Vacuum in Particle Accelerators

Oleg B. Malyshev is a Lead Scientist for Vacuum Science and Technology in Accelerator Science and Technology Centre at STFC Daresbury Laboratory near Warrington, UK.

• Acknowledgements xvNomenclature xviiIntroduction 1Oleg B. MalyshevReferences 31 Vacuum Requirements 5Oleg B. Malyshev1.1 Definition of Vacuum 51.2 Vacuum Specification for Particle Accelerators 61.2.1 Why Particle Accelerators Need Vacuum? 61.2.2 Problems Associated with Beam–Gas Interaction 81.2.2.1 Beam Particle Loss 81.2.2.2 Background Noise in Detectors 81.2.2.3 Residual Gas Ionisation and Related Problems 91.2.2.4 Contamination of Sensitive Surfaces 91.2.2.5 Safety and Radiation Damage of Instruments 101.2.3 Vacuum Specifications 111.2.4 How Vacuum Chamber Affects the Beam Properties 121.3 First Considerations Before Starting Vacuum System Design 131.3.1 What is the Task? 131.3.2 Beam Lattice 141.3.3 Beam Aperture and Vacuum Chamber Cross Section 151.3.3.1 Required Mechanical Aperture 151.3.3.2 Magnet Design 171.3.3.3 Mechanical Engineering 171.3.3.4 Other Factors Limiting a Maximum Size of Beam Vacuum Chamber 171.3.4 Vacuum Chamber Cross Sections and Preliminary Mechanical Layout 181.3.5 Possible Pumping Layouts 191.4 First and Very Rough Estimations 201.5 First Run of an Accurate Vacuum Modelling 221.6 Towards the Final Design 221.7 Final Remarks 25References 252 Synchrotron Radiation in Particle Accelerators 29Olivier Marcouillé2.1 Emission of a Charged Particle in a Magnetic Field 292.1.1 Radiated Energy Density and Power Density 312.1.2 Angular Flux 322.2 SR from Dipoles 322.2.1 Emission Duration and Critical Energy 332.2.2 Photon Flux 342.2.3 Vertical Angular Distribution of Photon Flux 372.2.4 Photon Power 392.2.5 Vertical Angular Distribution of Power 412.3 SR from Quadrupoles 422.4 SR from Insertion Devices 432.4.1 Motion of Charged Particles Inside a Planar Insertion Device 442.4.2 Resonance Wavelength 452.4.3 Radiation from Undulators and Wigglers 462.4.4 Angular Aperture of ID at Resonant Wavelength 512.4.5 Estimation of Power Distribution Radiated in a Wiggler 522.4.6 Estimation of the Power Collected by Simple Geometry Aperture 542.4.7 Method for Estimation Absorbed Power on the Complex Shapes 542.5 Software Dedicated to Evaluation of the Photon Flux and Power Distribution from the Insertion Devices 552.5.1 XOP 562.5.2 Synchrotron Radiation Workshop (SRW) 562.5.3 SPECTRA 572.5.4 SYNRAD 582.5.5 OSCARS 59Acknowledgements 59References 60Further Reading 603 Interaction Between SR and Vacuum Chamber Walls 61Vincent Baglin and Oleg B. Malyshev3.1 Photon Reflectivity 613.2 Photoelectron Production 693.2.1 Total Photoelectron Yield 693.2.2 Effect of the Photon Energy 723.2.3 Effect of the Incidence Angle 76References 764 Sources of Gas in an Accelerator Vacuum Chamber 79Oleg B. Malyshev and Junichiro Kamiya4.1 Residual Gases in Vacuum Chamber 794.2 Materials Used for and in Vacuum Chambers and Built-In Elements 814.2.1 Stainless Steel 824.2.2 Aluminium Alloys 834.2.3 Copper and Its Alloys 844.2.4 Titanium and Its Alloys 