, P.A. Whitlok. Monte Carlo Methods, vol.1 . New York / USA: Wiley, 1986.

[65] M.J., Berger. Monte Carlo calculations of the penetration and diﬀusion of fast charged particles. Academic Press New York / USA: Methods of Computational Physics - vol.1,pp.135-215,eds.B.Alder,S.Fernbach,M.Rotenberg,1963.

[66] M.J., Mueller. Generation Cross Sections with NJOY . AUSTRIA / Graz: Mario J. Mueller, 2000.

[67] M.J. Berger, St.M. Seltzer. Bremsstrahlung und Photoneutrons from Thick Tungsten and Tantalum Targets. National Bureau of Standards, Washington, D.C 20234 / USA: Physical Review V, vol.2, number 2, Aug. 1970.

[68] M.J. Mueller, G.R. Stevenson. Radiation levels in ECA5 due to Proton loses in ECX5 . Switzerland / CERN-Geneva: Technical Note CERN-TIS-2003-020-RP-TN, 2003.

[69] M.L., Ter-Mikaelyan. Bremsstrahlung radiation spectrum in a medium.Dokl.Akad. Nauk SSSR 94, 1033, 1954.

[70] on Radiation Protection, NCRP National Council and Measurements. The Ex- perimental Basis for Absorbed-Dose Calculations in Medical Uses of Radionuclides. Bethesda / USA: NCRP, 1985.

[71] Pelliccioni, M. Overview of fluence to effective dose and fluence to ambient dose equivalent conversion coefficients for high-energy radiation calculated using the FLUKA code. Great Britain / Cambridge: Radiation Protection Dosimetry 80, p279-297, 2000.

[72] Publication, ICRP. Conversion Coeﬃcients for use in Radiological Protection against External Radiation. The International Commission on Radiological Protection, 1995.

[73] R.E. Prael, A. Ferrari, R.K. Tripathi and A. Polanski. Comparison of nucleon cross section parameterization methods for medium and high energies. Knoxville, Ten- nessee: Proc. of 4th Workshop on Simulating Accelerator Radiation Environments (SARE4), Sept. 14-16 1998, 1998.

[74] R.E. Prael, A. Ferrari, R.K. Tripathi and A. Polanski. Plots supplemental to: "Com- parison of nucleon cross section parameterization methods for medium and high energies". LANL-New Mexico / USA: Los Alamos report LA-UR-98-5843, 1998. BIBLIOGRAPHY 121

[75] Report, ICRP. Neutron Dosimetry for Biology and Medicine. Bethesda, Maryland / USA: The International Commission on Radiation Units and Measurements, 1977.

[76] Report, ICRP. Conversion Coeﬃcients for use in Radiological Protection against External Radiation. Bethesda, Maryland / USA: The International Commission on Radiation Units and Measurements, 1998.

[77] R.M. Sternheimer, M.J. Berger, S.M. Seltzer. Density eﬀect for the ionisation loss of charged particles in various substances. Data Nucl. Data Tab. 30, 261, 1984.

[78] R.Y., Rubinstein. Simulation and the Monte Carlo Method.NewYork/USA:Wiley, 1981.

[79] S. Roesler, G.R. Stevenson. DEQ: a routine for dose equivalent and eﬀective dose conversion in Monte-Carlo programs. Switzerland / CERN-Geneva: CERN Internal Report TIS-RP/TN/2002 in preparation, 2002.

[80] S.G. Mashnik, A.J. Sierk, O. Bersillon and T.A. Gabriel. Cascade-Exciton Model Detailed Analysis of Proton Spallation at Energies from 10 MeV to 5 GeV . LANL / USA: Nucl. Instr. Meth. A414, (1998) 68 and Los Alamos National Laboratory Report LA-UR-97-2905, 1998.

[81] S.M. Seltzer, M.J. Berger. Bremsstrahlung spectra from electron interactions with screened nuclei and orbital electrons. Nucl. Instr. Meth. B12, 95, 1985.

[82] S.M. Seltzer, M.J. Berger. Bremsstrahlung spectra from electrons with kinetic energy 1 keV-10 GeV incident on screened nuclei and orbital electrons of neutral atoms with Z = 1-100 . Data Nucl. Data Tab. 35, 345, 1986.

[83] sourceforge. MayaVI . http://mayavi.sourceforge.net.

