Doctoral Dissertation
博士論文

Search For the Vacuum Polarization
using a high-field laser and an XFEL
(高強度レーザーと X 線自由電子レーザーを用いた真空偏極の探索)

A Dissertation Submitted for the Degree of Doctor of Philosophy
December 2020
令和２年１２月博士 (理学) 申請

Department of Physics, Graduate School of Science,
The University of Tokyo
東京大学理学系研究科物理学専攻

Yudai Seino
清野 結大

Abstract
This thesis reports a vacuum polarization search with a new experimental
scheme. X-ray diﬀraction caused by polarized vacuum under a high laser field(vacuum diﬀraction, VD) is searched. In the VD experiment, the high-intensity
laser pulse and the x-ray pulse are collided to diﬀract the x-ray. This new scheme
overcomes the problem of small signal statistics in previous vacuum polarization
searches. However, this scheme has not been performed since it is diﬃcult to collide both pulses due to their small sizes (∼ 1 µm) and their short pulse durations(∼ 100 fs). I developed the spatially and temporally precise alignment techniqueto collide both pulses. In addition, I derived the theoretical formula of the signal
distribution of the VD.
A first experimental search for VD was performed at the beamline 3 of SACLA,an X-ray Free Electron Laser (XFEL) facility at Hyogo, Japan. It is expectedthat a vacuum is polarized by the focused 0.6-TW laser field and an XFEL beam
is diﬀracted. A precise control system of a laser phase using an adaptive optics
is constructed to focus the laser pulse. A novel x-ray optics is also developed tosuppress backgrounds from the XFEL beam. Both pulses are collided in headon collision geometry using the developed alignment techniques, and diﬀracted xrays are searched. No significant signal is observed, and the upper limit of VD
is obtained with 90% C.L. The limit is obtained as the ratio of the number ofthe observed x rays, nxray,sum = (1.02 ± 1.07) × 104 photons, to the number of the−14 photons,
expected x rays in quantum electrodinamics, nQED,sum = (3.9+6.1−2.5 )×10
as follows:
nxrays,sum< 2.3 × 1018
nQED,sum(90% C.L.).

(1)

This is the first limit on vacuum polarization by the VD experiment and is also
the first experimental restriction on VD. The developed experimental scheme andthe techniques pave the way for observation of vacuum polarization in a future
experiment.

iContents
1 Introduction
1.1 Vacuum polarization . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Vacuum polarization and motivation for search . . . . . . . .
1.1.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Previous searches for vacuum polarization . . . . . . . . . . . . . . .
1.2.1 Photon-photon scattering experiment . . . . . . . . . . . . .
1.2.2 Vacuum birefringence experiment . . . . . . . . . . . . . . . .
1.3 Vacuum diﬀraction experiment using high-field laser and XFEL . . .
1.4 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
1
2
3
3
4
7
7

2 Formula of Vacuum Diﬀraction signal
92.1 Vacuum diﬀraction formula . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Assumed setup . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Signal formula . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Vacuum diﬀraction formula with XFEL curvature eﬀect . . . . . . . 14
3 Setup and devices
3.1 Probe XFEL system . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 XFEL beamline and devices . . . . . . . . . . . . . . . . . . .
3.1.2 Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Shaper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 XFEL beam . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Pump laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 0.6-TW laser system . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Optical system . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Laser beam and image . . . . . . . . . . . . . . . . . . . . . .
3.3 Signal detection system . . . . . . . . . . . . . . . . . . . . . . . . .

17
17
17
20
23
25
28
28
28
33
35

4 Alignment of two beams
4.1 Spacial alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Adjustment of the laser position . . . . . . . . . . . . . . . .
4.1.2 Measurement of laser position . . . . . . . . . . . . . . . . . .
4.1.3 Measurement of XFEL position . . . . . . . . . . . . . . . . .

37
37
37
38
41

iii

4.1.4 Result of spacial alignment . . . . . . . . . . . . . . . . . . .
Time alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Measurement of the focal position of the laser . . . . . . . . .
4.2.2 Adjustment of the delay time of the laser . . . . . . . . . . .
4.2.3 Precise measurement of the collision timing . . . . . . . . . .

42
45
45
46
46

5 Data taking and analysis
5.1 Data taking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Data acquisition of vacuum diﬀraction . . . . . . . . . . . . .
5.1.2 Monitoring of position drift of both pulses . . . . . . . . . . .
5.2 Expected signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 BG sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Timing distribution of detected x rays . . . . . . . . . . . . . . . . .
5.5 Analysis of the upper limit on VD . . . . . . . . . . . . . . . . . . .
5.5.1 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . .
5.5.2 Final result . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51
51
51
54
57
60
61
63
63
66

6 Discussion and prospect
6.1 Significance of the experimental result . . . . . . . . . . . . . . . . .
6.2 Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Upgrades for the future experiment . . . . . . . . . . . . . . .
6.2.2 Future experiment . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Requirement for the future experiment . . . . . . . . . . . . .

69
69
70
70
72
73

7 Conclusion

75

A Shaper77

B Polarizer

81

C List of symbols

83

Acknowledgements

85

4.2

iv

List of Figures
1.1
1.2
1.3

Vacuum polarization loop in QED. . . . . . . . . . . . . . . . . . . . 2
Processes of photon-photon interaction in a vacuum. . . . . . . . . . 2
Comparison of experimental sensitivities of previous experiment against
VP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1
2.2
2.3
2.4

Schematic views of the experimental conditions. . . . . . . . . . . . .
Angle distributions of the signal x rays and the probe XFEL pulse. .
Validation of the short-pulse approximation. . . . . . . . . . . . . . .
Schematic view of the focused XFEL pulse at the collision point. . .

10
13
14
14

3.1 The apparatuses in SACLA BL3. . . . . . . . . . . . . . . . . . . . .
3.2 A pair of total reflection mirrors (TRMs). . . . . . . . . . . . . . . .
3.3 Top view of the timing monitor (TM). . . . . . . . . . . . . . . . . .
3.4 Screen monitor (SCM). . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 The 4-jaw slit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Top view of the vacuum chamber. . . . . . . . . . . . . . . . . . . . .
3.7 The sample folder. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 The shaper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Setup of the Slit1 and the shapers at EH1. . . . . . . . . . . . . . . .
3.10 Images of the XFEL pulse with the x-ray camera. . . . . . . . . . . .
3.11 XFEL profiles at the collision point. . . . . . . . . . . . . . . . . . .
3.12 The vertical beam size of the XFEL pulse at each position on the
beam axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 A schematic of the whole setup of the optical system. . . . . . . . .
3.14 A system to cancel an aberration by the DM and the WFS. . . . . .
3.15 The focal spot of the laser pulse monitored by the Camera1. . . . . .
3.16 Laser beam size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 Ratio of eﬀective pulse energy concentrated in the spot. . . . . . . .
3.18 Image of PD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18
18
19
20
20
21
22
23
24
25
25

4.1
4.2
4.3

27
30
32
33
34
34
35

The microscope image of the irradiation traces of the laser pulse andthe XFEL pulse on the Au foil. . . . . . . . . . . . . . . . . . . . . . 38
The height profile of the crater of the laser irradiation traces. . . . . 39
Height profile of the crater. . . . . . . . . . . . . . . . . . . . . . . . 40v

4.4 Closed view of Fig. 4.3. . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 The image of the hole of the XFEL irradiation traces. . . . . . . . .
4.6 The projections of the binarized image of the hole. . . . . . . . . . .
4.7 The image of the irradiation traces on the Au foil. . . . . . . . . . .
4.8 The distributions of the XFEL positions and the laser positions. . .
4.9 Irradiation traces of the laser pulse. . . . . . . . . . . . . . . . . . . .
4.10 Depth of irradiation traces of the laser pulse at each position along
the beam axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.11 The image of the laser through the GaAs crystal. . . . . . . . . . . .
4.12 Left: Schematic of the GaAs crystal and both pulses at the collision
timing. Right: Laser transmittance versus delay time in the ideal
situation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.13 The pulse-by-pulse distributions of the laser transmittance of the
GaAs crystal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.14 Two kind of sources of GaAs position uncertainty. . . . . . . . . . .

40
41
42
43
43
45
46
47

48
48
49

5.1

Illustration of the way of the scan of the delay time with the wide
range (6.9 ps). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2 The jitter of each pulse during the data acquisition. . . . . . . . . . 52
5.3 The timing distribution of the collision data. . . . . . . . . . . . . . 53
5.4 The number of photons in the XFEL pulse during the data acquisition. 53
5.5 The timing distribution of the number of photons in the XFEL pulse
at the collision point. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.6 Images of the laser pulse and the XFEL pulse measured by the Camera2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.7 Drifts of the peaks of the laser and the XFEL images on the picture
taken with the Camera2. . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.8 Drift of displacement of the laser pulse position against the XFEL
pulse position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.9 Profiles of the interaction volume, the XFEL pulse, and the laser
pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.10 The phase space of the signal distribution in the vertical direction. . 58
5.11 Timing distributions of interaction probability and acceptance. . . . 59
5.12 Timing distribution of the number of expected signal x rays. . . . . . 59
5.13 The distribution of the intensity of x rays at the Slit6. . . . . . . . . 60
5.14 (Right) The schematic of the position of the slits. (Left) The dataof the knife-edge scan by the upper blade of the Slit4. . . . . . . . . 61
5.15 Detected x rays of each pulse during the data acquisition. . . . . . . 62
5.16 The timing destribution of the detected x rays. . . . . . . . . . . . . 62
5.17 The timing distribution of the diﬀerence of the number of detected
x rays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.1
6.2

Comparison of experimental sensitivities against VP. . . . . . . . . . 70
Experimental setup of the future experiment. . . . . . . . . . . . . . 72
vi

A.1 Comparison of the raw XFEL profile and the profile with the shaper. 78
A.2 Comparison of the XFEL beams focused by the shaper and the Be
lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
A.3 The x-ray camera images of the focused XFEL beam by the Be lensand the shaper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
B.1 Polarizer made of Si. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
B.2 Extinction ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

vii

List of Tables
1.1
1.2

The summary of the latest photon-photon experiments. . . . . . . .
The summary of vacuum birefringence experiments. . . . . . . . . .

4
6

3.1
3.2
3.3

The summary of main experimental parameters. . . . . . . . . . . . 17
Positions of shapers, slits and the x-ray camera. . . . . . . . . . . . . 27
The summary of optics parameter . . . . . . . . . . . . . . . . . . . 31

4.1
4.2

The summary of the uncertainties of the displacements. . . . . . . . 44
The summary of the temporal uncertainties. . . . . . . . . . . . . . . 50

5.1
5.2

The summary of the data acquisition of vacuum diﬀraction. . . . . . 51
The summary of systematic uncertainties on nQED,sum . . . . . . . . . 64

6.1
6.2

Expected gain factor by upgrades. . . . . . . . . . . . . . . . . . . . 70
The summary of the experimental parameters of the future experiment. 74

C.1 List of main symbols used in this theses. . . . . . . . . . . . . . . . . 83
C.2 List of abbreviations used in this theses. . . . . . . . . . . . . . . . . 84

ix

Chapter 1

Introduction
1.1

Vacuum polarization

1.1.1

Vacuum polarization and motivation for search

The discovery of the Higgs boson in 2012 shows that the vacuum is filled withquantum fields [1, 2]. This means that a vacuum is not an empty space and hides
various properties. This discovery opens a new era that exploring properties of avacuum.
Vacuum polarization (VP) is one of the most interesting vacuum properties in
the quantum electrodynamics (QED), which has not been observed yet. VP is abasic radiative correction that modifies the propagation of photons in the vacuum
through a virtual pair of an electron and a positron [3]. The Feynman diagram of
VP is shown in Fig. 1.1. Due to the eﬀect of VP, photons are able to interact witheach other, though a photon does not have an electric charge. A photon-photon
interaction causes various physical phenomena [4]. The representative phenomenon
is a photon-photon scattering, that is a scattering process of two photons (Fig. 1.2(a)). A polarization flip and diﬀraction of a propagating photon in a vacuum arealso caused by a photon-photon interaction (Fig. 1.2 (b)).
Since VP is a fundamental process in QED, the confirmation of it is important.
However, it has not been observed yet in a vacuum. Many experiments have been
performed using a laser or a magnet [5–9] to observe VP via the phenomena caused
by VP. However, anyone has not observed because of its small probability of theinteraction.
The phenomena caused by VP also provide a probe for a new physics. As a
new particle beyond the standard model, some particles are predicted, for example, Axion, axion-like particles and millicharged particles [10–12]. The phenomena
caused by VP are easily aﬀected by these particles since these particles have aneﬀective coupling to two photons. Therefore, we can search for these particles withthe search of the phenomena caused by VP.
The observation of VP is also the verification of physics under a strong electromagnetic field. Behaviors of photons and electrons under a strong electromagnetic
1

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Figure 1.1: Vacuum polarization loop in QED. Wavy lines and a circle represent
photons and virtual electron-positron, respectively.
(a)

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(b)

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Figure 1.2: Processes of photon-photon interaction at the lowest-order QED in a
vacuum. (a) Photon-photon scattering. Two photons are collided and scattered.
and vacuum birefringence.
A photon interacts with two(a) (b) Vacuum diﬀraction(b)(c)
photons in an electromagnetic fields.
field have not been studied, and various phenomena are predicted, for example,
Shwinger eﬀect that electrons are created by a strong electromagnetic field [13],and Unruh eﬀect that accelerated charged particles will feel a thermal bath [14].
Strength of the interaction of a photon and an electron under a strong electromagnetic field is important to estimate these phenomena and can be measured byobserving VP. Therefore, the observation of VP is the first step of the verificationof these predicted phenomena.

1.1.2

Properties

The properties of VP is mathematically expressed as the Euler-Heisenberg eﬀective
lagrangian [15]. It is an eﬀective lagrangian for the non-linear dynamics of an electromagnetic field in the QED vacuum. The lagrangian is written in Eq. (1.1) withassumptions that photon energies are well below the electron mass me and electromagnetic field strengths are much smaller than the QED critical values (electricfield E ≪ 1.3 × 1018 Vm−1 , magnetic field B ≪ 4.4 × 109 T),
[(
( 2
)
)2
(
)2 ]
2
1
E
A
E
E
e
L=
− B2 +− B2 + 7·B,(1.1)
2µ0 c2
µ0
c2
c
where
Ae =

2α2 ℏ3= 1.32 × 10−24 [T2 ]45µ0 m4e c5

(1.2)

3

CHAPTER 1. INTRODUCTION

with the magnetic permeability of vacuum µ0 , the speed of light in vacuum c, reduced Planck constant ℏ and fine structural constant α. The second term represents
the eﬀect of VP and causes photon-photon interactions.
A change of a refractive index of a vacuum caused by VP under an electromagnetic field is written as [16]{ [n = 1 + Ae

(
[
(
)]
)] }
E 2
E 2
7 (êe · B) + êb ·+ 4 (êb · B) − êe ·
,
c
c

(1.3)

where êe and êb are unit vectors of electro and magnetic field of a propagating
photon, respectively.
Due to the property of VP, three phenomena are caused (Fig. 1.2). The firstis photon-photon scattering which is an elastic scattering of two photons [17]. The
second is vacuum birefringence which is a phenomenon that a refractive index ofa vacuum has birefringence under an electromagnetic field. The third is vacuum
diﬀraction (VD) which is a diﬀraction of a photon propagating in a vacuum. Undera local electromagnetic field, the vacuum has the gradient of the refractive index,
and photons propagating in that local electromagnetic field are diﬀracted. We cansearch for VP by observing these phenomena.

1.2

Previous searches for vacuum polarization

Many experimental groups have searched for VP by measuring the phenomena
caused by VP,, as shown in this section. However, mainly due to an insuﬃcient
statistic of signals, anyone has not observed yet.

1.2.1

Photon-photon scattering experiment

Signature of photon-photon scattering
When the photon energy in the center of mass system, ωcms , is less than the energyof an electron mass, the diﬀerential cross-section of the scattering of two photons
with the same linear polarization is given by [18, 19],(dσγγ→γγdΩ)(

α2 re2=(180π)2
QED

ωcms
me c2

)6
× (260 cos4 θscat + 328 cos2 θscat + 580),
(1.4)

−70

σQED = 3.5 × 10

(ωcms [eV])

6

2

[m ],

(1.5)

where re = e2 /4πϵ0 me c2 is the classical electron radius, and θscat is the scattering
angle in the center of mass system. The cross-section is proportional to the sixth
power of ωcms .

CHAPTER 1. INTRODUCTION

4

Experiments and problems
Two lasers are collided in photon-photon scattering experiments. A signal is ascattered photon, and two patterns of an experimental scheme are taken to obtainsignal statistic. One scheme is the use of a laser whose pulse has many photons[5, 20, 21]. A high-field optical laser is used. Another is the use of high energy
photons, which has a large cross-section [6,22]. An x-ray free electron laser (XFEL)
which is a strong intensity x-ray laser is used. In both scheme experiments, lasers
are focused to enhance signals. For example, the size of the focused optical lasers is
4 µm, and that of the XFEL beams is 2 × 200 µm in the latest experiments [6, 21],respectively. Experimental parameters of these latest experiments are summarizedin Tab. 1.1.
However, signal statistics obtained by these experiments are not enough though
the pulse energy of both latest experiments (100 mJ and 1 µJ for [21] and [6],respectively) is a very strong class as the laser with each wavelength. Expectedsignals are very small and are about ∼ 10−19 photons during data acquisition. The
number of background (BG) photons was expected to be O(1 − 10) photons. The
observation of the photon-photon scattering using existing devices is statisticallydiﬃcult.
Table 1.1: The summary of the latest photon-photon experiments. σlimit is theobtained limit of the cross-section of photon-photon scattering.

