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Contents
I

Introduction

7

1 The International Linear Collider
1.1 Particle Physics at the Energy Frontier . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The International Linear Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Luminosity and the Final Focus System . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Chromaticity Correction Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Global Chromaticity Correction Scheme . . . . . . . . . . . . . . . . . . . . .
1.4.2 Local Chromaticity Correction Scheme . . . . . . . . . . . . . . . . . . . . . .
1.4.3 Comparing FFS Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 ATF / ATF2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Beam Line Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.2 Goals of ATF2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Beam Size Monitors at ATF2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.1 Shintake Monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.2 Other Types of Beam Size Monitors . . . . . . . . . . . . . . . . . . . . . . .
1.7 Beam Focusing History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8 About this Doctoral Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8.1 The Hi-lights of My Personal Contributions . . . . . . . . . . . . . . . . . . .
1.8.2 Structure of Doctoral Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7
7
7
9
11
11
12
12
13
13
14
17
17
18
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22
22
22

II

24

Concept of Beam Size Measurement by the Shintake Monitor

2 Description of Shintake Monitor
2.1 Measurement Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Beam size Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Measurable Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Laser wire mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Upgrades from Use at the FFTB . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Physics of Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24
24
25
27
30
31
32

3 Description of Individual Components
3.1 Overall Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Laser Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Expander and Reducer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Laser Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Laser Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Attenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Vertical Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Optical Delay Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Laser Crossing Angle Adjustment . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Laser Timing System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Q-switch Timing and Laser Pulse Output . . . . . . . . . . . . . . . . . . . .
3.4.2 Monitoring of Relative Timing . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Detector Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36
36
36
37
38
39
45
46
49
50
54
54
56
58
58

2

3.5.2 Separation of Signal and Background . . . . . . . . . . . . . . . . . . . . . . .
3.5.3 Collimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.4 Methods for Analysis and Signal Digitization . . . . . . . . . . . . . . . . . .
Estimation of Statistical Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Compton Photon Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Detector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Signal Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60
63
65
68
68
70
71

4 Procedures of Beam Size Measurement
4.1 Beam Tuning at ATF2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Linear Optics Tuning Knobs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Nonlinear Tuning Knobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Setup Procedure for the Shintake Monitor . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Transverse Laser Position Alignment . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Longitudinal Position Alignment . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Focal Lens Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Collimator Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.5 Relative Timing Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74
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76
77
77
79
80
82
83

III

85

3.6

Performance Evaluation of Shintake Monitor

5 Evaluation of Laser Properties
5.1 Adjustment of Laser Spot Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Representation of Laser Propagation by Transfer Matrices . . . . . . . . . . .
5.1.2 Laser Focusing at the IP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Laser Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Laser Pointing Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Laser Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Polarization Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Laser Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85
85
85
86
88
90
92
92
96

6 Modulation Reduction Factors
6.1 Methods to Evaluate Modulation Reduction . . . . . . . . . . . . . . . . . . . . . . .
6.2 Measurement of Total Modulation Reduction . . . . . . . . . . . . . . . . . . . . . .
6.3 Phase Related Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Introduction of Phase jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Causes of Phase Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.3 Phase Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Fringe Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Laser Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Power Imbalance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1 Static Factors for Power Imbalance . . . . . . . . . . . . . . . . . . . . . . . .
6.6.2 Power Imbalance Due to Incoherent Power Jitter . . . . . . . . . . . . . . . .
6.7 Laser Path Misalignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.1 Description of Laser Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.2 Longitudinal Misalignment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.3 Transverse Misalignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.4 Evaluation of Misalignment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Spherical Wavefront Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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101
101
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105
106
109
110
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111
112
113
113
114
115
115

3

6.9

Change of the Beam Size within the Laser Fringes . . . . . . . . . . . . . . . . . . . 117

7 Study of Signal Jitters and Drifts
118
7.1 Signal Jitter Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.1.1 Phase Jitter (Vertical Relative Position Jitter) . . . . . . . . . . . . . . . . . 118
7.1.2 Statistical Fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.1.3 Background Energy Fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.1.4 Laser Timing Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.1.5 Total Laser Power Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.1.6 Horizontal Relative Position Jitter . . . . . . . . . . . . . . . . . . . . . . . . 120
7.1.7 Electron Beam Intensity Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2 Modeling of Signal Jitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.3 Calibration of Detector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.4 Method for Deriving Phase Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.5 Simulation Test of Phase Jitter Extraction Method . . . . . . . . . . . . . . . . . . . 125
7.5.1 Gaussian-like Phase Jitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.5.2 Complex Phase Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.5.3 Interpretations of Modulation Reduction due to Phase Fluctuation . . . . . . 131
7.6 Eﬀect of Vertical Jitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.6.1 Eﬀect on Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.6.2 Eﬀect on Phase Jitter Extraction and Compensation . . . . . . . . . . . . . . 134
7.7 Conclusion on the Precision of Correction for Phase Fluctuation . . . . . . . . . . . 136
7.8 Extraction of Phase Jitter from Beam Time Data . . . . . . . . . . . . . . . . . . . . 136
7.8.1 Evaluation of Phase Jitter in Fringe Scans . . . . . . . . . . . . . . . . . . . . 136
7.8.2 Modulation Correction using the Extracted Phase Jitter . . . . . . . . . . . . 138
7.8.3 Comments about Electron Beam Jitter . . . . . . . . . . . . . . . . . . . . . . 141
7.9 Status of Signal Jitter in Fringe Scans . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8 Summary146
8.1 Beam Time Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.1.1 Evaluation of Measurement Stability . . . . . . . . . . . . . . . . . . . . . . . 146
8.1.2 Evaluation of the Smallest Beam Sizes . . . . . . . . . . . . . . . . . . . . . . 149
8.2 Future Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.2.1 Remaining Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.2.2 Possibility of Using the Shintake Monitor at the ILC . . . . . . . . . . . . . . 151
8.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
9 Acknowledgment

154

10 Appendix

155

A Laser Cavity

155

B Gauss Beam Focusing
156
B.1 Properties of an Ideal Gaussian Beam . . . . . . . . . . . . . . . . . . . . . . . . . . 156
C Damage Threshold for Optical Components

158

D Alternative Scenarios of Simulation Test for Phase Jitter Extraction

159

E Extraction of Clinear

161
4

F Details of Beam Time Results

163

G Wake Field Eﬀects

164

H Cross-check of Analysis Methods

166

I

168

DAQ

5

Abstract
The International Linear Collider (ILC) is essential for the precise measurement of the properties of
Higgs boson and new physics beyond the Standard Model for particle physics. The current ILC design
and physics program requires a high luminosity of about 2 ⇥ 1034 cm 2 s 1 while minimizing power
consumption. This calls for the focusing of its electron (e ) and positron (e+ ) beams to nanometersizes at the interaction point (IP). The Accelerator Test Facility 2 (ATF2) was constructed at KEK
as a realistic scaled down test prototype of the final focus system (FFS) of the ILC. The Goal 1 of
ATF2 is to focus the vertical e beam size ( y ) to 37 nm, scaled by energy from the ILC design yof 5.9 nm; the purpose is to demonstrate the design of a FFS for the ILC featuring a novel beamfocusing method called the Local Chromaticity Correction scheme, whose merits are a shorter FFS
beam line and less beam halo compared to preceding designs. The subject of this thesis, the Shintake
Monitor, is a beam size monitor installed at the virtual IP of ATF2 for the purpose of measuring
its O(10) nm y . Featuring a technique of using laser interference fringes as a probe to scan thee beam, the Shintake Monitor is the only existing device that has demonstrated measurement ofy below 100 nm. The collision of the e beam with a target of laser interference fringes ejects
photons by inverse Compton scattering. A modulation pattern is produced in the photon energy byscanning the fringe phase with respect to the electron beam using a piezo-electric stage. The y iscalculated from this signal modulation measured by a downstream gamma-ray detector. The laser
optics are designed to accommodate a wide range of y from about 25 nm to a few µm with better
than 10% precision. The eﬀective beam tuning using the Shintake Monitor contributed essentiallyto the ATF2 beam focusing progress; by June 2014, the focusing of y to below 45 nm has been
demonstrated on repeated occasions with a measurement stability of about 5%.
This thesis describes the design concepts and performance of the Shintake Monitor, focusing on
an extensive study of systematic errors which enabled the precise extraction of y from the measured
signal modulation. In particular, an original method was developed for the analysis of one of themost dominant errors, the fluctuation of the relative phase between the laser and the e beam. The
reliability of the method was demonstrated using simulation assuming realistic ATF2 conditions.
Other modulation reduction factors are related to laser properties e.g. polarization, profile, power,
and the position alignment precision with respect to the electron beam at the IP. Based on various
measurements conducted of laser properties and of the gamma-ray detector response, systematic
errors were evaluated for beam time data collected in spring of 2014. Applying the error study
results to a set of world record continuous y measurements in June, 2014 gives the full evaluationof 39.7 ± 0.6(stat.)+2.6
4.0 (syst.) nm; the beam size resolution is about 10%. This indicates that the
ATF2 Goal 1 has been achieved within error ranges. The results of the error studies demonstrate
the means to suppress systematic errors so as to allow the precise measurement of the smaller y at
the future ILC.

6

Part I

Introduction
1

The International Linear Collider

1.1

Particle Physics at the Energy Frontier

The current perception of particle physics is based on the “Standard Model”, which has explained andin turn been verified by the results of a variety experiments up to the TeV scale. The Standard Model(SM) attributes the fundamental constituents of matter to quarks and leptons, and the interactions
between particles to the exchange of gauge bosons. It provides a crucial base for the constructionof new models in search of new physics beyond the SM.
The most recently discovered particle in the SM is the Higgs boson, which is responsible forthe mass of all elementary particles. In 2012, a new particle consistent with the Higgs boson was
discovered at the Large Hadron Collider (LHC), thereby completing the SM particle spectrum.
However there are various unresolved issues in high energy physics which prevent the SM frombeing a complete theory. For instance, it does not incorporate the gravitational force, account for thecause of electroweak symmetry breaking, or provide a solution to the hierarchy problem. The Higgs
boson mass is unstable under quantum corrections, which is a problem that can be cancelled by
the introduction of new physics e.g. supersymmetry (SUSY) particles. The lightest SUSY particle
is also a strong candidate for dark matter possibly satisfying properties derived from cosmologicalobservations. Intense eﬀorts are being put into the discovery of new physics beyond the SM at LHC,
for which there is compelling motivation from theory.
As a synergy with the LHC, the International Linear Collider (ILC), an electron-positron collider,
has been proposed as a precision machine essential for the discovery and research of new physics
and more accurate measurement of Higgs boson properties. In contrast to proton collisions at the
LHC, the ILC collides electrons (e ) and positrons (e+ ), which are point-like particles and antiparticles whose colliding energies are precisely controllable. This realizes clean interactions withmuch less background than LHC, thus enabling better knowledge of the initial states and particle
mass resolution. Electrons and positrons collisions also enable precise prediction of theories, as
opposed to proton collisions, for which the precision is limited by higher order QCD eﬀects. Circularelectron-position colliders e.g. the 209 GeV LEP are limited from advancing to higher collisionenergies by the emission of synchrotron radiation as the beam trajectory is bent. Energy loss per
E4
one turn scales as E / ⇢1 m
4 , proportional to the fourth power of energy (E) and to the inverseof the fourth power of particle mass (m) for a fixed curvature radius (⇢). The linear ILC does not
suﬀer from energy loss due to synchrotron radiation, and thus can reach TeV scale energies which ismuch more promising for measuring new physics beyond the Standard Model.
The following sections will describe the ILC, focusing on the final focusing system in relation to
the main theme of this thesis.

1.2

The International Linear Collider

This section describes the basic components of the ILC accelerator.
The ILC accelerator design is a result of worldwide eﬀort, and takes into account the possibilityof changes in order to accommodate upgrades. The Reference Design Report (RDR)[1], issued inAugust 2007, was the first detailed technical report of R&D progress and preliminary cost estimatesfor each accelerator component. This was followed by the Technical Design Report (TDR)[2], issuedin June 2012, which provided comprehensive technical and engineering details, and serves as the7

final document to be submitted to funding agencies for project approval. The construction of the
ILC is anticipated to commence in the Kitakami mountain site in Japan within a few years.
Figure 1.1 shows the current layout of the baseline ILC accelerator with center of mass energy(ECM ) = 500 GeV and a total machine length of about 31 km. The major sub-systems consist of:• a polarized e source with a 5.0 GeV linac;• damping rings (DR) of 5 GeV and 6.4 km circumference for each of the e
the center region of the complex;

and e+ beams in• 13.6 km beam transport lines from the DRs to the ends of the two main linacs;• in the linacs (11 km each), each beam is accelerated up to 250 GeV;• an undulator-based positron source in the middle of the e linac;• a 4.5 km long beam delivery system (BDS) with 14 mrad crossing angle, including the final
focusing system (FFS) ; and• the interaction region with its detectors installed around the interaction point (IP).
The ECM at ILC can be varied from < 250 GeV to 1 TeV by adjusting linac length and the RF
power supplies of klystrons. Figure 1.2 shows the structure of beam trains and bunches. There are1312 bunches with 554 ns spacing are accelerated in a single RF power pulse induced in the 1.3
GHz superconducting radio-frequency accelerating cavities of the main linac, designed to deliver an
average accelerating gradient of 31.5 MV/m.

Figure 1.1: The current layout of the ILC accelerator for center of mass energy 500 GeV, according
to the TDR baseline design[2].

8Figure 1.2: The beam train and bunch structure. For the ILC baseline design, there are 1312 bunches
in a single train, with bunch spacing of about 554 ns. Since the repetition rate is 5 Hz, the spacing
between trains is 200 ms. [3]1.3

Luminosity and the Final Focus System

The most important parameters for a high energy collider are the center of mass energy (ECM )and the luminosity (L). To deliver the required rate of particle interactions to the detectors for theplanned physics program, the ILC baseline design (ECM =500 GeV) demands a high instantaneous
luminosity of 2 ⇥ 1034 cm 2 s 1 . Luminosity can be expressed as:L=

Nb Ne2 frepHD4⇡ x⇤ y⇤(1.1)

Here, Nb is the number of bunches per train, Ne is the number of particles in a bunch, frep is⇤the repetition rate, HD is the luminosity enhancement factor, and x(y)is the horizontal (vertical)
beam size at the IP. In order to achieve high L within the given limits on power consumption, it
is important not only to realize small beam size focusing at the IP, but also to suppress luminosity
loss due to beam-beam eﬀects e.g. beamstrahlung. Because energy loss due to beamstrahlung scales
inversely with x⇤ + y⇤ , x⇤ is chosen to be much larger than y⇤ by a factor of ⇠80 given the design
IP beam sizes at ILC of ( x⇤ , y⇤ ) = (474, 5.9) nm. Another important issue is nm level beam position
stabilization at the IP, for which intra-pulse orbit feedback in the final focus beam line is planned
to be utilized.
The beams are focused by the final doublet (FD) quadrupole magnets to a tight waist at the IP(see Fig. 1.3). The FD consists of the upstream quadrupole (QF), which focuses x⇤ and defocuses⇤⇤⇤
y , followed by the downstream quadrupole (QD), which focuses y and defocuses x . One majordiﬃculty in beam focusing arises from the chromaticity generated at the FD. Particles with lower
energy are focused more tightly than those with higher energies, similar to how light with longer
wavelengths (lower energy photons) receive stronger focusing by a lens in ordinary optics. The beam
size growth caused by the energy spread among particles in a bunch reduces the attainable L at theIP, which is critical issue for linear colliders. The beam size at the IP can be represented as the
combined contribution from betatron oscillation and momentum spread as :
q
q
q
2
⇤
⇤
⇤·
'
1
+
(⇠
)
=
"
1 + (⇠y E )2
(1.2)
y
y
E
y
y0
y
⇤ is the “nominal” vertical beam size without
Here, y⇤ is the vertical beta function at the IP, y0
chromaticity, E is the relative beam energy spread, and ⇠y is the vertical chromaticity. Section 1.4

9describes the methods for correcting the unavoidable chromaticity created in the strong quadrupole
fields, referred to as “natural chromaticity”. These methods use sextupole magnets arranged in a
special configuration with respect to other FFS magnets. This is because the sextupole produces
a quadrupole field whose strength is proportional to the horizontal position oﬀset of the particle
passing the sextupole. Because the horizontal position oﬀset is generated through the existence ofhorizontal dispersion, its is necessary to introduce non-zero horizontal dispersion into the correction
regions in order to separate particles of diﬀerent energies.
p
From Eq. 1.2, it can be seen that a small beam size y0 ⌘ "y y⇤ calls for a small verticalemittance "y . The Accelerator Test Facility (ATF) at KEK is a DR test facility constructed for thispurpose. ATF has demonstrated success in creating beams with "y ' 10 pm · rad. There has also
been intense R&D eﬀorts towards realizing a beam delivery system that oversees beam extraction
and transportation while preserving a small "y , including the FFS for the focusing and dynamic
manipulation of the colliding particle bunches. The ATF2 [4] is a prototype FFS constructed as anextension of the ATF with the primary goal of verifying a novel FFS design featuring the “Local
Chromaticity Correction” scheme selected for use at the ILC [5]. Details of ATF/ATF2 are foundin Sec. 1.5. Table 1.1 shows the major FFS parameters for ILC and ATF2, including the severity ofchromatic y⇤ growth. From the point of view of beam line design, the vertical chromaticity scales
approximately with y⇤ , L⇤ (= distance between FD and the IP), and LF (= FD quadupole length)as:⇠y ' (L⇤ + LF /2)/ y⇤(1.3)

In practice, chromaticity is determined by the level of demagnification required of the FFS optics.
Equation 1.3 indicates that tighter focusing (realized by a smaller y⇤ ) enhances chromatic y⇤ growth.
Smaller beam size requirements also demand more strict control of the placement precision and fieldstrength precision of the FFS beam line magnets in order to suppress higher order errors in themagnetic transport lattice1 . In the absence of chromaticity correction, ⇠y E would blow up y⇤ byas much as a factor of 10 at ILC/ATF2, even for a relatively mild E . 0.1%. This stresses theimportance of chromaticity correction.

Figure 1.3: Focusing of the e beam in the vertical plane. The beam enters parallel into the QF,
where it is first defocused, then enter with a large size into the QD, where it receives abrupt focusing
to a tight waist at the IP.
1
Before beam tuning begins, the FFS magnets are aligned with a precision of 50-100 µm[4]. When evaluating
the eﬀect on beam size, each magnet is required to have O(µm) placement precision and O(10 6 ) field strength
precision[4]. However, in reality tolerance is looser if the optics errors can be cancelled through beam tuning.

10parameters
Beam energy [GeV]
no. of bunches per train Nb
repetition rate frep [Hz]bunch population Ne
beam energy spread E [%]L⇤ [m]"y [pm · rad]"y [nm · rad]⇤⇤x , y [mm]⇤ , ⇤ [nm]x y⇠y ⇠ (L⇤ + LF /2)/ y⇤⇤⇤y / y ⇠ E · ⇠y

ILC (TDR, ECM = 500 GeV)
250
1312
5
2 ⇥ 1010
0.07 (e+ ), 0.12 (e )
4.5
0.07
35
(11, 0.48)(474, 5.9)9400
7 (e+ ), 11 (e )

ATF2
1.3
1
3.12
1 ⇥ 1010
0.07
1.0
12
31
(4, 0.1)(2200, 37)
10000
8Table 1.1: Key design FFS parameters of ILC (TDR, ECM = 500 GeV, ILD detector design) andATF2[2]. Here, L⇤ is the distance from QD0 to the IP, "y and "y are the geometric and normal⇤
ized vertical emittances, respectively, x(y)is horizontal (vertical) IP beta function. ⇠y is vertical⇤⇤chromaticity, andy / y indicates the beam size blow-up due to chromaticity (without correction).
The values are for the nominal beta function optics, whereas at ATF2 occasionally x⇤ is increased
by a factor of 10 for the “10⇥1” optics.

1.4

Chromaticity Correction Scheme

As mentioned in Sec. 1.3, the “natural chromaticity” generated the FD can be cancelled by the useof correction sextupoles in regions with non-zero horizontal dispersion. However in reality, there
are other diﬃculties; the unavoidable nonlinear fields of correction sextupoles themselves cause
higher order aberrations which also blow up the beam size and must be corrected. These consistof “geometrical aberrations” proportional to the quadrature of position and second order dispersion
proportional to E 2 ( E : beam energy spread). Below, I will describe two chromaticity schemes eachfeaturing its own special magnet configuration which seeks to correct natural chromaticity while also
compensating for the higher order aberrations that accompany the use of the nonlinear fields of thecorrection sextupole; first an older design called the “Global Chromaticity Correction” scheme, thena newer one called the “Local Chromaticity Correction” scheme. The contents are mainly based on[5] and [6].
1.4.1

Global Chromaticity Correction Scheme

Figure 1.4 (top) shows the magnet configuration of the “Global Chromaticity Correction” scheme.
The name “global” comes from the fact that the correction sextupoles are placed in regions separate
from the FD, the dominant chromaticity source. Here, chromaticity in the horizontal (vertical) planes(⇠x(y) ) are each corrected in separate dedicated regions, each consisting of a pair of sextupoles. The
sextupole strengths are optimized to correct ⇠x(y) as well as to enable the downstream sextupole
to cancel the nonlinear kick produced by its upstream partner. Because the chromaticity due to
sextupoles are proportional to beta function, the ⇠x(y) correction regions have high x(y) (y(x) ).
The two sextupoles in a region are linked by a transfer matrix of I, and the beta function anddispersion are equal between their locations. A FFS based on this design was tested at the FFTB
project [7] at SLAC. The merit of this beam optics design is its symmetry which allows for relatively
simple beam tuning procedures. However the demerits (when compared to the Local Chromaticity
Correction scheme) are the limitations on the energy bandwidth of the system, and that the FFS
11

beam line is longer.
1.4.2

Local Chromaticity Correction Scheme

A major challenge accompanying the aim for higher energies in linear colliders is that their FFS
beam lines rapidly become longer, more complex and thus more costly. This is a consequence of theenergy errors created inside the FFS amid the chromaticity sources. Some potential energy error
sources are wakefield eﬀects and bremstrahlung due to bending by the dipoles. The FFS dipoles
would have to be made weak and long. Also, long collimator sections are required to eliminate
oﬀ-energy particles which would otherwise hit the FD and create background in the detectors at theIP. Energy spread also makes the chromaticity correction ineﬀective since the sextupole’s focusing
strength depends on the energy of the beam particles.
To counter these obstacles, a novel FFS optics design was proposed by P. Raimondi and A.
Seryi in [5] which features the “Local Chromaticity Correction” scheme. Its name stems from thefeature that the natural chromaticity is compensated “locally” by placing the downstream sextupoles
adjacent to the FD. Figure 1.4 (bottom) shows a simplified configuration of the Local Chromaticity
Correction scheme. Here, a pair of sextupoles is interleaved with the FD. Higher order aberrations
generated by the sextupoles themselves are cancelled using the necessary chromaticity generated
by at least two additional sextupoles placed upstream. The horizontal dispersion necessary forseparating particles of diﬀerent energies is generated throughout the FFS using dipole magnets.
1.4.3

Comparing FFS Designs

The newer Local Chromaticity Correction scheme was chosen over the Global Chromaticity Correction scheme to be used at future high energy lepton colliders such as the ILC. This owes to thefollowing merits [5]:• The length of the FFS beam line is reduced, while still maintaining beam focusing performance.
This is attributed to the fact that chromaticity is corrected locally, in contrast to having to
make space for separate ⇠x and ⇠y correction sections upstream of the FD. The overall FFS
beam line length now scales slower than linearly with energy, allowing for more flexibility in
upgrading to higher collision energies. A compact beam line significantly reduces the numberof beam line components and tunnel cost as well.
• The energy bandwidth is wider, i.e. the tolerance for energy errors is looser from the point ofview of beam size focusing.
• L⇤ is increased about two-folds, which enlarges the dynamic aperture of the FD by several orders of magnitude. Although a longer L⇤ means larger amount of natural chromaticity needs
to be corrected (from Eq. 1.3), this one shortcoming is compensated by the following advantages: the background (BG) from synchrotron radiation is reduced; collimation requirements
are relaxed; the simplified vicinity of the IP allows for the installation of a larger variety ofphysical detectors; beam distortion (beam halo) is reduced (see Fig. 1.5).
However, the optics of the local correction method is more complicated since its ⇠x and ⇠y correction
sections are overlapped, in contrast to the symmetry and strictly separated sections in the global
correction method. This demands more advanced beam tuning procedures, which motivated theconstruction ATF2, where they have been successfully developed and tested.

12

Figure 1.4: Simplified configuration of the Global chromaticity Correction scheme (top) and of the
Local Chromaticity Correction scheme (bottom). Here, only the sextupoles (SF1, SF2) and (SD1,
SD2) and the FD are shown. In reality other quadrupoles and dipoles co-exist among them. -I, P,
M, Q, N represent the transfer matrices linking the magnets [4].

Figure 1.5: The comparison of beam halo particle distribution at the face of the FD between the
traditional (= global correction) and the new (= local correction) FFS designs, based on simulation
[5].

1.5

ATF / ATF2

1.5.1

Beam Line Layout

As introduced in Sec. 1.3, the ATF was constructed at KEK as a general-purpose accelerator researchfacility for ILC-like linear colliders. A 70 m S-Band linac accelerates the e bunches produced by a
RF gun to 1.3 GeV. The beam is fed into a 140 m circumference damping ring (DR). In operation
since 1995, the ATF DR has succeeded in realizing single 1.6 nC bunches at 3.12 Hz with an extremely
small normalized vertical emittance of "y ' 10 pm · rad [8].
The ATF2, consisting of a new extraction beam line and FFS, completed its construction onto
13the existing ATF DR in December 2008. The extraction line prepares the beam emerging fromthe DR for injection into the FFS by correcting for residual energy dispersion, cross-plane (xy) coupling and optics mismatch. Figure 1.6 shows a schematic layout of the ATF2 beam line.
The beam orbit is monitored by a system of beam position monitors (BPMs): stripline BPMs
(resolution 1-5 µm) and cavity BPMs (resolution 40-200 nm). There are also the “IPBPM” (Cband cavity)[9, 10] featuring O(nm) design resolution installed inside the IP vacuum chamber toprovide beam position information nearest to the IP. Various technologies are being developed at
ATF/ATF2 by international collaborators, such as kicker magnets, beam profile monitors, polarized
positron production, BPMs, and beam position feedback systems.
1.5.2

Goals of ATF2

The ATF2 is designed as an energy-scaled test prototype of the ILC FFS, with basically the same
optics, similar beam energy spread, natural chromaticity, and tolerances for alignment and magnet
field strengths. This means that a good estimate for the diﬃculty of ILC beam tuning can be obtained
from ATF2 beam operation. The prominent ATF2 beam time results reported in this thesis served
to experimentally verify the design feasibility of a FFS featuring the Local Chromaticity Correction
method for the ILC. Table 1.1 compares between ILC and ATF2 the basic design parameters, as well⇤⇤as the beam size growth due to chromaticity i.e.
y / y ⇠ E · ⇠y . Figure 1.7 shows a schematiclayout of the ATF2 FFS optics. Figure 1.8 shows the FD magnets and the FFS sextupole magnets
used for chromaticity correction at ATF2. The primary goals of ATF2 can be summarized as thefollowing:• [Goal 1] Demonstrate focusing of y⇤ to 37 nm, the design size scaled from the ILC by beamenergy and y⇤ , and by doing so, verify the Local Chromaticity Correction scheme selected foruse at the ILC.
• [Goal 2] Demonstrate O(nm) level IP beam position stabilization under the “Goal 1” beam
size.
Regarding Goal 1; using theparameters of beam energy, "y , and y⇤ from Table 1.1, thep design⇤
nominal beam size y0 ="y y⇤ , is 5.9 nm for ILC and about 35 nm for ATF2. Since FFS
L⇤
chromaticity scales as ⇤ , ATF2 ’s y⇤ = 0.1 mm and L⇤ =1 m yields nearly the same chromaticityyas ILC with y⇤ = 0.4 mm and L⇤ = 4 m. The oﬃcial ATF2 y⇤ milestone is scaled from ILC usingqq
GeV
0.1 mmboth beam energy and y⇤ as 5.9 nm ⇥ 250⇥
1.3 GeV
0.48 mm '37 nm. The measurement of O(10) nm
beam sizes at ATF2 by a laser interferometer type beam size monitor called the “Shintake Monitor”
is essential for achieving Goal 1.
Regarding Goal 2; commissioning and performance studies are ongoing for the high resolution
IPBPMs [9, 10] installed around the IP. Furthermore, specialized hardware referred to as “FONT”(Feedback On Nano-Second Timescales) [11] is undergoing tests in the extraction line beam diagnostic region to demonstrate a nm precision intra-pulse orbit feedback system.

14

Figure 1.6: The schematic layout of the extraction line and final focus section of ATF2 after extraction from the damping ring. [8]15Figure 1.7: Beam optics of (a) the ILC final focus beam line and (b) the ATF2 beam line. For the
ATF2, both the 1⇥1 optics and the 10⇥1 optics are shown [12]. The beam travels from the initialpoint (end of the extraction line) on the far left towards the IP on the far right.

16

Figure 1.8: (top) the Final Doublet quadrupole magnets at ATF2, QF1 (yellow) and QD0 (red),shown together with the FFS sextupole magnets interleaved with the FD.
(bottom left) A close-up view of the SD0, the sextupole magnet placed next to the QD0. (bottom
right) One of the skew setupoles in the FFS for correction of nonlinear errors.

1.6

Beam Size Monitors at ATF2

Throughout the rest of this thesis, the vertical beam size at the IP will be generally denoted without“*”, as just “ y ”.
1.6.1

Shintake Monitor

The Shintake Monitor, installed at the virtual IP of ATF2, is the only system at present thathas demonstrated the measurement of y < 100 nm, surpassing conventional beam size monitors
described in Sec. 1.6.2. Its stable y measurements are essential for beam tuning and achieving the
ATF2 Goal 1. The Shintake Monitor, invented by Dr. T. Shintake [13], was first used at the FFTB
(Final Focus Test Beam) experiment (1994-97) at SLAC, where it succeeded in measuring y ' 70
nm with approximately 10% resolution[13, 7]. Section 2.5 describes its upgrade for measuring theeven smaller design y of 37 nm at ATF2.
Figure 1.9 shows the location of the Shintake Monitor in the ATF2 beam line. Laser interference
fringes are formed at the IP, which is the focal point of both the e beam and the laser. The phase17

of the interference pattern is scanned with respect to the beam by altering the path length of one
arm of the interferometer using a delay line. Beam sizes are inferred from the modulation of theresulting Compton scattered photons as measured by a downstream calorimeter-type gamma-ray
detector. The comprehensive description of the Shintake Monitor system is found in Part II. Section
4 explains the use of the Shintake Monitor in beam tuning. The major theme of this thesis is theevaluation of its precision in y measurements.

Figure 1.9: The location of the Shintake Monitor in the ATF2 beam line (circled in red)
1.6.2

Other Types of Beam Size Monitors

There are various other types of beam size monitors besides the Shintake Monitor in use at ATF
for diﬀerent purposes. Some, such as wire scanners and laser wires use the “scan” method, whileothers such as screen monitors, optical transition radiation (OTR) monitors and x-ray synchrotron
radiation (XSR) monitors use imaging. Non-destructive methods, such as laser wire and XSR allow
repeated measurements and thus can be used for beam tuning at the DR. Wire scanners and OTR
monitors measure the beam with destructive methods. This section describes a few systems closely
related to the Shintake Monitor. Details on other systems can be found in [15, 16].
Wire Scanner
A wire scanner measures beam sizes by scanning a tungsten or carbon wire across the beam, whichcauses photon emission due to bremsstrahlung, the dominating process for a highly relativistic beam.
The energy of the emitted photons, which extends up to the beam energy, are measured using a
gamma-ray detector. If the wire diameter is suﬃciently thin compared to the beam size, a Gaussianlike beam profile is obtained by plotting the photon signal as a function of the scanned wire position(see Fig. 1.10). The beam size is inferred from the fitted sigma of the profile after subtracting
the wire thickness in quadrature. Beam sizes as small as 1/4 - 1/2 of the wire diameter can bemeasured. For any beam thinner than this, either correction for wire thickness is diﬃcult, or thewire may be burnt by the high beam intensity. The wire cannot be too thin either since it would not
be durable enough. Wire scanners are used at various locations in the ATF(2) beam line. Near theIP, carbon wires of 5 µm diameter are scanned using a mover to measure x and y & 1 µm. The
bremsstrahlung photons are measured using a “background monitor” located about 10 cm upstreamof the Shintake Monitor gamma-ray detector (see Fig. 3.30). It is a calorimeter made of a 5 mm
plastic scintillator with a 10 mm thick lead converter attached to its front surface. Scintillation lightis read out by a photomultiplier tube (PMT). The background monitor is installed on a mover which
18

allows it to be inserted for the wire scanner measurement and removed before using the Shintake
Monitor. The IP wire scanners play an important role in initial beam size tuning before y getssmall enough to be measured by the Shintake Monitor.
Screen Monitor
The screen monitor is a thin screen made of a fluorescent material. Its collision with the e beam
releases fluorescent light which is monitored by a CCD camera to observe the beam profile. Its merits
are that measurement is simple and not time consuming. However the blurring of the image limits
the resolution to a few tens of µms. Screen monitors are installed at a few places in the ATF/ATF2
beam line. At the IP, there is a screen monitor attached together with the IP wire scanners to acomplex target system which is slid in and out of the IP using an auto-stage. For example, the IP
screen monitor is inserted for the initial position alignment of the Shintake Monitor laser to the ebeam (see Sec. 4), then ejected before the interference fringe scans.
Laser Wire
The laser wire measurement method is similar to that of the wire scanner, except that the solid
wire in the latter is replaced by a laser beam, thus photon emission is due to inverse Compton
scattering. A single laser beam path is scanned across the e beam, and the energy of scatteredphotons measured at every laser position forms a distribution of the e beam profile convoluted
with the laser beam profile. Laser wire can measure beam sizes above 1 µm, smaller than those ofwire scanners. The usage of a laser beam as the target for the e beam avoids its destruction due
to heat. However, it is diﬃcult to maintain suﬃcient S/N ratio in the gamma-ray detector since
photon energy for Compton scattering is low compared to bremsstrahlung. The compensation for
signal rate requires high photon density i.e. powerful short laser pulses and strong laser focusing.
The laser wire mode of the Shintake Monitor (see Sections 2.4 and 4.2) performs similar functions
during preparation for use during beam time.

Figure 1.10: An example of the measurement of the vertical beam size by the IP carbon wire scanner.
The horizontal axis is the position of the mover stage of the wire scanner (in [mm]). [17]1.7Beam Focusing History

Figure 1.11 and Table 1.2 show the important benchmarks in the history of the minimum y stably
measured at ATF2 from Dec. 2010 to June 2014. Note that these are the upper bound on y , before
correcting for bias factors intrinsic to the Shintake Monitor to be described in Chap. 6. In Dec.
2012, Compton signal modulation corresponding to y . 70 nm was detected in fringe scans for the
first time. By Mar 2013, y < 65 nm had been stably measured[8]. By spring of 2014, y close to
the Goal 1 size has been routinely achieved. What is remarkable is not only how small a y can
19be focused to and measured, but also the reproducibility of beam focusing and measurement. The
stable y measurements by the Shintake Monitor enable very eﬃcient beam focusing. For example,
as shown in Fig. 1.11 ((b) and (c)), after start-up at the beginning of each “beam ON week”, y
can be squeezed from a few µm to < 100 nm in a couple of days, then further down to < 60
nm in just half a day. In fact, y . 65 nm was achieved during the first week of operation after
more than 3 months of shutdown during 2014 summer. The progress in focusing and measuring of
small y owes to various improvement made over time on beam tuning methods, the beam line, andinstrumentation. The most prominent improvements are grouped into the following two upgrade
phases (#1 and #2) in Table 1.2:
Upgrade#1: These played a large part in the achievement ofy < 70 nm.

• A major improvement of the Shintake Monitor laser optics in 2012 summer by the ATF2 groupat KEK (see [40]).
• The installation of skew sextupoles in the FFS line and the installation of OTR monitors in
the extraction line; these enabled more eﬀective beam tuning.
• The QF1 was replaced to one with a larger aperture which realized better field quality (Nov.
2012); the beam is very sensitive to the higher order multipole magnetic field errors of QF1
since the nominal beta function at QF1 is O(10000) m, i.e. the beam size is large.
• The improvement of tuning knobs (see Sections 4.1.1 and 4.1.2) by exchanging the relevant
FFS sextupoles found to have field errors.
Upgrade#2: The items below enabled the achievement of the smallest
nm).

y ever measured (< 50• The stabilization of the Shintake Monitor laser (see Sec. 8.1.1 for details)• The improvement of tuning knobs (see Sections 4.1.1 and 4.1.2); the sextupole setting of thetuning knobs was recalculated in order to omit one of the FFS sextupoles whose field wasfound to be abnormally weak (April 2014).
• The stabilization of the e beam; the orbit feedback was improved by introducing the use ofcorrector magnets, which reduced beam orbit drifts.
• The mitigation of wakefield eﬀects: the y < 100 nm were generally measured with low beam
bunch charge (. 1 ⇥ 109 ) to minimize the beam size growth due to wakefield eﬀects. A large
fraction of ATF2 beam time has been dedicated to the investigation of wakefield eﬀects since
early 2013 (see Appendix G and [18, 20] for details).