854.2.5 Ceramics 854.2.6 Other Vacuum Materials 864.3 Thermal Outgassing 874.3.1 Thermal Outgassing Mechanism During Pumping 884.3.2 Equilibrium Pressure 894.3.3 Vapour Pressure 914.3.4 Thermal Outgassing Rate of Materials 934.3.5 Outgassing Rate Measurements 974.3.5.1 Throughput Method 974.3.5.2 Conductance Modulation Method 984.3.5.3 Two-Path Method 984.3.5.4 Gas Accumulation Method 994.3.6 Thermal Desorption Spectroscopy 1004.4 Surface Treatments to Reduce Outgassing 1024.4.1 Cleaning 1024.4.2 Bakeout 1054.4.3 Air Bake 1064.4.4 Vacuum Firing 1064.4.5 Surface Coatings 1084.4.5.1 Coating the Surface by Thin Films of Material with Low Hydrogen Permeability and Low Outgassing 1084.4.5.2 Coating the Surface by Thin Film of Getter Materials 1084.5 Electron-Stimulated Desorption 1094.5.1 ESD Definition and ESD Facilities 1094.5.2 ESD for Different Materials as a Function of Dose 1124.5.3 ESD as a Function of Amount of Desorbed Gas 1134.5.4 Effect of Pumping Duration 1144.5.5 ESD as a Function of Electron Energy 1194.5.6 Effect of Bakeout on ESD 1224.5.7 Effectiveness of Surface Polishing and Vacuum Firing on ESD 1234.5.8 A Role of Oxide Layer on Copper 1254.5.9 Effect of Surface Treatment 1254.5.10 Effect of Vacuum Chamber Temperature 1254.6 Photon-Stimulated Desorption 1284.6.1 PSD Definition and PSD Facilities 1284.6.2 PSD as a Function of Dose 1314.6.3 PSD for Different Materials 1314.6.4 PSD as a Function of Amount of Desorbed Gas 1354.6.5 PSD as a Function of Critical Energy of SR 1364.6.6 Effect of Bakeout 1374.6.7 Effect of Vacuum Chamber Temperature 1404.6.8 Effect of Incident Angle 1424.6.9 PSD versus ESD 1444.6.10 How to Use the PSD Yield Data 1454.6.10.1 Scaling the Photon Dose 1454.6.10.2 Synchrotron Radiation from Dipole Magnets 1454.6.10.3 PSD Yield and Flux as a Function of Distance from a Dipole Magnet 1484.6.10.4 PSD from a Lump SR Absorber 1514.6.10.5 Combining PSD from Distributed and Lump SR Absorbers 1534.7 Ion-Stimulated Desorption 1554.7.1 ISD Definition and ISD Facilities 1554.7.2 ISD as a Function of Dose 1564.7.3 ISD Yield as a Function of Ion Energy 1584.7.4 ISD Yield as a Function of Ion Mass 1594.7.5 ISD for Different Materials 1604.7.6 Effect of Bakeout and Argon Discharge Cleaning 1614.7.7 ISD versus ESD 1614.7.8 ISD Yield as a Function of Temperature 1614.7.9 ISD Yields for Condensed Gases 163Acknowledgements 166References 1665 Non-evaporable Getter (NEG)-Coated Vacuum Chamber 175Oleg B. Malyshev5.1 Two Concepts of the Ideal Vacuum Chamber 1755.2 What is NEG Coating? 1775.3 Deposition Methods 1795.4 NEG Film Characterisation 1815.5 NEG Coating Activation Procedure 1825.6 NEG Coating Pumping Properties 1885.6.1 NEG Coating Pumping Optimisation at CERN 1885.6.2 NEG Coating Pumping Optimisation at ASTeC 1905.7 NEG Coating Lifetime 1935.8 Ultimate Pressure in NEG-Coated Vacuum Chambers 1955.9 NEG-Coated Vacuum Chamber Under SR 1965.10 Reducing PSD/ESD from NEG Coating 2005.10.1 Initial Considerations 2005.10.2 ESD from Vacuum Chamber Coated with Columnar and Dense NEG Films 2015.10.3 Dual Layer 2025.10.4 