Experiment

D. Bernard, et. al. [21]T. Yamaji, et. al. [6]Deviceωcms
σlimit /σQEDExpected signals
Detector
Problems

100 mJ optical laser
0.4 eV
8 × 1017
7 × 10−18 photons/100 seconds
Spectrometer· Insuﬃcient statistic of signals· BG photons from residual gas(66 photons/100 seconds)

1 µJ XFEL
6.5 keV
7 × 1019
3 × 10−19 photons/34 hour
Germanium detector· Insuﬃcient statistic of signals· BG photons ofenvironmental radiation(0.4 photons/34 hour)

1.2.2

Vacuum birefringence experiment

Signature of vacuum birefringence
Vacuum birefringence has been searched for by pumping the vacuum with magnets.
Under a magnetic field B, the horizontal and the vertical refractive indices of the5

CHAPTER 1. INTRODUCTION

vacuum and their diﬀerence are described as [16]n∥ = 1 + 7Ae B 2for êe ∥ B

(1.6)

2

for êe ⊥ B(1.7)

n⊥ = 1 + 4Ae B∆n = n∥ − n⊥ = 3Ae B 2 ≒ 4 × 10−24 B 2

[T2 ]

(1.8)

where êe is the polarization vector of a propagating photon in the magnetic field.
Since the refractive index depends on the direction of the magnetic field, the vacuum
has birefringence.
Experiments and Problems
Some groups have searched for vacuum birefringence [9, 23, 24] (Tab. 1.2). In theseexperiments, a linearly polarized optical laser probes the vacuum which has birefringence due to a magnetic field of a magnet. Signals are laser lights whose polarization are changed, and the amount of the signals is proportional to B 2 L, where L
is a length of the magnetic field. A high-finesse optical cavity, whose mirror reflects
a laser light about 106 times, is used to enhance a slit signal in a single path.
It seems to be diﬃcult to improve their sensitivity by the cavity. A fake signal
is generated every time when the laser light is reflected on the cavity mirror andlimits the current sensitivity. They have studied the origins of the fake signal, andthe strong candidate is birefringence of a mirror coating [7] or vibrations of themirror smaller than 1 pm [8]. Because these origins are unavoidable for the mirror,
the reduction of the fake signal seems to be diﬃcult.
The improvement of the sensitivity by increasing the magnetic field is also
diﬃcult because they already use world-class strong magnets (about 10 T). Anotherway to increase the signals without the cavity is required, and the VD experimentis considered. Table. 1.3 shows experimental sensitivities of previous experiment
against VP. The signals expected by QED, which is proportional to the square of
the fine structure constant α2 , is normalized to 1, and a sensitivity to the signals
are shown with 90% C.L.

CHAPTER 1. INTRODUCTION

6

Table 1.2: The summary of vacuum birefringence experiments. Alimit is an obtained
1σ limit of Ae .
Experiment

PVLAS [7, 23]

BMV [8, 24]

OVAL [9]Magnet type
Magnetic field
Field length
Alimit /Ae
Problems

permanent
2.5 T
1.6 m
1 × 101· Birefringence ofcavity mirror coating

pulsed
6.5 T
0.1 m
4 × 103· Vibration ofcavity mirrors

pulsed
9.0 T
0.2 m
4 × 105· Not identified

Photon-photon scattering experiment
Vacuum birefringence experiment

90%Limit

1020
1018

h1d_waku

Yamaji [6]Bernard [21]

1016
1014
1012

OVAL[9]1010
108

BMV [8]106
104

PVLAS [7]

102
1

2000

2005

2010

2015

2020

QED calculationyear

Figure 1.3: Comparison of experimental sensitivities previous experiments against
VP.

7

1.3

CHAPTER 1. INTRODUCTION

Vacuum diﬀraction experiment using high-field laser
and XFEL

Vacuum diﬀraction (VD) and search method
Another method to observe VP has been considered, and the search for VD wasproposed in 2006 [25]. Probe photons are diﬀracted under a local electromagnetic
field, and then diﬀracted probe photons are searched.
A high-field femtosecond (fs) optical laser is used to locally pump the vacuum.
A focused fs laser pulse generates a locally and instantaneously strong field. As aprobe light, the x-ray pulse of XFELs is used. Because the XFEL pulse is also fs
laser pulse, the XFEL pulse can probe the instantaneously pumped vacuum.
Benefits of vacuum diﬀraction experiment
Traditionally, VP has been searched for by the photon-photon scattering experiment or the vacuum birefringence experiment. In 2009, the first XFEL was constructed, and it enabled us to perform the VD experiment.
There are benefits in the VD experiment. The VD experiment can obtain large
signal statistics, which were small in previous VP experiments. An electromagnetic
field of a focused laser (for example, O(106 )T with a peta-watt (PW) class laser) is
significantly stronger than that of the magnets (O(1–10)T). Since the signal statistics are proportional to the fourth power of the electromagnetic field, large signal
statistics are generated. Furthermore, even larger signal statistics are generated byusing x-ray as the probe light instead of an optical laser. The signal statistics in
VD and vacuum birefringence experiments are proportional to the square of thewavenumber of probe photons. Since the wavenumber of the x-ray is four digits
larger than the visible light, the signal statistics increase about 108 times. Observable signals are given without an optical cavity, and O(1) photons of VD signals
are expected by one collision of the PW laser pulse and the XFEL pulse.
Another benefit is the applicability of the experimental method of the VD
experiment. Since the strong pumping field of the laser can excite other quantum
fields which are hidden in the vacuum, the pump-probe method can be applied toexperiments to search for the unknown fields, for example, axion and millicharged
particle [10–12].
We have performed the first VD experiment in the world. First VD experimentin the world is challenging and important because it creates a new way for VP
search.

1.4

Outline of this thesis

In this thesis, I report the first experimental search for VD. The XFEL of SPring-8
angstrom compact free electron laser (SACLA) [26] was used as the probe laser,
and a 0.6-TW laser was used as the pump laser. Both fs pulses were collided in

CHAPTER 1. INTRODUCTION

8

the head-on geometry, and the first experimental limit on the VD probability was
obtained.
In Chapter 2, a formula of VD signal is calculated. The detail experimental
setup is explained in Chapter 3. Developed alignment methods of the XFEL pulse
and the laser pulse are shown in Chapter 4, and the experimental result is shownin Chapter 5. The discussion about the result and a future experiment is shown in
Chapter 6, and then I conclude the thesis in Chapter 7.

Chapter 2

Formula of Vacuum Diﬀraction
signalFormulae of VD signal have been calculated under various situations [27–33]. In
this chapter, I derive the formulae of the signal for my experiment, which is ahead-on geometry illustrated in Fig. 2.1. Details of the calculation in this chapter
were published [34].

2.1

Vacuum diﬀraction formula

2.1.1

Assumed setup

A so-called “pump-probe” setup illustrated in Fig. 2.1 is considered. The electricalfield amplitude of the XFEL pulse is[](Z/c − t)2
J (x) =J0 cos(k(Z − ct) + ψ0 ) exp −(τX /2)2
[
]
[
]
X2
Y2
× exp − 2 exp − 2 ,
(2.1)
wXh
wXv
with

 


tan2 Θ
tan Θ tan Θ
1 + tan2 Θy ( cos1 Θ − 1) − tanx 2 Θ y ( cos1 Θ − 1) − tan Θx
X
x
 
2Θ
tan
Θ
tan
Θ
tan
 Y  = cos Θ 
x
y
y
1
1
y
,
 −
( cos Θ − 1) 1 + tan2 Θ ( cos Θ − 1) − tan Θy 
tan2 Θ
Zztan Θxtan Θx1(2.2)
where J0 is the peak field strength, τX is the pulse duration, k is the wavenumber ofthe x-ray, and ψ0 is a constant phase. The X , Y and Z-axes are the rotated x, y andz-axes by Θ. The XFEL pulse propagates in the Z-direction and has an incident
angle, Θ, against z-axis. Θx (Θy ) denotes the incident angle between Z-axis andthe y-z (x-z) plane, and satisfies cos12 Θ = 1 + tan2 Θx + tan2 Θy . Equation (2.1)
9CHAPTER 2. FORMULA OF VACUUM DIFFRACTION SIGNAL
(a)

y

x

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10

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Pump

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signal x-ray

ê⇥=0

E(x)

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xL , yLProbe

XFEL pulse

J (x)<latexit sha1_base64="cFPHzL9Cgfq8xMRW+d1h82kAvPw=">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</latexit>

wXh , wXvêX

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z<latexit sha1_base64="WuqC/D1SdcwO9VF5CFCXAs3GiHY=">AAACj3ichVG7SgNRED1Z3++ojWATDBGrMBuDUQsJ2mjnKw9Qkd31qqub3WX3JqAhP2BlJ2qlYCH+ga2NP2DhJ4hlBBsLZzcRsVDncu+dOXfO3DOM7lqmL4meI0pLa1t7R2dXd09vX/9AdHAo7ztlzxA5w7Ecr6hrvrBMW+SkKS1RdD2hlXRLFPTDheC9UBGebzr2ujxyxVZJ27PNXdPQJEP5TbkvpLYdjVNyZnoqlZ6KUZIoo6bUwEll0pPpmMpIYHE0bdmJ3mMTO3BgoIwSBGxI9i1o8HltQAXBZWwLVcY89szwXaCGbuaWOUtwhsboIZ97HG00UZvjoKYfsg3+xeLtMTOGBD3RLdXpke7ohT5+rVUNawRajvjWG1zhbg+cjKy9/8sq8S2x/836U7PELqZDrSZrd0Mk6MJo8CvHZ/W12dVEdZyu6ZX1X9EzPXAHduXNuFkRq5d/6NG5b41jwTVrPKavWcR+d/KppEpJdSUdz843B9aJUYxhgqeSQRaLWEaOfznAKc5xoQwqGWVOyTZSlUiTM4wfpix9Aj/TlB4=</latexit><latexit<latexit sha1_base64="KuSATb6zDgW0vTRPWFfX7drp8D8=">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</latexit><latexit

Probe
XFEL pulse

J (x)<latexit sha1_base64="cFPHzL9Cgfq8xMRW+d1h82kAvPw=">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</latexit>✓y ✓x<latexit sha1_base64="IM4uemDOaRPvpY+SPpgPnOIJ/Bo=">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</latexit><latexit sha1_base64="lULVK88R/e3aqzwpspIo6Tu0mUI=">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</latexit>

Pump
laser pulseE(x)<latexit sha1_base64="us3uArvEokfV0j0tQHSYdaOK8J4=">AAACu3ichVFNS9xQFD2mtbV+1LTdFLoJHRS7CTdxpDOFwlApuPRrVHBkSJ5Pjb58kGSGTsP8gf6BLupGQUH8Gd2U7rvwJ5QuFdy48CYzUroYe8PLu/e8e+479103Ul6SEl0MaQ8eDj96PPJkdGx84umk/uz5WhK2YiHrIlRhvOE6iVReIOuplyq5EcXS8V0l192D+fx8vS3jxAuD1bQTyS3f2Q28HU84KUNNXc8awlHGx+5Mw/WzT903Tb1EZrVK5fKcQeYc2bZdYYdm7UrVMiyTCiuhb4uh/hMNbCOEQAs+JAKk7Cs4SPjbhAVCxNgWMsZi9rziXKKLUea2OEtyhsPoAf93OdrsowHHec2kYAu+RfGKmWlgin7RGV3SDzqn33QzsFZW1Mi1dHh3e1wZNSe/vFy5/i/L5z3F3l/WvZpT7KBSaPVYe1QgeReix29//nq58m55KpumY/rD+o/ogr5zB0H7SpwsyeVv9+hxuW+HY8k1B79cnuejy2O8m5Ux2FmzTYtMa6lcqn3oD3QEr/AaMzy1t6hhAYuoc/U2DnGCU+29JrR9TfVStaE+5wX+Ma11C3MinxM=</latexit>

Figure 2.1: Schematic views of the experimental conditions. The XFEL pulse andthe laser pulse collide in the head-on geometry. (a) Magnified view from the sidearound the collision point. The laser pulse propagates in the negative direction of
the z-axis. The Z-axis is the beam axis of the XFEL pulse. The XFEL pulse has
incident angles, Θx and Θy , from the z-axis, and its beam size has been modelled
to be constant. The laser focus has transversal displacements (xL , yL ) from thez-axis. (b) Bird’s eye view. êX (êL ) is the polarization vector of the XFEL (laser)
pulse. êΘ=0 , which is on the x-y plane, is the polarization vector of the XFEL
pulse without the incident angle. δ is an angle between êL and êΘ=0 . k⃗′ is the
wavevector of the signal x-ray with a diﬀraction angle, θ, from the z-axis. θx (θy )is an angle of θ in the x-z (y-z) plane.
corresponds to a Gaussian beam with infinite Rayleigh length, which has constantbeam sizes, wXh and wXv , in the horizontal and the vertical directions, respectively.
The assumption that the beam sizes are constant is reasonable for the calculationof VD because the beam sizes are almost constant during the interaction due to thelong Rayleigh length of the XFEL pulse. Typically, an XFEL beam has Rayleighlength of 0.01 m with the divergence of 100 µrad and the focal spot of 1 µm.
The laser pulse is also modelled as a pulsed beam with an electrical field amplitude,[](z/c + t − tL )2
E(x) =E0 cos(Φ(x)) exp −(τL /2)2
] √
]
[
[
√
(x − xL )2(y − yL )2
wL0h
wL0v
×
,
×
exp −
exp −
(2.3)
wLh (z)wLh (z)2wLv (z)wLv (z)2
where E0 is the peak field strength. Φ(x) is a term which denotes a phase of thebeam, and τL is the pulse duration. wLh (z) and wLv (z) are the horizontal andvertical beam sizes as a function of z, respectively, and wL0h and wL0v are values
at the focus of the beam. The beam is focused on the x-y plane, and the focus has
the horizontal and vertical displacements, xL and yL , from the origin. tL is time ofa delay of the laser pulse.
Since the photon-photon interaction due to VD is almost unaﬀected by the
wavelength of the pump laser, the oscillating term cos(Φ(x)) in Eq. (2.3), which

11

CHAPTER 2. FORMULA OF VACUUM DIFFRACTION SIGNAL

depends on the wavelength of the pump laser, can be averaged over the oscillation of
the laser field [28,29]. This gives cos2 (Φ(x)) → 12 . I calculate the pulse energy of thelaser, W , to express the peak intensities, E02 and J02 , with measurable quantities as∫(2π)3/2 E02 wL0h wL0v cτL
W = dxdydzϵ0 E 2 (x) ≃ ϵ0
, where ϵ0 is the dielectric constant.
32
andFrom this, the peak intensities can be written as E02 ≃ (2π)3/2 ϵ 32W
w
w
cτ
0

L0h

L0v

L

ℏck
J02 ≃ (2π)3/232N, where N is the number of x rays in the XFEL pulse andϵ0 wXh wXv cτXℏck is photon energy of the x-ray.

2.1.2

Signal formula

In the assumed setup, an interaction probability of VD for each x-ray, P , is written
as [29],1 22 α4 ℏ5 ϵ30 ′d3 P=
k (1 + cos θ)2 (16 + 33 sin2 δ)
k ′2 dk ′ dϕd cos θ N 452 π 3 m8e c9× J0 2 E0 4 |M|2 ,

(2.4)

with
∫
M=

(
) J (x)d4 X exp iK ′ X
J0

(

E(x)
E0

)2
,

(2.5)

where X = (ct, x) = (ct, x, y, z) and K ′ = (k ′ , k⃗′ ) are four-vectors with the metric(−1, 1, 1, 1), and k ′ = |k⃗′ |. k⃗′ = k ′ (sin θ cos ϕ, sin θ sin ϕ, cos θ) = k ′ cos θ(tan θx , tan θy , 1)
is the wavevector of the diﬀracted x-ray, which is the signal. θ is the diﬀraction
angle of the signal x-ray from the z-axis. δ, which is illustrated in Fig. 2.1 (b), is
the angle between the polarization vector of the laser pulse, êL , and a vector, êΘ=0 ,where êΘ=0 is a polarization vector of the XFEL pulse without the incident angle.
The calculation is performed with realistic approximations [34]. One of theimportant approximation is against the pulse durations. The pulse durations oftypical fs lasers and XFELs are short and satisfy cτL ≪ zRL and cτX ≪ zRL , wherezRL is Rayleigh length of the laser beam. For example, the pulse length of typicalfs lasers satisfies cτL < 30 µm (τL < 100 fs), and cτX is much shorter than that,
whereas zRL is ∼ 400µm for 10 µm of the minimum beam size and λ = 800 nmof the wave length. In this short-pulse condition, we can approximate wLi (z) to
be constant during the interaction as wLi (z) = wLi (ctL /2) ≃ wLi (i = h, v). The

CHAPTER 2. FORMULA OF VACUUM DIFFRACTION SIGNAL

12

interaction probability, P , is approximately calculated asdP
26 α4 ℏ6
= 2 2 8 10 (16 + 33 sin2 δ)k 2 W 2
d cos θ 45 π me c
1
1
1
√
√
×
wLh wLv w2 + 2w2
w2 + 2w2
[

Lh

x2L

Xh

Lv

Xv

yL2

]

× exp −4 2
2 − 4 w 2 + 2w 2
wLh + 2wXh
Lv
Xv
√
[
]
2
2
2
2
wLh wXhk
1 wLh wXh22
×√
2 + 2w 2 exp − 2 w 2 + 2w 2 k (θx − Θx )2π wLh
Xh
Lh
Xh
√
[
]
2
2
2
2
wLv wXv
k
1 wLv wXv
22
×√.
2 + 2w 2 exp − 2 w 2 + 2w 2 k (θy − Θy )2π wLv
Xv
Lv
Xv

(2.6)

By assuming a symmetrical beam shape (wXh = wXv = wX and wLh = wLv = wL ),I shows the more simple formula. The formula becomesdP
26 α4 ℏ6
= 2 2 8 10 (16 + 33 sin2 δ)k 2 W 2
d cos θ 45 π me c
∫
1
2
× 2 2
IIV (x, y)dxdy
2 ) × πw 2wL (wL + 2wX
[
]
1
2
2
2
2
× (kw) exp − (kw) {(θx − Θx ) + (θy − Θy ) } ,
2

(2.7)

with
wL wX
,
w =√
2
wL2 + 2wX[]
x2 + y 2
IIV (x, y) = exp −2
2
wX
])2
(
[
(x − xL )2 + (y − yL )2,× exp −2
wL2

(2.8)

(2.9)

It consists of three parts; the parameter dependency part (the first line of Eq.(2.7)),
the form part of the two pulses (the second line) and the angular distribution part(the third line). It provides a valuable approximation to understand VD and to
optimize experimental setups since the parameter dependence of the interaction
probability is clear.
In the second line of Eq. (2.7), IIV (x, y) is the product of intensity distributionsof the two pulses, (J (x)2 ) × (E(x)2 )2 , at the collision point. The exponents of
the intensities agree with the number of photons of the leading-order Feynman
diagram for VD (one x-ray and two laser photons, Fig. 1.2). This overlap of thetwo pulses can be thought of as an eﬀective interaction volume. The interaction

CHAPTER 2. FORMULA OF VACUUM DIFFRACTION SIGNAL
Photons [a.u.]

