ALICE Tomography Section: Phase-Space Measurements and Analysis Thesis submitted in accordance with the requirements of the University of Liverpool for the degree of Doctor in Philosophy by Mark Gerard Ibison September 2013 Abstract The technique of phase-space tomography applies the principles of tomographic re- construction to the diagnostics of particle accelerator beams. It is one of the few methods capable of mapping phase-space in detail, using instrumentation commonly available on research accelerator beam-lines, that is, beam profile imaging and variable focussing magnets. This thesis studies the effects of space-charge in the particle bunch on the measure- ment of transverse phase-space, in the horizontal and vertical dimensions, by the beam tomography method. It applies a novel `comparative' method of using quadrupole to- mography scanning to look for these effects, over the length of the diagnostic section of the injection line which transfers the electron beam from the ALICE accelerator to the Electron Model for Many Applications (EMMA) ring at the Daresbury Laboratory. Simulations of the full tomographic process, from beam profile imaging to reconstruc- tion, are developed in the particle tracking code GPT. These are used to investigate space-charge effects, in support of the experimental studies. The concept of `normalised phase-space' is described, in the context of tomography with a very limited number of views, presenting its advantages as applied to a specific type of reconstruction algorithm, the Maximum Entropy Technique. Recommendations for future work in this field are suggested, with possible application both for new machines at the Daresbury Laboratory, and at other accelerator facilities. i Contents Abstract i Contents v List of Figures ix Acknowledgements x List of Publications xi 1 Introduction 1 1.1 Overall Objectives of the Project . 1 1.1.1 Statement of Contribution to Accelerator Science . 2 1.2 Modern Particle Accelerators . 3 1.3 The EMMA Concept . 5 1.4 ALICE Diagnostics . 7 1.5 Beam Diagnostics Methods . 8 1.5.1 Principles of Transverse Linear Beam Dynamics . 8 1.5.2 Practical Diagnostic Techniques . 10 1.6 Review of Reconstruction Techniques for Phase-Space Tomography . 11 1.6.1 Computed Tomography . 11 1.6.2 Reconstruction Algorithms . 14 1.7 Theory of the Filtered Back Projection Algorithm . 15 1.8 Review of Previous Work in Beam Tomography Research . 20 1.9 Basic Theory of Space-Charge in Particle Beams . 21 1.10 Overview of Contents of Chapters . 23 1.11 Summary . 25 2 Phase Space Measurements at ALICE 27 2.1 Relationship between Real-Space and Phase-Space Tomography . 27 2.2 Experimental Methods for Beam Tomography . 31 2.3 Proof of Concept Experiments (Phase 1) . 33 2.3.1 Camera Requirements for Tomographic Imaging . 33 ii 2.3.2 Phase-Space Measurement by Standard Techniques . 37 2.4 Quantitative Measurements (Phase 2) . 46 2.4.1 Screen Camera Calibration . 46 2.4.2 Horizontal and Vertical Tomography Experiments . 47 2.4.3 Dispersion . 48 2.4.4 Variable Bunch-Charge Experiments . 49 2.5 Beam Tomography: Applications for EMMA . 51 2.6 Summary . 51 3 Detailed Analysis and Parameter Extraction from Phase-Space Re- constructions 52 3.1 Principles of Analysis Techniques based on Linear Beam Dynamics . 52 3.1.1 Parameters derived from 2nd Order Moments . 52 3.1.2 Rebinning of Image Data before Reconstruction . 55 3.1.3 Fitting of Idealised Distributions . 56 3.1.4 Additional Corrections in Tomography Data Processing . 57 3.2 Alternatives to Tomography: Other Beam Diagnostic Methods . 59 3.2.1 Quadrupole-Scan Beam-Size Fitting Analysis . 59 3.3 Application of Analysis Techniques to Experimental ALICE Data . 60 3.3.1 Comparison of Experimental Beam Parameter Results . 61 3.4 Summary . 62 4 Space-Charge Simulation Studies 63 4.1 Modelling with Space-Charge using Particle Tracking Codes . 63 4.1.1 Particle Tracking Simulations using GPT . 63 4.1.2 Fundamental Principles of the GPT Code . 64 4.1.3 Application of Space-Charge Theory in Particle Tracking Codes . 64 4.1.4 Initial Demonstration of Space-Charge in GPT . 65 4.1.5 Benchmarking the Magnitude of Space-Charge Effects in GPT . 66 4.1.6 Description of GPT Processing and Interface Features . 70 4.1.7 Detailed Space-Charge Modelling in GPT . 71 4.2 GPT Modelling for Tomography Studies . 