Search for Axion-like Particles
using Strong Pulsed Magnets at SPring-8
Ph. D. thesis

Toshiaki Inada

Department of Physics
Facalty of Science, The University of Tokyo
December 2015

Abstract
This thesis reports the first X-ray light shining through a wall (LSW) search foraxion-like particles (ALPs) using strong pulsed magnets. Using the LSW method,
photons are converted to ALPs in magnetic field and then re-converted from the
ALPs. The magnet system is a key technology in this search. A transportable
magnet system for high-repetition use has dedicatedly been developed. The experiment has been carried out at the BL19LXU beamline of SPring-8, which produces
the world’s strongest X-ray beams. During two days of net run time, four magnets
are operated at a mean peak field of 8.3 T and 5.7 T (the first and the second
pulse, respectively) with a pulse repetition of about 0.2 Hz. After a total of 27,676
pulses, no signal events are observed. A new limit on ALP-two-photon coupling
constant gaγγ is obtained as
gaγγ < 2.51 × 10−4 GeV−1
below∼ 0.1 eV at 95% C.L. This is the most stringent LSW limit around 0.1 eV
and rules out the possibility of ALP re-absorption in the Sun.

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Contents
1 Introduction
1.1 Axions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Origin: the strong CP problem . . . . . . . . . . . . . . . . .
1.1.2 Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Invisible axion model . . . . . . . . . . . . . . . . . . . . . . .
1.2 ALPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Searching for ALPs . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 LSW experiment and its history . . . . . . . . . . . . . . . .
1.3 Motivation of the terrestrial ALP search . . . . . . . . . . . . . . . .
1.3.1 General motivations . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Interests of X-ray terrestrial experiments . . . . . . . . . . .
1.4 Features of the experiment . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Pulsed magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Conventional magnets and banks . . . . . . . . . . . . . . . .
1.5.2 Pulsed magnets with a long field region . . . . . . . . . . . .
1.6 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . .

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2 Magnets and bank
2.1 Usage of words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Design of the magnets . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Coil structure and the Maxwell stress . . . . . . . . . . . . .
2.2.3 Eddy current and divided backups . . . . . . . . . . . . . . .
2.3 Basic performance . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Measurement of the field and the current . . . . . . . . . . .
2.3.2 Field eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Field map . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Heat loss and thermal time constant . . . . . . . . . . . . . .
2.3.5 Destruction and repetition field . . . . . . . . . . . . . . . . .
2.3.6 Durability test . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.7 Leakage field . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.8 Oscillation test . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.3.9 Summary of the basic performance . . . . . . . . . . . . . . .
Capacitor bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Principle of the capacitor bank . . . . . . . . . . . . . . . . .
2.4.2 Circuit and operation sequence . . . . . . . . . . . . . . . . .

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3 Setup and devices
3.1 Whole setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 OH: beamline components . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Summary of the beam property . . . . . . . . . . . . . . . . .
3.2.2 BL19LXU undulator . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Double crystal monochromator . . . . . . . . . . . . . . . . .
3.2.4 Double mirror . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Slits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 EH1: field generation system . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Control system . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Safety measures . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Base table and electrodes . . . . . . . . . . . . . . . . . . . .
3.3.4 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.5 Other devices and components . . . . . . . . . . . . . . . . .
3.4 EH2: detection system . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Summary of detector performance . . . . . . . . . . . . . . .
3.4.2 Shield and alignment . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 Energy resolution . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.4 Detection eﬃciency . . . . . . . . . . . . . . . . . . . . . . . .
3.4.5 Time resolution . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Intensity measurement . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Intensity measurement between data sets: PIN A . . . . . . .
3.5.2 Intensity monitor during the run: PIN B . . . . . . . . . . .

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4 Run and analysis
4.1 Beamtime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Procedure of measurement . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Summary of run . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Field distribution . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Event timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Constraining the coupling constant . . . . . . . . . . . . . . . . . . .
4.7 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.1 Small uncertainties . . . . . . . . . . . . . . . . . . . . . . . .
4.7.2 Temperature increase at thermal equilibrium . . . . . . . . .
4.7.3 Alignment of the magnets . . . . . . . . . . . . . . . . . . . .
4.8 Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Discussion and prospect
5.1 Comparison with previous LSW limits . . . . . . . . . . . . . . . . .
5.1.1 Laser LSW limits . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 An X-ray LSW limit . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Another terrestrial search . . . . . . . . . . . . . . . . . . . .
5.2 Physical significance of the result . . . . . . . . . . . . . . . . . . . .
5.2.1 Significance to the general motivation . . . . . . . . . . . . .
5.2.2 Significance to the interests of X-ray terrestrial experiments .
5.3 Upgrades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Improvements of magnet operation . . . . . . . . . . . . . . .
5.3.2 XFEL SACLA . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Expected total gain on gaγγ . . . . . . . . . . . . . . . . . . .

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6 Conclusion

99

Acknowledgements

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List of Figures
1.1
1.2
1.3
1.4
1.5

Bounds of invisible axion models between the axion-two-photon coupling constant and the axion mass . . . . . . . . . . . . . . . . . . . 4
Principal of LSW search . . . . . . . . . . . . . . . . . . . . . . . . . 7
Limits on the ALPtwo-photon coupling constant as a function of theparticle mass obtained by experimental searches . . . . . . . . . . . . 9
SPring-8 and SACLA . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Left: a picture of a conventional pulsed magnet, right: a picture ofa conventional capacitor bank . . . . . . . . . . . . . . . . . . . . . . 14

2.1
2.2
2.3

Schematic view of the magnet . . . . . . . . . . . . . . . . . . . . . .
Pictures of the magnet . . . . . . . . . . . . . . . . . . . . . . . . . .
Field eﬃciency with divided backup along with the beam path calculated with 3D finite element simulation . . . . . . . . . . . . . . .
2.4 Pickup coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Current transformer . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Typical shapes of the measured field and current with 2.75 kV . . .
2.7 Field-current ratio of the four magnets . . . . . . . . . . . . . . . . .
2.8 Configuration of the map measurement . . . . . . . . . . . . . . . . .
2.9 Measured map with diﬀerent configurations . . . . . . . . . . . . . .
2.10 Comparison of the measured map and the calculation of finite element simulation (ANSYS) . . . . . . . . . . . . . . . . . . . . . . . .
2.11 Measured map of the four magnet . . . . . . . . . . . . . . . . . . .
2.12 Relation among thermal parameters . . . . . . . . . . . . . . . . . .
2.13 Time development of the heat loss measured by changing durationof the repetition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14 Measured field and inductance of a weakly-backuped magnet . . . .
2.15 Measured magnitude of leakage field in three directions from thecenter of a prototype magnet . . . . . . . . . . . . . . . . . . . . . .
2.16 Output of the laser power meter during the oscillation test . . . . . .
2.17 Basic circuit of the capacitor bank . . . . . . . . . . . . . . . . . . .
2.18 Circuit diagram of the capacitor bank . . . . . . . . . . . . . . . . .
2.19 Measured time variation of the capacitor voltage with a shot repetition of 0.5 Hz at 1 kV . . . . . . . . . . . . . . . . . . . . . . . . . .
2.20 Whole picture of the bank . . . . . . . . . . . . . . . . . . . . . . . .
vii

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2.21 Lower floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.22 Upper floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1 Top view of the whole system . . . . . . . . . . . . . . . . . . . . . .
3.2 BL19LXU undulator . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Double crystal monochromator . . . . . . . . . . . . . . . . . . . . .
3.4 Bragg angle as a function of the X-ray energy . . . . . . . . . . . . .
3.5 Total reflection mirrors . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Four-jaw slits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Measured width of the beam . . . . . . . . . . . . . . . . . . . . . .
3.8 The first experimental hutch and the control panel . . . . . . . . . .
3.9 Mask test in a repetition mode . . . . . . . . . . . . . . . . . . . . .
3.10 Base table of the magnets . . . . . . . . . . . . . . . . . . . . . . . .
3.11 Terminal boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Central space below the CT . . . . . . . . . . . . . . . . . . . . . . .
3.13 Vessels of liquid nitrogen placed at the outside of EH1 . . . . . . . .
3.14 X-ray windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15 Germanium detector and its inner shield . . . . . . . . . . . . . . . .
3.16 Outer shield of the detector . . . . . . . . . . . . . . . . . . . . . . .
3.17 Measured background energy spectra . . . . . . . . . . . . . . . . . .
3.18 Measured resolution as a function of the energy . . . . . . . . . . . .
3.19 Measurement of the detection eﬃciency . . . . . . . . . . . . . . . .
3.20 Measurement of time resolution . . . . . . . . . . . . . . . . . . . . .
3.21 57 Co level diagram and geometry of the crystal electrodes . . . . . .
3.22 Calculation and measurements of the time spectra . . . . . . . . . .
3.23 Silicon PIN photodiode . . . . . . . . . . . . . . . . . . . . . . . . .
3.24 Absorption rate of the photodiode as a function of the X-ray energy
3.25 Another photodiode used to monitor the beam intensity at the shield

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4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

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Field distribution of a magnet . . . . . . . . . . . . . . . . . . . . . .
Change of field of the most downstream magnet . . . . . . . . . . . .
Time spectrum of all events . . . . . . . . . . . . . . . . . . . . . . .
Measured energy spectrum of all events . . . . . . . . . . . . . . . .
Current shape of a shot . . . . . . . . . . . . . . . . . . . . . . . . .
Field maps of the upstream and the downstream regions . . . . . . .
Ratio of the two currents measured by the CT . . . . . . . . . . . .
The field map of the transverse direction along the X-ray polarization
at the central cross section of the magnet (simulation) . . . . . . . .
4.9 Uncertainty from the deviation of the beam path . . . . . . . . . . .
4.10 Limit on gaγγ at 95% C.L. obtained by this search . . . . . . . . . .
5.1

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Diﬀerence of the connection between series and parallel . . . . . . . 97

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List of Tables
1.1
1.2

gaγγ dependence on experimental parameters . . . . . . . . . . . . .
Previous laser-LSW experiments . . . . . . . . . . . . . . . . . . . .

2.1
2.2
2.3

Specification of the magnet . . . . . . . . . . . . . . . . . . . . . . . 18
Specification of Pearson Model 1439 . . . . . . . . . . . . . . . . . . 26
Basic performance described in the previous sub-sections . . . . . . . 40

3.1
3.2

Beam property from the undulator . . . . . . . . . . . . . . . . . . . 51
Detector performance . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.1
4.2
4.3
4.4

Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters used to calculate the limit . . . . . . . . . . . . . . . . .
Circuit parameters obtained by fitting the current shapes . . . . . .
Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . .

5.1
5.2

Light source parameter of SACLA . . . . . . . . . . . . . . . . . . . 97
Expected gain factors of the future experiment at SACLA . . . . . . 97

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8

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Chapter 1

Introduction
This thesis describes a search for axion-like particles (ALPs). ALPs have a similar
property to that of axions. Axions are therefore introduced in the first place. Then
ALPs and their history of search using LSW method is described. The motivationof the experiment is then presented. After that, features of the experiment aredescribed. Among them, the use of pulsed magnets is a key technology, and they are
introduced in the following section. Finally the structure of this thesis is described.

1.1

Axions

The axion is one of the best motivated particles. It was conceived to solve a longstanding issue of the standard model, known as the “strong CP problem”. Thissection briefly describes its origin and property.

1.1.1

Origin: the strong CP problem

In the QCD Lagrangian, there is an explicitly CP violating term,
gs2
Gµν G̃aµν ,(1.1)
32π 2 awhere gs the strong coupling constant, Gaµν the gluon field strength tensor. andits dual of G̃aµν = 21 ϵµναβ Gαβa . θ is a CP violating parameter. There are no
theoretical preference to it; it can take any value of 0–2π. It is therefore natural toexpect it to be of order unity.
This parameter also gives neutrons a measurable value of its electric dipole
moment dn (nEDM). Experimentally, however, the nEDM is bounded to |dn | <2.9 × 10−26 e cm (90% C.L.) using polarized ultra-cold neutrons [1]. It corresponds
to
|dn |
θ=
< 5.6 × 10−11 .
(1.2)
5.2 × 10−16 e cm
This diﬀerence from the expected value of ∼1 is referred to as the strong CP
problem [2, 3].
Lθ = θ

1

2

1.1 Introduction
θ consists of two parameters,θ = θ + arg det M,(1.3)

where θ an angle decided by the QCD vacuum and M the quark mass matrix
accounting the weak interaction. Eq. (1.3) hence means that strong CP problem
also requires a fine-tuning of more than 1010 for the two independent interactionsof the strong and the weak force. A solution to this problem is therefore considered
to expand the standard model naturally.
The simplest extension of the standard model, providing a solution to the problem was first given by R. Peccei and H. Quinn [4, 5]. They proposed an additional
global chiral symmetry U(1)PQ , which is spontaneously broken in the early universe.
The breaking of U(1)PQ at the energy scale fa generate a pseudo Nambu-Goldstoneboson, the axion. To make the standard model Lagrangian invariant under U(1)PQ
symmetry, the new axion field a gives an additional term to the Lagrangian,a gs2
1
Gµν G̃aµν .
La = − ∂µ a ∂ µ a + Lint + ξ2
fa 32π 2 a(1.4)

The first and the second term account the kinetic energy of axions and their interactions, respectively. The third term describes a coupling of axions and gluons.
ξ is anomaly coeﬃcient and a model dependent parameter. The third term also
represents an eﬀective potential for the axion field. Its minimum occurs at thevacuum expectation value ⟨a⟩ = −θ fa /ξ and is written as
⟨
⟩
⟩
∂Veﬀ
ξ gs2 ⟨ µν
=−
G
G̃
.
(1.5)
aµν
a
∂a
fa 32π 2⟨a⟩=−θ fa /ξThus ⟨a⟩ dynamically cancels out the θ-term at the minimum and therefore provides
a solution to the strong CP problem.