13

1

XFEL pulse

8.4keV
Signal x rays
wX=2µm, wL=1µm

0.8
0.6

70 µrad0.4

23 µrad0.2
0−100 −80 −60 −40 −20

0

20

40

60

80 100Diffraction angle θ [µrad]

Figure 2.2: Angle distributions of the signal x rays (red line) and the probe XFEL
pulse (blue line).
volume shows how good the two pulses overlap in space-time and gets decreased
by large displacements, (xL , yL ). w is the 2σ size of this interaction volume.
The third line of Eq. (2.7) shows that the angular distribution has a Gaus2
sian profile with the signal divergence, kw, and the center of the distribution is
the incident angle. The uncertainty principle binds a relation between the signal divergence and the size of the interaction volume in the transverse direction;1∆p∆x = kwℏk × w2 = ℏ2 . A relation between the signal divergence and the sizeof the interaction volume in the transverse direction is bound by the uncertainty
1principle as the following: ∆p∆x = kw
ℏk × w2 = ℏ2 .
Figure 2.2 shows angular distributions of the signal x rays (red line) and theprobe XFEL pulse (blue line). For these calculations, wL = 1 µm, wX = 2 µm
and 8.4 keV of x-ray photon energy are used. Both distributions are a Gaussian
profile. Due to the eﬀect of VD, signal divergence (70 µrad) is larger than that ofthe probe XFEL pulse (23 µrad).
Equation (2.7) is validated by comparing with a previous calculation [29] in[34], The ratios of the signal divergence and the interaction probability are shownin Fig. 2.3. In the calculation, perfect alignment and same pulse durations are
assumed (Θ = 0, xL = yL = 0, tL = 0, τ = τX = τL ). The beam sizes at the focus
are assumed as 1 µm for the laser pulse and 2 µm for the XFEL pulse. For the′previous calculation, a Gaussian beam and its Rayleigh length zRL= 3.9 µm areassumed. The calculated results show good agreement in the short pulse condition
and become the same in the limit of τX , τL → 0.

tg_ratio_sigma_THALES
Pulse duration τ [fs]
20
40
60
80
100

0

2.2
2
1.8
1.6

PEq.(2.7)/PPrevious

ΦEq.(2.7)/ ΦPrevious

CHAPTER 2. FORMULA OF VACUUM DIFFRACTION SIGNAL

0

2
1.8
1.6
1.4

1.2

1.2

0

tg_ratio_Probability_THALES
Pulse duration τ [fs]
20
40
60
80
100

2.2

1.4

1

14

1
1

2

3
4
5
6
7
8
cτ/z' RL (τ = τX = τL, z'RL = 3.9 µm)

0

1

2

3
4
5
6
7
8
cτ/z' RL (τ = τX = τL, z'RL = 3.9 µm)

Figure 2.3: Validation of the short-pulse approximation. The signal divergence andthe interaction probability calculated by Eq. (2.7), ΦEq.(2.7) and PEq.(2.7) , are compared with those calculated by the previous calculation [29], ΦPrevious and PPrevious ,respectively. Left: ΦEq.(2.7) /ΦPrevious . Right: PEq.(2.7) /PPrevious .

x, y

k~0

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xCP , yCP
Probe
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zX

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Figure 2.4: Schematic view of the focused XFEL pulse at the collision point. The
XFEL pulse is away from its focus by zX . The wavefront is drawn as a thick line.
Θnx (Θny ) is an angle between the y-z (x-z) plane and the normal direction of the⃗ n . These angles eﬀectively give the incident angles to the x-ray.
wavefront, Θ

2.2

Vacuum diﬀraction formula with XFEL curvature
eﬀect

So far, the simple formula of VD without the curvature of the XFEL pulse has been
considered. However, in realistic experiments, the XFEL pulse has the curvature.
The x-ray is eﬀectively given the incident angle by the curvature. In order toestimate the eﬀect by the curvature, the XFEL pulse as a Gaussian√ beam, as
zX φ 2) ,shown in Fig. 2.4, is considered. The beam size is given as wX = wX0 1 + ( wX0
where wX0 is a minimum beam size, zX is the distance from the collision point to
the focus along the z-axis, and φ is the divergence. The curvature radius of the15

CHAPTER 2. FORMULA OF VACUUM DIFFRACTION SIGNAL

wavefront is(R(zX ) = zX

1+

(

wX0
zX φ

)2 )
(2.10).

At a position (xCP , yCP ) on the wavefront, which is the x-y coordinate at the⃗ n , is given as the following:
collision point, the normalized normal direction, Θ⃗ n = cos Θn (tan Θnx , tan Θny , 1)
Θ
)
(
xCP
yCP
= −
,−
, cos Θn ≒ (Θnx , Θny , 1),R(zX ) R(zX )(Θn ≪ 1),

(2.11)

where Θnx (Θny ) is an angle between the y-z (x-z) plane and the normal direction
and satisfies cos21 Θn = 1 + tan2 Θnx + tan2 Θny . These angles are approximately
given by the x and y components of the normal direction.
Under the situation that Θn ≪ 1, the new VD formula is given by the convolution of the original angular distribution, Eq. (2.6), and the angle of the normal
direction with the weight, IIV (xCP , yCP ). The convolution is given by the integrations over xCP and yCP as
dPcurve
IIV (xCP , yCP )dP=∫.
dxCP dyCP d cos θ
IIV (xCP , yCP )dxCP dyCP d cos θ Θx =Θnx ,Θy =Θny

(2.12)

Due to the convolution, the divergence caused by the curvature at the collision
point, w/R(zX ), smears the original
divergence, 2/kw. The signal divergence be√comes their root sum square, (2/kw)2 + (w/R(zX ))2 . The center direction of theangular distribution is shifted to the normal direction at the center of the interaction
volume, and the central angles become (−2w2 xL /wL2 R(zX ), −2w2 yL /wL2 R(zX )).

Chapter 3

Setup and devices
The experiment is performed at SACLA during a beam time between 2019/06/27
10:00 and 2019/07/01 10:00 JST (96 hours). In this section, I describe the experimental setup about the probe XFEL system, the pump laser system and a signal
detection system. In Tab. 3.1, main experimental parameters are summarized.
Table 3.1: The summary of main experimental parameters.
Parameters
X-ray photon energy
XFEL beam size (Horizontal)
XFEL beam size (Vertical)
XFEL pulse duration
Pump laser
Pump laser pulse energy
Laser beam size (Horizontal)
Laser beam size (Vertical)
Laser pulse duration

ℏck
wXh
wXv
τX

8.4 keV22.0 µm
14.8 µm
17 fs

W
wLh
wLv
τL

0.6-TW laser
0.47 mJ
1.9 µm
1.9 µm48 fs

Signal selection angle by Slit6
Collision rate

38.8 µrad < θy < 58.6 µrad
15 Hz

3.1

Probe XFEL system

3.1.1

XFEL beamline and devices

Figure 3.1 is a schematic of experimental apparatuses related to the XFEL beamline. SACLA XFEL beamline 3 (BL3) is used as the source of the probe light. The
undulator of BL3, which oscillates an electron beam by a periodic magnetic field of17

CHAPTER 3. SETUP AND DEVICES

18

LH
Laser pulse

OH
XFEL BL3

XFEL
pulse

EH1
Shaper Slit2,3

TRM2
TRM1

EH2

TM

EH3

Slit4,5
Slit6

Chamber

Slit1

EH4c

PD

SCM
4.99 m

0.39 m

10.18 mFigure 3.1: The apparatuses in SACLA BL3. All components are connected withvacuum pipes. (TRM1, TRM2: Total reflection mirrors; SCM: Beam intensity
monitor; TM: Arrival timing monitor; Shaper: One-dimension x-ray lens; Chamber:
Vacuum chamber in which the both beams are collided; Slit1–4,6: 4-jaw slit withtantalum blades; Slit5: Vertical slit with a tantalum blade; PD: Photodiode)TRM2

XFEL pulse

2 mrad
TRM1

20 mm

5m

Figure 3.2: A pair of total reflection mirrors (TRM).
magnets, generates a horizontally polarized
x-ray pulse with ∼ 1011 photons/pulse,2
and each pulse duration, τX , is below 17 fs [26]. The photon energy of the x-ray,ℏck, is set to 8.4 keV, and its bandwidth is 25 eV (2σ).
The XFEL pulse is collided with the laser pulse in the vacuum chamber at
experimental hatch 2 (EH2). The XFEL pulse passes through the following opticaldevices and monitors before the collision.
Total reflection mirror (TRM)
A pair of total reflection mirrors (TRM) [35] as shown in Fig. 3.2 is used to remove
the second harmonics of x rays (16.8 keV) whose contamination fraction is about∼ 3×10−4 . Substrates of the TRM1 and the TRM2 are silicon (Si), and the surfaceof the TRM2 is coated by carbon. The incident angle of the TRM is set to 2 mrad,
which corresponds to the critical angle of 15 keV x-ray. Since the critical angle isinversely proportional to x-ray photon energy, high energy photons are decreased
with the reflection. The reflectivity of the two TRMs are ∼ 3 × 10−2 for 16.8 keV

19

CHAPTER 3. SETUP AND DEVICES
Laser
Grating

XFEL
pulse

(to EH2)

Diﬀracted x rays
(2%)

GaAs crystal(5 µm thick)

CCD camera

Figure 3.3: Top view of the timing monitor (TM). The relative timing of the
XFEL pulse and the laser pulse is monitored by measuring the laser transmittanceof the GaAs crystal.
x-ray, and the contamination is suppressed below 10−5 by the TRMs.
Timing monitor (TM)A relative timing between the XFEL pulse and the pump laser pulse is measured bya timing monitor (TM) [36], as shown in Fig. 3.3. The TM consists of a transmission
grating, a CCD camera and a 5-µm-thick GaAs crystal, which is glued on a 500µm-thick sapphire substrate. 2 % of x rays in the XFEL pulse are diﬀracted by thegrating and irradiated to the GaAs crystal. At the same time, the laser pulse isalso irradiated, and a part of the laser photons are transmitted. The transmittanceof the laser pulse is monitored by the CCD camera.
The relative timing of the two pulses can be measured by monitoring the lasertransmittance. The GaAs crystal which absorbs x rays changes its optical transparency because x rays ionize GaAs atoms and decrease the permittivity of the
GaAs crystal [36, 37]. As the result, power of the transmitted laser light changes
depending on the relative timing of the XFEL pulse and the laser pulse. A resolution of the relative timing is 6 fs.
Screen monitor (SCM)
A screen monitor (SCM) is inserted on the XFEL beam axis to measure an intensityof the XFEL pulse, as shown in Fig. 3.4. The SCM consists of a CCD camera anda 30-µm-thick boron-doped diamond film. The diamond film, which is tilted at
45 degrees against the XFEL beam axis, is a fluorescence screen. The intensityof its fluorescence light, which corresponds to the intensity of the XFEL pulse, ismeasured by the CCD camera. The transmittance of an 8.4 keV x-ray is 95 %, anda resolution of the intensity is 3 %.

CHAPTER 3. SETUP AND DEVICES

20

Boron-doped
diamond ﬁlm(30µm)

XFEL

45

pulse
Fluorescence
CCD
cameraFigure 3.4: Screen monitor (SCM). The intensity of the XFEL pulse is monitored
by measuring the intensity of the fluorescence of the boron-doped diamond film.

XFEL
pulse

XFEL
pulse

Slit4

Figure 3.5: The 4-jaw slit. Left: Schematic of a 4-jaw slit. Each blade can be
moved against the XFEL beam axis. Right: A side view of the Slit4. Four blades
are in the container of the slit, which can be evacuated.
Slit
Slits are used for three purposes. The first purpose is to make the size of the XFEL
pulse small. The second is to measure the size of the XFEL pulse. The third is toseparate the diﬀracted x rays from the XFEL pulse. Blades of the slits are madeof tantalum. Each slit is composed of four blades as shown in Fig. 3.5 Left. The
fifth slit (Slit5) from the upstream position of the XFEL beamline is composed ofonly a lower blade. Each blade can be moved with about 1 µm step by a motorized
position stage.

3.1.2

Chamber

Figure 3.6 shows the top view of the vacuum chamber. The XFEL pulse and thelaser pulse are collided in the chamber. A sample stage, which is a motorized
position stage, is set to study the XFEL pulse and the laser pulse properties at the21

CHAPTER 3. SETUP AND DEVICES

Figure 3.6: Top view of the vacuum chamber. (OAP: 90-degree oﬀ-axis parabolic
mirror with a 3-mm diameter hole; Mirror: Plane mirror with a 2-mm diameter
hole; Sample; A sample placed at the collision point; Lens5: Achromatic doublet
lens with 10-mm focal length and 8-mm diameter; Lens7: Achromatic doublet lenswith 400-mm focal length and 50.8-mm diameter) The samples, the Lens5 and theLens7 are mounted on the motorized position stage, and these can be inserted on
the laser beam axis. In the figure, the Lens5 is inserted.
collision point. A sample on a sample folder can be mounted on the sample stage
and be moved in x, y and z-directions around the collision point. Figure 3.7 showsa test film and a wire on the sample folder. The chamber and the XFEL beamline
were evacuated below 4 × 10−3 Pa.

CHAPTER 3. SETUP AND DEVICES

22

64 mm

70 mm

y
x

z

Figure 3.7: The sample folder. The 30-µm-thick Au foil, the 5-µm-thick GaAs
crystal glued on a 500-µm-thick sapphire substrate and the 1 mm diameter golden
wire are set on the folder. Left: Front side view of the folder. Right: Back sideview of the folder.







23











CHAPTER 3. SETUP AND DEVICES

Structure ofquadratic function

XFEL
pulse

350µm
550µm

1.1mm
名

日付

作成

内

5.4m

室

Paper_shaper
2019/12/07 材 一

YudaiSeino
井
室
24231
数

Figure 3.8: The shaper. Left: SEM image of the shaper. Right: Schematic of the
shaper.
1
A4

尺度 50 : 1

シート 1/1

Size

Shaper

N/A

3.1.3

The shaper is developed to suppress the BGs in the VD experiment. The shaper
is a one-dimensional optical device for x rays made of a Si crystal. The shaper
has been developed with Yamamura laboratory, department of precision scienceand technology, graduate school of engineering, Osaka University. I devised anddesigned the shaper. The shaper was manufactured by Yamamura laboratory andstudied its performance by me. Figure 3.8 (Left) shows a scanning electron microscope(SEM) image of a shaper. A structure of quadratic function is made by areactive ion etching method. Reactive ion etching is a kind of a dry etching, andwe can make an arbitrary structure with a few hundred µm of depth. When an
uniform x-ray pulse passes the shaper, its profile becomes gaussian distribution due
to the attenuation by the shaper with the quadratic function structure.
There are two roles of the shaper. One role is a lens for the XFEL pulse.
Since the refractive index of silicon for x rays is smaller than 1, an XFEL pulse
passing through the shaper is focused as shown in Fig. 3.8 (Right). The shapers
are designed with 5.4 m of a focal length (f) and 350 µm of an aperture whichcorresponds to the depth of the etching. Two shapers are used to focus the XFEL
pulse in the horizontal and the vertical directions, respectively.
Another role is to reduce BGs. There are two main BGs. First is diﬀused xrays by a lens. Second is a part of probe x rays which have large divergence due tothe focusing. By using a shaper, these BG x rays are suppressed or absorbed by ashaper. These eﬀect is detailed in App. A.
Figure 3.9 shows the setup of the shapers. From the upstream side, the Slit1,
the vertical focusing shaper, and the horizontal focusing shaper are placed. The
shapers are mounted on the motorized position stages and inserted on the XFEL
beam axis. The vacuum pipe containing the shaper is also mounted on the othermotorized position stages which move in transverse directions against the beamaxis, and the position of the shaper can be adjusted by the stages.

CHAPTER 3. SETUP AND DEVICES

24

Slit1

XFEL

0.22 m0.19 mpulse
Vertical focusing
shaperHorizontal focusing
shaperFigure 3.9: Setup of the Slit1 and the shapers at EH1. The shapers are in thevacuum pipe and mounted on the motorized position stages to be inserted on the
XFEL beam axis. The distance between the Slit1 and the shaper for the verticalfocusing is 0.22 m, and the distance between the two shapers is 0.19 m.

25

CHAPTER 3. SETUP AND DEVICES

1.2

x-ray intensity [a.u.]

x-ray intensity [a.u.]