Vacuum Firing Before NEG Deposition 2045.11 ESD as a Function of Electron Energy 2045.12 PEY and SEY from NEG Coating 2045.13 NEG Coating Surface Resistance 2065.14 NEG at Low Temperature 2075.15 Main NEG Coating Benefits 2075.16 Use of NEG-Coated Vacuum Chambers 208References 2096 Vacuum System Modelling 215Oleg B. Malyshev6.1 A Few Highlights from Vacuum Gas Dynamics 2156.1.1 Gas in a Closed Volume 2166.1.1.1 Gas Density and Pressure 2166.1.1.2 Amount of Gas and Gas Flow 2176.1.2 Total Pressure and Partial Pressure 2186.1.3 Velocity of Gas Molecules 2186.1.4 Gas Flow Rate Regimes 2206.1.5 Pumping Characteristics 2216.1.6 Vacuum System with a Pump 2236.1.7 Vacuum Conductance 2236.1.7.1 Orifice 2246.1.7.2 Vacuum Conductance of Long Tubes 2246.1.7.3 Vacuum Conductance of Short Tubes 2256.1.7.4 Serial and Parallel Connections of Vacuum Tubes 2266.1.8 Effective Pumping Speed 2266.2 One-Dimensional Approach in Modelling Accelerator Vacuum Systems 2286.2.1 A Gas Diffusion Model 2296.2.2 A Section of Accelerator Vacuum Chamber in a Gas Diffusion Model 2316.2.3 Boundary Conditions 2326.2.4 Global and Local Coordinates for Each Element 2386.2.5 Using the Results 2406.2.6 A Few Practical Formulas 2416.2.6.1 Gas Injection into a Tubular Vacuum Chamber 2416.2.6.2 Vacuum Chamber with Known Pumping Speed at the Ends 2416.2.6.3 Vacuum Chamber with Known Pressures at the Ends 2446.3 Three-Dimensional Modelling: Test Particle Monte Carlo 2456.3.1 Introduction 2456.3.2 A Vacuum Chamber in the TPMC Model 2466.3.3 TPMC Code Input 2466.3.4 TPMC Code Output 2486.3.4.1 Gas Flow Rate 2486.3.4.2 Gas Density and Pressure 2506.3.4.3 Transmission Probability and Vacuum Conductance 2506.3.4.4 Pump-Effective Capture Coefficient 2516.3.4.5 Effect of Temperature and Mass of Molecules 2516.3.5 What Can Be Done with TPMC Results? 2516.3.5.1 A Direct Model with a Defined Set of Parameters 2526.3.5.2 Models with Variable Parameters 2536.3.6 TPMC Result Accuracy 2566.4 Combining One-Dimensional and Three-Dimensional Approaches in Optimising the UHV Pumping System 2576.4.1 Comparison of Two Methods 2576.4.2 Combining of Two Methods 2586.5 Molecular Beaming Effect 2606.6 Concluding Remarks 2656.A Differential Pumping 2656.B Modelling a Turbo-Molecular Pump 266Acknowledgements 267References 2677 Vacuum Chamber at Cryogenic Temperatures 269Oleg Malyshev, Vincent Baglin, and Erik Wallén7.1 Pressure and Gas Density 2697.2 Equilibrium Pressure: Isotherms 2727.2.1 Isotherms 2737.2.2 Cryotrapping 2797.2.3 Physisorption on Gas Condensates 2817.2.4 Temperature Dependence of the H2 Isotherms 2827.2.5 Choice of Operating Temperature for Cryogenic Vacuum Systems 2867.3 Gas Dynamics Model of Cryogenic Vacuum Chamber Irradiated by SR 2897.3.1 Infinitely Long Vacuum Chamber Solution 2917.3.1.1 Vacuum Chamber Without a Beam Screen 2927.3.1.2 Vacuum Chamber with Holes in the Beam Screen 2927.3.2 Short Vacuum Chamber Solution 2947.3.2.1 Solution for a Short Vacuum Chamber with a Given Pressure at the Ends 2967.3.2.2 Solution for a Short Vacuum Chamber with a Given Pumping Speed at