20

(a)

(b)

(c)
Figure 1.11: (a) The history of stably measured beam sizes (without correction for systematic errors
intrinsic to the Shintake Monitor which cause beam size over-evaluation) at ATF2 from Dec 2010 toJune 2014.
(b, c) Examples of eﬃcient beam tuning of y from > 1 µm to < 60 nm. The diﬀerent colors signify
diﬀerent crossing angle modes of the Shintake Monitor system explained in Sec. 4 (b) start-up after
3 weeks of shutdown (c) start-up after 3 days of shutdown [18]

21

time
Dec., 2010
Feb. -June, 2012
Dec., 2012
Mar., 2013
Apr., 2014
May, 2014
June, 2014

stably measured y⇠ 300 nmdisturbance due to Mar 2011 earthquake⇠ 150 nmUpgrade#1. 70 nm. 65 nmUpgrade #2. 55 nm. 50 nm. 45 nmTable 1.2: The history of stably measured beam sizes at ATF2 from Dec. 2010 to June 2014. The
major upgrades contributing to this progress are explained in the main text.

1.8

About this Doctoral Thesis

1.8.1

The Hi-lights of My Personal Contributions

The specialties of my studies in this thesis are that they are the first and only ever to be applied tothe measurement of beam sizes < 50 nm, and that they demonstrate a way to achieve the smaller
beam sizes at the ILC in the future. My major personal contributions to the research on the Shintake
Monitor are the following:
1. I studied and analyzed a wide variety of systematic errors which aﬀect the precision of beam
size measurements. In particular, I developed an original method for deriving the dominantsystematic error, which is the fluctuation of the relative phase (or equivalently the vertical
relative position) between the laser and the e beam at the IP. The reliability of this method
was verified using simulation. These analysis are based on recent and realistic conditions of
the Shintake Monitor system and the ATF2 beam operation.
2. I analyzed the measurement by the Shintake Monitor of world record small beam sizes. These
take into account the above-mentioned systematic error studies, which are based on the measurements I conducted of the laser optics and the gamma-ray detector properties. My analysis
results indicate that the ATF2 goal beam size has been achieved.
3. I also participated in the following since the first year of my Masters course research (2010⇠):the development and improvement of the Shintake Monitor hardware; the regular ATF2 beamtuning shifts during which the beam size measurements by the Shintake Monitor play anessential role.
4. I presented my research results at a number of conferences (international and within Japan),as well as in published papers (some are listed in the bibliography of this thesis).
1.8.2

Structure of Doctoral Thesis

This thesis consists of three major parts:• In Part I, Chap. 1 begins with an introduction of the ILC, then describes the ATF/ATF2 andthe role of the Shintake Monitor.

22• In Part II, Chap. 2 describes the measurement scheme of the Shintake Monitor, while Chap.
3 provides the details on each of its components (e.g. the laser optics and the gamma-ray
detector); Chap. 4 describes the beam tuning procedures at ATF2 and the preparation of the
Shintake Monitor for beam size measurement.
• Part III, about the performance of the Shintake Monitor, is the most important part of thisthesis; Chap. 5 evaluates various properties of the laser based on actual measurements e.g.
focusing, profile, power, polarization, and angular stability; Chapters 6 and 7 describe an
extensive study and analysis of the systematic errors and signal fluctuations aﬀecting beam
size measurements; based on these error analysis, Chap. 8 provides the complete evaluationof the smallest beam sizes ever measured. This is followed by the conclusion.

23

Part II

Concept of Beam Size Measurement by the
Shintake Monitor
2

Description of Shintake Monitor

2.1

Measurement Scheme

Figure 2.1: The schematic layout of the Shintake Monitor (modified from [22]).
Figure 2.1 shows the schematic layout of the Shintake Monitor system, which consists of laser optics
and a gamma detector. The Nd:YAG Q-switch laser source located outside the accelerator tunnel
generates laser pulses of wavelength 532 nm, pulse energy of 0.41 J, and FWHM pulse length of
8 ns. The laser pulses are delivered to an upright standing optical table (“vertical table”) at the
IP through an approximately 20 m transport system containing lenses to adjust the spot size anddivergence. On the vertical table, the laser beam is split into upper and lower paths by a 50% beam
splitter. The laser paths propagate to lenses which focus them to tight waists at the IP, where they
cross to form the interference fringes that the e beam collides perpendicularly against. The fringe
phase is scanned relative to the beam using a delay line consisting of prisms and a piezoelectric
stage. The Compton scattered photons resulting from the laser-beam collision enter a downstream
electromagnetic calorimeter-type detector made up of layers of CsI(Tl) scintillators which measuresthe energy deposited by the photons. The e beam is bent by a dipole magnet safely into a dump.
The detector measures the variation in Compton signal intensity as the fringe phase is scanned,
called “modulation depth” (denoted as “M ”). The M spectrum consists of Compton signal energy
24plotted as a function of fringe phase. Figure 2.2 shows the relationship between M and beam sizes.
The number of signal photons is large when the beam collides against the fringe peak, and small
when it collides against the fringe valley. A well focused beam is more sensitive to this diﬀerence.
Therefore, M is large if the beam size is small compared to the fringe pitch, whereas M is small fora large beam size.

Figure 2.2: Relationship between modulation depth (M ) and beam sizes (modified from [22]).

2.2

Beam size Calculation

This section explains how the beam size is derived from the measured modulation. First, the relevant
parameters will be defined:•y : vertical beam size at the IP• ✓ : laser beam crossing angle• ky = ksin (✓/2) : wave number component normal to laser fringe•: laser wave length (532 nm for the Shintake Monitor at ATF2)• y 0 : vertical relative position at the IP between the laser and the e beam
• N : number of Compton scattered photons ( = signal intensity)• ↵ : relative phase between upper and lower laser paths
Figure 2.3 defines the coordinates surrounding the IP. The e beam propagates in the z directionin the laboratory frame, while the laser interference fringe is formed in the transverse plane, where
x and y are the horizontal and vertical directions, respectively. The wave number vectors of themagnetics fields for the upper and lower laser paths are:!
k1 = (kcos (✓/2) , ksin (✓/2) , 0) ⌘ (kx , ky , 0)25!
k2 = (kcos (✓/2) , ksin (✓/2) , 0)

(2.1)

Figure 2.3: Relationship between electromagnetic fields and the propagation of the e
the two laser paths.

beam andIn this experiment, the laser beam is set to be linear S polarization (see Sec. 5.4), for which
the electric field of the laser beam is parallel to the surface of the mirrors on the vertical table2 .
The laser spot size is focused by a lens to a waist of about 10 - 15 µm at the IP. Because thelaser spot size is much larger than y , the e beam is assumed to interact with homogenous planar!
!
electromagnetic fields. The electric (Eelec ) and magnetic ( B ) fields of the upper and lower laser
paths can be expressed as:
⇣
⌘
!
!
↵
Eelec,1 = Eelec (0, 0, 1)cos !t k1 · !
x
2⇣! ! ↵⌘!
Eelec,2 = Eelec (0, 0, 1)cos !t k2 · x + 2
⇣
⌘
(2.2)
!
!
↵
B1 = B(sin (✓/2) , cos (✓/2) , 0)cos !t k1 · !
x
2
⇣
⌘
!
!
B = B( sin (✓/2) , cos (✓/2) , 0)cos !t k · !
x +↵
2

2

2

After Lorenz transformation to the rest frame of a relativistic particle, only the field components
transverse to the Lorentz boost direction contribute to inverse Compton scattering since these areenhanced by a factor of . In the lab frame, the laser fringe intensity can be expressed as thefollowing superposition of magnetic fields from the two laser paths:
01
sin (✓/2) sin (!t kx x) sin ky y + ↵2!
! !
B = B1 + B2 = 2B @ cos (✓/2) cos (!t kx x) cos ky y + ↵2 A
(2.3)
0Equation 2.3 shows a traveling wave along the x axis and a standing wave along the y axis. The
magnetic field intensity, averaged over time, is expressed as 3 :!2! !2
B = B1 + B2 = B 2 (1 + cos ✓ cos (2ky y + ↵))(2.4)

Equation 2.4 indicates that the visibility of the interfere pattern depends on the crossing angle✓. It also indicates that the magnetic field intensity changes as cos (2ky y + ↵), which is a function
2
The electric field of the Shintake Monitor laser is parallel to the e beam (longitudinal) direction. The interference
fringes form upon a vertical table standing upright perpendicular to the beam direction.
3
For relativistic energy beams, the fringe intensity can be expressed either using magnetic field in the lab frame orelectric field in the e rest frame. Averaging the magnetic field intensity over time is valid since the longitudinal e
beam bunch length (⇠8 mm) is much longer than 1/kx , and thus the magnetic field oscillates many times along thex axis during the passing of the e beam bunch.

26

of the relative position (y) between the laser and the e beam at the IP, and the relative phase ↵.
An optical delay line installed in the upper path is used for changing ↵ during interference fringescans. The pitch (d) of the interference fringes i.e. the distance between adjacent peaks, depends
on the laser crossing angle ✓, and is expressed as:
d=

⇡
=
ky
2 sin (✓/2)(2.5)

The signal intensity N , which is proportional to the luminosity of collision between the e beamand laser fringes, is derived as the convolution between fringe intensity and e beam profile as:
N/

ˆ

!2 0
dxdy 0 Pbeam (x, y 0 ) B
y

(2.6)

Here, y 0 is the vertical distance between the crossing point of the two laser paths and the ebeam. Integration in theis equal to 1. Assuming a Gaussian vertical e beam profile as:⇣ x02plane⌘y10
Pbeam (y ) = p2⇡ exp, Eq. 2.6 can be rewritten as :
2 y2
y
✓
◆
ˆ
!2 0
1
y 02
0
N / dy p
exp
B
y
(2.7)
2
2 y
2⇡ y
= B 2 [1 + cos ✓ cos(2ky y + ↵) exp( 2(ky y )2 ]Equation 2.7 indicates that the Compton signal intensity changes according to the fringe phase,and that the degree of variation i.e. the “modulation depth” (M ), depends on the vertical e beam
size y . M is related to maximum and minimum signal intensity (N± = N20 B 2 [1±cos(✓) exp( 2(ky y )2 ]
) as:
M=

N+ N
N+ + N= | cos ✓ exp

2(ky y )2 |(2.8)

y can then be calculated as a function of M and fringe pitch d as:

d
y =
2⇡

s

2 ln

✓

| cos(✓)|
M

◆

✓

⇡
d=
=
ky
2 sin(✓/2)

◆

(2.9)

In practice, the Compton energy spectrum measured by the gamma-ray detector is plotted asa function of the fringe phase, and fitted with the following cosine-like function (as in Fig. 2.2) toextract M , Eavg (average energy), and '0 (initial phase).
E (y) = Eavg (1 + M cos (2ky y + '0 ))(2.10)

Examples of fringe scans from actual beam time can be found in Sec. 8.1. From Eq. 2.10, M canbe interpreted as Amplitude
Average of the measured energy. The contrast, or “visibility” of the laser fringes
is defined using the highest and lowest intensity interacting with the beam in the e rest frame asImin
I = IImax. A clear contrast is important for measuring a large M (i.e. a small y ), whereas amax +Imindegraded contrast leads to the under-evaluation of M (i.e. over-evaluation of y ).

2.3

Measurable Range

From Eq. 2.9, it can be seen that the measurable beam size range is determined by the fringe pitchd which depends on the crossing angle ✓. In order to be able to measure a wide range of y from 25
nm to a few µm with better than 10% resolution, the laser optics is designed to enable the switching27

between several ✓ modes according to e beam focusing status. This is explained as follows. Using
Equations 2.8 and 2.9, the beam size resolution can be expressed as a function of y /d, the ratio ofbeam size to fringe pitch, as:| M/M |⇣⌘
y2 ln | cos(✓)|
M⇣⌘
exp 2⇡ 2 ( y /d)2=
· | M|
4 |cos ✓| ⇡ 2 ( y /d)2y=(2.11)

Equation 2.11 is plotted in Fig. 2.4 assuming a constant | M |=0.02 and |cos ✓| = 1. From Fig.
2.4, we can observe the following:• resolution is best when

y is around 1/5 of d.

• resolution worsens suddenly as y exceeds 1/2 of d; this is because as y approaches the scaleof d, the e beam loses its sensitivity to the contrast of the interference fringes.
• resolution worsens slowly as y decreases below 1/10 of d; this is because if d is large compared
to y , the fringe loses its sensitivity to the narrow scale of the e beam.
The Shintake Monitor has a stricter limit on a larger y for a fixed d. This is why several crossing
angle modes are necessary in order to widen the range of measurable beam sizes.
For several representative modes of ✓ = 2, 8, 30, and 174 deg, Fig. 2.5 shows M (Eq. 2.8),
while Fig. 2.6 shows beam size resolution (Eq. 2.11) assuming | M |=0.02, both as a function of
y . Table 2.1 shows d and the measurement range for y ; the standard for the upper limit ( y,max )is based on M =0.1 since the typical amount of signal jitter limits detection of M smaller than this.
The standard for the lower limit ( y,min ) is based ony / y =10% in Fig. 2.6.
For the larger y , 2 - 8 deg modes (continuously adjustable) are used. As y is focused down
smaller (using the tuning procedures in Sec. 4.1), mode is switched to 30 deg, and finally to 174
deg mode. Mode switching is carried out via the remote control of auto-stages carrying actuatorcontrolled mirrors. In practice, the typical M for each mode is typically 0.1-0.9, with the exceptionof the upper limit for 30 deg mode, for which cos ✓ comes up to only about 0.86 (=cos (⇡/6)). The
lower limit for the measurable y (as M approaches 1), where switching to a larger ✓ mode is usually
carried out, is determined by the bias eﬀects from systematic errors.

28

Figure 2.4: The relative beam size resolution
beam size to fringe pitch assuming a constanty / y plotted as a function of

M =0.02 and |cos ✓| = 1.

y /d i.e. the ratio of

Figure 2.5: For the crossing angle modes of 2, 8, 30, and 174 deg: the relationship between modulation (M ) and vertical beam size ( y ). For a fixed y , M takes on very diﬀerent values for diﬀerent
modes. The maximum M comes up to |cos ✓|.

29

Figure 2.6: For the crossing angle modes of 2, 8, 30, and 174 deg: the relationship between beam
size resolution ( y / y ) and y , assuming a constant M =0.02.
crossing angle ✓fringe pitch drange y,min / y,max

174 deg
266 nm20 nm / 90 nm

30 deg1.028 µm
85 nm / 340 nm

8 deg
3.81 µm
290 nm / 1.3 µm

2 deg
15.2 µm
1.2 µm / 5.2 µm

Table 2.1: Beam size measurement range for each crossing angle mode.

2.4

Laser wire mode

In addition to the interference modes in Table 2.1, there is a “laser wire mode” which consists ofscanning a single laser path in the transverse plane relative to the e beam using mirrors controlled
by actuators. This serves to measure x and/or laser spot size laser . In this case, the “beam size
seen from the laser ( beam )” depends on crossing angles (✓) as:
q
2
2
2
2
(2.12)
beam =
x sin (✓/2) + y cos (✓/2)
Assuming Gaussian profiles for both the laser and the e beam, the Compton signal also takes
on a Gaussian distribution; its spread is the convolution of laser and beam :q22(2.13)
lw =beam + laser

Equation 2.13 shows that passing the laser horizontally i.e. ✓ !0 deg allows measurement of y ,while passing it vertically i.e. ✓ ! 180 deg makes it sensitive to x . In this way, the horizontal beam
size x can be measured using laser wire scan at 174 deg mode. During recent ATF2 operations,
x is of similar size to laser , and is typically measured using the IP wire scanners (see Sec. 1.6.2).
By the time the Shintake Monitor is used in beam tuning, y would already been tuned to be muchsmaller than laser , also using the IP wire scanners. Thus most of the time the Shintake Monitor
laser wire mode is used for the following purposes (see Sec. 4.2 for details):
1. Measure laser spot size laser . This is subtracted from the 1- spread of the measured laser
wire scan signal using Eq. 2.12 and Eq. 2.13.
30

2. Align laser position in the transverse plane to enable collision with the e beam.

2.5

Upgrades from Use at the FFTBThe Shintake Monitor had first been used at the FFTB experiment (at SLAC), where it had succeeded in measuring y ' 70 nm with approximately 10% resolution[13, 7]. The discrepancy between
the 70 nm and the FFTB goal y of 60 nm is possibly attributed to e beam jitter and beam size
monitor related systematics, and has not been made certain. The measurement of e beam jitterat the IP would require the yet to be commissioned O(nm) resolution cavity BPMs. There may
also have been some residual non-linear aberrations which blow up y since the Local Chromaticity
Correction scheme was developed after FFTB had ended. In the years that followed, various proposals for FFS design in linear colliders prompted the construction of ATF2. This section describes
the changes made to the Shintake Monitor to adapt it for achieving goals specific to ATF2. Table
2.2 compares the design parameters between ATF2 and FFTB. Compared to FFTB, the Shintake
Monitor at ATF2 faces the following challenges:[1] Repetition rate is lower for ATF2 (1.56 Hz at first, later 3.12 Hz) than for FFTB (30 Hz) by afactor of about 10. To compensate this limit on signal statistics, precision must be improvedby suppressing bunch-to-bunch signal fluctuation factors such as laser power, position, phase,and background. Also, fringe scans at ATF2 are more time consuming, which is unfavorablefrom the point of view of maintaining stability against slow position drifts of the laser and/or
the e beam. For instance, at ATF2, typically about 200 pulses are used for a scan taking over
1 min (10 pulses at each of the 20 phases). At FFTB, about 900 bunches can be measured
in much shorter scans of about 30 s. The higher FFTB repetition rate enables 10 times more
pulses to be used at each phase for the same length of time.
[2] Beam energy is lower for ATF2 (1.3 GeV) than for FFTB (46.6 GeV) by a factor of about 36.
Therefore single photon energy is also much lower for ATF2, making signal detection morediﬃcult.
Despite the above-mentioned challenges, the Shintake Monitor realized at ATF2 succeeded in measuring smaller beam sizes than FFTB with similar resolution. This owes to the following improvements:⇣⌘
Laser wavelength:
Because a smaller fringe pitch d = 2sin(✓/2) is required for measuring asmaller design y , the laser wavelength ( ) was halved from 1064 nm to 532 nm by second
harmonics generation (SHG).
Wider measurement range:
The laser optics was upgraded to measure a wider range of beam
sizes (25 nm - a few µm) than at FFTB (40 - 720 nm). In particular, continuously adjustablelaser crossing angle modes between 2-8 deg were implemented for more eﬀective tuning oflarge beam sizes during initial tuning stages. This allows the overlap and crosscheck with wire
scanner measurements. In addition, a “laser wire mode” (see Sec. 2.4) enables the convenientmeasurement of the larger horizontal beam sizes using a single laser path.
Scan method: For fringe scans at FFTB, the vertical position of the e beam itself is shiftedusing steering magnets w.r.t. a fixed laser fringe. This method is unsuitable for ATF2 because(a) very slight shifts of the beam are diﬃcult given the low ATF2’s beam energy, and (b) it
is unfavorable to jeopardize beam position stability from the point of view of the Goal 2 of
ATF2, which is nm precision stabilization of e beam position at the IP. At ATF2, modulation
is produced by scanning the relative phase of the two laser paths using a phase control system(see Sec. 3.3.1) w.r.t. the e beam position fixed at the IP. The prevention of e beam position
instability is more positive for measurement accuracy.
31

design parameters
beam energy
1 photon energy
repetition rate
⇤
⇤
x, y
⇤
⇤
x, y
( "x , "y )aspect ratio ( x⇤ / y⇤ )Nbunchenergy spread

FFTB
46.6 GeV
8.6 GeV
30 Hz(900 nm, 60 nm)(10, 0.1) mm(3 ⇥ 10 5 , 3 ⇥ 10 6 ) m · rad15
1 ⇥ 1010
0.3%

ATF2
1.3 GeV
15 MeV3.12 Hz(7 µm , 37 nm)(40, 0.1) mm(2.8 ⇥ 10 6 , 3.1 ⇥ 10 8 ) m · rad189
1 ⇥ 1010
0.7-0.9%

Table 2.2: Comparison between FFTB and ATF2 (status in 2014) of design parameters related to
the Shintake Monitor (modified from [7]).

2.6

Physics of Compton Scattering

The physics process of inverse Compton scattering between laser photons and electrons in the beam
will be described, with the aim to derive the following in the lab frame:• total cross section of Compton scattering• energy and angular distribution of the Compton scattered photons
The following notations are used:• 4 momentum vector : p for e , k for photon• ✓ : scattering polar angle,: azimuthal angle,⌦ : solid angle• with ’ : “after collision”, without ’ : “before collision”• with * : e rest frame, without * : lab framep2• : Lorentz boost factor, = 1/ 1
• !
" : photon polarization vector• m : e rest mass
Figure 2.7 shows the diagrams for Compton scattering in the e rest frame and the lab frame.
Kinematics will be calculated in the comparatively simpler e rest frame, then the results will be
converted using Lorentz transformation to the lab frame. Assuming that incident photon propagatesin the z direction, the following 4 momentum vectors will be used:p⇤ = (m, 0, 0, 0)
k ⇤ = (k ⇤ , 0, 0, k ⇤ )k 0⇤ = k 0⇤ , k 0⇤ sin ✓0⇤ cos0⇤, k 0⇤ sin ✓0⇤ sin

The diﬀerential cross section in the e rest frame is:320⇤, k 0⇤ cos ✓0⇤(2.14)

d
1
=
0⇤
d⌦
64⇡ 2 m2

✓ 0⇤ ◆2k|M |⇤2⇤k(2.15)The squared matrix element of Compton scattering is [14]:

0
p·k
2
2
4 p·k
+
2 + 4 " · "0
|M | = 2e
0
p·k
p·k

(2.16)

Equation 2.16 is based on linearly polarized photons and the gauge " · p = "0 · p = 0. It can beshown that after summing over all final polarization states (since the Shintake Monitor detector isnot sensitive to polarization) and integrating over all azimuthal angles, this can be expressed as the
Klein-Nishina equation [22]:
 ⇤
ˆ 2⇡
1
k 0⇤
⇤2
⇤
4 k
d |M | = 2e+
1 + cos2 ✓0⇤(2.17)
2⇡ 0
k 0⇤
k⇤
The relationship between parameters in the eLorentz transformation as the following:

rest frame and lab frame are obtained fromk⇤ = k⇤cos ✓0⇤ =d⌦0⇤ =

2=cos ✓01
cos ✓01+

cos ✓0⇤2d⌦0(2.18)

From kinematics i.e. conservation of momentum, the energy of the scattered photons is calculated
to be Eq. 2.19 and Eq. 2.20 in the e rest frame and the lab frame, respectively:
k 0⇤ =
k0 '

k

mk ⇤
m + k ⇤ (1 cos ✓0⇤ )mk0 ) + m (1k sin ✓0 cos ('(2.19)cos ✓0 )mk
k + m (1cos ✓0 )(2.20)In Eq. 2.20, the approximation sin ✓0 ⌧ 1 is applied based on the very forward distribution of
scattered photons. The maximum and minimum energies of the scattered photons are
0
kmax
=

mk
k + m (1

' 29.5 MeV✓0 = 0(2.21)

0
kmin
=

mk
' 1.17 eV
k + m (1 + )✓0 = ⇡(2.22))

Using Equations 2.15, 2.17, and 2.18, the cross section is distributed in terms of cos ✓0 as :dd⌦0 d⌦0⇤ d==dcos✓0dcos✓0 d⌦0 d⌦0⇤

ˆ

d

0⇤ 2

1
(1 + cos✓ ) ⇥64⇡ 2 m2330⇤ 2

✓ 0⇤ ◆2k|M |⇤2
k⇤

↵2 ⇡
= 2
m

✓ 0⇤ ◆2
k
k⇤

2

(1 +

0⇤ 2

cos ✓ )



k⇤
k 0⇤
+
k 0⇤
k⇤

2

1 + cos ✓

0⇤

✓

e2
↵=
4⇡

◆

(2.23)

Integration over the entire solid angle gives the total cross section for Compton scattering as :⇢2⇡↵2 1 + q 2q(1 + q)ln(1 + 2q)
1 + 3qln(1 + 2q) +(2.24)
total =
23m
q
1 + 2q
2q(1 + 2q)2Here, the parameter q ⌘ k/m represents the energy ratio between the incident photon and theelectron in the e rest frame. In can be seen that total declines with the increase of q, i.e. witheV
the increase of e beam energy ( ) or incident laser photon energy k. For ATF2, q ' 2544⇥2.33'
511 keV
0.0116, which gives total = 0.65 barn.
The angular distribution and energy distribution of Compton scattering cross section are calculated as Eq. 2.25 and Eq. 2.26, respectively. Inserting Equations 2.18, 2.19 , and 2.23, these areplotted as in Fig. 2.8, along with the scattered photon energy as a function of scattered angle (Eq.
2.20).
d
=
dk 0

✓

dk 0
d cos ✓0◆ 1

d=d cos ✓0kd02
k d cos ✓0(2.25)

dd cos ✓0 dd== sin ✓0(2.26)000d✓d✓ d cos ✓d cos ✓0
In Fig. 2.8 (top right), the angular spread of the scattered photons corresponding to 95% of thetotal number of photons is about 1.7 mrad. This signifies that the photons are nearly all projectedalong the e beam direction. Their angular spread is increased slightly by the divergence of the ebeam : ✓xe ' 0.17 mrad, ✓ye ' 0.35 mrad.

Figure 2.7: Schematics of Compton scattering between laser photons and electrons: (left) in the erest frame {right) in the lab frame.

34f_angle
dsigma/ dtheta [barn/rad]dsigma/dk [barn/MeV]

f_energy
0.04
0.035
0.03
0.025
0.02

1200

1000

800

600

0.015
400
0.01
200

0.005
0
0

5

10

15

20

0
0

25
30
35
scattered energy [MeV]

0.00050.001

0.00150.002
0.0025scattered angle [rad]scattered energy [MeV]

f_EAng
30

25

20

15

10

5

0
0

0.00050.001

0.00150.002
0.0025scattered angle [rad]Figure 2.8: (top) The distribution of Compton scattering cross section w.r.t. final state photon
energy (left) and final state photon scattered angle (right).
(bottom) The energy of Compton scattered photons plotted as a function of their angle.

Figure 2.9: The dependence of the total Compton scattering cross sectionin the range of q = 0 - 0.25. The blue line indicates the case of ATF2.

35

total on q =k/m, shown

3

Description of Individual Components

3.1

Overall Layout

3.1.1

Laser Transport

Figure 3.1 shows the schematic overview of the laser optics. On a laser table outside the accelerator
tunnel, the laser light is generated inside an optical cavity and is transported to the upright standing
main optical table (“vertical table”) in the IP area. The interference fringes are formed on the vertical
table. The transport system (⇠ 20 m) shown in Fig. 3.2 consists of a pipe passing over the topof the concrete shield of the accelerator tunnel and mirrors placed inside boxes located beside theoptical tables to guide laser beam propagation. Figure 3.3 shows examples of the laser sent up fromthe laser table, guided through the transport line, and ejected onto the vertical table.

Figure 3.1: The overall layout of the Shintake Monitor system. The laser beam, after being generated
and adjusted at the laser table, is transported through a transport line to the main vertical table in
the IP area. [22]36Figure 3.2: The transport line sitting on the roof of the accelerator tunnel.

Figure 3.3: (left) The laser reflected up from the laser table through a pipe into the transport pipeline. (center) The laser reflected down into the accelerator tunnel. (right) The laser emerging onto
the vertical table.
3.1.2

Expander and Reducer

Prior to transport, the laser spot size ( laser ) is magnified approximately two-folds by the “expander”
on the laser table in order to prevent divergence during transport. Magnification by M times isachieved by pairing an upstream concave lens with focal length f with a downstream convex lenswith focal length M f . After emerging onto the vertical table, laser is restored using the “reducer”,
which consists of the opposite, an upstream convex lens and a downstream concave lens. The coatedlenses (Fused Silica) are manufactured by Sigma Koki Inc. (SLSQ-50-(f)PY2 for convex and SLSQ50-(f)NY2 for concave; f is focal length). In practice, the distance between the lenses receive slightadjustments in order to realize the desired laser focusing. More details on laser adjustment are
given in Sec. 5.1. Figure 3.4 shows the schematics and photos of the expander and the reducer.
Alignment irises (Thorlab) are placed before and after the expander/reducer lenses to ensurethat the laser passes precisely through the lens centers. Irises are also used for alignment at several
other locations on the optical tables. The laser path is adjusted to pass the center of the irises,
which are closed for alignment, then opened again afterwards.

37

Figure 3.4: (top) The schematics of the expander and the reducer. (bottom left) The expander on
the laser table. (bottom right) The reducer on the vertical table.

3.2

Laser Table

Figure 3.5 shows the schematic layout of the laser table in the “laser hut” 4 . The laser cavity andoptical components are kept inside a box to maintain a dust-free and temperature stable environment.
Inside the laser cavity, the Nd:YAG Q-switched pulsed laser is generated and amplified at wavelength =1064 nm. Then is down-converted to 532 nm by second harmonics generation (SHG).
The laser pulse output is triggered by an upstream master signal. A laser power attenuator composed of two highly reflective mirrors and beam dumps is inserted and ejected on a motorized stage
to switch between low power for diagnostics and alignment, and high power for interference scans.
Diagnostic devices monitor various properties e.g. laser timing, power, profile, before transport tothe vertical table at the IP. Figure 3.6 shows the photodiode and the PIN-photodiode which are used
for monitoring the laser’s total power and temporal profile, respectively. The power supply for thelaser is also inside the laser hut. The major components on the laser table are described in detailbelow:
4

Locating the laser hut outside the accelerator tunnel is convenient arrangement for checking on the condition of
the laser even during beam time as well as for preventing damage due to radiation

38

Figure 3.5: The schematic layout of the laser table inside the laser hut

Figure 3.6: The weakened light transmitted by a mirror enters a PIN-photodiode (hidden here undera cylinder carrying ND filters), which monitors the laser timing. Next to it is a photodiode whichmonitors the stability of total laser power.
3.2.1

Laser Cavity

This section describes the basic properties of the Nd:YAG Q-switched pulsed laser (Quanta-Ray
Pro-350, manufactured by Spectra Physics)[24] of the Shintake Monitor. Table 3.1 displays its
catalogue specifications. More details are found in Appendix A. Its pulse width is 3.4 ns (RMS), or
8 ns (FWHM), which is more than 100 times longer than the e bunch length of about 20 ps. The
laser temporal profile is approximately Gaussian (confirmable from Fig. 3.24). Precise beam size
39

measurements require the laser system to have high stability, good coherence, and the intensity togenerate suﬃcient Compton photons.
Figure 3.7 shows the laser source. The laser beam is initially generated from population inversion
in the Nd:YAG medium of the oscillator, then amplified in the resonator cavity. The cavity consistsof two mirrors which are coated to reflect photons of a particular wavelength while transmitting
others. One mirror (the “high reflector”) reflects all light back into the cavity, while the other mirror(the “output coupler”) is made to be semi-transparent as to transmit the energy stored in the cavity
as the output laser beam. In the amplifier section two pump chambers add energy to the laser beam.
mediumwavelength
peak energy
pulse width
repetition rateline widthtiming stabilityenergy stability

Nd:YAG
532 nm (SHG)
1.4 J
8 ns (FWHM)
6.24 Hz< 0.003 cm 1
< 0.5 ns
±3 %Table 3.1: The basic design parameters of the Pro-350 Nd:YAG pulsed laser of the Shintake Monitor.

Figure 3.7: (top) The optical components in the laser cavity [23]. (bottom) A photo of the laser
cavity.

40

Q-switching
The Q-switch (Fig. 3.7) is an electro-optic device used for realizing laser emission with short pulse
width and high peak intensity. It comprises of a polarizer, a quarter wave ( /4) plate, and a Pockels
Cell. It allows the abrupt switching between a high loss state in the resonator, during which energy
stores up, and a low loss state during which oscillation occurs and energy is released from the cavity
as light output. The details of Q-switch mechanism are as follows:
1. Initially the Q-switch is set to a low Q state. Here, no voltage is applied to the Pockels cell
crystal, thus it does not aﬀect the polarization of the light passing through it. The lightentering the Q-switch is first horizontally polarized by the polarizer, then converted to circularpolarization by the /4 plate. After the circular polarized light is reflected back from the highreflector (rear mirror), it is converted to vertical polarization by the /4 plate and remains thatway as it passes through the zero voltage Pockels cell crystal. Because the polarizer transmits
only horizontal polarized light, light is reflected out of the resonator. In this way, the cavity
is kept at a high loss state, thus light feedback is prevented.
2. During Q-switched operation, the flash lamp excites the Nd ions (= pumping) for approximately 200 µs to build up a large population inversion. Here, excitation of the laser crystal
energy levels takes place. At the instant of maximum population inversion, a fast and highvoltage pulse is applied to the Pockels cell which switches from a high loss to a low loss state in
the cavity. When voltage is applied to the Pockels cell, it cancels the polarization retardationby the /4 plate, thus allowing the light to remain horizontally polarized and be transmitted by
the polarizer. This sudden switching to a low loss state leads to abrupt increase in oscillation of
the light released during the de-excitation of the laser crystal energy levels. The cavity releases
the large amount of energy stored up within the resonator during the excitation process all at
once in the form of very short and high peak intensity laser light pulses. This amplified light
output induced by stimulated emission is coupled out through the “output coupler” mirror.
Injection Seed laser
An injection seeding laser (Model 6350 manufactured by Spectra Physics)[24] is used for achieving
oscillation in a single longitudinal mode. For unseeded Q-switch operation, spontaneous noise emission is oscillated in multiple longitudinal modes. For seeded Q-switch operation, a small amountof single-frequency seed laser light is directed on-axis into the host cavity. Because the intensity ofthe seed laser is higher than that of spontaneous emission by more than 6 orders of magnitude, theQ-switch pulse builds up much faster around the seed light. As a result, the amplification of spontaneous emission is inhibited, and a single frequency light output is achieved. The use of injection
seeding reduces the line width by a factor greater than 300, from about 1.03 cm 1 to 0.003 cm 1 .
This enables the smooth temporal coherence required for high quality interference fringes.
One measure of the stability of a Q-switched laser is the “buildup time”, defined as the interval
between the Q-switch opening and the laser pulse output. For unseeded operation, the buildup timecorresponds to the time taken by the weak spontaneous emission light to make many round trips
in the oscillator to be amplified up to the intensity of saturation flunk level. For seeded operation,buildup timing is much reduced, as shown in Fig. 3.8.
The stability of the laser output depends on the control of the frequency locking of the host laser
to the seed laser. This is done by minimizing the buildup timing. Frequency is directly linked to thelength of the host cavity i.e. the distance between its two mirrors. The position of the high reflector
is tuned using a feed back loop based on a piezoelectric frequency tuning element (FTE). For eachlaser pulse, a small oﬀset voltage (“buildup voltage”) is applied to the FTE to enable it to provide
the mechanical mirror position translation for fast frequency correction. The relationship between
41

buildup timing and voltage is 0.05 V/ns. Frequency and energy instabilities translates to jitters in
Q-switch buildup timing. Therefore, the buildup voltage is read out as a means to monitor buildup
timing stability (Fig. 3.9), especially when adjusting the delay of the laser timing triggers.
Laser tuning is conducted regularly by an engineer from Spectra Physics. In practice, the seedlaser is tuned to optimize temporal coherence while monitoring the buildup timing and the temporalprofile measured by a PIN photodiode. The laser profile is tuned by coarse adjustments of the screwsof the rear mirrors by hand, which changes the angle of the laser passing through the components
in the cavity.
The feedback correction of the cavity length also compensates for the eﬀects due to temperaturechanges. Both the seed laser and the main laser are sensitive to temperature. Some potential eﬀects
are the changes in the optical length of the laser cavity due to thermal expansion of the support
structure, and temperature changes in the laser rods. The stabilization of environmental temperatureand the temperature of the internal cooling water supply are important. The laser system is also
sensitive to mechanical vibration transmitted through the support structure, the cooling water andits hoses.
The laser table containing the main cavity and seed laser is kept in a laser hut whose temperature
is maintained stable at all times. The location of the laser power source (Fig. 3.10), which also
carries the cooling water tank, is selected to minimize the eﬀect of vibration from surrounding
devices. Thermocouple wire sensors are strung in various locations around the system, and theirreadout values are logged to monitor temperature stability[29]. Figure 3.11 shows the temperaturemonitored at various locations in the laser optics. Table 3.2 lists the representative temperature
values in June 2014. The temperature of the laser hut is maintained stable using a control unit
located immediately outside the hut walls (Fig. 3.10 right). It can be seen that the temperaturein the laser box, where stability is most important, remains almost constant between the diﬀerent
months. There are very slight variations of 1-2 deg for the other locations aﬀected by ambient
temperature.
Second Harmonics Generator
The wavelength ( ) of the light output from the cavity is changed by the second harmonics generator(SHG) from the primary Nd:YAG of 1064 nm to 532 nm. The shorter is required for producing
the narrower laser fringe pitches required for measuring smaller beam sizes. The crystals in the SHG
are arranged in a particular sequence and orientation to generate the second harmonics. A mirror
directs the = 532 nm light to the Beamlok (see below) for stabilization while transmits the residual= 1064 nm light to a beam dump.
Beamlok
The Beamlok system is an optional component installed into the laser system for the purpose ofstabilizing the pointing jitter of the laser beam. It consists of a pointing sensor and a control mirror.
The pointing sensor detects the deviation of the laser beam position at the far field (the laser beamis reflected many times and transferred about 20 m). Then it provides feedback to the control
mirror, which is moved by a piezoelectric element to stabilize the position of the output laser beam.
From catalog specifications, pointing stability is smaller than ±50 µrad and smaller than ±25 µrad
without and with the Beamlok system, respectively[24].