Figure 3.10: Images of the XFEL pulse with the x-ray camera. Left: Raw beam
image of the XFEL pulse. Right: Image of the XFEL pulse with a collimation by
Slit1.
Scan data
0.8 Proﬁle fXh(x)
1

0.6
0.4

1.2
1
0.8

Proﬁle fXv(y)

0.6
0.4

0.2

0.2

0

0

−0.2

−0.2

−0.4

Scan data

−0.4
− 40

− 20

0

20

40

x [µ m]

− 40

− 20

0

20

40

y [µ m]Figure 3.11: XFEL profiles at the collision point. Black markers show the intensityof the transmitted x rays during the knife-edge scan, and blue markers show the
XFEL profile at the collision point. Left: In horizontal direction; Right: In verticaldirection.

3.1.4

XFEL beam

Figures 3.10 shows a x-ray camera images of the original XFEL pulse without theshapers. The x-ray camera is composed of a screen of a scintillator and a CCD
camera and is placed 7.5-m downstream from the shaper for a vertical focusing.
The beam sizes of the original XFEL pulse (Fig. 3.10 Left) are 524 µm and 588 µm(FWHM) in the vertical and the horizontal directions, respectively. Since theoriginal XFEL pulse is larger than the aperture of the shaper (350 µm), the XFEL
pulse is cut by the Slit1 and made rectangular (Fig. 3.10 Right). The FWHM sizesof the rectangular XFEL pulse are (262 ± 3) µm and (195 ± 3) µm in the verticaland the horizontal directions, respectively, where errors show fluctuations of thesizes. This rectangular XFEL pulse is focused with the two shapers.
At the collision point, the beam sizes of the focused XFEL pulse were measured

CHAPTER 3. SETUP AND DEVICES

26

using crossed 1-mm diameter golden wires mounted on the sample stage (Fig. 3.7).
The beam size was measured with the knife-edge scan method. The position of thewire was scanned, and the intensity of the transmitted x rays was measured witha PIN photodiode (PD, HAMAMATSU, S3590-09), which has 3% of an energy
resolution. The wire position was scanned from four directions (from upper, lower,right, left). At each wire position, about one hundred pulses of the x-ray intensity
were measured and averaged.
The distributions of the x-ray intensity in the horizontal and the vertical directions are shown in Fig. 3.11 with black points. The profile of the XFEL pulse iscalculated using a slope of the intensity distribution. The profiles in the horizontal
and the vertical directions are shown with blue points and defined as fXh (x) andfXv (y), respectively. The slope is evaluated with three to seven points, and blue
points show the case evaluated with five points. The beam sizes in the horizontal
and the vertical directions were wXh = (22.0 ± 3.5) µm and wXv = (14.8 ± 4.3) µm,
respectively, which are 2σ beam sizes calculated from the FWHM of the profile.
Dominant uncertainties of the beam size are due to the direction of the knife-edge
scan and the number of points to calculate the slope. The position of the beamaxis (x = 0, y = 0) is defined as the position where the transmitted x rays is 50%
and measured with accuracies of 3.1 µm and 1.7 µm horizontally and vertically,
respectively.
The divergence of the XFEL pulse in the vertical direction was estimated byfitting the beam sizes along the beam axis. The beam sizes were measured by knifeedge scan method using the Slit2—6. The x-ray camera was also used. Positionsof these devices are summarized in Tab. 3.2. Light blue points in Fig. 3.12 show
the measured beam sizes. A blue line shows the fitting result of the beam sizes by
the following function of a gaussian beam√()(z − zX )φ 2
wX (z) = wX0v 1 +
(3.1)
wX0v
where z is a distance from collision point, zX is a focal position of the XFEL
pulse, wX0v is a minimum beam size and φ is a divergence. Fitting results ofthese parameters are zX = (1.76 ± 0.08) m, wX0v = (3.1 ± 1.8) µm and φ =(10.6 ± 1.1) µrad.

27

CHAPTER 3. SETUP AND DEVICES

Table 3.2: Positions of shapers, slits and the x-ray camera from the collision point.
Devices

z [m]

Slit1
Shaper for vertical focusing
Shaper for horizontal focusing
Slit2
Slit3
Collision point
Slit4
Slit5
X-ray camera
Slit6

-5.22
-4.99
-4.81
-2.11
-0.99
0
0.39
1.53
2.29
10.18

wXv (= FWHM) [µ m]2log2tge_Paper_2sigma
2

4.438 / 4

h1d_waku
χ

160

/ ndf

w
X0

3.105 ± 1.814

Entries
ϕ

140

Mean
z
0

Std Dev

010.58 ±

1.13

0
1.764 ± 0.08201

0

120
100
80
60
40
20
0

−4

−2

0

2

4

6

8

10

z (distance from the collision point) [m]Figure 3.12: The vertical beam size of the XFEL pulse at each position on the
beam axis.

CHAPTER 3. SETUP AND DEVICES

3.2

Pump laser system

3.2.1

0.6-TW laser system

28

The 0.6-TW laser is a Ti:sapphire laser of a 800 nm wavelength [38]. The laser
system is composed of a mode-locked oscillator, a chirped-pulse amplifier and amultipass amplifier in the laser hatch (LH). The laser pulse is delivered from LH
to the EH2, and its pulse duration is compressed to τL = 48 fs (4σ). The intensityof the laser pulse is monitored by a photo diode after the compression. Maximum
pulse energy is 3 mJ with 60 Hz. The laser pulse has a gaussian profile of a 7-mm
beam size (2σ). The polarization is in the vertical direction, and the angle against
the XFEL polarization is δ = 90◦ . The timing of the laser pulse can be tuned with
6.7 fs step by an optical delay unit that can change the optical path length of thelaser pulse.

3.2.2

Optical system

Figure 3.13 shows a whole setup of the optical system. The laser pulse is focusedin the chamber. Before the focusing, the laser pulse is expanded by a pair ofachromatic lenses. Focal lengths of the Lens3 and the Lens4 are f = −100 mm
and 250 mm, respectively. The magnification is 2.5.
In the chamber, the laser pulse is focused at the collision point by a 90-degree
oﬀ-axis parabolic mirror (OAP, Thorlabs, MPD229H-M01) with f = 50.8 mm. The
OAP has a 3-mm diameter hole on the XFEL beam axis. The hole corresponds to30 mrad of an angular acceptance from the collision point, which is enough larger
than the signal divergence (O(10) µrad). The OAP is mounted on six-axis stages(three translations and three rotations) to adjust the position and the direction of
the laser pulse.
The focal spot is optimized by a deformable mirror (DM, Imagine optic, Mirao 52-e, Fig. 3.14 Right) and a wavefront sensor (WFS, Imagine optic, HASO4FIRST), which are placed upstream of the OAP. The DM is composed by a silver
membrane mirror, and 52 actuators support the back side of the membrane. The
membrane mirror has a 17.5-mm diameter of the aperture. The membrane mirror
can be deformed and generate an arbitrary aberration by pushed or pulled by theactuators within ±50 µm. Figure 3.14 (Left) shows a system to optimise the focal
spot. An aberration of optics is evaluated from the focal spot image. The information on the aberration is fed back to the operation of the DM, and the aberration
is canceled. The WFS is used for calibration of the size of the aberration generated
by the DM. The WFS is composed of an array of 32×40 microlenses and a CCD
sensor. The light passing through the microlenses is focused and makes spots on
the CCD sensor. Since the tilt of the wavefront of the laser pulse depends on thepositions of these spots, the tilt can be measured from the image of the CCD sensor
with a resolution of 5 µrad.
The focal spot of the laser pulse was monitored by the two CCD cameras (Cam-29

CHAPTER 3. SETUP AND DEVICES

era1,2 in Fig. 3.13). The Path1 and the Path2 are optical paths for the two cameras,
respectively. The Camera1 is used with the Lens5,6, and the Lens5 is the collimation lens. This imaging system has 100 magnifications and is used to measure andoptimize the focal spot size. The Camera2 is used with the Lens7,8,9 and Lens10,
and the Lens7 is the collimation lens. This imaging system has 7.6 magnifications
and is used to measure the focal spot when the XFEL pulse was irradiated. The
two imaging systems are switched by inserting or removing a moving mirror andlenses by motorized stages.

CHAPTER 3. SETUP AND DEVICES

ND2 Lens6

Camera1

f=1000 Path1

30

Path2

Lens8
f=1000Moving mirror
for Path2

Lens9
f=30 Camera2

ND3
Lens7 for Path2
f=400

Sample
XFEL
pulse

Lens1
f=400

Mirror

WFS
Lens2
f=75

Beam
samplerDM

Lens10
f=100
VacuumchamberOAP
f=50.8

Lens5
for Path1
f=10

Lens3

Lens4
f=-100 f=250

ND1
Laser
pulse

Figure 3.13: A schematic of the whole setup of the optical system. (DM: Deformable mirror with a 17.5-mm diameter aperture; Beam sampler: Beam sampler.
70 % light is reflected and 30 % light goes through.; WFS: Wavefront sensor; OAP:
90 degree oﬀ-axis parabolic mirror with a 3-mm diameter hole; Mirror: Plane mirror
with a 2-mm diameter hole; Lens1-10: Achromatic doublet lenses; Moving mirror:
76.2-mm diameter mirror for Path2; ND1,ND2 and ND3: Neutral density filter;
Camera1 and Camera2: CCD cameras) The collimation lenses (Lens5 and Lens7)
and the moving mirror are mounted on the motorized position stage, and can beinserted on the laser beam axis for the two optical paths (Path1 and Path2).

31

CHAPTER 3. SETUP AND DEVICES

Table 3.3: The summary of optics parameters. (f: Focal length; d: Diameter)

Lens1
Lens2
Lens3
Lens4
OAP
Lens5
Lens6
Lens7
Lens8
Lens9
Lens10f [mm]

d [mm]

400
75
-100
250
50.8
10
1000
400
1000
30
100

50.8
12.7
25.4
50.8
50.8
8
50.8
50.8
50.8
30.5
30.5

lens for WFS
lens for WFS
lens for expanding the beam size
lens for expanding the beam size
focusing optics
lens for Camerea1
lens for Camerea1
lens for Camerea2
lens for Camerea2
lens for Camerea2
lens for Camerea2

CHAPTER 3. SETUP AND DEVICES

32

Laser pulse with
an aberration to cancel
the OAP aberration

OAP that has
the aberration

Beamsampler

Actuators

DM

Membrane

Lens5

Microlens
array

CCD
sensorLens6

mirrorLaser pulse

WFS
Camera1

20 µm

Figure 3.14: A system to cancel an aberration by the DM and the WFS. Left:
Schematic of the system. In the figure, the aberration of the OAP is canceled by
20 µm
the aberration generated by the DM. Right: Picture of the DM.

33

h2d_LaserImage
Laser beam and image
y[um]

3.2.3

CHAPTER 3. SETUP AND DEVICES

20
18
16
14
12
10
8
6
4
2
0

2500

2000

1500

1000

500

0 2 4 6 8 10 12 14 16 18 20

0

x[um]

Figure 3.15: The focal spot image of the laser pulse monitored by the Camera1.
The horizontal and the vertical sizes are both 1.9 µm (2σ).
The image of the focal spot was measured using the Camera1. Since the Lens5
is thermally damaged if the laser pulse with full pulse energy is irradiated, the pulse
energy was reduced using the ND1 during the focal spot measurement. The image
with 13% of the full pulse energy is shown in Fig. 3.15. The image was measured
with several values of the pulse energy from 10% to 10−2 % of the full pulse energy
by the ND1. The focal spot was well fitted by two-dimensional gaussian function,and the beam sizes are wL0h = 1.9 ± 0.2 µm and wL0v = 1.9 ± 0.2 µm, where
dominant uncertainties are the resolution of the imaging system and dependence
on the pulse energy.
An eﬀective pulse energy focused in the peak of the image is calculated sincea part of the pulse energy is spread over the tail of the peak. The eﬀective pulse
energy is evaluated using a total energy in a measured image and an energy ina region of interesting (ROI) with ±2σ width. The ratio of the eﬀective pulse
energy was measured as a = (30 ± 3)% against the full pulse energy. The full
pulse energy is 1.6 mJ considering a loss by optics, and the eﬀective pulse energy
is W = a × 1.6 mJ = (0.47 ± 0.06) mJ, where a dominant error comes from adependence of a on the pulse energy.
The beam size and the ratio of concentrated energy around the focus are measured by moving the Lens5. Figure 3.16 shows the horizontal and vertical beam
sizes, wLh , wLv . The position, z = 0, is corresponding to the image of Fig. 3.15.
The horizontal beam size dose not take local minimum due to aberrations of optics. Figure 3.17 is the ratio of the concentrated energy. The ratio becomes large
around the focus. In front and back of the focus, the ratio decreases because a partof energy is spread over a tail of the image due to aberrations of optics.

CHAPTER 3. SETUP AND DEVICES

34

Beam size (2σ) [µ m]tge_wLh

●：wLh
●：wLv

3
2.5
2
1.5
1
− 30

− 20

− 10

0

10

20

30

z[µ m]

Figure 3.16: Laser beam size. The horizontal and vertical beam sizes, wLh , wLv ,are shown with red and black markers, respectively.

Ratio of effective pulse energy, a [%]tge_EnergyRatio_per

35
30
25
20
15
10
5
− 30

− 20

− 10

0

10

20

30

z[µ m]

Figure 3.17: Ratio of eﬀective pulse energy concentrated in the spot against the
total pulse energy at the collision point.

35

3.3

CHAPTER 3. SETUP AND DEVICES

Signal detection system

The signal x rays were separated from the probe XFEL pulse by the Slit6 andmeasured by the PD at EH4c. The vertically diﬀracted x rays were only selected
as the signal. The edges of the blades of the Slit6 and the Slit4 were set upper fromthe XFEL beam axis. The distance between the XFEL beam axis to the edge of
the Slit6 lower blade was S6l = (395.0 ± 3.0) µm and that of the upper blade was
S6u = (596.2 ± 4.4) µm. To block the pass of stray x rays from the XFEL, I use
the Slit4 and set the edge of the upper blade at S4u = (77.2 ± 2.2) µm from the
XFEL axis. The uncertainty of these edge positions comes from the accuracy of themeasurement of the beam axis position. These positions of the blades correspondto the selection angles of θy < 200 µrad with the Slit4 and 39 < θy < 59 µrad with
the Slit6.
Figure 3.18 shows a image of the PD (HAMAMATSU, S3590-09). The PD
is the equipment of the XFEL beamline, and placed in the vacuum pipe of thebeamline. The PD has 10 mm×10 mm aperture and 300 µm-thick depletion layer.
An energy resolution is measured by simultaneous measurement of XFEL pulse
with the SCM, and the energy resolution is 2.8%. A detection eﬃciency for 8.4 keV
x-ray is evaluated with a Monte Carlo simulation using Geant4 as (97.8 ± 0.8)%.

Figure 3.18: Image of PD (HAMAMATSU, S3590-09, [39]).

Chapter 4

Alignment of two beams
4.1

Spacial alignment

The position of the laser pulse is adjusted to make both pulses collide head-on.
The positions of the laser pulse and the XFEL pulse are measured using the Au
foil. The spacial alignment has been performed by iterating the adjustment of thelaser position and the measurement of both pulse positions. The adjustment of
the laser position is summarized in Sec. 4.1.1, and measurements of the positionof both pulses are summarized in Sec. 4.1.2 and Sec. 4.1.3, and the result of thespatial alignment is shown in Sec. 4.1.4.

4.1.1

Adjustment of the laser position

The position of the laser pulse is adjusted using the six-axis stages on which the
OAP is mounted. The position and the direction of the laser pulse were adjustedwith 0.25 µm or about 10 µrad step using the stages.
After the adjustment, the displacement between both pulses was measured using
the Au foil set around the laser focus. Both pulses were irradiated to the 30-µmthick Au foil mounted on the sample folder (Fig. 3.7). The displacement wasmeasured from the position of the irradiation trace of both pulses. Figure. 4.1
shows the image of the irradiation traces. The irradiation trace of the XFEL pulse
is a hole shown at the top in the figure. Totally 150 XFEL pulses were irradiated.
The irradiation trace of the laser pulse is a crater shown at the bottom in the figure.
One laser pulse was irradiated. In order to avoid overlapping of both traces, theAu foil was moved upward by 100 µm after the irradiation of the XFEL pulse.
37

CHAPTER 4. ALIGNMENT OF TWO BEAMS

38

Irradiation traceof the XFEL pulse(Hole)
100-µmshift

Irradiation traceof the laser pulse(Crater)yzx

Figure 4.1: The microscope image of the irradiation traces of the laser pulse
and the XFEL pulse on the Au foil. The top hole is the irradiation trace of the
XFEL pulse (150 pulses), and the bottom crater is that of the laser pulse (1 pulse),
To avoid the overlap between the two traces, I shifted the Au foil by 100 µm in atransverse direction against the beam axis after the irradiation of the XFEL pulses.
A red dot shows the estimated center position of the crater.
The coaxiality of two beams is also measured by measuring the displacement
at two positions along the beam axis.
After taking the Au foil from the chamber, the irradiation traces were measured
by a laser microscope (Olympus, OLS4100). The laser microscope can measure a
black-and-white or a three-dimensional image with 405 nm light.