the Ends 2987.4 Experimental Data on PSD from Cryogenic Surface 3007.4.1 Experimental Facility for Studying PSD at Cryogenic Temperatures 3017.4.2 Discovery of Secondary PSD 3017.4.3 Calculation of the Desorption Yields from Experimental Data 3067.4.4 Primary PSD Yields 3087.4.5 Secondary PSD Yields 3107.4.6 Photon-Induced Molecular Cracking of Cryosorbed Gas 3127.4.6.1 Experimental Measurements 3127.4.6.2 How to Include Cracking into the Model 3157.4.6.3 Example 3167.4.7 Temperature of Desorbed Gas 3187.5 In-Depth Studies with COLDEX 3217.5.1 COLDEX Experimental Facility 3217.5.2 PSD of Cu as a Function of Temperature 3247.5.3 Secondary PSD Yields 3257.5.4 PSD of a BS with Sawtooth for Lowering Photon Reflectivity and PEY 3267.5.5 Vacuum Transient 3287.5.6 Temperature Oscillations 3297.6 Cryosorbers for the Beam Screen at 4.5 K 3317.6.1 Carbon-Based Adsorbers 3337.6.1.1 Activated Charcoal 3337.6.1.2 Carbon Fibre 3347.6.2 Amorphous Carbon Coating Absorption Properties 3377.6.3 Metal-Based Absorbers 3387.6.3.1 Aluminium-Based Absorbers 3387.6.3.2 Copper-Based Absorbers 3407.6.3.3 LASE for Providing Cryosorbing Surface 3417.6.4 Using Cryosorbers in a Beam Chamber 3417.7 Beam Screen with Distributed Cryosorber 3427.8 Final Remarks 343References 3448 Beam-Induced Electron Multipacting, Electron Cloud, and Vacuum Design 349Vincent Baglin and Oleg B. Malyshev8.1 BIEM and E-Cloud 3498.1.1 Introduction 3498.1.2 E-Cloud Models 3518.2 Mitigation Techniques and Their Impact on Vacuum Design 3568.2.1 Passive Methods 3578.2.2 Active Methods 3638.2.3 What Techniques Suit the Best 3658.3 Secondary Electron Emission (Laboratory Studies) 3658.3.1 SEY Measurement Method 3658.3.2 SEY as a Function of the Incident Electron Energy 3678.3.3 Effect of Surface Treatments by Bakeout and Photon, Electron, and Ion Bombardment 3678.3.4 Effect of Surface Material 3688.3.5 Effect of Surface Roughness 3698.3.6 ‘True’ Secondary Electrons, Re-Diffused Electrons, and Reflected Electrons 3718.3.7 Effect of Incidence Angle 3748.3.8 Insulating Materials 3748.4 How the BIEM and E-Cloud Affect Vacuum 3768.4.1 Estimation of Electron Energy and Incident Electron Flux 3768.4.2 Estimation of Initial ESD 3788.5 BIEM and E-Cloud Observation in Machines 3798.5.1 Measurements in Machines 3798.5.1.1 Vacuum Pressure 3818.5.1.2 Vacuum Chamber Wall Properties 3828.5.1.3 Specific Tools for BIEM and Electron Cloud Observation 3868.5.2 Machines Operating at Cryogenic Temperature 3908.5.2.1 Surface Properties at Cryogenic Temperature 3918.5.2.2 Observations with Beams 3948.5.2.3 The CERN Large Hadron Collider Cryogenic Vacuum System 4018.6 Contribution of BIEM to Vacuum Stability 4058.7 Past, Present, and Future Machines 407Acknowledgements 409References 4099 Ion-Induced Pressure Instability 421Oleg B. Malyshev and Adriana Rossi9.1 Introduction 4219.2 Theoretical 4229.2.1 Basic Equations 4229.2.2 Solutions for an Infinitely Long Vacuum Chamber 4259.2.2.1 Room Temperature Vacuum Chamber 4259.2.2.2 Cryogenic Vacuum Chamber 4269.2.2.3 Summary for an Infinitely Long Vacuum Chamber 4279.2.3 