42Figure 3.8: The reduction in Q-switch buildup timing as a result of using seeded operation.[24]Figure 3.9: The distribution of buildup voltage monitored during a single fringe scan (about 2
minutes) in June, 2014.

43

Figure 3.10: (left) The tank containing the power source of the Shintake Monitor laser and thecooling water circulation system. (center) The control panel for the laser oscillation. (right) Goingfrom left to right, the temperature control unit for the laser hut, the nitrogen gas tank with valves
to control gas pressure, and the tank for external cooling waterlocationlaser box (bottom)
above laser box (inside plastic curtains)
DAQ room (just outside laser hut)laser transport line
vertical tableinternal cooling water (supply)internal cooling water (return after circulation)

temperature [o C]
25.4
21.4 ± 0.1
23.0 ± 0.1
25 - 27
26.7
29.9
32.5

Table 3.2: The temperature measured using thermocouple sensors at various locations in the laser
optics for a single scan on June 12, 2014.

44

Figure 3.11: The temperature measured by thermocouple sensors during a single fringe scan in April,May, and June of 2014 (vertical axis). The horizontal axis is time during the scan. For some, thered line (June) is overlapped i.e. hidden by the blue line (May).
(top left) Inside of the laser box containing the cavity. (top right) The laser hut.
(middle left) The temperature control unit which works to stablize the temperature of the adjacentlaser hut. (middle right) The vertical table.
(bottom left) The internal cooling water supply. (bottom right) The internal cooling water returning
to the tank after circulating through the system.
3.2.2

Attenuator

For the protection of human and diagnostic components during alignment, laser power needs to beattenuated while still maintaining laser path accuracy. An “attenuator” composed of two dumps andtwo highly reflective mirrors is inserted and ejected on a motor stage to switch between low power
for alignment and high power for fringe scans. For the “inserted” state, nearly all of the laser power
is directed into dumps by mirrors with reflectivity close to 100%. The laser beam is reflected twotimes and the laser beam is weakened by a factor of R2 (R : mirror reflectivity > 99.5%). Figure 3.12
shows the schematics and photo of the attenuator, as well as the propagation of the laser emerging
from the source until the attenuator.

45

The two mirrors are placed in opposite directions in order to cancel the position shift of the transmitted laser beam. This position shift ( x ) at the vertical table about 20q
m downstream is estimatedfrom the parallelism of the mirrors (. 5 [arcsec]) to be
140µm. This x is suﬃciently small for alignment.

x  20m⇥

5 [arcsec]2 + 5 [arcsec]2 Figure 3.12: The attenuator, comprised of two highly reflective mirrors and beam dumps, is inserted
and ejected on the laser table to allow selection of high laser intensity for interference scans andlow intensity for alignment (modified from [25]). (left) The schematics of the attenuator (right) the
actual photo.

3.3

Vertical Table

Figures 3.13 and 3.14 show the upright standing main optical table, called the “vertical table”, wherecollision between the e beam and the laser interference fringes takes place5 . The transported laser
beam emerges from the bottom-right corner, looking from downstream of the IP (also see Fig. 3.2).
After the laser spot size is restored by the reducer, it propagates to a 50% beam splitter, called the“half mirror” (Fig. 3.15), into upper and lower paths. These are then focused at the IP by focal
lenses and cross to form the interference fringes inside the IP vacuum chamber. The reflectance ofthe half mirror is measured to be 50.3 % for the S-polarized light of the Shintake Monitor laser.
This is consistent with catalog specification.
The mirrors and focal lenses are made from optical glass BK7. The vacuum chamber windows
are made of quartz for radiation hardness, since they are not easy to replace 6 . The coating on the
mirror surfaces provide the appropriate reflectance of > 99%. The damage thresholds for the mirrors(10-20 J/cm2 @ =1064 nm and 10 ns pulse width) are confirmed to withstand the intensity densityof the laser pulses with =532 nm, total energy of about 0.56 J/pulse, pulse width 8 ns (FWHM)
and laser spot radius of about 3 mm downstream of the reducer. Appendix C provides the details
on damage thresholds. The weak light transmitted through the mirrors is used for diagnostics, suchas profile monitors and PIN-photodiodes.
The optical components are aligned using a green continuous wave (CW) Nd:YAG laser (CrystaLaser GCL-005-S, see Fig. 3.16) of = 532 nm, spot size 0.36 mm (diameter) and beam pointing
5

The vertical table is made of steel honeycomb and supported by a rigid frame to suppress vibration. It is been
confirmed to move synchronized with ground motion.
6
The mirrors, focal lenses, and vacuum windows are manufactured by Lattice Electro Optics. The model numbers
are: for the mirrors: RX-532-45S-B-2038, RX-532-22.5S-B-2038, and RX-532-37.5S-B-2038 for reflection angles 45
deg, 22.5 deg, and 37.5 deg, respectively; for the lenses: B-PX-100-250(300)-532 for focal length f = 250 (300) mm;
for the vacuum windows: WA2-UF-WP-130mmD⇥13mmT-532 (174 deg mode), WA2-UF-WP-40mmD⇥5mmT-532(30 deg mode), and WA2-UF-WP-60mmD⇥8mmT-532 (2-8 deg mode).

46

stability . 20 µrad. Its low output power of 5 mW guarantees safety during alignment. The pulse
laser cannot be used for component alignment because of its strong intensity and large spot size
(diameter ⇠ 5 mm).
The following sub-sections explain in detail the mechanisms for optical delay and crossing angle
adjustment.

Figure 3.13: An actual photo of the vertical table, looking from downstream of the IP.

47

M8U-x/y

M174U-x/yM3U

toPhase Monitor

PSD
check theinjection orbit

MI-5

CCD

MI-6

F174U
M30U-x/y
M1U

F30U

M2U
S-up

M2L

Delay

P8
F8

S-low

Half-mirror

M1L

F30L

M30L-x/y
F174L
PSD
check theinjection orbit

MI-3

MI-4
Polarizer

Reducer

Profile Monitor
CCD

MI-1

to
Phase Monitor

MI-2
M3L

M8L-x/y

M174L-x/yFigure 3.14: The layout of the main optical table, the “ vertical table” on which the laser interferometer is formed as a target for the e beam, including the schematics showing the propagation of
the laser beam: the CAD drawing by N. Terunuma[17] for the 174 deg mode path.

48

PSD
check theinjection orbit

Figure 3.15: (left) The half mirror on the vertical table which split the laser beam into upper andlower paths which cross at the IP to form the interference fringes against which the e beam collides.

Figure 3.16: The CW laser used for alignment on the vertical table.
3.3.1

Optical Delay Control

For the Shintake Monitor at ATF2, signal modulation is produced by scanning the phase of the laser
fringes against the e beam. This is carried out by an optical delay line (Fig. 3.17) installed into
the upper path consisting of two triangular prisms, one of which is mounted on a piezoelectric stage(P-752.1C, Physik Instrumente). By adjusting the distance between the prisms (d) using the piezo
stage, the phase between the two laser paths (↵) changes as:↵ = 2kd = 4⇡d/

(3.1)

Here, k = 2⇡ is laser wave number. Table 3.3 shows the basic specifications of the piezo stage.
Its DAC system has design position resolution of 0.2 nm (close loop) and O(10) ms position setting
time (response speed), which is suﬃcient for the ATF2 repetition rate of 3.12 Hz. These meet thedemands for controlling ↵ with a precision of a few mrad. The piezo stage position is monitored
by a inner capacitance sensor. The set and read voltages are recorded in a fringe scan data set
synchronized with the signal energy measurement.
The movement of the piezo stage was tested through measurement using a distance meter (Iwatsu.
ST-3541).

49

While the delay line was moved to scan the fringe phase (↵), the readout voltage of the piezo
stage was observed to rise in steps of 17 mV per ↵ step of 0.6 rad, and 45 mV per ↵ step of 1.5 rad.
From Eq. 3.1, since 1 rad correspond to 42 nm in optical path length, the derived relationship isapproximately 15 µm per input voltage of 10 V. Consistent results were reproduced over repeatedscans. This test confirms the linear relationship between voltage input and the scanned phase.
stage
controller
resolution
response time
conversion time
reproducibility
input voltage
travel range
load tolerance

Physik Instrument, P-752.21C
Oriental Motors, E-661K005
0.2 nm (closed loop)
O(10 ms)
16 µs maximum± 2 nm (full range)± 10 V
30 µm per ± 10 V of input voltage
30 N

Table 3.3: The specifications of the piezoelectric stage [26]Figure 3.17: [left] The schematics of the delay line for fringe phase scan installed into the upper
path. [right] A photo of the piezo stage. Also shown here is the half mirror located below the piezo
stage.
3.3.2

Laser Crossing Angle Adjustment

In order to measure a wide range of y , the laser optics is designed to switch between 3 types of
optical paths, referred to as “crossing angle (✓) modes”: 2-8 deg (continuously adjustable), 30 deg,and 174 deg. Figure 3.18 shows the optics layout for each mode. Precise and eﬀective interchanging
between ✓ modes in accordance to the target y is extremely important for beam tuning. Modeswitching is carried out via remote PC control of compact linear stages carrying mirrors. Since there
is no need to divide up the laser power into more than pre-determined laser modes, this method
retains the full laser power of each of the two paths and thus contributes to a higher S/N ratio.
Continuous mechanical adjustment between 2-8 deg is made possible by a linear stage carrying a
prism (Fig. 3.19), whose position is changed continuously. This is desirable because it allows more
freedom in the tuning of large y , explained as follows: Measurement resolution depends on the50⇡ cos(✓/2)⇡
fringe pitch d = k sin(✓/2), which changes more abruptly as ✓ gets smaller ( * @d@✓ = 2k sin2 (✓/2) ).
The relationship between ✓, the focal length of the 2-8 deg lens (f =250 mm), and the distance (h)between the two paths on the prism is 7 :✓ ◆h✓ = 2 arctan
(3.2)
2f

The mirrors (Fig. 3.20) on the linear stages are also responsible for extremely precise alignmentof laser paths. The angles of the mirrors are steered by a pair of rotating actuators (Thorlab Optics,
ZST13) that move in X and Y controlled by stepping motors with 10 nm resolution. This allows
mirror angles to be controlled within O (1) mrad precision. The mirror angle changes as :( d ⌧ D)= 2 d/D(3.3)

d is the change in actuator length. D (=61.9 mm) is the distance from the actuator to themirror rotation axis i.e. the kinematic mount support. The resulting shift in laser position at the
IP ( xIP ) is:xIP = f
= (2f /D) d(3.4)
Equation 3.4 can be rewritten as xIP = C d. The table below summarizes the scaling factor
C is for each ✓ mode: C = 8.08 for the 2-8 deg and 174 deg modes, and by C = 9.7 for the 30 deg
mode. This scaling relationship is applied when calculating xIP from the actuator movement d,
as well as when estimating the laser spot size from the measured sigma of a laser wire scan, wherea single laser path w.r.t. the e beam at the IP using the X actuator (see Sections 2.4 and 4.2.1).
mode: ✓ [deg]2-8, 17430C=7xIP / d8.08
9.7

The theoretical calculation for ✓ assumes parallel propagation from the prism to the focal lens. The realistic laser
beam may have a slight divergence. Although prism is also set via remote PC control, we sometimes confirm theprecision in ✓ by measuring by hand the distance between laser spots on the final lens . The ±1mm precision of thismeasurement correspond to error of ✓/✓ ~ 10 %.

51

Figure 3.18: The optical path (in green) for each crossing angle mode. From top to bottom: 174
deg mode, 30 deg mode, 2-8 deg mode.

52

Figure 3.19: (top) The schematics of the prism stage for continuous mode adjusting between 2 and8 degrees.
(bottom) The area of the vertical table surrounding the prism (circled in red). Also shown here are
the delay line, the laser shutters for the upper and lower paths, and part of the focal lenses.

53

Figure 3.20: (top) One of the mirrors in the Shintake Monitor optics mounted on an linear motorizedstage that is slid in and out during mode switching. Mirrors have actuators attached to them for
precise adjustment of laser beam position and angle. (bottom) The schematics of adjusting the laser
position at IP by rotating the mirrors using actuators [22]3.4

Laser Timing System

3.4.1

Q-switch Timing and Laser Pulse Output

Figure 3.21 shows the logic diagram of the laser timing system. The laser output timing is determinedby inputting a properly delayed trigger signal into the Q-switch. The timing trigger inputs for thee beam and for the pulse laser are generated and adjusted using digital modules called event
generators “EVG” and event receivers “EVR” (Micro-Research Finland Oy; VME-EVG-230 and
54

VME-EVR-230RF). Because the trigger signals for the e beam and the laser are made from acommon upstream master signal generated by a synthesizer, they are synchronized with each other.
In Fig. 3.21, the “LAMP” and “Q-SW” represent the start of flash lamp excitation and Q-switch,
respectively. These are made to be 6.25 Hz to match the laser repetition rate. “BEAM” represents
the trigger signal for the e beam timing. The frequency of “BEAM” is halved from the laser trigger
to 3.12 Hz. The EVRs are scanned in sub-ns steps in order to carry out the fine timing delay
adjustment for the following purposes:
1. optimize the proper relative delay between laser timing and escattering.

beam timing for Compton

2. optimize the timing interval between “LAMP” and “Q-SW” in order to achieve stability of thebuildup timing, which directly aﬀects the stability of laser output timing and power.
Figure 3.22 shows the timing relationship between flash lamp trigger, flash lamp light pulse, Qswitch trigger, and laser light output. The flash lamp creates a laser light pulse after it receives a
TTL level input signal. If the Q-Switch is triggered within the proper delay from flash lamp trigger((Q-SW)- (LAMP) interval ⇠ 180 µs), maximum laser power is extracted 100 ns later. This process
is important for achieving high Compton signal intensity. Occasionally e.g. after laser oscillator
tuning, the flashing interval needs to be re-optimized by adjusting the EVR while monitoring thebuildup timing. The distribution of buildup voltage was shown in Fig. 3.8.

Figure 3.21: The schematic layout of the timing control system. The trigger signals for the e beamtiming and laser oscillation timing are generated and controlled using event generators (EVGs) andevent receivers (EVRs). The trigger signals are made from a common upstream master signals, thus
are synchronized with each other. “BEAM” represents the trigger signal for the e beam timing.
“LAMP” and “Q-SW” represent the start of flash lamp and Q-switch, respectively. The EVRs arescanned in sub-ns steps in order to precisely adjust the relative timing between the laser and the ebeam, as well as for the timing interval between “LAMP” and “Q-SW”.[17]55Figure 3.22: The timing relationship between flash lamp trigger, flash lamp light pulse output, Qswitch trigger, and laser light output. The flash lamp creates a laser light pulse after it receives a
TTL level input signal. If the Q-Switch is triggered within the proper delay from flash lamp trigger(⇠ 180 µs), maximum laser power can be extracted another 100 ns later.
3.4.2

Monitoring of Relative TimingThis section describes the process for monitoring and adjusting the relative timing between the laser
and the e beam. More details are found in Sec. 4.2.5.
Laser timing is monitored by fast response Si:PIN photodiodes (PIN-PD) (see Fig. 3.6). A
PIN-PD is a semiconductor photodiode with an insulator “i-layer” sandwiched between the P layer
and N layer of a typical PN junction diode. When incident light hits the deletion layer, which isalso the sensitive area, charge carriers are generated. An inverse bias voltage is applied to the diodeeﬀectively widens the depletion layer. The resulting reduction in the junction capacitance increases
the bandwidth i.e. enables faster response. The PIN-PD for the Shintake Monitor optics (Thorlab,
DET025A) has a fast rise time and fall time of 150 ps each, and a frequency bandwidth of 2 GHz.
There is one PIN-PD for each of the laser table and the vertical table.
The electron beam timing is monitored using the signal taken from an electrode extending froma stripline BPM into the beam pipe. As the beam pass through the beam pipe, output signals withshort rise times are triggered in the electrode.
Figure 3.23 shows the PIN-PD and the stripline BPM located next to an upstream quadrupole
magnet.
Fluctuation in relative timing leads to Compton signal energy jitters in fringe scans (see Sec.
7.1.4). Timing jitter is generally suppressed to .1 ns (from observing the PIN-PD waveform), which
contributes < 5% to Compton signal energy jitters. However there are also much finer zig-zagged
56

structures with a time scale of O(10) ps which may cause pulse by pulse fluctuations in the laser
intensity colliding with the e beam.
First, in order to trigger initial collision between the laser pulses and the e beam, their timing
signals are matched with O(ns) precision while observing the signals from a PIN-PD and a stripline
BPM electrode using an oscilloscope (see Fig. 3.24). Next, fine sub-ns timing adjustment is conducted in order to maximize Compton signal intensity and minimize the signal jitters due to timing
jitters. This is done by scanning the EVR delay setting in steps of 0.4 ns while colliding one of thelaser paths with the e beam. The LAMP delay is also scanned to optimize the interval between
LAMP and Q-SW for stable buildup voltage.

Figure 3.23: (left) The PIN-PD (Thorlab, DET025A) which is used for measuring the timing of thelaser. (right) The stripline BPM next to an upstream quadrupole magnet, whose signal is used formonitoring e beam timing.

Figure 3.24: Relative timing of the laser and the beam observed on an oscilloscope. Red shows thebeam timing (BPM), green shows the laser hut PIN-PD. Blue shows the vertical table PIN-PD.
The PIN-PD waveform corresponding to Laser ON timing is shown to the left, while those for Laser
OFF timing is shown to the right, 40 ns ahead. The distance between the peaks of each waveform
indicate the appropriate relative timing delay between the beam and the laser at the time (Phototaken by N.Terunuma[17]).

57

3.5

Detector

3.5.1

Detector Layout

The Shintake Monitor uses a calorimeter-type detector to measure the total energy of photons from
Compton scattering. Figure 3.25 shows the beam line components surrounding the detector positioned 6.2 m downstream of the IP. The energy deposit from the electromagnetic showers triggeredby the incident photons is transformed into scintillation light in layers of CsI(Tl) scintillators, whichthen enters photomultiplier tubes (PMTs) coupled to the scintillators to be processed. Tables 3.4 and3.5 list the basic specifications of the scintillators and the PMTs (Hamamatsu Photonics, R7400U),
respectively.
Figure 3.26 shows the structure of the detector. The transverse dimension is (100 mm ⇥50 mm).
The longitudinal length is 330 mm, which is about 17.7 times of the CsI(Tl) radiation length of 18.6
mm. It is composed of five layers of scintillators: the front four layers are each 10 mm thick. The
fifth “bulk layer” is 290 mm thick and is divided into three transverse sections. Doping CsI with Tl
increases light output. However, CsI(Tl) is slightly hygroscopic (as opposed to pure CsI), therefore
the scintillators are enclosed in Al housing purged with nitrogen gas for protection. The housing
walls are 10 mm thick, with the exception of the front surface through which photons enter, which
is only 1 mm thick to minimize energy loss. Each layer is wrapped with fluorocarbon polymer sheet
and alumimylar to prevent optical cross talk and improve light collectivity.
Figure 3.27 shows the naming of the PMTs (12 in all) which are coupled to the scintillators
through cylindrical light guides. Two PMTs (left and right) are attached to each of the front four
layers. For the fifth layer, two are attached to the large center section, and one to each of theside sections. The compactness of the PMTs (50 mm long, 8 mm ) is favorable for attaching to
the thin scintillators and for fitting into the tight space among the collimator blocks. The PMTs
operate under positive HV applied to their anodes, while their photocathode surfaces are grounded
to prevent electrical discharge due to direct contact with the Al housing.

Figure 3.25: The layout of the beam line components surrounding the Shintake Monitor gamma-ray
detector. [22]58Figure 3.26: The structure of the Shintake Monitor gamma-ray detector. [25]Figure 3.27: (left) The photo of one of the PMTs of the detector[25] (right) The naming andarrangement of the 12 PMTs coupled to the left and right of each scintillator.

59

density
radiation length
photon emission
decay constantreflective index
photon wavelength at max. intensity

4.51 g/cm2
1.86 cm
59000 / MeV
1 µs
1.79
565 nmTable 3.4: Basic specifications of the CsI(Tl) scintillators of the Shintake Monitor gamma-ray detector.
dynodephotocathodeouter / eﬀective diameter
length (PMT + socket)
nominal gain
max. / standard voltage
rise timeelectron transit time
spectral range
dark current (after 30 min.)quantum eﬃciency

metal channel, 8 stages
Bialkali
16 / 8 mm
50 mm
7⇥105 at 800 V
1000 / 800 V
0.78 ns (typical)
5.4 ns (typical)
300-650 nm
0.2 nA (typical)
25% (at 420 nm)

Table 3.5: Basic specifications of the Hamamatsu Photonics (R7400U) PMTs of the Shintake Monitor
gamma detector [27].
3.5.2

Separation of Signal and Background

The multi-layer detector design had originally been intended for separating signal and BG by taking
advantage of the significant diﬀerence in their shower development with energy[28]. The mean energyof a single photon is inferred from simulation to be about 15 MeV for Compton signal, and about 50
MeV for BG (see Table 3.6)[22]. Analysis methods were developed accordingly for optimizing S/Nratio and the tolerance for BG fluctuation.
The incident photon energy is estimated by measuring the energy deposit in the scintillators.
Figure 3.28 shows the longitudinal distribution of energy deposit in the detector for signal and BG
photons, generated by GEANT4 simulation[22]. Higher energy photons deposit more energy in the
deeper layers because the depth of electromagnetic shower maximum is logarithmly proportional toenergy. The shower development of signal photons is concentrated to the front layers, peaking inthe second layer. About half of the total energy deposit is in the front four layers. In contrast, most(⇠80%) of the BG energy is deposited into the thick fifth layer. The suﬃciently large number ofincident Compton photons (O(100) per bunch) maintains the statistical fluctuation of shower shape
to a negligible level.
BG from Bremsstrahlung
The majority of BG comes from bremsstrahlung photons emitted due to the collision of the beam
halo with the beam pipe. The beam pipe wall is more than a few sigmas away from the beam halo.
However, in order to focus to a tight waist at IP, the beam size is first abruptly defocused immediately
before the FD. In particular, the expansion of x to as large as 3 mm before entering QF1 enhances
the interaction between the beam halo and the beam pipe at that location. Figure 3.29 shows the60energy spectrum of bremsstrahlung BG photons, from the simulation of interaction between the
beam and the beam pipe at the FD. Plotted together is the energy spectrum of Compton signal
photons calculated in Sec. 2.6. The energy distribution of signal photons show a sharp “Comptonedge” (around 30 MeV for ATF), while the BG energy distribution has a tail extending up to thee beam energy (1.3 GeV for ATF).
Another major source of bremsstrahlung BG photons is the post-IP dipole magnet for bending
the e beam into its dump (see Fig. 3.30).

Figure 3.28: (top) The distribution of energy deposit per unit distance per photon in each scintilator
layers for Compton signal and bremsstrahlung BG, from GEANT4 simulation[22]. The amount of
BG is input according to the status in 2010 operation, for which the S/N ratio of .1 is lower than
1/25 of that in 2014.
(bottom) From the GEANT4 simulation results [22]: the ratio of energy deposit in each detector
layer (1, 2, 3, 4, 5) is (0.093, 0.139, 0.125, 0.107, 0.535) for Compton signal photons (left), and(0.021, 0.045, 0.061, 0.071, 0.802) for bremsstrahlung BG photons (right).

61

Figure 3.29: The energy spectrum of bremsstrahlung BG photons (blue) from the simulation ofinteraction between the beam and the beam pipe at the FD[22]. Plotted together is the energy
spectrum of Compton signal photons (red) calculated in Sec. 2.6.

signalbackgroundaverage [MeV]
14.7
53.0

RMS [MeV]
9.3
14.7

Table 3.6: The average and RMS of the energy of signal and BG photons from simulation[22]Slow Neutron BG
Most of the hadrons produced in the post-IP beam dump (about 50 cm to one side of the detector)
are absorbed by the dump itself. However, some neutrons, being long-lived and neutral, leak out
and deposit energy in the detector. Paraﬃn absorber plates are inserted between the dump andthe detector to block these neutrons (see Fig. 3.30). The high H atom content (close to neutron
in mass) in the inexpensive paraﬃn eﬀectively absorbs the neutrons’ kinetic energy through elastic
scattering. Since BG neutrons are slower than signal photons, they can also be separated by adjusting
the detector’s ADC gate timing. The “slow BG” was confirmed to be indeed neutrons by observing
the change in signal on an oscilloscope when the paraﬃn plates were inserted and removed.
Negligible BG Sources
Some minor sources of BG photons are synchrotron radiation when the beam passes the FD and thebremsstrahlung from scattering with the residual gas in the vacuum pipe.
The critical energy for synchrotron radiation is about EC,SR [keV] = 0.665 (E [GeV])2 B [T]. Thisis about 1.1 keV for the beam energy (E⇠1.3 GeV) and the FD magnet field (B⇠1 T) at ATF2.
Thus the energy loss due to synchrotron radiation is at the most a few keV. This is more than threeorders of magnitude smaller than the average signal energy of about 15 MeV. Almost all SR photons
should lose their energies inside the ATF2 beam pipe which is made from stainless steel (SUS304)
of thickness 1.6 mm. Therefore, BG from synchrotron radiation is negligible.
The vacuum inside the FFS beam pipe at ATF2 has been measured to be better than 10 6 Pa
8 . The cross section for the production of bremssstrahlung photons > 1 eV due to residual gas
8

The IP beam chamber has a larger volume per length, thus the vacuum in the beam pipe at IP should be evenbetter than this value.

62scattering is gas < 1.5 ⇥ 10 23 cm 2 . From these, the estimated density of residual gas particles isngas < 2.7 ⇥ 1010 /cm3 . Assuming a beam bunch charge of Ne ⇠ 109 , the number of bremsstrahlung
BG photons due to residual gas scattering produced after traveling L=50 m through the beam pipe
is estimated to be N gas ⇠ gas ngas Ne L < 2/bunch. Since average energy is about 15 MeV and
53 MeV for signal and BG photons, respectively, this correspond to .1 % in energy for every 1000
signal photons, and is thus negligible.

Figure 3.30: The area surrounding the “Gamma Detector” in Fig. 3.25:(top left) The Pb blocks to cut breamstrahlung BG photons and parafine shielding (in white) placedaround the detector to cut BG neutrons backscattered from the beam dump.
(top right) The CsI(Tl) gamma detector (upstream) and the BG monitor (downstream) shown sitting
amid the Pb blocks after the top of the shielding has been removed.
(bottom) The close up view of the CsI(Tl) detector (left) and the BG monitor (right).
3.5.3

Collimation

There are in general three types of collimators installed in the beam line between the IP and the
Shintake Monitor gamma-ray detector sitting 6.2 m downstream of the IP (see Fig. 3.31):
63

1. To cut the bremsstrahlung BG generated at the FD, there are two types of lead collimators
installed; a collimator of 20 mm aperture fixed at just 340 mm upstream of the detector,
and a movable collimator of 10 mm aperture is installed further upstream at about 3200 mm
from the detector, immediately after the exit of the final bending magnet.
2. To cut the bremsstrahlung BG generated at the post-IP dipole magnet, an intermediate collimator was installed into the beam chamber there in summer 2012[29]. This significantly
reduced the amount of BG photons and increased the S/N ratio in fringe scans.
The position of the movable collimator in 2. is scanned using a movable stage (Sigma Koki, SGSP26100(X)) during beam time with the purpose of optimizing signal acceptance in accordance with slightshifts in signal photon path which result from e beam orbit tuning. More on “collimator scans” arefound in Sec. 4.2.4. The relative position between the movable collimator and fixed collimator iscalibrated using an alignment laser. The table below lists their aperture, distance, and polar angle
acceptance when looking from the IP.

distance from IP
aperture (radius)polar angle acceptance9

movable collimator⇠ 3000 mm
5 mm
1.67 mrad

fixed collimator
5860 mm
10 mm
1.71 mrad

Assuming perfect alignment w.r.t. the center of the signal photon distribution, the aperture of
the entire collimator system yield a signal acceptance of 94% for the number of photons and > 99%
for signal energy. Because the bremsstrahlung BG photons generated at the FD propagate nearlyparallel to the signal photons projected from the IP, it is diﬃcult to collimate a suﬃcient amountof BG while still maintaining signal acceptance. Thus bremsstrahlung photons remain the major
source of BG in the detector. This is compensated by separating signal from BG in analysis.
The detector is surrounded by additional Pb blocks to reduce any residual BG photons. Also
inside this barrier is the BG monitor (see Sec. 1.6.2) about 10 cm upstream of the main detector.
The BG monitor is inserted on a mover to measure the energy of bremsstrahlung photons for theIP wire scanner, and is removed afterwards.

64Figure 3.31: (top left) A photo of the beam line leading up to the CsI(Tl) gamma-ray detector.
(top right) The movable collimator scanned during beam time to maximize signal. It has 10 mm
aperture and dimension of (50 mm ⇥ 50 mm ⇥ 200 mm).
(middle) The schematics of the movable collimator which is scanned to maximize the amount ofsignal passing to the gamma-ray detector.[30](bottom) The schematics of BG photons generated at the final bending dipole, and the “intermediate
collimator” inserted into the beam pipe to cut this BG (modified from [31]).
3.5.4

Methods for Analysis and Signal Digitization

The measured Compton signal energy is analyzed using the “ON/OFF” method. The energy of “ONevents” (EON ) are measured with collision between laser and e beam. The energy of “OFF events”(EOF F = BG energy) are measured without collision by shifting the laser trigger timing away by
about 40 ns. The total signal energy is calculated as Esig = EON EOF F . At each fringe scan phase,65

1 OFF event is measured, followed by subsequent “Nav ” pulses of ON events. The energy deposit
for the i-th detector layer is defined as the average of the left and right PMTs : Ei = (EiL + EiR ) /2
(i = 1-4) 10 . Typically, the sum of ADC counts in only the front 4 layers is used in analysis. This
custom is meant for accommodating any S/N ratios since under high BG circumstances, the last
bulk layer is dominated by BG 11 .
In the past, another more sophisticated analysis method called the “shot by shot method” hadbeen used. This had been developed in accordance to the multi-layer design of the detector. The
information of all layers are used, and BG is separated from signal shot by shot by fitting their
shower shapes. Compared to the “ON-OFF” method, the “shot-by-shot” method has the merit ofbeing more robust against BG fluctuation; however there are more ambiguities and complexities,
such as systematic errors due to unexpected changes in the shower shape of BG photons due tobeam angular jitter. Thus the “ON-OFF” method became the recent choice for analysis. The detailsof both methods are found in [22][32].
The detector signals are digitized using a charge sensitive ADC (Hoshin, v005), shown in Fig.
3.32. In order to suppress the eﬀect of e beam intensity jitters, the measured energy is normalized
by the beam bunch charge (Ne ) measured using an “integrated current transformer (ICT) monitor”.
An ICT monitor consists of cables wrapped around a toroid ferrite core (Fig. 3.34). The variationin the magnetic field induced by the beam pulse passing through the core results in a voltage output
signal directly proportional to Ne . The beam current of multiple pulses is integrated over about 70
ns, and bunch charge is measured as the area under the signal pulse. The signals are then amplified
and digitized by the charge sensitive ADC (RPV-171), whose gate signal is synchronized with thatfor the ADC measuring energy. Figures 3.32 and 3.33 show the schematics of DAQ (inputs of signal
and gate triggers) of the ADCs. Table 3.7 shows the ADC specifications.
10
In recent operation, an equal weighting is applied to all PMTs. This should not cause a significant miscalibrationeﬀect since the measured PMT gains are not very diﬀerent[25].
11
The S/N ratio was improved from < 5 before 2014 to > 50 due to improvements in beam tuning and collimation.
The custom of using only the front 4 layers has continued. Some alternative methods are to use the ADC counts fromall 5 layers, or to use the 2nd layer only, as it has the highest S/N ratio. It has been confirmed that the fitted beam
size is consistent within the fitting errors regardless of which method is used. It has also been confirmed that there isless than 1 % additional statistical fluctuation due to sampling from only the front 4 layers as opposed to using all 5
layers.

66

Figure 3.32: (left) The two charge sensitive ADCs (v005) for the gamma-ray detector. (right) Input
of PMT output signal and gate trigger signals into the ADC. “Ref” is a reference PMT for calibration.

Figure 3.33: The schematics of gate trigger signal input into the ADC v005 for digitizing Compton
photon energy measured by the gamma-ray detector and the ADC RPV-171 for digitizing beam
intensity measured by the ICT monitor. The trigger signals for laser timing are shown together
here.

67

Figure 3.34: The schematics of an ICT monitor used for measuring e beam intensity at ATF2[22].

product
no. of channels
full range
resolution
gate widthv005, Hoshin
80-1000 pC
14 bit30 - 1000 ns

product
no.of channels
full range
resolution
gate width

RPV-171, Repic Corporation
16
0-1000 pC
12 bit100 - 1000 ns

Table 3.7: Basic specifications for the charge sensitive ADCs (VME modules) of the Shintake Monitor: (left) v005 for the photon energy measured by the gamma-ray detector[33] (right) RPV-171 forthe beam intensity measured by the ICT monitor.

3.6

Estimation of Statistical Fluctuations

The gamma-ray detector measures the total energy of Compton signal photons bunch by bunch.
The statistical error of the measured energy depends on Compton photon statistics, collimation anddetector response.
3.6.1

Compton Photon Statistics

The number of Compton scattered photons Nsig entering the gamma detector is calculated as :Nsig = Ne · ⌃laser ·(3.5)

c · (collimator acceptance)

Ne is e beam bunch population. c is total Compton cross section (= 0.65 barns). ⌃laser is thesurface density of laser photons interacting with the beam, and is calculated as :⌃laser =Elaser(3.6)

2⇡"laser laser c t

Inserting the values of the relevant laser parameters in Table 3.8 gives ⌃laser = 1.7 ⇥ 1022 /m2 .
Since the e beam pulse (⇠20 ps) is much shorter than the laser pulse (3.4 ns), it is assumed tointeract with constant laser photon density.
1-photon energy"laser2.33 eVlaser pulse energy
Elaser
0.41 J 12

laser spot size
laser

10 µm

laser pulse width (RMS)t

3.4 nsTable 3.8: The realistic values of the laser related parameters used in the calculation of Nsig

68

The collimators upstream of the detector are optimized as to cut as much BG as possible while
maximizing signal acceptance. Assuming perfect alignment w.r.t. the center of the Compton photon
trajectory, the signal angle acceptance of the collimation system is about 1.67 mrad based on thegeometry given in Sec. 3.5.3. From integration of the angular distribution in Fig. 2.8 (top right),
this corresponds to 94% of all photons.
Furthermore, the power loss during the transport from the laser source to the IP is estimated to
be about 57%. This assumes the reflectivity R⇠99% of each of the 20 mirrors, and the transmittance(T⇠90%) of each of the 5 lenses and the vacuum chamber viewport window 13 . In addition, because
there are multiple (2⇠3) non-Gaussian modes observed in the laser profile14 (see Sec. 5.2), it ispossible only 30-70% of the total laser energy contributes to the collision with the e beam.
From all of the above and Eq. 3.5, Nsig is calculated to be 100-350/bunch for the relatively
low Ne = 1.0⇥109 in recent ATF2 beam operation. From this, the statistical fluctuation due toCompton photon statistics (without detector eﬀects) is evaluated using simulation as follows:
0 photons from Compton scattering are generated according to a Poisson distribution with
1. Nsig
the mean changed in the range of 100-350.

2. Each photon is randomly assigned an energy from the energy distribution in Fig. 2.8 (top0 photons.
left). The sum is taken of the energy of the Nsig
3. The above is repeated for 10000 pseudo experiments. The relative energy fluctuation isevaluated as E/Emean , where Emean and E represent the mean and standard deviationof the 10000 events. Figure 3.35 shows a histogram for the case of Nsig =200, for which
E/Emean '7%. For the Nsig =100-350/bunch estimated above, the statistical fluctuation isestimated to be 5-10% .
13

The catalog R of the mirrors (Lattice Electro Optics) is >99%. The T of the lenses and vacuum windows (also
Lattice Electro Optics) take into account their thickness and the properties of their materials (BK7 and Fused Silica,
respectively). In addition, a margin is included for possible deviation from catalog specifications due to radiation
damage and/or dust on the component surfaces.
14
There are typically 2⇠3 high intensity spots, among which one spot has the apparently highest intensity. Before
fringe scans, the laser position is adjusted to allow the location with the highest intensity to collide with the e beam.

69

Figure 3.35: The sum of the energy of Nsig =200 Compton signal photons generated by simulation for
10000 pseudo experiments. Each photon is randomly assigned an energy from the energy distribution
in Fig. 2.8 (top left).
3.6.2

Detector Response

When a photon deposits an energy of E MeV into the detector scintillators, the number of photoelectrons emerging from the PMT photocathode is:
Npe = Nsig ⇥ E ⇥ "sci ⇥ "coll ⇥ Q.E.

