Development of Longitudinal Diagnostics for Electron Beams ... · Abstract A setup for the investigation of Coherent Di raction Radiation (CDR) from a con-ducting screen as a tool

Development of Longitudinal Diagnostics for Electron

Beams based on Coherent Diffraction Radiation

Maximilian Micheler

Department of Physics

Royal Holloway, University of London

A thesis submitted to the University of London for the degree of Doctor of

Philosophy

December 2010

Fur meinen Großvater, Max Vetter, undmeine Eltern, Karin und Hermann Micheler.

Declaration

I hereby confirm that the work presented in this thesis is my own. Where information

has been derived from other sources, I confirm that this has been indicated in the

document.

Maximilian Micheler

3

Abstract

A setup for the investigation of Coherent Diffraction Radiation (CDR) from a con-

ducting screen as a tool for non-invasive longitudinal electron beam diagnostics has

been designed and installed in the Combiner Ring Measurement (CRM) line of

the Compact Linear Collider (CLIC) Test Facility (CTF3) at the Organisation for

Nuclear Research (CERN). Due to the short electron bunch spacing at CTF3, a

detection system using ultra-fast room-temperature Schottky Barrier Diode (SBD)

detectors was chosen. The system was fully automated and results on the commis-

sioning of the system are given. Studies of CDR properties and the CDR signal

correlation with an RF pickup and a streak camera are reported on and spectral

CDR measurements are discussed. Moreover, simulations based on the theoreti-

cal diffraction radiation (DR) model are used to obtain the DR spectra which are

needed for the deconvolution during the signal analysis. These are compared to the

simulation of CDR from a conducting screen using the state-of-the-art Advanced

Computational Electromagnetics 3P (ACE3P) suite from the Stanford Linear Ac-

celerator Center (SLAC).

4

Acknowledgements

First and foremost, I would like to express my sincere gratitude to my supervisor, Dr

Pavel Karataev, for his supervision and guidance over the last three years. Without

his support and help this thesis would not have been completed.

I would like to thank Professor Grahame Blair for giving me the opportunity

to study at Royal Holloway and perform research in such a competent and friendly

group, that has provided me with a very stimulating atmosphere. I would like to

thank Dr Stewart Boogert for his useful advise on object-oriented programming and

convincing me to buy the right personal computing equipment. I am very grateful

to Dr Stephen Molloy for introducing me to the world of supercomputing and letting

me steal some of his precious CPU hours at NERSC. I would like to thank Gary

Boorman for his help with the electronic equipment and the abundance of well

documented LabVIEW routines.

I would like to express my gratitude to Dr Thibaut Lefevre for all his help

during my stay at CERN. During these two years, he has always provided support

and guidance whenever it was needed. It would also like to thank Dr Gunther

Geschonke, Dr Roberto Corsini, Dr Anne Dabrowski, and all other members of the

CTF3/CLIC collaboration for their help during my time at CERN.

I would like to thank John Taylor for his workshop efforts and David Howell for

his useful advise on designing the setup at CTF3.

I would also like to mention the people at Royal Holloway who have made my

time more enjoyable during coffee breaks, lunches, and beers. Thanks go to Dr

5

Matt Tamsett, Dr Neil Cooper-Smith, Dr Sudan Paramesvaran, Dan Hayden, Tom

Aumeyr, Robert Ainsworth, Konstantin Lekomtsev, Nirav Joshi, and Dr Lawrence

Deacon. There are also a lot of friends who took care that I get enough time to

socialise. Special thanks to Nico Linder, David Pade, Christoph Zettler, Christian

Richter, Toots (James) Gardner and his fiancee Jemma O’Shaughnessy, and Olga

Roshchupkina.

Furthermore, I would like to thank the Science and Technology Facilities Council

(STFC) for providing funding for this project and supporting me to carry out this

research.

Moreover, I would like to acknowledge the help of the University of London

Central Research Fund, who have provided me with funding for hardware, which

was necessary to carry out the experiment at CTF3.

Finally, a very big thanks goes to my parents for their endless support and

devotion, not only during the last three years, but since I was born. Thanks for

always enabling and encouraging me to pursue all the things I wanted to do. I

would also like to thank my granddad for his never-ending supply of pocket money

and my sister Franziska, and brothers Simon and Manuel for their support.

6

Contents

1 Introduction 17

1.1 Particle physics and the Standard Model . . . . . . . . . . . . . . . . 17

1.2 High-energy particle colliders . . . . . . . . . . . . . . . . . . . . . . 19

1.2.1 Hadron colliders . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.2.2 Lepton colliders . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.2.3 Necessity for a high-energy linear collider . . . . . . . . . . . 21

1.3 CLIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.3.1 The CLIC concept . . . . . . . . . . . . . . . . . . . . . . . . 22

1.3.2 General layout of CLIC . . . . . . . . . . . . . . . . . . . . . 23

1.4 Beam-beam effects in a linear collider . . . . . . . . . . . . . . . . . 26

1.4.1 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.4.2 Disruption effect . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.4.3 Beamstrahlung effect . . . . . . . . . . . . . . . . . . . . . . . 27

1.4.4 Hour-glass effect . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.5 RF power production in the PETS . . . . . . . . . . . . . . . . . . . 29

1.6 Bunch length measurement techniques . . . . . . . . . . . . . . . . . 29

1.6.1 Streak camera . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.6.2 Transverse deflection cavities . . . . . . . . . . . . . . . . . . 30

1.6.3 Electro-optic techniques . . . . . . . . . . . . . . . . . . . . . 31

1.6.4 Frequency domain techniques . . . . . . . . . . . . . . . . . . 32

1.7 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7

Contents

1.8 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.8.1 Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.8.2 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.8.3 Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.8.4 Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.8.5 Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2 Theory 37

2.1 Virtual photon model . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2 Transition radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.2.1 Transition radiation phenomenon . . . . . . . . . . . . . . . . 42

2.2.2 Virtual-photon method derivation of transition radiation . . . 43

2.2.3 Far-field approach and infinite target size approximation . . . 45

2.2.4 Pre-wave zone approach . . . . . . . . . . . . . . . . . . . . . 46

2.2.5 Validity of the far-field approach and infinite target size ap-

proximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.3 Diffraction radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.3.1 Diffraction radiation process . . . . . . . . . . . . . . . . . . 48

2.3.2 Diffraction radiation theory . . . . . . . . . . . . . . . . . . . 49

2.4 Coherent radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.5 Kramers-Kronig analysis . . . . . . . . . . . . . . . . . . . . . . . . . 53

3 Simulation studies 56

3.1 DR simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.1.1 Evolution from TR to DR from a half-plane . . . . . . . . . . 57

3.1.2 Polarisation components of DR . . . . . . . . . . . . . . . . . 61

3.1.3 Diffraction radiation spectra . . . . . . . . . . . . . . . . . . 62

3.1.4 Impact parameter variation . . . . . . . . . . . . . . . . . . . 63

3.1.5 Total radiation spectrum . . . . . . . . . . . . . . . . . . . . 64

3.1.6 Power production . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.2 Time domain simulations . . . . . . . . . . . . . . . . . . . . . . . . 67

3.2.1 Computational technique . . . . . . . . . . . . . . . . . . . . 68

8

Contents

3.2.2 Simulation model . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.2.3 DR from the modelled target . . . . . . . . . . . . . . . . . . 71

3.2.4 DR time domain signal . . . . . . . . . . . . . . . . . . . . . 72

3.2.5 DR spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.2.6 Modified model . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.3 Comparison of the simulation models . . . . . . . . . . . . . . . . . . 77

4 Setup for the Investigation of Coherent Diffraction Radiation at

CTF3 80

4.1 Description of CTF3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.1.1 Drive beam injector and accelerator . . . . . . . . . . . . . . 81

4.1.2 Delay Loop, Combiner Ring, and Combiner Ring Measure-

ment line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.1.3 CLIC Experimental Area . . . . . . . . . . . . . . . . . . . . 85

4.2 CDR Setup in the CRM line . . . . . . . . . . . . . . . . . . . . . . 86

4.2.1 Installation location . . . . . . . . . . . . . . . . . . . . . . . 86

4.2.2 Vacuum hardware . . . . . . . . . . . . . . . . . . . . . . . . 90

4.2.3 Target and target holder . . . . . . . . . . . . . . . . . . . . . 94

4.2.4 Off-centre adapter flange . . . . . . . . . . . . . . . . . . . . 95

4.3 Michelson interferometer . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.3.1 Fourier transform spectroscopy . . . . . . . . . . . . . . . . . 97

4.3.2 Interferometer components . . . . . . . . . . . . . . . . . . . 99

4.3.3 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.4 Detection system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.4.1 Schottky barrier diode detector . . . . . . . . . . . . . . . . . 105

4.4.2 Standard gain horns . . . . . . . . . . . . . . . . . . . . . . . 107

4.4.3 Detector holder . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.5 Hardware control interface and software . . . . . . . . . . . . . . . . 108

4.5.1 Translation stage and manipulator control . . . . . . . . . . . 109

4.5.2 Data acquisition and synchronisation . . . . . . . . . . . . . . 110

4.5.3 Machine parameter readout and device control . . . . . . . . 111

9

Contents

4.5.4 Principles of operation with the LabVIEW software . . . . . 111

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5 Properties of Coherent Diffraction Radiation measured at CTF3 115

5.1 Schottky Barrier Diode signal . . . . . . . . . . . . . . . . . . . . . . 115

5.1.1 Bunch length variation . . . . . . . . . . . . . . . . . . . . . . 116

5.1.2 Bunch spacing frequency and sampling time . . . . . . . . . . 117

5.1.3 Dynamic range of the SBD detectors . . . . . . . . . . . . . . 119

5.2 Beam line backgrounds in the CRM line . . . . . . . . . . . . . . . . 120

5.3 CDR distribution measurements . . . . . . . . . . . . . . . . . . . . 124

5.4 Current dependence of the CDR signal . . . . . . . . . . . . . . . . . 127

5.5 Klystron phase dependence of the CDR signal . . . . . . . . . . . . . 128

5.6 Correlation measurements with other bunch length monitoring systems130

5.7 Interferometric CDR measurements and spectra . . . . . . . . . . . . 133

5.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6 Conclusion 138

6.1 Summary and main conclusions . . . . . . . . . . . . . . . . . . . . . 138

6.2 Suggestions for future work . . . . . . . . . . . . . . . . . . . . . . . 139

A Ginzburg-Frank formula 142

10

List of Figures

1.1 Schematic general layout of CLIC at 3 TeV. Courtesy of the CLIC

Study group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.2 Principle of a streak camera. . . . . . . . . . . . . . . . . . . . . . . 30

2.1 Lorentz boost of initial frame K to frame K ′. . . . . . . . . . . . . . 38

2.2 Ex (β−1By) and Ez component of the electromagnetic field for two

different particle energies γ. . . . . . . . . . . . . . . . . . . . . . . . 39

2.3 Change of the Coulomb field of a charged particle in the laboratory

frame under a Lorentz transformation from a stationary rest frame

to a moving rest frame with γ 1. . . . . . . . . . . . . . . . . . . . 40

2.4 Plot of ζK1(ζ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.5 Ginzburg-Frank TR distribution in the relativistic limit. . . . . . . . 43

2.6 TR emission scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.7 DR emission scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.8 Particle distributions and resulting form factor. . . . . . . . . . . . . 52

3.1 Infinite slit between two half-planes for different slit widths (in mul-

tiples of rfield) for γ = 235 in the far-field limit. . . . . . . . . . . . . 58

3.2 Withdrawal of a half-plane for different offsets (in multiples of rfield)

for γ = 235 in the far-field limit. . . . . . . . . . . . . . . . . . . . . 59

3.3 Variation of the DR distribution with impact parameter (in multiples

of rfield) for γ = 235 in the far-field limit. . . . . . . . . . . . . . . . . 60

11

List of Figures

3.4 DR spatial distribution for distance a = 10γ2λ

2π and a target size of

10γλ2π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5 DR polarisation components in the far field. . . . . . . . . . . . . . . 61

3.6 DR spectra for a 40 mm×40 mm target and a DXP-19 detector at a

distance a = 1.5 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.7 Variation of the DR spectra for different impact parameters at an

energy γ = 235. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.8 DR intensity variation with impact parameter for different observa-

tion wavelengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.9 Example CDR power spectrum obtained by the multiplication of the

single electron spectrum by the bunch form factor of a 2 mm Gaussian

beam for the setup at CTF3. . . . . . . . . . . . . . . . . . . . . . . 65

3.10 Average CDR power production for a Gaussian beam with bunch

charge 2× 1010 and energy γ = 235 for different impact parameters b. 66

3.11 CAD drawing of the simulated setup for DR from a rectangular target

tilted by 45 into a cylindrical viewport. The electron beam propa-

gation direction is illustrated by the dark grey line through the model. 69

3.12 Evolution of the electric DR field for given times after the simulation

start time (the beam entry time). . . . . . . . . . . . . . . . . . . . . 71

3.13 Electric and magnetic fields read-out from the simulation model. . . 72

3.14 Power readings of the DR propagating through the viewport of the

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.15 Spectral DR power density for the simulated model. . . . . . . . . . 74

3.16 Spectral DR power density for the simulated model with the trailing

signal excluded. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.17 Electric and magnetic fields read-out from the modified simulation

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.18 Spectral DR power density for the modified simulated model. . . . . 77

3.19 CDR power spectrum obtained by the convolution of the single elec-

tron spectrum calculated from the virtual photon model with the

bunch form factor of a 2 mm Gaussian beam. . . . . . . . . . . . . . 78

12

List of Figures

3.20 Normalised DR power spectra obtained for a 2 mm Gaussian beam

for the different simulation methods. . . . . . . . . . . . . . . . . . . 78

4.1 General Layout of CTF3. . . . . . . . . . . . . . . . . . . . . . . . . 82

4.2 Pulse compression by a factor 2 in the Delay Loop. The principle of

the phase coding with the Sub-Harmonic Bunchers (SHB) is shown on

the top left and the bunch frequency multiplication is shown on the

top right. The pulse structure before and after the pulse compression

stage in the Delay Loop is shown at the bottom. . . . . . . . . . . . 83

4.3 The principle of the bunch frequency multiplication by a factor 4 in

the Combiner Ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.4 PETS structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.5 CR with CRM line. The following devices are shown on the plot:

bending magnets (denoted by BHFx) in red, quadrupole magnets

(denoted by QDx and QFx) in blue, small deflector magnets (denoted

by DHFx and DVFx) in black, BPMs (denoted by BPMx) in dark

green, beam instrumentation devices including the CDR setup in the

CRM line (denoted by CDRx and MTVx) in magenta, septa (denoted

by SHx) in green, and RF deflectors (denoted by HDSs) in orange. . 87

4.6 Technical drawing of the CRM line. . . . . . . . . . . . . . . . . . . 88

4.7 Vacuum assembly and vacuum support. . . . . . . . . . . . . . . . . 91

4.8 Simulated diamond transmission properties. . . . . . . . . . . . . . . 92

4.9 Comparison of the transmission properties of diamond and quartz. . 93

4.10 Aluminised target and target holder. . . . . . . . . . . . . . . . . . . 95

4.11 Off-centre flange with a 15 mm offset of the inner bore. . . . . . . . . 96

4.12 Schematic diagram of a Michelson interferometer. . . . . . . . . . . . 97

4.13 Typical interferograms for a narrow band and broad band detector. . 99

4.14 Picture of the Michelson interferometer at CTF3. . . . . . . . . . . . 100

4.15 Calculated splitting efficiencies for the S-polarised radiation. . . . . . 101

4.16 Custom beam splitter holder. . . . . . . . . . . . . . . . . . . . . . . 102

13

List of Figures

4.17 Polariser transmission for the polarisation component parallel to the

wires. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.18 Attenuator transmission for the four different attenuation levels. . . 104

4.19 Metal and semiconductor band profiles. . . . . . . . . . . . . . . . . 106

4.20 Schottky Barrier Diode detector response plotted against the relative

frequencies from the lowest (0%) to the highest frequency (100%) in

the individual frequency bands shown in Table 4.3. . . . . . . . . . . 107

4.21 SGH gain plotted against the relative frequencies from the lowest

(0%) to the highest frequency (100%) in the individual frequency

bands shown in Table 4.3. . . . . . . . . . . . . . . . . . . . . . . . . 108

4.22 Detector holder with a detector. . . . . . . . . . . . . . . . . . . . . 109

4.23 Schematic diagram of the hardware control interface. . . . . . . . . . 110

4.24 Schematic layout of the LabVIEW software. . . . . . . . . . . . . . . 112

5.1 Typical SBD signal and the corresponding beam current reading from

the CR.SVBPM0195 in the CR. . . . . . . . . . . . . . . . . . . . . . 116

5.2 Typical SBD signals for a 3 GHz and 1.5 GHz beam repetition rate. . 118

5.3 Sampling of a simulated simplified signal for a 3 GHz and 1.5 GHz

beam repetition rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.4 Dynamic range of the SBD detector illustrated by the signal of CDR

for two different target orientations. . . . . . . . . . . . . . . . . . . 120

5.5 CDR distribution scan before and after the installation of the off-

centre flange for a beam centred in the beam pipe and a beam tra-

jectory below the beam pipe centre. . . . . . . . . . . . . . . . . . . 122

5.6 Schematic drawing explaining the origin of the backgrounds. . . . . . 123

5.7 3D plot and contour plot of the CDR distribution measured with a

target raster scan for the two different polarisation components. . . . 126

5.8 Typical beam current stability. . . . . . . . . . . . . . . . . . . . . . 127

14

List of Figures

5.9 RF accelerating voltage impact on the bunch length. By changing the

Klystron MKS15 phase, the bunch length at the end of the Frascati

chicane can become shorter (green), longer (blue) or just be preserved

(red). This is due to the different time-of-flight of particles with

different momenta in the chicane. . . . . . . . . . . . . . . . . . . . . 129

5.10 Evolution of the SBD signal measured with the DXP-12 as a function

of the klystron phase. . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.11 Correlation measurements of the SBD detectors of two different band-

width with a streak camera in the CR and a waveguide pickup in the

TL1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.12 Example DR interferogram and corresponding spectrum. . . . . . . . 134

15

List of Tables

1.1 Nominal design parameters for CLIC at 500 GeV and 3 TeV. . . . . . 23

1.2 Beam parameters at the IP for CLIC at 500 GeV and 3 TeV. . . . . 25

3.1 Main CTF3 parameters used in the simulations. . . . . . . . . . . . . 57

3.2 Mesh properties and technical information for the DR simulation model. 70

4.1 CRM line devices, as displayed in Figure 4.6. . . . . . . . . . . . . . 89

4.2 Manipulator axis calibration. . . . . . . . . . . . . . . . . . . . . . . 94

4.3 SBD detectors used in the experiment. . . . . . . . . . . . . . . . . . 106

5.1 Parameters of the exponential fit, as defined in Equation (5.1), of the

translation scan in Figure 5.5(c) and Figure 5.5(d). . . . . . . . . . . 124

16

Chapter 1Introduction

This chapter aims to briefly introduce the reader to the experiment carried out. It

explains the importance of particle physics for the understanding of our universe and

the need for high-energy collider experiments to test some of the proposed theories.

In order to obtain sufficiently large data sets from these experiments and therefore

a certain statistical confidence in the measurement, the concept of luminosity of a

collider is discussed. The influence of the bunch length on the luminosity and on

the overall performance of the machine is taken into consideration, and existing and

developing techniques to measure this important beam parameter are described.

1.1 Particle physics and the Standard Model

Particle physics as a tool to understand the nature of the universe and the parti-

cles within it became an important instrument with the invention of the first basic

particle accelerators in the 1930s [1, 2]. The use of particle accelerators laid the

foundations for the formulation of the Standard Model (SM) of Particle Physics,

which is one of the major successes of physics of the 20th century. For example, the

SM was able to predict the existence of a third generation of quarks, namely the

“bottom” and “top” quark, for which Kobayashi and Maskawa were awarded the

Nobel Prize of Physics in 2008. Indeed, the bottom quark was discovered in 1977 at

the E288 experiment at Fermilab [3] and the top quark was discovered in 1995 by

the CDF and DØ experiments at Fermilab [4].

17

1.1. Particle physics and the Standard Model

Not only has the SM celebrated enormous successes in the past, but it also

postulates the Higgs mechanism. The Higgs mechanism and a resulting particle, the

so-called Higgs boson, have moved into the centre of attention of modern particle

physics. Particle physicists around the world are eagerly awaiting the latest data

from the recently commissioned Large Hadron Collider (LHC) at CERN and the

discovery of this particle. It is hypothesised that elementary particles acquire mass

by interacting with this Higgs field. Moreover, the Higgs field is suggested to provide

the mechanism by which the symmetry of the electroweak force is broken, causing

the separate observation of electromagnetic and weak phenomenologies [5].

Despite its tremendous success, the SM does not explain some of the most fun-

damental questions of particle physics and has at least a couple of severe problems

it can not account for:

Dark matter Dark matter, which makes up around 25% of the energy of the uni-

verse, is currently not explained in the SM as it does not include a par-

ticle which is stable, fairly massive, electrically neutral and only weakly-

interacting [6].

Grand Unified Theory The Grand Unified Theory (GUT) postulates that the

couplings of the electromagnetic, weak, and strong interactions unify at an

energy scale of 1016 GeV. For the SM on its own, however, an extrapolation of

the gauge couplings to higher energies shows that the couplings become very

similar but do not precisely unify [7].

Hierarchy problem The SM is also faced with a hierarchy problem as the Higgs

boson will be subjected to large radiative corrections to its mass from loop

interactions with fermions and bosons which are quadratically divergent. Al-

though the Higgs mass is expected to be found in the range of the electroweak

symmetry breaking scale, O(100) GeV, the loop correction terms in the SM

would prefer to be closer to the cut-off scale beyond which the theory ceases to

be valid, namely the GUT or Planck scales. In order for the Higgs to remain

light, i.e. O(100) GeV, a fine-tuning of some of the SM parameters would be

necessary which is very unnatural [8].

18

1.2. High-energy particle colliders

Several theories exist to answer some of the problems outlined above. One of the

most promising candidates to answer these shortcomings is Supersymmetry (SUSY).

The SUSY model proposes that every SM fermion has a bosonic super-partner and

that every SM boson should have a fermion super-partner. For an in-depth expla-

nation of the SUSY model, the reader is directed towards [9].

In order to test theories like the proposed Higgs mechanism and the SUSY model,

and to discover unknown phenomena and particles, high-energy particle colliders are

utilised.

1.2 High-energy particle colliders

Particle accelerators such as the Large Electron Positron Collider (LEP) at CERN

and the Hadron Elektron Ring Anlage (HERA) at DESY have done an outstand-

ing job in exploring the particle physics landscape and the SM in energy regions

just below the TeV scale. After the many successes LEP and HERA celebrated,

they were decommissioned in 2000 and 2007, respectively. Another particle accel-

erator which took a vital role in advancing the understanding of particle physics

is the TEVATRON at Fermilab with a centre-of-mass energy (Ecm) of 2 TeV. The

TEVATRON is still running and is delivering many results, including some very

interesting exclusion regions for the mass of the Higgs boson in the SM [10].

As previously mentioned, the LHC recently began operation and has set the

record for the most energetic particle collisions, with Ecm of 7 TeV. The LHC has a

design Ecm of 14 TeV and is expected to deliver a lot of new interesting results as it

surpasses previously explored energy regions and has a direct look at physics at the

TeV scale.

When talking about the discovery potential and performance of modern particle

accelerators, one needs to distinguish between the different types of accelerators.

Generally, high-energy particle colliders can be divided into two main categories by

the kind of particles they are colliding, i.e. hadron or lepton colliders. There is

also HERA at DESY colliding a hadron and a lepton beam but it is omitted in this

discussion.

19


1.2.1 Hadron colliders

Hadron colliders have used either proton-proton or proton-antiproton beams and are

normally based on a ring-shaped layout of the accelerator. Hadron accelerators are

an outstanding tool for reaching into higher energy regions and are generally used

as discovery machines. They can reach much higher energies than lepton colliders,

even after taking the degradation of the beam energy due to the parton model

into account. As hadron colliders also allow gluon as well as quark and antiquark

collisions, a higher production cross section can be achieved.

There are, however, some disadvantages that hadron colliders inherently have.

The parton distribution functions introduce a spread of hard-scattering centre-of-

mass energies making the reconstruction of the collisions more difficult. Additionally,

remnants of the initial hadrons can be present in the final state of the collisions.

1.2.2 Lepton colliders

Lepton colliders normally go hand in hand with hadron colliders. Lepton colliders

usually utilise electron-positron beams to perform accurate measurements on dis-

coveries made by hadron colliders. The possibility to use polarised beams and the

resonant production of particles makes these machines ideal for these kind of pre-

cision measurements. Moreover, lepton colliders benefit from the direct access to

the centre-of-mass energy due to the collision of elementary particles and very clean

signatures in the particle detectors.

Nevertheless, lepton colliders also have drawbacks that limit their performance.

Due to the use of electron-positron beams, one can not easily produce particles that

do not couple to a γ or Z. Furthermore, the electron-positron annihilation cross

section is relatively small and decreases nearly quadratically with increasing Ecm.

As mentioned in Section 1.1, many interesting new discoveries are expected to

be seen at the LHC within in the next years, including the possible discovery of

the Higgs and SUSY particles. A next generation lepton collider in the TeV energy

region would be able to accurately measure properties of the Higgs and other possible

new findings at the LHC.