[84] W.R. Nelson, H. Hirayama, D.W.O. Rogers. The EGS4 code system. SLAC-265, 1985. Index

(AP) anterior-posterior, 45 biological cell (AP) posterior-anterior, 45 CNS, 36 (ISO) isotropic, 46 damage, 35 (LAT) lateral, 45 gastrointestinal syndrome, 36 (ROT) rotational, 45 genetic effect, 35 hematopoietic syndrome, 36 absorbed dose, 41 mitochondria, 35 accelerator shielding, 49 somatic effect, 35 activation, 49 biological cells ALARA, 47 somatic effect, 35 ambient dose equivalent Boltzman equation, 57 H*(10), 44 Boltzman Transport Equation, 24 H*(d), 44 boson angula deflection, 27 W, 8, 16—18 annihilation, 16 Z, 8, 16—18 anorexia, 35 Brookhaven National Lab, 4 atomos, 12 Austria, 5 calorimetry, 49 Avogadro number, 27 Central Limit Theorem, 26 CERN, 5 Bertini-Dresner-Atchison, 56 combinatorial geometry, 50 Betatron, 3 conversion coefficient, 44 Bethe Bloch Equation, 20 cosmic rays, 49 Biasing Cross Section FLUKA-russian roulette, 58 total, 28 FLUKA-surface splitting, 58 cross section Geometry, 33 DCS - Differential, 24, 27 geometry splitting, 57 differential, 29 Importance, 33 macroskopic, 31 MCNPX-russian roulette, 59 nucleon-nucleon, 51 MCNPX-surface splitting, 58 current, 39 Russian Roulette, 33 Cyclotron, 2 russian roulette, 58 Dees, 2 Surface Splitting, 33 surface splitting, 57 DeBroglie, Louis, 4 BigBang, 5 deep penetration, 49

122 INDEX 123

Democritus, 12 GSI, 56 distribution exponential, 30 Hadron Interactions, 19 Gaussian, 26 IAEA, 27 uniform, 31, 32 ICRP, 39, 46 DNA molecule, 35 ICRP74, 46 DNA-strand, 37 ICRU, 39 Doppler Broadening, 51 sphere, 43, 44 dosimetry, 49 INC, 19, 21, 50 DPM, 20, 21 GINC, 50 DPM - Dual Parton Model, 50 INCL4/ABLA, 56 DPMJET, 50 INFN, 49 Dubna, 3 interaction ECA5, 18, 65 electromagnetism, 14 ECX5, 18, 65 gravity, 14 Effective dose, 43 strong, 14 Efficiency, 26 weak, 14 EGS4, 27 ionizing energy, 20 Eightfold Way, 12 Joyce, James, 13 EM-interactions, 20 Empedocles, 11 K1200, 2 energy threshold, 32 KERMA, 41 Equivalent dose, 42 evaporation, 21, 51 laboratory reference, 31 LAHET, 56 Fermilab, 4 LEP, 4, 5, 7, 8 Feynman lepton, 14 diagram, 16 leptons, 14 Feynman, Richard, 16 Leucippus, 12 Finnigans wake, 13 leucippus, 14 flow, 39 LHC, 5, 7 fluence, 39 LINAC, 1 fluence-to-dose-conversion, 46 LSS, 7 FLUKA, 49, 65 material definition, 27 Manhattan project, 35 flux, 39 Markov Process, 32 FOM - Figure of Merrit, 26 MARS, 65 mass density, 27 gamma deexitation, 51 Maxwell, James Clerk, 17 Gell-Mann, Murray, 12 MCNPX, 49, 65 Glashow, Sheldon, 17 FLUKA comparison, 50 gluon, 16 IMP-card, 58 graviton, 16 material definition, 27 124 INDEX

PRINT card - table 120, 59 deuterium, 15 mean free path length, 30 down, 13 total inverse, 31 strange, 13 Mendeleev, Dmitri Ivanovich, 12 top, 13 Meson Decay, 20 up, 13 messenger particles, 16 Monte Carlo Rabi, Isidor, 5 integration, 24 Radiation Area high radiation, 48 Ne’eman, Yuval, 12 limited stay, 48 NEA, 27 non-designated, 48 neutrino, 14 prohibited, 48 physics, 49 simple controlled, 47, 48 neutron supervised, 47, 48 thermal, 23 radiotherapy, 49 neutrons Reggeon, 20 elastic scattering, 23 residual nucleus, 51 resonance, 22 Resonance Production, 50 NJOY, 27 ROI - Region of Interest, 33 nucleus Rubbia, Carlos, 7, 8 evaporation, 21 pre-equilibrium, 21 Salam, Adbus, 17 scattering process, 28 operational quantities, 39, 44 SLAC, 2 SPS, 5, 7, 18, 65 particle history, 27, 32 Standard deviation, 26 particle-transport, 19 STP, 68 PEANUT, 50 symmetry, 12, 17 PEG ﬁles, 27 synchrocyclotron, 2 Periodic Table of Elements, 12 Synchrotron, 3 phase space, 31 Cosmotron, 4 phasotron, 3 polar scattering, 27 target design, 49 Polar scattering angle, 28 Thucydides, 1 Pomeron, 20 TID, 21 PREPRO2000, 27 Probability Density Function, 24 UA1,7,8,18,65 protection quantities, 39, 42 UNESCO, 5 PS, 5 Uniﬁcation Theory, 17