(3.7)

Qout = Npe ⇥ (PMT gain) ⇥ e(3.8)

Here, "sci is scintillation eﬃciency. "coll is light collectivity between the scintillators and thePMTs, and Q.E. is PMT photocathode quantum eﬃciency. The final output charge from a PMT
and the corresponding ADC counts can be expressed as Eq. 3.8 and Eq. 3.9, respectively.

ADC = Qout ⇥ADCmaxQmax(3.9)

Here, e is the elementary charge = 1.6 ⇥10 19 [C]. Qmax and ADCmax are the maximum charge
and maximum ADC count of the charge sensitive ADC module (see Sec. 3.5.4) used for the detector.
The factors aﬀecting statistical fluctuation are estimated as follows:
The Npe emerging from the photocathode is estimated to be about 104 using Equations 3.8
and 3.9, the PMT gain of 4 ⇥ 104 for the typically applied HV of 500 V [27], ADC ⇠1000 (fromobservation), and Qmax = 1000 pCp
and ADCmax =214 (from ADC specifications). The contribution
to signal fluctuation, scaling as 1/ Npe , is > 1%.
In Sec. 3.6.1, the statistical error due to photon counting statistics i.e. the fluctuation of Nsig
was estimated to be 5-10%. However, from the GEANT4 simulation results in [22] about 10% of
the total Compton signal energy leaks out of the detector without being detected. Most of thisleakage is from the top and bottom of the detector, since the vertical dimension of 50 mm is not
suﬃciently long compared to the CsI(Tl) Moliere radius of 37.5 mm. Furthermore, from Fig. 3.28,
only about 50% of the total energy is deposited into the front four layers. Therefore only about7090%⇥50%=45% of the total incoming signal energy ends up as energy deposit to be used in the
typical analysis (see Sec. 3.5.4). When combined with shower development fluctuation, this detector
sampling eﬀect leads to statistical fluctuation, estimated as follows. From the GEANT4 simulationin [22], the mean and rms. of the energy deposit of a single photon in the first detector layer are
1.2 MeV and 3.2 MeV, respectively. WhenpNsig photons enter the detector, the resulting statisticalfluctuation is approximately 3.2 MeV ⇥ Nsig / (1.2 MeV ⇥ Nsig ). From the observation of thesignal in each PMT, the diﬀerence in fluctuation between the sum of the front four layers andthat in a single layer is generally < 15% 15 . When taking into account the correlation between
layers, the statistical fluctuation due to shower development fluctuation for a single layer can beconsidered a pessimistic evaluation for the sum of the front four layers: 27% and 14% for Nsig =100
and Nsig =350, respectively. Convoluting this with the fluctuation from photon counting statistics,
the total statistical fluctuation is estimated to be 15-28%.
3.6.3

Signal Acceptance

There are additional factors that may change the Nsig and photon energy (Esig ) reaching the detector. The two major factors are:
1. The angular jitter of the e beam directly leads to the angular jitter of Compton photons.
This causes shot by shot fluctuations in Esig .
2. The misalignment of the movable collimator reduces signal acceptance. This may occur if thecollimator is not re-optimized after unexpected changes in the e beam trajectory and thus
the signal photon path.
Regarding 1: the angular jitter of the e beam is generally about 30% of its divergence.
p Basedon recent ATF2 design parameters,qthe horizontal and vertical divergences are about "x / x⇤ =p
p
1.1 nm/40 mm ' 0.17 mrad and "y / y⇤ = 12 pm/0.1 mm ' 0.35 mrad, respectively. These

yield angular jitters of ( ✓ex , ✓ey )'(0.05 mrad, 0.1 mrad). The resulting shot by shot signal
fluctuation depends on the collimator alignment precision in 2.
Regarding 2: from experience, the movable collimator could be misaligned by as much as 2-3
mm. A misalignment of 2 mm in either X or Y could reduce Nsig by about 10% and Esig by about
1%, w.r.t. the case when photons pass exactly through the collimator centers.
Figure 3.36 (top left) shows the spatial distribution of Nsig generated from the angular distribution in Fig. 2.8 (top right). Figure 3.36 (top right) shows the distribution of Esig with each event
weighed by the distribution of Nsig , based on the angle-energy correlation of the scattered photons
in Fig. 2.8 (bottom).
A simulation was conducted to evaluate the eﬀect on signal acceptance (Nsig and Esig ) from the
combination of collimator oﬀset and beam angular jitter. The input conditions assume the actual
geometry of the collimator and the beam line, as well as the following:• The spatial projections in Fig. 3.36 (top).
• Collimator oﬀsets (X,Y) are changed in 1 mm steps over a range of 0-3 mm.
• Photon angular jitter with a Gaussian distribution whose sigmas are ( ✓ex , ✓ey ) ' (0.05 mrad,
0.1 mrad).
Figure 3.36 (bottom) shows the results of 1000 pseudo experiments in the form of Nsig /Nsig,0(Esig /Esig,0 ), defined as the ratio of the Nsig (Esig ) that made it past the collimators to the detector
15

The diﬀerence in signal fluctuation between diﬀerent detector layers is also generally < 15%.

71

w.r.t. total angular coverage. Table 3.9 lists the results for a few particular collimator oﬀset scenarios. A perfectly aligned collimator i.e. (X, Y)=(0, 0) yields Nsig /Nsig,0 =94.1% and Esig /Esig,0 =99.6%. For a pessimistic case of (X, Y)=(3 mm, 2 mm), Nsig and Esig are reduced to 87% and 95%
w.r.t. the case of no collimator oﬀset; this would increase statistical fluctuation by . 1% 16 .

Figure 3.36: [top] (left) The spatial distribution of Nsig generated from the angular distribution ofCompton scattering cross section in Fig. 2.8. The origin represents the photon path center. This
does not take into account beam angular jitter. (right) The distribution of the scattered photon
energy (Esig ) generated from the plot of angle vs energy in Fig. 2.8 (bottom). Each event is weighedby the distribution of Nsig .
[bottom] Simulation is carried out using the projections above. The inputs are: actual beam line
geometry, X and Y collimator oﬀsets in 1 mm steps over a range of 0-3 mm, and Gaussian distributed
photon angular jitter with the sigma being ( ✓ex , ✓ey ) '(0.05 mrad, 0.1 mrad). The plots show
the results of 1000 pseudo experiments in the form of Nsig /Nsig,0 and Esig /Esig,0 as a function of
X-Y collimator oﬀsets. Nsig (Esig ) is the number (energy) of signal photons that reach the detector.
Nsig,0 ( Esig,0 ) is the number (energy) of signal photons for total angle acceptance.
pThis assumes that the stochastic term in relative signal jitter scales approximately as 1/ Esig . In this case, theangular acceptance is reduced by as much as 1 mrad on one side. Although ✓ex 6= ✓ey , the distribution in Fig.
3.36 (top) is almost symmetrical between X and Y, since the eﬀect of angular jitter is small compared to that of thecollimator oﬀsets. In addition, when the Compton photon angular distribution is smeared with e beam divergence,the eﬀect on Esig is less than a few % even for a pessimistic case of collimator oﬀset.
16

72

X [mm]0
1
2
3

Y [mm]
0
1
2
2

Nsig /Nsig,0
94.1%
93.0%
88.4%
82.1%

Esig /Esig,0
99.6%
99.4%
98.1%
94.8%

Table 3.9: A few cases for the simulated plots in Fig. 3.36 (bottom).

73

4

Procedures of Beam Size Measurement

This chapter briefly describes the procedures of beam tuning and beam size measurement at ATF2.
Section 4.1 explains about the e beam orbit tuning both in the upstream sections of the beamline and at the IP. Section 4.2 describes the process of preparing the Shintake Monitor for use in IP
beam tuning.

4.1

Beam Tuning at ATF2

ATF2 beam tuning begins in the extraction line upstream of the FFS. First, the beam is steered intoa straight trajectory through the magnetic field centers of the beam line magnets using correction
dipole magnets and quadrupole magnets while referring to the beam position measured by BPMs.
Then dispersion incoming into the FFS is measured by changing the RF frequency in the DR,
and comparing the BPM orbit readings to energy. The dispersion is matched into the FFS using
two quadrupoles and two skew quadrupoles. In the diagnostic section, the multi-OTR (Optical
Transition Radiation) monitor system [34] provides fast shot-by-shot measurements of beam profile,emittance, and Twiss parameters 17 . Based on these, the FFS optics is adjusted to the measured
Twiss parameters using quadrupoles at the FFS entrance and x-y coupling is corrected using 4 skew
quadrupoles. All FFS magnets are placed on movers which allow their positions and roll angles inthe transverse plane to be changed by remote control.
The first-order correction for the errors at the IP e.g. horizontal and vertical waist oﬀset,
dispersion, and x-y coupling is performed by changing the field strength and rotation angles of
the FD quadrupoles. Figure 4.1 shows an example of a “QD0 scan”. This stage in tuning typicallyyields x⇤ ⇠ 10 µm and y⇤ . 3 µm, which are measured using carbon wire scanners.
Then more precise correction of residual linear aberrations is performed using the “linear tuning
knobs” (see Sec. 4.1.1) calculated as the horizontal and vertical motion of the FFS sextupole magnets.
The combination of sextupoles for each knob can be orthogonized i.e. chosen independently of eachother. Usually linear knob tuning is first done using beam size measurements by wire scanners, thenrepeated using measurements by the Shintake Monitor after y⇤ has been tuned down to . 2 µm.
In the final stage of beam tuning, higher order aberrations may be corrected using the “non-linear
knobs” (see Sec. 4.1.2), which are calculated as the combination of the strength of normal and skew
sextupoles. The alternate reiteration of linear knobs and non-linear knobs enabled y⇤ to be focused
to .40 nm in 2014 operation 18 . The descriptions of tuning knobs in this thesis are mainly basedon [12] and [35].
4.1.1

Linear Optics Tuning Knobs

The linear tuning knobs are calculated as orthogonal sets of the horizontal and vertical oﬀsets of
the FFS sextupoles. There are five sextupoles (SF6, SF, SD4, SF1 and SD0) in the ATF2 beam line
(similar to the ILC FFS) whose transverse positions can be scanned using magnet movers. The fieldpotential of magnets [36] can be represented in the form of Vn⇤ = Vn + iVsn , where the normal fieldcomponent Vn and the skew field component Vsn are expressed as:
Vn =

kn n
r cos n✓
n!

(4.1)

17
The Twiss parameters ↵i , i , i (i=x, y) describe the shape and orientation of the phase space ellipse for a single
particle. Their adjustments can be expressed by the transfer matrices of the particle trajectory for a particular beamline lattice. The Twiss parameters are related to emittance " as " = x2 + 2↵xx0 + x02 , where x and x0 are theposition and angle of a single particle, respectively.
18
In 2014, an “10⇥1” optics was used, for which x⇤ is increased to 40 mm, by a factor of 10 larger than the nominal
4 mm. The purpose was to reduce the eﬀect of the multipole errors of QF1.

74

ksn nr sin n✓(4.2)
n!
Here, n = 1, 2, 3 represent dipole, quadrupole, and sextupole, respectively. For example, fora normal quadrupole: V2 = k22 x2 y 2 ; for a skew quadrupole: Vs2 = ks2 xy; for a normal
sextupole: V3 = k63 x3 3xy 2 ; for a skew sextupole: Vs3 = k6s3 3x2 y y 3 .
For the case of a normal sextupole, a horizontal oﬀset x ! x + x changes the field potential
as:
Vsn =

V3 !

k3 h
(x +
6

x)3

3 (x +x) y 2i

k3 3
k3 x 2x3xy 2
xy 2 + O x2
62
The last term represents higher order dispersion eﬀects. A vertical oﬀset y ! y +the field potential as:
=

V3 !
=

k3 3
x
6

k3 h 3x
6

3x (y +y)2

(4.3)
y changesi

3xy 2 + k3 y · xy + O

y2

(4.4)

The second term in Eq. 4.3 can be rewritten as k22 x2 y 2 = k22 r2 cos 2✓. This indicates thatthe horizontal movement of a sextupole generates a quadrupole field whose strength k2 = k3 x
is proportional to the horizontal motion x. This changes the horizontal and vertical beam waist
positions (Wx and Wy ), the horizontal dispersion at the IP (⌘x ) and its derivative (⌘x0 ) w.r.t. thelongitudinal coordinate. The linear knobs AX, AY, EX, and EPX, calculated as orthogonal sets of
the horizontal oﬀsets, change Wx , Wy , ⌘x , and ⌘x0 , respectively.
Similarly, the second term in Eq. 4.4 can be rewritten as ks2 xy = k2s2 r2 sin ✓. This indicates thatthe vertical movement of a sextupole generates a skew quadrupole field whose strength ks2 = k3 y
is proportional to the vertical motion y. This changes the vertical dispersion at the IP (⌘y ), its
derivative (⌘y0 ), and coupling components between the x and y plane. The linear knobs EY, EPY,
and Coup2, calculated as orthogonal sets of the vertical oﬀsets, change ⌘y , and ⌘y0 , and x’-y coupling
respectively. The y at the IP is sensitive to Wy , ⌘y , and x’-y coupling. Therefore linear knob tuning
typically comprises of the knobs AY, EY, and Coup2. Their contribution to y can be expressed as:

Here, y0 =listed below:

p

2
y =

2
2
2
2
2
2
2
y0 + C↵y (AY ) + C⌘y (EY ) + Cx0 y (Coup2)(4.5)

y "y is the nominal vertical IP beam waist size. The functions of each knob are• AY: the deviation from 0 of the Twiss parameter ↵y , which represents the shift of the verticalbeam waist along the beam direction;• EY: the deviation from 0 of ⌘y ;• Coup2: the deviation from 0 of x’-y coupling.
The eﬀect represented by each coeﬃcient C↵y , C⌘y , and Cx0 y are listed below:• C↵y : the eﬀect of waist position; depends on vertical beam divergence;• C⌘y : the eﬀect of ⌘y ; basically constant; depends on momentum spread;75

• Cx0 y : the eﬀect of x’-y coupling; depends on horizontal beam divergence.
At locations away from the waist,y is sensitive to the vertical divergence angle

y0 =

r

✏y (1+↵2y )y.

If the knobs are independent, the measured modulation (M ) is expressed using the response of eachknob by:
M = Ctotal |cos✓|exp

2ky2 y22= Ctotal |cos✓|exp 2ky2 y0
⇣
⌘
⇣
⌘
⇣
⌘
2
2
·exp
2ky2 C↵y(AY )2 exp
2ky2 C⌘y(EY )2 exp
2ky2 Cx20 y (Coup2)2

(4.6)

2
Here, ✓ is the crossing angle of the Shintake Monitor laser. |cos✓|exp 2ky2 y0
indicates the
maximum achievable M (corresponding to the minimum achievable y ). Ctotal (<1) is the total
systematic error intrinsic to the Shintake Monitor which acts to under-evaluate M (see Chap. 6).
The orthogonality of the linear knobs has been tested by particle tracking simulation using SAD
[12].

4.1.2

Nonlinear Tuning Knobs

The strengths of the FFS sextupoles are set so as to cancel the chromaticity generated at the FD.
However, the presence of sextupole field errors causes additional higher order aberrations. In order
to correct second order optics errors, “nonlinear tuning knobs” are applied in the final stage of IP
beam size tuning. There are six nonlinear knobs in use: {Y22, Y44, Y66, Y26, Y24, and Y26},
calculated as the strengths of the FFS sextupoles. Y24 and Y46 correct normal sextupole fielderrors. Y22, Y44, Y66, and Y26 correct skew sextupole errors. Here, the indices 2, 4, 6 represent x’,y’, and energy, respectively. For example, Y66 is eﬀective for 2nd order dispersion. The nonlinear
knobs are almost orthogonal to each other, but not completely so. Because there are cross terms, theknob settings are optimized through reiteration. Reiteration is sometimes also carried out between
linear knobs and nonlinear knobs.
Figure 4.2 (shows an example of linear knob tuning and nonlinear knob tuning using measurements by the Shintake Monitor. The response of M to the knob strokes is fitted with a Gaussianfunction. The setting of each knob is optimized so as to yield the Gaussian peak.

76

Figure 4.1: An example of a QD0 scan [17]. Here, y is measured using the IP wire scanner asa function of the scanned strength (current) of the vertically focusing quadrupole QD0, and fittedwith a parabolic function.

Figure 4.2: An example of multi-knob tuning [17]: (left) linear knob AY (right) non-linear knob Y46.
The horizontal axis indicates the strengths of the knobs. Here, M is measured using the Shintake
Monitor as a function of the knob amplitudes, then fitted with a Gaussian function.

4.2

Setup Procedure for the Shintake Monitor

This section describes the process of preparing the Shintake Monitor system for use in beam tuning.
This comprises of the adjustment of the laser timing and position w.r.t. those of the e beam at theIP, the adjustment of the focal lenses, and the optimization of collimation. After these preparations
have been completed, the Shintake Monitor stably measures beam sizes as part of the e beamtuning process described in Sec. 4.1. The laser crossing angle mode is switched in accordance to thebeam focusing status.
4.2.1

Transverse Laser Position Alignment

The laser position must be kept constantly under strict alignment relative to the e beam at the IP
in order to measure M precisely. This section describes the routinely performed position alignment77

process, which is repeated throughout the beam tuning process to compensate for drifts in theposition of either laser or beam over time.
Preliminary Alignment by Screen Monitor
First, the laser paths are made to overlap with the beam using a CCD camera to monitor theirpositions on a screen (see Sec. 1.6.2) which allows a simultaneous view of both laser spots and thee beam spot. The screen is mounted on the “IP target” mover and inserted into (out of) the IP
before (after) this process. The CCD camera views the e beam by the fluorescent light generated
when it passes through the screen, and the laser spots by the light reflected from the screen. To
prevent the screen from being burnt, the laser intensity is first weakened by the attenuator before
the screen is inserted. The laser paths are aligned one at a time to the center of the e beam spotby adjusting the angles of the actuator-attached mirrors. This is capable of alignment precision of. 1 ⇥ t,laser . Figure 4.3 shows the IP target and an example of alignment on the screen.

Figure 4.3: (left) The complex IP target system carrying the wire scanner and the screen. The
weakened laser light (in green) is shown hitting the screen monitor.
(right) An example of laser position alignment using the IP screen monitor. The bright spot is thelaser profile while the marker in its center indicates the e beam position. The grey panel on thebottom right shows the mirror actuator settings being adjusted.
Fine Alignment by Laser Wire Scan
After the alignment using the IP screen monitor, finer position alignment with precision of about
1/10 of t,laser is carried out using collision between high power laser and the e beam. In thetransverse plane, alignment is carried out by the “laser wire scan” introduced in Sec. 2.4. The
position of one path at a time is scanned in the horizontal (x) direction w.r.t the beam by scanningthe mirror actuators in fine steps of typically 0.5 µm, corresponding to a laser position shift at the
IP of about 1/2 of t,laser . The range of the scan is typically wider than ±5 ⇥ t,laser . The primary
purpose is to locate x0 , the position that yields the peak in the Gaussian-like laser wire signal. Thisis obtained by plotting the Compton signal energy resulting from collision as a function of position
x, then fitting it by the following Gaussian function:!
(x x0 )2
E (x) = E0 exp(4.7)
2
2 t,laser
78

Here, E0 is the peak energy, which ideally corresponds to 1/2 of Eavg in a fringe scan. The
accuracy in determining x0 depends on the fitting precision, and is typically about 1/10 of t,laser .
Figure 4.4 shows the eﬀect of transverse laser position misalignment and an example of a laser
wire scan. Another laser wire scan with 50 pulses measured at each x is shown in Fig. 5.5. The
Gaussian-like signal is a convolution of the laser spot size t,laser and e beam size (mostly just x, since y ⌧ x ), and is expressed as :
q
q
2
2
2
2
2
2
2
+
=
(4.8)
lw =
t,laserx,relt,laser + x sin (✓/2) + y cos (✓/2)
q
2
2
2
2
Here, x,rel ⌘x sin (✓/2) + y cos (✓/2) , interpreted as the “e beam size seen by the laser”,
approximately equals to just x for the 174 deg mode. The horizontal beam size is inferred fromwire scanner measurements (see Fig. 1.10), and is typically 9-12 µm during operation in 2014.

Figure 4.4: (top) The schematics of transverse laser position misalignment at the IP. Here, the upper
path is assumed to be oﬀset w.r.t. the e beam center by l1 , while the lower path is assumed to
be precisely aligned. (bottom) A set of upper and lower path laser wire scans conducted in the 174
deg mode [17].
4.2.2Longitudinal Position Alignment

The laser wire scan enables the laser to collide with the beam. However, fringe contrast would
be degraded if the two laser paths are oﬀset in the longitudinal (i.e. e beam) direction. Precise
longitudinal alignment is done using the “z-scan”. Figure 4.5 shows the eﬀect of longitudinal oﬀset
and an example of z-scan. The “Y” actuator of the lower laser path is scanned with about the same79

steps and as the laser wire scan. Fringe scan is conducted at each step. The M response is fittedwith the following Gaussian function:!
(z z0 )2
M (z) = M0 exp(4.9)
2
8 z,laser
Here, z,laser is the longitudinal laser spot size. z is the lower path’s longitudinal position being
scanned, z0 is the optimum position which yields zero oﬀset and thus realizes the sharpest fringe
contrast, i.e. largest M . The actuator is set to align the laser to z0 with a precision of typically 1/10
of z,laser ( z,laser ' t,laser ). The 1-sigma of the Gaussian-like signal corresponds to 2 ⇥ z,laser .

Figure 4.5: (top) The schematics of longitudinal laser position misalignment. The two paths are
assumed to be oﬀset by z in the e beam direction. (bottom) An example of a z-scan conducted atthe 4.6 deg mode; here, five pulses are measured at each step of the mirror actuator being scanned
[17].
4.2.3

Focal Lens Scan

The focal lenses are able to be scanned in the laser beam propagation direction by placing themon movers of resolution 0.1 µm and stroke 30 mm (Figures 4.6 and 4.7). The “focal lens scan” isconducted during the setup of the Shintake Monitor for the following purposes:• To optimize the laser profile balance between upper and lower paths; profile imbalance would
cause bias of fringe contrast. (see Sec. 6).
80• To realize a well focused laser spot size at the IP to maximize Compton signal intensity 19 .
The procedures are as follows: the lens position is scanned in the laser beam propagation direction.
Laser wire scan is conducted at each step while recording lw , the sigma obtained from fitting thelaser wire scan signal. q
The laser spot size ( t,laser ) is calculated from lw by subtracting the e

2
2
2
2
2
beam size as t,laser =x sin (✓/2) + y cos (✓/2) (modified from Eq. 4.8). The focal lenslw
position (z) is set to the waist position (z0 ) which yields the minimum t,laser . The lens should
be scanned over a wide range e.g. more than one Rayleigh length away from z0 . Figure 4.8 shows
an example of a “focal lens scan” conducted using the 174 deg mode upper laser path. Here, themeasured laser spot radius ! ' 2 ⇥ t,laser is plotted as a function of focal lens position. The waist
spot size is !0 = 25.9± 2.2 µm (at z0 = 6 mm). Section 5.1.2 gives a detailed evaluation of laser
focusing status.

Figure 4.6: The vacuum chamber with viewports facing the focal lenses of the Shintake Monitor.
19

Usually, the laser spot size is focused to the smallest possible while checking the status of signal jitters. Because
a very small laser spot size may lead to larger pointing jitters at the IP, the focal lens position may be adjusted toslightly enlarge the laser spot size.

81

Figure 4.7: (left) The focal lens of the 174 deg mode upper path. (right) The focal lenses of the 30
deg mode upper and lower paths on either side of the 2-8 deg mode focal lens.

Figure 4.8: A focal lens scan conducted in the 174 deg mode (in May 2014).
4.2.4

Collimator Scan

The tuning of the e beam trajectory aﬀects the path of Compton signal photons, possibly causing
them to lose energy by brushing against the collimators on their way to the detector. There may also
be an increase in BG energy fluctuation due to unpredicted changes in the location of BG sources.
Section 3.5.3 introduced two types of collimators for cutting bremstrahlung BG generated at
the FD: a downstream fixed collimator, and an upstream movable collimator which is scanned via
remote control using an automatic stage for the following purposes:82

1. To maximize the amount of signal entering the detector; this re-adjustment is necessary when
signal path is altered along with the e beam orbit. Figure 4.9 shows an example of the resultsof a collimator scan. Here, signal intensity is measured by the detector while the collimator isscanned in X and Y directions.
2. To detect sudden changes in the e beam trajectory; in Fig. 4.9, if the peak of the measured
signal intensity i.e. the photon distribution center is significantly deviated from the initialcollimator center, it may be a sign that the e beam orbit needs re-adjustment.

Figure 4.9: The result of a collimator scan conducted in June 2014, shown on the online ATF panel
as a 2D histogram: The horizontal and vertical axis indicate the X and Y positions of the movable
collimator stage, respectively. The center of the collimator was adjusted to the red area, whichindicates the peak of signal intensity measured by the detector. [17]4.2.5

Relative Timing Adjustment

Section 3.4.2 explained the monitoring of the timing of the laser and the e beam using the signalsof a PIN-PD and strip line BPM, respectively, and timing control using digital modules (EVR). The
laser-beam relative timing require fine adjustment of precision better than 1 ns in order to maximize
signal intensity and suppress Compton signal jitters to <5% (see Sec. 7.1.4 for detail). For this, Qswitch timing is changed in steps of 0.4 ns by scanning the delay setting of the EVR, while colliding
one laser path against the e beam. The online panel of this “timing scan” is shown in Fig. 4.10.
The vertical axis is the Compton photon energy measured by the detector. The horizontal axis is
the Q-switch timing scanned in sub-ns steps.
The timing scan is typically reiterated with laser wire scans before measuring M in z-scans.
Because the laser path length to the IP diﬀers for each crossing angle mode, the laser timing trigger
setup must be re-adjusted after mode-switching. This is done automatically by software (timing
control panels) using the appropriate recorded values.

83

Figure 4.10: An example of a timing scan. This was conducted in the 4.6 deg mode, with 3 pulsesof Compton energy (vertical axis) measured at each step of the laser trigger timing (horizontal axis)
being scanned. [17]84Part III

Performance Evaluation of Shintake Monitor
5

Evaluation of Laser Properties

5.1

Adjustment of Laser Spot Size

5.1.1

Representation of Laser Propagation by Transfer Matrices

When describing the propagation of the laser through a lattice comprised of optical components, it
is convenient to use transfer matrices in the following form:
✓ ◆
✓ ◆
r2
r
= A 10
(5.1)
r20
r1

Here, the position r and angle r0 of the laser beam are represented by a vector, where the indices
1 and 2 ✓represent◆ the initial and final states, respectively. ✓The 2 ⇥◆2 propagation matrix A is
1 L
10
D (L) =
for a drift space of length L, and F (f ) =for focusing due to a thin
0 1
1/f 1
lens of focal length f ; det A = 1 is satisfied based on the conservation of phase space area underlinear transformation.
Propagation through the expander/reducer
Section 3.1.2 explained the magnification of the laser spot size ( laser ) by the expander on the laser
table, and the restoration of laser by the reducer after transportation to the vertical table. Using
transfer matrices, propagation through an ideal expander can be expressed as:
Aexpander = F (f2 ) D (f2=✓f1 ) F ( f1 )

◆✓
◆✓
◆ ✓
◆
1
0
1 f2 f1
10
f2 /f1 f2 f1=
1/f2 10
1
1/f1 10
f1 /f2In Eq. 5.2, the degree of magnification ofin the form of(5.2)

laser is M = f2 /f1 . Therefore Eq. 5.2 can be rewritten

Aexpander =

✓

M
0

L
1/M

◆

(5.3)

Propagation through an ideal reducer with a demagnification of 1/M can be expressed by exchanging f1 and f2 in Eq. 5.2 :Areducer = F ( f1 ) D (f2
=

✓

1/M
0

L
M

◆

=

✓

f1 ) F (f2 )f1 /f2 f2 f1
0
f2 /f1◆(5.4)

In practice, the setup of the expander and reducer lenses is more complex. The focal lengths
and the drift lengths between the lenses need to be optimized to meet the following requirements:
1. The laser must propagate parallel after emerging from the expander/reducer and pass throughthe center of mirrors all the way to the focal lens. An angular error when injecting into thelens leads to profile imbalance between the two paths at the IP.
85

2. The laser spot size must be adjusted as not to cause damage to optical components due tohigh laser intensity (also see Appendix C).
3. The laser must be focused at the IP to a spot size small enough for a suﬃcient rate of Compton
signal, while not too small as to cause too much laser pointing jitters.
Regarding 1, it is important not to strike the walls of the transport line. The magnification of the
expander should be maximized within this limit. The diameter of the transport line is about 100
mm, while the typical laser spot diameter emerging from the laser source is about 10 mm. Therefore,
there is a tolerance of about a factor of 5 even after a two-fold magnification.
Propagation through the focal lens
The propagationof◆the laser beam from the focal lens entrance to the IP can be expressed✓✓ using◆
10
1 f
F (f ) =for the focusing due to a thin lens of focal length f , followed by D (f ) =
1/f 1
0 1
for a drift space of length f until the IP as:
✓ ◆ ✓
◆✓
◆✓ ◆
r2
1 f
1
0
r1
=
(5.5)
0
r2
0 1
1/f 1
r10
From Eq. 5.5, we obtain:

r2 = f · r10(5.6)

Equation 5.6 indicates that the position oﬀset at the IP is determined by the initial angular error
when injecting into the lens, whereas initial position oﬀset has no eﬀect. Therefore it is important
for the laser to propagate parallel from the reducer exit to the focal lens. Otherwise there would be
an insuﬃciently focused laser and/or profile imbalance between the upper and lower paths. Howeverthese can be compensated by conducting the focal lens scan for each path (see Sec. 4.2.3).
5.1.2

Laser Focusing at the IP

It is important to focus the laser to a small waist size in order to realize suﬃciently high laser
intensity for generating Compton signal and maintaining a high S/N ratio. One quantitative measureof whether the laser spot size can be focused suﬃciently at the IP is the “M 2 factor”; it defines thedeviation of the actual beam from an ideal Gaussian beam (i.e. M 2 = 1). The waist size at the IP!0 (= 2 ⇥ t,laser 20 ) depends on M 2 , the lens’s focal length (f ), and the spot size injected into thelens (!i ) as:
!0 =

fM2
⇡!i

(5.7)

The laser spot size can be expressed as a function of the coordinate in the laser propagation
direction (z) w.r.t. the waist position (z0 ) as:
s
s
⇢ 2
✓
◆
M (z z0 ) 2
z z0 2! (z) = !0 1 += !0 1 +
(5.8)
zR
⇡!02
20
The laser spot radius !, defined as the width at which intensity falls to 1/e2 of the peak, is the parameter
typically used in optical calculations. For a perfect Gaussian beam of sigma , the beam radius is ! = 2 , and thebeam diameter is 2! = 4 .

86

p Here the Rayleigh length zR , defined as the distance over which ! (z) increases by a factor of
2, is expressed as:
zR ⌘

⇡!02
M2

(5.9)

A larger M 2 indicates more sudden focusing, i.e. ! (z) changes at a faster rate with distance z.
M2
This is understandable from the fact that the beam divergence ⇥ = !0 zR = ⇡!
is proportional to02
2
M . Figure 5.1 shows the dependence of laser beam divergence on M .
In reality !i can be adjusted using reducer lens setup. The initial spot size immediately before
the focal lens was observed to be !i ⇠2.5 mm in 2014 spring (see Sec. 5.2). If we assume a perfect
Gaussian profile (M 2 = 1) and parallel injection into the focal lens with !i = 2.5 mm, the waist sizeat the IP is calculated to be:(
16.9 µm : 2 8 deg, 174 deg (f = 250 mm)f!0 ==(5.10)⇡!i20.3 µm :30 deg (f = 300 mm)
Using the focal lens scan shown in Fig. 4.8 (Sec. 4.2.3), M 2 is evaluated as follows. The waist
spot size !0 is measured to be 25.9± 2.2 µm (at z0 = 6 mm). Using this, the observed !i =2.5 mm,
and Eq. 5.7, M 2 is calculated to be 1.5± 0.1. The Rayleigh length zR is calculated using Eq. 5.9 tobe 2.6±0.2 mm, which is approximately
consistent with the distance observed in Fig. 4.8 over whichp! increases by a factor of 2. For this measurement, t,laser at the waist is = 13.0± 1.1 µm. Thet,laser inferred from laser wire scans in 2014 is typically 10-15 µm. From Sec. 3.6.1, the number ofCompton signal photons (Nsig ) is proportional to the inverse of t,laser . At the low e bunch chargeof Ne = 1 ⇥ 109 , t,laser should be focused to < 16 µm in order to obtain suﬃcient Nsig to suppress
the statistical errors due to photon statistics to < 7%. The typical t,laser meets this expectation.
In reality, t,laser varies with occasional slight adjustments of the focal lenses or the reducer lenses.
In 2014 spring, the reducer lenses were adjusted as to yield a very relaxed focusing; a smaller spot(!i ) was injected into the lens in order to realize a larger waist size so as to mitigate eﬀects fromlaser pointing jitter. The resulting long zR serves to reduce the bias from wave-front eﬀects (see Sec.
6.8).

Figure 5.1: Dependence of laser beam divergence on M 2 factor.

87

5.2

Laser Profile

The spatial laser beam profiles are measured using profile monitors consisting of CCD cameras,
lenses, and targets (Fig. 5.2). The CCD camera (JAI, CM-030GE) has 640 (H) ⇥480 (V) pixels
and pixel size 7.4µm ⇥ 7.4 µm. It monitors a laser image formed by shining weakened laser light(transmitted from a mirror) upon a paper target. This method is more convenient in terms of visible
range given the frequent adjustments of the laser spot size and/or position, as opposed to injecting
light directly into the camera lenses.
Figure 5.3 shows images of the laser profiles measured before the expander lenses (left), in theinjection line on the vertical table (middle), and next to the most downstream mirror in the 174
deg lower path (right). Round and concentric Gaussian profiles are observed on the laser table.
However, after the transportation (⇠20 m) to the vertical table, the profile becomes triangularand shows multi-mode characteristics. The causes for the degraded spatial profile are still underinvestigation. One possibility is that the laser wavefronts become distorted due to complications
during the amplification process21 . The distortion become noticeable after the propagation of eachof the higher order modes through multiple mirrors and lenses from the laser source to the vertical
table. The multi-components are indicated by the occasionally observed two-peak structure in thelaser wire profile. Also, it becomes diﬃcult to overlap the profiles of the two laser paths by z-scan
if the focal points in their multi-components diﬀer. These factors aﬀect the peak search precisionin laser wire scans and z-scans, and thus lead to fringe contrast reduction due to laser position
misalignment. In addition, the interference of multiple transverse modes in the laser profile maylead to further distorted laser wavefronts at the IP.
In the past, the laser wavefronts on the vertical table had been measured using a Shack-Hartmann
wavefront sensor (see Thorlabs manual [37]), which measures the deviations from a reference wavefront. The incoming laser beam is divided by a lenslet array into several smaller beams. Eachsmaller beam is then imaged by a CCD camera placed at the focal plane of the lenslet array. For
the case of a uniform plane wave incident on the sensor, a regularly spaced grid of focused spots areformed in the focal plane. For the case of a distorted wavefront, the focused spots are displaced fromthe optical axis, thus yielding a disrupted formation on the grid. The wavefront can then be reconstructed from the spot displacement information since each spot centroid is proportional to the local
wavefront slope at a single lenslet. The measured results[25] indicate neither significantly unevenspot distribution on the grid, nor significantly distortion of the reconstructed wavefronts. However,this measurement was only conducted on the optical tables i.e. the near-field. It is necessary to also
conduct it at various other locations, including in the transport line i.e. the far-field. Furthermore,
it is suspected that the laser spots size at the time of the measurements may have been slightly toolarge to fit completely into the camera lens. Thus it is not possible to draw a reliable conclusion
about the laser wavefronts from these results. Future measurements need to be conducted in a more
systematic method and with better resolution.
The following improvements have been made to improve the quality of the laser profile. A partof these also served to reduce signal jitters and drifts:• In order to lighten the eﬀect of laser pointing jitters at the IP: (a) the spot size at the focal
point was enlarged by injecting a smaller spot size into the focal lens; (b) the reducer lenses
were adjusted to realize a longer Rayleigh length i.e. a more relaxed focusing. This appeared
to smooth out some of the higher order mode components in the profile.
• In order to reduce profile fluctuation: (a) a window was inserted in the laser transport to
reduce air flow; (b) an iris was used on the laser table to clip the outer part of the profile
21

Other possible causes include the oﬀset of the optical axis between the main laser and the seed laser, and either
the aging or slight damage of the seed laser and/or main laser YAG rod.

88

which fluctuates more apparently. After these eﬀorts, the fluctuation of the profiles w.r.t. a
fixed reference marker was observed to be < 5% of the laser spot diameter in all locations.
• The laser spatial profile was tuned by adjusting the angles of the rear mirrors in the laser cavity(also see Sec. 3.2.1). This optimized the angle of the laser passing through the components ofthe cavity. As a result, the profile emerging from the laser source became rounder and moreconcentric, and its intensity bias (“hot spots”) were reduced.
The laser profile is also observed by the eye at various locations such as by using a concentric paper
target to roughly measure the laser spot size. Figure 5.4 shows some examples from April-Juneof 2014. During this period, the expander lenses had focal lengths f1 = -150 mm (concave) and
f2 = 350 mm (convex), while the reducer lenses had f1 = 450 mm (convex) and f2 = - 150 mm(concave). From this, the magnification by the expander of |f2 /f1 | = 2.3 times followed by thedemagnification by the reducer of |f2 /f1 | = 3 times should give a net demagnification of 1.3 times
for the spot size injected into the focal lenses. From actual observations, the laser spot diameter
before and after the expander were 8 mm and 16 mm, respectively; the diameter of ovalish profile
before and after the reducer were 15⇥17 mm and 5⇥6 mm, respectively. These direct spot size
observations are consistent with the (de)magnification calculated from the focal lengths. The spot
size was observed to be preserved all the way from the reducer exit to the focal lens, which indicatesparallel propagation.