20


1.2.3 Necessity for a high-energy linear collider

Building a circular electron-positron collider as in the past with Ecm in the TeV

range, however, would be extremely difficult and costly due to the emission of syn-

chrotron radiation (SR). SR is emitted by an accelerated charged particle due to

the rearrangement of the electric field. In a circular collider a large amount of SR is

produced as the particles pass through the bending magnets, which keep the beam

in orbit. The instantaneous synchrotron radiation power is [11]

Pγ(GeV s−1) =cCγ2π

E4

ρ2(1.1)

where c is the speed of light, E is the particle energy, ρ the bending radius of the

particle in the magnetic field, and Cγ is the radiation constant

Cγ =4π3

rc(mc2)3

= 8.85× 10−5 m

GeV 3(1.2)

where rc is the classical particle radius and mc2 is the particle rest energy. Therefore,

the synchrotron radiation power does not only scale with E4 and ρ−2, but also

depends on the type of particle, a reason why it is possible to build circular hadron

colliders with a high Ecm.

The energy loss due to synchrotron radiation per revolution ∆E in a circular

accelerator is given by

∆E(GeV ) = CγE4

ρ. (1.3)

The circular electron-positron collider with the highest Ecm was LEP at CERN

with a tuneable energy of up to 209 GeV, or 104.5 GeV per beam. For a bending

radius of ρ = 3096 m [12], the particle energy loss per turn was 3.4 GeV or 3.3% and

needed to be compensated by accelerating structures.

Assuming a similar bending radius as for LEP and an electron beam at 1 TeV,

the particle energy loss per turn would be 28585 GeV, the compensation of which

is essentially unfeasible by RF acceleration. Since the energy loss per turn scales as

E4, it is also very difficult and costly to counteract the energy loss by increasing the

bending radius. Therefore, it is significantly more favourable to consider a linear

21

1.3. CLIC

accelerator (linac) for a future electron-positron collider.

Currently, two major R & D programmes for a future linear collider are being per-

formed: the International Linear Collider (ILC) and the Compact Linear Collider

(CLIC) which are based on a different linac technology. The ILC aims to accelerate

the electron and positron beams in a superconducting linac with an average accel-

erating gradient of 31.5 MV/m up to 500 GeV (Ecm) with an option to upgrade to

1 TeV in a later stage of the experiment [13].

1.3 CLIC

CLIC is based on a room-temperature two-beam acceleration concept, where the

accelerating RF power is provided by a drive beam running parallel to the main linac.

A high current, low energy drive beam is decelerated in special cavities producing

RF power and the RF power is transferred onto the low current, high energy main

beam. CLIC aims to accelerate the electron and positron beams with an accelerating

gradient of 100 MV/m up to 3 TeV (Ecm). Currently, a possibility to build a 500 GeV

(Ecm) CLIC and to later upgrade the accelerator to 3 TeV is considered.

1.3.1 The CLIC concept

The energy for RF production is initially stored in a long-pulse electron beam, the

so-called drive beam, which is accelerated to about 2.38 GeV by a fully-loaded, low-

frequency (1 GHz) linac. The initial bunch repetition rate of the drive beam will

be 0.5 GHz. The drive beam then passes through subsequent rings where groups of

leading bunches are delayed in order to fill in the gaps between succeeding bunches.

This bunch interleaving is performed by transverse RF deflectors. The resulting

effect is to multiply the bunch repetition rate of the long-pulse beam and to therefore

increase the peak power of the drive beam.

This high power drive beam is then distributed in transport lines along the two

linacs in the opposite direction of the main beam. Along this transport line, pulsed

deflector magnets deflect the drive beam into turn-around loops starting at the

beginning of the linac towards the interaction point (IP). Once the drive beam has

22

1.3. CLIC

been turned around in the direction of the main beam, it is decelerated in 876 m long

sectors of decelerating structures. The resulting output power is then transferred

into the accelerating cavities of the main linac and the low-current main beam is

accelerated to high energy.

The drive beam repeatedly joins the main beam to run in parallel, but slightly

ahead of it, to produce the necessary power for the individual sectors. At the end

of each sector, the decelerated drive beam is terminated in the beam dump and the

next part of the drive beam takes over the acceleration of the main beam in the next

sector.

Therefore, the initial long-pulse beam can be converted into a high-power drive

beam in the same accelerator and beam manipulation system to supply the necessary

RF power for the entire main linac [14].

1.3.2 General layout of CLIC

The two-beam acceleration scheme of CLIC, as explained in Section 1.3.1, dictates

the general layout of CLIC, as seen in Figure 1.1. The main design parameters, as

of September 2010, for a 500 Gev (Ecm) and 3 TeV (Ecm) configuration of CLIC

are shown in Table 1.1. More detailed information on the design parameters can be

found in [14].

Parameters unitCentre-of-mass energy (Ecm) 0.5 3 TeV

Instantaneous luminosity 2.3 5.9 1034 cm−2 s−1

Linac repetition rate 50 HzLoaded accel. gradient 80 100 MV/m

Main linac RF freq. 11.994 GHzBeam pulse duration 177 156 nsProposed site length 13 48.3 kmTotal site AC power 129.4 415 MW

Table 1.1: Nominal design parameters for CLIC at 500 GeV and 3 TeV [14].

The machine consists of an injector complex for the main beams including the

electron and positron sources producing polarised beams, the pre-damping rings and

damping rings to minimise the horizontal emittance, a bunch compressor after the

23

1.3. CLIC

(c)FT

TA ra

dius

= 1

20 m

BC

2

del

ay lo

op1

km

dec

eler

ator

, 24

sect

ors o

f 876

m

326

klys

tron

s33

MW

, 139

µs

CR

2

CR

1

circ

umfe

renc

esde

lay

loop

73.

0 m

CR1

146.

1 m

CR2

438.

3 m

BD

S2.

75 k

mIP

TA r=

120

m

BC

2

245

m

del

ay lo

op1

km

326

klys

tron

s33

MW

, 139

µs

dri

ve b

eam

acc

eler

ator

2.38

GeV

, 1.0

GH

z

CR

2

CR

1

BD

S2.

75 k

m

48.3

km

dri

ve b

eam

acc

eler

ator

2.38

GeV

, 1.0

GH

z

BC

1

245

m

CR

c

omb

iner

rin

gTA

turn

arou

ndD

R

dam

pin

g r

ing

PD

R

pre

dam

pin

g r

ing

BC

b

unch

com

pre

ssor

BD

S

bea

m d

eliv

ery

syst

emIP

inte

ract

ion

poi

nt

dum

p

e+ in

ject

or,

2.86

GeV

e+

PD

R

398

m

e+

DR

49

3 m

boo

ster

lina

c, 6

.14

GeV

e+ m

ain

linac

e– in

ject

or,

2.86

GeV

e–

PD

R

398

m

e–

DR

49

3 m

e– m

ain

linac

, 12

GH

z, 1

00 M

V/m

, 21.

02 k

m

Figure 1.1: Schematic general layout of CLIC at 3 TeV. Courtesy of the CLIC Studygroup.

24

1.3. CLIC

damping rings, and a booster linac to accelerate the main beams up to 6.14 GeV.

Long transfer lines then deliver each of the beams to a turnaround loop at the

beginning of the linacs, where it is compressed again and prepared for acceleration

in the main linac.

For the production of the drive beam, two drive beam injectors are utilised. As

explained in Section 1.3.1, the two drive beams are accelerated to 2.38 GeV and

the bunch repetition rate is doubled in the delay loop, tripled in the first combiner

ring, and quadrupled in the second combiner ring, yielding a bunch frequency mul-

tiplication factor of 24 thus achieving a 12 GHz beam for the power production in

the decelerating structures, the so-called Power Extraction and Transfer Structures

(PETS). The PETS are located in the 24 sectors of 876 m length along the main

linac where the power transfer to the main beam takes place. The design efficiency

for the power transfer from the drive beam to the accelerating structure in the main

beam is 65%.

Parameters unitCentre-of-mass energy (Ecm) 0.5 3 TeV

BDS length 1.87 2.75 kmBunch charge 6.8 3.72 109

Bunch separation 0.5 nsBeam power/beam 4.9 14 MWHor. IP beam size 202 40 nmVert. IP beam size 2.2 1.0 nmHor. norm. emitt 2400 660 nm radVert. norm. emitt 25 20 nm rad

Crossing angle at IP 20 mradBunch length 44 µm

Table 1.2: Beam parameters at the IP for CLIC at 500 GeV and 3 TeV [14].

After the two main beams have been accelerated to 3 TeV, they are prepared

for collision at the IP in the 2.75 km long beam delivery systems (BDS). The beam

parameters at the IP are shown in Table 1.2 and give rise to intense electromagnetic

fields. These fields strongly affect the motion of the particles in the opposing beams.

The influence of the different parameters at the IP on these beam-beam effects and

on the luminosity of the collider are explained in the following section.

25

1.4. Beam-beam effects in a linear collider

1.4 Beam-beam effects in a linear collider

The beam-beam effects in a collider can be divided into two categories, namely the

disruption effects and the beamstrahlung effects. Before discussing these effects,

however, the concept of luminosity is briefly explained in this section.

1.4.1 Luminosity

Luminosity is the key issue for colliders since the production rate for a particle

of interest is given as the product of luminosity and cross section for the desired

reaction. The luminosity of a collider can be interpreted as the particle flow of two

opposing beams through a certain area at the IP,

L =N1N2f

A(1.4)

where N1 and N2 are the number of particles per bunch, f is the frequency of the

particle beam crossing, and A is the cross-sectional area. Assuming equal bunch

charges for the opposing beams, the luminosity of a linear collider, can be written

as

L =N2frepnb

4πσxσy(1.5)

where frep is the repetition rate of the particle train, nb is the number of bunches

per train, and σx and σy are the horizontal and vertical beam sizes, respectively.

1.4.2 Disruption effect

Due to the large beam fields of the opposing, oppositely charged beams, the reduction

of the nominal beam sizes causes an enhancement of luminosity. When discussing

the enhancement, the disruption parameter D can be introduced, which in the x

and y direction is given by [15]

Dx,y =2reNσz

γσx,y(σx + σy)(1.6)

26


where σz is the rms bunch length, γ is the Lorentz factor, and re is the classical

electron radius. For e+e−-colliders, an enhancement of luminosity occurs due to

the mutual pinching of the two colliding beams. Note that the bunch length has

a significant impact on the disruption parameter and can be used to increase the

luminosity. For circular beams and in the weak disruption limit where D 1, the

luminosity enhancement factor HD can be found from computer simulations and can

be expressed by a semi-empirical scaling law [16]

HD = 1 +2

3√πD +O(D2) (1.7)

and one can therefore re-write the luminosity as

L =HDN

2frepnb4πσxσy

. (1.8)

1.4.3 Beamstrahlung effect

The disruption at the IP, however, is just a strong deflection of particles and therefore

synchrotron radiation is emitted, referred to as beamstrahlung. This beamstrahlung

causes an unwanted spread of centre-of-mass energy, undesirable pair creation, and

resulting detector backgrounds. Therefore, the requirement of a very high luminosity

is not the only important parameter for the design of a collider.

All beamstrahlung effects can be described by the beamstrahlung parameter Υ,

which can be written as [17]

Υ = γ〈E +B〉Bc

≈ 56

r2eγN

ασz(σx + σy)(1.9)

where 〈E + B〉 is the mean field strength, Bc is the Schwinger critical field (Bc =

4.4×1013 Gauss), and α is the fine-structure constant. The beamstrahlung parameter

signals the onset of non-linear QED effects and is to be kept as low as possible. Again,

the bunch length is an important parameter when trying to minimise beamstrahlung.

27


1.4.4 Hour-glass effect

Moreover, a geometrical effect plays an important role when considering the perfor-

mance of a collider. The transverse bunch size at the IP σ∗x,y of a collider is strongly

reduced using quadrupole magnets and is proportional to the β-function

σ∗x,y ∝√β∗x,y(s). (1.10)

Due to the focusing of the beam, the β-function depends on the position s from

the IP and can usually be approximated as

βx,y(s) = β∗x,y

(1 +

(s

β∗x,y

)2)

(1.11)

and therefore the bunch size near the IP can be formulated as

σx,y(s) = σ∗x,y

√√√√(1 +(

s

β∗x,y

)2). (1.12)

The variation of the transverse beam size then looks very much like an hour-

glass, hence the “hour-glass effect”. Therefore, if the bunch length σz is comparable

to or larger than β∗x,y, the variation of the transverse beam size has an impact on

the reduction of the luminosity. The relative luminosity reduction for circular beams

can then be formulated as [17]

L(σz)L(0)

=

∫ +∞

−∞

1√π

e−u2[

1 +(

uux,y

)2] du =

√π · ux,y · eu

2x,y · erfc(ux,y) (1.13)

with ux,y = β∗x,y/σz and erfc(ux,y) the complementary error function, indicating that

a long bunch length at the IP leads to a reduction of luminosity and is to be avoided.

Consequently, the bunch length has an important impact on the performance

of a linear collider and should neither be too large nor to small, as shown in this

section. Therefore, the bunch length needs to be carefully monitored and optimised

in order to achieve the best possible performance of such a machine.

28

1.5. RF power production in the PETS

1.5 RF power production in the PETS

Besides the influence of the bunch length on the luminosity and optimisation of the

collision rate, the bunch length also plays an important role for the power extraction

in the PETS at CLIC. The RF power generated by the bunched beam in a periodic

structure can be expressed as [14]

P = I2L2F 2b ω0

R/Q

4Vg(1.14)

where I is the beam current, L the active length of the structure, Fb is the single

bunch form factor, ω0 the bunch frequency, R the impedance per metre length, Q

the quality factor, and Vg is the group velocity. Again, the bunch length, which

manifests itself in the single bunch form factor Fb, as explained in Section 2.4, plays

a crucial role in achieving the desired power extraction in the PETS.

1.6 Bunch length measurement techniques

As described in the previous sections, the bunch length has a significant impact on

the performance of a particle collider, especially for a linear collider such as CLIC.

Therefore the bunch length needs to be measured as accurately as possible. In this

section, an overview of existing and developing techniques is laid out. For the case

of CLIC, the measurement of the bunch length at the IP of 147 fs (44 µm) is very

challenging. Different bunch length measurement techniques are outlined in this

section and their resolution limits are given.

1.6.1 Streak camera

The streak camera generally uses optical radiation emitted by the particle beam

to measure the bunch length. This optical radiation can either be synchrotron ra-

diation or transition radiation from a screen. Inside the streak camera, photons

emitted by the particle beam hit a photocathode of a vacuum tube where electrons

are emitted and accelerated. After acceleration, the electrons are quickly deflected

by a transverse time-dependent electric field. Successive electrons emitted by the

29

1.6. Bunch length measurement techniques

Figure 1.2: Principle of a streak camera [18].

photocathode, which correspond to the longitudinal particle distribution of the orig-

inal particle bunch, are deflected more strongly, thus rotating the particle bunch in

space. The electrons then strike a phosphor screen and a copy of the original bunch

can be observed from the side, yielding a possibility for measuring the bunch length.

The principle of a streak camera is shown in Figure 1.2.

During normal operation, a slit is used in front of the streak camera to minimise

the effect of the transverse beam size on the bunch length measurement as the

rotation is never exactly 90. The resolution of the streak camera is determined by

the quality of the optical transport system, finite sweep speeds, photoelectron energy

spread and the resolution of the CCD camera used to acquire the rotated image. The

fastest streak camera on the market, the Hamamtsu “FESCA-200” (Femtosecond

Streak Camera), has a quoted resolution of 200 fs [19].

Moreover, to measure the bunch length, a streak camera also requires radiation

emitted by the bunch. Therefore, it can easily be used in circular machines. In

linear parts of a machine, however, an additional light generation system is needed,

which might make the method destructive.

1.6.2 Transverse deflection cavities

The RF transverse deflection cavity, similar to the streak camera, uses a rotation of

the particle bunch to measure the bunch length. In this case, however, the rotation

30


of the bunch is performed on the original bunch, rather than a copy of it in the

streak tube. For this purpose, a transverse RF cavity is used to deflect particles

along the particle bunch more or less strongly to separate the head from the tail of

the bunch. The RF phase of the deflection cavity is set at the zero-deflection point,

such that the longitudinal phase space of the bunch is swept transversely, but does

not experience a mean deflection.

The resulting rotation of the particle bunches can then be observed on an optical

transition radiation (OTR) screen and the transverse size is directly proportional to

the bunch length. The RF deflector has a certain resolution limit and for the case

of the transverse deflection cavity “LOLA” at SLAC the best possible resolution is

15 fs [20]. This ultimate resolution depends on the streak speed and the unstreaked

transverse beam size on the OTR screen. The RF deflector has the disadvantage

of being an invasive bunch length measurement technique and is therefore not suit-

able for accelerators with high-energy beams or particle beams with a high current

density as this would cause damage to the OTR screens and give rise to signifi-

cant beam losses. Moreover, a transverse deflection cavity requires relatively large

infrastructure and significant beam-line space.

1.6.3 Electro-optic techniques

The electro-optic (EO) technique uses the change of the birefringence of an electro-

optical crystal (e.g. a ZnTe crystal) with external electric fields to measure the lon-

gitudinal beam profile. The Coulomb field of a particle beam passing such a crystal

changes the refractive index of the crystal. Using a linearly polarised laser cross-

ing such a crystal, the information can be extracted via laser ellipsometry. Laser

ellipsometry relies on directing the laser through an arrangement of polarisers, and

hence the change of the birefringence manifests itself as an intensity modulation.

The bunch length can then be extracted from the laser pulse. There are different

ways of modifying the initial laser pulse to allow the crystal properties to be en-

crypted onto the laser beam. Depending on the chosen method, the change of the

crystal properties can be decoded from the laser in two ways, spectral decoding or

temporal decoding [21].

31


For the spectral decoding, a linear chirp is introduced to stretch the short laser

pulse to a duration longer than the bunch length. The associated Coulomb fields

along the bunch are encoded onto the optical beam modifying different frequencies

in the chirped pulse. The chirped pulse can then be analysed with a spectrometer

and the longitudinal beam profile can be extracted. This form of the electro-optical

technique can be performed as a single-shot measurement.

For the temporal decoding, the short laser pulse is split into two beams. One of

those is functioning as the gate, while the other is acting as the probe. The probe

is again stretched to a length longer than the bunch length. This pulse samples

the birefringence in the electro-optical crystal. The modified probe pulse is then

cross-correlated with the short gate pulse in a crystal, where the temporal particle

distribution in the bunch is translated into a spatial position which can be observed

by a CCD camera.

For the EO techniques, it is possible to achieve a bunch length resolution of down

to 60 fs [22], but this is still a challenging resolution to achieve. Despite its good

performance, one of the main drawbacks of the EO technique is the cost involved in

setting up the measurement station and its operation.

1.6.4 Frequency domain techniques

Besides the time domain sampling methods outlined above, one can apply frequency

domain techniques in order to obtain the longitudinal beam profile. These frequency

domain techniques use beam-induced radiative processes, such as coherent transition

radiation (CTR), diffraction radiation (CDR), synchrotron radiation (CSR), Smith-

Purcell radiation (SP), and Cherenkov radiation. These spectral techniques depend

on causing the Coulomb field to radiate in a controlled manner and subsequently

obtaining the longitudinal charge distribution from the emitted radiation spectrum.

For this purpose, components such as gratings, crystals or screens are used in the

beam line to induce this kind of radiation and, depending on the type of radiation,

can be designed to be invasive or non-invasive. The radiation is then observed with

a spectrometer and the spectral information of the beam induced radiation can be

obtained.

32

1.7. Motivation

When retrieving the spectrum from the measurement, it has to be taken into

account that only the power density spectrum can be measured. The power density

spectrum, however, does not explicitly contain information about the phase of the

radiation. Therefore, one has to apply a minimal phase approximation to retrieve

the phase of the radiation. A commonly used technique, which is known as Kramers-

Kronig relation, is discussed in detail in Section 2.5.

There is essentially no intrinsic limit to the resolution of these frequency domain

techniques. There are, however, some technical challenges due to the detection

and transfer of far-infrared radiation, i.e. the alignment of the optical spectrometer

system becomes more challenging for higher frequencies.

1.7 Motivation

As shown in Table 1.2, the parameters for CLIC at the IP are quite challenging. Be-

sides the short bunch lengths of 147 fs (44 µm), the bunch separation in the electron

bunch train of 0.5 ns is also very small. Since the longitudinal beam profile has an

important impact on the luminosity of CLIC and on the power production in the

PETS, this profile and a variation thereof needs to be known all along the electron

bunch train. Therefore, a sufficiently fast longitudinal beam profile measurement

system which is able to resolve the bunch profile along the electron bunch train is

essential. For CLIC, over 200 longitudinal measurement stations along the drive

beam and the main beam will be needed and therefore the implication of the cost

of the longitudinal beam profile monitoring on the project needs to be taken into

consideration.

As discussed in Section 1.6, a streak camera can efficiently be used in circular ma-

chines. In linear sections, however, an additional light generation system is needed

which can be destructive. Moreover, due to its resolution limit, a streak camera will

not be able to monitor bunch lengths down to around 147 fs. A transverse deflection

cavity, on the other hand, is able to cope with bunch lengths as short as 15 fs. The

RF deflector, however, as already explained, has the disadvantage of being an inva-

sive measurement which is not suitable for accelerators with particle beams with a

33

1.7. Motivation

high population, such as CLIC. Moreover, the large footprint and the infrastructural

requirements of a transverse deflecting cavity limit its usage at CLIC.

The electro-optic technique has been developed extensively over the last decade

and bunch lengths down to sub-100 fs have been successfully measured. The need for

high-power laser system to perform the electro-optic measurements and the required

maintenance, however, has an impact on the costs of setting up and operating the

system over a longer period of time. Solely relying on the electro-optic technique

for the 200 measurement stations at CLIC, would imply a significant contribution

to the overall cost of the project.

A very promising alternative is the frequency domain technique, which shows

some very good characteristics, making it suitable for its use at CLIC. CDR, as

the source of controlled beam-induced radiation, is used in this project. Interest-

ing results on CDR as a longitudinal bunch profile monitoring technique have been

obtained before [23] and the technique is aimed to be expanded in this thesis. As

will be shown, a setup using CDR can be designed minimally invasive and has the

advantage over the aforementioned techniques that it does not have an intrinsic res-

olution limit. Moreover, the frequency domain technique provides a direct measure-

ment of the longitudinal form factor, which many applications, such as luminosity

estimations, require. The complicated requirements for a longitudinal beam profile

monitoring system for CLIC based on CDR, however, and challenges which the tech-

nique is faced with had to be identified and addressed. These challenges included

the accurate prediction of the emission of CDR from a conducting screen, which is

brought into close proximity to the electron beam. Therefore, an analytic model

needed to be constructed, which can be used to determine the CDR spectrum for

a specific setup. The CDR spectrum plays an important role during the analysis

of the observed signal since the reconstructed longitudinal bunch profile is sensitive

to it. Moreover, Kramers-Kronig reconstruction technique needed to be developed

further in order to reliably reconstruct the bunch profile.

Experimentally, the suppression of beam-based backgrounds for a setup needed

to be investigated in order to improve the performance of the longitudinal beam

profile reconstruction. Since CDR for bunch lengths at CLIC and CTF3 is mostly

34

1.8. Thesis overview

emitted in the far-infrared and millimetre wavelength region, the components to

build such a system needed to be chosen carefully. Additionally, a system being able

to cope with a high bunch spacing frequency at CLIC needed to be designed.

It was therefore intended to design and install a system for the investigation

of CDR from a conducting screen in CTF3 at CERN, which is based on ultra-

fast room-temperature Schottky Barrier Diode (SBD) detectors, in order to meet

the requirement for the observation of an electron bunch train with a high bunch

spacing frequency.

1.8 Thesis overview

1.8.1 Chapter 2

Chapter 2 includes an overview of the theory which is needed in the scope of this

thesis. It introduces the reader to the virtual photon model which can be used to

describe the emission of diffraction radiation (DR) from a conducting screen. It is

then explained how collective effects in a particle bunch can be used to determine the

longitudinal electron beam profile by determining the minimal phase with Kramers-

Kronig reconstruction technique.

1.8.2 Chapter 3

Chapter 3 demonstrates how two different simulation models were established by

the author to predict DR properties and outlines the results obtained from the

two models. It shows the spatial distributions of DR obtained by the virtual photon

model for various target configurations and beam parameters, and the spectra which

can be determined therefrom. With the aid of a time-domain simulation package,

the DR emission from a simplified replica of the setup at CTF3 is investigated and

again the spectra are determined.

1.8.3 Chapter 4

In Chapter 4, the setup which was designed and installed in CTF3 by the author

is explained. This includes a description of the key elements of the vacuum hard-

35

1.8. Thesis overview

ware, which was integrated in the CTF3 beam line, and the spectral dependencies

of the optical components of the Michelson interferometer, which was used to per-

form spectral measurements of CDR. Moreover, the acquisition and control software

developed by the author is briefly explained.

1.8.4 Chapter 5

In Chapter 5, the characteristics of the Schottky Barrier Diode signal are discussed

and the CDR spatial distributions are measured. Moreover, the effect of an upgrade

to minimise beam-based backgrounds is shown, and the performance of the setup

and the spectral measurements are discussed.

1.8.5 Chapter 6

In Chapter 6, the results obtained are summarised and the main conclusions are

drawn. From those conclusions, issues and challenges which need to be addressed

further are discussed and suggestions from the author for future experiments are

given.

36

Chapter 2Theory

In this chapter, the theory relevant to the understanding of the project is described.

It will introduce the reader to the virtual photon model and the resulting explanation

of diffraction radiation, and will summarise the basic properties thereof. Moreover, it

will explain how coherent radiation can be used to determine the longitudinal beam

profile and how the missing phase information can be inferred by the Kramers-Kronig

dispersion relation.

2.1 Virtual photon model

For a Lorentz transformation, corresponding to a boost along the z axis with speed

βc from a frame K to the boosted frame K ′, the transformation of the components

of the electric and magnetic fields, E and B, to the boosted fields E′ and B′ are [24]

E′z = Ez B′z = Bz

E′x = γ(Ex − βBy) B′x = γ(Bx + βEy)

E′y = γ(Ey + βBx) B′y = γ(By − βEx).