QCD, 20 Van de Graaﬀ Generator, 1 quark, 13, 14 van der Meer, Simon, 8 bottom, 13 Van der Waal, Johannes Diderik, 15 charm, 13 Variance, 25 INDEX 125

Variance Reduction Technique, 24, 33 VRT, 57

Weight molecular, 27 Weighting factor radiation, 42 tissue, 43 Weinberg,Stephen,18 WORST, 46 126 INDEX Appendix A Tables of Dose Rates in Critical Volumes

127 128 APPENDIX A. TABLES OF DOSE RATES IN CRITICAL VOLUMES 129 130 APPENDIX A. TABLES OF DOSE RATES IN CRITICAL VOLUMES 131 132 APPENDIX A. TABLES OF DOSE RATES IN CRITICAL VOLUMES 133 134 APPENDIX A. TABLES OF DOSE RATES IN CRITICAL VOLUMES Appendix B Visualization in 3D for FLUKA MC Simulation of SPS5

135 136APPENDIX B. VISUALIZATION IN 3D FOR FLUKA MC SIMULATION OF SPS5

The situation of visualization for FLUKA Monte-Carlo calculation results before that thesis was done had allowed only two-dimensional contour-plots obtained with CERN’s in-house PAW[39] software. To obtain a more intuitive form of analysis several software- tools have been developed. These oﬀer presentations, giving simpliﬁed explanations to technicians and other persons who could be exposed in areas like the SPS accelerator at CERN. Now it is possible to combine geometry data with the corresponding results in one interactively movable, three-dimensional body.

B.1 Introduction to visualization - state before thesis

Basically, there is a real difference between data and information. Visualization is one way to help mapping the former to the latter. Therefore an increased need for flexible visualization systems were observed, which can process huge amounts of data, so that a scientist can make a correct interpretation of his data. A major difference between pure graphics software and visualization systems is the emphasis on rendering realism. Most of the 3-D graphics one can see today is oriented towards photo-realistic rendering, at the expense of system interactivity. In contrast, visualization systems stress information display and interactivity, since these are the features that best enable exploration of large data sets. Plots of FLUKA - MC simulation results are cuts (see Figure B.1) of data that have been calculated in a 3D environment. Both are visualized, the geometry combined with the user-defined color-coded MC results.Hence it was a natural consequence to use a 3D

Figure B.1: Before thesis situation, a PAW - 2D contour plot of FLUKA dose-rate results visualization approach additionally to present results. This is especially useful when one B.2. HOW TO VISUALIZE ? 137 has to deal with complex and large data sets and geometries (see Figure 5.2, as it is given inside the SPS-Point 5 housing). This kind of visualization facilitates perception and understanding also for a less experienced audience and users (e.g. for the special case of SPS5 the communication with the technicians and subsurface-workers inside the SPS accelerator tunnel). It is important to keep in mind that the purpose of computing is insight and not numbers.

B.2 How to visualize ?

Generic 3D visualization can be performed with a number of available packages like ParaView[56] (see ﬁgure 3) or MayaVi[83]. These frameworks allow the analysis of 3D datasets by applying cutplanes (orange colored plane in Figure B.2), thresholds, iso- surface creation and a wide range of additional ﬁlters.