Figure 5.2: Examples of laser profile monitors (circled in red), consisting of CCD cameras and lenses(left) just after injection onto the vertical table (right) at one end of the laser table (surrounded byblack-out shading)Figure 5.3: Images of laser profile monitored by CCD cameras just in front of the expander lenses
on the laser table (left) vertical table , injection line (middle) vertical table, at the mirror M174L
closes to the 174 deg mode lower path focal lenses (right). The concentric circular structure can beinterpreted as Fraunhofer diﬀraction.
89

Figure 5.4: Images of laser profile observed with the eye by shining the laser light on a thin paper,at various locations on the laser table and vertical table. : From left to right: just before expander,
just after expander, at an intermediate mirror (M3), at the focal lens of the 30 deg mode upper
path.

5.3

Laser Pointing Jitter

Relative position jitter between the laser beam and the e beam at the IP causes signal jitters.
This section evaluates horizontal relative position jitter ( x ) and laser pointing jitter using theupper path laser wire scan shown in Fig. 5.5, which was taken in the 174 deg mode. To improveanalysis precision, Nav = 50 pulses were measured at each mirror position (x), whereas Nav =3-5 aremeasured for the typical alignment.
Using Eq. 4.7, the contribution fromx to the energy jitter can be expressed in first orderapproximation as :dErel (x) =dx

E0 expx0 ) 2

(x

2
2 lw

!!

x =

E0 (x

x0 )
2
lw

Therefore, the relative signal jitter due to relative position jitterfrom the laser wire peak position (x0 ) is :Erel (x)
x x0
=
·
2
E (x)
lw

x

exp

x0 ) 2(x

22 lw

x at an oﬀset of |xx!

(5.11)
x0 | away(5.12)For example, the jitter expected at 1 sigma from the laser wire scan peak is
x / lw . Assuming
a Gaussian laser wire profile,isderivedbythefollowingprocess:theenergyjitter i.e. thexstandard deviation of the Nav is plotted as a function of mirror position (x) (Fig. 5.6), then fitted
by a model written as:q
2 (x)E (x) =
EV2 (x) + Erel
(5.13)
Equation 5.13 assumes thatjitter is modeled as :EV (x) =E is a convolution ofrErel and vertical jitters

⇣
⌘2
p
2
Cconst+ Cstat E (x) + (Clinear E (x))2

EV . Vertical(5.14)

Each component in Eq. 5.14 will be explained in Sec. 7.1. Here,x , Cconst and Clinear are freeparameters, while Cstat is fixed according to detector calibration results (see Sec. 7.3). Table 5.1
displays the relevant parameters obtained from fitting, as well as parameters calculated using these.
The laser wire scan sigma lw is obtained from the fit in Fig. 5.5. The horizontal e beam sizex is measured by wire scanner to be 9.1 ± 0.2 µm . Inserting the measured x and lw into Eq.
4.8, laser spot size t,laser is calculated to be 12.2 ± 0.2 µm.
90

For this data, the horizontal relative position jitterx is obtained from the fit in Fig. 5.6 to be
2.4 ± 0.8 µm. By subtracting horizontal e beam jitter (assumed to be 15% of x [38]) in quadraturefromx , the pointing jitter of the laser only is estimated to bex,laser = 2.0 ± 0.9 µm, which is
16 ± 8 % of the laser spot sigma t,laser 22 .

lwt,laserx

from laser wire scan (Fig. 5.5)
15.2 ± 0.3 µm
12.2 ± 0.2 µm

x,laserx / lwx,laser / t,laserfrom jitter plot (Fig. 5.6)

2.4 ± 0.8 µm
2.0 ± 0.9 µm
16 ± 5 %16 ± 8 %Table 5.1: The analysis results for horizontal relative position jitter and laser pointing jitter.

Figure 5.5: A laser wire scan using the upper laser path in the 174 deg mode. The horizontal axis
is the position of the mirror M174U being scanned. The vertical axis is the statistical results of the
50 pulses measured at each position of the mirror M174U being scanned. This is fitted with Eq. 4.7
to obtain the peak height and position, and the sigma of the Gaussian-like profile.
22

This is approximately consistent with the laser profile fluctuation observed using CCD cameras upstream of theIP (in Sec. 5.2).

91

Figure 5.6: The plot used for deriving horizontal relative position jitter using the laser wire scan in
Fig. 5.5. The horizontal axis denotes the mirror position being scanned. The vertical axis is thesignal jitter, i.e. standard deviation of the 50 pulses measured at each mirror position. This is fittedwith Eq. 5.13 to obtain the horizontal position jitter.

5.4

Laser Polarization

The Shintake Monitor optics is designed for purely linearly S polarized laser. Any deviation from thiswill cause M reduction. This is because the half mirror has a design reflectivity of 50% for S polarized
light, thus any “contamination” from elliptical P components will lead to intensity imbalance between
the upper and lower paths. P components can mix in through the transportation to the vertical
table. Section6.5 explains the M reduction due to polarization and power imbalance 23 .
5.4.1

Polarization Measurement

The results of laser polarization measurement indicated the laser to be very close to pure S state.
The setup is shown in Fig. 5.7. The location is just after injection onto the vertical table at theIP, at the label “polarizer” in Fig. 3.14 (top)). The polarization of the laser is rotated by a half
lambda ( /2 ) plate over a full 360 deg range in fine steps. Rotating the /2 plate introduces aphase shift between the horizontal and vertical electric electric field components. Downstream ofthis a beamsplitter reflects the S light component upwards into a power meter to be measured, whiletransmitting the P light component. The /2 plate (rotator: Sigma Koki, SGSP-80YAW) and thebeam splitter (Sigma Koki, PBSHP-20-5320) are shown in Fig. 5.8. The power meter (VEGA Ophir
Photonics) is shown in Fig. 5.9.
Polarization can be explained using Jones matrix as follows[39]: Assuming light propagates inthe z direction, the x (y) components of its electric field, with phase x(y) and amplitude Ex0(y0) ,respectively, are expressed as :
✓ 0
◆
✓
◆
Ex (t)
E x0 exp (i x )
=
exp
{i
(kz
!t)}
(5.15)
Ey0 (t)E y0 exp (i y )23
On the optical table, polarization is defined with respect to the surfaces of optical components. Therefore special
care is taken to align all mirrors.

92

Here, x and y represents the S and P polarization components, respectively. The phase diﬀerence⇡⌘| x
y | is 0 for a linear polarized laser, and ± 2 for a circularly polarized laser.
✓◆cos 2✓
sin 2✓The Jones matrix for a /2 plate being rotated by ✓ is represented as. The
sin 2✓ cos 2✓
beamsplitter transmits S polarized light with the (1,0) component of its Jones matrix. Using these,
the light propagation in Fig. 5.7 (left) can be expressed as:
✓ 0
◆ ✓
◆✓
◆✓
◆
Ex (t)
1 0
cos 2✓
sin 2✓E x (t)=(5.16)
Ey0 (t)0 0
sin 2✓ cos 2✓
E y (t)The optimum settings of the /2 plate which maximizes the ratio of S light will be referredto here as “S peaks”. The measured cosine-like power spectrum (Fig. 5.11 (left)) is fitted by thefollowing function:
P =P0(1 + C1 cos4✓ + C2 sin4✓)
2(5.17)

2 + E 2 [PThe relationship between field amplitudes and total power is P0 = Ps + Pp = Ex0s(p)y0: power of S (P) light]. P0 is set to 1.12 ± 0.01 W, which is the average of the power measured atseveral “S-peaks” (0, 90, and 180 deg). The coeﬃcients C1 and C2 , to be obtained from fitting, areexpressed as a function of field amplitudes and as the following:

C1 =

2
Ex0

2
Ey0

Ps Pp
=
= cos 22
2
Ps + Pp
Ex0 + Ey0p
2 Ps Pp
2Ex0 Ey0
C2 = cos
2 + E 2 = cos P + P = cos sin 2
Ex0
s
p
y0
Here, the eccentricity
ellipse as:(5.18)(5.19)

is defined as the ratio between the long and short axis of the polarization

tan

Ey0
=
=
Ex0

r

Pp
Ps

(5.20)

Table 5.2 shows the fitted results for C1 and C2 and using these, the results calculated for ,Pp /Ps , and . The small eccentricity angle = 6.9±0.1 deg and “P contamination” Pp /Ps < 1.5 %indicate the laser to be very close to pure S linear polarization 24 . The “S peaks” angles of the /2
plate were cross-checked by confirming that they yield the best power balance. The power of eachpath was measured as a function of /2 plate rotation angle immediately before the focal lenses (seeFig. 5.10). Additionally, the reflectivity of the 50% beam splitter was measured to beRs = 50.3%
for S light, well within catalog specifications. Rp = 20.1% was measured for P light. By setting
the /2 plate to the “S peak” angles, any residual P components are prevents from entering the half
mirror, thereby eliminating nearly all polarization related systematic errors. This is demonstrated
in Sec. 6.5 using beam time fringe scans in which M is maximized while scanning /2 plate angle
over a wide range.
Before the above-mentioned measurements, a calibration linking the set values of the rotation
angles of the /2 plate and its controller (Sigma Koki, Shot204) was carried out. Figure 5.12 shows
the satisfactorily linear relationship.
24
It was confirmed that the lowest power values are well within measurable range of the power meter, and thatsensitivity of the measurement is finer than 5 deg.

93

C1
0.971± 0.001

C2
0.013± 0.012[deg]
86.8±3.0

Pp /Ps [%]1.47±0.06

tan
0.121±0.002[deg]
6.9±0.1

Table 5.2: The coeﬃcients from Eq. 5.17 obtained from the fitting of the measured polarization
spectrum in Fig. 5.11 and the phase shift and Pp /Ps calculated from these.

Figure 5.7: Setup for measurement of laser polarization.

Figure 5.8: (left) The half lambda plate which rotates the polarization state of the laser. (right)
The beam splitter for high intensity laser which reflects S light.

94

Figure 5.9: ( left) The power meter (VEGA, Ophir Photonics) used for measuring total laser power.
( right) The sensor attached to the power meter.

Figure 5.10: Setup for laser power measurement before the focal lenses.

95

Figure 5.11: (left) laser power spectrum measured as a function of rotated angle of the /2 plateusing the setup in Fig. 5.7: Plotted here are the average of 5 points for each step with error bars
assuming 1% design resolution of the power meter sensor. The fitted result shows the laser to bevery close to S linear polarization. (right) Laser power measured using the setup in Fig. 5.9. Thisshows that the optimum /2 plate setting, “S peaks” yields the best power balance between theupper and lower laser paths for both 30 deg and 174 deg modes. Meanwhile the “P peak” settings
yield the worst balance

Figure 5.12: The linear relationship resulting from the calibration between /2 plate rotation angle(vertical axis [a.u.] ) and set value of its controller Shot204 (Sigma Koki) (horizontal axis).

5.5

Laser PowerThe power of the laser was measured using the power meter in Fig. 5.9 in the following locations:• In the 174 deg mode upper path (174 U), immediately in front of the focal lens
• In the 174 deg mode lower path (174 L), immediately in front of the focal lens
• Before dividing up into two paths on the vertical table, just after the /2 plate in the injectionline
96• On the laser table, before the expander
These measurements were all done within about two hours in 2014 spring when the Shintake Monitor
was stably measuring y < 60 nm. The e beam was turned oﬀ. The results are shown as histogramsin Fig. 5.13 and in the table below. These values are the mean and RMS of 20-30 events read out
at each location.
location
power [W] (mean±RMS)
power jitter = RMS/mean

174 U
0.356±0.002
0.5%

174 L
0.357±0.003
0.8%

vertical table
0.799±0.004
0.5%

laser table
0.857±0.005
0.6%

The following observations are made based on the results:
1. The power balance between the upper and lower paths of the 174 deg mode is PU /PL =95±1%. This result is important for the analysis of systematic errors in fringe scans (see Sec.
6.6).
2. The power jitter is < 1%.
3. The power retained after transport to the vertical table is 93±1%.
4. The sum of the power measured for the upper and lower paths is 91±1% of the power measured
in the injection line.
Some possible causes of the power loss in 3. and 4. are the non-ideal reflectivity (R) of mirrors
and/or the non-ideal transmittance (T) of lenses. Under assumption of the design R⇠99% andT⇠90% for the 6 mirrors and 4 lenses respectively between the measuremet locations on the laser
table and the vertical table, the power loss is calculated to be about 10%. Similarly, for the 11
contacts with optical components in each path from the injection line to the focal lens, the power
loss is calculated to be about 11%.

97

Figure 5.13: Results of power measurement at various locations in the laser optics: Clockwise fromtop left: 174 deg mode upper path, 174 deg mode lower path, vertical table injection line, laser
table. The values in these histograms are read out consecutively by the eye with intervals of 1-2 sfrom the display panel of the power meter shown in Fig. 5.9.

98

6Modulation Reduction Factors

The systematic errors on the measured beam size are interpreted using “modulation reduction factors”. These smear the fringe contrast and cause the measured M (Mmeas ) to be smaller than theideal M :!
Y
Mmeas =Ci Mideal = Ctotal Mideal(6.1)
iHere Ci represents the individual M reduction factors. This bias leads to an over-evaluation of
the measured beam size y,meas as:
2y,meas =2y,ideal +

1 X
ln Ci
2ky2

(6.2)

Most M reduction factors are laser-related, due to its alignment, profile, power, and polarization.
There are also some factors related to the e beam position. These will be described in the following
subsections, and summarized in Chap. 8.1. Details can also be found in [40][41]. The first priority
should be to suppress error sources by improving hardware and/or alignment methods. Then residual
systematic errors can be evaluated oﬄine to the best precision possible in order to approach an
estimate of the true beam size.

6.1

Methods to Evaluate Modulation Reduction

The correction of y,meas requires the estimation of the total M reduction factor Ctotal . This can bedone using the following two methods:
1. Each individual
Q bias source is quantitatively evaluated, then Ctotal is calculated as their product: Ctotal ⌘ Ci .
i

2. The total M reduction for a particular ✓ mode is observed by comparing the inconsistency iny,meas immediately before and after mode switching.
Method 1 is diﬃcult because for some types of Ci , only the lower limits (i.e. the worst scenario)
can be obtained from the available data 25 . In some cases, a theoretical estimation is made basedon realistic assumptions and/or simulation.
Regarding Method 2., the y has to be within the measurable range for both the higher and lower✓ mode. The fringe contrast at the lower ✓ mode would have to be clear enough to measure a verylarge M close to the resolution limit. For example, when comparing results between the 30 deg and
174 deg modes, y must be focused down to . 90 nm in the 30 deg mode in order to be able to detect
modulation after switching to the 174 deg mode. Assume that the M measured immediately before
mode switching reaches only 0.6, despite that theoretically y = 90 nm corresponding theoreticallyto M = 0.74 in the 30 deg mode (from Eq. 2.8). This inconsistency indicates a Ctotal ⇠ 80% for
the 30 deg mode. However, this Ctotal cannot be applied universally to any ✓ mode because somesystematic errors are mode dependent and/or vary over time. After subtracting the eﬀects of mode
dependent factors, the residual M reduction due to the common factors can be compared between
the two modes. The following Sec. 6.2 shows a detailed example of such a study.
The evaluation of systematic errors is very complex. Nevertheless, the merit of using the Shintake
Monitor in beam focusing is that we can observe the relative changes in M ( y ) regardless of M
reduction, provided that e beam conditions remain stable.
25

Since multiple types of bias aﬀect Mmeas at once, it is diﬃcult to single out each type .

99

6.2

Measurement of Total Modulation Reduction

This section gives an example of the estimation of the total M reduction factor Ctotal using consecutive Nav = 50 fringe scans immediately before and after switching from 174 deg to 30 deg mode.
This study of about 1 hour was conducted under constant condition of the e beam and Shintake
Monitor setup. M was measured continuously three times in the 174 deg mode, which resulted
in Mmeas = 0.285 ± 0.025 (stat.). After switching to the 30 deg mode, M was again measured
continuously three times, which resulted in Mmeas = 0.765 ± 0.006 (stat.).
Table 6.1 shows the most important M reduction factors evaluated for each mode: C' fromphase jitter ' (see Sections 6.3 and 7.4) and Calign related to laser position alignment (see Sec.
6.7). First, the total M reduction factors Ctot ' C' · Calign are evaluated independently for eachmode as: Ctot (174 deg) > 0.655 and Ctot (30 deg) > 0.932. The apparent diﬀerence in Ctot ismainly due to ' , which averaged at 0.792±0.047 (stat.) rad for the 174 deg mode, in contrast to
0.265±0.051 (stat.) rad for the 30 deg mode. Section 6.3.1 explains the mode dependence of ' .
Next, the total M reduction for the 30 deg mode is derived using an alternative method, bycomparing with the 174 deg mode results as follows:
1. By correcting for Ctot (174 deg), the supposedly “true” M for 174 deg mode is Mcorr =Mmeas /Ctot < 0.473, which corresponds to y,corr > 51.6 nm.
2. Assuming y remains constant (since no beam tuning was conducted), the M expected for 30
deg mode is Mexp < 0.824.
3. Comparing the Mexp in 2. with the actually measured Mmeas (30 deg) = 0.765±0.006, thetotal M reduction is Ctot,exp =Mmeas (30 deg)/Mexp > 0.921.
It can be seen that the worst limits for the indirectly obtained Ctot,exp in 3 and the directly estimatedCtot (30 deg) are almost the same; their discrepancy is about 1%. This is a demonstration of the
precision in evaluating M reduction factors.
174 deg
Mmeas
meas
'

C'
CalignCtot (174 deg)
Mcorr
corr

0.285 ± 0.025
66.9 ± 2.3 nm
0.792±0.047 rad
0.731±0.027> 0.93> 0.655< 0.473> 51.6 nm

30 deg
Mmeas
meas
'

C'
CalignCtot (30 deg)
Mexp
Ctot,exp

0.765±0.006
81.3±2.5 nm
0.265±0.051 rad
0.965±0.014> 0.98> 0.932< 0.824> 0.921

Table 6.1: The measured M and the dominant M reduction factors evaluated for consecutive fringescans. The results are shown for 3 Nav =50 scans before/after switching from the 174 deg mode to
the 30 deg mode.
The statistical errors are defined as the statistic standard deviation of the N scanspdivided by N 1, whereas N = the number of scans (in this case 3). These data were collectedin Apr., 2014.
The following sections 6.3- 6.9 in this chapter describes and evaluates the individual M reduction
factors aﬀecting beam size measurement. These are related to fringe phase fluctuation, the rotation of
the fringes and laser path misalignment w.r.t. the beam, laser polarization and power, the sphericallaser wave-fronts, and the growth of within the fringes. For phase fluctuation, which is the dominanterror source, Chap. 7 is added to provide further details.
100

6.3

Phase Related Systematic Errors

Because the study of phase fluctuation is one of the most important topics of this thesis, its description will be divided as follows: the following Sec. 6.3.1 introduces phase jitter, while Sec. 6.3.2
estimates the contribution to it from the laser optics. Section 6.3.3 shows the eﬀect from slow phasedrift. The following Chap. 7 demonstrates using simulation the precision of a method developed forextracting phase jitter from fringe scans, then applies it to analyzing actual beam time data.
6.3.1

Introduction of Phase jitter

Phase jitter can be interpreted as the relative vertical position jitter between the laser and the ebeam at the IP. The relationship between the relative position jitter ( y) and the phase jitter ( ' )is:' = 2ky ·

(6.3)

y

Phase jitter is one of the dominant M reduction factors. Assuming Gaussian jitters,
Mmeas as Mmeas = M0 · C' . Here, the M reduction factor due to ' is expressed as:⇣⌘
2
C' = exp
2 (ky ·y)2
' /2 = exp' reduces(6.4)

This can be explained through the smearing of the amplitude of the cosine-like modulation curve
as follows:
✓
◆
ˆ
1
'2
C' cos (2ky y + '0 ) = d' · pexpcos (2ky y + '0 + ')
(6.5)
2 '2
2⇡ '
From the point of view of relative position jitter, the impact on the beam size is:2y,meas =Using the method described in Chap. 7,
correct the measured M as:

2
y,0 +

y2

' can be extracted from fringe scan data and used toMcorr = Mmeas /C'
6.3.2

(6.6)

(6.7)

Causes of Phase Jitter

Phase jitter ' (or relative position jittery) is the convolution of the laser fringe phase jitter andthe vertical e beam jitter at the IP. It is diﬃcult to distinguish which is dominant given the current
lack of the means of independent measurement for either eﬀect26 . Electron beam jitter is mainly
caused by the vibration of beam line magnets, especially the FD quadrupoles. The information from
BPMs and FD vibration measurements indicate that the vertical beam jitter is generally < 40%of y [38, 30]. Future precise measurements of IP beam position by the nm resolution “IPBPMs”
under commissioning at ATF2 are anticipated[9, 10]. The laser fringe phase fluctuation (without thee beam) had been measured by T.Yamanaka in 2009[32] using a diﬀerent laser from the current
one and a previously installed phase monitor. The measured phase variation pattern is used for
simulation in Sec. 7.527 . The controller of the piezo stage for fringe scan is ruled out from being asignificant ' factor since the jitter of its readout values is monitored, and has been confirmed to
be < 40 mrad (see Fig. 6.1).
26
27

If e beam jitter is dominant, real beam size growth issues may need to be addressed.
There is no guarantee that this measured laser phase represents the current condition.

101

Figure 6.1: An example of the jitter of the piezo stage controller used for phase delay, monitored
during a single fringe scan. The horizontal axis is (set value) - (read value) of the piezo controller.
The jitter is typically < 40 mrad, thus does not contribute significantly to phase jitter.
The dominant cause of ' related to the Shintake Monitor laser optics is thought to be theangular jitter of the laser (i.e. laser pointing jitter) when injecting into the half mirror. There
may also be a small eﬀect from the independent vibration of the mirrors in each path downstreamof the half mirror. Assuming (a) a laser angular error of ✓ when injecting into the half mirror,and (b) the rotation
j of each mirror “j” (j=1,..., n : n = number of mirrors downstream of
the half mirror),
P the clockwise/counterclockwise angle change of the laser reflected from mirror j is
✓0j ! ✓0j + 2 ji=1
i + ✓. The schematics of this can be seen in Fig. 6.2. These change thelength of each of the upper path (LU ! LU + LU ) and/or the lower path (LL ! LL + LL )between the half mirror and the focal lenses. The phase in fringe scan is directly related to the “pathlength diﬀerence” L = |LU LL |. The jitter ( L ) of L leads to phase jitter at the IP as 28 . :
' =k·

L=

2⇡·

L

(6.8)

p
For the case when each path jitters completely incoherently by l w.r.t. each other,
L = 2 · l. Given the lackof a means for measuring the realistic mirror angular error, only a pessimistic estimation can be made as follows: fora pessimistic case of mirror actuator error d < 0.0001 mm (about 1/10⇥ t,laser at the IP), and given the rotational
axis length D = 61.9 mm, the corresponding mirror angular error is d/D ' 1.5 µrad; this is still about an ordersmaller than laser angular jitter.
28

102

Figure 6.2: The schematics of a combination of (a) a laser angular error of ✓ when injecting
into the half mirror, and (b) the rotationof a mirror (downstream of the half mirror); theclockwise/counterclockwise angle change of the laser reflected from the mirror (red path) becomes✓0 ! ✓0 + 2+ ✓. The green path represents the nominal case i.e. neither laser angular error
nor mirror rotation. Here, the injection position oﬀset at the half mirror is ignored for simplicity.
Simulation of laser pointing jitter
Monte Carlo simulation is used to estimate the ' due to laser angular jitter as in Eq. 6.8. Here, theoptical components on the vertical table are placed according to the geometry shown in Fig. 3.1429 .
When entering the half mirror, the laser beam is given an angular jitter which follows a random
Gaussian distribution i.e. ✓ = Gauss (0,✓), as well as a position oﬀset in accordance to theactually observed laser profile fluctuation of < 5% of the profile radius (see Sec. 5.2). Figure 6.3
shows the simulation results of 10000 pseudo experiments for the 174 deg and 30 deg modes. The
plot in Fig. 6.3 (top) shows the resulting ' as a function of✓ which is changed as {10, 20, 25,
30, 40} µrad. From catalog specifications, laser pointing jitter is below 25 µrad when the Beamlok isused for pointing stabilization[24]. Figure 6.3 (bottom) shows histograms of path length diﬀerence
L = |LU LL | assuming✓=25 µrad, whose RMS values correspond to the path length jitter
L in Eq. 6.8. For the 174 deg mode,
L is 54 nm, corresponding to ' =0.64 rad. For the 30
deg mode,
L is 39 nm, corresponding to ' =0.46 rad. These can be considered the worst limit
for the ' due to the laser optics.
Interpretation
For the same amount of laser pointing jitter, more ' is generated for the 174 deg mode than forthe 30 deg mode because of the diﬀerence in laser optics design. The total path length (LU ' LL )29

2
The path variation after focusing by the lens (with focal length f ) is approximately f ✓out
, where the angularerror after emerging from the lens is expressed as ✓out = ✓in
xin /f , where ✓in and xin are the incident
angular and position error, respectively. This eﬀect is negligibly small (about a few mrad) compared to the angularjitter of O(100) mrad from upstream.

103

downstream of the half mirror for the 174 deg mode (about 2000 mm) is longer than that of the 30
deg mode (about 1000 mm) by a factor of 2. In each of the upper and lower paths between the half
mirror and the focal lenses, there are four mirrors for the 174 deg mode and three mirrors for the
30 deg mode.
The ' resulting from simulation of the 174 deg mode is not significantly diﬀerent from thephase variation of the previous Shintake Monitor laser measured by T. Yamanaka [32], which also
used the 174 deg mode. However, note that the discussion in this section considers only the eﬀect
from the laser optics, whereas the phase jitter extracted from actual fringe scan data in Sec. 7.8 isa convolution of the laser fringe jitter and the e beam jitter.

Figure 6.3: Simulation results of the phase jitter due to laser pointing jitter ( ✓), shown as theresult of 10000 pseudo experiments. [top] ' plotted as a function of✓. [bottom] Histograms of
the path length diﬀerence L = |LU LL | for the 174 deg mode (left) and 30 deg mode (right),
assuming✓=25 µrad; the RMS values correspond to the path length jitterL.

104

6.3.3Phase Drift

Phase fluctuation consists of not only fast jitters but also slow drifts. The two types of components
may be hard to distinguish within the short time scale of a single fringe scan. The eﬀect on Mmeas
depends on the ratio of jitters to drifts, as well as on the time structure (determined by Nav ) of thescan. These are studied in detail in Sec.7.5.
Figure 6.4 shows the drift of the fitted initial phase during several sets of continuous fringe scans.
Over a linear range, phase drift is typically about 50 mrad/min. A relatively bad case is about 80
mrad/min. The overall phase shift throughout the entire set of about 10 scans is typically < 1 rad.
Phase drift is the convolution of the drift of laser and beam position, both of which are aﬀectedby changes in environmental temperature. When phase drift is detected by a sudden decrease inCompton signal intensity, the laser is realigned to the beam by scanning the mirror actuators.
Simulation of fringe scans was conducted to evaluate the eﬀect of linear phase drift on Mmeas
with the following input conditions: M0 =0.636 ( y0 = 40 nm for 174 deg mode), and a typical signal
jitter of 23% w.r.t. Eavg . Figure 6.5 shows the M reduction due to a linear phase drift for Nav =10, 50, and 100. The larger Nav scans are more aﬀected because they take a longer time. Within arealistic drift range of 30-80 mrad/min, the M reduction factor Cdrif t for is >0.97 for Nav = 100,
> 0.99 for Nav = 50 and Nav = 10.

Figure 6.4: (left) The drift of the initial phase obtained by fitting the measured M spectrum during
several sets of continuous fringe scans from Apr-Jun 2014. (right) The drift of the initial phase forone particular set of continuous scans on Jun. 12, plotted as a function of time. Here, the phasedrift is about 30-35 mrad/min over the entire period.

105

Figure 6.5: Simulated M reduction due to a linear phase drift for Nav = 10, 50, and 100. Shown
here are the results of 100 pseudo experiments assuming M0 =0.636 and a signal jitter of 23% w.r.t.
Eavg . Within a realistic range of phase drift 30-80 mrad/min, M reduction is < 1% for both Nav =10 and Nav = 50, and <2.7% for Nav = 100.

6.4

Fringe Rotation

The mismatch between the e beam and the axis of the laser fringes leads to rotated fringe in theform of “tilt” and “pitch” in the transverse (xy) plane and longitudinal direction, respectively. Figure
6.6 show the schematics. Fringe tilt
tilt aﬀects y,meas approximately as Eq. 6.9, and depends on.
Fringepitch
aﬀectsxy,meas approximately as Eq. 6.10, and depends on the longitudinalpitchlaser spot size z,laser .
2y,meas '2y,meas '

2
y0 +

2
y0 +

2
x·

2
z,laser ·

2
tilt
2
pitch

(6.9)
(6.10)

Both z,laser and x are typically around 10 µm. For example, a rotation of 5 mrad would cause
a nominal y = 40 nm to be over-evaluated by about 25 nm. Laser fringe rotation is caused by
the oﬀset of laser spot on the lens w.r.t the lens center. Although this can be prevented by carefulalignment prior to beam time, the laser spot position may drift over time. Furthermore, the ebeam itself may be rotated in the transverse plane. Therefore fringe rotation is corrected using thee beam as a reference by conducting “tilt scans” and “pitch scans” in the final stage of beam tuningin the 174 deg mode. Figure 6.7 shows the online plot of pitch and roll scans. M is measured while
deliberately rotating the laser fringes by manipulating intermediate mirrors in the lower path. M3
in Fig. 3.18 is rotated in x and y to generate tilt and pitch, respectively, while M174L is moved
simultaneously with the same stroke to compensate for the variation in injection angle into the focal
lens. In the end, the mirror actuators are set to values that yield the peak in the measured M
response.
In Fig. 6.6, the oﬀset of upper (lower) laser w.r.t. lens center is represented by XU (L) . The
longitudinal distance from the vertical table is represented by ZU (L) . Using these, tilt and pitch are
expressed as Eq. 6.11 and Eq. 6.12, respectively.
✓✓◆◆
1
XU + XLXU + XL
Arctan'(6.11)
tilt =
2
f
2f
106

1
pitch =
2✓

Arctan✓ZU YL
f sin (✓/2)

◆◆

'

ZU ZL
2f sin (✓/2)(6.12)

Here, f is the focal length of the lens, and ✓ is the crossing angle. For example, in Fig. 6.7(bottom), the M3Y actuator was moved by 0.05 mm from 0 mm to -0.05 mm. This rotates the laserby 2⇥ 0.05 mm / 61.9 mm = 1.6 mrad. Given the distance of 625 mm between M3 and M174L, thisresulted in a longitudinal oﬀset of Z w1.0 mm. Using Eq. 6.12, the original fringe pitch error was
about 2 mrad. Similarly, for the tilt in in Fig. 6.7 (top), the M3X stroke of 0.012 mm moved thelaser on the lens by 2⇥ 0.012 mm ⇥ 625 mm/ 61.9 mm = 0.24 mm. Using Eq. 6.11, the original
fringe tilt error was about 0.5 mrad. These calculations are consistent with the observed change inthe measured M in Fig. 6.7.
The M reduction factor due to tilt and pitch are expressed approximately as Eq. 6.13 and Eq.
6.14, respectively, assuming a Gaussian laser profile.
!
Ctilt ' exp

2 · ky22x1+

Cpitch ' exp

2
x sin

2

2
(✓/2) / t,laser

22 · ky2 z,laser
·

2
pitch

·

2
tilt

(6.13)(6.14)The detailed calculations, found in [22] 30 , assume
tilt ,
pitch ⌧ 1, y ⌧ x , and y ⌧
,
,
which
is
in
valid
for
measuring
<
100
nm
since
y
x ⇠ t,laser ⇠ z,laser ' 10 µm.
t,laserz,laser
From the precision in determining the optimum mirror actuator setting by the fit shown in Fig. 6.7,
the residual M reduction factors after performing tilt and pitch scans are Ctilt > 0.999, and Cpitch> 0.989, respectively.
30
Equation 6.9 had assumed y ⌧ x and x sin (✓/2) ⌧ t,laser . The latter does not necessarily stand for 174
deg mode since typically x ⇡ t,laser ' 10µm, thus x sin (174o /2) ' t,laser . In this case, the precise expression in
Eq. 6.14 must be used.

107

Figure 6.6: The schematics for fringe tilt (top) and fringe pitch (bottom) (figure modified from [25]).

108

Figure 6.7: Example of the online plots made during ATF2 beam time (June 2014) for “tilt scan”(top) and “pitch scan” (bottom). The horizontal axis is the stroke of the mirror M3 actuator being
scanned.

6.5

Laser Polarization

Section 5.4 explained that because the half mirror by specification has 50% reflectivity for S polarized
light, any “contamination” from elliptical P polarized components will lead to intensity imbalance
between the upper and lower laser paths. The resulting M reduction factor is expressed as [22]:q
Cpol = (A B cos tan ✓)2 + (C sin tan ✓)2(6.15)
A=2

B=2

p
Rs (1

p
Rs (1

Rp )

p
Rs )Ps + Rp (1Ptot

Rp )Pp

p
Rp (1
Ptot

p
Ps Pp

Rs )

=2

p
Rs (1

p
Rs ) + Rp (1Rp/s + 1

=2

p
Rs (1

Rp )

109

p
Rp (1
Rp/s + 1

Rp )Rp/s

Rs )

p

Rp/s

C=2

p
Rs (1

Rp ) +

p
Rp (1
Ptot

Rs )

p
Ps Pp

=2

p
Rs (1

p
Rp ) + Rp (1Rp/s + 1

Rs )

p
Rp/s

Here, for S and P polarized light, Rs and Rp are the reflectivities of the half mirror, respectively.
“P contamination” Rp/s is defined as Pp /Ps , where Ps and Pp are the power entering the half mirror.
If the half mirror were perfect i.e. Rs = 1 Rp = 50%, Eq. 6.15 would be rewritten as:
v
!2
u
p
q
u
2
P
P
s
p
0
Cpol
= t1 +
sin
tan2 ✓ = 1 + sin2 2 tan2 ✓(6.16)Ptot

Rs and Rp were measured to be 50.3%
p and 20.1%, respectively. From Eq. 6.16, the fringe0
contrast can be written as cos ✓ · Cpol
= cos2 ✓ + sin2 2 sin2 ✓. Although circular polarization( = 45o ) maximizes contrast, elliptical components may mix in after reflection by several mirrors.
Thus the linear polarization, which is easier to handle, is selected for the Shintake Monitor laser.
The polarization measurement results in Table 5.2 showed very little P contamination. Inserting
those results into Eq. 6.15 yields negligible M reduction factors due to polarization: Cpol (174o )= 0.999 for 174 deg and Cpol (30o ) = 0.998 for 30 deg. Furthermore, by optimizing the /2 plateangle to the “S peaks” (see Sec. 5.4), any residual P components are prevented from entering thehalf mirror, thus Cpol w100%. During beam time, these “S peaks” were confirmed to yield the
maximum M by conducting fringe scans as a function of the /2 plate angle scanned over a wide
range (>180o )[40]. This is consistent with the fact that these angles also yield the best power balance
between the upper and lower paths as demonstrated in Sec. 5.4.

6.6

Power Imbalance

The calculations in Sec. 2.2 had assumed equal magnetic field amplitudes for both laser paths i.e.
!
B1 = B2 (B1(2) ⌘ B1(2) ). In order to represent the case of power imbalance i.e. B1 6= B2 , themagnetic fields are rewritten as :⇣!
!
↵⌘B1 = B1 (sin (✓/2) , cos (✓/2) , 0) cos !t k1 · !
x
2
⇣
!
!
↵⌘
B2 = B2 ( sin (✓/2) , cos (✓/2) , 0) cos !t k2 · !
x +(6.17)
2
Consequently, the field intensity in Eq. 2.4 is modified to Eq. 6.18 and M is reduced as in Eq.
6.19:
✓
◆
! ! 2 B12 + B22
2B1 B2B1 + B2 =1+ 2
cos (2ky y + ↵) cos ✓(6.18)
2
B1 + B22hi
2B1 B22B1 B2
2
Mred = 2
|cos
✓|
exp
2
(k
)
= 2
·M
(6.19)yy
B1 + B22
B1 + B22
From Eq. 6.19, the M reduction factor due to power imbalance is expressed as :p
p
2 P1 /P2
2B1 B2
2 R12
Cpower = 2==
1 + P1 /P2
1 + R12
B1 + B22

110

✓

!2

P1(2) ⌘ B1(2) ;R12 ⌘ P1 /P2◆(6.20)

6.6.1

Static Factors for Power Imbalance

The static factors that contribute to power imbalance are:• the non-zero reflectance of lenses and prisms, the deviation from the ideally 100% reflectanceof mirrors (> 99% by design), and the deviation from the ideally 50% reflectance of the half
mirror for S polarized light (< 0.5 % from both catalogue and measurement). There are nearly
the same number of optical components in each path, thus these small factors should not causea significant M reduction.
• incoherent misalignment of each laser path downstream of the half mirror.