1.1.2

Property

The second expansion of Veﬀ around its minimum gives the axion a mass⟩⟨ 2⟩
ξ gs2 ∂ ⟨ µν
∂ Veﬀ
2
=
−
G
G̃
.
ma =
aµν
a
∂a2
fa 32π 2 ∂a⟨a⟩=−θ fa /ξ

(1.6)

The mass is thus given by its gluon coupling. This calculation gives [6, 7]
√
mπ fπ
z
106 GeVma == 6.3 eV,
fa 1 + z
fa(1.7)

where mπ the pion mass, fπ its decay constant, and z = mu /md the quark mass
ratio between u and d. The axion thus directly acquires its mass by mixing with
π 0 , which occurs with the gluon coupling.

3

1.2 Introduction
The π 0 -mixing then induces another coupling of the axion to two photons
1Laγγ = − gaγγ Fµν F̃ µν a = gaγγ E · B a,
4

(1.8)

where Fµν is the electromagnetic field strength tensor, F̃ µν its dual, E · B the
product of the electric and the magnetic field. gaγγ is the axion-two-photon coupling
constant and is written as
α
Cγ ,
(1.9)
gaγγ =
2πfa
where α the fine structure constant. Cγ is a model dependent parameter is written
as
E
2 4+z
E
Cγ =
−
=
− 1.95 ,(1.10)
N
3 1+z
N
where E the electromagnetic anomaly and N the color anomaly.

1.1.3

Invisible axion modelInvisible axion models take fa larger than the electroweak scale. The axion hence
becomes lighter and interacts weakly with matter. There are two typical invisible
axion models.
KSVZ model
The Kim-Shfman-Vainshtein-Zakharov (KSVZ) model [8, 9] postulates that no leptons carry PQ charge. The charge is instead assigned to an exotic heavy quark.
The axion interacts with matter only through the gluon coupling and is therefore
referred to as “hadronic axion”. When the electric charge of this new quark istaken to be zero, the model gives E/N = 0.
DFSZ model
The Dine-Fischles-Srednicki-Zhitnitskii (DFSZ)) model [10, 11] postulates thatelectrons carry PQ charge. Since many grand unification theories (GUT) introduce this model, this model is referred to as a “GUT-embedded model”. The
model does not require any exotic quarks and takes E/N = 8/3.
The mass of the axion and its coupling to two photons are related by Eq. (1.7)
and Eq. (1.9) and are shown in Fig. 1.1. The two solid lines are the bounds of thetypical invisible models. As can be seen in Eq. (1.10), Cγ varies from its center
value of 1.95. The value expresses a model independent contribution, which comesfrom the π 0 -mixing. It is possible to cancel out Cγ by some artificial fine-tune of
E/N , however, it is natural to take Cγ as order unity. Typical invisible models
take Cγ as 0.07–7. This region is referred to as the “invisible band” and is also
shown in the figure with broken lines.

4

ga" " [GeV-1]

1.2 Introduction

10!7
10!8
10!9
10!10
10!11
10!12 !3
10

10!2

10!1

1

10

ma [eV]

Figure 1.1: Bounds of invisible axion models between the axion-two-photon coupling constant and the axion mass. The blue line is standard KSVZ model(E/N = 0), and the red line is DFSZ model (E/N = 8/3). The broken lines
show the region of typical invisible models with Cγ of 0.07–7, which is referred toas the “invisible band”.

1.2

ALPs

Despite of its strong theoretical motivation, the axion has not been observed up
to now. Therefore relatives of the axion have also intensively been searched in
the mass-coupling plane other than the typical invisible band; the mass and thecoupling are no longer bound. They are referred to as axion-like particles (ALPs).
This section describes its origin and reviews the history of ALP search.

1.2.1

Origin

ALPs arise from a general consideration of the physics beyond the standard model.
Most theories which go beyond the standard model have new symmetries, someof which are global. Any time such global symmetry is spontaneously broken, aNambu-Goldstone or a pseudo Nambu-Goldstone boson appears. Corresponding
scalar or pseudoscalar particles are referred to as ALPs. As examples of suchgeneral consideration, ALPs are predicted in supersymmetric theories [12], in string
theory [13, 14], and in conformal standard model [15]. ALPs thus originally include
both scalar and pseudoscalar cases, however, only the latter one is considered inthis thesis.
Quite generally, the new particle couples to two photons. The coupling is written as the same expression of Eq. (1.8) for the pseudoscalar case. Some literatures1.2 Introduction

5

distinctively use gAγγ as the ALP-two-photon coupling constant. Most of axion
searches, however, are also sensitive to ALPs. Thus sometimes the same notation
gaγγ is also used for ALPs, and it is followed here. Their mass and their coupling
to two photons are not related as it is in the case of the axion. They are hence
searched in a plane of the two independent parameters.

1.2.2

Searching for ALPs

There are two methods to seach ALPs experimentally. Both apply the same mechanism. The last expression of Eq. (1.8) induces photon-ALP conversion in an
external field. Here E is the incident photon field, and B is an external magnetic
field. This conversion is referred to as the Primakoﬀ eﬀect. The inverse process
also occurs and converts ALPs to outgoing photons in an external field. The two
methods are distinguished whether the γ → a conversion takes place on the earth
or not.

Astrophysical observations
Astrophysical observations have searched axions and ALPs from the Sun or in
our galactic halo. Their techniques are referred to as helioscope or haloscope,
respectively, both of which were proposed by Sikivie [16] in 1983. The helioscope
technique is applied to detect solar axions or ALPs with masses below 0.1–1 eV [17,18, 19, 20]. Crystal detectors are also used to search for solar axions and ALPs.
The a → γ conversion occurs in the electric field of the crystal lattice with the
Bragg condition [21, 22, 23, 24, 25] The haloscope technique is, on the other hand,applied to detect cold dark matter (CDM) axions or ALPs with masses around
1–10 µeV [26, 27, 28, 29].

Terrestrial experiments
Although a helioscope is not purely a laboratory experiment since they assume
ALP flux from the Sun. There seems to be nothing wrong with it. After all solar
neutrinos, which have also produced in the core of the Sun, are detected with its
measured number consistent with the solar model, However it is desirable to haveexperiments in which both the production and the detection of ALPs are carriedout on the earth. An experiment on this scheme was first proposed in 1982 [30]in the context of a search for hidden photons. It is now referred to as the “Light
Shining through a Wall” (LSW) [31]. In the LSW experiment, a terrestrial lightsource is prepared, which is an alternative to the Sun or the galactic halo.

6

1.2.3

1.2 Introduction

LSW experiment and its history

Principle
Here the principle of the LSW method is described (for detailed theoretical discussions, see Ref. [32, 33]). Figure 1.2 shows principle of the LSW experiment.
A high-flux beam from a light source goes through an external field of a magnet.
The region works as γ → a conversion region. Here only pseudoscalar particles are
considered as ALPs. From Eq. (1.8) the external field needs to be parallel to theelectric field, or polarization, of the photon. Most of the unconverted photons are
dumped at a shield placed downstream of the magnet. Only ALPs pass throughthe shield due to their weak coupling to the matter. Behind the shield, the inverse
process re-converts the ALPs to photons in the second field of another magnet.
There is no energy loss in these conversions, and the regenerated photons havethe same energy of the incident photons. Detection of ALPs is claimed whether
the events of the regenerated photons surpass the background counts at a detector
placed downstream of the second magnet.
The expected signal count N is expressed as [34]N = η Pa→γ Pγ→a F ttot ,(1.11)

where η the detector eﬃciency, F the photon flux in time, and ttot the total livetimeof measurement. The probability of Primakoﬀ conversion is written as
Pa→γ = Pγ→a =

(g

aγγ

)2

2

√

ω
ω 2 − m2a∫ L

2

B(z) eiqz

dz ,(1.12)

0where ω the photon energy, B(z) the field map along the beam direction of z, andL the field length. q is the momentum transfer to the magnetic field and is writtenasm2γ − m2a(1.13)
q=2ω
with the eﬀective photon mass of
√
√
4παne
Z
= 28.9
ρ,
mγ ≃
me
A

(1.14)

where α the fine structure constant, ne the number density of electrons in thegas, and me the electron mass. The second expression is more convenient for the
calculation of mγ with Z the atomic number of the gas, A its atomic mass, and ρ
the gas density in g cm−3 .
The approximation of uniform field (B(z) = B) makes Eq. (1.12) to(gaγγ BL2)2√

ω

sin qL2ω 2 − m2a

qL
2

2

.

(1.15)

7

1.2 Introduction

1$",23&.$(%(/!

4!

4!

.$(%(/!

0!.'!
!"#$%&'()*+,&-,%,+%(*!
1!

1!

Figure 1.2: Principal of LSW search.
If q is small so that the oscillation length q −1 becomes suﬃciently larger than
L (qL/2 ≪ 1), sin (qL/2)/ (qL/2) becomes unity. In vacuum, where mγ ≃ 0,
this corresponds to a low mass region of ma . As can be seen in Eq. (1.15), gaγγ
dependence on ma vanishes for the mass region.
Parameter dependence of gaγγ for the low mass region is summarized in Tab. 1.1.
A major contribution comes from the performance of magnets, which is expressedas the product of their field and their length. The magnet needs to produce atransverse field along the polarization of the incident photon. This means that it is
not useful to apply a conventional solenoid placed with its axis along the directionof the beam. Thus dipole magnets are typically used in LSW search. To obtain alarger field-length product, racetrack dipoles are usually selected.
Compared with its strong dependence on the magnet performance, gaγγ weakly
depends on the other parameters. These contributions are at most fourth root of
the magnet performance. This feature comes from the fact that the LSW method
uses the two Primakoﬀ conversions on the earth; before and after the shield. The
probability of each conversion is proportional to the square of (gaγγ B L).
Parameter
Magnets (field-length product)
Photon flux
Detector eﬃciency
Background count rate
Measurement timegaγγ dependence(factorial)
−1
−1/4
−1/4
+1/8
−1/8 (−1/4)

Table 1.1: gaγγ dependence on experimental parameters for the low ALP mass.
The bracketed value of measurement time corresponds to the case of observing anull count.

8

1.3 Introduction

History
The first LSW experiment to search for ALPs was proposed in 1985 [35, 36]. In
early 1990s, this was realized by BFRT collaboration using an optical laser witha Fabry Perot cavity and superconducting dipoles of Brookhaven National Laboratory. Since then many experiments have been carried out to detect any signalof ALPs with every occasion of upgrades in the performance of optics or magnets.
They are summarized in Tab. 1.2. All of them use a laser as their light source.
Optical lasers can easily produce large photon flux by itself or using a Fabry Perotcavity. Pulsed lasers can also produce high intensity photons and are used in the experiments. In terms of magnets, which is the key factor of the LSW experiments,
racetrack dipoles are typically used. They are commonly used as bending magnets in a circular accelerator. Due to the availability of spare or decommissioned
magnets and the convenience of their transportation, most experiments have been
carried out in the site of an accelerator. Their best limits are obtained by the ALPS
and the OSQAR experiment using a HERA magnet at DESY [37] and two LHC
magnets at CERN [38]. respectively. They now can be seen as two benchmarks of
the LSW limits.
In addition to these optical searches, experiments with other light sources haverecently been carried out to cover the wider range of the ALP mass. The first
implementation of ALP search using a microwave cavity can be found in Ref. [39].
Another pioneering search using X-ray beams is performed by Battesti et al. [40] as
the BMV project. They used 50.2 keV and 90.7 keV X-ray beams of synchrotron
radiation at ESRF (European Synchrotron Radiation Facility). These energies are
more than 104 higher than the energy of the previous laser experiments. Theirlimit on gaγγ has thus extended the previous limits to higher mass region, and isshown in Fig. 1.3.
Experiment

Site

Year

ω
[eV]

β

F
[photon/s]

B
[T]

L
[m]

BFRT
BMV

Brookhaven
LULI

1992 [41], 1993 [42]2007 [43], 2008 [44]

2.5
1.2

100
1

3.7
12.3

4.4
0.4

GammeV

Fermilab

2008 [45]

2.3

1

5

3

LIPSS
ALPS
OSQAR

JLab
DESY
CERN

2008 [46], 2009 [47]2009 [48], 2010 [37]2008 [49], 2015 [38]

1.0
2.3
2.3

1
300
1

7.6 × 1020
8 × 1021(14 shots)
4 × 1017(3600 shots)
1.1 × 1021
3.2 × 1021
5.0 × 1019

1.7
5
9

1
4.2
14.3

Table 1.2: Previous laser-LSW experiments, where ω the photon energy, β thebuilding-up factor of a Fabry Perot cavity, F the photon flux taking β into account,
B the field, and L its length of one side. The number in the bracket shows thetotal shots of a pulsed light source.

