Validation of Method of Input of Particles to GPT

A number of tests were carried out to verify that the specification of particles input to the GPT model were as expected. This was to increase confidence in the tomography model as a whole, illustrated in Fig. 4.9, of which GPT was a key component. These test methods included:-

1. Comparison of GPT inputs with measured outputs from GPT utility programs (known as GDFA modules) which calculate emittance and Courant-Snyder (Twiss) parametersβ, αdirectly

2. Empirical analysis of GPT particle data (exported in text format), extracting emittance and Twiss parameters by applying the equations of Section 3.1.1

3. Analysis of tomographic reconstructions of phase-space, from screen image sets generated by GPT quadrupole tomography scanning, using the Section 3.1.3 method

4. Independent beam-size quadrupole-scan analysis (fitting a parabolic function) using the method described in Section 3.2.1

Table 4.2 shows the results of testing GPT Output against Input, using Method 1; values in the ‘GPT Input’ column should match corresponding values in the first ‘GPT Output’ column (at the Start):

GPT Input: GPT Output (from GDFA):

Position Start Start QUAD-07 YAG-02

(m) at 0.006 at 0.006 at 0.295 at 0.631 Parameter αx 0.1139 0.0678 -2.46 -2.66 βx (m) 0.1295 0.128 0.851 2.32 αy -2.2797 -2.31 -1.62 -6.55 βy (m) 1.109 1.14 1.99 5.28 x (m-rad) 4.33 x 10−7 4.51 x 10−7 4.51 x 10−7 4.51 x 10−7 y (m-rad) 9.03 x 10−8 9.40 x 10−8 9.41 x 10−8 9.42 x 10−8

Table 4.2: Set values for parameters βx, αx, βy, αy, and x, y, are input to GPT at

the Start position. The function GDFA is used to calculate the parameters at other positions; specifically,x, y are expected to be conserved.

Table 4.3 contains the results of testing with Method 4. It should be noted that in this case, only the vertical (y) data is meaningful, as the quadrupole scanned (QUAD- 06) is vertically-focussing; also, to reduce uncertainty the input emittances have been increased by a significant factor from the realistic values in Table 4.2. Good agreement is seen in all 3 parameters, within the limits of precision of the fitting technique used in the quadrupole-scan method, and its assumption of a ‘thin-lens’ model for the quadrupole, probably not fully justified in this case.

GPT Input: Quadrupole-Scan Beam-Size Analysis Position Start (m) at 0.006 Parameter αx 0.1139 βx (m) 0.1295 αy -2.2797 -2.44 βy (m) 1.109 1.13 x (m-rad) 1.084 x 10−5 y (m-rad) 2.256 x 10−6 γy (m-rad) 55.19 x 10−6 55.56 x 10−6

Table 4.3: For a given set of input parameter values, GPT is used to scan a vertically- focussing quadrupole (QUAD-06). Beam profiles from extracted (x, y) GPT particle data are used in the ‘quadrupole-scan beam-size analysis’ method to deriveβy, αy and

γy, to provide independent validation by comparison with the known inputs.

Because GPT keeps track of all particles as they move along the beam-line, it provides for output, at any selected position, in terms of particle coordinates in phase-space. In this way, a visual check may be made to ensure that the developing beam is as expected, according to the beam input parameters. For the ALICE tomography line, a reference position at the entrance to the quadrupole QUAD-07 was chosen, for all four types of quadrupole tomography scan modelled. Plots are shown in Fig. 4.12, where ‘H’ in the Scan column refers to Horizontal phase-space (x, x0) and ‘V’ to Vertical (y, y0). Quadrupole magnets are identified in Fig. 4.5.

Figure 4.12: GPT supports the visualisation of phase-space at any selected ‘screen’ position, here chosen as the QUAD-07 entrance. Checks are made that distributions related to different quadrupole scans are similar, both in the horizontal and the vertical.

It will be seen from Fig. 4.12 that as expected, the shape of the horizontal phase- space is the same in case of both QUAD-07 and QUAD-10 scans, as is the shape of the vertical for QUAD-06 and QUAD-11 scans. The size of the distribution appears reduced for the two quadrupoles further down the line (QUAD-10 and QUAD-11).

4.3

Summary

In this chapter, the particle tracking code GPT has been introduced and its fundamental principles briefly described, with the various built-in models for incorporating space- charge effects. After a first simple demonstration of space-charge causing an initially parallel beam to diverge along a drift-space, a more rigorous benchmarking exercise based on bunch radius is reported. This directly compares the results of an analytical calculation with the equivalent GPT results, for a uniform and for a Gaussian bunch. The required inputs and outputs for running GPT models, and the user interface, are outlined. A systematic investigation of space-charge, using the RMS beam-size as a metric, applied to a full ALICE tomography section model in GPT, is presented. Plots of high/low charge beam-size difference against quadrupole current and screen position are shown, highlighting regions of rapid change. A check is also made to see the expected convergence of beam-size difference with number of particles simulated, setting a lower limit for accurate modelling.

GPT is then incorporated into a comprehensive model of the phase-space tomography process, starting with the generation of initial particle specifications based on previous experimental results. Detailed steps in the creation of GPT input particle files are given, and some limitations of the process discussed. The methods used to verify that inputs are actually as specified, by matching to outputs, are summarised with tabulated examples. GPT plots of phase-space made from its internal data are included. Discussion of simulated reconstructed output is postponed until Chapter 5, where it is compared with the corresponding experimental data.

Chapter 5

Space-Charge Experiments and

Data Analysis

Introduction

To carry out experimental investigations of the effects of space-charge in ALICE, which had already been predicted in simulation, preparations were made for a systematic study. The phase-space tomography experiments were to use some or all of the facilities of the diagnostic section of the ALICE to EMMA injection line. To support these experiments and to improve the quality of results, a number of modifications were also proposed to the camera systems used for screen image capture. This chapter describes the preparation and experiments, and discusses the findings, including investigatory work into an important anomaly discovered between results from sets of scans expected to be consistent.

5.1

Detailed Space-Charge Experiments (Phase 3)

In Phase 3, screen imaging cameras were prepared by fitting optical filtration for inten- sity control. Tomography experiments were planned and performed to measure hori- zontal phase-space in detail for a study of space-charge effects, using analysis results for calculating emittance and Twiss parameters.