(2.1)

To illustrate the transformation of the fields, a point charge q is considered. This

point charge is at rest in the system K ′ and moving in a straight line with velocity

v in system K, as seen in Figure 2.1. In frame K, the charge is moving past an

observer along the positive z axis. The closest distance between the charge and the

37

2.1. Virtual photon model

x

z

x′

z′

y

y′

q

P

b

r′=pb2 + (vt′)2

Figure 2.1: Lorentz boost of initial frame K to frame K ′.

observer at point P , i.e. the impact parameter, is b. At t = t′ = 0, the origins of

the two coordinate systems coincide with the charge closest to the observer, and the

coordinates of point P in frame K ′ can be expressed as x′ = b, y′ = 0, and z′ = −vt′.

Therefore the observer is a distance r′ =√b2 + (vt′)2 away from q in frame K ′.

In the rest frame K ′ of charge q, the electric and magnetic fields at the observa-

tion point P can be written as

E′z = −qvt′

r′3E′x =

qb

r′3E′y = 0

B′z = 0 B′x = 0 B′y = 0.(2.2)

The non-vanishing components of the electric and magnetic fields can be ex-

pressed in terms of the coordinates of frame K. Subsequently, using the inverse of

Equations (2.1) they can be written as

Ez = E′z = − qγvt

(b2 + γ2v2t2)3/2

Ex = γE′x =γqb

(b2 + γ2v2t2)3/2

By = γβE′x = βEx.

(2.3)

38


Time [vt]-0.3 -0.2 -0.1 0 0.1 0.2 0.3

) co

mpo

nent

[ar

b.u.

]-1 β y

(an

d B

xE

0

0.2

0.4

0.6

0.8

1 = 10γ = 50γ

(a) Ex (β−1By) field

Time [vt]-0.3 -0.2 -0.1 0 0.1 0.2 0.3

com

pone

nt [

arb.

u.]

zE

-1

-0.5

0

0.5

1 = 10γ = 50γ

(b) Ez field

Figure 2.2: Ex (β−1By) and Ez component of the electromagnetic field for twodifferent particle energies γ.

Equations (2.3) illustrate the changes of the electric and magnetic fields for dif-

ferent particle Lorentz factors γ. For a particle approaching the speed of light, i.e.

β → 1, the observed transverse magnetic field By becomes almost equal to the trans-

verse electric field Ex. For the ultra-relativistic case, i.e. γ 1, the peak transverse

electric field is a factor γ larger than the transverse field in the non-relativistic case.

The three non-vanishing field components at the stationary observation point, as a

function of time, are shown in Figure 2.2.

Figure 2.2(a) shows the transverse electric and magnetic field for two different

γ, where the peak field is proportional to γ. It can also be inferred that the time

interval for which the fields are significant is

∆t =b

γv. (2.4)

This means that, while the transverse peak fields are linearly proportional to

γ, the durations of the fields are inversely proportional. Figure 2.2(b) also shows

that the longitudinal electric field changes more and more rapidly from positive to

negative strength for increasing γ and has zero time integral.

A spatial representation of how the lines of electric force for a particle at rest

change to the lines of electric force for a particle in motion is shown in Figure 2.3.

39


γ 1

Figure 2.3: Change of the Coulomb field of a charged particle in the laboratoryframe under a Lorentz transformation from a stationary rest frame to a moving restframe with γ 1.

It indicates that the lines are compressed to an increasingly transverse direction for

increasing particle Lorentz factors.

Hence, in the relativistic case, i.e. γ 1, the observer sees nearly equal trans-

verse and mutually perpendicular electric and magnetic fields. Additionally, due to

the zero time integral of the longitudinal electric field and the rapid polarity change,

this longitudinal electric field can not be observed by a real detector with a certain

inertia. Moreover, the amplitude of the longitudinal component does not scale with

γ and is much smaller than the transverse field in the relativistic limit. For high

enough γ, the three field components therefore reduce to the two transverse and

mutually perpendicular electric and magnetic fields and just appear to be the fields

of a pulse of linearly polarised radiation propagating in the z direction.

The consideration so far is based on the electric field constraint to the x-axis,

since E′y = 0 was set in Equations (2.2), and therefore resulted in the pulse of linearly

polarised radiation. Due to the azimuthal symmetry of the Coulomb field, however,

the model can easily be extended to a two-dimensional case in order to allow for a

pulse of elliptically polarised radiation. For the two-dimensional case one would set

b =√b2x + b2y, where bx,y are the impact parameter components.

The interpretation of the particle field as the field of a plane wave is known as

the virtual photon or Weizsacker-Williams method and will be used to describe the

transition and diffraction radiation theory in this chapter.

Moreover, Equations (2.3) can be Fourier transformed to obtain the harmonic

content of the Coulomb field components of the charged particle. Since only the

40


ζ0 1 2 3 4 5 6

)ζ( 1 Kζ

0

0.2

0.4

0.6

0.8

1

Figure 2.4: Plot of ζK1(ζ).

transverse electric field component is of real interest in this discussion, it can be

shown that the Fourier transform of this component is [24, 25]

Ex(ω) =q

bv

(2π

)1/2

ζ K1(ζ) (2.5)

where ζ =ωb

γv, ω is the angular frequency, and K1 is the first order MacDonald

function. A plot of ζK1(ζ) is shown in Figure 2.4 and illustrates the dependence of

the transverse electric field component on ζ. Recalling that v = βc → c for γ 1

and ω = 2πc/λ, we can therefore formulate an approximate condition for which the

transverse field component has a significant strength

ζ =ωb

γv≤ 1⇔ b ≤ γλ

2π(2.6)

and therefore the transverse electric field component is confined within a disk of

radius γλ. Since the electric and magnetic transverse fields for γ 1 are equal,

this also applies to the transverse magnetic component. The confinement of the

Coulomb field gives rise to some experimental benefits as well as limitations for the

application of diffraction radiation. These are are discussed in Section 5.2.

41

2.2. Transition radiation

2.2 Transition radiation

2.2.1 Transition radiation phenomenon

A relativistic charged particle travelling along a constant direction does not emit

radiation unless it is accelerated or it moves in a medium with changing dielectric

properties. In the case of an accelerated charge, synchrotron radiation or undu-

lator radiation is emitted. A charged particle moving in a medium in which the

speed of light is smaller than the particle speed emits Cherenkov radiation. Simi-

larly, a charged particle traversing a boundary of two media with different dielectric

constants also emits radiation, the so called Transition Radiation (TR). TR has

been observed in the late 1960’s and its applications to beam diagnostics have been

studied [26]. TR as a beam diagnostics tool is widely used and is still developing.

When the charged particle traverses the boundary, the Coulomb field needs to

adjust itself to the varying conditions, i.e. the dielectric constant. This change of

the Coulomb field is only possible if radiation is emitted. TR is therefore emitted in

the forward direction, i.e. along the particle trajectory, and the backward direction,

i.e. in the mirror reflection direction from the boundary.

By solving Maxwell’s equations, the TR process can be calculated analytically.

Assuming a thin, infinitely large, and ideally conducting target, the TR spatial-

spectral power distribution in the far-field limit can be expressed by the Ginzburg-

Frank formula. The Ginzburg-Frank formula expresses the backward TR power dW

radiated into a solid angle dΩ and frequency dω [27]

d2W

dω dΩ=

e2

π2c

β2 sin2θ

(1− β2 cos2θ)2(2.7)

where θ is the observation angle and β = vc . In the relativistic limit, i.e. γ

1, the intensity of the radiation is zero at θ = 0 and maximum at θ = 1γ , as is

the case for radiation emitted by an accelerated charge. These properties of the

TR spatial-spectral distribution can be seen in Figure 2.5. One should also notice

that the spatial-spectral energy distribution does not depend on the frequency ω

within the limits of validity of the Ginzburg-Frank formula, i.e. within the ideal

42


]-1γ [θ-10 -8 -6 -4 -2 0 2 4 6 8 10

Inte

nsity

[ar

b.u.

]0

0.2

0.4

0.6

0.8

1

Figure 2.5: Ginzburg-Frank TR distribution in the relativistic limit.

conductor approximation. The ideal conductor approximation is valid up to the

plasma frequency of the conducting target; e.g. for aluminium this is 15.8 eV or

3.8×1015 Hz [28].

This frequency independent characteristic, however, is not accurate for a realistic

setup as the infinite target assumption and the far-field approximation do not nec-

essarily hold any longer at high energies. One can therefore use the virtual photon

method, as described in Section 2.1, to derive the spatial-spectral TR distribution

with a different approach. The approach explained follows the derivation in [29].

2.2.2 Virtual-photon method derivation of transition radiation

The virtual photon model in the relativistic limit can be used to describe TR and

the analogy between the processes of radiation and light scattering is used, which

is already established if the electromagnetic field of an uniformly moving particle

is represented as a sum of pseudo-photons. Hence, the processes of radiation are

reduced to those of the scattering of pseudo-photons [30]. In this discussion, a

vacuum-metal interface is considered and the metal is referred to as a target. When

the particle field traverses the boundary, i.e. the vacuum-metal interface plane, the

pseudo-photons are scattered off the target and converted into real photons [29].

Assuming an electron is travelling along the positive z-direction and the vacuum-

metal interface is in the x-y-plane, the TR field is a superposition of the real photons

created on the target surface and observed at the ξ-η-observation plane. The super-

43


x

z

y

~r

η ξ

ys

xs

a

e

γλ

Figure 2.6: TR emission scheme.

position can be written as

Elx,y =1

4π2

∫∫Eix,y (xs, ys)

eiϕ

rdys dxs (2.8)

where Elx,y is the amplitude of the x- and y-polarisation components of TR, re-

spectively. Eix,y is the amplitude originating from a point source on the target at a

position (xs, ys), ϕ is the phase advance of the photons and r is the distance from the

point source to the observation point. A simple diagram of the scheme can be found

in Figure 2.6. It shows the target plane on the left hand side with the point source

position (xs, ys), the observation plane on the right hand side with the observation

point (ξ, η), and the vector ~r between the two points.

The amplitude Eix,y that one needs to substitute into Equation (2.8) is just the

Fourier transform of the incident particle field. The two polarisation components

are [29, 30]:

Eix,y(xs, ys) =ie

2π2

∫∫ k′x,y exp

[i(k′xxs + k

′yys

)]k′2x + k′2y + k2γ−2

dk′x dk

′y (2.9)

=iek

πγ

cosψs

sinψs

K1

(k

γρs

)(2.10)

where ρs =√x2s + y2

s , and xs = ρs cosψs and ys = ρs sinψs, relating Cartesian

44


(xs,ys) to polar (ρs,ψs) coordinates. k′x,y are the pseudo-photon wave vectors, k =

2π/λ is the modulus of the radiation wave vector, λ is the Backward TR (BTR)

wavelength, γ is the charged particle Lorentz-factor, K1 is the first order MacDonald

function, and e is the electron charge. A natural unit system is also used, where

h = me = c = 1 [29]. Equation (2.10) contains the expression for the Fourier

transformed particle field as shown in Equation (2.5).

Substituting Equation (2.9/2.10) into Equation (2.8), one obtains equations for

the correct amplitudes and the TR spatial-spectral distribution can be calculated

using

d2W TR

dωdΩ= 4π2k2a2

[∣∣ETRx ∣∣2 +∣∣ETRy ∣∣2] (2.11)

where ETRx and ETRy are the x- and y-polarisation components of TR and a is the

distance between the target and the observation plane.

Having introduced the general approach to derive the spatial-spectral distribu-

tion, two cases can be considered when discussing the phase advance ϕ of the photons

at the observation plane. These two approaches can be divided into the far-field and

the pre-wave zone approach and are discussed in the subsequent sections.

2.2.3 Far-field approach and infinite target size approximation

In the far-field approach, the distance between the target and the observation plane

is considered large enough for the Fraunhofer approximation to be valid. In the

Fraunhofer limit, the radiation from each source of the target can be considered as a

plane wave. The superposition of wavelets with different amplitudes yields the TR

amplitude in the observation plane. In the Fraunhofer diffraction theory, one can

express the phase ϕ as

ϕ = −(~r · ~ρs) = −xskx − ysky (2.12)

45


where kx,y ≈ kθx,y. Substituting Equation (2.9) and (2.12) into Equation (2.8) yields

Elx,y(xs, ys) =ie

8π4a

∫∫∫∫ k′x,y exp

(i[(k′x − kx)xs + (k

′y − ky)ys

])k′2x + k′2y + k2γ−2

dk′x dk

′y dxs dys

(2.13)

where a = |r| is the distance between the target and the observation plane. This

expression now allows the calculation of the spatial-spectral distribution for various

target shapes by choosing the correct integration limits.

Integrating over an infinite target, i.e. xs, ys from −∞ to ∞, and using the

inverse Fourier transform of a δ-function [31], it can be shown that the spatial-

spectral distribution in the far-field limit is [29]

d2W TR

dωdΩ=

α

π2

θ2x + θ2

y

(θ2x + θ2

y + γ−2)2(2.14)

which is the same as the Ginzburg-Frank formula in Equation (2.7). The deriva-

tion of Equation (2.14) from the Ginzburg-Frank formula is quickly demonstrated in

Appendix A.

2.2.4 Pre-wave zone approach

In the pre-wave zone, the phase ϕ can be derived from a simple geometrical discussion

where the distance from a source point to an observation point |~r| is given by

|~r| =√a2 + (xs − ξ)2 + (ys − η)2 (2.15)

which can be substituted into the phase factoreiϕ

rof Equation (2.8) to obtain

eiϕ

|~r|=eik|~r|

|~r|=

exp(ik√a2 + (xs − ξ)2 + (ys − η)2

)√a2 + (xs − ξ)2 + (ys − η)2

(2.16)

and thus can then be simplified assuming an ultra-relativistic case where (ξ− xs)/a

and (η − ys)/a, i.e. the observation angles, are of the order γ−1 1 [29] yielding

eiϕ

|~r|=eika

aexp

[ik

2a(x2s + y2

s

)− ik

a(xsξ + ysη) +

ik

2a(ξ2 + η2

)](2.17)

46


which contains factors for the Fraunhofer and Fresnel diffraction. The second term of

the exponential, ka (xsξ + ysη), is of the same nature as Equation (2.12) and is respon-

sible for the Fraunhofer diffraction. The first term in the exponential, k2a

(x2s + y2

s

),

is the first order Fresnel correction to the far-field approximation.

Again, substituting Equations (2.9), or (2.10), and (2.17) into Equation (2.8), the

correct TR amplitudes are obtained in the pre-wave zone. Using Equation (2.11) and

the correct integration limits over the target surface, TR spatial-spectral distribu-

tions can be obtained for different parameters.

2.2.5 Validity of the far-field approach and infinite target size ap-

proximation

In Section 2.2.3 and 2.2.4, the two different approaches to derive TR have been

discussed. As mentioned above, Equation (2.17) contains the Fresnel correction to

the far-field approximation. In order to obtain the Fraunhofer diffraction, the Fresnel

term, k2a

(x2s + y2

s

), must be much less then unity. Since the intensity of the radiation

sources at distances of more than γλ2π from the particle trajectory is significantly

suppressed, one can write xs = ys = γλ2π and the limiting case can be expressed as

k

2a(x2s + y2

s

)=k

a

γ2λ2

4π2=γ2λ

2πa 1⇔ a γ2λ

2π(2.18)

which for the beam energy of γ = 235 and a typical observation wavelength of

λ = 5 mm at CTF3 is a = 44 m. Since the distance between the target and the

observation point for the setup at CTF3 is much smaller than this limit, the pre-

wave zone approach needs to be applied.

The infinite target size approximation is valid when the target size is larger than

the transverse dimension of the Coulomb field. Therefore, the approximation of an

infinite target can be used as soon as the target size is larger then 10γλ2π . For the

setup at CTF3, this parameter is significantly larger than the target dimensions.

Hence, the infinite target size approximation can not be applied.

47

2.3. Diffraction radiation

2.3 Diffraction radiation

2.3.1 Diffraction radiation process

Diffraction radiation (DR) is a very similar process to TR and is essentially based

on the same process. DR is caused when a charged particle moves in the vicinity of

a target or edge which has a different dielectric constant than the current medium

the particle propagates in.

x

bz

y

~r

η ξ

ys

xs

a

e

γλ

Figure 2.7: DR emission scheme.

As shown in Equation (2.6), the Coulomb field is transversely confined to a disc

and therefore DR only occurs if the distance between the charged particle and the

target/edge, i.e. the impact parameter b, meets the condition

b ≤ γλ. (2.19)

Similarly to TR, DR is also emitted in the backward direction along the mirror

reflection direction from the target and in the forward direction along the parti-

cle trajectory. Different target configurations utilising DR are possible. The most

common configurations range from a rectangular or circular hole in an infinite or

rectangular target to just a simple rectangular target brought into proximity of the

48

2.3. Diffraction radiation

particle beam as seen in Figure 2.7.

2.3.2 Diffraction radiation theory

The spatial-spectral distributions for the various target shapes can be calculated

using the same approach as in Section 2.2.3 and 2.2.4, depending on the distance

between the target and the observation plane, and choosing the integration limits

carefully. Where necessary Babinet’s principle can also be exploited.

Babinet’s principle states that the diffraction fields of a diffraction screen are

the same as the sum of the diffraction fields of the complementary screens. For a

diffraction screen A with complementary screens A1 and A2, the relation between

the complementary diffraction fields, ψ1 and ψ2, and the overall diffraction field ψ

can be written as [32]

ψ = ψ1 + ψ2. (2.20)

To illustrate the use of Babinet’s principle, the concept of the derivation of

the DR spatial-spectral distribution for a slit between two semi-planes is quickly

outlined. Assuming a slit of width w between two semi-planes, one can write the

superposition of the photons created on the target surface, i.e. Equation (2.8), as

Elx,y =1

4π2

[∫ ∞−∞

∫ ∞−∞

Eix,y (xs, ys)eiϕ

rdys dxs−

−∫ ∞−∞

∫ w2

−w2

Eix,y (xs, ys)eiϕ

rdys dxs

] (2.21)

where the first integral is the superposition of the photons from the entire plane and

the second integral is the superposition of the photons from a strip-like target along

the x-axis with width w. As the Coulomb field is transversely confined, the infinite

integration limits correspond to a distance larger than 10γλ2π from the electron, since

for distances further away, the contribution to the amplitude Elx,y is negligible.

For numerical calculations, the dimensions for an infinite screen can therefore be

approximated as 10γλ2π .

For the experiment described in this document, one single target of dimensions

l and h is brought into the vicinity of the particle beam with impact parameter b.

49

2.4. Coherent radiation

The superposition of the photons created on the screen can then be written as

Elx,y =1

4π2

∫ l2

− l2

∫ b+h

bEix,y (xs, ys)

eiϕ

rdys dxs (2.22)

where the phase termeiϕ

ris given by Equation (2.17) since the distance between the

target and the observation plane is less than γ2λ2π .

For some of the expressions obtained by the use of Babinet’s principle or the care-

ful choice of integration limits, it is possible to write down an analytic expression,

but for most of the cases, especially in the pre-wave zone and for non-infinite tar-

gets, one needs to use numerical calculations in order to obtain the spatial-spectral

distributions. Numerical calculations of the spatial-spectral distributions and the re-

sulting spectra for the target configuration, as used in this experiment, are therefore

necessary and are explained in greater detail in Chapter 3.

2.4 Coherent radiation

In the previous sections, the radiation emitted by a single charged particle has

been considered. When charged particles in a bunch emit TR or DR, however, a

collective effect can be observed which depends on the particle distribution in the

bunch. As previously mentioned, the TR and DR emission occurs primarily in the

forward and backward direction with emission angles of θ ≈ γ−1. Since θ ' 0 at

small observation angles, the following discussion is reduced to the one-dimensional

longitudinal particle distribution. Assuming that the particles in the bunch only

differ in the relative position along the z-axis, the field of the radiation emitted by

N particles in a bunch EN , can be written as

EN (ω,Ω) = E1(ω,Ω)N∑j=1

eiωczj (2.23)

where E1(ω,Ω) is the radiation field emitted by a single particle. The total intensity

of radiation emitted by N particles, SN (ω,Ω), is therefore the intensity of a reference

50


particle, S1(ω,Ω), multiplied by the squared modulus of the phase components

SN (ω,Ω) = |E1(ω,Ω)|2 ·N∑j=1

eiωczj

N∑k=1

e−iωczk (2.24)

= |E1(ω,Ω)|2 ·N∑j=1

N∑k=1

eiωc

(zj−zk) (2.25)

= S1(ω,Ω)[N +

N∑j=1

N∑k=1k 6=j

eiωc

(zj−zk)

](2.26)

and introducing the particle densities along the z-axis, S(zj,k), one can re-write the

total intensity as

SN (ω,Ω) = S1(ω,Ω)[N +

N∑j=1

N∑k=1k 6=j

eiωc

(zj−zk)N(N − 1)S(zj)S(zk)]. (2.27)

Since the number of particles in a bunch is generally large, e.g. for CTF3 this is

around 1010 particles, the summation can be replaced by an integral. Thus, the

previous expression can be written as

SN (ω,Ω) = S1(ω,Ω)[N +N(N − 1)

∫ ∞−∞

S(zj)eiωczj dzj

∫ ∞−∞

S(zk)e−iωczk dzk

]= S1(ω,Ω)

[N +N(N − 1)

∣∣∣∫ ∞−∞

S(z)eiωcz dz

∣∣∣2]. (2.28)

One can therefore rewrite the previous equation as

SN (ω,Ω) = S1(ω,Ω)[N +N(N − 1)F (ω)

](2.29)

where the longitudinal form factor F (ω) is defined as

F (ω) =∣∣∣∫ ∞−∞

S(z)eiωcz dz

∣∣∣2. (2.30)

and is just the squared modulus of the Fourier transform of the longitudinal particle

distribution, i.e. the longitudinal beam profile.

As seen from Equation (2.29), the intensity of emitted radiation from N parti-

51


cles consists of two parts. An incoherent part which is proportional to N and a

coherent part which is proportional to N(N − 1), which for sufficiently populated

particle bunches can be approximated as N2. The coherent part also depends on

the form factor F (ω). For wavelengths much shorter than the bunch size, the form

factor is negligibly small and the total intensity is just the incoherent part. On the

other hand, for longer wavelengths, the phase components add constructively to a

maximum of F (ω) = 1 and the total intensity is dominated by the coherent part.

Figure 2.8 shows examples of how different particle distributions S(z) along

the bunch, as shown in Figure 2.8(a), are transformed into the form factor F (ω),

as shown in Figure 2.8(b). Besides an ordinary Gaussian distribution, a double-

Gaussian, and a square distribution, an asymmetric Gaussian with skew parameter

α is used, which is of the form

S(z) =1√

2πσ2exp

(− (z − µ)2

2 [(1 + α · sgn(z − µ))σ]2

). (2.31)

All particle distributions S(z) have the same full-width at half maximum (FWHM),

in order to be able to compare the resulting form factors. It can be seen that the

form factor amplitude for high frequencies is different for all 4 bunch shapes and

that the form factors can have long tails for certain distributions.

Distance [mm]4 6 8 10 12

Cha

rge

[arb

.u.]

0

0.2

0.4

0.6

0.8

1Asymmetric Gaussian

Symmetric Gaussian

Square distribution

Double Gaussian

(a) Bunch distribution

Frequency [GHz]0 20 40 60 80 100 120 140

Form

fac

tor

[arb

.u.]

0

0.2

0.4

0.6

0.8

1Asymmetric Gaussian

Symmetric Gaussian

Square distribution

Double Gaussian

(b) Form factor

Figure 2.8: Particle distributions and resulting form factor.

52

2.5. Kramers-Kronig analysis

In order to obtain the longitudinal particle distribution in the bunch from the

longitudinal bunch form factor F (ω), an inverse Fourier transform needs to be per-

formed. Experimentally, the form factor is usually obtained by a spectrometer of

some kind. Since only the magnitude of the form factor can be obtained from the

spectrometer, it is not possible to obtain information about the asymmetry of the

longitudinal particle distribution, since this manifests itself in the missing phase in-

formation. In order to extract this missing phase information from the form factor,

Kramers-Kronig dispersion relation is used. This relation and its use to reconstruct

the minimal phase is explained in the following section.

2.5 Kramers-Kronig analysis

The explanation of Kramers-Kronig relation for the reconstruction of longitudinal

bunch distributions follows the discussion by Lai and Sievers [33] and the reader

is directed to this article for a more detailed derivation. Kramers-Kronig relation

connects the real and imaginary parts of a complex function which is analytic in

the upper half complex plane. The problem given in this section has very strong

similarities with the input-output response function analysis used in optics to obtain

the complex reflectivity of an interface. The conditions for this approach to be valid

can be directly translated for the case of the longitudinal form factor and are as

follows:

• S(ω) analytic in the upper half complex plane, by assuring that S(z) = 0 for

z < 0.

• S(ω) decays in a power law with |ω| → ∞

The integral in Equation (2.30) can be redefined as the product of the amplitude

ρ(ω) and a phase term eiψ(ω) as follows

S(ω) ≡∫ ∞

0S(z)ei

ωczdz ≡ ρ(ω)eiψ(ω) (2.32)

53


such that the form factor can be expressed as

F (ω) = S(ω)S∗(ω) = ρ2(ω) (2.33)

where a measurement of the form factor F (ω) directly yields the form-factor ampli-

tude ρ(ω). Additionally, Equation (2.32) can be written as

ln S = ln ρ(ω) + iψ(ω). (2.34)

Finally, Kramers-Kronig relation connecting the modulus and the phase can be

written as

ψm(ω) = −2ωπ

∫ ∞0

ln ρ(x)x2 − ω2

dx (2.35)

where ψm is the minimal phase. In order to remove the singularity at x = ω the

following term is added to Equation (2.35)

−2ωπ

∫ ∞0

ln ρ(ω)x2 − ω2

dx = 0. (2.36)

Thus to final expression for calculating the minimal phase can be obtained as

ψm(ω) = −2ωπ

∫ ∞0

ln[ρ(x)/ρ(ω)]x2 − ω2

dx (2.37)

with which ρ(ω) can be used to find the frequency dependent phase ψm(ω) to de-

termine the frequency dependence of the complex form-factor amplitude. Thus, the

longitudinal bunch distribution function can be obtained from the inverse Fourier

transform of Equation (2.32),

S(z) =1πc

∫ ∞0

ρ(ω) cos[ψm(ω)− ω

cz]dω (2.38)

which only depends on the cosine term as S(z) is real. If the minimal phase ψm(ω)

contains components non-linear in frequency ω, the longitudinal particle distribution

S(z) in Equation (2.38) must be asymmetric.