4.1.2

Measurement of laser position

When a laser pulse is irradiated to the Au foil, a high-pressure vapour of plasma
is generated by Au atoms on the surface of the foil. This high-pressure vapour
becomes a shock wave and creates the irradiation traces like a crater on the foil.
Thus, the center of the laser pulse corresponds to the deepest position of the crater.
The deepest position of the crater is observed by the three-dimensional image

39

CHAPTER 4. ALIGNMENT OF TWO BEAMS

Figure 4.2: The height profile of the crater of the laser irradiation traces. The
profile is fitted by paraboloid function (red line).
measured by the laser microscope. The image is shown in Fig. 4.2. The deepest
position is measured by fitting the ROI in the image with a paraboloid function.
The size of the square ROI is changed from 8 µm to 18 µm. The uncertainty of the
deepest position due to a fitting error is ±0.04 µm and that due to a dependence
on the ROI size is ±0.5 µm.
Since each crater shape around the deepest position is slightly diﬀerent, thestability of the deepest position against the crater shape is investigated. Figure 4.3
is a height profile of the crater taken by projecting the three-dimensional image with
13 µm width. The origin is the bottom of the fitted paraboloid function. Each pointshows an average of the profile of the six crater data (shown in Sec. 4.1.4). Eachprofile is normalized by a depth of the crater before the averaging to compare theshape of the profile. An error bar shows root mean square (RMS) of a fluctuationof the height of each profile. The shape of the profile is very stable. An intensity
profile of the laser pulse, which is the projection of the two-dimensional intensity
profile, is also shown as a green line for the comparison. The center position of thetwo-dimensional intensity profile corresponds to the origin of the graph. Although
the profile in the horizontal direction is asymmetry due to a tail of the laser profile,the shape of the crater is stable as well as the vertical profile. Figure 4.4 is a closed
view of Fig. 4.3 around the deepest position. Due to the instability of the shape,
the deepest position has the uncertainty of 1.4 µm and 2.3 µm in horizontally andvertically. Summarizing all the uncertainties, a total accuracy of the laser position
measurement is a quadratic sum of all uncertainties and is ±1.5 µm and ±2.4 µm
horizontally and vertically, respectively.

0
−0.2

−5

−0.4

tge_Hy_Norm
Vertical

5

0.2

0

0
−0.2

−5

−0.6

−10

40

−0.4
−0.6

−10

−0.8

−0.8

−15
−20

−15

−1
− 20

− 10

0

10

−1.2

20

Laser Intensity [a.u.]

0.2

0Depth [µ m]tge_Hx_Norm
Horizontal

5

Laser Intensity [a.u.]

Depth [µ m]

CHAPTER 4. ALIGNMENT OF TWO BEAMS−20

Horizontal direction [µ m]

−1
− 20

− 10

0

10

−1.2

20

Vertical direction [µ m]tge_Hx_Norm_wE
Horizontal

−13

−13.5

−13

−13.5

−14

−14.5

−14

−14.5

−15

−15

−15.5

−15.5

−16

−16

−16.5

−16.5

−17− 8

Verticaltge_Hy_Norm_wE
Depth [µ m]Depth [µ m]Figure 4.3: Height profile of the crater. For a comparison, a laser intensity profileis also shown with a green line. Left: in the horizontal direction. Right: in thevertical direction.

1.4 µm
−6

−4

−2

0

2

4

6

8

Horizontal direction [µ m]−17− 82.3 µm
−6

−4

−2

0

2

4

6

8

Vertical direction [µ m]Figure 4.4: Closed view of Fig. 4.3. Left: in the horizontal direction. Right: inthe vertical direction.

41

CHAPTER 4. ALIGNMENT OF TWO BEAMS
h2d_ZeroIchi
Vertical direction [µm]

40 µm

1
0.9

35

0.8

30

0.7

25

0.6

20

0.5

15

0.4
0.3

10

0.2

5
0 µm

0 µm

40 µm

0

0

0.1

5

10

15

20

25

30

35

0

Horizontal direction [µm]Figure 4.5: The image of the hole of the XFEL irradiation traces. Left: The
black-and-white image of the hole taken by the laser microscope with 405 nm light.
Right: The binarized image. The threshold of the brightness for the binarization
is 15% to 35% against the maximum brightness in the black-and-white image. The
25% case is shown. The black cross marker shows the center of the hole.

4.1.3

Measurement of XFEL position

When the XFEL pulse is irradiated to the Au foil, Au atoms on the surface arevaporized as well as the laser irradiation. Since the intensity of the XFEL pulse(∼ µJ) is smaller than that of the laser pulse (∼mJ), an influence of the shock
wave is weak, and a crater is not created. Instead of a crater, a through hole iscreated by repeating the irradiation and the vaporization. Since the hole is createddepending on the x-ray intensity, the center of the hole is estimated as the peak
position in the XFEL profile.
The center of the hole is observed by a black-and-white image measured by thelaser microscope. Figure 4.5 left shows the image. The region of the hole is dark
since lights of the laser microscope, which illuminate the foil, are not reflected by
the hole. The brightness of the image is binarized to observe the shape of the hole.
Figure 4.5 right is the binarized image. Figure 4.6 is the projection of the binarized
image, and the red line shows the FWHM of the histogram, which is a width of
the hole. The centers of the FWHM shown with black crosses are estimated as thepeak positions of the horizontal and the vertical XFEL profiles. Considering thatthe peak position of the XFEL profile is certainly in the√region of the hole, theuncertainty of the peak position is calculated as FWHM/ 12. Three data of theholes (shown in Sec. 4.1.4) are evaluated, and averages of the FWHM are 3.5 µm
and 2.9 µm in the horizontal and the vertical directions, respectively. From these,
the uncertainties of the peak positions are ±1.0 µm and ±0.9 µm in the horizontal
and the vertical directions, respectively. Dependence of the peak position on thethreshold of the brightness for the binarization is also evaluated. The dependences

CHAPTER 4. ALIGNMENT OF TWO BEAMS

Horizontal

42

Vertical

h1d_ZeroIchi_ProjectionY
pixelspixelsh1d_ZeroIchi_ProjectionX

22
20
18
16

20

14
12
10
8
6
4
2
0

0

25

15
10
5

5

10

15

20

25

30

35

Horizontal direction [µ m]

0

0

5

10

15

20

25

30

35

Vertical direction [µ m]Figure 4.6: The projections of the binarized image of the hole (Fig. 4.5 right)
shown by the blue histogram. The red line shows the FWHM of the histogram.
The black cross marker shows the center of the hole, which is the center of theFWHM. Left: The projection to the horizontal direction. Right: The projection
to the vertical direction.
are ±0.3 µm and ±0.1 µm in the horizontal and the vertical directions, respectively.
The XFEL position (x = y = 0 in the profile of Fig. 3.11) is calculated by considering a gap from the XFEL position to the peak position of the XFEL profile.
The gaps are (2.2 ± 3.1) µm and (3.4 ± 1.7) µm in the horizontal and the verticaldirections, and these uncertainties of the gap are mainly caused by the interval of
the knife-edge scan for the XFEL profile measurement. Summarizing all uncertainties, the accuracies of the XFEL position measurement are ±3.3 µm and ±1.9 µm
in the horizontal and the vertical directions, respectively.

4.1.4

Result of spacial alignment

After a few iterations of the adjustments and the displacement measurement, thedisplacement was measured. Data of the irradiation traces were taken six times, andthe images of the traces are shown in Fig. 4.7. The hole was created only three times
out of six times of the x-ray irradiation due to the fluctuation of the pulse energy.
Figure. 4.8 shows the measured position of each pulse. Blue and Orange markers
show the XFEL position and the laser position, respectively. An average of the
XFEL position is taken as the origin. The distance of the horizontal or vertical shift
to avoid the overlap of the irradiation trace is corrected in the calculation. From
the average of the laser positions, the displacements are calculated as xL = 0.7 µm
and yL = 4.8 µm. From the fluctuation of the measured positions, the fluctuationof both pulses is evaluated as about 0.4 µm.
The coaxiality is also measured. The foil position was moved ±25 µm, and ateach foil position, the position of pulses was measured. The angle between bothaxes of beams was (0 ± 67) mrad. If there is a small angle between both axes, the43

CHAPTER 4. ALIGNMENT OF TWO BEAMS

Irradiation tracesof the laser pulse

Hole was not created.

Holes

Irradiation tracesof the XFEL pulse

Fig 4.1100-µmshifty200-µm

z

shift

x

y [um]

Figure 4.7: The image of the irradiation traces on the Au foil. The area surrounded
by a green rectangle is Fig. 4.1.
6
4
2
0
−2
−4
− 6− 6

−4

−2

0

2

4

6

x [um]

Figure 4.8: The distributions of the XFEL positions (blue) and the laser positions(orange) against the averaged XFEL position. The averaged position of the XFEL
pulse is set to be the origin (x = y = 0).
displacement changes along the z-direction. The laser size was measured in theregion of z = ±30 µm. The uncertainty of the displacement due to the coaxiality
uncertainty is ±30 µm × 67 mrad = ±2.0 µm.
The total uncertainties of the displacement are calculated by the quadratic sumof all uncertainty, and are ±4.2 µm and ±3.7 µm, in the horizontal and the verticaldirections, respectively. The uncertainties are summarized in Tab 4.1.

CHAPTER 4. ALIGNMENT OF TWO BEAMS

44

Table 4.1: The summary of the uncertainties of the horizontal displacement, xL ,and the vertical displacement, yL .
Uncertainties
of xL [µm]

Uncertainties
of yL [µm]Measurement of the XFEL position
Measurement of the laser position
Fluctuation of the XFEL position
Fluctuation of the laser position
Uncertainty of coaxiallity

3.3
1.5
0.3
0.4
2.0

1.9
2.4
0.5
0.3
2.0

Total uncertainty of the displacement

4.2

3.7

Sources of uncertainty

45

CHAPTER 4. ALIGNMENT OF TWO BEAMS
Irradiation traceat z = -66µm

200-µmshift
z = 0µmz = 51µm

Figure 4.9: Irradiation traces of the laser pulse. The foil is moved about ±60 µm
along the beam axis, and the laser pulse is irradiated five times at each foil position.

4.2

Time alignment

To collide both pulses when the laser pulse is focused, the delay time of the laser
pulse is adjusted. The focal position of the laser is measured using the Au foil.
A timing when both pulses are collided at the focus is measured using the GaAs
crystal set at the focus. The accuracy of the time alignment is determined by thismeasurement.

4.2.1

Measurement of the focal position of the laser

The focal position of the laser in the z-direction is measured using the informationof the depth of the irradiation trace since a focused laser creates a deep crater.
Figure 4.9 shows the created craters on the Au foil. The laser pulse was irradiatedfive times, and the foil was moved by about ±60 µm in the z-direction. In order
to avoid the overlap of craters, the foil was transversely shifted 200 µm against thez-axis after the irradiation.
The depth of the craters is measured by the three-dimensional image of thelaser microscope, and the average of the depth at each position of the foil is shownin Fig. 4.10. The vertical error shows a fluctuation of the depth, and the horizontal
error is mainly caused by a warp of the foil. The deepest position in Fig. 4.10
(z = 0 µm) is estimated as the focal position, and the uncertainty corresponds to17 µm of the interval between points, which is shown by a green arrow.

CHAPTER 4. ALIGNMENT OF TWO BEAMS

46

Depth of crater [µ m]tge_depth_paper

25
20
15

17 µm

10
5
0

− 80

− 60

− 40

− 20

0

20

40

60

z [µ m]Figure 4.10: Depth of irradiation traces of the laser pulse at each position along
the beam axis.

4.2.2

Adjustment of the delay time of the laser

The delay time of the laser is adjusted in a two-phased approach. First, both pulses
are detected by a photodiode set around the focal position, and a time to oscillate
the laser pulse is adjusted. By this adjustment, a diﬀerence of timings when bothpulses arrive becomes within ∼ 100 ps.
Next, the delay time of the laser is adjusted using a GaAs crystal. A GaAs
crystal irradiated by x rays is ionized and becomes opaque against the laser lights[36,37]. Since this process is very fast (< 0.1 ps), using this process, the delay timeof the laser can be adjusted to about 0.1 ps accuracy. The used GaAs crystal isshown in Fig. 3.7. The 5-µm-thick GaAs crystal glued on a 500-µm-thick sapphire
substrate is placed around the focal position and irradiated by the XFEL pulse.
The laser pulse is also irradiated, and transmittance is monitored by the Camera2.
The delay time of the laser was adjusted by the optical delay unit with a 6.7 fs
step. Fig. 4.11 is the image detected by the Camera2. In the left (right) imageof Fig. 4.11, the laser pulse was irradiated earlier (later) than the XFEL pulse.
In the right image, the transmittance of the laser is decreased. By detecting thisphenomenon, the diﬀerence of timings of both pulses is adjusted within about
0.1 ps.

4.2.3

Precise measurement of the collision timing

Measurement of the collision timing
After the adjustment of the delay time, a collision timing when both pulses collide
at the focal position (tL = 0) was measured by the transmittance of the laser.
The surface of the GaAs crystal was placed at the focal position as shown in
Fig. 4.12 (Left), and the transmittance of the laser was measured against the delay
time. If the duration of both pulses and a time of the optical response of GaAs
against the x rays irradiation are very short, the transmittance of the laser decrease

47

CHAPTER 4. ALIGNMENT OF TWO BEAMS
h2d_ThreeImg_1

h2d_ThreeImg_3
2500

80

2000

100

y [µm]

y [µm]

100

2500

80

2000

60

1500

60

1500

40

1000

40

1000

20

500

20

500

00

20

40

60

80

100

x [µm]

0

00

20

40

60

80

100

0

x [µm]

Figure 4.11: The image of the laser through the GaAs crystal detected by the
Camera2. The image is distorted by the GaAs crystal and the substrate. Left:
The laser pulse was irradiated to the GaAs crystal earlier than the XFEL pulse.
Right: The laser pulse was irradiated to the GaAs crystal later than the XFEL
pulse. The irradiation of the XFEL pulse makes the GaAs opaque against the laser
lights, and the transmittance of the laser lights is decreased.
as shown in Fig. 4.12 (Right). When tL is 0, the transmittance gets down. The
width of the slope (0.08 ps) corresponds to the sum of a time when the laser pulse
passes through the GaAs crystal and a time when the XFEL pulse passes through.
Figure 4.13 shows the pulse-by-pulse distribution of the laser transmittanceversus the delay time. The delay time was scanned around the timing when thetransmittance decreases. Since there is the jitter (∼ 0.3 ps), the delay time of eachlaser pulse is calculated using the TM. The transmittance is calculated using theenergy in the square ROI whose center is the peak of the image (Fig. 4.11 (Right)).
The analysis is evaluated with the size of the square ROI from 6 µm to 65 µm, andthe result with a 35 µm case is shown in Fig. 4.13. The timing when the transmittance gets down, t0 , is observed by the fitting the transmittance by following
function{1(tL < t0 )f (tL ) =(4.1)
1 − b(tL − t0 ) (t0 ≤ tL )where b is a constant. Since the collision timing (tL = 0) agrees with the timing
when the transmittance gets down (t0 ), t0 is 0.

CHAPTER 4. ALIGNMENT OF TWO BEAMS

48

Focal positionof the laser

Transmittanceof the laser

Laser pulse

XFEL pulse

GaAs

0.08 pscrystalDelay timeof the laser tL

1.2

8
7

1

pulsesTransmittance of the laser [a.u.]

Figure 4.12: Left: Schematic of the GaAs crystal and both pulses at the collision
timing. Right: Laser transmittance versus delay time in the ideal situation. The
durations of both pulses and the optical response of the GaAs are assumed to bevery short (≪ 1 fs).

6

0.8

5

0.6

4
3

0.4

2

0.2
0

1

− 0.5 −0.4 − 0.3 − 0.2 − 0.1

00.1 0.2

0.3 0.4

0.5

0Delay time of the laser t [ps]L

Figure 4.13: The pulse-by-pulse distributions of the laser transmittance of the
GaAs crystal. The horizontal axis is the delay time of the laser. Since the irradiation of x rays makes the GaAs opaque against the laser lights, the transmittancebecomes less than 1 in the region tL > 0.

49

CHAPTER 4. ALIGNMENT OF TWO BEAMS①Uncertainty of tilt of
the sample folder

Area of focal
position measurementLx
1.6 mmLy
13.6 mm

Front view ofthe sample folderof the sample stageΔθun
GaAs position
uncertainty

Au foil

Position of collision
timing measurement②Uncertainty ofthe moving direction

Δθun

GaAs

crystalMoving directionof the sample stage

Side view ofthe sample folder

Figure 4.14: Two kind of sources of GaAs position uncertainty in the beam axis
direction. The schematic of the sample folder is shown with the front view andthe side view. One of the sources is the uncertainty of the tilt of the sample folder(middle schematic). The other is the uncertainty of the moving direction of thesample stage (right schematic).
Uncertainty of the collision timing
Large uncertainties of the collision timing measurement are caused due to theanalysis and misalignment of the GaAs crystal. In the analysis, dependencies of thecollision timing on the ROI size and the fit width are evaluated. The uncertainties
due to these dependencies are 20 fs and 18 fs, respectively. Due to the finite pulse
duration, the edge in the ideal transmittance graph (at tL = 0 in Fig. 4.12) isrounded. The uncertainty due to this eﬀect is 28 fs.
Other sources of uncertainties are the misalignment of the GaAs crystal in the
beam direction. Figure 4.14 shows a schematic of the sample folder and sources of
the GaAs position uncertainty. The tilts of the sample folder and the moving directions of the sample stages have an uncertainty, ∆θun , as shown in the middle andthe right of Fig. 4.14. The tilt uncertainties of the sample folder were ±0.3 mradand ±0.7 mrad in the horizontal and the vertical direction, respectively. The moving direction uncertainties of the sample stage were ±2.1 mrad and ±0.9 mrad. On
the sample folder, the distances from the position of the collision timing measurement to the position of the focal point measurement are horizontally Lx = 1.6 mm

CHAPTER 4. ALIGNMENT OF TWO BEAMS

50

Table 4.2: The summary of the temporal uncertainties of the collision timing.