1.3 Introduction

9

Figure 1.3: Limits on the ALPtwo-photon coupling constant as a function of theparticle mass obtained by experimental searches (the figure is from Ref. [40]). In
the legend, “Our experiment” is the previous X-ray LSW search at ESRF [40],“ALPS” is a laser LSW search at DESY [37], “Microwave cavity” is searches forcold dark matter axions [26, 27, 28, 29], “CAST” is a search for solar axions [20],and “Axion models” are described in Sec. 1.1.3.

1.3

Motivation of the terrestrial ALP searchThis experiment is the second LSW search carried out at a synchrotron radiation
facility. Using the world’s strongest X-ray beams and multiple pulsed magnets
with a racetrack shape provides a better sensitivity for the ALP mass region below∼ 10−1 eV. Figure 1.3 [40] shows previous limits on gaγγ as a function of ma . X-ray
source is suited to search for this mass region. This region also corresponds to an
extremely-higher mass region of the laser-LSW limits, where dumping oscillationof the limit dominates. Therefore the result obtained by X-ray experiments is also
considered to have significant information around 10−2 eV.
This section describes the motivation for the ALP search. First, motivations
which are common to all ALP searches are described. Then a couple of interests

10

1.3 Introduction

which are peculiar to X-ray terrestrial experiments are pointed out.

1.3.1

General motivations

Since the mass and the coupling of ALPs are not bound to the invisible band, they
can be applied to explain long standing puzzles of cosmology and astrophysics.
For example, they might become alternative candidates for dark matter [50, 51],
explain the universe transparency to very high energy photons (>100 GeV) [52],the anomalous white dwarf cooling [53], or the recent excess of a 3.6 keV line fromgalaxy clusters [54]. These are the common motivations of all the terrestrial or
extraterrestrial ALP searches. They push experiments to an unsearched parameter
space in the mass-coupling plane.
There is also one remark that it is better not to stick too much to the mass
relation of Eq. (1.7). As pointed out in many literatures [55, 56, 57], it could nolonger be valid even in an axion model where the axion mass has other exotic
contributions, such as gravity.

1.3.2

Interests of X-ray terrestrial experiments

Another X-ray search other than astrophysical observations
In the ALP mass-coupling plane, there are stringent bounds obtained by the astrophysical observations [17, 18, ?]. There have been so much arguments about thepossibility of evading these astrophysical bounds. Most of them postulate somemodels and new physics at low energies [58, 59, 60, 61, 62]. Some of them were,
however, conceived to evade the contrary between these bounds and the PVLAS
result [63]. The PVLAS result was ruled out later on by other LSW experiments
and its signal was found to be an artifact of the instruments.
Although evading these astrophysical bounds are not an easy task, it is clearthat they inevitably have some model dependencies. Apart from those previous
arguments, it seems to be desirable from the scientific point of view to have other
X-ray searches using a diﬀerent method. They are considered to have a goodcomplementary relation with the astrophysical observations.
Possible solutions to some solar problems
The standard solar model seems to be reliable and agrees with helioseismologicaland neutrino observations. However there are still many problems with the Sun.
One of them is the well-known “solar coronal heating problem”; the outer layeror the solar surface is hotter than its inner layer. As the world’s consensus, thisanomalous heat transportation is considered to be connected with solar magnetic
activity.
Recently a striking possibility is pointed out by Zioutas et al. [64] proposing an
ALP with its mass of 10–20 meV. A rapid change of the solar plasma density in
its radial direction satisfies the resonance condition of ma = ωpl (ωpl the plasma1.4 Introduction

11

frequency) at a depth of ∼400 km from its surface. The solar axions are re-converted
to X rays with the resonance in the strong solar magnetism. The re-converted X
rays go through down-comptonization and deposit their energy while propagating to
the surface. If the ALP mass is taken as 10–20 meV, the a → γ conversion restoresthe coherence inside ≲400 km, and thus the anomalous heat transportation could
become possible. Furthermore, this mechanism could also explain another problem
with the Sun. Expected X-ray spectra reconstructed with this ALP contributionagree with the measured spectra.
In this case, the ALP flux from the Sun could become smaller and they could
escape from the detection of the astrophysical observations. This intriguing scenario
gives another interest to terrestrial X-ray searches.
Re-absorption in the Sun
Apart from the previous argument, which assumes some models and the ALP
mass, re-absorption of the solar ALPs in the Sun was considered long time ago (seelike [65]). This possibility seems to take place with a very strong ALP coupling to
two photons of gaγγ ∼ 9 × 10−4 GeV−1 . It is more than 107 times larger than theastrophysical bounds, and such a large gaγγ is not preferred by considerations of thesolar age and the helioseismology [66]. These observations and considerations arequite reliable, and therefore the possibility of the re-absorption has been naturally
excluded.
On the other hand, one question still remains; has it been ruled out experimentally? The previous X-ray LSW search has not ruled out gaγγ ∼ 9 × 10−4 GeV−1 ,and strictly speaking, any terrestrial experiment has not excluded this extraordinary possibility yet. The reason is quite simple since there are only two powerful
X-ray sources available to us. One is the Sun, and the other is synchrotron light.
The experimental exclusion of this possibility is hence possible only by using astrong X-ray source and strong magnets.
The X-ray LSW experiment using synchrotron light was first proposed in 2006 [67,68] and was realized in 2010 [40]. Although its photon flux is smaller than that of
optical lasers, using X rays is one of the best way to increase the parameter space in
the ALP mass-coupling plane. As described above, it also helps and compensates
the astrophysical observations.

1.4

Features of the experimentSignificance of this experiment
In this thesis, another X-ray LSW experiment is described. An X-ray LSW experiment is carried out in a synchrotron radiation facility. As radiation control,
setup of the experiment has to be contained in an experimental hutch, and humanbodies are kept out from the hutch while the beam is on. A hutch typically has an

12

1.4 Introduction!"#$%&'(!

)*+,-.!/0,/1!
2,34,)5!
Figure 1.4: SPring-8 and SACLA
inner width of 3–4 m along the beam axis, and this restricts the space available tomagnets. Large bending magnets used in previous LSW experiments are therefore
not usable, and small magnets are required.
Recently, a new X-ray source, an Free Electron Laser (FEL), has become available. The world’s second XFEL, SACLA (SPring-8 Angstrom Compact Free Electron Laser), has started its operation since 2013. It is located next to SPring-8(Fig.1.4). It outputs pulsed X rays with one of the world’s strongest peak intensities. If pulsed beam is used as light source of an LSW experiment, DC magnets
are not necessarily required. Instead, strong pulsed-field which coincides with the
X ray gives better sensitivity to gaγγ . This pulsed field is generated by a pulsed
magnet. It has a typical size of 0.1–1 m and satisfies the restriction of hutch space.
A long field is obtained by placing many magnets along the beam axis. In thisthesis, combination of pulsed magnets and pulsed beam from SACLA is consideredas the final goal of X-ray LSW experiments.
A typical beamtime assigned at SACLA is 2.5 days. This includes a time for
setup and carry-out of the system from a hutch. They have to be minimized toobtain a suﬃcient time for measurement, Moreover, since SACLA is a new device,
there are many applications of experiments, and obtaining a beamtime is highly
competitive. Therefore, feasibility of the experiment has to be shown in advanceto the one at SACLA. This demonstration is the theme of this thesis and is carriedout using DC beam from SPring-8. Although DC beam gives a better sensitivity
to gaγγ when it is used with DC magnets, pulsed magnets are used with DC beamin this thesis for this demonstration. Nevertheless, this experiment has the best
sensitivity ever to gaγγ around 0.1 eV as an LSW experiment.
Features
The system used in this experiment has totally diﬀerent features from the previous
searches:• strong pulsed magnets with:

1.5 Introduction

13– unique design– high field eﬃciency– high repetition– high durability• transportable capacitor bank with high repetition use• the world’s strongest DC X-ray beam from a long undulator• the first LSW search using multiple magnets for each side of the shield
Among them, the pulsed magnets play a key role in the experiment. The use of
pulsed magnets has not been decided from the beginning. In fact it has been taken
about a year for the selection of the magnet. Careful investigations have been
carried out for each possibility from water-cooling iron core dipoles to superconducting ones. Then a conclusion has been reached that only pulsed magnets havea potential of producing stronger field by far than that of magnets used in previous
LSW searches. As an example, peak field of 85.8 T has been obtained by Kindo etal. [69] with simple structure of single solenoid.
On the other hand, length of the field is also an important factor. Previous
searches used bending magnets of an accelerator with a length of ∼10 m. There
are many proposals for the “next generation” LSW search [34, 70]. If the previous
LSW searches are referred to as the first generation, the key feature of the second
generation setup is to use multiple magnets to obtain the long field. As an example,
21 magnets of 5 T×8.8 m each are planned to be used in the ALPSII experiment [70]The total length of the setup is expected to be ∼200 m. Up to now, any LSW
experiments have not used multiple magnets for each side of the shield to obtain alarge length, though it is a key feature of the next generation LSW experiment. In
this thesis, it is tried to demonstrate the use of multiple magnets for each side of
the shield, which is the first great step toward the future LSW searches.

1.5

Pulsed magnets

1.5.1

Conventional magnets and banks

Pulsed magnets [71] are used to produce stronger field which cannot be obtainedby DC magnets. They are divided into two categories. One is non-destructive
magnets producing field below 100 T with pulse duration in the range of 1 ms–1 s.
The other one produces field above 100 T with pulse duration of order microsecond
due to self-destruction of its coil. The magnet concerned in this experiment is
non-destructive type.
During the field generation, magnets are adiabatically heated up by strong
pulsed current. The pulse width is determined by the inductance of a magnet andcapacitance of a bank, which stores electric energy. To increase the heat capacity
and reduce the resistance, magnets are cooled down with liquid nitrogen.

14

1.6 Introduction!!""#$$!

Figure 1.5: Left: A picture of a conventional pulsed magnet [72]. The inner coil isbackuped with a maraging steel ring, and its outer diameter is typically ∼200 mm.
Right: a picture of a conventional capacitor bank of 500 kJ at SPring-8 BL19LXU.
Figure 1.5 shows pictures of a conventional pulsed magnet with solenoid structure and of a capacitor bank. High-density fluxes generated in the bore repulse
with each other and cause outgoing pressure to the coil. This stress is referred toas the “Maxwell stress” and is proportional to the square of the field. It becomes
4 GPa at 100 T. The maximum field, or destruction field, is determined by themechanical strength of the wire and the backup metal used to reinforce the barecoil.
The bank shown in the right picture is a typical capacitor bank of 500 kJ locatedoutside of SPring-8 BL19LXU. Although most pulsed magnets are portable since
they are not so large, a bank is generally fixed in a site of experiment or in alaboratory. This limits the possibility of using pulsed magnets in many experiments.
One of the key works is to make a transportable bank. If a field generation
system is fixed, a light source must be portable to realize the LSW setup. Thisis one of main reasons why many previous searches have used a laser as a lightsource. On the other hand, if the field generation system becomes transportable,
it widens the possibility of many experiments. In the case of LSW searches, it
becomes possible to use various types of light sources, which are fixed in a facility
or in a laboratory. As the first example, an LSW search using an X-ray source isdemonstrated in this thesis.

1.5.2

Pulsed magnets with a long field region

The length of the field is another key factor of LSW searches. A unique design
which produces transverse pulsed field over a long range can be found in Ref. [73].
This dipole magnet has a structure with two racetrack coils crossing at its body
center. It produces peak field of 14 T with the body length of 480 mm.

1.6 Introduction

1.6

15

Organization of the thesis

This thesis is organized as follows.
Chaper 2 describes the design and the study of the magnets in detail. The
transportable capacitor bank is also explained there. Then the setup and devices
used in the experiment is written in Chapter 3. In Chapter 4, data acquisition runs
and the analysis are described. The results and future prospects are discussed in
Chapter 5. Finally this thesis is concluded in Chapter 6.

16

1.6 Introduction

Chapter 2

Magnets and bank
Magnets play a key role in LSW experiments. The largest contribution to thesensitivity on gaγγ comes from the field-length product of the magnet. Strong andlong fields are hence required to improve the sensitivity. To achieve this, pulsed
magnets are selected from many other types of magnets. The magnets used in thissearch are dedicatedly developed for the X-ray LSW experiment.
In this chapter, definitions of words are shown in the first place. The design andthe performance of the magnets are then described in detail. In order to provide
pulsed current to the magnet, a capacitor bank is also needed. The rest of thischapter explains the design and the operation sequence of the bank. It is also
dedicatedly developed along with the magnets.