54


From an experimental point of view, the form factor can be measured using a

spectrometer of some kind and hence ρ(ω) can be found. Using Kramers-Kronig re-

lation, the minimal phase can be determined with Equation (2.37) and assumed to be

the real phase. Hence, the asymmetric bunch distribution can then be reconstructed

with the aid of Equation (2.38).

55

Chapter 3Simulation studies

The objective of this chapter is to introduce the properties of TR and DR by per-

forming numerical calculations based on the derivation given in Sections 2.2.3, 2.2.4,

and 2.3.2. Firstly, a parametric discussion of the two processes is conducted, which

shows the similarities between TR and DR, and subsequently the evolution from TR

to DR from a single half-plane is outlined. Thereafter, the spatial-spectral distribu-

tions are calculated numerically and used to determine the single electron spectra

for the given hardware at CTF3. To obtain the form factor F (ω), the single electron

DR spectrum Se(ω) needs to be known in order to normalise the acquired spectrum

from the experiment S(ω). They are linked by the expression in Equation (2.29),

namely

S(ω) = Se(ω) [N +N(N − 1)F (ω)] (3.1)

where Se(ω) is just a different notation for dWedω . It originates from the integration

of the spatial-spectral DR distribution dWedωdΩ , which is used throughout Section 2.2

and Section 2.3, over the solid angle Ω, i.e.

dWe

dω=∫∫Ω

dWe

dωdΩ. (3.2)

Additionally, a time domain simulation technique is performed from which the

CDR spectra can be determined. This time domain simulation technique allows the

construction of more complex target layouts and takes the surrounding hardware

56

3.1. DR simulations

into consideration.

3.1 DR simulations

The simulations carried out in this section are based on the typical parameters at

CTF3, unless it is stated otherwise. The main parameters for the setup at CTF3

are shown in Table 3.1.

Parameter Value UnitBeam energy (γ) 235 –Target distance 1.5 m

Observation wavelength (typical) 5 mmTarget dimensions (projected) 40×40 mm

Bunch charge 2.3 nCBunch spacing frequency 1.5 or 3 GHz

Table 3.1: Main CTF3 parameters used in the simulations.

3.1.1 Evolution from TR to DR from a half-plane

For the simulation studies, the phase expression for calculating the spatial-spectral

distributions in the pre-wave zone, i.e. Equation (2.17), is used. This expression is

also valid in the Fraunhofer limit, as discussed in Section 2.2.5, and therefore a valid

model for the pre-wave zone and the far-field can be established.

Substituting Equation (2.10) and (2.17) into Equation (2.8) yields the following

expression

Elx,y =1

4π2

∫∫D

Eix,y(xs, ys)eiϕ

rdysdxs (3.3)

=1

4π2

∫∫D

iek

πγ√x2s + y2

s

xs

ys

K1

(k

γ

√x2s + y2

s

)×

× 1a

exp[ik

2a(x2s + y2

s

)− ik

a(xsξ + ysη)

]dysdxs (3.4)

where the integration is performed over the target area D and where phase terms

independent of the integration have been omitted. Choosing the target area to be

57

3.1. DR simulations

sufficiently large and setting the distance a γ2λ2π , the spatial distribution is as

described by the Ginzburg-Frank formula in Equation (2.7).

As a starting point for the parametric discussion of the evolution from TR to

DR, an infinite slit between two half-planes for different slit widths is considered.

The integration is then performed over the target area such that

Elx,y =1

4π2

∫ y′s

−y′s

[∫ −s/2−x′s−(s/2)

Eix,y(xs, ys)eiϕ

rdxs +

∫ x′s+(s/2)

s/2Eix,y(xs, ys)

eiϕ

rdxs

]dys

(3.5)

where s is the width of the slit between the two half-planes with dimensions x′s and

y′s.

First of all, an important parameter which is repeatedly used in this discussion

is redefined as follows

rfield =γλ

2π(3.6)

which is just the effective electron field radius, the dimension of which gives rise to

many of the characteristics of TR and DR. The change of the spatial distribution

depending on the variation of the slit width between two infinite half-planes is shown

in Figure 3.1.

]γ [a/η-5 -4 -3 -2 -1 0 1 2 3 4 5

]m

axT

RIn

tens

ity [

I

0

0.2

0.4

0.6

0.8

1fieldSlit width in r

0.1 0.61.2 2.5

Figure 3.1: Infinite slit between two half-planes for different slit widths (in multiplesof rfield) for γ = 235 in the far-field limit.

The plot clearly indicates a decreasing maximum intensity for increasing slit

widths since the Coulomb field interacting with the target surface reduces. For a

vanishingly small slit, e.g. 0.1 · rfield, the maximum intensity is still at the maximum

58

3.1. DR simulations

TR intensity ITRmax = αγ2

4π2 and therefore DR in the limit of small slit width, i.e. the

slit width being much smaller than rfield, is just the TR case. On the contrary, for

a slit width of 2.5 · rfield, only the tails of the Coulomb field interact with the target

and therefore the intensity has significantly diminished. The effect of the slit size

on the DR intensity is well studied and has been observed before [34].

Secondly, the effect of retracting one of the half-planes from the centre is studied.

Starting from two half-planes with no slit between them, the distance of one half-

plane to the centre is increased. Figure 3.2 illustrates the impact of this retraction

on the DR distribution.

]γ [a/η-5 -4 -3 -2 -1 0 1 2 3 4 5

]m

axT

RIn

tens

ity [

I

0

0.2

0.4

0.6

0.8

1fieldOffsets in r

0 13 10

Figure 3.2: Withdrawal of a half-plane for different offsets (in multiples of rfield) forγ = 235 in the far-field limit.

It can be observed that for increasing distances of the retracted plane from the

centre, the minimum between the two peaks, which is at 0 for the case without a

retraction, increases in intensity. At very large distances of the retracted plane from

the centre only one predominant peak is produced. In this limit, the distribution is

just the distribution of DR from a single half plane, which is used in the experiment

at CTF3.

To complete this parametric discussion of the evolution from TR to DR from a

single half-plane, the dependence of the DR distribution from a single half-plane on

the impact parameter is illustrated. This dependence can be observed in Figure 3.3.

The maximum intensity of the distribution for a zero impact parameter is just ITRmax

and the intensity decreases for increasing impact parameters, again, because of the

decreasing Coulomb field strength at distances much larger than rfield from the

59

3.1. DR simulations

]γ [a/η-5 -4 -3 -2 -1 0 1 2 3 4 5

]m

axT

RIn

tens

ity [

I

0

0.2

0.4

0.6

0.8

1field

Impact param. in r

0 0.1

0.2 0.5

1

Figure 3.3: Variation of the DR distribution with impact parameter (in multiples ofrfield) for γ = 235 in the far-field limit.

electron. The distribution, as already mentioned in the discussion of Figure 3.2, is

just a single central peak.

As explained in Section 2.3.2, the DR setup at CTF3 consists of a single rectan-

gular target which is brought into close proximity to the electron beam. Figure 3.4

shows the DR distribution observed at a distance of a = 10γ2λ

2π and a target size

of 10γλ2π , where an observation wavelength of λ = 5 mm and an electron energy of

γ = 235 were used. The impact parameter for the given simulation was chosen to be

b = 0. The resulting distribution from this target configuration is then just a single

]γ [a/ξ-4 -3 -2 -1 0 1 2 3 4]γ

[a/η

-4-3

-2-1

01

23

4

]m

axT

RIn

tens

ity [

I

0

0.2

0.4

0.6

0.8

1

Figure 3.4: DR spatial distribution for distance a = 10γ2λ

2π and a target size of 10γλ2π .

60

3.1. DR simulations

central peak as one would expect for DR from a single target.

3.1.2 Polarisation components of DR

The DR distribution is also polarised and depends on the orientation of the target

edge. In the case of the rectangular target, the vertical polarisation axis is defined

as the direction perpendicular to the target edge closest to the electron beam. The

horizontal polarisation component is defined in the direction perpendicular to both

the vertical polarisation component and the mirror reflection direction from the

target. Figure 3.5 shows the polarisation components of DR from a rectangular

target. It shows a single central peak for the vertical polarisation component, as seen

in Figure 3.5(a), and two horizontally separated peaks for the horizontal polarisation

component, as seen in Figure 3.5(b). One should also notice the differences in the

maximum intensities for the two components. While the vertical component has a

maximum intensity of ITRmax, the horizontal component is significantly weaker, i.e.

0.24 · ITRmax.

]γ [a/ξ-4 -3 -2 -1 0 1 2 3 4]γ

[a/η

-4-3

-2-1

01

23

4

]m

axT

RIn

tens

ity [

I

0

0.2

0.4

0.6

0.8

1

(a) Vertical component

]γ [a/ξ-4 -3 -2 -1 0 1 2 3 4]γ

[a/η

-4-3

-2-1

01

23

4

]m

axT

RIn

tens

ity [

I

0

0.2

0.4

0.6

0.8

1

(b) Horizontal component

Figure 3.5: DR polarisation components in the far field.

61

3.1. DR simulations

3.1.3 Diffraction radiation spectra

The DR distribution shown in Figure 3.4 is just valid for one chosen wavelength. In

order to obtain the DR spectra for the setup at CTF3 one needs to integrate over

the DR distribution for a specific detector aperture at every given wavelength one

is interested indWe

dω=∫∫

detector

dWe

dωdΩdΩdetector. (3.7)

The integration limits used for this integration are the dimensions of the detector

opening along the x and y axis, i.e. xdetector = 46 mm and ydetector = 35 mm. These

dimensions correspond to the DXP-19 detector, which will be discussed in detail in

Section 4.4.1. The correct distance between the detector and the target, a = 1.5 m,

and the correct target size was taken into account, which in the case at CTF3 is just

40 mm×40 mm. A zero-impact parameter was used.

Wavelength [mm]5 10 15 20 25 30 35

]m

axT

RIn

tens

ity [

I

-910

-810

-710

-610

-510

-410 γParticle energy 160 235400 6001000

Figure 3.6: DR spectra for a 40 mm×40 mm target and a DXP-19 detector at adistance a = 1.5 m.

A plot of the DR spectra for different particle beam energies can be seen in

Figure 3.6. One should note that, despite the impression of obtaining more intense

spectra for lower electron energies, this is actually not the case. This impression

arises from the fact that the normalisation constant ITRmax = γ2λ2π is used. These DR

spectra can then be used in normalising the spectrum acquired during the experiment

as mentioned above.

62

3.1. DR simulations

3.1.4 Impact parameter variation

The variation of the impact parameter is also an important aspect for the setup at

CTF3 as this determines the working point of the target with respect to the electron

beam. The following plots give a good indication of the intensity changes for different

impact parameters and information about a good working point at CTF3.

For the CTF3 parameters, the spectra for different impact parameters are shown

in Figure 3.7. Overall, the DR spectra show a similar decrease in intensity for in-

creasing wavelength. The spectra, however, behave slightly differently at shorter

wavelengths for different impact parameters. While the spectrum for a zero impact

parameter is monotonically increasing for shorter wavelengths, the DR intensities

for increasing impact parameters are decreasing towards very short wavelengths, an

indication of which can be seen for the b = 10 mm case. Due to limited computation

time, a detailed study in this region was not performed as this is not the region of

interest and since the radiation is strongly suppressed by the form factor, as shown

in Figure 2.8(b).

Wavelength [mm]5 10 15 20 25 30 35

]m

axT

RIn

tens

ity [

I

-710

-610

-510

-410Impact parameter [mm]

0 12 410

Figure 3.7: Variation of the DR spectra for different impact parameters at an energyγ = 235.

Another interesting investigation is the change of intensity with impact param-

eter for fixed wavelength, which is shown in Figure 3.8. Arbitrarily chosen wave-

lengths in the DXP-19 spectral range were used to perform the simulation. The

other parameters are again the parameters for the setup at CTF3.

An interesting feature of the impact parameter variation is that the intensity

63

3.1. DR simulations

Impact parameter [mm]0 2 4 6 8 10 12 14

]m

axT

RIn

tens

ity [

I

0

1

2

3

4

5

6

7

8-610×

Wavelength [mm]5 5.56 6.57

Figure 3.8: DR intensity variation with impact parameter for different observationwavelengths.

for a 15 mm impact parameter only decreases by a factor of 2 compared to a zero

impact parameter. This means that the signal levels are still comparatively high

when keeping the target at that distance from the electron beam. Therefore a

working point between b = 10 mm and b = 15 mm is perfectly acceptable and the

system can be designed to be non-invasive.

3.1.5 Total radiation spectrum

As demonstrated in Section 2.4, the longitudinal bunch form factor is just the squared

modulus of the Fourier transform of the longitudinal particle distribution S(z). As-

suming a Gaussian electron bunch with bunch length σ

S(z) =1√

2πσ2exp

[− z2

2σ2

](3.8)

the form factor F (ω) is just

F (ω) =∣∣∣∣∫ ∞−∞

1√2πσ2

exp[− z2

2σ2

]× e−ikz dz

∣∣∣∣2 =

= exp[−k2σ2

]= exp

[−ω

2

c2σ2

] (3.9)

which yields another Gaussian-like function, the width of which depends on the

electron bunch length σ.

Recalling that the relation for the coherent radiation emitted by a particle bunch

64

3.1. DR simulations

Frequency [GHz]0 10 20 30 40 50 60 70 80

]m

axT

RPo

wer

[I

0

0.1

0.2

0.3

0.4

0.5

-610×

Figure 3.9: Example CDR power spectrum obtained by the multiplication of thesingle electron spectrum by the bunch form factor of a 2 mm Gaussian beam for thesetup at CTF3.

is given by Equation (3.1), one can write

S(ω) ∝ dWe

dω· F (ω). (3.10)

Taking dWedω from Figure 3.6, the combined spectrum of radiation emitted by a

Gaussian bunch due to CDR is shown in Figure 3.9. The combined spectrum shows

a suppression at low as well as at high frequencies. The low frequency suppression

is due to the finite outer target dimensions which are used for the experiment.

The effect occurs when the parameter γλ exceeds the transverse dimensions of the

target [35]. The high frequency suppression, on the other hand, is due to the form

factor F (ω), since the amount of coherent radiation reduces for higher frequencies.

3.1.6 Power production

In order to determine whether the power emitted by CDR is large enough to be

detected, the power radiated into the frequency range corresponding to the detector

sensitivity is calculated. Since the average power is just the energy emitted by a

single bunch divided by the temporal bunch spacing, the energy emitted by the

bunch due to CDR needs to be determined. An estimation of the energy emitted by

the bunch with a bunch length σ due to CDR – neglecting the incoherent part – is

given by the expression

65

3.1. DR simulations

W (σ) =∫ ωhigh

ωlow

n2 S(ω) dω (3.11)

where n is the bunch charge and S(ω) is the combined spectrum of CDR emitted by

the particle beam, as shown in Section 3.1.5. From the integration of the combined

spectrum in the correct frequency range, i.e. integrating Equation (3.11) over the

detector bandwidth, the power emitted by an electron bunch due to CDR can be

obtained. Therefore, a perfectly Gaussian electron bunch with a charge of 2.0×1010

electrons and an energy of γ = 235 is assumed. The bunch spacing is chosen for the

two different settings at CTF3, i.e. 1.5 GHz and 3 GHz respectively. The resulting

average power emitted is shown in Figure 3.10 and shows the dependence of the

power on the bunch length.

[mm]σBunch length, 1 1.5 2 2.5 3

Ave

rage

pow

er p

er tr

ain

[W]

50

100

150

200

250

300

350

400

450

Bunch spacing3 GHz1.5 GHz

(a) b = 0 mm

[mm]σBunch length, 1 1.5 2 2.5 3

Ave

rage

pow

er p

er tr

ain

[W]

50

100

150

200

250

Bunch spacing3 GHz1.5 GHz

(b) b = 10 mm

Figure 3.10: Average CDR power production for a Gaussian beam with bunch charge2× 1010 and energy γ = 235 for different impact parameters b.

Different impact parameters were also assumed in the simulations. Figure 3.10(a)

shows the power generated by the bunch due to CDR with a theoretical zero-impact

parameter. For the simulations shown in Figure 3.10(b), an impact parameter of

b = 10 mm is assumed.

For a typical 2 mm long bunch at CTF3 and for a zero impact parameter, the

average power per train is 10.3 W and 22.7 W for 1.5 GHz and 3 GHz operation,

66

3.2. Time domain simulations

respectively. For an equally long bunch and for the impact parameter b = 10 mm,

the average power per train is 5.5 W and 11.0 W for 1.5 GHz and 3 GHz operation,

respectively.

The energy contribution per electron for this kind of bunch is therefore 1.7 eV and

0.9 eV for a zero impact parameter and b = 10 mm impact parameter, respectively.

This is an overall emitted energy per bunch of 3.4× 1010 eV and 1.8× 1010 eV, i.e.

5.4 nJ and 2.9 nJ, respectively.

This kind of power estimated to be emitted by the bunch due to CDR is suffi-

ciently large in order to be detected with the Schottky barrier diode type detectors

used in the experiment. For shorter bunches, one even needs to be careful not to

damage the detectors by exposing those to such an intense radiation. Therefore,

attenuators, as explained in Section 4.3.2, were utilised.

3.2 Time domain simulations

Besides the idealised target configurations in the previous section, a different simu-

lation technique is used in this section to account for the surrounding hardware of

the real setup. For this purpose, state-of-the-art simulations were performed using

a time-domain simulation on the Franklin supercomputer at the National Energy

Research Scientific Computing Center (NERSC) [36] at the Lawrence Berkeley Na-

tional Laboratory.

The simulations are based on SLAC’s Advanced Computations Department

(ACD) suite of 3D parallel finite-element based electromagnetic codes for accelera-

tor modelling, called Advanced Computational Electromagnetics 3P (ACE3P) [37].

The package contains various methods for calculating electromagnetic fields, e.g.

an Eigenvalue solver for finding the normal modes in an RF cavity (Omega3P), a

particle-in-cell code to simulate self-consistent electrodynamics of charged particles

(Pic3P), and a S-parameter solver to calculate the transmission properties of open

structures (S3P), among others.

Moreover, the suite is equipped with a 3D parallel finite-element time-domain

solver to calculate the transient field response of an electromagnetic structure to

67


imposed fields, and dipole or beam excitations (T3P). This suite can therefore be

used to calculate DR from a target since the target is just an electromagnetic struc-

ture which is subjected to an imposed field, i.e. the Coulomb field surrounding an

electron beam.

3.2.1 Computational technique

The T3P suite is based on the finite-difference time-domain (FDTD) [38, 39] tech-

nique and is very briefly introduced in this section. The technique uses Maxwell’s

equations, explicitly Ampere’s and Faraday’s laws in partial differential form, which

can be combined to obtain the inhomogeneous vector field equation for the time

integral of the electric field E

(ε∂2

∂t2+∇× µ−1∇×)

∫ t

E dτ = −J (3.12)

with permittivity ε and permeability µ. The electric current source density J is

given by an one-dimensional Gaussian particle distribution moving along the beam

line at the speed of light.

The time-integral of the electric field∫ t E(x, τ)dτ can be decomposed into a

chosen set of spatially fixed finite element basis functions Ni(x) with time-dependent

coefficient vector e(t) such that [40]

∫ t

E(x, τ) dτ =∑i

ei(t) ·Ni(x) (3.13)

which is the basic principle of the finite element computational model utilised in this

simulation study.

3.2.2 Simulation model

In order to obtain the finite elements, a model of the setup to be simulated needs

to be created. A computer-aided design (CAD) program is used to construct such

a model and can also be used to mesh the model into finite elements utilised by

the T3P suite. For this purpose, the free space within the model is meshed with

68


tetrahedrons of a desired maximum size, which sets constraints on the minimum

radiation wavelength to be modelled. Additionally, electromagnetic properties can

then be assigned to the surfaces surrounding the free space, i.e. the walls of the

setup and the DR target, to represent the hardware setup.

Figure 3.11: CAD drawing of the simulated setup for DR from a rectangular targettilted by 45 into a cylindrical viewport. The electron beam propagation directionis illustrated by the dark grey line through the model.

A model created with the CAD program is shown in Figure 3.11. The model fea-

tures a target with dimensions in the projection perpendicular to the electron beam

of 40 mm× 20 mm. An impact parameter of 10 mm is chosen for the simulations and

a viewport diameter of 30 mm is considered. When the model is designed, the total

volume of the model needs to be kept at the lowest possible since the computation

time scales with the volume.

Once the model is designed, the CAD program also allows the volume to be

meshed with tetrahedrons and a second order correction can be applied to curved

surfaces to obtain a greater accuracy of the simulations. During the meshing proce-

dure, a mesh with the properties shown in Table 3.2 is obtained.

Upon successful meshing of the model within the CAD program, the mesh needs

to be converted by the SLAC ACDTool to a format readable by the T3P suite.

Moreover, a setup file needs to be created specifying the surface and beam properties

69


Properties ValueVolume numbers:

Total no. 7506506Edge length [mm]:

Minimum 0.257Maximum 1.040Average 0.523Std. dev. 0.095

Technical information:CPU hours 239No. of cores used 1024Raw data 182 GBSupercomputer Franklin (Cray XT4)

Table 3.2: Mesh properties and technical information for the DR simulation model.

used by the T3P code, the time discretisation, and the lower and upper time limits

for which the simulation is to be performed for. Furthermore, the setup file also

contains information on the parameters the T3P suite extracts from the simulation

and saves to file.

For this particular model, all surfaces except the viewport surface and the sur-

faces through which the beam enters and leaves the model were set to be a conductor.

Electromagnetic radiation was allowed to freely propagate across these excluded sur-

faces, which is the case for the real setup. A Gaussian electron beam with a bunch

length of σz = 2 mm, which is within the bunch length range found at CTF3, and

a total bunch charge of 1 pC was selected for this model. The choice of the bunch

charge of 1 pC arises from the fact that the output field strengths are given per pC.

The output from the simulation can easily be scaled to obtain the absolute field

strengths for the electron beam at CTF3 with a bunch charge of 2.3 nC. The time

discretisation steps and the time limits need to be carefully chosen in order to obtain

a spectrum via a Fourier transform. For this model, a time discretisation of 2 ps

for an interval from 0 ps to 900 ps was chosen. For every time step, the electric and

magnetic field strengths in all 3 dimensions are read out for each mesh point and

the total power at the viewport surface for every time step was also read out.

70


3.2.3 DR from the modelled target

The data from the simulation can then be post-processed with a special visualisation

software. Figure 3.12 shows the DR fields calculated with the T3P code for the model

described above. The plot shows the total magnitude of the electric field in the plane

which vertically divides the model into two equal halves. The electron beam enters

the model from the bottom and the DR field is generated at the target tilted by 45

with respect to the beam propagation direction. The BDR propagates in the mirror

reflection direction into the cylindrical viewport towards the left as shown. The

forward DR (FDR) generated from the target propagating in the beam propagation

direction is also displayed.

(a) 30 ps (b) 50 ps (c) 70 ps

(d) 90 ps (e) 110 ps (f) 130 ps

(g) 150 ps (h) 170 ps (i) 190 ps

Figure 3.12: Evolution of the electric DR field for given times after the simulationstart time (the beam entry time).

71


3.2.4 DR time domain signal

A useful property is the DR intensity which propagates though the viewport on the

left. This power can be obtained in two different ways. The T3P suite allows the

power across predefined surfaces to be read out, which in this case was chosen to be

the viewport surface of the model. The T3P suite determines the intensity and a

data file with the power for every time step is written to disk.

Besides the possibility of visualising the DR field with the visualisation software,

the Python libraries, on which the software is based, can be used to extract other

information from the simulation output and save them as a new dataset. Since

the power is not one of the parameters that is saved as part of the default simula-

tion output, the power needs to be determined from the electric and magnetic field

strengths. The electric and magnetic fields integrated across the viewport surface

are shown in Figure 3.13(a) and 3.13(b), respectively.

Time [ps]0 200 400 600 800

Am

plitu

de [

arb.

u.]

-1

-0.5

0

0.5

1 E fieldxE yE

zE

(a) Electric field

Time [ps]0 200 400 600 800

Am

plitu

de [

arb.

u.]

-1

-0.5

0

0.5

1 B fieldxB yB

zB

(b) Magnetic field

Figure 3.13: Electric and magnetic fields read-out from the simulation model.

The power can be determined by integrating the magnetic and electric field

strengths across the viewport surface and using the Poynting vector

|S| = 1µ0|E×B| (3.14)

in order to obtain the power which flows across the surface for each time step. A

72


comparison of the power read out by the two different methods is shown in Fig-

ure 3.14. The two power readings shown in Figure 3.14(a) and Figure 3.14(b) are

the direct power reading from the simulation and the power reconstructed via the

Poynting vector using the electric and magnetic fields, respectively.

Time [ps]100 200 300 400

Pow

er [

arb.

u.]

0

0.2

0.4

0.6

0.8

1

(a) Direct readout from the simulation

Time [ps]100 200 300 400

Pow

er [

arb.

u.]

0

0.2

0.4

0.6

0.8

1

(b) Reconstructed by reading out via the li-braries and the Poynting vector

Figure 3.14: Power readings of the DR propagating through the viewport of themodel.