Figure B.2: Geometry of SPS5 visualized with Paraview

Still they have to create surfaces which is not always the best way to deliver intuitive results. Another applicable method is the creation of volume renderings of voxel data which is especially useful in MC applications because:

Information inside exploration of inner/unseen structures without applying a cut • Subtle surfaces can be maintained • 138APPENDIX B. VISUALIZATION IN 3D FOR FLUKA MC SIMULATION OF SPS5

Voxels represent sampled data, so there is no need to recover the exact surface. • Our new Tools : VolVis (see window-capture in Figure B.3) is a proprietary tool which creates volume renderings of arbitrary voxel data that can be imported using diﬀerent ﬁle formats:

ASCII XYZ Value format • FLUKA Userbin outputs •

Figure B.3: Window-capture of the VolVis tool

Two different algorithms (Maximum intensity projection, Composite Raycasting) for the creation of volume renderings are supported. The decision which delivers the better result must be made on a case to case basis because this depends heavily on the visualized data. Both approaches share the basic idea of sampling a volume to determine the values of the voxels along the sampling path. The resulting value is then mapped onto a user configurable color table and folded with a linear opacity function for which the range can be specified. As a result a transparent 3D volume with an appropriate color mapping is created. To facilitate interpretation of the results it is possible to overlay the data with actual 3D geometries (which have been used in the MC programs to obtain the results). Currently 3 formats are supported :

STL Stereo-lithography (with user conﬁgurable transparency) • B.3. THE RESULTS WITH NEW VISUALIZATION 139

OBJ Wavefront (with user configurable transparency) • 3DS 3D-Studio (using the original materials) • The user has the possibility to save the created renderings using one of the following formats: BMP, JPG, PNG or PS. In case that the user wants to perform specific analyses by applying for example cutplanes or iso-surfaces with thresholds VolVis can export files which can be used with ParaView and MayaVI.

B.3 The results with new visualization

After MC-calculations with FLUKA (USRBIN effective dose-rate detectors defined), the resulting data are ASCII formatted and directly readable by VolVis. For the geometry, as a basis for the 3D-MC-model additional preparation steps are necessary. These data have to be converted via AutoCAD to STL/3DS format, which is free available and standardized. All the data-flow between geometry-construction and finally visualization is shown in Figure 4.4. Due to the FLUKA - results, which are basically given per primary particle, it is necessary to normalize them to a given beam intensity. Therefore a scaling factor has to be selected which converts the data to the present dose-rate situation. In combination with the 21 color-table the visualization results in 3D-plots (see Figure B.4, which completely corresponds to the PAW contour-plots in Figure B.1).These new methods will not replace

Figure B.4: 3D plots of the dose-rate situation along the beamline in SPS5 housing - generated corresponding to contour plot of Figure B.1. the current used techniques with PAW, but will extend them to a more intuitive form. 140APPENDIX B. VISUALIZATION IN 3D FOR FLUKA MC SIMULATION OF SPS5 Appendix C Particle spectra for the SPS5 liaison area

141 142 APPENDIX C. PARTICLE SPECTRA FOR THE SPS5 LIAISON AREA C.1 Boundary-crossing particle spectra for Level 9 C.1. BOUNDARY-CROSSING PARTICLE SPECTRA FOR LEVEL 9 143 144 APPENDIX C. PARTICLE SPECTRA FOR THE SPS5 LIAISON AREA C.2 Boundary-crossing particle spectra for Level 7 C.2. BOUNDARY-CROSSING PARTICLE SPECTRA FOR LEVEL 7 145 146 APPENDIX C. PARTICLE SPECTRA FOR THE SPS5 LIAISON AREA C.3 Boundary-crossing particle spectra for Level 6 C.3. BOUNDARY-CROSSING PARTICLE SPECTRA FOR LEVEL 6 147 148 APPENDIX C. PARTICLE SPECTRA FOR THE SPS5 LIAISON AREA C.4 Boundary-crossing particle spectra for Level 5 C.4. BOUNDARY-CROSSING PARTICLE SPECTRA FOR LEVEL 5 149 150 APPENDIX C. PARTICLE SPECTRA FOR THE SPS5 LIAISON AREA C.5 Boundary-crossing particle spectra for Level 4 C.5. BOUNDARY-CROSSING PARTICLE SPECTRA FOR LEVEL 4 151 152 APPENDIX C. PARTICLE SPECTRA FOR THE SPS5 LIAISON AREA C.6 Boundary-crossing particle spectra for Level 3 C.6. BOUNDARY-CROSSING PARTICLE SPECTRA FOR LEVEL 3 153 154 APPENDIX C. PARTICLE SPECTRA FOR THE SPS5 LIAISON AREA C.7 Boundary-crossing particle spectra for Level 1 C.7. BOUNDARY-CROSSING PARTICLE SPECTRA FOR LEVEL 1 155 156 APPENDIX C. PARTICLE SPECTRA FOR THE SPS5 LIAISON AREA