2.1

Usage of words

First, usage of words from this chapter is mentioned:• field: always means magnetic field, and also means peak field of a pulse except
as otherwise noted. Moreover, it represents the field at the center of themagnet for the most cases.
• pulse: unit of a pulsed field with a shape of half-sinusoidal wave.
• shot: unit cycle of a bank operation; a shot contains one pulse in the “single
pulse mode”, whereas it contains two pulses in the “repetition mode”.
• heat loss: energy loss of a shot, expressed in Joule• heating: heat loss × shot repetition, expressed in W
17

18

2.2 Magnets and bank

2.2

Design of the magnets

2.2.1

Specification

Table 2.1 shows specification of the magnet. The coil is wound with a wire, which
has a cross section of 1 mm×3 mm rectangle. Copper is selected as the materialof the wire since it has a small resistance at a temperature of 77 K. The coil has
a shape of single racetrack. The straight section of the racetrack has a lengthof 200 mm. The length is decided from the feasibility of coil winding. A beam
pipe diagonally passes through the center of the magnet with an angle of 2.75◦ .
A small diameter of the pipe contributes to the decrease of the field volume andthus increases the field eﬃciency characterized by field-current ratio. On the other
hand, too small diameter requires a technique of precise alignment. A pipe withan outer diameter of 1/4 inch and a thickness of 0.5 mm is used for the beam path.
Body length of the magnet becomes 350 mm after enclosing the coil with backup
metals. Its weight is 16 kg. 15 turns of the wire gives its inductance and resistanceof 40 µH and 23 mΩ, respectively at 750 Hz.
Parameter
Wire
Coil shape
Length of straight section
Number of turns
Pipe
Pipe tilting angle
Body length
WeightResistanceInductanceValue
Cu (1 mm×3 mm)single racetrack
200 mm15
ϕ1/4 inch (=6.4 mm), t0.5 mm
2.75◦∼350 mm
16 kg
9 mΩ @ DC
23 mΩ @ 750 Hz
40 µH @ 750 Hz

Table 2.1: Specification of the magnet
Development of magnets is a series of production and destruction. It has taken
nearly two years to fix the design of the magnet suited to the high-repetition use.
So far a total of about 30 magnets have been produced and tested. Although theirdesign are not still completely optimized and are still on the way of optimization,
seven magnets have been produced with the same structure for this experiment.
The first produced magnet, referred to as magnet1, is used to test its durability
for many shots before the experiment. Four of them, magnet2-magnet5, are usedin the experiment. The rest two, magnet6 and magnet7, are reserved as spares incase of destruction.

2.2 Magnets and bank

2.2.2

19

Coil structure and the Maxwell stress

Figure 2.1 shows a schematic view of the magnet. It has a simple structure of
single coil. X-ray beams diagonally pass through the center of the magnet. They
are polarized along the horizontal direction. The magnet therefore stands at rightangles so as to produce parallel field to the polarization of the X rays.
The reason of using the single-coil structure comes from the Maxwell stress.
Some early prototypes have a typical dipole structure. In terms of field uniformity,
the dipole structure is more preferred than the single-coil one. Moreover, racetrack
dipoles are commonly used as bending magnets in a circular accelerator. Miniatureversion of such a magnet is thus easily conceivable from a sense of particle physics.
There is however critical defect in this dipole structure. To improve the fieldeﬃciency, compactification of the field volume is necessary. The beam path, on theother hand, requires a suﬃcient diameter by taking into account the beam size andmargin of arraignment. When the thickness of the support material is not enough,mechanical strength around the hole becomes weaker. The Maxwell stress causes
an attracting force between the dipole coils. It acts as a collapsing force to thebeam hole. As an example, one prototype has a hole diameter of 3 mm. Both theinner width of the coil and the distance between the poles are taken to be 4.5 mm.
The hole has been collapsed with 9 T at the center of the magnet. The Maxwell
stress scales to the square of the field. Field generation of, for example, 20 T hence
requires more than 4 times larger mechanical strength. Thickness around the hole
contributes to an increase of this strength. This however severely degrades the fieldeﬃciency. As a countermeasure, the single-coil structure is selected. This structure
avoids the attracting force which appears in the dipole structure. In exchange, thisstructure has bad uniformity and symmetry due to the diagonal beam pipe crossing
the center of the coil.

2.2.3

Eddy current and divided backups

Figure 2.2 shows pictures of the magnet. The top figure is the bare coil woundaround a bobbin. The straight section of the coil has a length of 200 mm. Cu wirewith cross section of 1 mm×3 mm is used for the coil winding. The resistance of Cu
becomes 1/8 when it is cooled with liquid nitrogen. Cu wire therefore has a good
property of small heat loss. The wire is coated with a half-wrapped dielectric tapeof polyimide. It is tightly wound around the GFRP (glass-fiber reinforced plastics)
bobbin with 15 turns. The GFRP material is commonly used as a coil bobbin ofa pulsed magnet. The bobbin has a diagonal hole with a crossing angle of 2.75◦ .
The hole diameter is 1/4 inch (6.4 mm). A stainless-steel pipe with a thickness of
0.5 mm passes through the hole.
The bottom figure shows the fully backuped magnet. The bare coil is backupedwith 20 divisions of stainless-steel metal. It is then compressed in the longitudinal
direction by two thick plates with M20 bolts and nuts. The total body length isabout 350 mm. Its weight is 16 kg.

20

2.2 Magnets and bankFigure 2.1: Schematic view of the magnet with simple structure of a single coil.
X-ray beams diagonally pass through the center of the magnet. They are polarizedalong horizontal direction. The magnet therefore stands at right angles so as toproduce parallel field to the polarization of the X rays.

2.3 Magnets and bank21

The use of the divided backups comes from two reasons. One is eddy current
which runs in the backup metal. For some early prototypes, a single backup which
also has a racetrack shape and fits to the outer surface of the bare coil is used. The
field eﬃciency of these magnets was measured to be significantly smaller by ∼15%
than that without the backup. The reason has been found to be the cancellationof field by eddy current running in the backup metal. As a countermeasure, thebackup is divided into pieces of metals. They are separated with each other using
dielectric sheets to reduce the volume of a single metal. Figure 2.3 shows fieldeﬃciency along with the beam path calculated with 3D finite element simulation.
The colored lines show the number of divisions: three (red), seven (blue), 19 (black)and 41 (magenta). Increasing the number of divisions clearly contributes to thedecrease of the field cancellation from eddy current.
The second reason is the mechanical strength of the backup. The single backupof this prototype is deformed by expansion of the coil at ∼10 T due to the Maxwell
stress. This deformation comes from the fact that straight section of the backup
receives all of the coil expansion pressure. The resulting stress concentrates on thecorner sections of the backup, which connect the straight and the round sections.
This problem is also avoided by changing the single metal into pieces. The expansion pressure of the coil is distributed to each division. The local concentration of
the whole stress thus does not occur.

2.3

Basic performanceThis section describes basic performance of the magnet. The performance is characterized by the following items:• field eﬃciency• field map along the beam path• heat loss
• thermal time constant• leakage field• destruction field• repetition field
Before the description of each items, the way of measuring of the field and thecurrent, which are common to all measurements, is explained. In the following
measurements, capacitance of the bank is set to 1.5 mF except as otherwise noted.

22

2.3 Magnets and bank!""#$$!

!""#$$!

Figure 2.2: Pictures of the magnet. Top: a bare coil of Cu wire wound arounda GFRP bobbin. Its straight section has a length of 200 mm. The beam pipe
diagonally passes through the center of the coil. Bottom: the fully backupedmagnet. The bare coil is backuped with 20 divisions of stainless-steel metal and iscompressed in the longitudinal direction by two thick plates with M20 bolts and
nuts.

23

B/I (T/kA)

2.3 Magnets and bank

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-150

-100

-50

0

50

100

150

Position (mm)Figure 2.3: Field eﬃciency with divided backup along with the beam path calculated with 3D finite element simulation. The colored lines show the number ofdivisions: three (red), seven (blue), 19 (black) and 41 (magenta). The increase of
the divisions clearly contributes to the decrease of the field cancellation from eddy
current.

24

2.3.1

2.3 Magnets and bankMeasurement of the field and the current

Field
The field is measured with a pickup coil. Figure 2.4 shows a picture and a schematic
view of the pickup coil. The field is measured by inserting the small coil along thebeam path. The wire is made of Cu core (ϕ0.1 mm) coated with enamel (t150µm) and is wound around a GFRP rod (ϕ1.5 mm) with five turns. The read line istwisted to cancel out an induced voltage from the field. In order to detect transverse
field, its head is cut oﬀ and is glued at right angles to the rod.
The pickup coil is produced and calibrated with the following procedure. First,
a coil before the cut-oﬀ, which is just wound around a rod, is calibrated using
a solenoid pulsed magnet with a large bore diameter of ∼10 cm. The large-bore
magnet is used due to its good uniformity of the field. The absolute value of the
field generated in the magnet is obtained by using another well-calibrated pickup
coil, a master coil, at the same time. Precise calibration of the master coil has been
carried out by measuring field from spin-flip transition of an anti-ferromagnetism.
In order to know the individual diﬀerence, two coils have been calibrated in thelarge-bore magnet with the mater coil. The diﬀerence is 0.6% and is relatively agood result for such a small structure This calibration procedure using the largebore solenoid has been carried out at IMSL, Kashiwa.
After that, one of the calibrated small coils is cut oﬀ at its head and is glued
at right angles to the previous rod. This picture is shown at the top of Fig. 2.4.
Misalignment of the gluing angle gives a measured field reduced by a cosine factor.
This means that if accuracy of the gluing is ten degrees, the field is conservatively
measured to be less by only 1.5%.
To measure the field at the center of the pipe, the head of the pickup coil isembedded into a GFRP centering. The bottom of Fig. 2.4 shows its schematic view
as well as its picture. Measured field changes with a rotation of the coil around
its long GFRP rod. The rotation is therefore always adjusted to the angle, which
maximize the measured field.
Current
Current is measured with a commercial current transformer (CT, Pearson Model
14239). Figure 2.5) shows its picture. It outputs a voltage proportional to thecurrent passing through the hole. The input current and the output voltage areelectrically isolated. Its sensitivity is 1 V/kA, and the maximum peak current is
500 kA. Cut-oﬀ frequencies are 1.0 Hz and 1.2 MHz. Its specification is summarizedin Tab. 2.2.
Shapes of field and current
Figure 2.6 shows a typical shape of the field and of the current with a charged
voltage of 2.75 kV. A raw signal of a pickup coil is the induced voltage of dΦ/dt.

25

2.3 Magnets and bank!"#$%&'(%)*+,-%../!

0123'&%415(%)-678&269':;%5&'82(%5%*+,-6..6&'(/! <:&19='2%'>%?1;(!

D15.%E:E1!
B1271&:2C!

@.A1((1(%415(!

Figure 2.4: Pickup coil. Top: Cu wire (ϕ0.1 mm) coated with enamel (t150 µm)
is wound around a GFRP rod (ϕ1.5 mm) with five turns. Bottom: a centering
used to measure the field at the center of the pipe. The head of the pickup coil isembedded into the GFRP centering.

!"#$%&'()!

Figure 2.5: Current transformer (Pearson Model 14239). It outputs a voltage
proportional to the current passing through the hole. The input current and theoutput voltage are electrically isolated.

26

2.3 Magnets and bank
Parameter

Value

Sensitivity
Output resistance
Maximum peak current
Maximum rms current
Current-rise productLow frequency 3 dB cut-oﬀ
High frequency 3 dB cut-oﬀ

1 V/kA50 Ω
500 kA
2.5 kA
75 A·s
1.0 Hz
1.2 MHz

Table 2.2: Specification of Pearson Model 1439
The field shape is obtained by integrating the the raw signal. Absolute value ofthe field is scaled with the calibration coeﬃcient described above. Current shape isalso measured with the CT and it agrees with the field shape. The current shapeis a half sinusoidal pulse with its frequency determined by the LC resonance of thecoil inductance L and the bank capacitance C. The frequency becomes about 750
Hz, which corresponds to a pulse width of 0.67 ms. If the two magnets are seriallyconnected, the total inductance doubles, and the pulse width becomes about 1 ms.

2.3.2

Field eﬃciency

Field eﬃciency is expressed by field-current ratio. The peak values of the fieldand current are used for this ratio. Figure 2.7 shows measured field and the fieldcurrent ratio of four magnets at the center of their beam path. All the magnets
reach around 9 T with a charged voltage of 2.75 kV. The red line shows a meanvalue of four measurements from 1.5 kV to 2.75 kV, which correspond to the field
range of ∼5–9 T. This region covers the√most of the field produced in the run(see Fig. 4.1). Note that during the run, 2-time-higher voltages around 3.5–4.00
kV are applied to two magnets, which are serially connected (Fig. 3.10). Their
total inductance becomes twice as much as that of each. From the relation of
LI2 /2 = CV2 /2, the measurements for single magnet in Fig. 2.7 provides
the same√
range of current as the run. The field therefore reaches 9 T with a 2-time-smaller
voltage than 3.5–4.00 kV. The mean values are used in the analysis in Chapter 4.

2.3.3

Field map

Field map is measured along the beam path. Figure 2.8 shows a schematic view ofthe measurement. The map is measured with both the position and the directionof the magnet unchanged. The field direction is shown with a black arrow. There
are two directions to insert a pickup coil into the pipe. Here the the electrode sideis defined as “back”, and the other as “front”. The beam direction is taken as z
axis with its origin at the center of the magnet. The z < 0 region corresponds tothe front side and z > 0 to the back side. When a positive field is detected by27

voltage (for dB/dt) [V]

2.3 Magnets and bank

0.6
0.4
0.2
0
-0.2
-0.4
0.5

1

1.5

2

2.5

B [T]

time [ms]

10
8
6
4
2
0
0.5

1

1.5

2

2.5

I [kA]

time [ms]

16
14
12
10
8
6
4
2
0
0.5

1

1.5

2

2.5

time [ms]Figure 2.6: Typical shapes of the measured field and current with 2.75 kV. Top: araw signal of the pickup coil, which is an induced voltage of dΦ/dt. Middle: thefield shape obtained by an integral of the raw signal. Bottom: the current shapemeasured with the CT.