One can clearly identify the two power peaks corresponding to the two DR

wavefronts propagating towards the viewport, as shown in Figure 3.12. Due to the

time discretisation, however, the two peaks of the power reading for both cases have

a slightly different ratio. Nevertheless, the two power readings show a very good

agreement between each other despite this minor difference. Moreover, one is also

able to identify the power which is caused directly by the Coulomb field of the

particle beam as it passes the viewport chamber. Figure 3.12(d) – 3.12(g) show the

beam field extending out to the viewport and contributing to the signal which is

read out at the viewport. Due to causality, however, this contribution to the signal

occurs much earlier than the actual DR signal and can therefore be excluded for

subsequent calculations.

73


3.2.5 DR spectrum

The ability to read out the individual components from the simulation output and

to reconstruct the power from the electric and magnetic fields is crucial for the full

power spectrum. Since the power in the time domain has a nonzero average, it is not

a square integrable function and the Fourier transform can not be directly obtained

from the power itself. By reading out the individual components of the electric

and magnetic fields, the fields can be Fourier transformed to obtain the electric and

magnetic field spectra E(ω) and B(ω). Thus, the Poynting vector can again be

found for each discrete frequency and hence S(ω) can be computed.

Frequency [GHz]0 10 20 30 40 50 60 70 80

Pow

er [

arb.

u.]

0

0.2

0.4

0.6

0.8

1

Figure 3.15: Spectral DR power density for the simulated model.

The spectral power density S(ω) for the model described above is shown in

Figure 3.15. The power density shows a suppression at high frequencies due to the

form factor cut-off from a Gaussian particle beam, as shown in Figure 2.8, and a low

frequency suppression due to the finite dimensions of the target and the viewport.

Despite the agreement with theory for large and small frequencies, the obtained

spectrum is not a smooth function. A smooth spectrum, however, is expected from

the simulation. As seen in Figure 3.13, there are still significant electric and magnetic

fields present long after the beam has left the model. A close investigation of the DR

fields with the visualisation software shows a reflection of the electromagnetic field

from the conducting surfaces within the model. Since the radiation is not allowed

to freely propagate away, some of the DR energy is still present after an unusually

long time, i.e. long after the beam has passed the target. Excluding any radiation

74


Frequency [GHz]0 10 20 30 40 50 60 70 80

Pow

er [

arb.

u.]

0

0.2

0.4

0.6

0.8

1

Figure 3.16: Spectral DR power density for the simulated model with the trailingsignal excluded.

more than 340 ps after the beam entry, i.e. 150 ps after the beam left the model, a

different spectrum than before, as seen in Figure 3.15, can be calculated. The cut

was chosen at 340 ps since the DR power decreases to a minimum here, which can be

seen in Figure 3.14(b). The DR spectrum obtained from this shortened time series

is shown in Figure 3.16.

From this modified spectrum, one can see that the high-frequency cut-off due to

the form factor is the same as in Figure 3.15. The low frequency region, however,

shows slightly different features. The power spectrum is a smooth curve as expected,

unlike that shown in Figure 3.15 which features several sharp peaks. The power

spectrum exhibits a monotonic decrease for decreasing frequencies due to the finite

outer target dimensions, as one would expect, and it has a similar absolute intensity

compared to that in Figure 3.15.

This analysis demonstrates the importance of the contribution from the sur-

rounding hardware. In a real experiment, however, the low frequency components

can easily be cut out by a high pass filter.

3.2.6 Modified model

The aforementioned model shows reflections of the electric and magnetic fields from

the conducting surfaces within the model. These surfaces, however, do not exist

in this way for the real setup at CTF3. The target is contained within a six-way

cross with cylindrical ports with inner diameter of 95.7 mm and the flanges are at a

75


distance of 135 mm from the centre of the beam pipe, as explained in Section 4.2.2.

Nevertheless, in order to save computing time and to keep the amount of data as

low as possible, it was necessary to minimise the model in such a way. In order

to investigate the agreement with the virtual photon model simulations, a modified

model was constructed. This modified model has the same geometry as the previous

model, but the surface properties are different. All surfaces except the surfaces

comprising the target were set to be transparent, i.e. the electromagnetic field is

allowed to freely propagate across these surfaces. This is expected to suppress the

reflections in the model long after the beam has left the model, which is in fact the

case as shown in Figure 3.17.

The plots of the electric and magnetic fields, in Figure 3.17(a) and Figure 3.17(b),

show the beam passing the viewport again within the first 180 ps and then the fields

generated by DR from the target. After the DR wavefront has reached the viewport,

the intensity thereafter is zero as expected.

Again, the components of the electromagnetic field are Fourier transformed and

the spectral power is found via the Poynting vector. The spectral power for the mod-

ified model is shown in Figure 3.18. This time, the Fourier transform was performed

over the entire time series. Compared to Figure 3.16, the power spectrum for the

Time [ps]100 200 300 400

Am

plitu

de [

arb.

u.]

-1

-0.5

0

0.5

1 E fieldxE yE

zE

(a) Electric field

Time [ps]100 200 300 400

Am

plitu

de [

arb.

u.]

-1

-0.5

0

0.5

1 B fieldxB yB

zB

(b) Magnetic field

Figure 3.17: Electric and magnetic fields read-out from the modified simulationmodel.

76

3.3. Comparison of the simulation models

Frequency [GHz]0 10 20 30 40 50 60 70 80

Pow

er [

arb.

u.]

0

0.2

0.4

0.6

0.8

1

Figure 3.18: Spectral DR power density for the modified simulated model.

modified model shows slightly different properties. The high frequency suppression

is very similar in both cases, but the low frequency suppression has different fea-

tures. This, however, can be explained by the truncation of the signal for the power

spectrum in Figure 3.16. Since the signal for the modified model was not truncated

and/or altered, it is assumed to show the correct low-frequency dependence.

3.3 Comparison of the simulation models

In order to compare the power spectra from the time-domain simulations to the

virtual photon model, the power spectrum from a 2 mm Gaussian beam obtained

with the virtual photon model simulation with the same parameters is calculated.

To take the short distance between the target and the viewport for the time-domain

simulation into account, the integration of the DR distribution for the virtual pho-

ton model is performed over ±0.2 rad. The resulting CDR spectrum is shown in

Figure 3.19.

In order to be able to compare the different spectra obtained by the different

methods, the spectra are drawn on the same plot, which is shown in Figure 3.20. As

expected, the two different time-domain (ACE3P) simulations show similar charac-

teristics because the two models had the same geometric dimensions. The internal

surfaces, however, had different dielectric properties, requiring the signal for the

original model to be truncated, thus introducing uncertainties in the low frequency

range, which can also be seen. The two time-domain simulation spectra also show

77


Frequency [GHz]0 10 20 30 40 50 60 70 80

Pow

er [

arb.

u.]

0

0.2

0.4

0.6

0.8

1

Figure 3.19: CDR power spectrum obtained by the convolution of the single electronspectrum calculated from the virtual photon model with the bunch form factor of a2 mm Gaussian beam.

a fairly good agreement with the spectrum obtained by the virtual photon method.

The overall shapes of the spectra show similar properties for both cases and the max-

imum intensities of the different spectra occur at a very similar frequency for the

two different methods. The high frequency characteristics, however, differ slightly.

This can be explained by the fact that the time-domain simulation method utilises

a finite size volume mesh, which sets constraints on the accurate computation of the

spectrum for higher frequencies.

Taking everything into consideration, similar results have been achieved for two

fundamentally different approaches to the same process. For future setups and

experiments, one is now able to use the ACE3P time-domain simulation technique

Frequency [GHz]0 10 20 30 40 50 60 70 80

Pow

er [

arb.

u.]

0

0.2

0.4

0.6

0.8

1 Simulation method

Virtual photon model

ACE3P simulation (orig.)

ACE3P simulation (mod.)

Figure 3.20: Normalised DR power spectra obtained for a 2 mm Gaussian beam forthe different simulation methods.

78


to calculate the CDR spectrum from more complex target configurations in the

surrounding hardware. The technique, for example, allows the consideration of

external surfaces, viewports and others. This makes it a great tool to design setups,

which successfully suppress unwanted backgrounds, are minimally invasive and cost

effective.

79

Chapter 4Setup for the Investigation of Coherent

Diffraction Radiation at CTF3

This chapter introduces the reader to the experimental setup at CTF3 at CERN.

Before explaining the details of the CDR setup, the overall layout and the key

features of CTF3 are discussed. Based on the discussion of CTF3, the Combiner

Ring Measurement (CRM) line and the modifications therein to accommodate the

CDR setup are displayed. Thereafter, the CDR vacuum hardware is explained and

the optical hardware is shown, followed by a description of the detection system

and the data acquisition. Finally, a brief overview of the software written to fully

automate the system and acquire various signals from the system and CTF3 is given.

4.1 Description of CTF3

The main purpose of CTF3 is to test the bunch frequency multiplication and two-

beam acceleration scheme for CLIC. It is designed for proving the feasibility of the

RF power transfer and to produce the RF power at nominal CLIC parameters. Ad-

ditionally, beam dynamics studies and beam diagnostics issues are also addressed.

CTF3 made maximum use of the already existing hardware of the former LEP Pre-

Injector (LPI) complex [41] at CERN, composed of a 3 GHz linear accelerator and an

accumulator ring. The accumulator ring was significantly modified from the Prelim-

80

4.1. Description of CTF3

inary Phase of CTF3 [42] to the existing CTF3 facility, which is shown in Figure 4.1.

The various sections of the present facility are explained in the subsequent sections.

4.1.1 Drive beam injector and accelerator

CTF3 consists of a drive beam injector which generates a 1.6 µs long e− pulse using

a 140 kV, 9 A thermionic gun. The gun is followed by an RF bunching system com-

posed of a set of 1.5 GHz subharmonic bunchers, a 3 GHz pre-buncher and a 3 GHz

travelling-wave buncher [44]. The phase of the subharmonic bunchers is switched

rapidly by 180 every 140 ns, which is crucial for the bunch frequency multiplication

process as explained in Section 4.1.2. Hence, the bunches are spaced by 20 cm (two

3 GHz buckets) and have a charge of 2.3 nC per bunch, which corresponds to an

average current of 3.5 A. Towards the end of the injector, the bunches are accel-

erated by two 3 GHz travelling wave structures, bringing the beam energy up to

20 MeV. After the drive beam injector, a magnetic chicane with collimators is used

to eliminate the low energy beam tails produced by the bunching process resulting

in a 1.4 µs long e− pulse.

In the drive beam accelerator, the beam is accelerated up to 150 MeV (115 MeV

at the time of the experiment) using 3 GHz RF travelling-wave accelerating struc-

tures. Full beam loading is applied during the acceleration stage resulting in an RF-

to-beam efficiency of around 94%. The needed RF power is supplied by klystrons

with a power ranging from 35 MW to 45 MW and compressed by a factor 2 to

provide 1.5 µs pulses over 30 MW at each structure input. In order to achieve a

rectangular compressed output pulse, an RF phase modulation of the klystron in-

put signal needs to be performed. To compensate the variation of the output RF

phase, which leads to a modulation of the beam energy, a slight RF frequency offset

is introduced. The residual RF phase sag is compensated by anti-phase operation

of alternate klystrons [45].

81


Driv

e be

am in

ject

orD

rive

beam

acc

eler

ator

Del

ay L

oop

Com

bine

r Rin

g

Tran

sfer

Lin

e 2

& B

unch

Com

pres

sor

Tran

sfer

Lin

e 1

Mai

n B

eam

Inje

ctor

Two-

Bea

m T

est S

tand

CR

M L

ine

Fras

cati

chic

ane

Figure 4.1: General Layout of CTF3 [43].

82


4.1.2 Delay Loop, Combiner Ring, and Combiner Ring Measure-

ment line

After the drive beam accelerator, i.e. the linac, the first stage of the electron pulse

compression and bunch frequency multiplication of the drive beam is performed in

the Delay Loop (DL). The bunch interleaving in the DL is obtained by a single

transverse RF deflector at 1.5 GHz and a delay loop circumference of 42 m. This

length corresponds to the length of a set of phase-coded sub-pulses, i.e. the so called

“even” and “odd” bunches [45], which is just 140 ns. Since the even and odd bunches

have a different phase advance with respect to the RF deflector, these bunches are

separated by the deflector, as shown in Figure 4.2. After half of the bunches, e.g.

the even buckets, have been delayed in the DL, they are recombined with the odd

buckets. Consequently, the original 1.4 µs long pulse is converted into a sequence of

five 140 ns long pulses with twice the initial current separated by 140 ns long pulse

gaps.

After the DL, a second stage of pulse compression and bunch frequency multi-

plication by a factor four is achieved in the Combiner Ring (CR). This is performed

3-4

The high beam current in the linac requires an effective damping of the beam induced higher order modes (HOMs) in the travelling wave structures. Two structure types have been developed with different damping schemes. They are described in chapter 9.2. The first design is derived from the 30 GHz Tapered Damped Structure (TDS) developed for the CLIC main beam linac. The damping here is achieved by four waveguides with wide-band Silicon-Carbide (SiC) loads in each accelerating cell. The waveguides act as a high pass band filter, since their cut-off frequency is above the fundamental frequency but below the HOM frequency range. The !-value of the first dipole is thus reduced to about 18. A further reduction of the long range wake-fields is achieved by a spread of the HOMs frequencies along the structure, obtained by varying the aperture diameter from 34 mm to 26.6 mm. The second approach called SICA, (Slotted Iris Constant Aperture) uses four radial slots in the iris to couple the HOMs to SiC RF loads. In this approach the selection of the modes coupled to the loads is not made by frequency discrimination but is obtained through the field distribution of the modes: therefore all dipole modes are damped. The !-value of the first dipole is reduced to about 5. In this case a frequency spread of the HOMs is introduced along the structure by nose cones of variable geometry. The aperture can therefore be kept constant at 34 mm, so that a smaller amplitude of the short range wake-fields is obtained. 3.3 Bunch interleaving One of the most important issues to be tested is the frequency multiplication by the novel bunch interleaving technique. In CTF3 a long train of short bunches with a distance of 20 cm between bunches is converted into a series of short bunch trains, with the individual bunches spaced by 2 cm. This is done in two stages, first by a factor of two in a Delay Loop, then by a factor of 5 in a Combiner Ring. In order to maintain the short bunch length, both rings must be isochronous. The issues to be studied in this context are: injection into the ring using RF deflectors, operation of the isochronous ring, phase extension of the bunches in the deflectors and impedance effects. 3.3.1 Phase coding of bunches and Delay Loop After the linac, a first stage of electron pulse compression and bunch frequency multiplication of the drive beam is obtained using a transverse RF deflector at 1.5 GHz and a 42 m circumference Delay Loop. The circumference of the loop corresponds to the length of one batch of "even" or "odd" bunches. The process is illustrated in Figure 3.3. The RF deflectors in the Delay Loop deflect every second batch of 210 bunches into the Delay Loop, and after one turn insert this batch between the bunches of the following batch. Therefore the timing of the bunches of subsequent batches is adjusted such that they have a phase difference of 180 ° with respect to the 1.5 GHz RF of the deflector.

odd buckets

evenbuckets

RF deflector1.5 GHz

Delay LoopAcceleration3 GHz

Deflection1.5 GHz

20 cmbetweenbunches

140 nssub-pulse length

1.4 µs train length - 3.5 A current

odd bucketseven buckets

140 nspulse length odd+ even

buckets140 nspulse gap

1.4 µs train length - 7 A peak current

10 cmbetweenbunches

180° phase switch inSHB

Figure 3.3 Schematic of (x2) bunch frequency multiplication in the Delay Loop.

Figure 4.2: Pulse compression by a factor 2 in the Delay Loop. The principle of thephase coding with the Sub-Harmonic Bunchers (SHB) is shown on the top left andthe bunch frequency multiplication is shown on the top right. The pulse structurebefore and after the pulse compression stage in the Delay Loop is shown at thebottom [45].

83


by two RF deflectors at 3 GHz and a CR length of 84 m, which is just the distance

between two 140 ns long pulses, i.e. 280 ns, and corresponds to two times the length

of the delay loop. The CR is connected to the DL by the Transfer Line 1 (TL1) and

consists of four isochronous arcs, two short straight sections, and two long straight

sections for injection and extraction.

At the injection region, a septum is placed symmetrically in the long straight

section and two horizontally deflecting RF structures are positioned in such a way

that they have a distance between them which corresponds to a horizontal betatron

phase advance of π.

As shown in Figure 4.3, the bunches of the incoming train always receive a max-

imum deflection from the RF deflector and are deviated onto the closed orbit in the

ring. The bunches of the first train, after one revolution in the CR, arrive at the

zero-crossing of the RF field, which means they are not deflected and stay on the

reference orbit. The second train is then injected into the ring receiving a maximum

deflection as before. After the second turn, the bunches of the first train are de-

flected towards the opposite direction by the first RF deflector due to the different

phase advance and the bunches of the second train arrive at the zero-crossing. The

bunches of the first train are then deflected back onto the reference orbit in the

The deflection varies rapidly with time, allowing theinterleaving of the bunches in the ring. The combinationis possible for various combination factors. CLIC is basedon two stages with a factor 4 each, while CTF3 withnominal current has a factor 5 in the ring. For didacticreasons, the principle of the injection with rf deflectors isexplained in the following for a frequency multiplicationfactor 4 and shown in Fig. 2.

(1) The bunches of the incoming train always receivethe maximum kick from the rf deflector and are deviatedonto the closed orbit in the ring.

(2) With the condition of Eq. (1) fulfilled (for thecombination factor N ! 4), the bunches pass the deflec-tors after one turn at the zero crossing of the rf field andstay on the unperturbed closed orbit. The second train isinjected into the ring.

(3) After a second turn, the first-train bunches arekicked in the opposite direction and follow a closedbump between the deflectors, the second-train bunchesarrive at the zero crossing, and the third train is injected.

(4) After the third turn, the first-train bunches arriveagain at the zero crossing, the second-train bunches arekicked away from the septum, the third-train bunches arealso at the zero crossing, and the fourth train is injected.The four trains are now combined into one single trainand the initial bunch spacing is reduced by a factor 4.

For combination factors other than 4, the phase of thedeflecting field at the passage of the bunches and hencethe trajectories between the two rf deflectors changeaccordingly (see Fig. 3 for a combination factor 5).

The rf deflectors are short resonant, traveling-wave,iris-loaded structures with a negative group velocity. Inorder to obtain the nominal deflecting angle of 4.5 mradfor injection with a beam energy of 350 MeV=c, a powerof about 7 MW is needed in each of the deflectors. Theyare powered by a common klystron with a phase shifterand a variable attenuator in one of the rf-network

branches in order to allow relative phase and amplitudeadjustments.

The first bunch train combination experiments wereperformed with already existing rf deflectors built byCERN. They were later replaced by newly designed struc-tures, with a bigger iris aperture (43 mm instead of23 mm). The latter were built by INFN-Frascati [5] andwill be reused in a later phase of CTF3.

As a consequence of the rapid change of the deflectingfield inside the deflectors, not only do the bunches ondifferent turns experience different deflections but alsothe head and the tail of individual bunches are deflectedmore or less, as shown in Fig. 4.

This enlarges the transverse size of the circulatingbeam in the region between the two rf deflectors andrepresents the main contribution to the beam size at theseptum location. Figure 5 shows the envelope of Gaussianbunches in the injection region.

5 cm)(2nruht5

o = 0 mc

t

! 1

/o!

FIG. 3. (Color) Fifth passage of the first injected bunch train inthe injection region for a combination with a multiplicationfactor of 5.

!

!

0inner orbits

localtransversedeflector

field

0 /4

2nd

3rd 4th

nd2 deflector st1 deflector

st1 turn septumline

injection

FIG. 2. (Color) Bunch train combination by injection with rf deflectors for a multiplication factor 4. The images show the injectionregion of the ring for four successive turns of injected bunches and the corresponding bunch distribution on the rf field of thedeflectors.

PRST-AB 7 ROBERTO CORSINI et al. 040101 (2004)

040101-3 040101-3

Figure 4.3: The principle of the bunch frequency multiplication by a factor 4 in theCombiner Ring [42].

84


second deflector and the third train is injected. After three turns, the bunches of

the first and third trains arrive at the zero-crossing and the bunches of the second

train are deflected towards the opposite direction in the first RF deflector. These

are then deflected back onto the reference orbit and the bunches of the fourth train

are injected.

Consequently, a 140 ns long drive beam pulse with 8 times the initial current,

typically around 28 A, and a final bunch spacing of 2.5 cm or 12 GHz is obtained. A

more detailed explanation of the pulse compression and bunch frequency multipli-

cation can be found in [45, 46].

Finally, the continuation of the straight injection section, which is located after

the first bending magnet of the CR, is the so called Combiner Ring Measurement

(CRM) line. The CRM line is equipped with an Optical Transition Radiation (OTR)

screen and the CDR setup, as explained in Section 4.2. A beam dump to safely

terminate the beam completes the line.

4.1.3 CLIC Experimental Area

The compressed pulse is then sent to the CLIC Experimental Area (CLEX) via the

Transfer Line 2 (TL2) in which the bunches are also compressed in a chicane. The

combined beam arriving from the CR area can be chosen to be injected into the

the Test Beam Line (TBL) or the Two-Beam Test Stand (TBTS). Besides the TBL

and the TBTS, an additional accelerator which resembles the CLIC probe beam

is installed, which is the so called Concept d’Accelerateur Lineaire pour Faisceau

d’Electrons Sonde† (CALIFES).

a) Test Beam Line

The TBL is composed of 16 PETS structures, which were already mentioned in

Section 1.3.2 and are positioned in a similar way as they are designed to be arranged

in the proposed CLIC module. Each PETS structure is followed by a quadrupole

magnet and a Beam Position Monitor (BPM). The aim of the TBL is to extract as

much energy from the drive beam as possible and to demonstrate the stability of the†English translation: “Conceptual linear accelerator for an electron probe beam”

85

4.2. CDR Setup in the CRM line

decelerated beam and the generated RF power. Additional objectives for the TBL

are the testing of alignment procedures and the study of the mechanical layout of a

CLIC drive beam module, including the PETS and RF components [47].

b) Two-Beam Test Stand

The TBTS on the other hand is used to demonstrate the power extraction from

the compressed drive beam and its transfer to the probe beam via the PETS, as

shown in Figure 4.4, which are just resonant cavities with output waveguides. In

order to do so, the 140 MeV CALIFES, which is running in parallel to the combined

drive beam, was built. Spectrometer lines are installed along the drive beam line

and the CALIFES to accurately monitor the beam energies before and after power

extraction and transfer [48].

Figure 4.4: PETS structure [49].

4.2 CDR Setup in the CRM line

4.2.1 Installation location

The CRM line, as mentioned in Section 4.1.2, is the elongation of the straight injec-

tion section of the CR. The general layout of the straight section, the first CR arc,

and the CRM line is shown in Figure 4.5. The schematic drawing shows the most

86


important devices in this region‡. A few metres upstream of the bending magnet

(CR.BHF0205) two quadrupole magnets (CR.QDF0160 and CR.QFF0190) are lo-

cated. These quadrupole magnets allow for the beam optics to be changed and to

deliver a transversely circular electron beam to the CDR setup in the CRM line.

A pair of corrector dipole magnets (CR.DHF0200 and CR.DVF0200) are installed

just upstream of the bending magnet and allows for the trajectory into the CRM

line to be adjusted without any optical elements thereafter. Additionally, two beam

position monitors (BPM) (CR.BPM0155 and CR.BPM0195) are installed in this

section, which can be used for a horizontal and vertical beam position reading, and

a beam current reading with a sampling rate of 5 ns.

QFG

0120

QD

G01

40

QD

F016

0

QFF

0190

QFJ0215QDJ0230

QFJ0245

QFJ0255

QDJ0270

BHF0205

BHF0250HD

S01

50

QD

G10

60

QFG

1080

HD

S10

50

CT.

SH

C 0

780

CT.

SH

D 0

790

DHF/DVF 0252

DHF/DVF 0242

DH

F/D

VF02

00

DH

F/D

VF 0

145

DH

F/D

V F10

5 5

DH

F/D

VF01

47

CRM.MTV 0210

CRM.CDR 0200

BPM

019

5

BPM

015

5

Figure 4.5: CR with CRM line. The following devices are shown on the plot:bending magnets (denoted by BHFx) in red, quadrupole magnets (denoted by QDxand QFx) in blue, small deflector magnets (denoted by DHFx and DVFx) in black,BPMs (denoted by BPMx) in dark green, beam instrumentation devices includingthe CDR setup in the CRM line (denoted by CDRx and MTVx) in magenta, septa(denoted by SHx) in green, and RF deflectors (denoted by HDSs) in orange [50].

A technical drawing of the CRM line is shown in Figure 4.6 and the components

installed in the CRM line are listed in Table 4.1. The reference beam height with re-

spect to the ground is 1350 mm. Originally, only the vacuum valve (CRM.VVS0150),

the OTR screen (CRM.MTV0210), and the vacuum pump (CRM.VPI0220) were

installed on the girder in the CRM line. In order to position the CDR setup

(CRM.CDR0200) in the line, a girder extension was designed, manufactured, and

installed. Additionally, the OTR screen and the vacuum pump were moved down-‡All devices around CTF3 are named uniquely. The characters ahead of the dot resemble the

section of CTF3, e.g. CR, CRM. The part after the dot indicates the device and the position.

87


Figure 4.6: Technical drawing of the CRM line [51].

88


stream towards the beam dump. The OTR screen contains two different screens, a

semi-transparent silica screen and a reflecting aluminised silica screen, and can be

used to monitor the transverse beam profile and the horizontal and vertical beam

position.

# Device/Component1 CR dipole2 CR beam pipe

3, 14, 16 Beam pipe4 Adapter vacuum bellows5 Vacuum valve

6, 10, 12 Bellows7 OTR screen8 Girder extension9 Vacuum pump11 CDR setup13 Support15 Beam dump

Table 4.1: CRM line devices, as displayed in Figure 4.6.