Sources of uncertainty

GaAs position
uncertainty [µm]Temporal
uncertainty [fs]

0.4
9
3
12
17

20
18
28
6
6
3
62
22
79
118

ROI dependence of t0
Fit width dependence of t0
Pulse width of both pulses
Resolution of TM
Thickness of the sapphire substrate
Horizontal tilt of the sample folder
Vertical tilt of the sample folder
Horizontal tilt of the stage moving direction
Vertical tilt of the stage moving direction
Focal position measurement
Total temporal uncertainty

160

and vertically Ly = 13.6 mm. Due to the distance, the position of the GaAs crystal during the collision timing measurement has uncertainty as ±Lx × tan(θun ) or
±Ly × tan(θun ), as shown in Fig 4.14. The maximum of these uncertainties is±12µm.
The uncertainty of the focal position measurement, 17 µm, also causes theuncertainty of the GaAs crystal position.
All uncertainties are summarized in Tab. 4.2. The uncertainty of the collision
timing in total becomes the quadratic sum of those and was ±160 fs.
Result and accuracy of the time alignment
The delay time of measured data in the VD search has a width of about 0.3 ps dueto the jitter of both pulses. Since the delay time is precisely measured by the TM,
the accuracy of the time alignment is determined by the accuracy of the collision
timing measurement. Thus, the accuracy of the time alignment is ±160 fs.

Chapter 5

Data taking and analysis
5.1

Data taking

5.1.1

Data acquisition of vacuum diﬀraction

Table 5.1: The summary of the data acquisition of vacuum diﬀraction. The
collision data and the BG data were measured alternately with the conditions
summarized in the table.
Wide range scanNarrow range scan

6.9 ps27
267 fs1552.9 ps12267 fs150
5Range of the scan
Number of steps for the scanInterval between steps
Statistics of data in one step
Repetition of scan

The VD search was performed for about 20 minutes on July 1, 2019. Both pulses
were collided, and diﬀracted x rays were searched. During the data acquisition, thedelay time of the laser was scanned using the optical delay unit. The delay time wasscanned with a wide range (6.9 ps) and a narrow range (2.9 ps), and each range wasscanned with 267 fs of the interval. The scan with the wide range was performed
to confirm a stability of BG amount in the timing distribution of the delay time.
The scan with the narrow range was performed to take a lot of data when bothpulses are collided at the focus of the laser. These scans were repeated five times.
Conditions of the scans are summarized in Tab. 5.1 and Fig. 5.1. Two kinds ofdata were taken. One is a collision data when both pulses are collided, and theother is a BG data when only XFEL pulse is irradiated. Both data were measured
alternately using the 30 Hz of the XFEL pulse, and both data were obtained at
15 Hz. One BG data observed after one collision data is used as BG of its collision51

CHAPTER 5. DATA TAKING AND ANALYSIS

52

Collision data1
BG data1 : Background of collision data1
Collision data2

Laser pulse
XFEL pulse
Time

30 pulses

Change delay time 267 fs

27 steps

Figure 5.1: Illustration of the way of the scan of the delay time with the wide
range (6.9 ps). During the data acquisition, the wide range scan was repeated fivetimes, and after that, the narrow range scan was also repeated five times.
Jitter [ps]h2d_Jitter_eachstep_Sig
1.5
22
20

1

18
16

0.5

14
12

0

10
8

− 0.5

6
4

−1

2
− 1.5

20

40

60

80

100

120

140

160

180

0

The number of steps

Figure 5.2: The jitter of each pulse during the data acquisition.
data. In total, 11025 pulses of both data were taken, respectively. The x rays
through the openings of the slits were measured and recorded for every pulse.
Figure 5.2 shows the jitter of the collision data of each pulse. The horizontal
axis shows each step of the scans, and the first 135 steps correspond to the scanwith the wide range. The vertical axis is the jitter, which is a delay time of theoscillation timing of the laser against the XFEL. The jitter shows a gaussian-like
distribution with the RMS of about 300 fs. Though the median of the jitter at eachstep has a slight drift (∼ 10 fs/step) during the scans, the drift is enough smaller
than the jitter size and the delay time added at each step.
Figure 5.3 shows the timing distribution of all collision data. The horizontal
axis shows the delay time of the laser. The timing distribution has finer structures
than the interval of the scan (267 fs) due to the jitter.
Figure 5.4 is the number of photons in the XFEL pulse for each step. The

53

CHAPTER 5. DATA TAKING AND ANALYSISCount [/50fs]

h1d_timing_e_x0_Sig
180
160
140
120
100
80
60
40
20
0

−4

−3

−2

−1

0

1

2

3

4

Delay time of the laser t [ps]
L

BG

Sig

Figure 5.3: The timing distribution of the collision data. The horizontal axis
shows the delay time of the laser. The vertical axis shows counts of the collision.
h2d_CPphoton_eachstep_Sig

× 10

h2d_CPphoton_eachstep_BG1

6

20
18

6000
16
5000

14
12

4000

10
3000

8
6

2000

4
1000

Photons in the XFEL pulse [photons]

Photons in the XFEL pulse [photons]

6

7000

7000

× 10

20
18

6000
16
5000

14
12

4000

10
3000

8
6

2000

4
1000

2

2
0

20

40

60

80

100

120

140

160

180

The number of steps

0

0

20

40

60

80

100

120

140

160

180

The number of steps

Figure 5.4: The number of photons in the XFEL pulse during the data acquisition.
Left: The collision data; Right: The BG data.
photons of each pulse are shown and have about 30% of the intensity fluctuation(RMS) at each step. Figure 5.5 shows a magnified view of the timing distributionof photons in the XFEL pulse. Each bin shows the average number of photons in
the XFEL pulse at the collision point. Black and magenta points show the collision
data and the BG data, respectively. A timing window for the analysis is the area
between green lines. In the analysis, the signal is calculated in the region where thebeam size of the laser was measured. This region is |z| ≤ 30 µm, which corresponds
to |tL | < 0.2 ps. The timing window is determined to be |tL | < 0.55 ps, whichcontains the region of the signal (±0.2 ps) with the accuracy of 2σ (±0.32 ps, 2σ ofthe time alignment accuracy). The number of photons of the collision data in thetiming window was N = (3.46 ± 0.02) × 109 photons/pulse on average.

0Photons in the XFEL pulse [photons/pulse/50fs]

CHAPTER 5. DATA TAKING AND ANALYSIS
×10

54

h1d_CPphoton_ave_Sig

6●：Collision data●：BG data

Timing window

3700
3600
3500
3400
3300
3200
3100

−1

− 0.5

0

0.5

1

1.5

Delay time of the laser t [ps]L

Figure 5.5: The timing distribution of the number of photons in the XFEL pulse
at the collision point. The collision data and the BG data are shown with blackand magenta points, respectively.

5.1.2

Monitoring of position drift of both pulses

The images of both pulses are measured by the Camera2 to monitor the drift of thepositions of both pulses. Figure 5.6 shows the images of both pulses. The image ofthe laser pulse has a diﬀraction pattern around its peak since the aperture of theLens7 (ϕ46 mm) is smaller than the laser pulse at the Lens7 (∼ ϕ60 mm). Diﬀerent
from the image of the laser pulse, the image of the XFEL pulse was measured using
the GaAs crystal. A GaAs emits fluorescence after absorption of the x rays. The
XFEL pulse was irradiated to the GaAs crystal set at the focus of the laser, andthe image of fluorescence was measured.
In my research, the position of the laser pulse was drifted due to a slight movement of the chamber. In this situation, the laser image on the picture does not movesince the laser pulse moves together with the imaging lens (Lens7). In contrast,
the XFEL image moves inversely with the Lens7.
The drift of both pulses was measured by tracing the peak of the images before
and during the data acquisition. Figure 5.7 shows the drift of the peaks of both
images. The average of the peak position with 150 pulses is shown with its error
due to the fluctuation. The orange and the blue points are the peaks of the laser
and the XFEL, respectively. The horizontal axis, T , is a time from the start ofthe data acquisition. The peak of the XFEL image changes due to the drift of thelaser pulse. In order to estimate this drift, the peak of the XFEL image is fit by ablue linear function. This function corresponds to the drift of the laser pulse, and alight blue hatch is its uncertainty due to the fluctuation, which is a maximum gap
from this function to the blue points (horizontally 0.6 µm and vertically 0.8 µm).
In order to cancel the displacement due to the drift, the laser pulse was verticallyshifted by 4.25 µm by the OAP stage before the data acquisition.
The displacement between both pulses after the spatial alignment is calculated
by comparing the peak of the laser and the linear function in Fig. 5.7, and the

55

CHAPTER 5. DATA TAKING AND ANALYSIS
h2d_GaAs_Paper
2500

y [µm]

y [µm]

h2d_Laser_Paper

60

60
140

50

50

120

2000

100

40

40
1500

80

30

30

60

1000

20

20
500

10

40
20

10

0

00

10

20

30

40

50

60

x [µm]

0

00

10

20

30

40

50

60

x [µm]

Figure 5.6:
Images of the laser pulse and the XFEL pulse measured by the
Camera2. Left: Image of the laser focal spot; Right: Image of the fluorescence of
the GaAs crystal which is irradiated by the XFEL pulse.
result is shown in Fig 5.8. A time when the spatial alignment has been performed(T = −1.4 hour) is shown with the red line. The green hatched area is the durationof the data acquisition, and the displacements at first 150 pulses of the ten delay
time scans and end 150 pulses of the last delay time scan are shown. Displacements
during the data acquisition, which is the average of displacements in the green
hatch area, are xL = (0.5 ± 4.2) µm and yL = (2.9 ± 3.8) µm, where each error
is a quadratic sum of the spatial alignment uncertainty and the fluctuation of theposition drift of the chamber.

1●：Laser●：XFEL

0

Vertical peak position on the picture [µm]

Horizontal peak position on the picture [µm]CHAPTER 5. DATA TAKING AND ANALYSIS−1−2●：Laser●：XFEL0
4.25 µm
shift

−1

−3

−4

−4

−5
−2

1

−2

−3

−6

56

−5
−1.5

−1

−0.5

0

−6

0.5

−2

Time from start of the data taking, T [hour]

−1.5

−1

−0.5

0

0.5

Time from start of the data taking, T [hour]

Displacement [µm]Figure 5.7: Drifts of the peaks of the laser the XFEL images on the picture takenwith the Camera2. Left: Horizontal direction; Right: Vertical direction.

8

Spatial alignment
T = -1.4 hour

7
DAQ

6

●：xL
○：yL

5
4
3
2
1
0
−1

−2

−1.5

−1

−0.5

0

0.5

Time from start of the data taking, T [hour]

Figure 5.8: Drift of displacement of the laser pulse position against the XFEL
pulse position. The green hatch (T = 0 to 0.3 hour) shows the duration of VD
search, and the displacements at first 150 pulses of the ten delay time scans andend 150 pulses of the last delay time scan are shown.

57

CHAPTER 5. DATA TAKING AND ANALYSIS(a) XFEL proﬁle(c) Interaction volume(b) Laser proﬁleFigure 5.9: Profiles of the laser pulse, the XFEL pulse and the interaction volume
at tL = 0. The profiles of both pulses are used for the calculation of the interaction volume. Maximum of three profiles [are normalized to 1. (a) ]XFEL profile,2−yL )2L)
fXh (xCP )fXv (yCP ). (b) Laser profile, exp −2 (xCPw−x− 2 (yCP
.
2
w2
Lh

L0v

(c) Interaction volume.

5.2

Expected signal

A distribution of the signal x rays at the collision point is calculated with thefollowing formula,
dPcurve
I˜IV (xCP , yCP )
dP
=∫
.
˜
dxCP dyCP d cos θdIIV (xCP , yCP )dxCP dyCP cos θ Θx =Θnx ,Θy =Θny

(5.1)

with
I˜IV (xCP , yCP ) =fXh (xCP )fXv (yCP ),([])2(yCP − yL )2(xCP − xL )2−
2
× exp −2
,
2
2
wLh
wLv

(5.2)
(5.3)
(5.4)

where I˜IV (xCP , yCP ) is an interaction volume considering the measured XFEL
profile. Equation (5.1) is obtained by replacing IIV (xCP , yCP ) in the fraction in
Eq. (2.12) with I˜IV (xCP , yCP ).
Figure 5.9 (c) shows the interaction volume at tL = 0. The XFEL profile andthe laser profile used for the calculation are also shown in Fig. 5.9 (a) and (b),respectively. The XFEL profile is the product of the horizontal and the verticalprofiles, fXh (xCP )fXv (yCP ). The laser profile is a two-dimensional Gaussian function, and its peak has the displacements (xL , yL ). The profile of the interaction
volume strongly depends on the laser profile since the beam size of the laser issmaller than that of the XFEL. The region (|xCP |, |yCP | < 15 µm), which is shownin Fig. 5.9, is used for the analysis.
Figure 5.10 is the expected signal distribution at tL = 0 as a phase space in thevertical direction. The signal has a Gaussian profile of the angular distribution with

CHAPTER 5. DATA TAKING AND ANALYSIS

58

Geometricalacceptance

Figure 5.10: The phase space of the signal distribution in the vertical direction.
The area between magenta lines shows the geometrical acceptance made by the
Slit6.
the divergence of 34 µrad. Due to the curvature of the XFEL pulse, the angle ofthe signal x-ray is slightly increased as yCP becomes smaller. The area between themagenta line shows the geometrical acceptance of the signals, which corresponds
to the opening of the Slit6. The interaction probability is P = 2.1 × 10−22 /1 xray, and an acceptance A which is the ratio of the signals through the geometricalacceptance is A = 9.5 × 10−3 , and the number of expected signal x rays is nQED =N P A = 7.0 × 10−15 photons/pulse.
The timing distributions of the interaction probability, the acceptance andthe expected signal x rays are shown in Fig. 5.11 and Fig. 5.12, respectively.
These parameters are calculated in the region where the laser size was observed(|z| ≤ 30 µm). The interaction probability becomes large around tL = 0 since theinteraction probability mainly depends on the eﬀective pulse energy of the laser.
Since the divergence of the signal is inversely proportional to the beam size of thelaser, the acceptance is large in the region (tL < 0) where the beam size is small.
The distribution of the number of expected signal x rays is obtained as the productof distributions of the interaction probability and the acceptance.

CHAPTER 5. DATA TAKING AND ANALYSIS

0.4

×10−21

tge_A

tge_P
Acceptance, AInteraction probability, P [photons/1 Xrays]

59

0.35
0.3

0.1
0.09
0.08
0.07

0.25

0.06

0.2

0.05
0.04

0.15

0.03

0.1

0.02

0.05

0.01

0

− 0.2 − 0.15 − 0.1 − 0.05 0

0.05 0.1 0.15 0.2

0− 0.2 − 0.15 − 0.1 − 0.05 0

0.05 0.1 0.15 0.2

Delay time of the laser, t [ps]Delay time of the laser, t [ps]L

L

Figure 5.11: Timing distributions of interaction probability P and acceptance A.

Expected signal x rays, n

QED[photons/pulse]

−15

20

×10

tge_Signal

18
16
14
12
10
8
6
4
2
0

− 0.2 − 0.15 − 0.1 − 0.05 0

0.05 0.1 0.15 0.2

Delay time of the laser, t [ps]L

Figure 5.12: Timing distribution of the number of expected signal x rays nQED .

CHAPTER 5. DATA TAKING AND ANALYSISXFEL beam

60

Diﬀused x rays

Intensity of XXrays
rays [a.u.]

tge_pdCP_bibun_allscan_fit_slit6Low
S6l

1

S6u

Geometrical

10−1

acceptance

10−2

0

200

400

600

800

1000

y [µ m]Figure 5.13: The distribution of the intensity of x rays at the Slit6. The area
between magenta lines shows the geometrical acceptance by the Slit6.

5.3

BG sources

BGs in the VD experiment are x rays passing the geometrical acceptance by the
Slit6 and derive from the x rays of the XFEL pulse. BGs are divided as follows:
i X-ray which has a large angle.
When the XFEL pulse is focused, x rays at the tail of the beam profile get alarge angle and become the BG. Since the shaper absorbs this BG, this BG
is negligible.
ii Diﬀused x-ray by the beamline optics.
A part of the x rays in the XFEL pulse is diﬀused when materials of thetransmission-type optics have a non-uniformity and when the TRM andtransmission-type optics have the roughness on the surface.
iii Diﬀracted x-ray by the slit and beamline optics.
X rays is diﬀracted when the XFEL pulse passes the small aperture of the
optics and when the blade of the slit cuts the XFEL pulse or the diﬀused xrays.
The distribution of the BGs at the Slit6 is shown in Fig 5.13. When the Slit4 is
opened, the distribution of x rays is measured by the knife-edge scan of the lower
blade of the Slit6. The XFEL beam, which corresponds to the large angle x-ray(i), has a gaussian distribution and is dominant near the beam axis. The diﬀused
x-ray (ii) has a larger divergence than the XFEL beam and is dominant at a regionaway from the beam axis.
The region where the diﬀused x-ray is dominant is better for the geometricalacceptance. The geometrical acceptance is shown by the magenta lines. Since
the divergence of the signal is larger than the XFEL beam and smaller than the

61

CHAPTER 5. DATA TAKING AND ANALYSIS
Slit4

Slit6

600

X rays passing the geometrical acceptance [a.u.]y [µm]

Slit1

500
400
300
200
100
0
− 100
− 200

Collision point

0

2

4

6

8

10

12

14

S4u

1

tge_pdCP_allscan_slit4Up

10−1

10−2

0

100

200

300

400

500

Position of the upper blade of the Slit4 [µ m]16Distance from the vertical focusing shaper [m]Figure 5.14: (Right) The schematic of the position of the slits. The horizontal
axis is the distance from the vertical focusing shaper. The blue line shows the edgeof the light ray of the XFEL beam. (Left) The data of the knife-edge scan by theupper blade of the Slit4.
diﬀused x-ray, the region where the diﬀused x-ray begins to dominate has a large
signal-to-noise ratio.
The position of the upper blade of the Slit4 is optimized to minimize the BGs.
Figure 5.14(Left) shows the position of the slits during the data acquisition. Figure 5.14(Right) is the data of the knife-edge scan by the upper blade of the Slit4.
The vertical axis shows the number of the BGs passing the geometrical acceptance.
The horizontal axis is the position of the edge of the upper blade of the Slit4. Whenthe blade is closed (When the coordinate of the horizontal axis becomes small), thenumber of diﬀused x rays is decrease. Whereas the number of diﬀracted x rays (iii)increase since the diﬀused x-ray is diﬀracted by the blade. The diﬀracted x-ray
becomes the dominant BG when the position the blade is near to the beam axis(∼ 20 µm). The blade is set at the position with fewer BGs shown as the red line.