76 4.2.1 Investigating Observed Differences in Reconstructed Phase-Space 76 4.2.2 Generating Input Particle Specifications for GPT . 78 4.2.3 Validation of Method of Input of Particles to GPT . 82 4.3 Summary . 84 5 Space-Charge Experiments and Data Analysis 85 5.1 Detailed Space-Charge Experiments (Phase 3) . 85 5.1.1 Camera Filter Installation . 85 iii 5.1.2 Measurement Design and Setup . 86 5.1.3 Analysis of Space-Charge - Part 1: First Evidence from Tomog- raphy Experiments . 89 5.1.4 Results of Analysis of Bunch-Charge Study Experiment . 90 5.2 Further Space-Charge Studies (Phase 4) . 92 5.2.1 Experimental Proposal . 92 5.2.2 Camera Filter-Changer . 93 5.2.3 Results of Phase-Space Reconstructions . 93 5.3 Analysis of Space-Charge - Part2: Evidence from Further Experiments and Comparison with Simulation . 95 5.3.1 Vertical Phase-Space: Investigations into Discrepancies . 97 5.4 Summary . 100 6 Normalised Phase Space 102 6.1 Normalised Phase-Space Technique . 102 6.2 Measurements in Normalised Phase-Space . 105 6.3 Summary . 107 7 Three-Screen Data: Reconstruction Approaches 108 7.1 Outline of the MENT Algorithm . 108 7.2 Comparison of MENT with FBP . 110 7.2.1 Problems with MENT . 111 7.3 Limitations and Optimisation of MENT . 113 7.3.1 Implementations of MENT . 113 7.4 Multiple-Screen Tomography . 114 7.5 Summary . 115 8 Conclusion 116 8.1 General Summary . 116 8.1.1 Detailed Summary by Chapter . 116 8.2 Overall Conclusions . 120 8.3 Further Work . 121 A Camera Performance and Specifications 123 A.1 Camera Specification for Improved Performance . 123 A.2 Focus Setting Procedure . 124 B List of Datasets Used 127 B.1 Experimental Data . 127 B.2 Simulated Data . 127 iv C Phase-Space Tomography Computer Processing 130 C.1 Sequence of Steps in Processing Raw Images into Reconstructed Phase- Space . 130 D An Implementation of the MENT Tomographic Reconstruction Code136 D.1 Data Preparation and Execution Environment . 136 D.2 Applying the MENT Code . 137 Bibliography 144 v List of Figures 1.1 Typical screen and camera layout . 5 1.2 EMMA Layout showing Injection Line from ALICE . 6 1.3 EMMA Injection Line with beam-line elements relevant to tomography . 7 1.4 ALICE Screen Station . 8 1.5 Diagram of phase-space plot . 9 1.6 Projection of f(x; y) at Angle θ ....................... 12 1.7 Sinogram of simple object . 12 1.8 CT Scanner in use . 13 1.9 Example of CT Slice Image . 13 1.10 Projection Test Image . 16 1.11 Projection Profile of Circle . 16 1.12 Ideal `Ramp' Filter Shape . 17 1.13 Backprojection Process . 18 1.14 Effect of Number of Projections . 18 1.15 Shepp-Logan Phantom . 19 1.16 Sinogram for Shepp-Logan . 19 1.17 Shepp-Logan Phantom Reconstructions . 20 1.18 Uniform Parallel Beam in Drift-Space . 21 1.19 Point Charge: Relativistic Fields . 23 2.1 Rotational Effect of Transform M on (x; x0) Distribution . 28 2.2 Projection Scaling . 29 2.3 Mapping the Projection from Original to Transformed Phase-Space . 30 2.4 Equivalence of Populations in Real and Phase Space . 30 2.5 EMMA Injection Line Tomography Section: Identification of Elements . 32 2.6 ISO 12233 Test Card; Slant Edge Image and SFR Output Plot . 35 2.7 Beam Focus Testing . 37 2.8 Typical arrangement for `Quadrupole Tomography Scanning': horizontal phase-space . 38 2.9 Drift Lengths for Specified Projection Angle . 39 2.10 Accessible Projection Angles against Quadrupole Strengths . 40 2.11 Example of Screen Image: Background . 41 vi 2.12 Typical Screen Images: Beam at various Quadrupole Currents . 42 2.13 Display of loaded Screen Images . 43 2.14 Window around Beam: interactive selection . 43 2.15 Display of sample of Projections . 44 2.16 Contour plot of Reconstructed Phase-Space . 44 2.17 Example of Quadrupole Tomography Scan Reconstruction . 45 2.18 Effect of Smoothing on a Reconstruction . 46 2.19 Comparison of Horizontal and Vertical Phase-Space Reconstructions . 48 2.20 Dispersion: Adjustment and Measurement Locations . 49 2.21 Horizontal Phase-Space: Variable Bunch-Charge . 50 3.1 Horizontal Phase-Space: effect of processing on analysis . 53 3.2 Effect of Filtering on Parameters . 55 3.3 Effect of Image Rebinning on Reconstructions . 56 3.4 Effect of Gaussian 2-D Fitting . 57 3.5 Effect of threshold in projections on emittance . 58 3.6 Effect of truncation of projections on reconstructed phase-space . 59 3.7 Quadrupole-Scan of EMI-QUAD-06 . 60 4.1 GPT: (x-y) profiles at start and end of drift space . ..