The CRM line was selected as the installation location due to the following

reasons. The CRM line – despite the need for a slight rearrangement – offered

sufficient space for the vacuum hardware, which will be described in Section 4.2.2 in

greater detail, as well as for the optical table which needed to be placed alongside

the beam line. Moreover, the availability of beam instrumentation in the proximity

of the CDR setup, not only in the CRM line but also in the CR and the TL1,

was of great importance. The CLEX area was still under construction at the point

of installation and other parts of the machine did not offer enough space and not

sufficient beam instrumentation. For these reasons, and due to the availability of

the beam in the CRM line, the CRM line was selected. Additionally, the CRM line

is equipped with a vacuum valve, a vacuum pump, and an ion pump, which allow for

minor vacuum installations to be done without breaking the entire CR vacuum and

compromising the vacuum levels in the machine. Finally, the installation location

also allows the measurement of synchrotron radiation, emitted in the CR.BHF0205

bending magnet, since the CRM line is just an elongation of the injection section.

89


The ability to measure synchrotron radiation offers the possibility to carry out

debugging processes of the CDR system, including the data acquisition, target move-

ment, etc. It also offers the opportunity to perform parasitic measurements and does

not require dedicated beam time with the electron beam in the CRM line.

4.2.2 Vacuum hardware

The CRM line, which is shown in Figure 4.6, contains the CDR vacuum assembly and

a more detailed description of the CDR vacuum hardware is given in the following

sections.

a) Vacuum tank and support structure

Two ultra-high vacuum (UHV) six-way crosses (VG Scienta, ZBX610RS) are in-

serted in the CRM line which are connected to each other and installed along the

beam line. An exact model of this configuration can be seen in Figure 4.7. The

diameter of the six cylindrical ports is 95.7 mm and the length of the six-way cross

is 270 mm. The diameter of the cylindrical ports coincides with the inner diameter

of the six-way cross flanges and the outer diameter is 150 mm. One flange of each

set of opposite flanges is rotatable, which allows for an easier installation of the

hardware.

The vacuum chambers are supported by a support structure which was designed

and manufactured at CERN. This support structure is the interconnection between

the vacuum chamber and the girder, which the CDR setup is placed on. The support

structure can also be seen in Figure 4.7 and – above the two (yellow) pillars – consists

of three base plates, which can be moved and tilted with respect to each other. A

clamp for the six-way crosses is mounted on top of the upmost base plate to ensure

a secure installation.

The support allows for an accurate installation of the CDR vacuum assembly,

which is held in place by the two vertical clamps. The yaw can be adjusted with

the top base plate as it can be moved in the horizontal plane with small adjustment

screws (light grey). The roll can be adjusted by the rotation of the vacuum chamber

as well as by the three adjustment screws (magenta) between the bottom and middle

90


e -

Six-way cross

Manipulator

Adapter flange(later replacedby a 15 mm

off-centre flange)

Support

Figure 4.7: Vacuum assembly and vacuum support.

91


plate. The three adjustment screws also control the correct vertical height and the

pitch of the setup.

b) Adapter flange and vacuum viewport

In order to install flanges with a smaller outer diameter onto the six-way cross, an

adapter flange needs to be mounted. For the smaller flanges used at this setup,

namely 70 mm outer diameter flanges and viewports, the adapter flanges have an

outer diameter of 150 mm with a concentric bore of 38 mm (VG Scienta, ZAZ7015).

The two downstream horizontal six-way cross openings perpendicular to the

beam line are equipped with viewports. Initially, the vacuum window through which

the radiation is detected was a quartz fused silica vacuum window with a viewing

diameter of 38 mm.

Frequency [GHz]0 50 100 150 200 250 300

Tra

nsm

issi

on

0

0.2

0.4

0.6

0.8

1

Figure 4.8: Simulated diamond transmission properties with data from [52] andcorrected for multiple reflections.

This window, however, was exchanged with a CVD diamond vacuum window

with a viewing diameter of 34 mm, since the diamond vacuum window has much

better transmission properties. Diamond exhibits a broadband transparency in the

far-infrared and millimetre wavelength range, as shown in Figure 4.8. The CVD

window also has a thickness of 0.5 mm, which is smaller than or comparable to the

observation wavelength, which minimises the viewport absorption and the distortion

of the transmitted radiation spectra due to multiple reflections.

Compared to a quartz window, diamond also has the advantage of a high trans-

mission without any resonant absorption down to the microwave region, which is

92


shown in Figure 4.9.

diamond

1

0.4

0.6

0.8

0.2

10 100 100020 50 200 500

quartz

Wavelength [μm]

Tran

smis

sion

Figure 4.9: Comparison of the transmission properties of diamond and quartz [53].

c) Other components

All remaining six-way cross openings, except the two upstream horizontal openings

perpendicular to the beam line, the opening adjacent to the diamond vacuum win-

dow, and the top opening of the downstream cross, are equipped with blank flanges

to seal the vacuum. A vacuum ion pump is attached to the the horizontal opening

facing the CR. Moreover, an adapter flange (VG Scienta, ZAZ7015) and a 70 mm

outer-diameter blank flange are installed at the adjacent opening, since this opening

will be equipped with a viewport during a future upgrade. The opening adjacent to

the diamond window is fitted with an adapter flange and a 38 mm Kodial viewport

(VG Scienta, ZVPZ38) and is only used for alignment purposes, which will be ex-

plained in Section 4.3.3. Finally, the top opening is equipped with another adapter

flange in order to accommodate the vacuum manipulator.

d) Manipulator

In order to suspend and control the target, which is described in Section 4.2.3, within

the vacuum chamber, the target is attached to the shaft of a 4D UHV manipulator

(VG Scienta, HPT High Precision Translator), which is mounted on top of the down-

stream cross. The manipulator provides precise remote control over the rotation and

vertical translation of the target. The remaining two dimensions, namely the two

93


Axis Position Error Encoder (steps)

Translation20 mm

± 0.1 mm0

25 mm 5,00030 mm 10,000

Rotation240

± 0.215,000

260 10,000300 0

Table 4.2: Manipulator axis calibration.

horizontal axes, can be controlled locally. The manipulator is equipped with stepper

motors which in turn are equipped with encoders. The range of the translation axis

is 50 mm and is set up such that the target edge reaches its lowest position 6 mm

below the beam pipe centre. Although the range of the rotation axis is theoretically

unlimited, limit switches are installed which prevent this free rotation. The stepper

motors are driven and the encoders are monitored with a BALDOR NextMove e100

motion controller via custom cable connections. To prevent radiation damage of the

motion controller, it was moved out of the experimental hall. With the aid of the

motion controller, each axis is equipped with a power supply for the stepper motors,

an encoder, and two limit switches. For each of the three channels, dedicated cabling

between the manipulator and the motion controller is necessary, and is described in

Section 4.5.1.

A mechanical calibration of the manipulator was performed before the instal-

lation in the CRM line. Within the range of motion, a few positions, for the ver-

tical axis as well as the rotation axis, and the corresponding steps of the motor

were recorded. These records are shown in Table 4.2 and calibration constants of

1000 steps/mm and 250 steps/1 can be inferred. The motors provide a single step

precision, relating to a 0.004 rotational and a 1 µm translational precision.

4.2.3 Target and target holder

As already mentioned, the downstream six-way cross contains the CDR target. The

target is a 60 mm×40 mm×0.3 mm silicon wafer coated with aluminium and is placed

to one side of the electron beam with impact parameter b. Aluminium was chosen as

the coating since the intensities of TR and DR depend on the reflection properties

94


2030

46

40

60

(a) Technical drawing of the targetand target holder

(b) Picture of the target and target holder from a view per-pendicular to the beam line. The beam pipe extending tothe CR area can be seen in the reflection from the targetwhich is tilted by 45

Figure 4.10: Aluminised target and target holder.

of the target. Since aluminium has a high refractive index in the far-infrared region,

it follows from the Fresnel reflection coefficients that aluminium has a reflectivity

of more than 99% [54]. Moreover, the skin depth of aluminium in the millimetre

wavelength region is less than 1 µm and aluminium is therefore an ideal coating for

the target.

A thin copper plate is glued to the coated silicon target such that it can be

held by a clamp without damaging the surface. The clamp which was designed and

manufactured at RHUL is used to safely attach the target to the shaft of the 4D UHV

manipulator. The design of the clamp holding the target is shown in Figure 4.10(a)

and a picture of the target clamped by the target holder is shown in Figure 4.10(b).

4.2.4 Off-centre adapter flange

Due to the reasons explained in detail in Section 5.2, an adapter flange with a shifted

inner bore was used. Such a flange is referred to as an off-centre adapter flange and

was manufactured at CERN. The design of the off-centre flange originates from

a standard 150 mm outer-diameter blank flange (VG Scienta, ZFC6), which was

95


15

(a) Technical drawing of the off-centre flange

(b) Picture of the off-centre adapter flange equipped with the diamondvacuum window at the setup in CTF3

Figure 4.11: Off-centre flange with a 15 mm offset of the inner bore.

96

4.3. Michelson interferometer

modified for this setup and fitted with a bore, taking the straddled configuration of

the six-way cross flanges into account. The offset of the inner bore was chosen to

be 15 mm in the upward direction and the off-centre flange is shown in Figure 4.11.

This new design allows a larger area of the target to be seen at the observation point

compared to a standard adapter flange, which is beneficial for the detection of CDR

from the target.

4.3 Michelson interferometer

At CTF3, a Michelson interferometer was used to analyse the radiation originating

from the target and to determine the spectrum of the radiation dWdω . A brief descrip-

tion of the Fourier transform spectroscopy technique is followed by a discussion of

the components used to build the interferometer at CTF3.

4.3.1 Fourier transform spectroscopy

A Michelson interferometer is based on dividing the amplitude of radiation from a

source and recombining the two wave forms with an optical delay τ . A schematic

diagram of an ordinary Michelson interferometer can be seen in Figure 4.12. It

consists of a radiation source, a beam splitter, a fixed mirror and a translating

mirror, and a detector.

Beam splitter

Radiation source

Mirrors

τ

2

Detector

Figure 4.12: Schematic diagram of a Michelson interferometer.

The radiation originating from the source with intensity I0(ω) is divided at the

97


splitter which is normally tilted by 45 and subsequently recombined at the same

location. Therefore, the intensity at the detector is

Itot(ω, τ) = RT (ω)I0(ω)∣∣1 + eiωτ

∣∣2 (4.1)

where RT (ω) is the splitter efficiency, which is represented by the splitter transmis-

sion and reflection coefficients. Consequently, the intensity of the interferogram as a

function of the optical path difference is given by the integration over all frequencies

Itot(τ) = 2∫ ∞−∞

RT (ω)I0(ω) dω + 2∫ ∞−∞

RT (ω)I0(ω) cos (ωτ) dω (4.2)

where the first term is independent of τ and corresponds to half the intensity at

zero path difference. The second term corresponds to the Fourier cosine transform

of 2RT (ω) times the radiation spectrum. The radiation spectrum can therefore be

obtained by an inverse Fourier cosine transform

I0(ω) =1

4πRT (ω)

∫ ∞−∞

[Itot(τ)− 1

2Itot(τ = 0)

]cos(ωτ) dτ. (4.3)

Practically, however, this inverse Fourier transform is replaced by a summation

over all 2N + 1 discrete optical delays τn separated by ∆τ , which is

I0(ω) =1

2RT (ω) ·∑nItot(τn)

N∑n=−N

[Itot(τn)− 1

2Itot(τ = 0)

]cos(ωn∆τ) ∆τ (4.4)

which sets limitations on the resolution and maximum frequency one can retrieve

from the interferogram. The maximum resolution is ∆ω = 2π/T , i.e. ∆f = 1/T ,

up to a maximum frequency of fmax = 1/2∆τ .

Figure 4.13 shows examples of two interferograms which are expected to be mea-

sured with a broad band and a narrow band detector. For the broad band detector,

as seen in Figure 4.13(a), it can be observed that the interferogram consists of one

main peak which on either side is accompanied by a deep minimum and two smaller

peaks, after which the peak intensity approaches half the intensity of the central

peak as the optical path differences tend to ±∞. For the narrow band detector,

98


Optical path difference [arb.u.]-1 -0.5 0 0.5 1

Inte

nsity

[ar

b.u.

]

0

0.2

0.4

0.6

0.8

1

(a) Broad band

Optical path difference [arb.u.]-1 -0.5 0 0.5 1

Inte

nsity

[ar

b.u.

]

0

0.2

0.4

0.6

0.8

1

(b) Narrow band

Figure 4.13: Typical interferograms for a narrow band and broad band detector.

on the other hand, as shown in Figure 4.13(b), the main peak is accompanied by

multiple oscillations around half the intensity of the central peak. The amplitude

of these intensity modulations becomes smallest furthest away from the zero path

difference and eventually the peak intensity approaches half the intensity of the cen-

tral peak as the optical path difference tends to ±∞. Therefore, the interferogram

for a narrow band detector needs to be recorded for larger optical path differences

than for a broad band detector, since the intensity approaches half the central peak

intensity much less rapidly.

4.3.2 Interferometer components

In this section the components of the interferometer setup at CTF3, as shown in

Figure 4.14, are explained.

a) Periscope

In order to avoid backgrounds from the horizontal particle beam plane and to observe

the radiation which is emitted by the target and extracted through the diamond

vacuum window at beam height, i.e. 1350 mm, the radiation needs to be translated

vertically to the optical setup on the optical table. The reference working point is

99


Figure 4.14: Picture of the Michelson interferometer at CTF3.

a height of 5 inches (127 mm) with respect to the table surface. For this purpose a

periscope is used which consists of two mirrors clamped to a rod mounted on the

optical table.

b) Mirrors

All mirrors that are used for the experiment are broad band aluminium coated

mirrors (Melles Griot, PAV-PM-4050-C) since aluminium has a very high reflectance

in the far-infrared and millimetre wave region. The mirrors have a diameter of

4 inches (101.6 mm) and are mounted in suitable mirror holders with the centres of

the mirrors at the working point of 5 inches. Two axes of each mirror holder can be

controlled with fine adjustment screws, which can potentially be motorised.

c) Translation stage

As already mentioned, a mirror in one of the interferometer legs is mounted on top of

a translation stage (Newport Corp., UTS150CC). The translation stage has a travel

range of 150 mm, a resolution of 0.1 µm, a minimum incremental motion of 0.3 µm

and an uni-directional repeatability of 1 µm. The translation stage is powered by

and interfaced with a controller (Newport Corp., SMC100CC) which can be accessed

100


from a computer via an RS232 serial connection.

d) Beam splitter

A choice of beam splitters including commercially available Mylar and Kapton films

were investigated analytically by calculating the Fresnel surface reflectance terms Rs

and Rp, where the subscripts refer to polarisations. The s polarisation represents the

component of the incoming radiation perpendicular to the plane of incidence and

the p polarisation represents the component of the incoming radiation parallel to

the plane of incidence. The refractive indices and absorption coefficients, as found

for Mylar [55] and Kapton [56], were extrapolated to lower frequencies in order

to perform the calculations [57]. The splitter efficiencies for the S-polarisation for

Frequency [GHz]0 50 100 150 200 250 300

Eff

icie

ncy

00.02

0.04

0.06

0.080.1

0.12

0.14

0.16

0.180.2

m]µThickness [13 2336 5075

(a) Mylar

Frequency [GHz]0 50 100 150 200 250 300

Eff

icie

ncy

00.02

0.04

0.06

0.080.1

0.12

0.14

0.16

0.180.2

m]µThickness [13 2536 5075

(b) Kapton

Figure 4.15: Calculated splitting efficiencies for the S-polarised radiation.

Mylar and Kapton films are shown in Figure 4.15. It was concluded that the best

compromise between splitter efficiency and linearity for commercially available films

was for a 50 µm thick Mylar film or a 50 µm Kapton film. For the experiment, a

50 µm Kapton film is used as the splitter material.

e) Splitter holder

In order to mount the splitter materials, custom splitter holders were designed and

manufactured. The design of the splitter holders is shown in Figure 4.16. The splitter

101


holders consist of two metal rings between which a rubber O-ring is placed. The film

is positioned between the two rings and upon screwing the two rings together the

O-ring is flattened. This flattening of the O-ring causes the polymer splitter films

to be stretched uniformly and a secure fit is obtained.

M3

450

Figure 4.16: Custom beam splitter holder.

f) Polariser

In order to be able to study CDR polarisation properties, it is desirable to separate

the polarisation components. In order to discriminate between the two polarisation

components of DR, a polariser is used. In the far-infrared and millimetre wavelength

region a simple wire grid polariser can be used. The wire grid polariser G80×15 used

at CTF3 consists of a 15 µm thick tungsten wire wound on a circular frame with a

spacing of 80 µm. The clear aperture of the polariser is 88 mm. A wire grid polariser

allows the polarisation component with the E-field perpendicular to the wires, E⊥,

to be transmitted, while the component with the E-field parallel to the wires, E‖, is

reflected in the mirror reflection direction. Figure 4.17 shows the transmission spec-

trum for the E‖ component and it can be seen that the chosen polariser discriminates

well between the two components in the region of interest. For frequencies lower

than 200 GHz, the polariser separates the E⊥ and E‖ components with an efficiency

102


0.1E || wires

Tran

smis

sion

Frequency (GHz)100010010

0.01

0.001

0.0001

G80 x 15

Figure 4.17: Polariser transmission for the polarisation component parallel to thewires [58].

of more than 99.5%.

g) Attenuator

Since the radiation emitted by the target can potentially be too intense for the

dynamic range of the detection system used in the experiment, attenuators (Mi-

croTech Instruments, THz Attenuators) are used to reduce the intensity. For this

setup, the attenuators are sputter-coated thin-film elements and are available in 4

different attenuation strengths. Figure 4.18 shows the transmission spectra for the

attenuators and a flat attenuation spectrum is expected for all 4 attenuators from

the far-infrared to the millimetre wavelength region. The attenuators, when used,

are placed right in front of the detectors. The attenuators have a clear aperture of

60 mm and may be used as individual attenuators or in combination as needed.

h) Shielding

As seen in Figure 4.14, lead shielding is utilised all around the equipment. It was

introduced to minimise the background from the beam dump, but also to reduce

103


100 10001E-3

0.01

0.1

1

Tran

smis

sion

Frequency (GHz)

30%

10%

3%

1%

Figure 4.18: Attenuator transmission for the four different attenuation levels [59].

the risk of damage to sensitive hardware. Lead shielding is used for protecting the

translation stages, since the optical encoders within them, which are used for the

position readings, are very susceptible to malfunction in a radiation environment

like CTF3. Furthermore, the motion controllers which are used to control the stages

also need to be protected since the electronics within them is prone to radiation

damage.

i) Detector

The detection system which is part of the interferometer will be discussed in greater

detail in Section 4.4.

4.3.3 Alignment

In order to align the interferometer, an optical laser alignment procedure is used. A

HeNe laser is stably mounted on the side adjacent to the beam line and directed into

the six-way cross through the Kodial viewport, which was mentioned in Section 4.2.2.

Consequently, the laser resembles the path of radiation originating from the target.

Subsequently, the interferometer mirrors are adjusted locally to minimise a vertical

and horizontal misalignment until a pattern of concentric rings is seen. This pattern

is the result of a best possible alignment for a diverging laser beam. Since the

104

4.4. Detection system

observation of CDR is performed at a wavelength of about 4 orders of magnitude

larger than the green HeNe laser at around 600 nm, a very accurate alignment of

the interferometer for millimetre radiation is obtained.

4.4 Detection system

In order to detect the radiation emitted by the target, a detection system based on

ultra-fast room-temperature Schottky barrier diode detectors is used. The properties

of a Schottky barrier are briefly introduced to explain the main properties of a

detector based on this technology.

4.4.1 Schottky barrier diode detector

A Schottky barrier is based on the direct contact of metal with a semiconductor,

which in this case shall be an n-type semiconductor. In order to understand the

properties of this metal-semiconductor junction, the band structures of a metal and

a n-type semiconductor without a contact between them, as shown in Figure 4.19(a),

and the change of the band structures after contact, as shown in Figure 4.19(b), are

discussed. The important feature, like in an ordinary p-n junction, is the bending

of the bands due to the coinciding of the Fermi levels EFm and EFs at the junction.

Due to this bending of the band, a depletion region is formed, leaving behind charged

ions near the junction, causing a change of potential across the junction of φm−φs,

i.e. the barrier voltage Vbi.

When the Schottky barrier is exposed to electromagnetic radiation, the electrons

in the epitaxial metal layer can cross the depletion barrier causing currents to flow

in the device. The depletion layer can be crossed by thermal activation over the

barrier or by quantum-mechanical tunnelling through the barrier. For a Schottky

diode at room temperature, however, thermal effects are dominant. The Schottky

diode is a majority carrier device and free of long reverse recovery times. Therefore,

the detector response can be designed to be very fast. The Schottky barrier diode

provides an output voltage without needing any external DC bias and the detector

response is proportional to the input radiation power. The electromagnetic radiation

105


n-typesemiconductor

Metal

Contact

≈ ≈

φm > φs n-type

EcEFs

n-semiconductorMetal

EFm

Ev

eφseχs

eφm +

EcEFs

Ev

EFm

eφm – eφs = eVbi

W

eφbeφm

eχs

++ ++––

VacuumEnergy

Vacuum

(a) Before contact

n-typesemiconductor

Metal

Contact

≈ ≈

φm > φs n-type

EcEFs

n-semiconductorMetal

EFm

Ev

eφseχs

eφm +

EcEFs

Ev

EFm

eφm – eφs = eVbi

W

eφbeφm

eχs

++ ++––

VacuumEnergy

Vacuum

(b) Metal-semiconductor contact

Figure 4.19: Metal and semiconductor band profiles [60].

is fed into the detector with an impedance-matched antenna, i.e. a Standard Gain

Horn (SGH). The radiation is then guided to the Schottky barrier diode chip within

the detector via wave guides, which cause the detector to be polarisation sensitive.

Until now, commercially available Schottky Barrier Diode (SBD) detectors are

faced with limitations on their spectral response. A waveguide cut-off at low fre-

quencies and a limited response at high frequencies reduce the bandwidth of such

types of detectors. Therefore, in order to cover a wide frequency range in the exper-

iment, a set of detectors was used. The detectors are polarisation sensitive and have

a typical response time of ∼ 250 ps (FWHM). It was already shown experimentally

that a detector response time of less than 1 ns can be achieved [61]. The detectors

used in the experiment with their corresponding frequency and wavelength regions

are shown in Table 4.3.

Detector Freq. band Freq. range [GHz] Wavelength range [mm]DXP-08 F-band 90 – 140 2.14 – 3.33DXP-12 E-band 60 – 90 3.33 – 5DXP-19 U-band 40 – 60 5 – 7.5DXP-28 Q-band 26.5 – 40 7.5 – 11.32

Table 4.3: SBD detectors used in the experiment.

The spectral sensitivity of the SBD detectors in their individual bands for a

1 MΩ termination are shown in Figure 4.20. At CTF3, however, a 50 Ω termination

106


Frequency band [%]0 10 20 30 40 50 60 70 80 90 100

Sens

itivi

ty [

mV

/mW

]

0

1000

2000

3000

4000

5000

DXP-08 DXP-12

DXP-19 DXP-28

Figure 4.20: Schottky Barrier Diode Detector response plotted against the relativefrequencies from the lowest (0%) to the highest frequency (100%) in the individualfrequency bands shown in Table 4.3 [62]. The frequency band is calculated by sub-tracting the lowest frequency of the respective band from the frequency at which theintensity is displayed and dividing by the detector bandwidth, i.e. fi,rel = fi−fmin

fmax−fmin.

is used. Since the diode sensitivity is expected to depend on the diode properties,

rather than the termination, the sensitivities for a 1 MΩ are assumed to be valid for a

50 MΩ termination. Since only a relative sensitivity is needed for the normalisation

of the spectra for the experiment at CTF3, the sensitivities for a 1 MΩ load can be

taken for this purpose.

4.4.2 Standard gain horns

As mentioned above, the electromagnetic radiation is fed into the SBD detectors

with Standard Gain Horns (SGH). The SGHs are connected to the front face of the

detectors and match the different sized waveguides. The gain horns are pyramidally

shaped and have different apertures and length for different frequency bands. The

gain of the antennas depends on the frequency and is shown in Figure 4.21. It can be

observed that the signal gain has a change of less than 1.5 dB across the individual

frequency bands.

107

4.5. Hardware control interface and software

Frequency band [%]0 10 20 30 40 50 60 70 80 90 100

Gai

n [d

B]

22.4

22.6

22.8

23

23.2

23.4

23.6

23.8

SGH-08 SGH-12

SGH-19 SGH-28

Figure 4.21: SGH gain plotted against the relative frequencies from the lowest (0%)to the highest frequency (100%) in the individual frequency bands shown in Ta-ble 4.3 [63]. The frequency band is calculated by subtracting the lowest frequency ofthe respective band from the frequency at which the gain is displayed and dividingby the horn bandwidth, i.e. fi,rel = fi−fmin

fmax−fmin.

4.4.3 Detector holder

In order to mount the detectors at the correct working point, detector holders were

designed and manufactured at the RHUL workshop. The design of a typical detector

and detector holder is shown in Figure 4.22. The holders were designed in such a

way that they can be rotated to measure different polarisation components as well as

to mount the detector facing upwards. The distances between the detector opening

and the mounting faces were designed to be 1.5 inch in order to establish the working

point of 5 inch above the optical table surface with commercially available mounting

posts.

4.5 Hardware control interface and software

In order to control all the hardware described in the previous sections, a hardware

control interface needed to be established, a diagram of which is shown in Figure 4.23.

This hardware control interface is also used to monitor the necessary parameters to

conduct the experiment. As shown in the diagram, all components are either situated

108


Figure 4.22: Detector holder with a detector.

in the Streak Camera Lab just outside the DL area or in the CTF3 accelerator tunnel,

separated by a distance of about 60 m between them. The devices are all controlled

with the DAQ computer in the Streak Camera Lab and the arrows in the diagram

indicate the direction of communication between them. The individual systems are

explained in greater detail in the following sections.