28

2.3 Magnets and bank

9
8
7
6
5
4
3
2
1
0
0

B/I [T/kA]

B [T]!2 / ndf

4.397e-05 / 3

p00.5846 ! 0.001914

0.592
0.59
0.588
0.586
0.584
0.582
0.58

1000

2000

3000
Vc [V]

0

1000

2000

3000
Vc [V]

9
8
7
6
5
4
3
2
1
0
0

B/I [T/kA]

B [T]!2 / ndf
p0

0.595
0.59
0.585
0.58
0.575
0.57
0.565

1000

2000

3000
Vc [V]

0

1000

2000

3000
Vc [V]

9
8
7
6
5
4
3
2
1
0
0

B/I [T/kA]

p0

0.62

0.000216 / 3
0.5954 ! 0.004242

0.615
0.61
0.605
0.6
0.595
0.59

1000

2000

0.585

3000
Vc [V]

B/I [T/kA]

B [T]

B [T]

!2 / ndf

9
8
7
6
5
4
3
2
1
0
0

0.0001754 / 3
0.5733 ! 0.003824

0

1000

2000

3000
Vc [V]!2 / ndf
0.0002118 / 3
p00.6009 ! 0.004201

0.62
0.615
0.61
0.605
0.6
0.595
0.59

1000

2000

3000
Vc [V]

0

1000

2000

3000
Vc [V]

Figure 2.7: Field-current ratio of the four magnets. Left: the measured fields atthe center of the magnets. Right: the measured field-current ratios.

2.3 Magnets and bank29

the pickup coil, rotating it by 180◦ gives a negative field. Hence there are also two
directions of the pickup coil, which is shown with a white arrow. The direction,
which detects a positive field by inserting the coil from the front, is defined as “0◦ ”.
Rotation of 180◦ from the 0◦ , which detect a negative field by inserting t from thefront, is defined as “180◦ ”. There are thus four ways to measure the map.
Left of Fig. 2.9 shows a measured map with a charged voltage of 0.2 kV with
diﬀerent configurations. The black line shows back-0◦ data and the red one shows
front-180◦ data. Their negative field is inversed for the visibility. The two measurements give the same deviation of the coil head from the center of the beampath, which may have occurred at gluing of the coil head to the GFRP rod (seeFig. 2.4). The blue data is the mean of the two measurements from the diﬀerent
directions. This mean cancels out the contribution from axial component of the
field, which is not detected by an ideal pickup coil.
Right of Fig. 2.9 compares the diﬀerence between the pervious measurement ofback-0◦ and front-180◦ (black), and the other measurement of back-180◦ and front0◦ (red). Diﬀerence of the two measurements show two contributions. The first one
is the deviation of the coil head from the center of the beam path (gluing). This
gives the diﬀerence of the two maps so that its sign changes for z > 0 and z < 0regions. Such an alternating diﬀerence is not seen in the figure and therefore thedeviation of the coil head from the pipe center is considered to be negligibly small.
The other contribution is an accuracy of the map measurement since they measure
the same map with a diﬀerent way. Its major diﬀerence comes from reproducibilityof the rotation angle of the coil. This gives a uniformly lower map than the other.
The observed diﬀerence is seem to be more likely for this case. The diﬀerence
between the areas of the two maps is 0.9%. The result is taken as a systematic
error, which is described again in the analysis.
Figure 2.10 shows a comparison of the measured map (the black line in theright of Fig.2.9) and the calculation of finite element simulation (ANSYS). The
simulation includes all the 3D geometrical information. Unsmooth structure at theedges of the simulation reflects the finite size of the mesh. Although non-magnetic
metal (stainless-steel 304) is used for the backup material, small magnetization
appears at low temperature on its surface after the machining. This inhomogeneous distribution of permeability in the backup metal, which is not reproduced in
the simulation, is considered to cause the diﬀerence from the measurement. The
diﬀerence of the area between the two maps is 0.2%.
Figure 2.11 shows measured maps of the four magnet used in the experiment.
Slight asymmetric structure can be seen in the figure; the half region of z < 0 isslightly small when compared with the other half region of z > 0. This feature
comes from the fact that the coil structure is not symmetrical due to the existenceof a pair of electrodes. They break the geometrical symmetry.

30

2.3 Magnets and bank-.(/!

!'*+,!
6"7#!

01!

4.5+#,!
8$#(,'*%#!

2301!
!"#$%&%"'#()*+!

B/I [T/kA]

B/I [T/kA]

Figure 2.8: Configuration of the map measurement. The field direction of themagnet is shown with a black arrow. The direction of the pickup coil is shownwith a white arrow. If the two arrows are in the same direction, a positive field ismeasured by the pickup coil. For the definition of “front” and “back”, or “0◦ ” and“180◦ ”, see the text.

0.7
0.6
0.5

0.7
0.6
0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

-0.1
-150

-0.1
-150

-100

-50

0

50

100

150

z [mm]

-100

-50

0

50

100

150

z [mm]

Figure 2.9: Measured map with a charged voltage of 0.2 kV with diﬀerent configurations. Left: comparison of the back-0◦ data (black) and the front-180◦ data(red). Their negative field is inversed for the visibility. The blue points show themeans of them. Right: comparison of the mean maps measured with the diﬀerent
configurations. The black line is the mean of back-0◦ and front-180◦ measurements,
and the red line is the mean of back-180◦ and front-0◦ measurements.

31

B/I [T/kA]

2.3 Magnets and bank

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.15

−0.1 −0.05

0

0.05

0.1

0.15

z [m]

B/I [T/kA]

B/I [T/kA]

Figure 2.10: Comparison of the measured map (the black line in the right of Fig.2.9)
and the calculation of finite element simulation (ANSYS). The simulation includes
all the 3D geometrical information. Unsmooth structure at the edges of the simulation reflects the finite size of the mesh. Inhomogeneous distribution of permeability
in the backup metal is considered to cause the diﬀerence from the measurement.
The diﬀerence of the area between the two maps is 0.2%.
0.7
0.6
0.5

0.7
0.6
0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

-0.1
-150

-0.1
-100

-50

0

50

100

150

-100

-50

0

50

100

0.7
0.6
0.5

0.7
0.6
0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

-0.1
-150

-0.1
-150

-100

-50

0

50

100

150

z [mm]

150

z [mm]

B/I [T/kA]

B/I [T/kA]z [mm]

-100

-50

0

50

100

150

z [mm]

Figure 2.11: Measured map of the four magnet with a charged voltage of 0.2 kV

32

2.3.4

2.3 Magnets and bankHeat loss and thermal time constant∫t
Heat loss of a magnet is expressed from its resistance and current as 0 1 I 2 Rdt,
where t1 a period of one shot. Since resistance is a function of temperature, heatloss gives information of the coil temperature. The thermal time constant, on theother hand, is a time for the magnet to reach a thermal equilibrium with a given
heating. Therefore it shows an eﬃciency of cooling with liquid nitrogen. This subsection first summarizes the relation between these parameters and the repetition or
the field. Measurements of heat loss and thermal time constant are then described.
Factors of the achieved repetition are finally considered.

Benefits from a small thermal time constant
The key point of repetition operation is to reduce the heat loss of the magnet. This
reduction also results in a reduction of the charging time and thus speeds up the
repetition. On the other hand, the time constant of the magnet to reach a thermal
equilibrium represents an accumulation of heat inside the magnet. A large time
constant means a large amount of heat is stuﬀed inside the magnet, which results
in an increase of the temperature of the coil. Since the coil resistance increases
with the increase of its temperature, it causes a large heat loss and lowers therepetition. This relation is schematically shown in Fig. 2.12 in case of a small time
constant. Another benefit from the small time constant is an increase of the field.
The decrease of the resistance gives a larger current. Field linearly scales to thecurrent and is thus increased by the reduction of the thermal time constant.

!"!"#$%&&"'()*+$%&",$*"-./#(%/(0!
1*2"!"#$%&&"
3*%("&.##"!"#$%&&"
9)%+57/5",$*"!"#$%&&"

9:++*/("!"&%+5*"
67*&8"!"&%+5*"

1*4*,,./"!"&%+5*"Figure 2.12: Relation among the thermal time constant τ , the resistance at thermal
equilibrium Req , the heat loss , the charging time, repetition, current, and field2.3 Magnets and bank33

Measurements
Heat loss of a shot is measured by the diﬀerence of a charged voltage before andafter the shot. Since the charged voltage is several kV, the read out voltage isdivided by 1/1000 using a pair of 1 MΩ and 1 kΩ resistance. The heat loss isdirectly calculated by CV02 /2 − CV12 /2.
On the other hand, thermal time constant is measured in several ways. The
most direct way is to measure time development of the resistance of the coil after ashot. The decay curve of the resistance is exponentially extrapolated to one rightafter the shot. The resistance is measured by connecting an LCR meter to theelectrodes of the magnet. The measurements are carried out by changing durationof the repetition. In terms of security, however, it is sometimes dangerous for a
person to wait near the magnet during the shot and to connect it by hand rightafter the shot.
Although time constant of some prototypes have been measured in this way,
the magnets used in this experiment are measured in other ways. Since the time
constant is measured with a time change of any parameter, which reflects thethermal equilibrium of the magnet. There are many ways to measure the time
constant other than the direct measurement of the coil resistance. The easiest way
is again to measure the voltage; the heat loss. Figure 2.13 shows time developmentof the heat loss measured by changing a duration of the repetition. The top left
shows heat loss of serially connected two magnets of magnet2 and magnet3 with ashot repetition of ∼0.12 Hz and a charged voltage of 4 kV, corresponding to heatloss of ∼1.2 kW. The voltage is assumed to be the same for the experiment at
SPring-8. The top right shows heat loss with the same condition of magnet4 andmagnet5. Both time constant agree with 13–14 s. Finally, the bottom shows heatloss with operation of the two pairs simultaneously, which is the same condition of
the experiment. Its total heating with a shot repetition of ∼0.12 Hz is therefore∼2.5 kW. The capacitor bank has an electric power capacity of 20 kVA. The half of
it is consumed as heat loss of charging resistances, and the rest half can be consumed
as heat loss of magnets and other resistance components like, for example, cables.
The shot repetition is assumed to be ∼0.1 Hz at the experiment, which corresponds
to be less than one fourth of the full power capacity of the bank.
Although measurement of the time constant from voltage is easy, the read line
contains a spike noise from switching a large current. As an alternative parameter,a peak value of current is used for the measurement of the time constant during theexperiment. The pulsed current is read out with the CT, which line is electricallyisolated.
Factors of high repetition
The measured thermal time constant τ is 13-14 s with a heating of each magnet with
∼0.6 kW. This value is so small at an unprecedented level from the sense of pulsed
magnets. A typical shot repetition of a conventional magnet is ∼1 mHz. The shot

2.3 Magnets and bank

!2 / ndf
0.002348 / 2
p0
9.569 ! 0.02585
p1-24.73 ! 2.125
p2
12.88 ! 1.133

9.8
9.6
9.4
9.2
9

Heat loss [kJ]

Heat loss [kJ]

34

9.8
9.6
9.4
9.2
9

8.8
8.6

8.8

8.4

8.6

8.2
0

!2 / ndf
6.275e-05 / 1
p0
9.549 ! 0.00876
p1-29.55 ! 0.7305
p2
13.99 ! 0.3636

20

40

60

80

8.4
0

100 120 140 160

10

20

30

Heat loss [kJ]Time [s]

40

50

60

Time [s]!2 / ndf
p0
p1
p2

9.4

0.01011 / 1
9.297 ! 0.1227-32.08 ! 12.34
14.65 ! 5.953

9.2
9
8.8
8.6
8.4
8.2
0

10

20

30

40

50

60

Time [s]Figure 2.13: Time development of the heat loss measured by changing duration of
the repetition. Top left: heat loss of serially connected two magnets (magnet2 andmagnet3) with a shot repetition of ∼0.12 Hz and a charged voltage of 4 kV. Topright: heat loss with the same condition of the other set (magnet4 and magnet5)
used in the experiment. Both time constants agree with 13–14 s. Bottom: heatloss with a simultaneous operation of the two pairs with shot repetition of ∼0.12
Hz, which assumes the same condition of the experiment at SPring-8.

2.3 Magnets and bank35

repetition is given as 1/τ for the most part and can be somewhat changed from thisvalue, depending on huw much temperature increase is allowed to the coil. In thisexperiment, the heatat thermal equilibrium can be read from Fig. 2.13 as 9.6∫ loss2
kJ. Dividing it by I dt gives resistance at the equilibrium. From the resistivityof copper as a function of temperature, the coil temperature is obtained as 215 K.
This corresponds to an increase of the temperature from 77 K by 138 K, whichis quite large though it is still well below the room temperature of ∼300 K. The
repetition of 0.12 Hz is hence larger than the inverse of the 13-14 s, which is around0.08 Hz.
The feature of high repetition mainly comes from the three factors. One is to
use Cu wire, which has the best thermal conductivity among all wires. The second
factor is to reduce materials with poor thermal conductivity such as GFRP as muchas possible. As can be seen in Fig. 2.2, the magnet consists of metals for the mostpart. The use of metal near the field volume causes an increase of field cancellationfrom eddy current, which runs in the metal. Thus it requires divided backups at
the same time. The third factor is the flat structure of the magnet to improve thecooling eﬃciency.