5.4

Timing distribution of detected x rays

The number of x rays detected by the PD is shown in Fig. 5.15. The number of xrays of each pulse is shown and have about 40% of the intensity fluctuation (RMS)at each step. The normalized number of detected x rays is shown in Fig. 5.16 as
the timing distribution. The black and the magenta point are the collision data
and the BG data, respectively. Each bin is normalized by the XFEL intensity as
follows: i th bin yi is yi = (average of detected x rays) × N/Ni , where Ni is thenumber of photons in the XFEL pulse shown by i th bin in Fig. 5.5. The errors
show uncertainties of the measurement of x rays. Both histograms have a 1 ps anda 0.1 ps scale of intensity fluctuations since the XFEL profile slightly fluctuates in
1 minute and 1 second scale. The intensity fluctuation in 1 ps scale is cancelledout by subtracting the BG data from the collision data.

BG

Sig

CHAPTER 5. DATA TAKING AND ANALYSIS
h2d_CPphoton_eachstep_Sig

× 10

18
6000
16
5000

14
12

4000

10
3000

8
6

2000

4
1000

0

h2d_CPphoton_eachstep_BG1

620

Photons in the XFEL pulse [photons]

Photons in the XFEL pulse [photons]

6

7000

62

7000

× 10

20
18

6000
16
5000

14
12

4000

10
3000

8
6

2000

4
1000

2

2
20

40

60

80

100

120

140

160

180

0

0

20

40

60

80

100

120

140

160

180

The number of steps

The number of steps

Detected X rays (Normalized) [photons/pulse/50fs]

Figure 5.15: Detected x rays of each pulse during the data acquisition. The
number of x rays is not normalized by the XFEL intensity. Left: The collision
data; Right: The BG data.
120 × 10h1d_PDphoton_Signal_Paper

3●：Collision data●：BG data

Timing window

115

110

105

−1

− 0.5

0

0.5

1

1.5

Delay time of the laser t [ps]L

Figure 5.16: The timing distribution of the detected x rays normalized by the
XFEL intensity. The black point and the magenta point show the collision data
and the BG data, respectively.
Since the intensity fluctuation in a 0.1 ps scale is not canceled out by the subtraction, the standard deviation of this fluctuation, σy is estimated by calculating
the following value Y√ ()
2
yi−1 + yi+1
Y =
yi −
.
(5.5)
3
2
Since the width of each bin is enough smaller than 1 ps, Y also has σy of thestandard deviation, approximately. The calculated σy was 1.61×103 photons/pulse.
The uncertainty of the BG due to the fluctuation of the XFEL profile, σBG , isalso estimated using σy . The standard deviation of Y , σy , is estimated as σy =√2 , where σ2σmeasure+ σBGmeasure is the statistical error of each bin due to themeasurement of the x rays. σmeasure is 0.55 × 103 photons/pulse, and σBG is 1.51 ×
103 photons/pulse.
Figure. 5.17 shows the diﬀerence of the BG data from the collision data, nxrays .

0

63

CHAPTER 5. DATA TAKING AND ANALYSIS[photons/pulse/50fs]

10000

5000

xrays

X rays, nTiming window0− 5000− 10000

−1

− 0.5

0

0.5

1

1.5

Delay time of the laser t [ps]L

Figure 5.17: The timing distribution of the diﬀerence of the number of detected x
rays. The diﬀerence between the collision data and the BG data is shown. The area
between green lines shows the timing window (|tL | < 0.55 fs). The red histogramshows the expected signal of VD, which is multiplied by 2.0 × 1017 for comparison.
The errors show the uncertainties of the BG and the measurement of the x rays. The
number of expected signal x rays is shown as a red histogram, which is multipliedby 2.0 × 1017 for the comparison. A sum of the number of x rays in the timing
window is nxray,sum = (1.02 ± 1.07(stat) ± 0.03(sys)) × 104 photons. A sum of thenumber of expected x rays in the timing window is nQED,sum = 3.9×10−14 photons.
No evidence for an excess of the number of x rays due to VD was not observed.

5.5

Analysis of the upper limit on VD

An upper limit for the interaction probability is calculated although significant
signals are not observed. The limit on the interaction probability is calculated by
the ratio of sum of the number of x rays in the timing window, nxray,sum , to thesum of the number of expected x rays in the timing window, nQED,sum , as follows
nxray,sum,nQED,sum
where

5.5.1

nxray,sum =1
1.1 psnQED,sum =1
1.1 ps

(5.6)∫ +0.55 ps−0.55 ps
∫ +0.55 ps−0.55 psnxrays dtL(5.7)

nQED dtL .

(5.8)

Systematic uncertainties

The parameters nxrays and nQED (= N P A) have an uncertainty. Table. 5.2 is asummary of systematic uncertainties on nQED,sum due to observed parameters.

CHAPTER 5. DATA TAKING AND ANALYSIS

64

Table 5.2: The summary of systematic uncertainties on nQED,sum calculated fromthe experimental parameters.

Parameters

Uncertainties on nQED,sum

The number of x rays in the XFEL pulse, N
Pulse energy of the laser, W
Horizontal beam size of the laser, wLh
Vertical beam size of the laser, wLv
Horizontal beam size of the XFEL, wXh
Vertical beam size of the XFEL, wXv
Pulse durations, τL , τX
Horizontal displacement, xL
Vertical displacement, yL
Lower blade position of Slit6, S6l
Upper blade position of Slit6, S6u
Distance from the collision point to the Slit6, DCP/Slit6
Distance from the shaper to the collision point, zX
Minimum XFEL beam size, wX0v
Divergence of the XFEL beam, φ−0.7% / 0.7%
−22% / 25%−13% / 17%−55% / 109%−14% / 19%−21% / 33%−25% / 42%−9%−43% / 36%−4% / 5%
−0.3% / 0.3%
−2% / 2%
−1% / 0.9%
−0.5% / 0.9%
−0.1% / 0.2%

Each uncertainty is subsequently explained in the following subsections.
Uncertainty on the x rays: nxrays
The x rays nxrays , which is the diﬀerence between the collision data and the BG
data, has uncertainties due to the fluctuation of BGs and the measurement of xrays. Dominant error source is the statistical uncertainty due to the fluctuation of
the BG. The uncertainty on nxrays,sum is ±1.07 × 104 photons in total.
uncertainty on the number of x rays in the XFEL pulse: N
The number of the x rays in the XFEL pulse, N , has uncertainty due to thecalibration of the SCM and the intensity fluctuation. The uncertainties on N andnQED,sum are both ±0.7%.
uncertainty on the pulse energy of the laser: W
The pulse energy of the laser, W , has ±12% uncertainty. The dominant uncertainty
is caused due to the estimation of the ratio of the eﬀective pulse energy. Since P
is proportional to W 2 , nQED,sum is nearly proportional to W 2 . The uncertainty on
nQED,sum is +25%
−22% .

65

CHAPTER 5. DATA TAKING AND ANALYSIS

Uncertainty on the horizontal beam size of the laser pulse: wLh
The horizontal beam size of the laser pulse, wLh , has ±0.2 µm uncertainty due tosystematic uncertainties of the measurement
dedicated in Sec 3.2.3. From Eq. (2.6),√
2 + 2w 2
P is nearly proportional to 1/wLh wLhXh ∼ 1/(wLh wXh ), (wLh ≪ wXh ).
nQED,sum is roughly proportional to 1/wLh , and the uncertainty on nQED,sum is+17%−13% .

Uncertainty on the vertical beam size of the laser pulse: wLv
The vertical beam size of the√laser pulse, wLv , also has ±0.2 µm uncertainty. P is

2 + 2w 2 ∼ 1/w , (wnearly proportional to 1/wLh wLv
Lv
Lv ≪ wXv ) and has about
Xv±10% uncertainty.
The acceptance A is also aﬀected. The geometrical acceptance corresponds tobetween 2.3σ and 3.5σ in the Gaussian√ angular distribution of the signals. Since thew2 +2w2

Xv
divergence (2σ) is proportional to wLv∼ 1/wLv (wLv ≪ wXv ), the divergence
Lv wXv
has about ±10% uncertainty and A has about ±70% uncertainty. In total, theuncertainty on nQED,sum is 109%−55% .

Uncertainty on the horizontal beam size of the XFEL pulse: wXh
The horizontal beam size of the XFEL pulse is wXh = (22.0 ± 3.5) µm. The systematic uncertainties come due to conditions for the measurement√
and the analysisof the knife edge scan data. P is nearly proportional to 1/wLh

2 + 2w 2 ∼wLhXh

1/(wLh wXh ), (wLh ≪ wXh ). The uncertainty on nQED,sum is +19%
−14% .
Uncertainty on the vertical beam size of the XFEL pulse: wXv
The vertical beam size of the XFEL pulse is wXv = (14.8 ± 4.3) µm. As with wXh ,wXv has the systematic uncertainties and the dependence on P . Although wXv also
depends on A, the uncertainty of A is less than 2%. In total, the uncertainty on
nQED,sum is +33%
−21% .
Uncertainty on the signal estimation due to both pulse durations: τL , τX
The signal has uncertainty depending on both pulse durations since the signal iscalculated under the limit that both pulse durations are short (τL , τX → 0). The
beam size of the laser slightly depends on z. Since the beam size of the laser is notconstant during the interaction due to both pulse durations, P and the divergenceof the signal have uncertainties. The maximum and the minimum sizes of thelaser beam during the interaction are calculated by assuming both pulses to be
the square wave in the time-domain. The laser beam size, P and A change about±10%, ±10% and ±30%, respectively. In total, the uncertainty on nQED,sum is+42%−25% .

CHAPTER 5. DATA TAKING AND ANALYSIS

66

Uncertainty on the horizontal displacement: xL
The horizontal displacement is xL = (0.5 ± 4.2) µm. The uncertainties come fromthe [spatial alignment
and the drift of the laser position. P is proportional to]x2L
exp −4 w2 +2w2 , which shows how well both pulses overlap. The uncertainty on
Lh

Xh

nQED,sum is −9%.
Uncertainty on the vertical displacement: yL
The vertical displacement is yL = (2.9±3.8) µm. As with xL , yL has the systematic
uncertainties and the dependence on P . The uncertainty on P is about −30%.
A is also aﬀected due to the wavefront curvature of the XFEL pulse. Depending
on yL , the eﬀect of the wavefront curvature shifts the median of the angle distribution of the signals. The shift of the angle is ±2.1 µrad, and A is changed by about±20%. In total, the uncertainty on nQED,sum is +36%
−43% .
Uncertainty on the position of the blade of the Slit6: S6l , S6u
The positions of the Slit6 blade are S6l = (395.0 ± 3.0) µm and S6u = (596.2 ±4.4) µm. The uncertainties come from the accuracy of the measurement of the beamaxis position and give the uncertainty of the size of the opening. The uncertainties+0.3%
on nQED,sum due to S6l and S6u are +5%−4% and −0.3% , respectively.
Uncertainty on the distance from the collision point to the Slit6: DCP/Slit6
The distance from the collision point to the Slit6, DCP/Slit6 , is 10.18 m. The halfsize of slits in the z-direction, 36 mm, is taken as the uncertainty of the positionof the blades. This uncertainty changes the selection angle for the signals. The
uncertainty on nQED,sum is +0.9%−1% .
Uncertainty from the XFEL beam parameters: zX , wX0v , φ
The distance between the XFEL focal spot and the collision point zX = (1.76 ±0.08) m, the minimum XFEL beam size wX0v = (3.1 ± 1.8) µm, and the divergenceof the XFEL beam φ = (10.6 ± 1.1) µrad, are determined by fitting the beam sizes
in the z-direction. The wavefront curvature of the XFEL pulse depends on theseparameters. The uncertainties on nQED,sum from these three parameters are +1%−0.9% ,
+0.9%
+0.2%
−0.5% , and −0.1% , respectively.

5.5.2

Final result

The uncertainties shown above are taken into account, and nQED,sum = (3.9+6.1−2.5 ) ×
10−14 photons and nxray,sum = (1.02 ± 1.07) × 104 photons are obtained.

67

CHAPTER 5. DATA TAKING AND ANALYSISIn order to calculate the limit, nQED,sum and nxrays,sum are estimated with Monte
Carlo calculations. As the probability density functions of the experimental parameters to estimate nQED,sum , a gaussian functions which have the standard deviation
same with the error of the experimental parameters is used. As the probability
density function of nxrays,sum , the following function is used{f (nxrays,sum ) =0nxrays,sum < 0(n−n0 )2− xrays,sum
2
2σun

e

0 ≤ nxrays,sum(5.9)

where n0 = 1.02 × 104 photons and σun = 1.07 × 104 photons are the measured
value of nxrays,sum and its uncertainty, respectively. The obtained upper limit with
the 90% confidence level isnxrays,sum< 2.3 × 1018
nQED,sum(90% C.L.).

(5.10)

Chapter 6

Discussion and prospect
6.1

Significance of the experimental result

The focus of my research was to establish a new VP search method to improvesignal statistics which limit the experimental sensitivity in the previous experiments[6–9, 21]. I established the new VP search method via VD search, which has notbeen searched so far and can generate large signal statistics. In the VD search,creating the focused laser field which generates large signals and colliding the laser
field with the sensitive XFEL pulse are needed. I made the optical system using theadaptive optics and focused the laser pulse to ∼ µm level. Using the Au foil and
the GaAs crystal, I developed the precise alignment techniques, and both pulses
were collided. The shaper was also developed, and BG was suppressed.
The first limit on VP by the VD experiment was obtained using the establishedmethod. This is also the first experimental restriction on VD, and the new information about the properties of VP regarding VD was obtained in addition tophoton-photon scattering and vacuum birefringence.
In Fig. 6.1, experimental sensitivities against VP by the VD experiment andprevious experiments are compared. The signals expected by QED, which is proportional to the square of the fine structure constant α2 , is normalized to 1, and asensitivity to the signals are shown with 90% C.L. The sensitivity of the VD experiment is better than the photon-photon scattering experiment using x rays [6]. Dueto the insuﬃcient suppression of BGs, the sensitivity is not good compared withthe vacuum birefringence experiments. The sensitivity of the previous experiments
is limited by various reasons, for example, BGs which can not be reduced and few
signal statistics. The VD experiment is very promising because the improvementof the sensitivity and the observation of VP are expected by upgrades.
69

CHAPTER 6. DISCUSSION AND PROSPECT70

VD experiment

Photon-photon scattering experiment
Vacuum birefringence experiment

90%Limit

1020
1018

h1d_waku

Yamaji [6]VD experiment

Bernard [21]

1016
1014
1012

OVAL[9]1010
108

BMV [8]106
104

PVLAS [7]

102
1

2000

2005

2010

2015

2020

QED calculationyear

Figure 6.1: Comparison of experimental sensitivities against VP.

6.2

Future prospects

6.2.1

Upgrades for the future experiment

Since the developments of the experimental techniques were taken as the toppriority issue in my research, there is still room for improvement of the experimental
parameters for the future experiment. Plans for upgrades of the experimental parameters are summarized in the following. The experimental parameters in myresearch and after the upgrades are summarized in Tab. 6.1. By considering the
upgrades, the experimental sensitivity of the VD experiment improves 9.5 × 1020
times.
Table 6.1: Expected gain factor by upgrades. The extinction ratio is the accuracyof the polarizer to separate an s-polarized x-ray and a p-polarized x-ray.
Parameters

My researchUpgradeGain

Laser pulse energy [J]Polarizer (Extinction ratio)
Beam sizes [µm]
Laser
XFEL

0.47×10−3
1.9 and 1.9
22.0 and 14.8

12.5
2 × 10−10
1.0 and 1.0
2.0 and 2.0

7.0 × 108
5.0 × 109

Total

2.7 × 102
9.5 × 1020

71

CHAPTER 6. DISCUSSION AND PROSPECT

Laser pulse energy
The 500-TW laser is installed in SACLA. The laser has 12.5 J of the pulse energy.
Using this laser, the sensitivity is improves (12.5 J/0.47 mJ)2 = 7 × 108 since theinteraction probability P is proportional to the pulse energy. The beam size of thelaser becomes larger (120 mm diameter) to avoid the thermal damage to the optics.
Beam sizes
The beam sizes of the XFEL and the laser are needed to decrease to 2 µm and1 µm to increase the interaction probability, respectively. The XFEL beam size
is decreased by colliding the XFEL pulse at its focus. The laser beam size isdecreased by using a DM which is already installed in the 500-TW laser system.
In my research, the laser beam size was larger than 1 µm because the astigmatismof the laser pulse was too large to correct higher-order aberration by the DM. If
the 500-TW laser pulse has a large lower-order aberration, the large aberrationis needed to be cancelled out by other optics. Otherwise, a DM which has moreactuators is needed. A group which uses the DM with three times more actuators
achieves 1 µm of the focus size [40].
The interaction probability P is proportional to P ∼ w 1w √ 2 1 2 √ 2 1 2 .
LhLvwLh +2wXh

wLv +2wXv

By decreasing the beam sizes, the interaction probability increase 2.7 × 102 times.
Background suppression

BGs, which are x rays of the XFEL pulse, are suppressed by its polarization. Since
the polarization of a part of diﬀracted signal x rays is changed, these x rays are
separated from BGs by a polarizer and observed. There is a high precision polarizer using the Bragg refection for an x-ray [41]. This polarizer only reflects ans-polarized x-ray with 2 × 10−10 of the accuracy. With the polarizer, the experimental sensitivity improves 5 × 109 . The development of this polarizer was alreadystarted, and a prototype polarizer is shown in App. B.
Alignments
The accuracy of the spacial alignment is needed smaller than the XFEL beam size
(2 µm). The accuracy is mainly determined by the uncertainty of both pulse positions. The uncertainty of the XFEL position shown in Tab.4.1 is 1/7 of the beam
size. This uncertainty becomes smaller than the beam size since this uncertainty
decreases proportionally to the beam size. The uncertainty of the laser position iscaused due to the instability of the shape of the irradiation trace. The cause of
the instability is thought to be the roughness on the surface of the Au foil (a fewµm) or the softness. Research and development of the spacial alignment using aflat and a hard foil are necessary.
The improvement of the time alignment accuracy is also important since thejitter between the 500-TW laser and the XFEL (56 fs) is smaller than that for theCHAPTER 6. DISCUSSION AND PROSPECT

72
Slit(40µrad to 46µrad)

Focused 500-TW
laser pulse

Horizontal
polarization

Analyzer

DetectorshaperXFEL

Signal x-ray
Polarizer

Verticalpolarization

Figure 6.2: Experimental setup of the future experiment.
0.6-TW laser (∼ 300 fs). The accuracy of the time alignment is mainly determinedby the uncertainty of the position of the GaAs crystal. Since this uncertainty canbe suppressed by a simple measurement and iterations, for example, a measurementof levelness of the chamber, the accuracy of the time alignment decrease to about
40 fs, which is the total of uncertainties due to other sources.