From Sec. 5.5, power imbalance was directly measured to be about 95% on Apr 30, 2014. This gives
a negligible Cpower > 0.999. Figure 5.11 shows another example of well balanced power provided
the /2 plate is set as to allow only S polarized light to enter the half mirror.
6.6.2

Power Imbalance Due to Incoherent Power Jitter

Apart from static power imbalance, if the power of each laser path jitters independently shot-byshot, the incoherent eﬀect can also lead to power imbalance. This eﬀect is studied using simulation
as follows. Here, fringe scans of Nav = 10 and nominal M0 = 0.636 are generated for 1000 pseudo experiments. The only input jitter is the power jitter P1(2) applied in a random Gaussian distribution
to the upper (lower) laser path. For ( P1 , P2 ) = (10%, 10%), (20%, 20%), (30%, 30%), (5%, 10%),(10%, 20%), (10%, 30%). Table 6.2 shows Cpower (defined in Eq. 6.20) as the statistical results of
the 1000 pseudo experiments. Figure 6.8 shows the simulation results of the measured modulation
Mmeas for the first 100 pseudo experiments.

power jitter ( P1 , P2 )(5%, 10%)(10%, 10%)
(10%, 20%)
(10%, 30%)
(20%, 20%)
(30%, 30%)

Cpower
0.998±0.000
0.997±0.000
0.993±0.000
0.985±0.001
0.989±0.001
0.972±0.002

Table 6.2: Cpower (defined in Eq. 6.20) as the statistical results of the 1000 pseudo experiments, forrandom power jitter ( P1 , P2 ) = (10%, 10%), (20%, 20%), (30%, 30%), (5%, 10%), (10%, 20%),(10%, 30%) applied to the upper (1) and lower (2) paths.

The following observations are made:• A larger power jitter in either path apparently leads to greater M reduction (from the meanof Mmeas and/or Cpower ) and a larger fluctuation in Mmeas .
• The M reduction due to incoherent power jitter is in general worse beyond the statistical error
ranges than that predicted from static power imbalance using Eq. 6.20. For instance, a static
P1 /P2 = 20% gives Cpower = 0.994, while the jitter simulation for ( P1 , P2 )=(20%, 20%)
gives 0.989±0.001; a static P1 /P2 = 30% gives Cpower = 0.984, while the jitter simulation for( P1 , P2 )=(30%, 30%) gives 0.972±0.002.
111

Some possible causes for incoherent power jitter are:
• The higher order eﬀects from timing jitters, including the fine O(10) ps components seen in
the temporal profile, may aﬀect the position /angle of the laser pulses when entering into thehalf mirror. This in turn may lead to incoherent angular jitters when entering the focal lenses
in each path, and thus power imbalance at the IP.
• The turbulence from air flow and the vibration of the mirrors in each path.
However, the power measurement in Sec. 5.5 indicates that the power jitter for each laser path is< 1%. Therefore, based on the above-mentioned simulation results, the M reduction due to power
jitter is confirmed to be negligible.

Figure 6.8: The simulation results of Mmeas (for the first 100 events out of 1000 pseudo experiments)
for the random power jitter P1(2) applied to each of upper (lower) laser paths. The left columns
are for equal jitter applied to both paths: ( P1 , P2 ) = (10%, 10%), (20%, 20%), (30%, 30%). The
right columns show the same for diﬀerent jitter applied to each path: ( P1 , P2 ) = (5%, 10%), (10%,20%), (10%, 30%).

6.7

Laser Path Misalignment

The misalignment of the laser position at the IP leads to fringe contrast bias i.e. the reduction of
Mmeas . The consequence can be classified as follows:
1. The precision of the laser position w.r.t. the e beam center position at the IP during collision
is aﬀected.
2. The overlap of the two laser beams at the IP is aﬀected, leading to profile imbalance (i.e. laser
imbalance). Some other possible causes for profile imbalance are the divergence of the laser
beam after emerging from the reducer, and the misalignment of the focal lens. Section 4.2.3
explained the lens adjustment for optimizing laser focusing.
The crossing of the laser paths is maintained well aligned to the e beam at the IP by adjusting
mirror angles using actuators (see Sec. 4.2.1). As position precision is generally better than 10% of
the laser spot size ( laser ), misalignment should not be a major issue. However, the realistic laser
profile has a certain degree of laser pointing jitter, as seen from the shot-by-shot fluctuation of thelaser profiles monitored by CCD cameras (see Sections 5.2 and 5.3). The bias from relative position
misalignment is worse for a smaller laser w.r.t. the horizontal e beam size. Also, either the laser
or beam position may drift over time before alignment is repeated. These non-static factors could
lead to unexpected M reduction.

112

The following subsections evaluate the M reduction due to misalignment. First, the intercorrelated eﬀects of relative position oﬀset and profile imbalance will be considered, then the two
factors will be separated. The calculations assume a Gaussian laser profile (as seen in Fig. 5.5),
equal total laser power for the two paths, and y ⌧ t,laser .
6.7.1

Description of Laser Profile

In Sec. 2.2, the Compton signal intensity is calculated by the integration of the e beam profile! !2
over the laser fringe intensity which is calculated as B1 + B2 i.e. the magnetic field averaged overtime in the lab frame. Here, Eq. 2.2 will be rewritten as Eq. 6.21 assuming Gaussian laser profiles
Pt,laser (x, y) and Pz,laser (z) in the transverse and longitudinal dimensions, respectively.
q
⇣
!
!
↵⌘
B1 = B (sin (✓/2) , cos (✓/2) , 0) P1z,laser (z)P1t,laser (x, y)cos !t k1 · !
x
2!
B2 = B ( sin (✓/2) ,cos (✓/2) , 0)q⇣
P2z,laser (z)P2t,laser (x, y)cos !t! ! ↵⌘
k2 · x +2(6.21)The schematics of transverse and longitudinal position misalignment were shown in Figures 4.4
and 4.5, respectively. When there is a transverse oﬀset of l1 and l2 from the e beam center (defined
here at (0, 0, 0)), the transverse distances from the laser beam center to coordinate (x,y) can be
expressed as t1 = xsin 2✓ ycos 2✓ + l1 and t2 = xsin 2✓ + ycos 2✓ + l2 31 . Using these, the transverse
laser profiles Pit,laser (zx, y) (i = 1 (2): upper (lower)) are expressed as:
✓
◆
✓
◆
t21
t22
exp
exp
2
2
2 1t,,laser
2 2t,laserqP1t,laser (x, y) =P2t,laser (x, y) = q(6.22)
2
2
2⇡ 1t,laser2⇡ 2t,laser
Similarly, for a longitudinal oﬀset of z between the two laser beams at the IP, the longitudinallaser profiles Piz,laser (z) (i = 1 (2)) are expressed as:
✓
◆
✓
◆
(z
z/2)2
(z+ z/2)2
exp
exp
2
2
2 1z,laser
2 2z,laserqqP1z,laser (z) =P2z,laser (z) =(6.23)
2
2
2⇡ 1z,laser2⇡ 2z,laser
6.7.2

Longitudinal Misalignment

The M reduction factor due to longitudinal position misalignment and profile is [22]:01s2
2 1z,laser 2z,laserz0⇣⌘ACz,align =
exp @
2
2
2
2
+
1z,laser2z,laser4+
1z,laser(6.24)

2z,laserThis is equivalent to the multiplication of two M reduction factors: Cz,pos due to a longitudinaloﬀset z between the two laser paths (Eq. 6.25) and Cz,pro due to profile imbalance (Eq. 6.26).
!
z2
Cz,pos = exp(6.25)
2
8 z,laser
31

l1 and l2 have the same sign if oﬀset is in the same direction, and vice versa

113

Cz,pro =6.7.3

s

2 1z,laser 2z,laser
221z,laser + 2z,laser(6.26)

Transverse Misalignment

In evaluating laser path misalignment in the transverse plane, we will assume that y cos (✓/2) ⌧32 , and l = 0 (since only the relative oﬀset |ll2 | is meaningful). The corresponding M
2
1t,laser
reduction factor is [22] :v
pu
2 exp (At ) / 1t,laser 2t,laser
1u
Ct,align =(6.27)⇣⌘2t⇣⌘2
x sin(✓/2)
l1
1
1
+
exp
/
+
1/
1,t,rel2,t,rel2t,l1t,rel

At =

q

⇣
⌘
2
l12 2 2,t,laser+ x2 sin2 (✓/2)✓⇣⌘2 ◆x sin(✓/2)
2
2
8 1t,laser 2t,laser 1 +t,lHere, the following notation is used:

t,l⌘i,t,rel⌘Equation 6.27 represents the coupled eﬀects ofprofile and position. On the other hand, they can be evaluated separately under certain assumptions.
If we assume no position misalignment i.e. |l1 l2 |=0 , the M reduction factor due to profile
imbalance only is expressed as:v
p
2/ 1t,laser 2t,laser u
1u
Ct,pro =(6.28)⇣⌘2t
1/ 1,t,rel + 1/ 2,t,rel
1 + x sin(✓/2)
t,l
2i,t,laser +2
2
x sin (✓/2) +2
y cos (✓/2) (i =1, 2).

⌘ 1/2
p ⇣
2
2
2 1/ 1,t,laser+ 1/ 2,t,laser
and

If we assume a perfectly balanced profile i.e. 1t,laser =transverse position alignment only is expressed as:

2t,laser , the M reduction factor due tov
u
2 exp (At ) / 1,t,laser1u
Ct,pos = ✓
⇣
⌘2
t
⇣
⌘2 ◆
x sin(✓/2)
l1
1
1+
1 + exp/
1,t,rel2
1t,laser
1t,relAt =⇣⌘2
l12 2 1,t,laser+ x2 sin2 (✓/2)✓⇣⌘2 ◆x sin(✓/2)
4
8 1t,laser 1 +1t,laser(6.29)

Figure 6.9 compares the M reduction for Ct,align (Eq. 6.27) and for the multiple of the two
individual factors Ct,pro · Ct,pos . The non-zero discrepancy is an indication of the coupled eﬀect
between the two factors. However, this discrepancy is a negligible level of < 1%.
simplified version
If

y ⌧
32

t,laser andx sin (✓/2) ⌧This is valid since thet,laser can be assumed, Eq. 6.27 can be simplified to:

y at interest < 100 nm, andt,laser is typically about 10µm

114

Ct,align '2t,laser exp



1
2

⇣

2

p

1t,laser 2t,laser

l1
1t,laser⌘2+

1t,laser exp

⇣l1

2 1t,laser⌘2(6.30)

However, since x ' t,laser ' 10 15 µm for recent ATF2 operation, the assumption x sin (✓/2) ⌧t,laser is not valid for ✓=174 deg mode. In this case, the precise expression in Eq. 6.27 must be
used.
6.7.4

Evaluation of Misalignment

Regarding profile imbalance, only the transverse profile t,laser can be inferred separately for eachlaser path, from laser wire scans. As for the longitudinal profile, the same ratio in z,laser between
the two paths is assumed as that for t,laser . The worst limits for Ct,align and Cz,align are estimatedassuming the following typical conditions (according to observations): t(z),laser w 15 µm, x w
12 µm, position alignment precision better than 10% of t(z),laser , profile balance better than 10:7.
These give Ct,align > 98.7% and Cz,align > 96.8%. The total M reduction factor due to position
misalignment is expressed as Calign = Ct,align · Cz,align >95.5%.

Figure 6.9: (left) The M reduction due to transverse position misalignment (Ct,pos : red) and profile
imbalance (Ct,pro : green) , as well as the multiple of the two uncoupled factors (Ct,pos · Ct,pro : blue).
(right) The comparison of Ct,pos · Ct,pro with the M reduction calculated using the precise expression
for Ct,align in Eq. 6.27.

6.8

Spherical Wavefront Eﬀects

The calculations in Sec. 2.2 used plane wave assumption for the laser colliding with the e beam.
However, realistically the laser has the spherical wavefronts characteristic of a Gaussian-like beam.
The plane wave approximation is valid only at the focal point where the curvature radius is infinite.
If the location of laser crossing and/or laser-beam collision is deviated from the laser focal point,
the e beam would interact with “distorted” fringes due to spherical wave-front eﬀects (Fig. 6.10).
This leads to M reduction calculated as follows[22]: Here, it is assumed that two Gaussian laser
beams propagate in y, and that the laser-beam collision is oﬀset by y w.r.t. the laser focal point (=crossing point) defined at (0,0,0). Defining y ⌘ y/zR to be the relative oﬀset w.r.t. the Rayleighlength zR , the resulting M reduction factor is:

Csphere = 1 + y 2

2

1/4 6

41 + ⇣

115

y2
y2
1 + zR 1+
2k x2

3 1/4

7
⌘2 5

(6.31)

In recent operation, the horizontal e beam size x is typically 12 µm, and zR is measured to be
2.6 mm (see Sec. 5.1.2). Figure 6.11 shows the dependence of Csphere on lens alignment precisionfor (left) zR = 2, 3.5, 5.1 mm, assuming x = 12 µm and (right) for x = 20, 12, 2.2 µm, assuming zR= 2.6 mm. It can be seen that the tolerance for lens misalignment is looser for a longer zR and/or
a smaller x . The measured zR = 2.6 mm and lens alignment precision of typically better than 0.5
mm gives y < 19%. Inserting these into Eq. 6.31, Csphere is estimated to be > 98.8%. This eﬀect
is a concern only for measuring the smallest y using the 174 deg mode.

Figure 6.10: The schematics of the eﬀect of Gaussian spherical wavefronts when the collision of laserand e beam is oﬀset from the laser waist.

Figure 6.11: The dependence of Csphere on lens alignment precision shown for (left) Rayleigh lengthzR = 2, 3.5, 5.1 mm, assuming x = 12 µm and (right) for x = 20, 12, 2.2 µm , assuming zR = 2.6
mm.

116

6.9

Change of the Beam Size within the Laser Fringes

The sudden strongly focusing of y to O(10) nm requires the beam to have a large divergence angle
at the IP (i.e. a short curvature radius). Therefore, the growth in y within the finite longitudinallength of the laser fringes needs to be taken into account (see Fig. 6.12). The “eﬀective beam size”
y,ef f can be written as a function of the longitudinal coordinate (z) on the laser fringe as:r"y 2
2(6.32)
y,ef f (z) =y (0) + ⇤ zyqThis shows the dependence on the beam divergence angle "y / y⇤ , which is determined by thepemittance "y and the IP beta function y⇤ . Here, y (0) = "y y⇤ is the nominal beam size, assuming
all chromatic aberrations have been corrected. Since the laser Rayleigh length (' 5 mm) is much
longer than y , the e beam is assumed to interact with laser fringes that stretch homogeneously
in y. On the other hand, in the longitudinal (z) direction,a finite
spread of about z,laser aﬀects⇣⌘
fringe intensity as : 1 + cos ✓ cos (2ky y + ↵) ! exp
reduction from this eﬀect is[22]:z22 z,laser{1 + cos ✓ cos (2ky y + ↵)}. The M

1
Cgrowth = q"y2
1 + 4ky2 z,laser⇤(6.33)yAssuming a typical z,laser w 10 µm, Cgrowth > 99.7%. This corresponds to a negligible beam
size growth of < 0.2 nm for y = 37 nm. This factor is nearly equally negligible for all modes, withexception of the 174 deg mode, which receives the heaviest impact relative to the minuscule y .

Figure 6.12: The schematics of the change of beam size inside the longitudinal spread of the laser
fringes.

117

7Study of Signal Jitters and Drifts

The previous Chap. 6 described the M reduction factors aﬀecting beam size measurements. The
most important M reduction factor is phase jitter. The purpose of this chapter is to provide theunderstanding of the other signal jitter sources which is necessary for the analysis of phase jitter. The
most important sections are Sections 7.4 - 7.7, where simulation assuming realistic ATF2 experimentconditions is used to demonstrate the extraction of phase jitter from fringe scan data. An original
method was developed for this purpose. Finally Sec. 7.8.1 evaluates phase jitter from actual beamtime data.

7.1

Signal Jitter Sources

This section describes the individual signal jitter sources (also see [40][41]). Out of these, phasejitter was first brought up in Sec. 6.3 as a M reduction factor, while the other jitter sources arenecessary for its understanding.
Fast signal jitter sources that vary shot-by-shot cause fluctuations of the measured signal energy
and consequently degrade beam size measurement precision and beam tuning eﬃciency. Detectionof smaller M values may even become impossible under very heavy jitters comparable in scale to thesignal modulation itself. At the low e bunch charge (. 1 ⇥ 109 ) used for small y measurements
during recent ATF2 operation, the relative signal jitter (w.r.t to Eavg ) is typically observed to be
15-25 % at peaks and bottom phases of fringe scans and and 25-35% at mid-points phases. Thisvaries depending on the conditions of the laser and/or the e beam. Individual jitter sources areassessed by improving hardware or oﬄine data correction.
7.1.1

Phase Jitter (Vertical Relative Position Jitter)

Section 6.3 introduced phase jitter ( ' ), or equivalently vertical relative position jitter ( y) as oneof the dominant M reduction factors. The signal jitter caused by ' depends on M and fringe scan
phase ', and can be expressed as :
r
⇣
⌘2 r
⇣
⌘2
Ep =
E (') E (') = E (')2
E (')
(7.1)
= Eavg M

r

1⇥
1
2

2 cos2 (') exp

2'+ cos (2') exp

2 '2

⇤

Here, E (') and E (')2 are expressed using the modulation already reduced by2
M · exp' /2 as:E (') =

ˆ

exp

✓
2

E (') =

'02
2 '2
ˆ

◆

⇥
⇤
Eavg 1 + M cos ' + '0 d'0 = Eavg (1 + Mred cos ')

exp

✓

'02
2 '2

◆

⇥
⇤ 2 0
Eavg 1 + M cos ' + '0
d'⇥2
2 /2 · exp= Eavg1 + 2Mred cos ' + Mred2'

+ cos (2') exp' :Mred =

(7.2)

(7.3)
2
'

⇤

Using a method described in Sec. 7.4, the ' extracted by fitting fringe scan data is typically
400 - 750 mrad for the 174 deg mode. For example, when measuring a nominal y of 45 nm (M0 =0.56 for 174 deg mode), a ' of 500 mrad ( y w 21 nm) causes signal jitter w.r.t Eavg of about
9% at the fringe peak or bottom, and about 25% at the mid-point.
118

7.1.2

Statistical Fluctuation

Section 3.6 gave the evaluation of the statistical fluctuation of the measured Esig , which is the combined eﬀect of Compton photon statistics and detector response. It was shown that the contribution
to relative signal jitter is < 1% from the fluctuation of the number of photo-electrons (Npe > 10000)
output from the PMT photocathodes, 5-10% from the statistical fluctuation of the number of Compton photons per bunch (Nsig =100-350), and 14-27% from the fluctuation of shower development.
Section 3.6.3 took into account the small eﬀect (> 1%) from photon angular jitter and the signal
reduction due to the possible misalignment of the movable collimator. From all of the above, thestatistical signal fluctuation is estimated to be about 15-28% 33 .
7.1.3

Background Energy Fluctuation

The Compton signal energy is measured using the “ON/OFF” method (see Sec. 3.5.4), for which
the signal energy (Esig ) is calculated by subtracting “OFF events” (EOF F ) from “ON events” (EON :signal+BG) as Esig = EON EOF F . Variations in BG conditions may arise from an enhancementin the interaction between the beam halo and beam pipe triggered by beam orbit instability. Given
the suﬃciently high S/N ratio of ?50 in recent operation, the relative signal jitter due to BG energy
jitter is < 5% w.r.t. Eavg and not problematic.
7.1.4

Laser Timing Jitter

Sections 3.4.2 and 4.2.5 described the mechanism of laser timing adjustment. Laser timing ande beam timing are monitored using the signals from PIN-PDs and strip-line BPMs, respectively.
Sub-ns precision matching is carried out during beam time by scanning laser Q-switch timing using
digital modules. The design FWHM laser pulse width is 8 ns, while the e beam pulse width isabout 20 ps. Therefore, relative timing jitter (dominated by laser timing jitter) on the order of O(1ns) would aﬀect the intensity of the laser colliding with the e beam pulse by pulse. This results insignal jitters expressed as:
⇣
⌘
´
t2
p 1 2
dt expPlaser (t)22 t
Etiming
2⇡ t
´
=1
(7.4)
Eavg
dt (t) Plaser (t)
s
✓
◆2
2
1
t,rms
t
=1
2
2 ⇡ 2
t,rms
t,rms +t
Here, t represents
the⌘relative timing between the laser and the e beam, andt its jitter.
⇣t2
Plaser (t) / exp
is
the
laser
temporalprofilewithadesign
RMS
pulse
width
of t,rms
2 2t,rms= 3.4 ns. In order to maintain signal jitters to < 5%,t should be suppressed to . 1 ns. The
horizontal fluctuation of the laser temporal profile observed using an oscilloscope (see Fig. 3.24)
indicates laser timing jitter to be about 1 ns (RMS)34 . From Eq. 7.4, this leads to a signal jitter ofabout 4.3%.
33
The evaluation of statistical fluctuations here does not take into account the eﬀect from other energy jitter sources
e.g. phase jitter or horizontal relative position jitter. These are mentioned separately in the following subsections.
34
There are finer structures of O(10) ps order observed in the temporal profile that could also possibly aﬀect theintensity of collision with the e beam pulse with has a similar time scale. However this is beyond the resolution of
the PIN-PD.

119

7.1.5

Total Laser Power Jitter

The signal jitter due to the total power jitter

P/P is:Epower
P
=
Eavg
P

(7.5)

The power measurements in Sec. 5.5 show total laser power jitter to be .1%. The contribution
to signal jitters is negligible compared to the change in laser intensity during collision with the ebeam such as due to position oﬀset at the IP.
7.1.6

Horizontal Relative Position Jitter

Laser pointing jitter and/or horizontal e beam position jitter leads to fluctuation in the laser
intensity intercepted by the e beam. Jitter conditions can change over time depending on thestability of the laser and the e beam. The estimated laser pointing jitter in Sec. 5.3 is approximately
consistent with the laser profile fluctuation (< 5% of the laser spot diameter) observed using CCD
cameras. Here, relative position and its jitter will be denoted as x andx , respectively. The
signal jitter due tocanbeexpressed
as:
x
⇣
⌘
´
x2
p 1 2
d x exp
Ppos ( x)
2
2⇡ x
Erel
2⇡ x
´
=1
(7.6)
Eavg
d x ( x) Ppos ( x)
s
=1

⇣

⌘
2

2
lw

2
lw +

2

x

x
Here, Ppos ( x) / exp
is the Gaussian profile based on relative position, whose width22 lw
x is evaluated using a laser wire scan tolw is the fitted sigma in a laser wire scan. In Sec. 5.3,
be 16±5% of lw . Using Eq. 7.6, this causes 1.3±0.9% in signal jitters.

7.1.7

Electron Beam Intensity Jitter

The jitter of the e beam intensity directly leads to jitters in the Compton signal energy. To
suppress this, the measured signal energy is normalized pulse by pulse by the beam bunch charge(Ne ) measured by the “ICT monitor” introduced in Sec. 3.5.4 (Fig. 3.34). Figure 7.1 shows the Ne
measured during a single fringe scan. The beam intensity jitter Ne /Ne is typically 5-10%. This
“ICT correction” process can reduce the signal jitter due to Ne /Ne down to the the resolution of
the ICT monitor, which was evaluated to be about 2 %[22]. However its resolution may become
degraded due to surrounding electronics noise. Typically, a jitter reduction of . 2% is observed
after ICT correction.

120

Figure 7.1: A histogram of the e beam bunch charge (unit: 109 / bunch) measured by the ICT
monitor during a single fringe scan. Here, the beam intensity jitter is about 6%.

7.2

Modeling of Signal Jitters

The signal jitter ( E) in a fringe scan is defined as the standard deviation of Nav (= number ofpulses) events of energy measured at each phase. Total signal jitter can be expressed approximately
as a convolution of vertical jitter ( EV ) and the jitter due to phase jitter ( Ep ) as :q
4E = 4EV2 + 4Ep2
(7.7)
The expression for

Ep was given in Eq. 7.1. Vertical jitter is expressed as :
r
⇣
p ⌘2
2
EV = Cconst+ Cstat E + (Clinear E)2(7.8)

Each jitter component is assumed to follow a Gaussian distribution. Cconst is mainly related toelectrical noise of the detector 35 . Clinear is related to laser related instabilities e.g. timing, power,
and position, as well as e beam intensity jitter. The stochastic term Cstat represents the statisticalsignal fluctuations, which depends on the fluctuation of the number of Compton signal photons
reaching the detector as well as detector response. Typically, the Cstat term is dominant over theterms Cconst and Clinear . The Clinear term may vary over time, while the terms Cstat and Cconst
remain relatively stable.

7.3

Calibration of Detector Response

The following calibration was performed to evaluate the linearity and the fluctuation related to the
response of the gamma detector response. Beam bunch charge (Ne ) was changed in steps while
recording E and E, defined as mean and standard deviation, respectively, of the measured signal
energy for each Ne . Only the upper laser path was made to collide with the e beam by setting its
position to the peak of a laser wire scan.
35
For the analysis of phase jitters, BG fluctuation is subtracted from the signal jitters. Thus the eﬀect of BG
fluctuation should not be included in the term Cconst

121

Figure 7.2 shows good linearity of E w.r.t. a wide intensity range from Ne ⇠ 0.5 ⇥ 109 to
Ne ⇠ 3.5 ⇥ 109 36 . Figure 7.3 shows E plotted as a function of E, and fitted with Eq. 7.9 with 3
free parameters Cconst , Cstat , and C2 .
r
⇣
p ⌘2
2
E = Cconst+ Cstat E + (C2 E)2(7.9)

Here, C2 is mainly caused by the intensity fluctuation of the e beam and the laser at the IP.
The terms Cconst and Cstat are approximatelypconsistent with those in Eq. 7.8 for the same detector
condition. The fitted p
result gives Cstat = 6.2· unit of E. The stochastic term contributes to relative
signal jitter as Cstat / E : about 17% (w.r.t. Eavg ) for low E corresponding to Ne = 1 ⇥ 109 , andabout 10% for a higher E corresponding to Ne = 3 ⇥ 109 . The relationship between Ne and E are
derived using the linearity plot in Fig. 7.2. The Cstat derived for each Ne is used for ' analysis in
Sec. 7.8.1.

Figure 7.2: The linearity of the gamma-ray detector response is demonstrated by plotting energy
measured as a function of e beam bunch charge (Ne [109 ]) . The fitted result is : E [a.u] = 650⇥
Ne .
36
In fact, the same linearity and slope was obtained when this measurement was conducted one month later, despitethat the e beam orbit conditions were diﬀerent from this measurement.

122

Figure 7.3: The calibration of the fluctuation related to detector response: energy jitter is plotted
as a function of energy, and fitted with Eq. 7.9. Here, energy is shown in the form of the sum of
ADC counts of the front four detector layers, which is the usual case for fringe scan analysis.

7.4

Method for Deriving Phase Jitter

An original analysis method has been developed for the purpose of extracting phase jitter ' fromfringe scan data; it is the first ever to be able to do so. In this section, this method will be explainedusing the Monte Carlo simulation plots in Fig. 7.4; here Compton signal energy E is generated
according to:
E = Eavg {1 + M · cos (' + '0 )}(7.10)In Eq. 7.10, the phase ' is jittered according to a certain distribution. In Sec. 7.5, both Gaussianlike phase jitters and complex non-Gaussian phase jitters are tested. Furthermore, vertical jitters are
implemented as Eq. 7.8 according to a random Gaussian distribution. The phase jitter extraction
method comprises of the following two steps:
Step1: Figure 7.4 (top): the fitting of the M spectrum in a fringe scan with Eq. 2.10 to obtain
Mmeas , Eavg and '0 ; here the measured signal energy is plotted as a function of '.
Step2: Figure 7.4 (bottom): the fitting of the “signal jitter plot” by Eq. 7.7 to obtain ' ; here themeasured signal energy jitter (defined as the S.D. of the Nav events at each ') is plotted as afunction of '.
q
The Eq. 7.7 4E = 4EV2 + 4Ep2 used in Step 2., as explained in Sec. 7.2, assumes a convolutionof Gaussian distributed jitters comprised of phase jitters and vertical jitters. The signal jitter due
to ' ( Ep ) is given by Eq. 7.1. Vertical jitters ( EV ) is written as [42]:q222 E (') + C 2
EV = Cconst+ Cstat(7.11)
linear E (')
In this model, E (') (Eq. ??) and E (')2 (Eq. ??) take into account the eﬀect of ' on
the measured energy. The free parameters extracted from fitting are ' and Clinear . The fixed123parameters are the Mmeas , Eavg and '0 obtained in Step 1, as well as the estimated values of
the relatively time stable terms Cconst and Cstat . The dominant Cstat term is estimated using thedetector calibration results in Sec. 7.3 according to the e beam bunch charge of each scan; theeﬀect of the uncertainty of Cstat is shown in Sec. 7.6. The Cconst term, whose eﬀect is small, is fixed
to a pessimistic value of 5% w.r.t. Eavg 37 .
The fitting of the measured energy jitters in Step 2 is carried out by 2 minimization. The
statistical error of a variance value “ ” ( E in this case) is estimated as follows [43]: Taking s tobe the estimation of , the test statistic ns2 / 2 follows 2n 1 (↵), based on a 2 distribution withn 1 degrees of freedom and probability ↵. Defining the statistical error as 1 standard deviation(68% C.L.), the probabilities 0.84 and 0.16 will be used in calculating the upper and lower limits of
2 /s2 = n/ 2
n 1 (↵) as (in this case n () Nav ):
s
s
( )
(+)
Nav
Nav
=
=
(7.12)22ss
Nav 1 (0.16)
Nav 1 (0.84)
Therefore, the error bars for each point of the “signal jitter plot” are expressed as:
"
#
s
s
Nav
Nav
s s·
, s+s·
2
2
Nav 1 (0.16)
Nav 1 (0.84)(7.13)For a larger sample size (Nav ), because the 2n (↵) distribution approaches a standard distribution, the error bars are more symmetrical. On the other hand, the errorbars are more asymmetricalfor a smaller sample size. For example, Eq. 7.13 gives [0.0059 · s, 0.084 · s] for Nav =100, as opposed
to [0.875 · s, 1.42 · s] for Nav =10. In Sec. 7.8.1, where this method is applied to data analysis,Fig. 7.6 shows a fitted jitter plot for an actual fringe scan.
37

It has been confirmed that the diﬀerence in the fitted result of
to 5%.

124' is .1 % when Cconst is fixed to 0, as opposed

Figure 7.4: The schematics of phase jitter extraction using a two step process: (top) Step 1: themeasured M spectrum is fitted with Eq. 2.10 in order to obtain Mmeas , Eavg and '0 . (bottom)
Step 2: the energy jitter (S.D. of the Nav events) of the same scan is plotted as a function of ',then fitted with Eq. 7.7 to extract ' and Clinear . The fixed parameters are Mmeas , Eavg and '0
obtained in Step 1 and the estimated values of the relatively time stable Cconst and Cstat .

7.5

Simulation Test of Phase Jitter Extraction Method

This section uses simulation tests to demonstrate the precision of extracting ' using the method
described in Sec. 7.4, and using it to correct the measured M . This is important for precise yevaluation since ' is one of the dominant systematic errors. In the simulations, fringe scans are
generated assuming nominal modulation M0 = 0.636, corresponding to y0 =40 nm for the 174 deg
mode, and a realistic scenario of vertical jitter and phase instabilities.
7.5.1

Gaussian-like Phase Jitters

In this section, fringe scans are generated with the following input conditions:• Phase jitter ' is input into the Compton signal energy according to a random Gaussian
distribution as: E(', ' ) = Eavg {1 + M · cos (' + '0 + Gaus(0, ' )}. The input ' ( ',in )125covers a wide range of {0, 0.23, 0.47, 0.71, 0.94} rad. For the 174 deg mode, this corresponds
to relative position jittery of {0, 10, 20, 30, 40} nm.
• Vertical jitter is input according to Eq. 7.8, consisting of (5%, 20%, 10%) w.r.t. Eavg from
(Cconst , Cstat , Clinear ), each following a random Gaussian distribution 38 . This gives a typical
total vertical jitter of about 23% at the mid-point fringe scan phases (where E = Eavg ).
The fitting process described in Sec. 7.4 is used to extract ' . Then, the extracted ',out is used tocorrect the reduced Mmeas back towards M0 as Eq. 6.7. Figure 7.5 shows the simulation results as
the mean and statistical error of 1000 pseudo experiments for Nav =50 and Nav =10; the precision of',out and Mcorr is generally within tolerable ranges; The systematic bias intrinsic to this method
are observed as follows:• The relative deviation of Mcorr w.r.t. M0 is . 1% for Nav =50, and < 4.5% for Nav =10.
• The deviation of ',out w.r.t.
(with exception of zero- ',in ).

',in is < 15 mrad for Nav =50, and < 55 mrad for Nav =10• For smaller Nav , M is not reduced as much as the theoretic expectation Mmeas = M0 ·2
exp
' /2 (pink curve). This will be explained in Sec. 7.5.3.

Figure 7.5: Fringe scan simulation with input of Gaussian-like ' ( ',in = 0, 0.23, 0.47, 0.71, 0.94rad), and realistic vertical jitters totalling to about 23% w.r.t. Eavg . Shown here are the statisticalresults of 1000 pseudo experiments for Nav = 50 (top row) and Nav = 10 (bottom row). The leftplots show the extraction precision for ',out (red) w.r.t. the input ',in (green). The right plotsshow the reduction of Mmeas by ',in , and its correction (Mcorr ) using the ',out extracted in theleft plots.
38
a fringe scan, relative vertical signal jitter is expressed as
EV /Eavg =q At the mid point ofp2
22(Cconst /Eavg ) + Cstat / Eavg + Clinear . Therefore, a more strict expression would be “5% w.r.t. Eavg fromp
Cconst , 20% w.r.t.
Eavg from Cstat , and 10% from Clinear ”. In this thesis, the expression will be simplified byreferring to all terms as “w.r.t. Eavg ”.

126

7.5.2Complex Phase Fluctuations

The aim of this section is to study the eﬀect of a more complex and realistic non-Gaussian phasefluctuation. The fringe phase variation for a previous laser was measured by T.Yamanaka in 2009[32] using a phase monitor which used to be installed on the vertical table. This took place during
beam oﬀ time, thus excludes e beam jitters. Figure 7.6 shows the reproduced version of this phasepattern, whose amplitude has an RMS of about 0.45 rad. The original amplitude of the phasepattern is multiplied by a factor of {0, 0.5, 1, 1.5, 2}, and input into fringe scan simulation similar
to that in Sec. 7.5.1, assuming M0 =0.636 and vertical jitter comprised of (5%, 20%, 10%) w.r.t.
Eavg from (Cconst , Cstat , Clinear ). The purpose is to observe the precision of ',out and Mcorr i.e.
the correction of Mmeas using ',out as in Eq. 6.7. Two types of simulations are conducted; keeping
all other conditions (e.g. vertical jitters) the same, their diﬀerence lies in the input phase, explained
as follows:
1. Just the measured phase variation in Fig. 7.6 alone. Figure 7.7 shows the precision ofand Mcorr for Nav =50 and Nav =10.

',out

2. The measured phase variation in Fig 7.6 as well as the following additional input phase instabilities: a linear phase drift of 80 mrad/min (worse than typical), and a 0.7 rad jump at '=11rad. Figure 7.8 shows the precision of ',out and Mcorr for Nav =50 and Nav =10.

Figure 7.6: The measured phase variation of the laser fringes reproduced for 150 pulses in 3 Hz
intervals.

127

Figure 7.7: Fringe scan simulation using various amplitudes of the phase variation in Fig. 7.6 andrealistic vertical jitters totaling to about 23% w.r.t. Eavg . Shown here are the simulation results for1000 pseudo experiments for Nav = 50 (top) and Nav = 10 (bottom).
The plots on the left show the extraction precision of ',out w.r.t. the input (green). The plotson the right show the Mmeas reduced by ',in , and the precision of its correction using the ',out
extracted in the left plots.

128

Figure 7.8: Fringe scan simulation with the same input conditions as in Fig. 7.7, as well as thefollowing additional phase instabilities: a linear phase drift of 80 mrad/min, and a 0.7 rad jump at
the fringe phase '=11 rad. Shown here are the simulation results for 1000 pseudo experiments for
Nav = 50 (top) and Nav = 10 (bottom).
The plots on the left show the extraction precision of ',out w.r.t. the input (green). The plotson the right show the Mmeas reduced by ',in , and the precision of its correction using the ',out
extracted in the left plots.
Regarding the case of the original phase RMS '0.45 rad in 2., results are compared between
Nav =10, 20, 50, and 100 in Table 7.1 and Fig. 7.9. Here, Mcorr ⌘ Mcorr M0 is the error of Mcorr ,2
Mmeas is the deviation of Mmeas w.r.t. the expected value i.e. M0 · exp' /2 , and ⇣ C' is the⌘2
2 /2
deviation of the correction factor C' = exp/2(using
)
from
the
ideal
exp
',out
',out
',in
(using ',in ).