2.3.5

Destruction and repetition field

Field of repetition is decided from the maximum field, or destruction field, by
taking a suﬃcient safety margin. The destruction field is decided by the mechanicalstrength of the wire and the backup. Left of Fig. 2.14 shows measured field of a
prototype magnet with an increase of charged voltage. Both ends of the magnet
are not enough backuped with M20 bolts and nuts as they are with the present
magnet (see Fig. 2.2). Here it is referred to as a “weakly-backuped” magnet.
Linearity of the field increase changes at around 3 kV. The right figure showsa corresponding measurement of its inductance at 750 Hz. The measurement iscarried out with an LCR meter after each shot. Since the Maxwell stress aﬀects inthe way to increase the field volume, its deformation also increases the inductance.
About 1%-increase of inductance is generally said to be a sign of deformation. In
this case, the increase of the inductance reaches 1% at 3 kV. Increase of the field
volume causes a decrease of the field eﬃciency. This corresponds to the observedchange of linearity at 3 kV. After that, the plastic deformation continues to occur
along with the increase of the inductance. The magnet finally destroys at 4 kVwith 14.4 T with an increase of the inductance of about 10%.
The destruction has occurred at both ends of the racetrack. Contact areas
between the coil and the backup at these end-sections become half-circle shape andthus become larger than areas of straight section backuped with divided metals foreach 10 mm. This causes a larger force against the backups of both ends and hence
they needs to be backuped with extra metals. After this prototype, two thick plates
are added to compress the weakly-backuped magnet at both ends. The destruction
field of the present magnets used in the experiment is therefore considered to belarger than 14.4 T.

36

2.3 Magnets and bank

L [µH]B [T]

The field at 3 kV gives an elastic limit of the weakly-backuped magnet, and
it is 12.5 T. Repetition field should be in the elastic region. Moreover, the highrepetition use requires a high durability of more than > 104 shots. Thus it also
requires a suﬃciently-lower repetition-field than the field at the elastic limit. Hereabout 30% of safety is taken from the elastic limit and it becomes 9.5 T. The
Maxwell stress scales to the square of the field, and hence it corresponds to a safety
factor of two for the force.
14

33

12

32.5

10

32

8

31.5

6

31

4

30.5

2
0
0

30
1000

2000

3000

4000
Vc [V]

0

1000

2000

3000

4000
Vc [V]

Figure 2.14: Measured field and inductance of a weakly-backuped magnet with anincrease of the charged voltage.

2.3.6

Durability test

Even if the repetition field is decided by taking a safety margin into account, there
are still some other destruction modes which appear during the repetition:• friction of dielectric coating between the wires• deterioration of wire strength due to repetitive high-density current• fatigue failure of backup metals
The durability test is therefore necessary before the experiment.
The first magnet (maget1) is produced for the test of durability and repetition.
11.5 T has been confirmed to be within the elastic region of the magnet. Afterthe shot of 11.5 T, the same magnet is tested its durability before the experiment.
A total of 2,700 pulses at 9.5 T are generated. Deformation of the coil appears
as the increase of the inductance. The test has thus been carried out checking
its inductance many times during the repetition. Since a significant change of theinductance is not observed after the test (∆L < 0.2%), the repetition field of 9.5 T
has been confirmed to be safe.

2.3 Magnets and bank

2.3.7

37

Leakage field

Leakage of the field is measured to evaluate the field at the SPring-8 storage ring.
The experimental hutches of BL19LXU are, as most of the other beamlines, locatednext to the electron ring. The electron orbit is well-tuned against the geomagnetic
field, and thus, existence of other field of ∼10 µT could disturb the orbit. Deviationfrom the stabilized electron orbit causes a severe problem to other users.
Figure 2.15 shows a measured magnitude of leakage field in three directions fromthe center of a prototype magnet. The magnets used in this experiment almost has
the same structure of this prototype and is therefore considered to have the same
property foe the leakage field. The measurement is carried out with a charged
voltage of 1.0 kV and capacitance of 1.6 mF. The data points are measured withanother pickup coil, which is wound around 10 turns with a diameter of 100 mm.
The leakage field is measured in the three directions for each data point, and themagnitude at the position is calculated. There are many obstacles in the way fromthe center of the magnet to the measurement positions such as a liquid nitrogencontainer and a safety barrier. The uncertainty of the length is therefore shown as
a horizontal error. The lines show the result of 3D finite element simulation andagree with the data. The leakage can be seen to decay in inversely proportional
to the cube of the length. This is a character of dipole radiation. The deviationfrom the decay law of simulation can be seen for the length over 1 m. It is anedge eﬀect of the volume input to the simulation. Even if field of 10 T is generated
at the magnet center, the leakage field decays to ∼100 µT (=1 G) at a length of
1 m. The length from the experimental hutch to the electron ring is 5.5 m andcorresponding decay factor is ∼ 6×10−3 . There is also an hutch wall of steel with athickness of 12 mm, resulting a shielding eﬀect of 1/10. There is also another wall,
which separates the experimental hall and the electron ring. The leakage field at
the electron ring with 10 T at the magnet center is thus estimated as less than 60
nT for each magnet. Moreover, the two pairs of magnets are placed in a direction
so as to cancel the field from each pair at the electron ring. Since the eﬀect ofthe magnets on the electron orbit is estimated to be negligible, pre-study of themagnets before the experiment is exempted.

2.3.8

Oscillation test

As supplemental information, oscillation of the magnet during the pulse is described
here. The peak current at a field of 9.5 T becomes 16 kA. Due to the Lorentz force,
this large current oscillates the cables, which connect the magnets with electrodes.
If the magnet also oscillates during the pulse, the motion would cut the beam path.
In order to test this oscillation, a test measurement has been carried out with thesame setup used in the experiment. The magnets are operated with 9.5 T and ashot repetition of 0.1 Hz. Laser light with the center wavelength of 650 nm passes
through the pipe. Its power is measured with a laser power meter. The gain of
its amplifier is adjusted to output 10 V for an input laser power of about 1 mW.

38

B/I (T/kA)

2.3 Magnets and bank

x
10−1

y
z

10−2
10−3
10−4
10−5
102

3

10

Position (mm)Figure 2.15: Measured magnitude of leakage field in three directions from the centerof the prototype magnet. The measurement is carried out with a charged voltageof 1.0 kV and capacitance of 1.6 mF. Results of 3D finite element simulation is also
shown with the corresponding line color.

39

12
10

14
12
10

8

8

6

6

4

4

2

2

0

voltage [V]voltage [V]

14

0

10

20

30

15

#!

10

"!

5
0
-5
-10

!!
0

$!

%!
10

20

30

0

40
time [ms]40time [ms]voltage [V]voltage [V]

2.3 Magnets and bank

18
16
14
12
10
8
6
4
2
0
-2

0.5

1

1.5

2

2.5
time [ms]2

2.5time [ms]

#!
0.5

1

1.5

Figure 2.16: Output of the laser power meter during the oscillation test. The gainof its amplifier is adjusted to output 10 V for an input laser power of about 1 mW.
The top left figure is its output, and the bottom left figure shows the corresponding
current. The pulse interval is set to 33 ms. The top right figure is the magnified
view around the first pulse, and the bottom-right figure shows the corresponding
current. Significant change is not measured.

40

2.4 Magnets and bank

The diameter of the laser beam is about 4 mm and almost the same of the innerdiameter of the pipe (5.4 mm).
Figure 2.16 shows the output of the power meter. The top left figure is its
output, and the bottom left figure shows the corresponding current. In this case,the pulse interval is set to 33 ms. The top right figure is the magnified view aroundthe first pulse, and the bottom right figure shows the corresponding current. Timeregions before the first pulse (a), in the first pulse (b), between the pulses (c), in thesecond pulse (d), and after the second pulse (e) are shown in the figure. The mean
power for these regions is 9.51 V (a), 9.52 V (b), 9.52 V(c), 9.51 V (d), and 9.52
V (e). All changes of the power is less than 0.1%. From Tab. 1.1, its contribution
to the ALP-two-photon coupling constant becomes less than 0.025% and is thus
negligible.

2.3.9

Summary of the basic performance

Table 2.3 summarizes the basic performance described in the previous sub-sections.
The field eﬃciency is a mean of the four magnets. The thermal time constant is
15 s at the heating of 2.5 kW for four magnets, which is the same condition of theexperiment. In this case, the total heat loss becomes 21 kJ at a shot repetition of
0.12 Hz. The leakage field decays to 10−5 at a distance of 1 m from the center ofthe magnet. The durability is tested with 2,700 pulses of 9.5 T.
Parameter

Value

Field eﬃciency
Field-length product
Thermal time constantHeat loss
Destruction field
Durability / repetition field
Leakage field

0.59 T/kA (center)1.12 × 10−1 T m/A
15 s (2.5 kW)
21 kJ (2.5 kW)>14.4 T
>2700 pulses / 9.5 T
10−5 (1 m)

Table 2.3: Basic performance described in the previous sub-sections The field efficiency is a mean of the four magnets. The thermal time constant is 15 s at theheating of 2.5 kW, which is the same condition of the experiment. In this case, theheat loss becomes 21 kJ at a shot repetition of 0.12 Hz. The leakage field decays to10−5 at a distance of 1 m from the center of the magnet. The durability is tested
with 2700 pulses of 9.5 T.

2.4

Capacitor bank

A capacitor bank is used to provide pulsed current to magnets. As well as themagnets, a transportable bank is newly designed and constructed. This section
describes the design and the operation sequence of the bank.

2.4 Magnets and bank

2.4.1

41

Principle of the capacitor bankAlthough most of the circuit components are custom-made, and some of them areso expensive, basic circuit of the bank is represented as a simple LCR discharge
circuit. Figure 2.17 shows a schematic diagram of the basic circuit. The left is aconventional type of the LCR discharge circuit. First, a capacitor (C) is charged
from a voltage supply through a charging resistor (Rc ). After the charging, thecapacitor is disconnected from the supply by a switch. A trigger pulse is then sent
to a cathode of a thyristor (SCR). The thyristor works as a switch which rectifies
the current in one direction. Electric energy stored in the capacitor is discharged
to a magnet. The magnet can be seen as a pair of serially connected inductanceand resistance. The frequency of √the pulse is decided from the capacitance C andthe magnet inductance L as 1/2π LC. After a quarter cycle, the magnetic energy(i.e. the current) generated by the magnet maximizes. The energy then returns
to the capacitor as electric energy at half cycle. The thyristor automatically turns
oﬀ at this time since the current becomes zero. The thyristor works as a rectifier,and the LC oscillation also stops at this time. The pulse shape thus becomesa half sinusoidal wave, shown in the bottom left figure. The capacitor is thengrounded, and the residual energy inversely stored in the capacitor is released.
This conventional operation sequence is used in the bank as a “single pulse mode”.
The right figure shows a circuit of a “repetition mode”, which produces twopulses in a shot. The diﬀerence from the single pulse mode is an additional thyristor
installed in anti-parallel to the original one. The energy which returns to thecapacitor by the first thyristor, is not grounded but discharged again with thesecond thyristor. The time interval between the turn-on of the two thyristors isadjustable. If the second thyristor is turned on right after the turn-oﬀ of the firstone, the two half sinusoidal waves are generated without a break, shown in thebottom right figure. The return energy of the capacitor is positively charged andhas been decreased by the two times of heat losses at the magnet. The decrease of
the energy is additionally charged from the supply. This repetition mode reduces
the charging time compared with the single pulse mode, where the charging starts
from 0 V every time.

2.4.2

Circuit and operation sequence

Figure 2.18 shows the circuit diagram of the capacitor bank. A charging section,
which provides a high voltage, is commonly used for the succeeding discharge section. The discharge section consists of two parallel components, and each drives
two magnets. They have the same structure and therefore only one of them is
described here.
A commercial AC 200V line is input to the bank. The bank is turned on bya circuit breaker (CB) of 75 A, which protects the line from overcurrent. The
mechanical contactor (MC) is a large relay with a thermal fuse (TH). By closing
the MC, the AC 200 V is applied to a primary side of a slidac (SL), which is42

2.4 Magnets and bank

!"!

$#!+!

$#!!

$#!,!

#!

I [kA]

I [kA]%&'()*!
10
8

10
8
6
4

6

2
4

0
-2

2

-4

0

-6
0.5

1

1.5

2

2.5

time [ms]

0

1

2

3

4

5
time [ms]Figure 2.17: Basic circuit of the capacitor bank. Left: a conventional LCR circuit
used for “single pulse mode”. Right: a circuit of the “repetition mode”. Antiparallel thyristors are triggered to produce a shot with two pulses.