4.5.1 Translation stage and manipulator control

In order to control the translation stage of the interferometer, a SMC100 single axis

motion controller is used, which requires a RS232 connection to the DAQ computer.

At a baud rate of 96 kBit/s, however, which is required by the stage controller, the

cable length is limited to a few metres. Therefore, a Serial-to-IP hub is used in

the accelerator to connect the RS232 cable via an ethernet connection to the DAQ

computer. The DAQ computer can then access the SMC100 controller to demand

a certain stage position and monitor the encoder of the translation stage for an

accurate position reading.

In order to control the position and orientation of the target in the vacuum pipe

with the 4D UHV manipulator, the stepper motors need to be managed and the

limit switches need to be monitored. As explained above, a BALDOR NextMove

e100 motion controller is used to carry out this task running a Motion INTelligence

109


FESA

Streak camera lab CTF3

IP to RS232

Stage(s)SMC100

MINTLimit

switches

Manip.motors

BPM

OTR

KlystronPhase

DC282 SBD

DA

Q C

ompu

ter

e guntrigger-

Figure 4.23: Schematic diagram of the hardware control interface. On the lefthand side the devices in the Streak Camera lab and on the right hand side thedevices in the CTF3 accelerator tunnel. The DAQ computer controls the IP-to-RS232 device, the MINT controller, the DC282 digitiser, and the FESA class viaa two-way communication (represented by the direction of the arrows). These fourmain devices in turn control all other hardware shown in the column on the righthand side, including the stages, manipulator motors etc.

(MINT) program and is linked to the DAQ computer. From the manipulator con-

troller, custom cables are laid into CTF3 to interface with the UHV manipulator,

which consist of ordinary multi-lead wires with 9-, 15-, and 23-pin serial connectors

for the power supplies, encoders and limit switches, respectively.

4.5.2 Data acquisition and synchronisation

The data acquisition is performed with a 10-bit Acqiris DC282 digitiser. The DC282

offers synchronous four channel sampling at up to 2 Giga-Samples/second (GS/s), or

interleaved dual- or single-channel sampling at up to 4 and 8 GS/s, respectively. The

input for an external trigger provides a precise synchronisation to the electron gun

trigger. The internal acquisition memory of the digitiser is 256 kSamples/channel

and is large enough to theoretically store around 100 bunch trains of 1.4 µs length.

The bunch train repetition rate, however, is 0.8 Hz and the data is read out to the

DAQ computer immediately after every single bunch train. In order to transmit the

110


signal from the SBD detector to the DC282 digitiser, high quality RF cables are

chosen with a bandwidth of 11 GHz.

4.5.3 Machine parameter readout and device control

Almost all devices around CTF3 are controlled and monitored with the so-called

Front-End Software Architecture (FESA) developed by CERN. It is a framework to

integrate and monitor any kind of equipment such as beam instrumentation devices,

magnet power supplies, vacuum- and RF components into the control system. The

FESA class was used to acquire necessary information, such as BPM readings, OTR

screen readings, and klystron phases, from the accelerator directly to the DAQ

computer via the technical network.

As part of the software, running on the DAQ computer, it also provides control

over the klystron phase which needs to be adjusted for some of the measurements,

which are taken during the experiment.

4.5.4 Principles of operation with the LabVIEW software

On the DAQ computer a LabVIEW program is run which, with the necessary drivers,

can control and monitor all devices. The LabVIEW software can also be designed

to read out the memory of the DC282 digitiser and is therefore a good choice for

integrating all hardware components into one program. A schematic diagram of the

LabVIEW program can be seen in Figure 4.24, which starts in the “Initialise” stage.

Upon the “Initialise” stage, the program enters the “Monitor & free move” stage,

in which all the devices are read out and with which all hardware components can

be moved and controlled. After every bunch train, the program enters the “Perform

scan” stage and checks if a scan is selected. If no scan is selected the program enters

the “Monitor & free move” stage again. If a scan is selected, on the other hand,

a movement of the hardware follows, which depends on the selected scan. Upon

successful movement, the “Acquire & Save” stage is entered where the signal traces

and the hardware positions are saved for future data analysis. Once the data is

saved, the program enters the “Perform scan” stage or the “Monitor & free move”

111


Initialise:- DC282- Stage- Target

Monitor & free move:- DC282- Stage pos.- Target pos.

- BPM- Phase

Perform scan:- Stage- Translation- Rotation

- Raster- Phase- None

Acquire & Save:- DC282- Stage pos.- Target pos.

- BPM- Phase

Change klystronphase

Move target

Move stage

Phase scan

none

Stage scanTranslation, Rotation, Raster scan

stop

scan

run scan

Figure 4.24: Schematic layout of the LabVIEW software.

stage, depending on whether the scan is still running or has finished, respectively.

The important stages are explained in more detail in the subsequent sections.

a) Initialising and monitoring

Upon starting the software, all hardware components are initialised, i.e. the DC282

is calibrated, the stage is reset and homed, and the connection to the manipulator

controller is established.

Following the initialisation, the program can be used to monitor all hardware

components and display them to the graphical user interface. While monitoring, it

can also be used to freely rotate and translate the target, move the translation stage

to a desired position, and adjust the phase of the last klystron in the linac. This

part of the software is generally used to set up the hardware for a subsequent scan.

Additionally, the digitisation level, the sampling rate and the sampling length of the

DC282 digitiser is adjusted here.

b) Selecting and performing scan

When the hardware is set and the settings are adjusted, a scan can be performed. A

scan usually consists of a hardware movement, followed by a short pause to ensure

the hardware movement is finished and by a number of data acquisitions, i.e. a

number of iterations, to achieve a certain statistical confidence. The data is saved

112

4.6. Summary

in data files along with the BPM recording of the CR.SVBPM0195, the settings of

the digitiser, and the hardware positions.

The scans conducted in the experiment are briefly described below:

Stage scan/Interferograms This scan consists of an incremental motion of the

translation stage changing the optical delay of the interferometer and therefore

obtaining an interferogram.

Translation scan For this type of measurement a vertical movement of the target

is followed by the acquisition. The target is usually brought into closest prox-

imity to the electron beam and is then moved out from the centre of the beam

pipe towards the manipulator.

Rotation scan Similar to the translation scan, in this case a target rotation is

performed instead of the target translation.

Raster scan For the raster scan, a range for the rotation scan is defined and af-

ter the rotation has been performed an incremental motion of the target is

performed. In this way, a 2D map or raster of the distribution is mapped

out. Again, after every rotation and translation a certain number of pulses are

acquired.

Phase scan For a phase scan, the RF phase of klystron MKS15 in the linac is

changed and an incremental phase change of the klystron is followed by a

subsequent number of data acquisitions.

After a scan has been completed, the LabVIEW software is again used to monitor the

entire system and freely move hardware components until another scan is performed.

4.6 Summary

In this chapter, the purpose and design of CFT3 has been introduced and all vital

components of the accelerator have been explained. The system which is installed in

the CRM line of CTF3 has also been discussed and all spectral dependencies of the

equipment have been determined. These dependencies are important to calculate

113

4.6. Summary

the transfer function through the optical system such that the measured spectrum

can be normalised in order to obtain the real spectrum of CDR emitted by the

electron bunch.

As discussed in this chapter, some of the hardware is susceptible to radiation

damage and the experience with the setup has shown that it is crucial to minimise

the number of electronic components near the accelerator. Translation stages, which

are equipped with optical encoders, were especially prone to radiation damage and

could be replaced with simple stepper motors in the future, which are currently used

with the manipulator, attached to a threaded rod translating a stage. A similar

controller as used for the manipulator could be used for this purpose and placed

outside the accelerator tunnel to avoid radiation damage. This would not only

improve the reliability and radiation hardness of the setup in the machine, but also

reduce the cost of components.

During the initial stages of the experiment, it was noticed that a high bandwidth

application like the detection system with SBD detectors in the CRM line requires

high-quality RF cabling connecting the detector in the machine to the digitiser in

the streak camera lab. Moreover, it was also experienced that high-quality RF

connectors are needed to connect the RF cables to the detectors and the digitiser to

achieve the best possible results.

Since the CDR setup was installed close to the CRM line beam dump, beam-

based backgrounds, as explained in Section 5.2, as well as minor, ordinary back-

grounds from the beam dump were observed. In order to minimise these ordinary

backgrounds, additional lead shielding or an installation location without a beam

dump behind might be considered in the future.

Altogether, however, the CDR setup in the CRM line performed well and most

of its components behaved as expected. Measurement of CDR obtained with the

system in the CRM line are shown in the next chapter.

114

Chapter 5Properties of Coherent Diffraction

Radiation measured at CTF3

This chapter outlines the measurements that were performed with the Coherent

Diffraction Radiation setup at CTF3. It explains some of the basic SBD detector

properties and the dynamic range of the detection system, which can be observed

while measuring the CTF3 electron bunch train. Moreover, the origin of back-

grounds in the CRM line, which were measured with the setup when the concentric

adapter flange was used, is discussed and the results of an upgrade to minimise

these backgrounds are given. Furthermore, the CDR distributions for two polari-

sation components are shown and the electron beam current stability is discussed.

Additionally, the dependence of the CDR signal on the phase of the MKS15 klystron

is outlined and the correlation of the CDR signal for two different SBD detectors

and two other bunch length monitoring systems is demonstrated. Thereafter, initial

results of interferometric measurements of CDR are shown and problems which need

to be addressed in the future are identified.

5.1 Schottky Barrier Diode signal

Before the discussion on the spatial and spectral properties of CDR, this section

introduces the properties of the SBD detectors with the help of the raw signals

115

5.1. Schottky Barrier Diode signal

measured with the CDR setup in the CRM line. The characteristics of SBD detectors

in extreme conditions of an accelerator with high bunch charge and high beam

repetition frequency have not been previously studied in detail. Therefore, time was

devoted to identify the capabilities as well as shortfalls of the SBD detectors in an

environment like CTF3.

5.1.1 Bunch length variation

As mentioned in Section 4.5.4, when any kind of scan or measurement is performed,

the trace of the SBD detector signal and the CR.SVBPM0195 current reading in the

CR is saved to file. A typical reading of the SBD detector and the corresponding

BPM current reading is shown in Figure 5.1.

When the electron beam passes the target, CDR is emitted and detected by the

SBD detector. The detector shows a similar time structure as the BPM current

reading shown in Figure 5.1(b), i.e. the detector signal lasts as long as the electron

pulse in the CRM line. After the electron train has passed the target, the SBD

reading decays quickly and remains at the noise level, which can be observed from

a typical SBD reading, which is shown in Figure 5.1(a). It also indicates that the

electron gun at CTF3 can be set up to deliver shorter electron pulses than the

nominal 1.4 µs, e.g. 200 ns in this case.

Time [ns]0 200 400 600

Sign

al [

mV

]

0

50

100

150

200

250

(a) SBD signal of CDR in the CRM line

Time [ns]0 200 400 600

Cur

rent

[A

]

-2.5

-2

-1.5

-1

-0.5

0

(b) Corresponding BPM0196 current reading

Figure 5.1: Typical SBD signal and the corresponding beam current reading fromthe CR.SVBPM0195 in the CR.

116


Since the response of the detector is less than 1 ns (FWHM), the detector is able

to record the SBD signal along the electron train in great detail. Therefore, the

narrow-band SBD is able to detect an intra-train variation of the intensity, visible

in Figure 5.1(a), caused by an electron bunch train with a fairly flat beam current,

as shown in Figure 5.1(b). From Equation (2.29), this change in intensity can be

interpreted as a change in the longitudinal bunch form factor F (ω), provided that

the electron beam current remains constant, which is the case for the presented

readings. The CDR signal recorded with the SBD can therefore be used as an intra-

train bunch profile monitor, indicating major relative longitudinal profile changes

throughout the train, with the requirement that the beam current is constant in

the region of interest. This property of the SBD detectors has been routinely used

in the control room for beam parameter optimisations. With the aid of the SBD

signal, the klystron phases in the linac can be adjusted in order to try to minimise

this longitudinal profile variation throughout the train.

Moreover, only the second term in Equation (2.29), which is responsible for co-

herent emission, depends on the longitudinal distribution of particles in the bunch.

It therefore demonstrates that the emitted radiation is coherent.

The SBD signal also shows the need for the use of ultra-fast detectors at CTF3,

since a measurement with a slow detector would not allow for this intra-train bunch

profile variation to be measured. With a slower detector, one would only be able to

measure a projection of the bunch length over the entire electron train.

5.1.2 Bunch spacing frequency and sampling time

Since a beam with a bunch spacing frequency of 1.5 GHz or 3 GHz can be delivered

to the CRM line from the linac, the different structure and properties of the SBD

signal for the two repetition rates are discussed. Two plots for the respective cases

are shown in Figure 5.2 and for both cases the sampling rate of the DC282 digitiser

was set to 4 GS/s. Figure 5.2(a) shows a typical signal for a bunch spacing frequency

of 3 GHz and Figure 5.2(b) a signal for a frequency of 1.5 GHz. The major difference

between the two signals is the detail, which the electron pulse structure can be

recorded with at 4 GS/s. At first sight, this difference in detail manifests itself in

117


Time [ns]500 1000

Sign

al [V

]

0

0.1

0.2

0.3

0.4

595 600

(a) 3 GHz

Time [ns]400 600 800 1000

Sign

al [V

]

0

0.1

0.2

0.3

0.4

595 600

(b) 1.5 GHz

Figure 5.2: Typical SBD signals for a 3 GHz and 1.5 GHz beam repetition rate.

Time [ns]0 1 2 30

0.2

0.4

0.6

0.8

1

Sampling rate (4GHz)

Simplified signal (3 GHz)

Simplified signal (1.5 GHz)

Sampling rate (4GHz)

Simplified signal (3 GHz)

Simplified signal (1.5 GHz)

(a) Simplified signal and sampling rate

Time [ns]0 1 2 3

0

0.2

0.4

0.6

0.8

1

DAQ Signal (3 GHz)

DAQ signal (1.5 GHz)

(b) Example DAQ digitised signal at 4 GS/s

Figure 5.3: Sampling of a simulated simplified signal for a 3 GHz and 1.5 GHz beamrepetition rate.

the width of the “band” on top of the signal but can be explained in more detail by

zooming into a smaller time interval. The magnified area in Figure 5.2(a) indicates

that it is not possible to clearly identify a single bunch due to the sampling rate

of 4 GS/s at this specific beam repetition rate. With a lower beam repetition rate,

however, it is possible to identify a single bunch, which is shown in the magnification

in Figure 5.2(b).

118


The effect of the sampling time on the ability to identify single bunches is illus-

trated in Figure 5.3. In Figure 5.3(a), the sampling of a 3 GHz and 1.5 GHz signal

with a sampling rate of 4 GS/s is shown and the corresponding DAQ signal is dis-

played in Figure 5.3(b). It can be seen that for a 1.5 GHz beam repetition rate one

is able to identify a single bunch, while for a 3 GHz beam this is not possible, which

is exactly what is shown in Figure 5.2.

The signal outlined in Figure 5.2(b) also indicates that the rise and decay time of

the detector is sufficiently fast, i.e. it is less than 500 ps in this case. A measurement

of CSR from a single bunch with an identical detector at the DIAMOND Light Source

clearly demonstrates that the response time is in fact around ∼ 250 ps (FWHM) with

a small ∼ 2 ns long tail [64].

In order to acquire a peak signal from every bunch, with a small amount of

cross-talk from neighbouring bunches, it is necessary to synchronise the digitiser

acquisition with an external clock signal of 1.5 GHz or 3 GHz.

5.1.3 Dynamic range of the SBD detectors

The SBD detector also has a specific dynamic range, which becomes apparent when

the detector is exposed to intense radiation. Figure 5.4 shows the SBD signal of CDR

for two different target orientation positions. Figure 5.4(a) shows a CDR signal from

the target at an angle further away from the mirror reflection direction than in the

case in Figure 5.4(b). The signal strength of the target rotated further away is

expected to be smaller than the target near the centre of the distribution, which is

seen in Figure 3.4.

The two signals were taken at a 1.5 GHz beam repetition rate and Figure 5.4(a)

shows the longitudinal bunch profile variation along the electron bunch train. With-

out any changes of the beam parameter settings, the signal shown in Figure 5.4(b)

was taken shortly after and therefore the bunch length variation is expected to man-

ifest itself in a similar way as in Figure 5.4(a). Due to a higher intensity, however,

caused by the rotation towards the centre of the distribution, the signal shows a

higher peak intensity and the SBD detector does not represent the expected radia-

tion intensity in the same places any longer. Spurious decreases in intensity can be

119

5.2. Beam line backgrounds in the CRM line

Time [ns]0 200 400 600 800 1000

Sign

al [

V]

0

0.2

0.4

0.6

(a) Before breakdown

Time [ns]0 200 400 600 800 1000

Sign

al [

V]

0

0.2

0.4

0.6

(b) Example breakdown

Figure 5.4: Dynamic range of the SBD detector illustrated by the signal of CDR fortwo different target orientations.

observed, which neither take place at a fixed position, nor reproduce in subsequent

electron bunch trains. For the signal shown in Figure 5.4(b), this decrease takes

place at around a time of 300 ns and 600 ns. Comparing the two signal shapes, one

could argue that the SBD detector experiences a breakdown or saturation as soon

as the input radiation power causes a response higher than around 500 mV and that

the diode seems to exhibit a highly non-linear behaviour.

Due to this breakdown or saturation of the SBD detectors, attenuators, as ex-

plained in Section 4.3.2, need to be used which, depending on the current bunch

length, have to be adjusted accordingly. Since the maximum signal response is well

above the noise level, the necessary attenuator can be selected in a way to avoid a

significant decrease of the signal to noise ratio.

5.2 Beam line backgrounds in the CRM line

Translation scans were routinely performed and the corresponding data plots were

obtained as follows. At every target position, the intensity is obtained by integrating

the SBD signal over a short region in time since the SBD signal changed along the

electron bunch train. This integration was performed for the chosen number of data

120


acquisitions per target translation, and the mean and the standard deviation of the

integrated intensities were calculated. The mean and the standard deviation were

consequently plotted on the graph against the target translation positions. As shown

in Figure 3.8, the DR intensity for such a translation scan is expected to decrease

exponentially with an increasing distance from the particle beam.

With the original configuration of a concentric adapter flange, translation scans

were performed and the results of a set of translation scans are shown in Fig-

ure 5.5(a). The translation scans, however, do not show a clear exponential be-

haviour. Upon changing the Optical Transition Radiation (OTR) screens behind

the setup, which was regularly done to set up the beam in the CRM line, a change

in CDR intensity could also be observed without changing the beam or the target.

For a beam centred in the beam pipe, Fig 5.5(a) displays the different CDR inten-

sities for the two different OTR screens inserted behind the system and the CDR

intensities without an OTR screen inserted at all.

The reason for the different intensities can be explained by Figure 5.6 and have

been published in [65]. When none of the OTR screens are inserted in the line, one

can observe a large contribution to the signal for large impact parameters in com-

parison to the other two cases when the screens are inserted. This contribution can

be attributed to the beam dump behind the setup. Before the beam is terminated

in the lead beam dump, the vacuum is sealed off by an aluminium vacuum flange

perpendicular to the beam line. When the beam is terminated, Coherent Transition

Radiation (CTR) is generated by the aluminium flange, and additionally potential

wake-fields and CSR backgrounds are reflected by this flange. With the CDR target

partially inserted, the radiation is reflected off the back of the target, by the vacuum

window facing the CR and into the detector. When the OTR screens are inserted in

the beam line, the OTR screens mask the radiation originating from the beam dump

and the signal decreases. For the semitransparent OTR screen, however, there is

still some contribution to the signal as the radiation is not completely attenuated.

For smaller impact parameters, when the OTR screens are inserted behind the

setup, CTR generated by the OTR screens is reflected by the OTR vacuum window,

the OTR screen, the back of the CDR target, the vacuum window towards the CR,

121


Impact Parameter [mm]10 15 20 25 30

Inte

grat

ed in

tens

ity [

V]

100

150

200

250

300

350

400

450

500Screens

NoneSemitransparent

Aluminised

Abs. position w.r.t. beam pipe centre [mm]10 15 20 25 30

(a) Centred beam before the installation of theoff-centre flange

Impact Parameter [mm]6 8 10 12 14 16 18

Inte

grat

ed in

tens

ity [

V]

100

150

200

250

300

350

400

450

500Screen

NoneSemitransparent

Aluminised

Abs. position w.r.t. beam pipe centre [mm]0 2 4 6 8 10

(b) Low beam before the installation of the off-centre flange

Impact Parameter [mm]10 15 20 25

Inte

grat

ed in

tens

ity [

V]

0

5

10

15

20

25Screen

NoneSemitransparent

Aluminised

Abs. position w.r.t. beam pipe centre [mm]

10 15 20 25

(c) Centred beam after the installation of theoff-centre flange

Impact Parameter [mm]10 15 20 25

Inte

grat

ed in

tens

ity [

V]

0

5

10

15

20

25Screen

NoneSemitransparent

Aluminised

Abs. position w.r.t. beam pipe centre [mm]5 10 15 20 25

(d) Low beam after the installation of the off-centre flange

Figure 5.5: CDR distribution scan before and after the installation of the off-centreflange for a beam centred in the beam pipe and a beam trajectory below the beampipe centre.

and eventually propagates to the SBD detector, where it is detected. Therefore, the

signal levels for smaller impact parameters for the case when the screens are inserted

are higher than the signal without an OTR screen behind. Since the CTR intensity

is proportional to the reflectivity of the OTR screens, the additional contribution to

the signal from the aluminised screen is higher than for the semitransparent screen.

The signals start converging for the smallest impact parameters because the

122


removable OTR screen

CDR

OTR vacuumwindow

vacuumwindow

reflected CTR lightbeam

beam pipe beam dumpvacuum window

CTR

Figure 5.6: Schematic drawing explaining the origin of the backgrounds.

target starts cutting off the light which is reflected by the vacuum window opposite

the detector. To verify this behaviour, the beam was lowered by 7 mm in the CRM

line using the CR.DVF0200 vertical corrector in the CR. This covered more of the

vacuum window with the target, while keeping the impact parameter similar to the

measurement in Figure 5.5(a) and not touching the beam with the edge, which would

introduce other possible backgrounds. The signals for such a beam setup are shown

in Figure 5.5(b). As discussed above, the signals start converging at a certain point

and most of the backgrounds from downstream of the CDR setup are cut off. For

impact parameters smaller than 9 mm the plots also show the expected monotonic

signal increase for decreasing impact parameters. This observation led to a decision

for an important upgrade to the system and the installation of an off-centre adapter

flange, which is discussed in Section 4.2.4 and has the bore for the diamond vacuum

window with smaller outer diameter shifted in the upward direction by 15 mm. This

vertical shift allows for the detector to “see” more of the CDR target for the same

impact parameters than it was the case for the concentric adapter flange, which was

expected to minimise the backgrounds.

After the installation of the off-centre flange, the same scans were performed

again with a centred and low beam, and are shown in Figure 5.5(c) and Figure 5.5(d),

respectively. For the centred and the low beam, the intensities now show a clear

exponential decrease for increasing impact parameters, as expected. This is shown

123

5.3. CDR distribution measurements

OTR Screen Param.Normal beam Low beam

Value Error χ2/NDF Value Error χ2/NDF

Nonea 55.9 1.3

145.1/4772.2 2.2

86.8/53b 0.137 0.003 0.178 0.003c 0.01 0.10 0.30 0.05

Semitransp.a 46.0 1.6

159.8/4736.0 1.1

116.0/48b 0.132 0.004 0.137 0.004c 1.95 0.11 1.30 0.07

Aluminiseda 41.3 1.4

73.9/4641.9 0.5

156.3/49b 0.112 0.004 0.119 0.002c 0.85 0.16 0.23 0.08

Table 5.1: Parameters of the exponential fit, as defined in Equation (5.1), of thetranslation scan in Figure 5.5(c) and Figure 5.5(d).

by fitting an exponential to the translation scan dependencies which has the form

y(x) = a exp (− b x) + c (5.1)

where a, b and c are the fitting parameters. The resulting parameters from the

individual fits including the absolute errors and the reduced Chi-square are shown

in Table 5.1. From the table, it can be seen that the exponential dependence is

similar for all 6 different measurements. It can therefore be concluded that the off-

centre flange significantly minimises the backgrounds from downstream of the CDR

setup. Therefore, its installation was a great success for the setup in the CRM line

and important conclusions for future investigations have been obtained.

The translation scans with the off-centre flange also show that measurements can

be performed with the target at quite a distance from the electron beam. This way,

the system can be designed to be much less invasive than with the target close to the

electron beam. With over 200 measurement stations at CLIC, this will minimise the

impact the CDR measurement stations have on the electron/positron beam quality.

5.3 CDR distribution measurements

Besides the translation scans, raster scans, which are 2-dimensional scans over the

target rotation and the target translation, can be performed. As explained in Sec-

124


tion 4.5.4, a rotation scan is followed by an incremental translational motion of the

CDR target in order to map out the region of interest. Similar to the analysis of

the translation scan, the SBD signal is integrated over a short region in time and

the integrated intensity is averaged as before. As shown in Figure 3.5, the CDR dis-

tribution depends on the polarisation which is measured with the detector. Based

on the theory and the results from the simulations shown in Figure 3.5, a two-peak

distribution is expected for the horizontal polarisation component and a single peak

distribution for the vertical component.

Figure 5.7 shows two raster scans of the CDR distribution for the two polarisation

components. Figure 5.7(a) and Figure 5.7(b) show the result of the raster scan of the

horizontal polarisation component, while Figure 5.7(c) and Figure 5.7(d) display the

result for the vertical polarisation component. As can be seen from the figures, the

result of each of the two different measurements is displayed as a 3D distribution

and a contour plot.