Nav
10
20
50
100

Mcorr /M0
- 0.1%- 2.1%⇠ 0%
0.3%

Mmeas /Mexp
4.8%
1.5%
0.9%
0.9%

C' /C',exp
5.3%
4.0%
0.9%
0.6%

Table 7.1: The comparison of results between Nav =10, 20, 50, and 100, for Mcorr w.r.t. M0 , andMmeas and C' w.r.t. their values expected from a Gaussian model. These are from simulation using
the particular input of phase amplitude RMS '0.45 rad, with all other input conditions same as inFig. 7.8.

129Figure 7.9: The measured phase variation in Fig. 7.6 with an amplitude RMS of about 0.45 rad is
input into fringe scan simulation along with a linear phase drift of 80 mrad/min, a 0.7 rad jump at thefringe phase '=11 rad, and realistic vertical jitters totaling to about 23% w.r.t. Eavg . Shown here
are the simulation results for 1000 pseudo experiments of the eﬀect on Mmeas and Mcorr (correctedusing ',out ) for Nav =10, 20, 50, and 100.

Interpretations:
The precision of ',out (w.r.t. the RMS of ',in ) and the precision of Mcorr (w.r.t. M0 ) is better fora larger Nav . These are explained as follows:
1. The realistic phase fluctuation is a combination of jitters and slower drifts. Its systematic
eﬀect on Mmeas depends on the time structure of the scan, which in turn depends on Nav i.e.
the time spent at each phase. The same phase variation ( ' ) behaves more like Gaussian-likejitters for a large Nav and more like slow drifts for a small Nav . Therefore, a large Nav is moresuited to the Gaussian model used for ' extraction.
2. Just as for the Gaussian jitters in Fig. 7.5, for a large Nav , Mmeas reduction is more in2
accordance with the expected M0 · exp' /2 . This will be explained in Sec. 7.5.3. Boththis and 1. explain the fact that the precision of Mcorr (obtained using Eq. 6.7) is better fora large Nav .
Regarding the most complex phase variation in Fig. 7.8, for Nav =50, good precision is observed
regardless of the amplitude of ',in 39 :• The deviation of',out (w.r.t. the RMS of',in ) is < 30 mrad,• The relative deviation of Mcorr (w.r.t. M0 ) is < 2 %.
For a smaller Nav =10, the ',out extracted using a Gaussian jitter model tend to be under-evaluatedw.r.t. the RMS of ',in . This is due to the eﬀect of drift components over-taking the eﬀect of jitter
components since less time is taken at each phase. However, the reduction of Mmeas itself tends tobe less apparent than that theoretically expected from a Gaussian model. Because the outcomes of
the two factors ',out and Mmeas partially cancel each other out, the relative deviation of Mcorr for
Nav =10 is still better than 4% for all inputs except the largest ',in =0.89 rad, for which it is better
than 10%. Note that ultimately, Mcorr is the factor important for precise beam size evaluation.
39

The discussions here are made with exception of the unrealistic case of zero- ',in . At zero input“fake ',out ” of about 48 mrad, due to the coupling to vertical jitters, to be explained in Sec. 7.6.

130',in , there is a

From Table 7.1 and Fig. 7.9, Mcorr precision is best for Nav =100 and Nav =50. Although theformer has a larger Nav , the more time consuming scan receives more M reduction from the significant input linear drift of 80 mrad/min, whereas the M correction only compensates for Gaussian-like
phase jitters. Similarly when comparing Figures 7.7 and 7.8, a slight diﬀerence can be seen for the
Nav =50 case, due to the eﬀect of the linear phase drift.
The extraction precision of Clinear , as well as the values extracted from actual fringe scan data
are given in Appendix E.
7.5.3

Interpretations of Modulation Reduction due to Phase Fluctuation

This section explains why the M reduction due to ' is more in accordance with the theoreti2
cal curve Mmeas = M0 exp' /2 for a larger Nav scan, and less apparent for a smaller Nav
scan [42]. Modulation is obtained by fitting the fringe scan data with the function (Eq. 2.10)
f (', Eavg , M, '0 ) = Eavg (1 + M cos (' + '0 )), based on the minimization of
2

=

N
X
{E ('i )f ('i , Eavg , M, '0 )}2
2
E,i

i

(7.14)The error bar ( E,i ) at each phase 'i (i=1, 2,..., N: N = numberof steps) is defined as thepstandard deviation of the Nav measured energy events divided by Nav 1.
Here we shall observe the distribution of cos ( ), where the set phase⌘ ' + '0 follows aGaussian distribution with sigma(= phase jitter). Figure 7.10 (top) shows the simulation resultsfor 1000 events assuming =0.7 rad at the fringe peak phase (mean =0), mid-point phase (mean= ⇡/2), and bottom phase (mean = ⇡).
The mean and standard deviation of cos ( ) for Nav events will be denoted as a and s, respectively.
Figure 7.11 shows the correlation between a and s at peak, mid-point, and bottom fringe phases,for 1000 pseudo experiments. At peak phase, the⇣ negative⌘ correlation between a and s indicatesthat the larger the mean of the measured energy E ( ) is, the smaller its standard deviation E
will be. In contrast, at bottom phase, the positive correlation between a and s indicates that thesmaller E ( ) is, the smaller E will be. In other words, the weight in Eq. 7.14 is “larger for larger
energy data” at fringe peaks and “larger for smaller energy data” at fringe valleys. Furthermore, thecomparison between Nav =10 and Nav =100 in Fig. 7.11 shows that this correlation trend is moresignificant for a smaller Nav . In conclusion, due to the enhancement in opposite directions at fringe
peaks and valleys, for the same amount of phase jitter, a smaller Nav scan tends to result in a larger
2
fitted Mmeas than the theoretical value M0 exp' /2 . Figure 7.12 shows the diﬀerence in M
reduction between Nav = 10, 50, and 100 with the same simulation input conditions as in Sec. 7.5.

Figure 7.10: The distribution of 1000 events of cos ( ), where is given a random Gaussian distribution with sigma=0.7 rad. From left to right: the distribution at the fringe peak phase i.e. mean
=0, mid-point phase i.e. mean = ⇡/2, and bottom phase i.e. mean = ⇡.
131

Figure 7.11: The correlation between the average and standard deviation of Nav events of cos ( ),where has a Gaussian distribution with sigma=0.7 rad. The red and green represent Nav =10 and
100, respectively. (top) at fringe peak phase i.e. mean =0 (middle) at mid-point phase i.e. mean
= ⇡/2 (bottom) at bottom phase i.e. mean = ⇡.

132

Figure 7.12: Simulation of M reduction due to a Gaussian-like ' inputs ( ',in =0, 0.23, 0.47, 0.71,
0.94 rad) and the same input conditions as in Fig. 7.5. Shown here for Nav = 10, 50, and 100 are
the statistical results of 1000 pseudo experiments.

7.6

Eﬀect of Vertical Jitters

This section uses simulation to evaluate the eﬀect of vertical jitters on the measured Mmeas and on
the extraction and compensation of ' . In this section, the vertical jitter terms Cconst , Cstat , andClinear in Eq. 7.8 are defined as the contribution to relative signal jitter w.r.t. Eavg in a fringe scan.
7.6.1

Eﬀect on Modulation

Fringe scan simulation was conducted as follows: vertical jitter was varied by changing only themost dominant term Cstat from 0% to 30%; ',in and the terms Cconst and Clinear are kept to 0.
Results are shown as the statistical results of 1000 pseudo experiments. Figure 7.13 (left) shows theeﬀect of vertical jitter on Mmeas for Nav =50 and Nav =10. It can be concluded that vertical jitters
do not cause apparent M reduction. Figure 7.13 (right) shows the relative error of Mmeas , definedas the standard deviation of 1000 events divided by their average; the standard deviation
increasespwith vertical jitters, and is larger for a smaller Nav by a factor of approximately Nav . It has been
confirmed that similar results are obtained when Cconst or Clinear are changed.

133

Figure 7.13: Simulation of the eﬀect of vertical jitter on Mmeas shown for fringe scans of Nav =50(red) and Nav =10 (blue); input conditions are: M0 = 0.636, (Cconst , Clinear ) = (0%, 0%), ',in = 0
rad, and Cstat changed in steps from 0% to 30% w.r.t. Eavg . Shown here are the statistical resultsof 1000 pseudo experiments as a function of vertical jitter (Cstat ): (left) Mmeas and (right) the
standard deviation of 1000 events of Mmeas divided by their average.
7.6.2

Eﬀect on Phase Jitter Extraction and Compensation

For the same simulation as in Fig. 7.13, keeping in mind that the input ',in is zero, Fig. 7.14
shows the “fake ',out ”, defined as the non-zero ',out extracted from fitting by the method in Sec.
7.4. This indicates the bias of ',out determination attributed to the coupling from vertical jitters
40 . For a typical C
stat = 15%, the fake ' is about 30 mrad and 55 mrad for Nav = 50 and Nav =10, respectively.

Figure 7.14: For the same simulation as in Fig. 7.13 with zero input
from fitting is plotted as a function of the input vertical jitter.

',in , the “fake',out ” extracted

Uncertainty of Vertical Jitter Estimation
The accuracy of ',out is aﬀected by the precision of the value of Cstat fixed during the ' extraction process (Cstat,f ix ). From the calibration results in Fig. 7.3, Cstat,f ix is estimated with a40

Here, the bias of',out is based on the average output value of the pseudo experiments in the simulation.

134

relative precision of about 20% 41 . For bunch charge 1 ⇥ 109 , Cstat is estimated as 17.2±3.8% i.e.
Cstat =±3.8%. Here, Cstat ⌘ Cstat,f ix Cstat is the absolute error of Cstat,f ix (i.e. the deviationfrom the true Cstat ).
Fringe scan simulation was conducted in order to evaluate the eﬀect of the uncertainty of Cstat,f ix
on the extraction and compensation of ' . The input conditions are: M0 = 0.636, ',in = 0.47 rad(Gaussian), and (Cstat , Cconst , Clinear ) = (17%, 5%, 10%). While the true Cstat (input) is 17%,
Cstat,f ix is changed as {12%, 13.5%, 17%, 20.5%, 22%} in the fitting process to extract ',out . The
extracted ',out is then used to correct Mmeas as in Eq. 6.7. Table 7.2 lists the results for theparticular cases of Cstat = 0%, 3.5%, and -3.5%, for Nav = 50 and Nav = 10:• The relative error of',out (|',out / ',in |) is < 6.5% for Nav = 50, and . 7.5% for Nav = 10.

• The relative error of Mcorr (| Mcorr /M0 |) is < 1.5% for Nav = 50, and < 4% for Nav = 10.
Figure 7.15 shows the simulation results as a function of Cstat,f ix . It can be seen that the underestimation of Cstat,f ix leads to the over-evaluation of ',out and thus the over-correction of Mmeas ;and vice versa, the over-estimation of Cstat,f ix leads to the under-evaluation of ',out and thus
the under-correction of Mmeas . This can contribute to the systematic error of ' extraction andcompensation.

Nav = 50
Nav =10',out / ',in
Mcorr /M0',out / ',in
Mcorr /M0

Cstat = -3.5%
4.9%
1.5%
4.7%
3.8%

Cstat = 0%
⇠ 0%
0.5%
- 0.2%
2.6%

Cstat =3.5%- 6.4%- 0.9%- 7.4%
1.0%

Table 7.2: Relative systematic errors ( ',out / ',in and Mcorr /M0 ) due to the under/overestimation of the Cstat value fixed in the ' fitting process; these result from fringe scan simulationfor 1000 pseudo experiments. Input conditions are: M0 = 0.636, (Cstat , Cconst , Clinear ) = (17%,5%, 10%) w.r.t. Eavg , and ',in = 0.47 rad.

Figure 7.15: From the same fringe scan simulation as as in Table 7.2: ',out (left) and Mcorr (right)
as a function of the fixed value of Cstat . Results are shown as the statistical results of 1000 pseudo
experiments for Nav = 50 (red) and Nav = 10 (blue).
41
This evaluation takes into account the uncertainty of the relationship between bunch charge and energy in Fig.
7.2 as well as the fitting precision of Cstat in Fig. 7.3.

135

7.7

Conclusion on the Precision of Correction for Phase Fluctuation

This section draws a conclusion on the precision of the evaluation of systematic errors due to phasefluctuation 42 . This was studied using simulation in Sections 7.5 and 7.6.
For a Gaussian-like phase jitter (Sec. 7.5.1):• The relative deviation of Mcorr w.r.t. M0 (| Mcorr /M0 |) is . 1% for Nav =50, and < 4.5% for
Nav =10.
• The deviation of
for Nav =10.

',out w.r.t.

',in (| ',out',in |) is < 15 mrad for Nav =50, and < 55 mrad

On the other hand, the more realistic and complex phase variation (Sec. 7.5.2) is a combinationof Gaussian-like jitters and slow drift components. In this case, it is more meaningful to focus
on the precision of Mcorr , rather than the value of the extracted ',out itself. Ultimately, Mcorris the important factor for precise y evaluation. For the same phase variation pattern, both theextracted ',out and the reduction of Mmeas are dependent on Nav . Therefore the outcome of Mcorr
2(= Mmeas / exp',out /2 as in Eq. 6.7) is the combined result of the two. This was explained inSec. 7.5.3. The relative deviation of Mcorr w.r.t. M0 is observed as follows:• For Nav =50, | Mcorr /M0 | is . 2%
• For Nav =10, out of the ',in RMS values tested, | Mcorr /M0 | is . 4% for the realisticof 0.22 rad, 0.45 rad, 0.67 rad, and . 10% for the extraordinarily large 0.89 rad.

',in

• Especially good precision was demonstrated for the ',in RMS of 0.45 rad, which is close tothat extracted from the most important beam time data in June 2014; | Mcorr /M0 | is lessthan 1% for both Nav =50 and Nav =10.
The above assumed the Cstat term being fixed accurately to its true value during the fitting process
to extract ',out . Section 7.6.2 showed that for the typical uncertainty of Cstat,f ix and assuming a',in of 0.47 rad, the additional relative error of Mcorr is < 1.5% for Nav = 50, and < 4% for Nav= 10.
In conclusion, for the realistic phase variation amplitude of approximately 0.2-0.7 rad, the precision of Mcorr w.r.t. M0 is estimated to be better than 2.5% for Nav =50 and better than 5.7%
for Nav =10. This takes into consideration both the complexity of a realistic phase pattern and theuncertainty of Cstat,f ix . This conclusion will be applied to the evaluation of systematic errors forthe most important beam size measurements in Sec. 8.1.2.

7.8

Extraction of Phase Jitter from Beam Time Data

7.8.1

Evaluation of Phase Jitter in Fringe Scans

In this section, the phase jitter ( ' ) in actual beam size measurements is evaluated using the method
given and verified in Sections 7.4 - 7.7. Figure 7.16 shows an example for a 174 deg mode Nav =50
fringe scan in May, 2014, where the extracted ' =0.73±0.03 rad corresponds to relative vertical
position jittery = 30.9±1.4 nm. This causes a y,meas over-evaluation of approximately 9.5 12.5 nm. Figure 7.17 shows the history of the estimated ' in fringe scans sampled from April toJune of 2014. For the smallest y measured in the 174 deg mode in June 2014, the typical ' is0.4-0.7 rad, corresponding toy of about 15-30 nm. For the 30 deg mode, ' is smaller, typically< 300 mrad. The mode dependence of ' can also be inferred from the simulation in Sec. 6.3.1 andthe data analysis in Table 6.1, and can be explained as follows:42

The discussions here are made with exception of the unrealistic case of zero- ',in136

1. The path length after the half mirror is longer for the 174 deg mode than that of the 30 deg
mode by a factor of 2; therefore laser pointing jitter leads to more path length variation andconsequently larger ' for the 174 deg mode.
2. The 174 deg mode is more sensitive to e beam jitter by about a factor of 4; relative position
jitter is related to phase jitter as ' = 2ky ·y. The factor 2ky = 2⇡/d is 0.0236 nm 1 for1
the 174 deg mode, as opposed to 0.00611nm for the 30 deg mode. For example,
y= 20
nm would cause ' = 0.47 rad for the former and only ' = 0.12 rad for the latter.

Figure 7.16: An example of ' extraction for a 174 deg mode Nav =50 fringe scan. Here, the signal
jitter (standard deviation of Nav events measured at each phase) is plotted as a function of phase,and ' is obtained by fitting. For this scan, ' is estimated to be 0.74±0.03 rad.

137

Figure 7.17: The history of ' extracted from randomly sampled single fringe scans in April - Juneof 2014. The red points and blue points represent the 174 deg and 30 deg modes, respectively. Bothmodes are a mixture of Nav =50 and Nav =10. The error bars are the fitting errors. The horizontal
axis represents time.
7.8.2

Modulation Correction using the Extracted Phase Jitter

Using the extracted ',out , the measured Mmeas can be corrected as Mcorr = Mmeas / exp(
(Eq. 6.7). The precision was demonstrated in Sections 7.5 - 7.7 to be better than a few %.

2
' /2)

Modulation correction in consistent scans
Table 7.3 lists the Mmeas , ',out , and Mcorr as the statistical results of a few sets of “continuous
scans” recorded in spring of 2014. These consist of consecutive Nav =10 (or 20) scans, with 1 ormore Nav =50 scans within the same time slot, under assumedly the same e beam conditions. As
explained in Sec. 7.5.2, the realistic phase variation is a combination of jitters and drifts. Thus,
both its eﬀect on Mmeas and the extracted value of ',out depend on the time structure (Nav ) of
the fringe scan. Therefore M correction needs to be conducted for each individual scan within eachNav group.
Figure 7.18 compares the results of Mmeas , Mcorr , ',out , andy (converted as
y = ',out /(2ky ))between small Nav (10 or 20) and large Nav (50) from May-June of 2014. Based on these, the following observations are made:
1. After correcting each individual scan using its ',out , the values of Mcorr are closer between
Nav =10 and Nav =50 within the same group than the values of Mmeas before correction.
2. The relative position jittersize.

y is in general between 50-70% of

138

y,corr i.e.

the “true” beamModulation Correction for Wakefield Studies
Stable measurements by the Shintake Monitor play an essential role in the study of e beam factors
which impose limitations on small y focusing. A possibly dominant factor is the wakefield eﬀect
due to the interaction of the beam with the electromagnetic fields generated at discontinuities inthe beam line (see [18] and Appendix G). Because wakefield eﬀects cause y to increase with bunchcharge (Ne ), they can be studied by measuring M while changing Ne in steps. An example isgiven in Fig. 7.19, where Mmeas is plotted as a function of Ne . Plotted together here is the Mcorr
calculated by inserting the ',out extracted for each scan into Eq. 6.7. These are then fitted withan exponential function. The consistency of the fitted sigma between Mmeas and Mcorr is anotherindication of the reliability of ' extraction and compensation: 2.48±0.11 for Mmeas and 2.64±0.12
for Mcorr . These indicate the growth of y w.r.t. Ne to be about 17 nm/109 .

Figure 7.18: [top] The measured M (left) and the M corrected using the extracted ' (right) for
representative 174 deg mode “continuous scans” in May-June of 2014. Red and blue represent large
Nav (50) and small Nav (10), respectively.
The data points and their error bars show the mean andpstandard deviation divided by N 1 (N = the number of scans), respectively, of the scans in eachset. The horizontal axis represents time.
[bottom] The ' extracted for the same continuous scans as the top plots (left) and the ratio ofrelative position jittery (= ' /(2ky )) w.r.t. y,corr (right).

139

Figure 7.19: A “beam intensity scan” (for ATF2 wakefield study) showing Mmeas as a function ofbeam bunch charge. Plotted together is Mcorr corrected using the ' extracted for each scan. The
sigmas of the fitted exponential functions are approximately consistent between Mmeas and Mcorr .
These indicate that the beam size growth w.r.t. the beam bunch charge is about 17 nm/109 .
date (in 2014)bunch charge [109 ]small Nav scans(Nav , no. of scans)Mmeasy,meas [nm]
' [rad]Mcorry,corr [nm]y [nm]
large Nav scans(Nav , no. of scans)Mmeasy,meas [nm]
' [rad]Mcorry,corr [nm]y [nm]

Apr. 90.7

Apr. 100.55

Apr. 17
0.53

May 22
0.6

June 13
1.1(10, 8)0.297±0.019
66.1±1.8
0.545±0.120
0.361±0.027
60.5±2.2
5.6±2.8(20, 6)0.333±0.012
62.6±1.0
0.720±0.064
0.435±0.010
54.5±0.88.1±1.3(20, 10)0.401±0.010
57.1±0.80.550±0.050
0.471±0.017
51.8±1.3
5.3±1.5(10, 10)0.507±0.013
49.2±0.6
0.637±0.043
0.625±0.012
40.8±0.98.4±1.1(10, 12)0.563±0.011
45.1±0.8
0.492±0.039
0.640±0.009
39.7±0.6
5.4±1.4(50, 3)0.285±0.025
66.9±2.3
0.792±0.047
0.419±0.037
55.6±1.8
11.3±2.9(50, 2)0.352±0.029
61.1±2.4
0.651±0.238
0.440±0.032
54.0±2.4
7.1±3.4(50, 2)
0.394±0.018
57.7±1.4
0.649±0.047
0.465±0.067
52.3±4.9
5.4±5.1(50, 2)0.443±0.064
53.9±4.8
0.722±0.012
0.569±0.088
44.8±5.6
9.1±7.4(50, 2)0.500±0.018
49.7±1.3
0.628±0.078
0.610±0.008
41.9±0.5
7.8±1.4

Table 7.3: The comparison between consecutive scans of small Nav (10 or 20) and large Nav (50),of the following: the measured Mmeas and y,meas , the extracted phase variation ( ',out ), and theMcorr and y,corr corrected using the ',out pfor each scan. The statistical errors are defined as thestandard deviation of the scans divided by N 1, where N is the number of scans.
y is thecontribution to y growth from ' .

140

7.8.3

Comments about Electron Beam Jitter

The direct measurement of vertical e beam jitter ( ye ) at the IP is not available yet since the
IPBPM is still under commissioning for electronics and alignment at ATF2. As a support for the
ATF2 Goal 1, the IPBPM aims to achieve a resolution of 10-20 nm with 30 µm dynamic range,
which contributes 1.3 - 4.7 nm to y w40 nm. This corresponds to a ' which is within the rangethat can be extracted precisely from fringe scans using the method given in Sec. 7.4.
The information from BPMs in the upstream sections of the FFS beam line indicate thatye ,
mostly due to the vibration of quadrupole magnets, is generally about 15% of y [38]. The
ye at
the IP is thought to the convolution of this and a significant additional jitter caused by the vibrationof the final doublet (FD) quadrupoles, QD0 and QF1 [30]. In the table below, the first column lists
the measured vertical vibrations ( ymag ) of QD0 and QF1[22]. The second column lists theyeat the IP translated fromymag . The third column lists the corresponding phase jitter in fringescans ' (estimated as 2ky ·ye ). The fourth column lists the contribution to the growth of anominal y = 40 nm. The first two rows are for each of QD0 and QF1, while the third row combinesthem as the FD, assuming they are non-correlated. The last row convolutes the FD vibration withtheye (assumedly 15% of y = 40 nm) coming in from upstream.

QD0
QF1
FD
total (FD+upstream)ymag
4.8 nm30 nm

ye
7.3 nm
12.6 nm14.6 nm15.8 nm'0.17 rad0.30 rad0.35 rad0.37 rady

0.7 nm
1.9 nm
2.6 nm3.0 nmThe smallest y measured in June 2014 are close to 40 nm. For the case of y =40 nm, the total
ye of about 16 nm is about 40% of y . Assuming a total ' of 0.5 rad (typical for June 2014), thesubtraction of the contribution fromye (0.37 rad) in quadrature would leave the contribution fromthe Shintake Monitor to be about 0.34 rad. This indicates that the contribution to the total phasejitter (relative position jitter) is about equal between the laser and the e beam. The estimatedcontribution from the laser is comparable in scale to (a) the laser-only phase jitter measured by
T.Yamanaka (RMS⇠0.45 rad) for a previous laser, and (b) the simulation results in Sec. 6.3.2 whichassumed a pessimistic value for laser pointing jitter.

7.9

Status of Signal Jitter in Fringe Scans

This section describes the status of signal jitters observed in actual fringe scans. The following
notations are used:•

E (') : signal jitter i.e. standard deviation of the Nav measured energy events at each phase.

• E (') : mean of the Nav measured energy events at each phase.
•

Erel ('): “relative signal jitter” i.e.

E (') divided by E (') at each phase.

The number of signal photons per bunch is estimated in Sec. 3.6.1 to be O(102 ); thus the total energy
deposit per bunch in the detector is expected to have a Gaussian-like distribution. Figures 7.20 and
7.21 show the distribution of energy measured at a single fixed phase of a Nav = 50 fringe scan. Figure
7.20 shows the sum of energy deposit in the front four detector layers. Figure 7.21 shows the energy
deposit in each of the eight PMTs. These distribution shapes and Erel from the real data arecomparable to those from simulation such as shown in Fig. 7.22. For the same scan, Erel (') and141

the M spectrum (E (')) are plotted together in Fig. 7.23 (left).

E (') =q

Ep2 (') +Ep2 (')and its two components, Ep (') and EV ('), are plotted together with the M spectrum in Fig.
7.23 (right). Both Erel (') and Ep are minimum at the fringe peaks and maximum at the
mid-points. EV ('), which scales with energy E ('), is in phase with the M spectrum.
Relative signal jitter Erel in a fringe scan is typically 15-25% at fringe peaks, and 25-35% at
fringe mid-points. Table 7.4 lists the contribution from the individual signal jitter sources describedin Sec. 7.1. Adding each component in quadrature yields a total approximately consistent with theErel observed in actual fringe scans at mid point phases for the similar beam bunch charge of 109 .

Figure 7.20: The distribution of energy events measured at a particular single phase in a Nav =50
fringe scan. (left) at peak (right) at mid-point. Here, signal jitter (= RMS/mean) is 22% and 33%
at the peak and mid-point phases, respectively.

142

Figure 7.21: The distribution of energy deposit measured by each of the eight PMTs of the front
four detector layers, at one of the mid points in the same Nav =50 fringe scan as in Fig. 7.20.

143

Figure 7.22: The distribution of Compton signal energy from the simulation of a Nav =50 fringe
scan assuming M0 =0.636, ' =0.59 rad, and vertical jitters consisting of (5%, 15%, 10%) w.r.t. Eavg
from (Cconst , Cstat , Clinear ); (left) at a single peak phase; (right) at a mid-point phase. Here, signal
jitter (= RMS/mean) is 18% and 37% at peak and mid-point, respectively.

Figure 7.23: For the same Nav =50 scan as in Fig. 7.20: (left) The M spectrum and the relative
signal jitter Erel (') are plotted together as a function of phase '. (right) Total signal jitter
E (') and its two components Ep (') and EV ('), are plotted together with the M spectrum
as a function of phase '. The dots and the solid curves are the real data and the fitted results,
respectively.

144

sourcephase jitter (vertical relative position jitter)
relative timing jitter
total laser power jitter
horizontal relative position jitter
BG fluctuation
statistical fluctuations
ICT monitor resolution
total

E/Eavg
28%
.5%
. 1%
.2%
< 5%
. 20%
⇠ 2%
. 35%

comments
assume ' = 500 mradsee Sec. 7.1.4
see Sections 5.5 and 7.1.5
see Sections 7.1.6 and 5.2
see Sec. 7.1.3
see Sec. 3.6
see Sec. 7.1.7
at fringe mid-point

Table 7.4: The contribution from individual sources to the signal jitter w.r.t. Eavg in a fringe scan.
The estimation here assume e bunch charge of 109 , Nsig =200 entering the detector, and y = 40
nm.

145

8

Summary

8.1

Beam Time Performance

By June 2014, the Shintake Monitor has been stably measuring a world record y of below 45 nm[19]. This section gives the full y evaluation based on the systematic error studies in Chapters 6
and 7. The results demonstrate that the ATF2 Goal 1 y of 37 nm has been achieved.
8.1.1

Evaluation of Measurement Stability

Section 4.1 described the factors that contributed to the ATF2 beam focusing progress, focusing
mainly on the improvements of the accelerator beam line and e beam stability 43 . As for the
Shintake Monitor system, the following improvements are thought to have contributed significantly
to the measurement of small y in 2014 spring:
1. The reduction of signal jitters by (a) the tuning of the laser profile and (b) adjustment of theinjection seed laser to stablize the laser Q-switch timing.
2. The speeding up of the Shintake Monitor control software from about 1 Hz to about 3 Hz; thismay have reduced eﬀect from drifts in the position of the laser and / or the e beam.
3. The reinforcement of the detector shielding by adding Pb blocks against bremstrahlung BG
and paraﬃn plates against neutron BG.
These eﬀorts realized eﬃcient beam tuning using the Shintake Monitor with a measurement stabilityof as good as about 5%. Table 8.1 and Fig. 8.1 show the results for two representative sets ofcontinuous Nav =10 scans conducted at the 174 deg mode under stable beam condition and a beam
bunch charge ' 1 ⇥ 109 . On June 12, 10 scans were taken within about 30 min. Just about 24
hrs later, on June 13, 12 scans were taken within about 50 min 44 . These are the results before
correcting for systematic errors, and are shown in the form of the mean and standard deviation(S.D.) of the scans in each set. The results of some other consecutive scans from 2014 spring wereshown in Table 7.3.
Figure 8.2 shows two examples of single fringe scans from the June 12 set in Fig. 8.1 (left).
Without correction for ' , nor taking into account any other systematic errors, the results are:(left) Mmeas = 0.660 ± 0.021(stat.), meas = 38.3 ± 1.5(stat.) nm; (right) about 17 min later:
Mmeas = 0.678 ± 0.020(stat.), meas = 37.1+1.4
1.5 (stat.) nm. For each fringe scan, at a single phase,
10 pulses (Nav =10) are measured with the laser colliding with the e beam (EON in Sec. 3.5.4)
and 1 pulse is measured without collision as the BG energy (EOF F in Sec. 3.5.4). This is repeatedfor each of the 20 phases in the scan. Then the mean of the 10 pulses of Compton signal energy
Esig = EONp EOF F is plotted as a function of phase, with the errorbars being the standard deviation
divided by Nav 1. This cosine-like curve is fitted with Eq. 2.10 to obtain the Mmeas shown in
the histograms in Fig 8.1.
Before each of the two continuous scan sets was conducted, the multi-knob tuning described inSec. 4.1 was carried out in order to focus the beam size. In addition, out of the setup proceduresin Sec. 4.2, the factors that could change over time were reoptimized: transverse and longitudinal
position alignment of the laser w.r.t. the e beam, and laser timing adjustment.
43

Because the e beam orbit feedback ceases to function below the threshold beam bunch charge of 0.8 ⇥ 109 , somemeasurements conducted at a bunch charge lower than that may have been aﬀected by beam instability. However this
could not be confirmed since the BPMs cannot record reliable beam orbit information at such low beam intensity.
44
Between the set on June 12 and the set on June 13, the position of the OTR monitors in the extraction line were
scanned and moved for the purpose of wakefield studies. It is not certain where this may have caused some slightchanges in the e beam orbit.

146

date
June 12 (10 scans)June 13 (12 scans)

Mmeas
0.589 ± 0.050 (S.D.)
0.563 ± 0.036 (S.D.)y,meas [nm]43.3 ± 3.7 (S.D.)
45.1 ± 2.7 (S.D.)

stability 45
8.5%
6.4%

Table 8.1: The results of two representative sets of continuous Nav =10 scans conducted in the 174
deg mode, before correcting for systematic errors, shown as the mean and standard deviation (S.D.)of the scans in each set. The common conditions are: Nav =10, beam bunch charge ' 1 ⇥ 109 , andthe normalization of the measured energy by the measured bunch charge pulse-by-pulse.

Figure 8.1: The two sets of continuous scans in the 174 deg mode, whose results before the correction
for systematic errors are shown in Table 8.1.

Figure 8.2: Examples of the high M measured in the 174 deg mode as part of the “consistency scan”
shown in Fig. 8.1. The results before correction for systematic errors are (left) Mmeas = 0.660 ±0.021(stat.), meas = 38.3 ± 1.5(stat.) nm. (right) about 17 min later: Mmeas = 0.678 ± 0.020(stat.),+1.4
meas = 37.1 1.5 (stat.) nm.

147

Figure 8.3: The plots for the extraction of phase jitter corresponding to each of the Nav =10 scansshown in Fig. 8.2. The extracted phase jitter values are (left) ' = 0.509 ± 0.037(stat.) rad, and(right) ' = 0.490 ± 0.040(stat.) rad.
As the counterparts of Table 8.1 and Fig. 8.1, Table 8.2 and Fig. 8.4 show the results after
correcting each individual scan for its ' extracted using the method described in Sec. 7.4. The
extracted ' is 0.509±0.023 rad and 0.492±0.039 rad for June 12 and June 13, respectively. The
corresponding relative position jittery ( y/ y,corr ) is 21.5±1.0 nm (57.3±7.8 %) and 20.8±1.7
nm (52.4±6.7 %), for June 12 and June 13, respectively.
date
June 12 (10 scans)June 13 (12 scans)

Mcorr
0.672 ± 0.051 (S.D.)
0.640 ± 0.029 (S.D.)y,corr [nm]37.5 ± 3.9 (S.D.)
39.7 ± 2.1 (S.D.)

stability
7.6%
4.5%

Table 8.2: The results of the two sets of continuous scans shown in Table 8.1 and Fig. 8.1, after
correction using the ' extracted for each individual scan.

Figure 8.4: The two sets of continuous scans shown in Fig. 8.1, after correction using theextracted for each individual scan: The corrected results are shown in Table 8.2.

148'

8.1.2

Evaluation of the Smallest Beam Sizes

Table 8.3 summarizes the M reduction factors evaluated for the smallest y measured in the two
sets of continuous scans mentioned in Sec. 8.1.1. If the correction for phase jitter ' (as in Table 8.2
and Fig. 8.4) is not carried out, the systematic errors on the measured y are evaluated based on
all of the M reduction factors i.e. Ctotal in Table 8.3; in this case, the smallest beam sizes measured
in continuous scans by the Shintake Monitor are:43.3 ± 1.2(stat.)+0.0
13.9 (syst.) nm(8.1)

45.1 ± 0.8(stat.)+0.0
8.0 (syst.) nm(8.2)

37.5 ± 1.3(stat.)+2.7
8.7 (syst.) nm(8.3)

39.7 ± 0.6(stat.)+2.6
4.0 (syst.) nm(8.4)

However, the full evaluation of Mmeas ( y,meas ) will be carried out after correcting for the extracted phase fluctuation ' for each scan. As explained in Sections 7.5 - 7.7, the precision of Mcorr
is a combined eﬀect of the extraction precision of ' as well as its eﬀect on Mmeas . Section 7.7 concluded from simulation test results that when the phase variation amplitude is within the realistic
range of 0.2-0.7 rad, the precision of Mcorr (w.r.t. the true M0 ) is better than 2.5% for Nav =50 andbetter than 5.7% for Nav =10. The propagation to y,corr can be evaluated using Eq. 2.11. For they =39.7 nm measured on June 13 (see Table 8.2), this corresponds to an uncertainty of at most 2.6
nm, which is about 6.5% of y . Below, this uncertainty of correction for ' i.e.
y,corr = 6.5%
⇥ y is taken into account when evaluating systematic errors. In this case, the smallest beam sizes
measured in continuous scans by the Shintake Monitor are:

For the systematic errors in Equations 8.3 and 8.4, the upper limit (+) is fromy,corr . The
lower limit (-) is the convolution of
and
the
other
factors
in
Table
8.3
excluding
C' i.e.
y,corr0
Ctotal = Ctotal /C' , which is 0.858 and 0.938 for June 12 and June 13, respectively.
The final results in Equations 8.3 and 8.4 indicate that the ATF2 Goal 1 has been achieved
within the range of the evaluated errors. The measurement resolution of the Shintake Monitor for
y = 39.7 nm is evaluated to be about 10%. Table 8.4 summarizes the full evaluation of the two setsof continuous scans. More details are given in Appendix F.
dateC'Ct,align
Cz,align
Ctilt
CpitchCsphereCgrowth
Cdrif tCpower
Cpol
CtotalJune 12 (10 scans)
0.879> 0.965> 0.915> 0.999> 0.989> 0.988> 0.997> 0.999> 0.9991.000> 0.754

June 13 (12 scans)
0.886> 0.991> 0.974> 0.999> 0.989> 0.988> 0.997> 0.999> 0.9991.000> 0.831

Table 8.3: The summary of M reduction factors evaluated for the two record sets of continuous
Nav =10 fringe scans on June 12 and June 13 mentioned in Sec. 8.1.1.
149

date
June 12 (10 scans)June 13 (12 scans)

M
0.672 ± 0.017(stat.)+0.118
0.038 (syst.)
0.640 ± 0.009(stat.)+0.056
0.036 (syst.)

y [nm]
37.5 ± 1.3(stat.)+2.7
8.37 (syst.) nm
39.7 ± 0.6(stat.)+2.6
4.0 (syst.) nm

Table 8.4: The full evaluation of the two record sets of continuous fringe scans on June 12 and June
13. Correction is carried out for the phase jitter extracted using the method described in Chap. 7.
The systematic errors take into account the M reduction factors in Table 8.3.