2.4 Magnets and bank43

an adjustable voltage transformer. The secondary side of the SL is connected toa primary side of a step-up transformer (TR) with a voltage ratio of 30. The
output high voltage from the TR is rectified by a diode bridge (DB) with full wave
rectification. By closing a charging relay (CR), the capacitor (C) is charged througha charging resistor (RC ). The time constant of the charging is given as the productof C and RC . In case of charging from 0 V, the initial high voltage causes a large
current at the beginning of the charging and heats up the RC . Since a fast charging
is not required for the initial charging, the capacitor is charged slowly through RCL
with 6 kΩ. In case of the additional charging, on the other hand, the voltage dropsby only the heat loss, and the fast charging is required for the repetition. The
capacitor is therefore charged rapidly through RCH with 900 Ω. The fast or slow
charging is selected by a resistor relay (RR). The voltage of the capacitor is divided
by a pair of resistors (Rm1 and Rm2 ). The 1/1000-divided voltage is read out by adigital meter relay (DMR), which turns on or oﬀ with a preset voltage. It is used
for the control of the operation sequence.
After the capacitor is charged up, the upstream charging section is disconnectedby opening the charging relay. The first trigger is then sent to the SCR1 and thefirst pulse is generated. Due to impedance mismatch between the output cable andthe magnet, a reflected voltage returns to the SCR. Since the voltage can cause
destruction of the SCR, it is absorbed by a pair of a terminal resistor (Rt ) andcapacitor (Ct ) inserted in parallel to the output terminal.
In case of a single pulse mode, the returned voltage is grounded through anearth resistor (Re ) by closing an earth relay (ER). In case of a repetition mode,on the other hand, the second trigger is sent to SCR2 and the returned voltage
positively charges the C. The amount of the energy loss is additionally charged
through the RCH by closing the CR. Due to the current capacity of the SCRs, thesame discharge section is connected in parallel to lower the current running to each
SCR by half. Each drives two magnets placed either upstream or downstream sideof an LSW shield.
Figure 2.19 shows a measured time variation of the capacitor voltage with ashot repetition of 0.5 Hz at 1 kV. The voltage is reversed after the first pulse,
and then reversed again after the succeeding second pulse. Right after that, an
additional charging starts until the voltage returns to its original value.
Figure 2.20 shows a whole picture of the bank. Four units of capacitors are seenin the front. Each unit has three capacitors and each of them is 0.25 mF. Unit1
and unit2 are connected in parallel and used as 1.5 mF. Similarly, the pair of unit3
and unit4 are used as another 1.5 mF. Behind these, the main body of the bank isseen. It has a four-story structure and its height is 2 m.
Figure 2.21 shows a picture of the inside. The transformer (6 kV, 20 kVA) is
seen in front of the left picture. Behind it is the slidac with 20 kVA. The charging
resistors are shown in the right picture. RCL is composed of 6 kΩ resistors connectedwith 2p2s (two-parallel of two-serial). RCH is, on the other hand, composed of 16
resistors of 900 Ω and 700 W each, connected with 4p4s.

44

2.4 Magnets and bank

,)'

$&'
&2*!

("!

(#&!

&!)!

$%!

,!&*!

&!%!&&! !&*!

!"!#!!

!*!

,!&+!
&.*!

&/*! #*!

-&*!

!/*!
#+!

&2+!

!&+!

,!&0!
,!&1!
!+! &.+!

&/+!

-&+!

!/+!

#0!

#1!

Figure 2.18: Circuit diagram of the capacitor bank with an additional charging
system. The left half is the charging section, and the right half is the discharge
section. The discharge section consists of two parallel components constructed withthe same structure. Each drives two magnets.

45

Vc [kV]

2.4 Magnets and bank

1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-2000

-1000

0

1000

2000

time [ms]Figure 2.19: Measured time variation of the capacitor voltage with a shot repetitionof 0.5 Hz at 1 kV. The voltage is reversed after the first pulse, and then reversed
again after the succeeding second pulse. Right after that, an additional charging
starts until the voltage returns to its original value.
Figure 2.22 shows a picture of the upper floors. The top picture shows thethird floor. It consists of high-voltage components including thyristors (SCR1 andSCR2). Coaxial cables connecting the capacitor and magnets are seen on the right.
Another set of components are symmetrically placed behind them. The bottom
shows the fourth floor. The trigger boards (TB1, TB2) receive optical signals froma control panel through optical fibers, and drive pulse transformers. There can beseen four sets of the pulse transformers. Each consists of a two-stage structure anddrives one thyristor. The dividing resistors (Rm1 and Rm2 ) are shown on the left.
Its lower voltage is read out by DMR.

46

2.4 Magnets and bank()#*&'+!
#&'!

!$!
!"!

!%&
!#!

Figure 2.20: Whole picture of the bank. Four units of capacitors are seen in thefront (left). Each unit has three capacitors and each of them is 0.25 mF (right).
Behind these, the main body of the bank is seen. It has a four-story structure andits height is 2 m.

#$!
"%(!

%&!
"%$!
!"!
'%!

Figure 2.21: Lower floors. Left: the first floor. The transformer (6 kV, 20 kVA)
is seen in front of the left picture. Behind it is the slidac with 20 kVA. Right: thesecond floor. RCL is composed of 6 kΩ resistors connected with 2p2s. RCH is, on
the other hand, composed of 16 resistors of 900 Ω and 700 W each, connected with
4p4s.

47

2.4 Magnets and bank#)*")!

!"#$%&!

#(!

'#!

+,$!
#-$!
#-&!

+,&!

Figure 2.22: Upper floors. Top: the third floor. Another set of components are
symmetrically placed behind them. Bottom: the fourth floor. The trigger boards(TB1, TB2) drive pulse transformers. There can be seen four sets of the pulse
transformers. The dividing resistors (Rm1 and Rm2 ) are shown on the left, and its
lower voltage is read out by DMR.

48

2.4 Magnets and bank

Chapter 3

Setup and devices
This chapter describes the setup of the X-ray LSW search. The whole system is
explained in the first section. The setup spreads to three hutches. The following
section describes the devices of each hutch in detail.

3.1

Whole setup

The top view of the whole system is schematically shown in Fig. 3.1. The experiment has been carried out at BL19LXU in SPring-8. Three hutches of the beamline
are used in this experiment. The role of each hutch is as follows:• optics hutch (OH): beamline components for the processing of direct beamfrom the undulator,• the first experimental hutch (EH1): a main hutch where the field generation
system is placed,• the second experimental hutch (EH2): detection of signal X rays and electronics of NIM and CAMAC.
Direct beams from the undulator goes to OH. In order to obtain a desired beam
quality, several fixed components in the hutch are used. The beam then goes to
EH1. It is a main hutch where the field generation system composed of the magnets
and the bank is placed. Four magnets are used for the LSW conversion regions.
They are placed in liquid-nitrogen containers and are cooled down to 77K. The
beam passes through the upstream conversion region (a → γ) and is dumped intoa hole of a lead shield. A silicon PIN photodiode (PIN B) is embedded in theshield and monitors the beam intensity. The ALP components pass through theshield and are re-converted in the downstream conversion region (γ → a). The
regenerated photons go to EH2, where a low-energy germanium detector is placed.
It detects the regenerated photons. All the conversion regions are evacuated. The
other beam paths are also evacuated to reduce air-attenuation of the X rays.
49

50

3.2 Setup and devices

Due to the safety from radiation, human bodies are kept out from these hutches
during the beam is on. The bank is therefore controlled from the outside of thehutch. There is a duct hole in each hutch, which leads to the outside. Signal
or control cables go through the duct. The liquid nitrogen is also filled from theoutside. The hose goes through the duct and reaches the containers.
The magnets and the bank are contained in the same hutch. This has two
reasons. First, the bank itself is a high-voltage and a large-current device. If
there is some problem, it might become dangerous in the worst case. Therefore
they are confined in the hutch and the door is closed. In this way, human bodies
cannot be harmed. The other reason is noisy environment. During the operationof the magnets, the hutch is filled with EMI (electromagnetic interference) noise.
The ground potential also becomes unstable during shots. If the operation-control
system or the data-acquisition electronics are placed in the same environment, thenoise causes malfunction of these devices or severely spoils the analog data. Thus
the hutch wall also works as a separator of the environment.

3.2

OH: beamline components

This section describes the beamline components. The beamline used in this experiment is BL19LXU (BeamLine 19 Long X-ray Undulator), which is located at thewest of SPring-8. First, property of the X-ray beam is summarized. The BL19LXU
undulator is then described. The X-ray beam from the undulator has the world’s
strongest intensity. Direct beam from the undulator goes to OH, where fixed components are placed. They are used to process the direct beam and to obtain adesired beam quality. Principle of these components is described in the following
sub-sections.

3.2.1

Summary of the beam property

Table 3.1 shows a summary of the beam property, which will be described in thefollowing sub-sections. The energy of the beam is selected to 9.5 keV. This energy isdecided from the eﬃciency of the detector, the energy spectrum of the undulator,
and the energy spectrum of the background spectrum. Intensity of the beam ismeasured in front of the detector (PIN A), and its mean value is about 3 × 1013
photon/s (Tab. 4.1). Since the undulator bends electron bunches in the horizontal
plane, the beam is polarized to the horizontal direction. Higher-order radiations
from the undulator are cut to be less than ∼1% by using a pair of total reflection
mirrors. The beam size has been measured in the previous beamtime, and it is 1.0
mm (H)×0.5 mm (V). The X-ray beam has the same time structure of electron
bunches. The bunch interval is 23.6 ns and is much smaller than a pulse width offield of ∼1 ms. The X-ray beam therefore is regarded as a DC X-ray source.

51

3.2 Setup and devices!"#$%&'(%)$(!

J,%/&.0,'$8/"80,0)?!

*+",-./,0)%&'(%)$('1!
@FB4'/80.)8-! @,%>'<&8$A! HCB'J!
2%3'1! 2%3'4!

*+",-./,0)%&'(%)$('4!
HCB'E'

2%3'5! 2%3'6!

7,),$)8-'

Iu! =L! Id!
9:-%;'<,%/!
=%"%$.)8-'<%0A'1!

=%"%$.)8-'<%0A''4!
L./.03'
BC2D'?8I-$,! =E2E=!
L-.33,-!

=(%-3,:>.?$(%-3,'$80)-8&!
@FB4'G,??,&!
=I--,0)'?(%",!

K,FI,0$,-D'=I--,0)'?(%",'"I&?%-'-,$8->,-!
=80)-8&'L-.33,-' H='4!
"%0,&! ?)8"!
=I--,0)'?(%",',--8-'>,),$#80!
H='1!

Figure 3.1: Top view of the whole system. The beamline components of the optics
hutch are used to obtain a good beam quality. The first experimental hutch is amain hutch of the experiment, where the field generation system is placed. The
bank is operated from the outside of the hutch. A detector and DAQ electronics
are placed in the next hutch. The upstream current Iu serially runs through Mag1
and Mag2, and the downstream one Id through Mag3 and Mag4. Although thesum of the two currents is read out with the CT during the run, their ratio is alsomeasured in additional measurements by passing each cable one by one to evaluate
their diﬀerence (Sec. 4.7).
Parameter
Photon energy
Intensity (in front of the detector)
Polarization
Higher-order radiation
Beam size (prev.)
Electron bunch intervalValue
9.5 keV∼ 3 × 1013 photon/shorizontal
cut by the double mirrors
1.0 mm (H)×0.5 mm (V)
23.6 ns (∼DC)

Table 3.1: Beam property from the BL19LXU undulator after beamline components
in OH.

3.2.2

BL19LXU undulator

An undulator is an important device since it works as a light source in this experiment and provides intense X-ray beams to the magnets. Electron bunches

52

3.2 Setup and devices

circulating in the storage ring go through the undulator. Their orbits are bent by
periodically aligned magnets. Synchrotron radiations are emitted at each bending.
They interfere with each other and generate phase-matched beams with a small
band width of about ∆ω/ω = 10−2 .
Undulators are characterized with field strength (Bu ), periodic length (λu ),periodicity (N ), and gap distance between the two arrays of permanent magnets.
Undulator radiations are, on the other hand, characterized with wavelength (λn ),band width, and intensity. Wavelength of undulator radiation is written as
(
)
λu
K2
λn =
1
+
,
(3.1)
2nγ 2
2
where n is degree of higher-order radiation, γ the Lorentz factor of 8 GeV/511
keV= 1.5 × 104 . λu is a common value of 32 mm for standard undulators in
SPring-8. K is a parameter proportional to the product of Bu and λu , and iswritten as
eBu λuK== 0.934Bu [T] λu [cm].
(3.2)
2πme cIf the magnet is divided in two to reduce λu , Bu is also reduced in accordancewith its size. This gives K to be unchanged. On the other hand, Bu can beincreased by closing the gap distance between the arrays of magnets. Hence K
can be seen as a parameter of the gap distance. In Eq. (3.1), both λu and γ are
fixed values. The wavelength is then changed by varying the gap distance. It can
be closed 12 mm at the minimum, which corresponds to a 0.57 T and K = 1.70.
From Eq. (3.1), this defines the maximum wavelength of 1.6 Å or 7.8 keV for thefundamental wavelength. On the other hand, the limit of K = 0, which corresponds
to a suﬃciently widened gap, defines the minimum wavelength of 0.65 Å or 19 keV
for the fundamental.
Large length of an undulator increases the beam intensity. Practically, however,
it is not so for the most cases. Since it is hard to produce a long undulator as one
body, it is divided into several segments when they are manufactured. If they aresimply connected, the expected intensity will not be obtained due to the distortionof phase-matching condition of the X rays, which occurs at the connections. This
limits the intensity of a long undulator.
The left of Fig 3.2 shows a picture of the BL19LXU undulator. It is composedof five segments and each segment has a length is 5 m. The right figure showsa cross section at the connection between the segments. The magnets (and ofcourse the path of the electrons) are contained in a cylindrical vacuum chamber.
It is referred to as an “in-vacuum undulator”. The in-vacuum undulator was used
for the first time in SPring-8 and then spread to world’s synchrotron radiation
facilities. In a conventional undulator, magnets are placed at outside of the vacuum.
This inevitably requires space for the connection. On the other hand, the invacuum undulators are connected without such space, keeping the phase-matchingcondition. Among all the beamlines in the world, the BL19LXU undulator has the

53

3.2 Setup and devices

0#1123%!"#$%#&'#"($)*$'+!
,-.#$%#&'#"(%$)/*$'+$

45$'6&"#($67768%$)9-4$:26(#5+!