Short Vacuum Chamber 4289.2.3.1 Solution for a Short Vacuum Chamber with a Given Gas Density at the Ends 4289.2.3.2 Solution for a Short Vacuum Chamber with a Given Pumping Speed at the Ends 4319.2.3.3 Solution for a Short Vacuum Chamber Without a Beam Screen Between Two Chambers With a Beam Screen 4349.2.3.4 Some Remarks to Solutions for Short Tubes 4379.2.4 Multi-Gas System 4379.2.5 Two-Gas System 4389.2.5.1 Solutions for an Infinitely Long Vacuum Chamber 4399.2.5.2 Solution for a Short Vacuum Chamber in the Equilibrium State 4399.2.6 Some Comments to the Analytical Solutions 4409.2.7 Effect of the Ion-Stimulated Desorption on the Gas Density 4419.2.7.1 Infinitely Long Vacuum Chamber (One Gas) 4419.2.7.2 Vacuum Chamber with a Given Pumping Speed at the Ends (One Gas) 4419.2.7.3 Two-Gas System 4439.2.8 Some Numeric Examples from the LHC Design 4439.2.8.1 The Critical Current for an Infinitely Long Vacuum Chamber 4449.2.8.2 Short Vacuum Chambers 4459.2.8.3 Effect of the Ion-Stimulated Desorption on the Gas Density 4459.3 VASCO as Multi-Gas Code for Studying the Ion-Induced Pressure Instability 4479.3.1 Basic Equations and Assumptions 4479.3.2 Multi-Gas Model in Matrix Form and Fragmentation in Several Vacuum Chamber Elements 4489.3.2.1 Boundary Conditions 4499.3.3 Transformation of the Second-Order Differential Linear Equation into a System of First-Order Equations 4509.3.3.1 Boundary Conditions 4519.3.4 Set of Equations to be Solved 4519.3.5 ‘Single Gas Model’ Against ‘Multi-Gas Model’ 4529.4 Energy of Ions Hitting Vacuum Chamber 4559.4.1 Ion Energy in the Vacuum Chamber Without a Magnetic Field 4559.4.1.1 Circular Beams 4559.4.1.2 Flat Beams 4589.4.2 Ion Energy in a Vacuum Chamber with a Magnetic Field 4609.4.2.1 Vacuum Chamber in a Dipole Magnetic Field 4619.4.2.2 Vacuum Chamber in a Quadrupole Magnetic Field 4619.4.2.3 Vacuum Chamber in a Solenoid Magnetic Field 4629.5 Errors in Estimating the Critical Currents Ic4649.5.1 Beam–Gas Ionisation 4659.5.2 Ion Impact Energy 4659.5.3 Ion-Stimulated Desorption Yields 4659.5.4 Pumping 4669.5.5 Total Error in Critical Current 4669.6 Summary 467References 46710 Pressure Instabilities in Heavy Ion Accelerators 471Markus Bender10.1 Introduction 47110.2 Pressure Instabilities 47210.2.1 Model Calculations of the Dynamic Pressure and Beam Lifetime 47610.2.1.1 Closed System (Vessel) 47610.2.1.2 Vessel Including Collimation 47810.2.1.3 Longitudinal Profile 47810.2.2 Consequences 47910.3 Investigations on Heavy Ion-Induced Desorption 48010.3.1 Desorption Yield Measurements 48110.3.2 Materials Analysis 48310.3.3 Dedicated Set-ups to Measure Ion-Induced Desorption Yields 48510.3.4 Results 48910.3.4.1 Materials 49010.3.4.2 Surface Coatings 49310.3.4.3 Cleaning Methods 49410.3.4.4 Energy Loss Scaling 49510.3.4.5 Angle Dependence 49610.3.4.6 Conditioning 49710.3.4.7 Cryogenic Targets 49810.3.5 Theoretic 49910.3.5.1 Interaction of Ions with Matter 49910.3.5.2 Inelastic Thermal Spike Model 50110.4 Conclusion: Mitigation of Dynamic Vacuum Instabilities 505Acknowledgement 507References 507Index 515