8.2

Future Goals

8.2.1

Remaining Issues

The full evaluation of the smallest y stably and continuously measured in June 2014 (Table 8.4)
indicate that the ATF2 Goal y of 37 nm has been achieved. However, the “raw” measured values
i.e. not taking into account the systematic errors, are still larger than the y expected from thedesign values of the optics and the vertical emittance. Some possible explanations are:
1. The systematic errors related to the Shintake Monitor laser; these are discussed extensively in
Chapters 6 and 7. Various eﬀorts have been ongoing to further improve the stability of thelaser.
2. The jitter and drift of the e beam orbit at the IP.
3. Residual beam size growth due to wakefield eﬀects. The smallest beam sizes were measured atvery low beam intensity in order to minimize the eﬀect from wake fields. This issue is discussed
in Appendix G and in references [20, 18, 19].
4. Measurements of the beam optics and the emittance may have some ambiguities. See [19, 18]
for details.
Regarding 2., the possible eﬀects of e beam instability can be further grouped as the following:• Contribute to phase jitter and drift, which are among the most dominant systematic errors.
• Cause actual

y growth.

• Degrade the eﬀectiveness of beam tuning. For example, the orbit drift of the e beam maychange its position at sextupole magnets and thus aﬀect the correction of chromaticity andhigher order aberrations.
The stabilization of e beam position at the IP is important for both achievement of Goal 2 and forthe reproductivity of the Goal 1 beam size. The O(nm) resolution cavity BPMs “IPBPMs” currently
under commissioning at ATF2 will be useful for measuring the beam orbit jitters and drifts.
The results of the error studies reported in this thesis indicate that the measured M can becorrected, provided precise measurement of phase jitter, thus suppressing systematic errors down
to only the contribution from the other factors, which have been confirmed to be less serious thanphase jitter. The method for compensating phase jitter can be verified even better if its precision
when applied to actual data could be directly confirmed. One possible way is to deliberately jitterthe piezo controller which shifts the phase during a fringe scan, described as follows:
1. First, measure M before jittering the piezo controller.
2. Deliberately jitter the piezo controller by a known amount so as to create phase jitter. Thee beam condition needs to be kept stable.
1503. Extract the phase jitter from the fringe scan using the method described in Sec. 7.4, and use
the result to correct the Mmeas in 2..
4. Compare Mcorr to the Mmeas in 1. i.e. before jittering the piezo controller. The extracted
phase jitter can also be compared to the monitored value of the piezo controller jitter.
Furthermore, the precision of evaluating and correcting for phase jitter can be improved by its direct
measurement using the IPBPMs for the e beam jitter at the IP, as well as a phase monitor for thelaser fringes. This would allow the precise measurement of even smaller y .
8.2.2

Possibility of Using the Shintake Monitor at the ILC

In recent years, international collaborations have been joining forces to realize the construction of
the ILC. This section gives my personal views on the prospects of using the Shintake Monitor at the
ILC in the future. There will be no space in the IP area of the ILC for the Shintake Monitor during
normal operation because physics detectors are installed there. However, a beam size monitor with
O(10) nm resolution is necessary for confirming that the e and e+ beams can be suﬃciently focusedat the IP to achieve the design luminosity. One candidate for this is the pair monitor[44]. However,there has been little development carried out on the pair monitor hardware. In contrast, the Shintake
Monitor has been proven capable of stable measurement of O(10) nm beam sizes at both ATF2 andSLAC. Therefore it is possible to upgrade the Shintake Monitor for initial commissioning of the
ILC beam line before detector installation. When the pair monitor hardware has been suﬃciently
developed, it may replace the Shintake Monitor when beam-beam collision actually commences.
As described throughout this thesis, the world record beam size measurements by the Shintake
Monitor has played an essential role in successfully verifying the FFS design featuring the Local
Chromaticity Correction Scheme for the ILC. The next step is to enable the Shintake Monitor to be
the utilized at the ILC by resolving the following issues intrinsic to the higher beam energy and thesmaller design y at the ILC.
Related to higher beam energy• The total Compton scattering cross section decreases as beam energy increases. This canbe seen from Eq. 2.8 and Fig. 8.5. Here, total is expressed as a function of the parameterq = k/m, which is scales linearly with both beam energy ( ) and incident laser photon energy(k). For ATF, q = 0.0116, assuming beam energy 1.3 GeV and =532 nm. For ILC, q = 2.23,
assuming beam energy 250 GeV and also =532 nm . From Fig. 8.5, the total for ILC would
be reduced to about 1/3 of that for ATF, which imposes a limit on signal statistics i.e. thenumber of Compton scattering photons. Although this could be compensated by increasing
the laser energy, additional eﬀort is needed in order to stabilize a more intense laser.
• Both the signal and BG energy spectrum will be changed. Since the signal energy will behigher and may approach that of bremstrahlung BG, some changes may be required for thedesign of the gamma-ray detector and/or analysis methods for separating signal and BG.
• The much higher radiation levels at ILC demands reinforced shielding of the Shintake Monitor
components to be placed inside the accelerator tunnel e.g. the laser optics, gamma-ray detector,
and controllers.
Related to smaller design beam size
• Laser wavelength . 250 nm is required for producing the fringe pitches narrow enough formeasuring the y < 10 nm at the ILC. For example, M = 0.95 at 174 deg mode yields y =12.8
151

nm for (d, ) = (266 nm, 532 nm), while halving the wavelength to (d, ) = (133 nm, 266nm) yields y = 6.4 nm. One option is to use 4th harmonics generation. Another option is
to change to UV lasers (e.g. ArF excimer lasers ( =193 nm) or F2 excimer lasers ( = 157nm)). However, these lasers outside the visible range are impractical in terms of alignment andstability control. For example, the essential process of overlapping the laser and the e beamon the current screen monitor would become diﬃcult. The practical usage of the Shintake
Monitor during the initial beam line commissioning may be to measure y ' 20 nm with alaser of =532 nm at a location slightly upstream of the IP, then use the results to estimate
the achievable y at the IP based on beam focusing optics design.
• Systematic errors need to be suppressed further to measure the smaller y at the ILC withsatisfactory resolution. Without correcting for phase jitter, the systematic error for y,meas '45 nm at ATF2 is about 8 nm (see Eq. 8.2), which corresponds to a measurement resolutionof about 20%. Assuming y w 20 nm at the ILC, the error needs to be suppressed below 4
nm to achieve a resolution better than for instance 20%. The suppression of the dominant
phase jitter i.e. relative position jitter calls for reinforced stabilization of both the e beamand the laser (e.g. laser pointing jitter and profile fluctuation). Residual phase jitter canbe compensated for by applying the phase jitter correction method described in this thesis.
Howerer, precison can be improved by the direct measurement of both e beam jitter and laser
fringe phase jitter. These emphasize the importance of the development of O(nm) resolution
BPMs and laser fringe phase monitors.
Furthermore, the operation of the Shintake Monitor needs to be adapted to the higher repetition
rate of 5 Hz and the multi-bunch operation at the ILC, as opposed to the single bunch 3 Hz
operation at ATF2. The O(10) ms time resolution of the Shintake Monitor piezoelectric stage forfringe phase control satisfies the demand from the higher repetition rate. On the other hand, multibunch operation calls for a more speedy beam size measurement methods than that for single bunch
operation. The R&D of multi-bunch operation is ongoing at ATF.

Figure 8.5: The dependence of total Compton scattering cross section total on q = k/m (m:erest mass; k : incident laser photon energy), shown here in a wider range of q = 0 - 5 (as opposedto the narrow range in Fig. 2.9).

8.3

Conclusion

At the International Linear Collider (ILC), the high luminosity of about 2⇥1034 cm 2 s 1 required forits physics program calls for the focusing of its e and e+ beams to nanometer sizes at the interaction152

point (IP). The Accelerator Test Facility 2 (ATF2) was constructed at KEK as a realistic scaled
down test prototype of the final focus system (FFS) of the ILC. The Goal 1 of ATF2 is to focus
the vertical e beam size ( y ) to 37 nm, scaled by energy from the ILC design y of 5.9 nm and by
doing so, demonstrate the design of a FFS that is to be used at the ILC. This FFS design features
a beam focusing method called the Local Chromaticity Correction scheme, which realizes a shorter
FFS beam line and less beam halo than preceding designs.
The Shintake Monitor is a beam size monitor installed at the virtual IP of ATF2 for the purpose ofmeasuring its O(10) nm y . Featuring a technique of using laser interference fringes as a probe to scanthe e beam, the Shintake Monitor is the only existing device that has demonstrated measurementof y below 100 nm. Its measurement scheme is as follows: a pulsed Q-switch Nd:YAG laser beam issplit into upper and lower paths which cross at the IP to form laser interference fringes. The collisionof the e beam against the fringes release photons from inverse Compton scattering. By scanningthe fringe phase with respect to the e beam using a piezo-electric stage, a modulation pattern is
produced in the photon energy measured by a downstream calorimeter-type gamma-ray detector.
The y is calculated from this modulation (M ). The laser optics are designed to accommodatea wide range of y from about 25 nm to a few µm with better than 10% accuracy. A series of
hardware improvements stabilized the timing, profile, and position of the laser. The eﬀective beamtuning using the Shintake Monitor contributed essentially to the ATF2 beam focusing progress; byJune 2014, the focusing of y to below 45 nm has been demonstrated on repeated occasions with ameasurement stability of about 5%.
The most important of my personal contributions to the development and performance evaluation of the Shintake Monitor is an extensive study of various systematic errors. These are called“M reduction factors” because they cause under-evaluation of M i.e. over-evaluation of y . The
dominant M reduction factor is found to be the fluctuation of the relative phase between the laser
and the e beam. An original method was developed for the extraction and correction of phasejitter. The reliability of this method was demonstrated using simulation assuming realistic ATF2
conditions; the M correcetd using the extracted phase jitter was shown to have a precision corresponding to better than 6.5% of the beam size. Based on various measurements of the laser andthe gamma-ray detector response, systematic errors were evaluated for beam time data collected in2014 spring. The full beam size evaluation for a set of world record continuous y measurements
in June 2014 is y = 39.7 ± 0.6(stat.)+2.6
4.0 (syst.) nm; the beam size resolution is about 10%. Thesestudies enabled the precise evaluation of y , and their results indicate that the ATF2 Goal 1 has
been achieved within error ranges.
Because the ATF2 is a scaled prototype of the ILC FFS with similar diﬃculties in beam tuning,
various technologies verified at ATF2 are applicable to the ILC. Therefore, the above-mentioned
precise y evaluation was a large step towards demonstrating the feasibility of realizing the ILC.
By resolving several issues in performance and design, the Shintake Monitor is also a promising
candidate for the O(nm) resolution beam size monitor necessary for the beam line commissioning at
the actual ILC. Furthermore, the results of the error studies reported in this thesis indicate that it
would be possible to suppress systematic errors so as to allow the measurement of the smaller O(nm)y at the ILC in the future, provided precise measurement of phase jitter using O(nm) precision
BPMs and laser fringe phase monitors.

153

9

Acknowledgment

I would like to express my gratitude to many who contributed to this thesis and my research life.
Firstly, I would like to express my deepest gratitude to my supervisor, Professor Sachio Komamiya. The immense support and opportunities he provided me during my student years at theGraduate School of the University of Tokyo enabled me to find my dream of working towards realizing the ILC, now and hereafter. It is one of my greatest pride and privileges to be his student. I
would also like to thank assistant professor Dr. Yoshio Kamiya for his expertise advice; his manykind encouragements meant a great deal to me. I am extremely grateful to Dr. Daniel Jeans for his
help on data analysis methods; being an amazing educator, his enthusiastic instructions enhanced
my passion for ILC related research.
Next, I express gratitude to the IPBSM study group at ATF2 for their advice and cooperation in
Shintake Monitor study and the publication of papers. Professor Nobuhiro Terunuma has provided
me constant guidance and support from the very beginning of my research at ATF2 five years ago. I
respect very much his immense eﬀorts and amazing energy in running ATF2. Dr. Toshiyuki Okugi
has given me much advice in various aspects of my studies; his expertise in beam tuning contributed
essentially to the beam focusing achievements reported in this thesis. The many upgrades made byProfessor Terunuma and Dr. Okugi on the Shintake Monitor hardware enabled stable beam size
measurements. I am very grateful to Professor Toshiaki Tauchi and Professor Kiyoshi Kubo for thelong term support on the development of the phase jitter analysis method. Professor Tauchi has
kindly educated me in physics and accelerator issues. Professor Kubo has given me an especiallygreat amount of advice during the completion of this thesis.
I would like to appreciate all colleagues at ATF(2) for their eﬀort in operating ATF(2). I am very
grateful indeed to Professor Phillip Bambade of LAL who had first encouraged me to commence thestudy of phase jitters. I would like to express special thanks to Dr. Alexander Aryshev (KEK), Dr.
Laura Corner (John Adams Institute), and the members of the ATF EXT-laserwire group for their
help pertaining the laser system.
I am thankful to the previous members of the Komamiya Laboratory with whom I have had theprivilege to work with on the Shintake Monitor. Dr. Taikan Suehara, Dr. Takashi Yamanaka, Dr.
Masahiro Oroku, and Dr. Yohei Yamaguchi provided valuable advice even after they had graduatedfrom the project. Their great previous eﬀorts in developing the Shintake Monitor had paved thefoundation for this research. In particular, Dr. Yamaguchi has taught me more than anyone about
the experiment for many years, and I shall continue to look up to him as a role model as a researcher.
The other members of our laboratory: Mr. Yuto Minami, Ms. Chihiro Kozakai, Mr. Shion Chen,
Ms. Mayuko Ogino, Mr. Yoshihiro Sasayama, and Mr. Yuya Kano has made daily life pleasant forme in the lab and provided helpful advice during weekly lab meetings. Ms. Kuniko Kono has been
most kind in supporting various aspects of my student life.
I would like to thank the Japan Society For The Promotion of Science for the financial support
throughout my PhD. research. I would also like to thank the Honjo International ScholarshipFoundation for their financial support and kind encouragements during my Masters course research.
I would like to thank Takuji Matsumoto for his sincere support for my goals and for always being
there for me; being able to share our dreams with each other has given me light during even thehardest days of my student life.
Lastly, I would like to appreciate my father for having demonstrated to me from a young age theimportance of diligence and responsibility. I share many of his values and aspire to one day becomea physicist just like him and a daughter he can be proud of.
Finally, I oﬀer my thanks once more to all of those who supported me in any respect during thecompletion of this thesis, including the authors mentioned in the bibliography page and many others
not specified in the limited space here. I thank them all.
154

10

AppendixA

Laser Cavity

Figure A.1 shows the layout of the laser head of a PRO-Series laser manufactured by Spectra
Physics[24]. The Shintake Monitor uses the Quanta-Ray PRO-350 laser. The major components
are described as the following. There are vertical and horizontal controls in various locations whichallow adjustment of the routing of the beam.
Oscillator section:
The components here make up the laser cavity where the initial laser beam is generated. The alignment of the oscillator cavity and the optimization of output power and mode quality are conducted
through vertical and horizontal controls, which are accessible when the head cover is removed.
• Rear mirror (“high reflector”) M1: one of the two oscillator cavity end mirrors. M1 reflects alllaser light back into the cavity.
• Output coupler M2: the other cavity end mirror. M2 allows a part of the light to pass throughas the output laser beam.
Q-switch system:
The Q-switch system is used for producing laser pulses of high intensity and short pulses. It iscomprised of a quarter-wave plate, a polarizer, and a Pockels cell.
• Quarter-wave plate: rotates the polarized cavity light by 90 deg. It suppresses laser oscillation
until the Q-switch is fired.
• Pockels cell: a crystal used as a high-speed optical shutter for Q-switch pulses. It is opaque(blocks light) until a voltage is applied to it. The Marx bank provides the power to drive the
Pockels cell and uses a TTL trigger source to turn the cell on and oﬀ.
• Polarizer: a coated optical component that allows only light with a selected polarization topass throughAmplifier section:
Two rectangular pump chambers add energy to the laser beam from the oscillator section. Thisamplified beam becomes the laser output. The pump chamber has a flash lamp at one focus point
and a YAG rod i.e. the lasing media at the other. The YAG rod is pumped by the flash lamp. Foldmirrors route the laser beam from the oscillator to the amplifier section.
Injection seeder:
The injection seeder provides a small amount of single-frequency laser light (wavelength ( )=1064nm) to stimulate emission at a single longitudinal mode in the host laser oscillator once the proper
threshold for lasing is reached in the rod. Its controls are provided on one of the laser side panels.

155

Second harmonic generator (SHG):
Crystals arranged in a particular sequence and orientation generate second harmonics from theprimary of 1064 nm to 532 nm. The dichroic mirror DM1 reflects and routes light of = 532
nm to DM2 while transmitting the residual = 1064 nm light to the beam dump. A temperature
controller stabilizes the temperature of the SHG crystals, thus maintaining stable output regardlessof changes in ambient temperature.
Beamlok:
The Beamlok is a device for position stabilization. The dichroic mirror DM2 mounted on an x-y
piezo servo routes the output beam through the BeamLok sensor and out of the laser head. The
BeamLok pointing sensor detects the far field beam position and provides feedback to the controller
for stable beam-pointing output. This controller then controls the piezo servo carrying DM2.

Figure A.1: The layout of the laser head of a PRO-Series laser manufactured by Spectra Physics
Inc. [23]B

Gauss Beam Focusing

B.1

Properties of an Ideal Gaussian Beam

Most of the discussion pertaining to laser beam propagation and focusing in this thesis are based ona model based on Gaussian beam physics. A Gaussian beam is the fundamental mode of a coherent
laser beam. For the realistic laser, there is a certain amount of deviation from Gaussian (see Sec.
5.2). Figure shows the schematics of the focusing of a Gaussian laser beam[45].

156

The electric field of the Gaussian beam has a radially symmetric distribution, and can be expressed as:✓◆r2
E (z, r) = E (z, 0) exp(B.1)! 2 (z)The intensity distribution of a Gaussian beam is also Gaussian, and can be expressed as:✓◆
2r2
I (z, r) = I (z, 0) exp(B.2)! 2 (z)Here, z is the direction of beam propagation, r is the radial direction. E (z, 0) is the field
amplitude on the axis (r=0). The beam radius w (z) is defined as the radius at which the intensity
decrease to 1/e2 of I (z, 0) = |E (s, 0)|2 , the intensity on axis. w (z) can be expressed as a functionof z, the propagation distance w.r.t. the waist position (z0 ), and waist size w0 as:
s
s
⇢
✓
◆
(z z0 ) 2
z z0 2! (z) = !0 1 += !0 1 +
(B.3)
zR
⇡!02
p
The Rayleigh length zR is defined as the distance over which the laser waist is increased by 2times, and can be expressed as:
zR ⌘

⇡!02

The curvature radius R (z) can be expressed as:(✓
R(z) = |zz0 | 1 +

(B.4)

⇡!02
(z z0 )

◆2 )

(B.5)

The beam divergence ⇥ is an important property in laser beam transportation, and can be
expressed as:✓◆
1⇥ = tanw(⇥ ⌧ 1)
(B.6)
⇡!0
⇡!0
The approximation ⇥ ⌧ 1 stands since =532 nm and !0 is about 20 µm. The waist radius !0at the focal point can be expressed using !i , the radius injecting into the focal lens, and f , the focal
length of the lens, as:
!0 =

f
⇡!i

(B.7)

A larger !i injecting into the focal lens and a shorter f leads to a larger divergence angle. Thiscan be understood by using Eq. B.7 and Eq. B.6 to rewrite beam divergence as:⇣! ⌘ !
ii⇥ = tan 1
'
(B.8)
f
f

157

Correction for a Non-Gaussian Beam The M 2 value serves as a beam quality factor which
represents the degree of deviation from an idealistic Gaussian beam (M 2 = 1). The waist sizeachievable by focusing at the focal point depends on M 2 . For the realistic beam, Eq. B.3 and Eq.
B.7 are corrected as Eq. B.9 and Eq. B.10, respectively.
s
s
⇢ 2
✓
◆
M (z z0 ) 2
z z0 2! (z) = !0 1 += !0 1 +
(B.9)
zR
⇡!02
!0 =

fM2
⇡!i

(B.10)

This indicates that the !i injecting into the focal lens need to be made smaller by a factor of M 2
in order to achieve the same waist radius !0 at the focal point. A larger M 2 indicates a more suddenchange in spot size as the beam propagates. This can be explained by that the beam divergence ismagnified by a factor of M 2 as:
✓ 2 ◆
M2
1 M
⇥ = tan'(B.11)⇡!0⇡!0
Accordingly, the Rayleigh length in Eq. B.4 and the curvature radius in Eq. B.5 are shortenedby a factor of approximately M 2 as:R(z) = |z

zR ⌘

⇡!02
M2

(

✓

z0 | 1 +⇡!02
2
M (z z0 )(B.12)◆2 )(B.13)

Figure B.1: The schematics of Gaussian beam focusing. [45]C

Damage Threshold for Optical Components

In order to prevent damage by high intensity laser, it is necessary to ensure that the damage thresholdfor the optical components withstand the intensity of the laser beam in contact. This section givesa theoretical calculation of laser energy density, which scales with total laser energy and the inverseof laser spot area.
For the case of a Gaussian intensity profile, a two dimensional distribution is written as:
!
1
x2
y2
P (x, y) =
exp
(C.1)
2
2
2
2⇡ t,laser
2 t,laser
2 t,laser158

Here, t,laser represents the transverse laser spot size radius on the surface of the component ofinterest. The peak energy density is expressed using total energy W as:
Ipeak (W,t,laser ) =W22⇡ t,laser(C.2)

The design total energy of 1.4 J/pulse is cut by 60% to 0.56 J/pulse by a beamsplitter on thelaser table to prevent damage of components. The typical t,laser is about 3 mm between the reducer
and the focal lens on the vertical table (see Sec. 5.2). W =0.56 J/pulse and t,laser w 3 mm gives
Ipeak = 0.3 J/cm2 .
In the past, some mirrors in the full power beam line that had damage threshold Ith = 10 J/cm2
had been replaced with mirrors of Ith = 20 J/cm2 . Using Eq.C.2, the corresponding lower limit on
laser spot size at a mirror is:(r
0.9 mm(Ith = 10 J/cm2 )
W
'
(C.3)
t,laser >2⇡Ith
0.7 mm(Ith = 20 J/cm2 )However, the above-mentioned thresholds are defined for wavelength = 1064 nm and pulse
width 10 ns (FWHM)[46], whereas the damage threshold scales with and the square root of time
domain. Therefore when setting the safety margin for pa laser of = 532 nm and pulse width = 8
nm (FWHM), Ith needs to be halved, then divided by 10 ns/8 ns w 1.25. Thus Eq. C.3 becomes:s(
1.5 mm(Ith = 10 J/cm2 )
W
'
(C.4)
t,laser >2⇡ (Ith /2/1.25)
1.1 mm(Ith = 20 J/cm2 )Furthermore, for a pulse laser, there may be hot spots in the profile. This requires another safetymargin of a factor of 2-3[48]. Taking this into account, the t,laser w 3 mm on the vertical tablebarely meets the stricter version of safety margin for mirrors of Ith = 20 J/cm246 . We must also
keep in mind the possibility of sudden changes in focusing patterns, and that the discussion here is
only on a theoretical basis.
For a CW laser, we think in terms of power density, which is simply written as (total power)/(beam2
spot area), where beam spot area = ⇡ t,laser. For example, for the Nd:YAG CW laser (50 mW,
532 nm, diameter 0.8 mm) used for the alignment of optical components, the power density is (50mW)/(⇡ · 0.42 mm2 ) = 9.95 W/cm2 .

D

Alternative Scenarios of Simulation Test for Phase Jitter Extraction

Section 7.5.2 demonstrated the results for the extraction and compensation of a complex and realistic
non-Gaussian phase fluctuation. The purpose of this section is to show that similar precision for
Mcorr can be achieved for some alternative scenarios of complex phase instabilities. The inputs into
these simulations are based on the same phase variation pattern (Fig. 7.6) and the same verticaljitter as in Sec. 7.5.2, whereas the following alterations are made upon the the order of the phasevariation in Fig. 7.6, the linear drift, or the phase jump.
1. Figure: D.1: the first half and second half of the phase pattern in Fig. 7.6 are interchanged.
46

Compared to a flat top distribution, a Gaussian intensity profile requires multiplying W by a factor of two toaccommodate the peak power density at the center of the beam. The actual laser beam is in between a flat top
distribution and the assumed Gaussian, thus the peak intensity is lower than a perfect Gaussian case, which slightly
lowers restrictions.

159

2. Figure: D.2: the linear drift is input as 60 mrad / min for the interval of '=0-10 rad, 0 mrad/ min for '=11-14 rad, and 80 mrad / min for '=15-19 rad. The linear drift in Fig. 7.8 wasa constant 80 mrad / min.
3. Figure: D.3: the location of the 0.7 rad phase jump is moved to '= 6 rad (fringe peak) and'=15 rad (fringe valley). The original location in Fig. 7.8 was at '= 11 rad (fringe mid-point).
In the plots below, the results of Mcorr (w.r.t. M0 ) are compared with that in Fig. 7.8, and areshown for 1000 pseudo experiments for Nav =50 and Nav =10. For the smallest y measurements inJune 2014, ' is approximately in the range of 0.4-0.7 rad. It can be seen that within this realistic' range, no significant diﬀerence can be seen in the precision of Mcorr between Fig. 7.8 and thealternative scenarios. The only points with discrepancy beyond the range of the errorbars are for
Nav =10 in Fig. D.3 and are only < 3.1%.

Figure D.1: The red points show the results of Mcorr w.r.t. M0 (green line) from an alternative
version of the fringe scan simulation in Fig. 7.8; here the first half and the second half of the phasevariation in Fig. 7.6 have been interchanged. The other input conditions are kept the same as inFig. 7.8. For comparison, the blue points show the original results in Fig. 7.8. These are the resultsof 1000 pseudo experiments for Nav = 50 (left) and Nav = 10 (right).

Figure D.2: The red points show the results of Mcorr w.r.t. M0 (green line) from an alternative
version of the fringe scan simulation in Fig. 7.8; here the linear drift is input as 60 mrad / min for
the interval of '=0-10 rad, 0 mrad / min for '=11-14 rad, and 80 mrad / min for '=15-19 rad.The
other input conditions are kept the same as in Fig. 7.8. For comparison, the blue points show theoriginal results in Fig. 7.8, where the linear drift is a constant 80 mrad / min. These are the resultsof 1000 pseudo experiments for Nav = 50 (left) and Nav = 10 (right).

160

Figure D.3: The red points show the results of Mcorr w.r.t. M0 (green line) from an alternative
version of the fringe scan simulation in Fig. 7.8; in the top row, the location of the 0.7 rad phasejump has been moved to '= 6 rad (fringe peak); in the bottom row, the phase jump has been
moved to '=15 rad (fringe valley). The other input conditions are kept the same as in Fig. 7.8. For
comparison, the blue points show the original results in Fig. 7.8, for which the phase jump is at '=11 rad (fringe mid-point). These are the results of 1000 pseudo experiments for Nav = 50 (left) andNav = 10 (right).

E

Extraction of Clinear

Clinear is the other free parameter extracted from fringe scan data alongside phase jitter ' using
the method given in Sec. 7.4. Figure E.1 demonstrates the extraction precision of Clinear for boththe simulation of Gaussian-like ' in Fig. 7.5 as well as the the simulation of realistic ' in Figures
7.7 and 7.8.
Figure E.2 shows a history of Clinear extracted from fringe scan data in May-June 2014. The
center of the data points are between 6-10% in general. The major factors contributing to Clinear
are laser timing jitter (. 5%), e beam intensity jitter (⇠ 2% = ICT monitor resolution), and the
reduction in the laser power interacting with the e beam due to fluctuation of the laser profile atthe IP (< few %).

161

Figure E.1: The simulation results for the extraction of Clinear . The horizontal axis is the RMS of
the input phase variation ( ',in ). The red and blue points are the extracted Clinear for Nav = 50
and Nav = 10, respectively, shown as the statistical results of 1000 pseudo experiments. The green
line is the input Clinear (=10% w.r.t. Eavg ). (top) From the simulation in Fig. 7.5; the absolutedeviation of the extracted Clinear w.r.t. to the input is < 1.5% for any amplitude. (bottom left)
From the simulation in Fig. 7.7. (bottom right) From the simulation in Fig. 7.8. With exception of
the largest RMS ',in = 0.90 rad, the absolute deviation of the extracted Clinear w.r.t. to the input
is . 3%. For ',in = 0.90 rad, the deviation is . 6%.

Figure E.2: A history of Clinear extracted from fringe scan data in May-June 2014. The center ofthe data points are between 6%-10% in general. Each data group is labeled by the date and Nav .

162

F

Details of Beam Time Results

For the continuous scans on June 12 and June 13 mentioned in Sec. 8.1, Figures F.1, F.2 and F.3
show the results of Mmeas , Mcorr , and ' respectively, as a function of time. For each scan, ' isderived using the method described and verified in Sections 7.4 - 7.7, and Mcorr is by correcting
Mmeas using the extracted ' as in Eq. 6.7.

Figure F.1: Mmeas shown as a function of time for the continuous fringe scans on June 12 (left) and
June 13 (right), mentioned in Sec. 8.1. The errorbars are the fitting errors.

Figure F.2: ' shown as a function of time for the continuous fringe scans on June 12 (left) and
June 13 (right), mentioned in Sec. 8.1. The errorbars are the fitting errors.

163

Figure F.3: Mcorr shown as a function of time for the continuous fringe scans on June 12 (left) and
June 13 (right), mentioned in Sec. 8.1.

G

Wake Field Eﬀects

The small beam sizes achieved by ATF2 as mentioned in this thesis were measured with very low
beam bunch charge (. 1.0 ⇥ 109 ). The beam size ( y ) is observed to depend strongly on bunch
intensity. Figure G.2 shows examples of the intensity dependence measurement.
The most probable cause of the intensity dependence is wakefield in the final focus beam line.
Figure G.1 shows the schematics of wakefield. Relativistic particles create electromagnetic fields
behind them as they travel down the beam line. The particles in the later part of the bunch are
kicked by the fields created by the preceding particles. In this way, wakefield causes particles to strayoﬀ course, thus leading to beam size blow up. In particular, when beam particles pass oﬀset fromthe center of the beam pipe, they are kicked by the wakefield generated from unleveled locations in
the beam line, where wake filed generation is enhanced.
Wakefield scales approximately inversely with beam energy when the distance between the beamand the beam pipe walls is much longer than the beam bunch length, and scales approximately
linearly to bunch intensity and beta function. Beam size focusing is aﬀected more by wakefield at
ATF2 than at the ILC because of the lower ATF2 beam energy and the longer bunch length (6-8mm for ATF2 as opposed to 300 µm for the ILC). Wakefield eﬀect should be less serious at the ILC
because of the higher beam energy, shorter bunch length, and better vacuum chamber material ofCu, as opposed to Al for ATF2 47 . The eﬀect of wakefield at ATF2 has been studied by simulation
during its design stage (see ATF2 Proposal [4], pg 31) for cavities, bellows, and flanges (in the formof average kick angles per unit oﬀset). However the significant intensity dependence observed inexperiment is larger than the theoretical calculations.
The contribution of wakefield to the measured beam size is expressed as:2y (q) =

22 2
y (0) + a q(G.1)

Here, y (0)is the beam size at zero-charge i.e. without wakefield eﬀect, q is the bunch charge in
nC, and a represents the wakefield contribution in nm · nC 1 . The contribution of wakefield to beam
size growth has been measured to be 100-140 nm · nC 1 [19]. This is more significant than the eﬀectcalculated from only cavity BPMs. To minimize wakefield eﬀect, ATF2 is usually operated in 2014spring at a very low charge of 80-200 pC, which correspond to bunch population of 0.5-1.25⇥109 .
47
The ILC vacuum chamber is to be made of Cu for the purpose of resistive wall wake, which is not necessary at
ATF2.

164

For example, using Eq.G.1, the typical bunch charge of 1.0⇥109 (160 pC) would cause a y of 45
nm to be blown up by about 2.8 nm.
A large part of beam time in 2014 spring was dedicated to the investigation of the reason for theunexpectedly large eﬀect on y : identify the wakefield sources and engineer solutions to mitigate
them. Most wake studies involve measuring M using the Shintake Monitor. When investigating
intensity dependence, M is measured as a as a function of bunch intensity as in Fig.G.2. Wheninvestigating the source of wakefield, M is measured as a function of the scanned position of beamline components, which are placed on a mover for this purpose. Figure G.3 shows one example,
where the vertical direction of one of the OTR monitors (OTR2) is scanned, while observing theeﬀect on the measured M .
The various eﬀorts to mitigate wakefield sources in the high beta region of the FFS line include:• the shielding of bellows and vacuum ports• the removal of some cavity BPMs, reference cavities, wire scanners, and some other components
from a large beta section to a lower beta section• the realignment of beam pipes
Owing to these prolonged eﬀorts, the eﬀect on y is thought to have become weaker, howeverstill remains one of the major limits in y focusing. A clear conclusion is yet to be reached andthe studies are still ongoing. The understanding of the bunch intensity dependence of y and thewakefield eﬀects are part of what is referred to as the “Goal 3” of ATF2. More detailed discussions
and study results are found in the references [21, 18, 30, 19, 20].

Figure G.1: The schematic diagram of wakefield in the beam line. Here, d is the distance between
the e beam and the beam pipe, and z is the longitudinal bunch length. [25]Figure G.2: Intensity dependence of the M measured by the Shintake Monitor [19, 18]: (left) using
the 174 deg mode (right) using the 30 deg mode.

165

Figure G.3: A scan of the OTR2 vertical position in order to investigate the impact on the beam
size from the wake field produced in this part of the beam line. The beam bunch intensity here isabout 3 ⇥ 109 . [21].

H

Cross-check of Analysis Methods

As mentioned in Sec. 3.5.4, typically the sum of ADC counts in only the front 4 layers is used inanalysis. This custom is meant for accommodating any S/N ratios since under high BG circumstances, the last bulk layer is dominated by BG. Some alternative methods are to use the ADC
counts from all 5 layers, or to use the 2nd layer only, as it has the highest S/N ratio.
It has been confirmed that the fitted beam size is consistent within the fitting errors for the sumof the ADC counts of the following:• the front 4 layers only (as typical)• all five layers• only the 2nd layer, which has the highest ratio of signal deposit
Figure H.1 shows an example of the above-mentioned three types of analysis results for the same
fringe scan (from the ATF2 control room panel). It can be seen there is no significant diﬀerence ineither the beam size, nor the signal fluctuation.

166

Figure H.1: The analysis results (from the ATF2 control panel) for the same fringe scan from June2014 shows no significant diﬀerence in M or y between alternative methods: (top) front 4 layers:
y = 42.4 ± 1.5 nm (b) all five layers: y = 42.3 ± 1.4 nm (c) second layer only: y = 42.0 ± 1.5 nm.
167

I

DAQ

The Shintake Monitor system is made up of many optical components and sub-monitors, theircontrollers, and digital modules. Furthermore, its operation requires experiment data and control
data to be shared on a time synchronized basis with other ATF2 beam monitors. The control anddata acquisition (DAQ) of the Shintake Monitor are performed on the EPICS (Experimental Physics
and Industrial Control System)[49] platform. It is a software environment capable of linking together
individually distributed control systems on a realtime basis. In EPICS, servers called Input/Output
Controllers (IOCs) pass on information to individual PCs through a network protocol called Channel
Access (CA).
Figure I.1 shows the schematics of the control system comprised of various devices each linked
to the EPICS via an IOC. Information is exchanged based on a “record” with a “PV name”. The ebeam related database channels (EPICS PVs) are synchronized and updated by a beam repetition
rate of 3.12 Hz. The EPICS IOC gather the status of the device (=DAQ), update the appropriate
EPICS PV, and control the device through individual computers.
In the Shintake Monitor system, the main computers for control and DAQ are called “lxs-ip” and“ip-ccnet”. These communicate with the EPICS.
lxp-ip: the EPICS IOC for most Shintake Monitor devices run on the lxp-ip. Each IOC acquires andexchanges information about the status of the device it’s responsible for. Some examples are:(a) The linear stage on which mirrors are mounted receive commands from their controllers
to move to the designated position in order to switch to a particular crossing angle mode. Its
position status is acquired by the IOC and updated to the EPICS PV. (b) The position of theattenuator is monitored using a infrared ray sensor and read out by a PLC. The information ofwhether the attenuator is inserted or ejected is update it to an EPICS PV by the IOC. Other
devices, such as the IP screen mounted on a mover, need to confirm the inserted state before
they are allowed to move to their designated position to prevent damage by high intensity
laser.
ip-ccnet: the ip-ccnet handles the DAQ and controls the synchronization of the VME modules:
the charge sensitive ADCs: V005 (for the gamma-ray detector) and RPV171 (for the ICT
monitor). It runs a reader process called “Event Collector” which gathers the ADC datafrom the VME modules and updates the EPICS PV called “IPBSM:AllData”. This allows
the measured Compton signal energy to be normalized precisely by the measured e beam
intensity during fringe scan using synchronized data for both.
Another computer, referred to as the “Windows machine” specially handles the control of the mirror
actuators.
These tasks (e.g. giving commands, acquiring information) can be done via PCs connected to
the EPICS with permission to “read” or “write”, such as through the control panels in the ATF
control room.
Owing to the EPICS, the information of other ATF2 beam monitors such as the BPMs could berecorded within the fringe scan data set on a synchronized basis.

168

Figure I.1: The schematics of control and DAQ based on the EPICS platform. [25]169

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