6.2.2

Future experiment

The future experiment is designed by considering the upgrades. The experimental
setup is shown in Fig. 6.2. The purity of the polarization of the XFEL pulse isenhanced by the polarizer, and the XFEL pulse is focused to 2 µm by the shapers.
The 500-TW laser pulse is focused to 1 µm and collided with the XFEL pulse. X
rays are diﬀracted with 66 µrad of the divergence, and 9/130 of the diﬀracted xrays are changed its polarization. These x rays are separated from BGs by theslit and the analyzer which is the same device with the polarizer. The separated xrays are observed by a photon detector. Considered experimental parameters are
summarized in Tab 6.2.
The selection angle for the signals by the slit is 40 µrad to 46 µrad since the incident angle at which the analyzer reflects photons is 45◦ ±3 µrad. The suppressionof BGs by silt is 1 × 10−5 by considering the decrease of the width of the selection
angle (20 µrad → 6 µrad). The suppression by analyzer is 2 × 10−10 , and the total
suppression of BGs is 2×10−15 . In order to estimate the expected signals, a perfectalignment (xL = yL = tL = 0) is assumed, and a loss due to a jitter between the
XFEL beam and the 500-TW laser (56 fs, RMS) is considered. The repetitions of
the XFEL and the laser are 60 Hz and 1 Hz, which are maximum repetitions of the
XFEL of SACLA and the 500-TW laser, respectively. The collision data and the
BG data are measured with 1 Hz and 59 Hz, respectively. The expected signals
reach 4.1+3−2 (stat) photons with 20 days of the data acquisition. In contrast, theexpected BGs are 1.6 ± 0.2(stat) photons, and VD is observed.

73

6.2.3

CHAPTER 6. DISCUSSION AND PROSPECT

Requirement for the future experiment

In the future experiment, a decrease of the energy bandwidth of the XFEL is
required (30 eV → 1 eV, FWHM) since the energy width of x rays reflected by
the polarizer is very small (50 meV). The energy bandwidth can be decreased to
1 eV, which is the target value of the future experiment, by a technique called as aseeding of the XFEL [42], and SACLA achieved to decrease the energy bandwidth
to 3 eV by the seeding. More improvement in the operation of the XFEL with theseeding technique is required.
Birefringence of the shaper should be lower than that of the polarizer in order
not to generate BGs. The shaper may have birefringence though the shaper ismade of Si crystal, which has symmetric structure. There are two possibilities ofbirefringence sources. One is the roughness of the surface on the shaper (∼ 1 µm),
which is made due to the etching process. The other is a solution for the etching,which is left on the surface of the shaper. These possibilities should be studied.

CHAPTER 6. DISCUSSION AND PROSPECT74

Table 6.2: The summary of the experimental parameters of the future experiment.

Parameters
Laser parameters

Laser
Pulse energy
Beam size
Polarization
Repetition

XFEL parameters

Photon energy
Pulse energy
Beam size
Polarization
Repetition
Divergence
Energy bandwidth
Transmittance of shaper
Transmittance of polarizer

BG separation

Slit : Direction of aperture
Selection angle
Fraction of BGs through slit
Polarizer : Crystal plane
A number of reflections
Extinction ratio

horizontal
40 µrad to 46 µrad
1 × 10−5
Si(511)
Eight times
2 × 10−10Signal parameters

Divergence
Acceptance by slit
Diﬀraction eﬃciency of analyzer
Interaction probability
Ratio of polarization flipped x rays
Loss due to Jitter
Rate of collision data
Rate of BG data
Time of data acquisition

66 µrad1.1%
0.40 (for eight times reflections)
7.2 × 10−12
9/130
0.34
1 Hz
59 Hz
20 days

Expected signals
Expected BGs

500-TW laser
12.5 J
1 µm
45◦ from horizontal direction
1 Hz
8.4 keV
4 × 1011 photons/pulse
2 µm
horizontal
60 Hz
20 µrad1 eV (FWHM)
6.3% (for two shapers)
1.8%

4.1 photons
1.6 ± 0.2(stat) photons

Chapter 7

Conclusion
This thesis reported a vacuum polarization search with the new experimental
scheme. Diﬀraction of the XFEL pulse under the strong laser pulse was searched.
This new scheme has not been done due to the diﬃcultly of the collision of bothpulses. To resolve this problem and establish the experimental method of the VD
experiment, I developed
1. the precise spatial and temporal alignment techniques with 4 µm and 160 fs
accuracies
2. the precise control system of the laser phase by the deformable mirror tofocus the laser pulse
3. the novel x-ray optics, shaper, to suppress BGs.
In addition, I derived the theoretical formula of the signal distribution of the VD.
The eﬀective signal distribution was calculated by considering the eﬀects whichhave not been considered so far, for example, the divergence of the XFEL beam.
The first experimental search for VD was performed at the beamline 3 of
SACLA, XFEL facility. The 0.6-TW laser is focused to 1.9 µm, and the 22.0 µm×14.8 µmof the XFEL pulse is precisely collided with the laser pulse by the developed alignment techniques. No significant signals are observed, and the 90% C.L. upper limiton the interaction probability of VD is obtained. The limit is obtained by the ratioof the number of the observed x rays, nxray,sum , to the number of the expected xrays in QED, nQED,sum , as follows:
nxrays,sum< 2.3 × 1018 (90% C.L.).
(7.1)
nQED,sumThis is the first limit on VP by the VD experiment and is also the first experimental
restriction on VD.
This experiment also demonstrates the feasibility of the observation of VD. VD
can be observed in the future experiment with the XFEL and the 500-TW laser of
SACLA. Requirements for the alignment accuracy and the BG suppression in the
future experiment will be achieved by the developed techniques and optics.
75

Appendix A

ShaperIn this section, the eﬀect of the suppression of the BG in the VD experiment by theshaper is discussed. BGs in a VD search is a part of probe x rays passing throughthe opening of the slit which is set in front of an x-ray detector. These x rays are
divided into three cases, as follows:i

X rays which have a large angle

ii Diﬀused x rays by the beamline optics
iii Diﬀracted x rays by the slit and beamline optics
It is possible to block the direct path to the opening for these x rays by using
the slit. However, enough suppression of BG x rays is impossible because theslit which blocks the direct path causes new diﬀracted x rays (iii). For example,
Fresnel diﬀraction is typical diﬀraction caused by the slit. The shaper is developed
to remove BG x rays without the new diﬀraction of x rays.
Since the shaper smoothly shapes the beam profile diﬀerent from the slit, diﬀraction is not caused. Figure A.1 shows the XFEL beam profile shaped by the shaper.
The blue point is the shaped beam profile, and the grey point is a raw XFEL beam.
The data was measured at SPring-8 beamline 19. Only one dimension of the profileis shaped. Since the shaped profile has a good gaussian profile, the diﬀraction due
to the shaping is well suppressed. The red line is a gaussian function fitted to theshaped profile and drown with 7σ of the width. Since the shaper also works as thefocusing lens, the diﬀraction due to the aperture of the focusing lens (iii) is also
decreased.
Since the shaper selectively absorbs the photon at the tail of the beam profile,
a divergence of the beam is decreased, and the large angle x rays (i) is suppressed.
Figure A.2 shows the focused XFEL beam of the SACLA BL3. The light blue
points show the focused beam by the shaper, and the orange points show thefocused beam by the beryllium (Be) lens equipped at the EH2. The blue and the
red lines are fitting functions of the Gaussian beam, respectively. By using the77

APPENDIX A. SHAPER

78[photon/um]

tmg_bibun_V

109

108

107

106
−400

−200

0

200

400

+direction = Up [um]Figure A.1: Comparison of the raw XFEL profile (grey) and the profile shapedby the shaper (blue). The red line is the fitted gaussian function drown with 7σ ofthe width.
shaper, the divergence of the beam is strongly decreased (65 µrad→ 10 µrad). Dueto this eﬀect, BG x rays are decreased about 3 digits.
The shaper also decreases the diﬀused x rays (ii). The Be lens, which is a typical
x-ray lens, has vacancies and distortion in the lens since it is created by pressing
the material. The x-ray is diﬀused by the vacancy and the distortion. Whereas theshaper does not have the vacancy and the distortion since it is made of a Si crystal.
Figure A.3 shows the x-ray camera images of the focused XFEL beam by the Be
lens and the shaper. The focused XFEL beam by the Be lens has many diﬀused xrays around the peak. By focusing the XFEL with the shaper, the diﬀused x rays
are well suppressed. The diﬀused x rays are caused due to pillars which are createdduring the etching process.

79

APPENDIX A. SHAPER

wXv [µm][0]*sqrt(1+pow([1]*([2]-x)/[0],2))

700

2 2
χχ
/ ndf
/ ndf

4.438// 1
4
0.3555

BeamSize0
p0± 1.8145.6913.105± 1.194600

Div_2sigmaByFWHM
p1± 1.1364.9610.58± 2.704

z0
p2

6.758
± 0.08201
5.1± 0.0066

500
400
300
200
100
0

0

2

4

6

8

10

12

14

16

Distance from the optics for focus [m]Figure A.2: Comparison of the XFEL beams focused by the shaper (light blue
point) and the Be lens (orange point). The blue and the red lines are fitting
functions of the Gaussian beam, respectively.

Noise

Figure A.3: The x-ray camera images of the focused XFEL beam by the Be lensand the shaper. The color of the image means the intensity of the x rays. (Left)
The image focused by the Be lens. (Right) The image focused by the shaper. The
spots circled by yellow lines are noise due to the thermal damage of the fluorescentscreen of the x-ray camera.

Appendix B

Polarizer
The polarizer has been developed for the future VD experiment. The target valueof the extinction ratio is < 2 × 10−10 . Amount of light transmitted through thepolarizer is depend on the direction of the polarization of lights. The extinction
ratio is the ratio of minimum and maximum amount of light transmitted throughthe polarizer. The polarizer in the x-ray region is a reflective type optics madeof a crystal. X rays enter the polarizer with Brewster’s angle (45◦ ), which is
the incident angle at which only s-polarized x rays are reflected, and reflected by
Bragg diﬀraction. The main cause which makes the extinction ratio worse is thephenomenon called as Multiple beam reflection (MBR). An x-ray is reflected several
times in the crystal and emitted to the same direction as the reflection at Brewster’sangle.
The polarizer with less MBR is created with the optimization of the crystal
plane, the x-ray energy and the azimuth angle of the crystal. Figure B.1 shows theimage of the polarizer made of Si crystal. The mirror index of the crystal planeis (511). The polarizer works as a polarizer for an 8.3878 keV x-ray. X rays arereflected eight times to improve the extinction ratio.
The extinction ratio was measured at SPring-8 BL19, which is an x-ray beamline. The azimuth angle and the angle between the polarizer and the analyzer were
adjusted. 1.3 × 10−7 of the extinction ratio was obtained with the best alignmentof the polarizer and the analyzer. Figure. B.2 shows the change of the extinction
ratio when the incident angle of x rays to the analyzer is changed. The polarizer
and the analyzer are crossed at θ = 0 µrad.
The obtained extinction ratio is three digits larger than the target value. Fromthe measurement of the dependence against the azimuth angle, it is confirmed thatthe crystal plane is the same as the designed plane, which has a small eﬀect of MBR.
A reason other than MBR makes the extinction ratio worse. One candidate to makethe extinction ratio worse is the scattered x-ray by the polarizer. More precise
polishing of the polarizer (∼10 nm class roughness on the surface) is considered.

81

APPENDIX B. POLARIZER

82

X raysFigure B.1: Polarizer made of Si.

Extinction ratio

h1d_waku

10−6

10−7
− 2000 − 1500 − 1000 −500

05001000 1500 2000

Analyzer angle [µ rad]Figure B.2: Extinction ratio as a function of the analyzer position. The analyzer
position θ = 0 µrad corresponds to the situation that the analyzer and the polarizer
are in the crossed position.

Appendix C

List of symbols
Table C.1: List of main symbols used in this theses.
SymbolAc
DCP/Slit6
e
fXh
fXv
ℏ
IIV
I˜IV
nQED
nQED,sumnxraysnxrays,sum
N
P
S6l
S6u
tL
W
xCP
xL
yCP
yL
zX
α
θ

Attribution
Acceptance of the signal x rays
The speed of light in vacuum
Distance from the collision point to the Slit6
Electron mass
Horizontal XFEL profile at the collision point
Vertical XFEL profile at the collision point
Reduced Planck constantInteraction volume
Interaction volume considering the measured XFEL profile
The number of expected signal x rays
The sum of nQED in the timing window
The diﬀerence of the number of x rays between the collision data and the BG data
The sum of nxrays in the timing window
The number of x rays in the XFEL pulse
Interaction probability
Lower blade position of Slit6
Upper blade position of Slit6
Delay time of the laser pulse
Pulse energy of the laser
x coordinate at the collision point
Horizontal displacement of the laser pulse against the XFEL pulse
y coordinate at the collision point
Vertical displacement of the laser pulse against the XFEL pulse
Distance from the shaper to the collision point
Fine structural constantDiﬀraction angle against z-axis
continued on the next page...
83

APPENDIX C. LIST OF SYMBOLS

84

continued from the previous page...
SymbolAttribution
θx
Diﬀraction angle in the horizontal direction
θyDiﬀraction angle in the vertical directionµ0
The magnetic permeability of vacuum
τL
Pulse duration of the laser pulse
τX
Pulse duration of the XFEL pulseφ
Divergence of the XFEL beam
wLh
Horizontal beam size of the laser
wLv
Vertical beam size of the laser
wX0v
Minimum XFEL beam size
wXhHorizontal beam size of the XFEL
wXv
Vertical beam size of the XFELEnd.

Table C.2: List of abbreviations used in this theses.
Abbreviation
BG
DM
EH
FWHM
LH
ND
OAP
PD
RMS
ROI
SACLA
SCM
TM
TRM
VD
VP
WFS
XFEL

Long form
Background
Deformable mirror
Experimental hatch
Full width at half maximum
Laser hatch
Neutral density filter
Oﬀ axis parabolic mirror
Photo diode
Root mean square
Region of interesting
SPring-8 angstrom compact free electron laser
Screen monitor
Timing monitor
Total reflection mirror
Vacuum diﬀraction
Vacuum polarization
Wavefront sensor
X-ray free electron laserEnd.

Acknowledgements
I would like to express the deepest appreciation to my supervisor Prof. Shoji
Asai and my former supervisor Prof. Hiroshi Sakamoto for providing me with theopportunity of this work. I was supported by their encouragements and assistance.
I also wish to express my great appreciation to Prof. Toshio Namba for his
many guidance. He gave me a lot of comments and useful advice every time. My
aim is to create logic, slide and paper which do not need to be corrected by him.
I am thankful to Prof. Takayuki Yamazaki, Dr. Toshiaki Inada and Dr. Tomohiro Yamaji. Daily discussions and experiments with them and sincere supports
make me grow up as a researcher.
The experiment has been performed in cooperation with researchers of SPring8/SACLA. I would like to express my gratitude to Prof. Kenji Tamasaku, Prof.
Yoshiki Komura, Prof. Yuichi Inubushi, Prof. Tadashi Togashi and Prof. Toshinori
Yabuuchi for providing technical advice and supports to my experimental studies
at SACLA. I would like to thank Prof. Shigeki Owada, Dr. Ichiro Inoue, Dr. Taito
Osaka, Prof. Makina Yabashi and Prof. Tetsuya Ishikawa for useful discussions
about x-ray physics and optics. I gratefully thank all engineers for kind supports
to my experimental studies.
I would also like to thank Prof. Kentaro Kawai for collaborative research forthe development of the new x-ray optics. Thanks to him and his techniques, theshaper was created.
I also express my sincere gratitude to Prof. Felix Karbstein for theoretical
discussion. My research started with his paper.
I would like to thank Prof. Katsumi Midorikawa, Prof. Akira Ishida, Prof.
Yoshio Kamiya, Prof. Kenji Shu and Shusei Kamioka for useful discussion. I would
also like to thank all staﬀs and colleagues of the University of Tokyo for their kind
supports.
Finally, my family are my emotional supports. I really appreciate what they
have done for me. Thank you.

85

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