The raster scan of the horizontal polarisation component was taken before the

installation of the off-centre flange. At the time, the optical system on the optical

table only consisted of the periscope and a DXP-08 detector facing the viewport. The

table layout, however, does not have an influence on the CDR distribution. From

Figure 5.7(a) and Figure 5.7(b), it can be seen that, for small impact parameters

below 8 mm, a two-peak distribution can be observed, as expected. The intensity

at the mirror reflection direction decays to a minimum and is accompanied by two

peaks. The intensity of the two peaks decays when the target is rotated further

away from the mirror reflection direction, which is also as expected. Nevertheless, for

increasing impact parameters above 8 mm, the two-peak distribution transforms into

a single peak centred at the mirror reflection direction. As discussed in Section 5.2,

large beam based backgrounds were present in the CRM line before the installation

of the off-centre flange and therefore the distortion of the CDR distribution is most

probably caused by the presence of backgrounds in the CRM line. For rotation angles

further away from the mirror reflection direction than the two peaks at ±1.5, the

intensity decreases monotonically with increasing impact parameters, as expected.

The CDR distribution measurements of the horizontal polarisation component have

125


Impact parameter [mm]

67

89

1011

1213

Rotation [deg]

-4-2

02

4

Inte

nsity

[m

V]

20

40

60

80

(a) 3D plot of the CDR distribution of the hor-izontal polarisation component

Impact Parameter [mm]6 7 8 9 10 11 12 13

Rot

atio

n [d

eg]

-5

-4

-3

-2

-1

0

1

2

3

4

Inte

nsity

[m

V]

20

30

40

50

60

70

80

(b) Contour plot of the CDR distribution of thehorizontal polarisation component

Rotation [deg]

-4-2

02

4

Impact parameter [mm]

1015

20

Inte

nsity

[m

V]

20

40

60

(c) 3D plot of the CDR distribution of the ver-tical polarisation component

Impact parameter[mm]10 15 20

Rot

atio

n [d

eg]

-4

-2

0

2

4

Inte

nsity

[m

V]

10

20

30

40

50

(d) Contour plot of the CDR distribution of thevertical polarisation component

Figure 5.7: 3D plot and contour plot of the CDR distribution measured with a targetraster scan for the two different polarisation components.

been published in [66].

The purpose of the detection system after the installation of the interferometer

was focused on the interferometric measurements. Since the CDR distribution has a

higher photon yield and a central maximum for the vertical polarisation, the detec-

tion of the vertical component is a better choice for these measurements. Therefore,

the horizontal distribution could not be measured after the installation of the off-

centre flange.

126

5.4. Current dependence of the CDR signal

The vertical polarisation component of the CDR distribution was measured with

the DXP-12 after the installation of the off-centre flange. As seen in Figure 5.7(c) and

Figure 5.7(d), the measurement of the vertical component of the CDR distribution

shows good agreement with the DR theory. A single central peak at the mirror

reflection direction can be observed and the intensity of the CDR signal decreases

monotonically with increasing impact parameters.

5.4 Current dependence of the CDR signal

As shown in Section 2.4, the coherent radiation – for a constant longitudinal form

factor – is proportional to N(N − 1), which for sufficiently intense bunches can be

approximated as N2. In order to determine the charge dependence of the signal,

which is usually necessary to normalise the SBD signal, the bunch charge is altered

and the dependence of the SBD signal on the bunch charge is recorded. The Nx

signal dependence can vary significantly for a given experiment and factors for x as

low as 1.4 have previously been observed [67].

It was intended to perform such a charge dependence scan with the CDR setup at

CTF3. Due to the fully-loaded RF acceleration at CTF3, however, the bunch charge

can not be changed without affecting the overall beam energy and the longitudinal

bunch profile, thus changing the longitudinal form factor. The scraping of the beam

at a collimator to reduce the bunch charge was also considered but it could not

Beam currentEntries 1067Mean 3.198RMS 0.01555

Beam current [A]3.1 3.2 3.3 3.4

Cou

nts

0

50

100

150

200

250Beam current

Entries 1067Mean 3.198RMS 0.01555

Figure 5.8: Typical beam current stability.

127

5.5. Klystron phase dependence of the CDR signal

be ensured that the form factor would stay constant. Therefore, the Nx signal

dependence can not be determined for the setup at CTF3.

Recording the beam current of the electron pulse from the CR.SVBPM0195

during a long-lasting scan, however, the typical current stability of CTF3 can be

determined. Figure 5.8 shows a histogram of the beam current of 1067 consecutive

electron beam pulses taken during such a lengthy scan. From the histogram, the

mean beam current of 3.198 A and the r.m.s. of 0.016 A can be determined. Setting

bounds on the beam current fluctuation of ±2.0%, the number of electron bunch

trains within this beam current fluctuation is 99.6% of all electron pulses. Taking

the high beam current stability into consideration, one can therefore safely assume

a constant bunch charge for a particular interferometric scan and not to normalise

the signal by the charge dependence.

5.5 Klystron phase dependence of the CDR signal

The performance of the accelerator depends on the control of the electron bunch

length. In the linac, the electron bunches must remain short (about 0.5 mm) to keep

the energy spread as low as possible during acceleration, but need to be stretched

(2 mm – 4 mm) before the DL and CR to minimise emittance dilution due to the

emission of CSR. In order to stretch or compress electron bunches, magnetic chicanes

are normally used.

In the Frascati chicane in CTF3, as shown in Figure 4.1, as well as in any other

chicane in an accelerator, electrons of different momenta travel different distances

due to the deflection in the dipole magnets. Since electron bunches in any accelerator

have a certain energy spread, this has an impact on the bunch length when an

electron bunch traverses the chicane due to the ballistic time of flight difference.

By changing the phase of the accelerating RF voltage, the energy spread can be

manipulated to some extent. Figure 5.9 shows how the change of RF phase changes

the bunch length after a chicane. Depending on whether the electron bunch is

accelerated on crest, the rising edge or falling edge, the bunch length is changed

differently. If the head of the bunch experiences a smaller accelerating gradient than

128

5.5. Klystron phase dependence of the CDR signal

Time t

V(t)

(a) Impact of the phase on the energy spread

p+∆p

p-∆p

(b) Schematic drawing of a magnetic chicaneand the different paths for particles of differentmomenta p±∆p

Figure 5.9: RF accelerating voltage impact on the bunch length. By changing theKlystron MKS15 phase, the bunch length at the end of the Frascati chicane canbecome shorter (green), longer (blue) or just be preserved (red). This is due to thedifferent time-of-flight of particles with different momenta in the chicane.

the tail of the bunch, the bunch is compressed. If the head, on the other hand,

encounters a higher accelerating gradient than the tail of the bunch, the bunch is

stretched. If the electron bunch is accelerated on the crest of the RF voltage the

bunch length is preserved assuming that the bunch length is much shorter than the

RF wavelength.

A phase scan was performed with the MKS15 klystron in the CTF3 linac and

the DXP-12 signal was recorded. Since a bunch length variation was present along

the electron bunch train, the signal was integrated over a short region of time and

the integrated intensities were averaged as before. The mean integrated intensity at

each klystron phase is then plotted against the klystron phase for which the scan

was performed. Before the scan, the MKS15 klystron phase was set at 69 and an

acceptable range for the scan, from 50 to 71 was established, beyond which the

electron beam current decreased, i.e. the beam was lost.

With this maximum phase range determined, the klystron scan was performed

and the result is shown in Figure 5.10. One can clearly observe a klystron phase

dependence of the DXP-12 signal, originating from a change in longitudinal bunch

form factor caused by the change in bunch length. Below a klystron phase of 60,

129

5.6. Correlation measurements with other bunch length monitoring systems

MKS15 Phase [deg]50 55 60 65 70

Inte

grat

ed in

tens

ity [

V]

10

20

30

Figure 5.10: Evolution of the SBD signal measured with the DXP-12 as a functionof the klystron phase.

the DXP-12 signal is constant and has decreased significantly with respect to the

normal operating phase at 69. In this region the bunch length has become so

large that the narrow-band SBD detector is no longer sensitive to any further bunch

length variation since only the tail of the form factor F (ω) is measured now. Above

a klystron phase of 60, a clear increase in signal up to the normal operating phase

at 69 is shown, corresponding to a shortening in bunch length towards a higher

klystron phase.

Since the absolute klystron phase can not be measured directly at CTF3, it is not

possible to evaluate exactly where on the RF phase the acceleration takes place. The

CDR setup, however, can be used to quickly establish if, by changing the klystron

phase, one is increasing or decreasing the bunch length. From an operations point of

view at CTF3, this enables the quick identification of a relative bunch length change

without having to perform a lengthy streak camera or RF deflector measurement.

Hence, the CDR signal can be used as a fast phase feedback system.

5.6 Correlation measurements with other bunch length

monitoring systems

As shown in Figure 5.1, the CDR setup allows to measure the intra-train bunch

length variation. For a fairly constant bunch charge along the train, as in CTF3,

130


any variation of the signal throughout the train corresponds to a longitudinal beam

profile variation. This bunch length variation is observed and is compared to a

streak camera measurement in the CR and a waveguide pickup in the TL1. The

results of the measurements, which were recorded within a short time of each other,

are shown in Figure 5.11.

For the CDR measurement outlined, an additional linear stage is installed just in

front of the primary SBD detector which allows for an additional SBD detector to be

utilised by introducing an optional 90 bend with a mirror. Hence, two SBD detec-

tors were used with a spectral response of 60 – 90 GHz (DXP-12) and 90 – 140 GHz

(DXP-08).

The two CDR signals recorded by the DXP-12 and the DXP-08 along the 1.3 µs

long train are shown in Figure 5.11(a) and Figure 5.11(b), respectively. The overall

shape of the signal for both the DXP-12 and the DXP-08 indicates a significant

longitudinal beam profile variation along the electron train. A higher SBD signal

indicates a larger form factor in this region of the electron bunch train. Therefore,

the two peaks in the signal suggest either shorter bunches or a change in the lon-

gitudinal profile, e.g. a high electron density in the core or a change of the overall

bunch shape. Due to the spectral response of the DXP-12 and DXP-08 the detail

of how this beam profile variation manifests itself in the signal is slightly different.

The DXP-12 is able to monitor longer bunches since it is able to detect coherent

radiation in the lower frequency band, whereas the DXP-08 is not capable of mea-

suring those low frequencies. At the time of the measurement, an attenuator with

30% transmission was installed in front of the DXP-12, leading to an even greater

difference in real intensity between the two detectors than the difference between

the signals shown on Figure 5.11(a) and Figure 5.11(b).

Additionally, in order to determine the consistency and proper functioning of

the CDR setup, measurements on other systems throughout the machine close to

the CDR setup were carried out at the same time. With the bending magnet at

the beginning of the CRM line in the CR turned on, a streak camera measurement

can be performed in the second 90 arc of the CR. Moreover, in the TL1 towards

the CR a waveguide pickup is installed and detects radiation in the spectral range

131


Time [ns]500 1000 1500

Inte

nsity

[V

]

0

0.05

0.1

0.15

0.2

0.25

(a) DXP-12 (60 to 90 GHz)

Time [ns]500 1000 1500

Inte

nsity

[V

]

0

0.01

0.02

0.03

0.04

(b) DXP-08 (90 to 140 GHz)

Time [ns]500 1000 1500

Inte

nsity

[V

]

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

(c) Waveguide pickup (26.5 to 40 GHz)

Time [ns]500 1000 1500

Bun

ch le

ngth

(FW

HM

) [m

m]

3

4

5

6

7

(d) Streak [68]

Figure 5.11: Correlation measurements of the SBD detectors of two different band-width with a streak camera in the CR [68] and a waveguide pickup in the TL1.

of 26.5 – 40 GHz. The longitudinal electron profile between the waveguide pickup

and the CR is expected to stay nearly unchanged providing a good comparison

between the different measurements. Therefore, streak camera measurements at

various times along the train and the waveguide pickup offer a possibility to check

for consistency between the CDR setup and other measurement techniques at CTF3.

A waveguide signal and the streak camera measurements are shown in Figure 5.11(c)

and Figure 5.11(d) which were taken at the same time as the measurements displayed

in Figure 5.11(a) and Figure 5.11(b).

132

5.7. Interferometric CDR measurements and spectra

The waveguide pickup in Figure 5.11(c) is in very good agreement with the SBD

measurements in Figure 5.11(a) and Figure 5.11(b). As the waveguide pickup offers

a spectral response in an even lower frequency band than the DXP-08 and DXP-12,

more detail between the two predominant peaks can be seen.

For the streak camera measurements, as shown in Figure 5.11(d), the bunch

length is obtained by fitting a suitable function to the streak camera CCD image.

In this case, an asymmetric Gaussian function was fitted to the trace and the FWHM

is taken to be the bunch length. In the region where the streak camera measures

short electron bunches, the waveguide pickup and Schottky diodes show a peak in

intensity as one would expect. In the region of large bunch length, however, both

the RF pickup and Schottky diodes show that the longitudinal profile is not uniform,

giving a sharp spike where the bunch length is longest. This suggests that there is

a dense, low intensity fraction of the beam within the entire bunch, which gives rise

to the emission of CDR in this spectral range.

The correlation measurements with other bunch length monitoring systems have

also been published in [69].

5.7 Interferometric CDR measurements and spectra

As described in Section 4.3, a Michelson interferometer is used to analyse the radia-

tion originating from the target and to determine the spectrum of the radiation dWdω .

In order to record an interferogram, which is needed to reconstruct the spectrum of

the radiation, the DR signal along the electron train for every single electron bunch

train is recorded for a specific optical path difference. Once the desired number of

readings for each optical path difference has been acquired, the delay line mirror

is moved and data for the next path difference is taken. As before, only a small

time slice along the train is used to obtain an interferogram since the bunch length

varies quite significantly along the train. The signal was integrated over a small

time window of 20 ns in the region of interest and the two integrated intensities for

each optical path difference were averaged.

An interferogram measured with the DXP-12 with a spectral response of 60 –

133

5.7. Interferometric CDR measurements and spectra

90 GHz is shown in Figure 5.12(a). The interferogram was taken with a 50 µm thick

Kapton beam splitter and the optical path difference step size was chosen to be

0.2 mm over a range from –9 mm to 74.4 mm. The resulting spectrum obtained from

the Fourier transform of the interferogram can be seen in Figure 5.12(b) and agrees

fairly well with the spectral response of the detector. There is, however, a peak in

intensity which is just at the edge of the expected detector response.

It has to be mentioned that the travel range of the linear stage and the incre-

ment of the optical path difference set constraints on the resolution and maximum

frequency of the spectrum one can achieve. The theoretical resolution for the spec-

trum is ∆f = 1/T . With the given optical path difference of the interferogram

d = 83.4 mm, i.e. T = 278 ps, the best resolution would be ∆f = 3.6 GHz. For the

DXP-12 used for this measurement one would only be able to obtain a maximum of

8 points within the given frequency band.

In order to achieve a better spectral resolution, the travel range would have

to be extended. The maximum travel limit of the stage currently installed would

allow for a best possible resolution of 1.5 GHz, yielding 20 points for the specified

frequency band. For a 0.8 Hz beam repetition rate, however, a scan over the entire

travel distance with a similar step size – to avoid statistical fluctuations – would be

far too time consuming and one could potentially be subjected to a beam parameter

Optical path difference [mm]

0 10 20 30 40 50 60 70

Inte

grat

ed in

tens

ity [

mV

]

6

7

8

9

10

11

(a) CDR interferogram

Frequency [GHz]40 50 60 70 80 90

Inte

nsity

[a.

u.]

0

0.2

0.4

0.6

0.8

1

(b) Resulting spectrum

Figure 5.12: Example DR interferogram and corresponding spectrum.

134

5.8. Summary

drift of the machine. The interferogram displayed in Figure 5.12(a), for example,

– with 418 path difference points with 2 iterations each, separated by 1 iteration

to allow for hardware movement – lasted half an hour. And although the recorded

interferogram has a clear central peak, it does not show a symmetric behaviour,

which can be seen in Figure 4.13 and which was expected. Moreover, there is also a

shift of the baseline amplitude decreasing from a path difference of –9 mm to 10 mm

and a slight increase of the baseline amplitude from 10 mm to 74 mm. This baseline

drift is most likely due to a klystron phase drift due to a temperature modulation

and has a direct impact on the bunch length and subsequently on the DXP-12 signal

level.

Since the spectral coverage obtained during the measurement is limited to one de-

tector, Kramers-Kronig reconstruction technique could not be applied at this stage.

Moreover, due to an experiment for the detection of CSR from the DIAMOND Light

Source, which was also conducted by the group, a collaboration with the Millimetre

Wave Technology group suggested that the splitter efficiency of Kapton and Mylar

was not high enough to conduct reliable interferometric measurements [70]. In or-

der to improve the interferometric measurements and to successfully reconstruct the

longitudinal beam profile, suggestions for future work are outlined in Section. 6.2.

5.8 Summary

In this chapter, the capability of the SBD detectors to resolve single electron bunches

has been shown, which allows the longitudinal beam profile variation along the elec-

tron bunch train to be measured. Large CDR signals from the conducting screen,

however, necessitate the use of attenuators in order to avoid a breakdown or satu-

ration of the SBDs.

When translation scans were performed after installing the setup, beam-based

backgrounds from downstream of the CDR setup were observed. An investigation

as to where the background originated from was conducted and the most likely

sources of background were identified. Therefore, an important upgrade to the

system in the form of an off-centre flange was carried out. The off-centre flange has

135

5.8. Summary

sufficiently reduced the observed backgrounds and an exponential dependence of the

SBD signal on the impact parameter was identified, which has been a great success.

The suppression of backgrounds, especially in the far-infrared and millimetre region,

is also an important aspect which needs to be considered for future hardware designs

of longitudinal diagnostics based on the detection of CDR.

Moreover, CDR distribution scans were performed, which show good agreement

with the theory outlined in Section 3.1.2, and the current stability of CTF3 was

identified to be sufficient to omit the N2 normalisation for this specific experiment.

Additionally, the dependence of the SBD signal on the MKS15 phase was observed,

which illustrates the use of CDR as a relative bunch length monitor and a fast feed-

back system in any accelerator, when the spectral range of the SBD detectors is cho-

sen carefully. This possibility is also demonstrated by the correlation measurements,

for which the CDR setup shows good agreement with other bunch length monitoring

stations. For the situation where the signals differ from the streak camera measure-

ment, this can be explained and attributed to a change of the longitudinal beam

profile. It can also be seen that this beam profile change is hard to detect with

a streak camera and that it is desired to use a coherent radiation technique with

Kramers-Kronig reconstruction to identify such changes.

For this purpose, interferometric measurements of CDR were conducted and first

interferograms have been obtained from the system. The interferometric measure-

ments with SBD diodes, however, have proven to be challenging. The accuracy of

the obtained spectra strongly depends on the travel range of the translation stage,

since this determines the resolution of the spectra and the number of points which

can be obtained in the spectra. Furthermore, the splitter efficiencies were chosen for

bunch lengths of 0.5 mm. The setup of CTF3 at the time, however, yielded longer

bunches at around 4 mm, which caused a decrease of the splitter efficiencies in this

spectral region. Moreover, the time it takes to perform interferometric scans with a

long travel range is significant. Therefore, one is running the risk of being subjected

to beam parameter changes.

Unfortunately, due to limited access to the machine, which resulted in fairly

long turn-around periods, and due to a fire accident in the klystron gallery above

136

5.8. Summary

the CTF3 linac, which severely delayed the restart in 2010, the identified problems

could not be incorporated in the timeframe of this thesis. The problems with the

interferometric measurements, however, that have been identified led to possible

solutions to these challenges and are discussed in Section 6.2.

137

Chapter 6Conclusion

6.1 Summary and main conclusions

The development of longitudinal diagnostics for electron beams based on CDR has

been discussed in this thesis and the main conclusions are drawn in this section.

With the theoretical model of diffraction radiation, which is based on the virtual

photon model, and with a time-domain simulation method, based on SLAC’s ACE3P

suite, two independent computations of the CDR spectrum emitted by an electron

bunch in the proximity of a conducting screen have been performed. The two models

yield spectra with very similar properties, which demonstrates that the two different

models are functioning well. Additionally, with the ACE3P suite, one is able to take

the surrounding hardware into account, which, for example, can be used for studies

for a prototype for CLIC.

Experimentally, a system for the detection of CDR has been designed and all

components have been carefully selected. The installation process was coordinated

with the engineers at CERN and a beam line space at CTF3 was created by re-

arranging the existing components in the CRM line. Upon successful installation

of the vacuum system, the hardware performance of the entire CDR system was

ensured and first CDR signals were observed.

After the working order of the system was established, the properties of CDR

emitted from the conducting screen were studied. As part of the study, beam-based

138

6.2. Suggestions for future work

backgrounds originating from downstream of the setup were discovered and the

sources of the backgrounds were identified. This discovery led to the installation of

an off-centre flange, which has noticeably reduced the backgrounds, such that a clear

exponential dependence of the signal on the impact parameter can be observed.

Moreover, the detector properties were studied and the possibility of identifying

an intra-train longitudinal beam profile variation was demonstrated. Correlation

measurements with other systems in the machine have shown that the CDR setup

performs well and that it can be utilised as a fast feedback system. As such a

feedback system, the CDR setup has already been used routinely in the CTF3 control

room for optimising the beam properties and the acceleration process in the linac.

With the aid of the SBD signal, the klystron phases in the linac can be adjusted in

order to try to minimise this longitudinal profile variation throughout the train.

Finally, interferometric measurements on CDR were performed and initial spec-

tra have been obtained. These measurements have proven to be challenging and

reasons as to why have been identified. As part of the design, the beam splitters

were initially chosen for a bunch length of 0.5 mm, but since the bunch length at

the time was significantly larger at around 4 mm the splitter efficiency was very low.

Additionally, the time required to obtain an interferogram with a sufficiently large

travel range for narrow band detectors is very long. Thus, the measurements can

become susceptible to a machine parameter drift, which has a negative impact on

the resulting spectra.

In order to further develop the CDR system, and thus improve the measurements

and results outlined above, suggestions for future work are proposed in Section 6.2.

6.2 Suggestions for future work

As previously mentioned, there are possibilities to increase the performance of the

system by incorporating some changes. Some of these possible additions to the CDR

system are explained in this section.

Generally speaking, the emission of CDR from the conducting screen and the

translation of the radiation via the periscope to the optical table is performing well.

139


There are, however, possibilities for changes within the interferometer. The two most

critical items, which can significantly effect the functioning of the interferometer, are

the detector and the beam splitter.

Recently, a lot of research and development has been carried out on developing

a broad band SBD detector and is still ongoing. The use of a broad band SBD

detector for the CDR setup in the CRM line would not only allow to measure a

broad spectrum with one single interferometric scan, but also allow the measurement

of the longitudinal beam profile variation along the electron bunch train at CTF3,

which will also be an important requirement for a bunch length monitoring station

at CLIC.

Moreover, the beam splitters were selected for a bunch length of around 0.5 mm

and showed a poor efficiency for measurements of bunches with a bunch length

of 4 mm. As indicated above, the Millimetre Wave Technology group suggested

that the splitter efficiency of Kapton and Mylar was not high enough to conduct

reliable interferometric measurements. Instead, commercially available silicon wafers

of 100 and 150 µm thickness can be used instead, which exhibit a much higher

efficiency in the region of interest. Such beam splitters have been used in a similar

experiment carried out by the group at the DIAMOND Light Source and have

performed well [70].

Besides these two main items, most of the other hardware used for the interfer-

ometer has certain spectral transmission characteristics. Some of these character-

istics have not been quantified precisely enough to carry out accurate and reliable

reconstructions of the longitudinal beam profile using Kramers-Kronig technique.

Currently, an infrastructure project for the development of a microwave laboratory

at the Physics Department at Royal Holloway is ongoing. Such a microwave labo-

ratory will allow for all the equipment to be extensively tested and their spectral

characteristics to be precisely quantified, which should lead to a better overall un-

derstanding of the interferometer in the millimetre wavelength region.

For the analysis of the spectra obtained from the experiment, it will also be

necessary to develop an algorithm that is able to reliably reconstruct the longitudinal

beam profile using Kramers-Kronig method, something yet to be understood in detail

140


by the accelerator community. A final goal would be the implementation of such

an algorithm in the control system of an accelerator where it can be used as a

non-expert bunch length monitor on a regular basis.

There are also possibilities for future work, which are directly concerned with

the development of a prototype of a longitudinal beam profile measurement station

for CLIC. For the design of such a prototype, the simulation model based on the

ACE3P simulation suite, which was used to carry out DR simulations in Section 3.2,

can be modified to construct a vacuum chamber that is cost-effective, minimally

invasive and reduces the backgrounds.

141

Appendix AGinzburg-Frank formula

The derivation of the virtual photon model formula of TR in the far-field case

from the Ginzburg-Frank formula is shown in this appendix. Recalling from Equa-

tion (2.7), the Ginzburg-Frank formula is given by

d2W

dω dΩ=

e2

π2c

β2 sin2θ

(1− β2 cos2θ)2. (A.1)

Using the small angle approximation with sin θ = θ and cos θ = 1 − θ2

2 , and for

high particle velocities β = 1− 12γ−2, Equation (A.1) can be written as

d2W

dω dΩ=

e2

π2c

θ2(1−

(1− 1

2γ−2)2 (1− θ2

2

)2)2 . (A.2)

Omitting terms smaller than γ−2 the expression can be simplified to yield

d2W

dω dΩ=

e2

π2c

θ2

(γ−2 + θ2)2 (A.3)

and with θ =√θ2x + θ2

y and α =e2

cis simply

d2W TR

dωdΩ=

α

π2

θ2x + θ2

y

(θ2x + θ2

y + γ−2)2(A.4)

which is them same as the equation for TR in the far-field obtained from the virtual

photon model, i.e. Equation (2.14).

142

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