Figure 3.2: BL19LXU undulator. Left: the undulator is composed of five segments,and has a total length of 25 m. Right: a cross section at the connection. The
magnets are contained in a cylindrical vacuum chamber, and it is referred to as
an “in-vacuum undulator”. The length and the in-vacuum technology used in theundulator make its intensity uniquely strong.
longest length of 25 m whereas the length of a standard undulator in SPring-8 is
4.5 m. This length and the in-vacuum technology used in the undulator make its
intensity uniquely strong. Without any losses in the air or in widows, its maximum
output reaches 2 × 1014 photon/s around 10 keV.

3.2.3

Double crystal monochromator

The oﬀ-axis components of the direct beam from the undulator is cut at the front
end. The beam then goes to a monochromator and is monochromated with Braggreflection at a silicon crystal. The beam is reflected again by the second crystal
to restore its horizontal direction. This type of monochromator is referred to as a
DCM (double crystal monochromator). Figure 3.3 shows a picture and a schematic
view of the DCM. The inside of the DCM is evacuated, and the crystals are cooledwith liquid nitrogen due to heat load of the beam. The two metal hoses, in which
the liquid nitrogen flows, are shown in front of the left figure.
Figure 3.4 shows the Bragg angle as a function of X-ray energy, calculated with
the Bragg condition of
2d sin θB = λ,(3.3)
where d the lattice spacing of silicon (d111 = 3.14 Å and d311 = 1.64 Å). Brassangles of the two crystals are tuned to pick up the peak intensity of the energy
spectrum of undulator radiation. If both of their positions are fixed, however, theheight of the outgoing beam is also changed. This requires height adjustments of all

54

3.2 Setup and devices!"#$%&'#()*+,-!
*+,$%&'"#()!

!"#$%&'"#()!

./(*+'#()*+,-!
Figure 3.3: Double crystal monochromator (DCM). Left: inside of the DCM isevacuated, and the crystals are cooled with liquid nitrogen due to heat load of
the beam. The two metal hoses, in which the liquid nitrogen flows, are shown infront of the left figure. Right: translation movement of the first crystal as well as
rotations of the both. In this way, height of the outgoing beam does not changewith the energy.
the downstream devices for diﬀerent energies. To avoid this, translation movement
is attached to the first crystal. Thus the first crystal moves with the change of theenergy to keep the height of the outgoing beam constant.
There is one remark about the DMC. The outgoing beams are monochromatedwith the level of ∆ω/ω = 10−4 whereas the direct beams from the undulator have∆ω/ω = 10−2 . A good monochromaticity is not required for this experiment since
the energy resolution of the detector is about 100 eV (σ). Intensity loss at the
DCM is quite large and reduces the intensity to about 1% of the original one. In
terms of the sensitivity, it is thus desirable not to use the DCM. It is, however,a fixed component, and removing it requires many applications and tests for thesafety.

3.2.4

Double mirror

In order to cut higher-order radiations from the undulator, a pair of total reflection
mirrors is used. Figure 3.5 shows a picture and a schematic view of the mirrors.
They are used as a pair to restore the horizontal direction. Since Eq. (3.3) is alsosatisfied for the higher-order wavelengths, they are contained in the beams fromthe DCM. Refractive index of X rays for materials is slightly smaller than unity
and is written as
2ne αλ2,(3.4)n(λ) = 1 − δ = 1 −me c2
where ne the electron number density, α the fine structure constant. From thisequation, high-energy X rays have a larger n(λ). Since the condition of totalreflection is expressed as n(λ) = cos θc , high-energy X rays have a shallow critical

55

Bragg angle (mrad)

3.2 Setup and devices

700
600
500
400
300
200

Si(311)100

Si(111)
5

10

15

20

25
30
energy (keV)

Figure 3.4: Bragg angle as a function of the X-ray energy, calculated with the
Bragg condition of 2d sin θB = λ, where d the lattice spacing of silicon (d111 = 3.14
Å and d311 = 1.64 Å).

!"#$%&'()**"*!
/0!
+&,('-,..!

Figure 3.5: Total reflection mirrors. Two mirrors are used torestore the horizontal
axis. They cut higher components of X rays, which have a shallow critical angle.

nagle θc . In this experiment, both angles of the mirrors are set to 4.5 mrad to cut
the higher components of the 9.5-keV X rays.

56

3.3 Setup and devices!""#$%&'(#!"#$%&'%()'*+,%)*#+,*-.#/0#4#
123*4##+.*"#-.$'/%(+'0%5#
6#

Figure 3.6: Four-jaw slits. Left: a schematic view. Right: a picture. Beam profile
is measured by scanning the blades along the horizontal or the vertical directions.

3.2.5

Slits

-1

ρ(y) (mm )-1

ρ(x) (mm )The beam size is measured in the previous beamtime using four blades of tantalum
slits. Figure 3.6 shows a schematic view and a picture. Beam profile is measured
by scanning the blades along the horizontal or the vertical directions. Figure 3.7
shows the measured profiles. The horizontal full width is about 1.0 mm and thevertical one is about 0.5 mm. Since the undulator bends electron bunches in thehorizontal plane, the horizontal width becomes larger than the vertical one. During
the run, the slit is loosely closed so as to cut only oﬀ-axis components.

1.5

2.5
2

1

1.5
1

0.5

0.5
0

-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8
x (mm)

0-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8
y (mm)

Figure 3.7: Measured width of the beam. The horizontal full width is about 1.0 mm
and the vertical one is about 0.5 mm. Since the undulator bends electron bunches
in the horizontal plane, the horizontal width becomes larger than the vertical one.

3.3

EH1: field generation system

Left of Fig. 3.8 shows a picture of the first experimental hutch in BL19LXU. The
hutch width is about 4 m along the beam axis. First, magnets on a base table are57

3.3 Setup and devices

5)7#*$/'89*0:#1;!

+*,-*#.*%!
!"#$%"&'()#*&!
456!

!-%%*#$'/0)(*'%*."%1*%!
<)#='8>%"#$;!

2-&/)%'
2!3!
!-%%*#$'/0)(*'*%%"%'1*$*.$!

Figure 3.8: The first experimental hutch and the control panel. Left: the hutch
width is about 4 m along the beam axis. First, magnets are installed into the backof the hutch. The capacitor bank is then installed at their front. Right: the control
system composed of the sequencer, the pulser, the current shape error detection,
the current shape recorder, and the control panel.
installed into the back of the hutch. After their alignment on the beam axis, thecapacitor bank is installed at their front. The magnets and the bank are containedin the hutch so as not to harm the human body in the worst case.

3.3.1

Control system

Right of Fig. 3.8 shows a picture of the control system. It consists of the following
items:• sequencer• pulser• current shape error detection• current shape recorder• control panel with a DMR (digital meter relay), which shows a charged voltage
The sequencer is placed on top of the system. It consists of PLC (programmable
logic controller) modules of Omron. It exchanges signals with contact relays in acontrol section of the bank (the charge-discharge control).
The pulser is used to send signals to the trigger boards placed on top of thebank. A high voltage appears at the pulse transformers on the board. The pulser

58

3.3 Setup and devices

is therefore electrically disconnected from the boards by sending signals through an
optical fiber. The optical signal is sent and received by photo-couplers. Since one
shot contains two pulses, the pulser sends two independent signals for each shot.
The time interval between the two signals is adjustable and has been written into
an FPGA board with a 50-MHz clock. In this experiment, it is set to generatecontinuous pulses without their time interval.
The control panel is operated by hand at the initial charging. The operation
sequence is as follows; first, a charging voltage is input to preset the DMR. Charging
is started by a push button and stops at the preset voltage. A charging resistanceis switched from 6 kΩ to 900 Ω by turning a toggle switch. Operation mode isthen switched by turning another toggle switch from the single pulse mode to therepetition mode.

3.3.2

Safety measures

The field generation system is composed of the magnets and the bank describedin the previous chapter. It also includes the control system of operation sequence.
During the run, inside of the hutch becomes dangerous environment, which is listedas;• X-ray radiation• high-voltage and large-current devices (the magnets and the bank)• low temperature of liquid nitrogen• low oxygen density• EMI noise
The environment is monitored from the outside with two web cameras. Some measured quantities are also monitored from the outside to check safety and stability.
They are listed as below:• peak current and current shape of each shot using the CT• temperature of the charging resistance and the thyristor using non-contact(i.e. radiation) thermometers• surface level of the liquid nitrogen in a container using thermometers with
diﬀerent heights• oxygen density of the atmosphere using oxygen density monitors• vacuum pressure using a vacuum gauge• beam intensity at the central shield

59

3.3 Setup and devices

2)34"5'$"6/+%!
8$/66"$'9:;3"'-<";;+(1!
7$"3"%0'()*"#+$,'-6$""%1!

!"#"$"%&"'()*"#+$,'-(./0"1!

Figure 3.9: Mask test in a repetition mode with a charged voltage of 3.75 kV. The
vertical scale of voltage is converted to the current by a coeﬃcient of the CT, whichis 1 V/kA. A trigger TTL pulse is shown with yellow. A reference current shape isshown with white. The green is a current shape of the present shot. Margin fromthe reference shape is set to ±0.2 div for the vertical scale, which corresponds to±0.8 V. For the horizontal scale, it is set to ±0.05 div corresponding to 20 µs.
Since the current shape directly reflects an anomalous behavior of the magnets andthe bank, It is compared with a reference shape with each shot at online. In caseof the detection of shape error, a signal is fed back to the sequencer and stops thenext shot. To do this, a “mask test” function of a digital oscilloscope (Rohde &Schwarz, RTO1044) is used. Figure 3.9 shows a display of the mask test in 3.75 kV
repetition. The vertical scale of voltage is converted to the current by a coeﬃcientof the CT, which is 1 V/kA. A trigger TTL pulse is shown with yellow. A reference
current shape is shown with white. The green is a current shape of the present
shot. Margin from the reference shape is set to ±0.2 div for the vertical scale, whichcorresponds to ±0.8 V. For the horizontal scale, it is set to ±0.05 div corresponding
to 20 µs. Sign of magnet destruction appears as a spike or deformation of current
shape. When it occurs, the current shape deviates from the reference one andenters the masked region. An error signal is then sent from the oscilloscope to thesequencer and stops the next shot.

3.3.3

Base table and electrodes

Figure 3.10 shows a picture of the base table. It is moved to the hutch with its
casters. It has five-axis alignment mechanism other than the translation along thebeam direction. Three of them including the height is realized using level adjusters
on its foot. Linear guide rails are used for another translation, which transversely

60

3.3 Setup and devices!"#$%&'(#)*'+#,!

;>?@)1',#)-:')849'%)1./("#,)
6+4,)'7)849'%!
-&./,".0'/)1./("#)2'/#)4/)*.$3),4(#5!
2*.$3),4(#5!
;#9#").(<=,%#&,)./()$.,%#&,!
Figure 3.10: Base table of the magnets. It has five-axis alignment mechanism
other than the translation along the beam direction. Three of them including theheight is realized using level adjusters on its foot. Linear guide rails are used foranother translation, which transversely crosses the beam axis. Swing of the baseaxis applies pivot mechanism.
crosses the beam axis. The rest degree of freedom, swing of the base axis, applies
pivot mechanism. The pivot axis is placed at the head of the base, and its tail is
moved with two handles.
A hose of liquid nitrogen is drawn from the outside of the hutch. It is divided
with a tee branch and they go to the containers. The magnet containers are madeof polystyrene boxes.
At the center of the base table, terminal electrodes and the CT is placed. They
are shown in Fig. 3.11, which is seen from the back of the hutch. There are twoterminal boxes and they are lined with polyimide sheets. Each of them has a highvoltage (HV) and a low-voltage (LV) electrode fixed with each other with insulators.
Coaxial cables are drawn from the bank and connected to them. The two cablesfrom each LV electrode go through the CT and are then connected to the inner

61

3.3 Setup and devices

%$!

#$!

#$!

Id!

!"!

%$!

Iu!

Figure 3.11: Terminal boxes seen from the back of the hutch. Each of them hasa high-voltage (HV) and a low-voltage (LV) electrode fixed with each other withinsulators. Coaxial cables are drawn from the bank and connected to them. The
two cables from each LV electrode go through the CT and are then connected tothe inner magnets. In this way, the sum of the two current (Iu and Id ) is read out
with the CT.

6789%:#;#53"<!

12#3'#4*5!

!"#$%&'$(%)*+,#-./0%

12#3'#4*5!

Figure 3.12: Central space below the CT. The beam dump is placed at the center.
There are X-ray windows of polyimide with a thickness of 12.5 µm. The air ofconversion regions is evacuated near these windows with a scroll pump. Behindthese components, a surface level balancer for liquid nitrogen is placed.

62

3.3 Setup and devices

magnets. On the other hand, the two cables from each HV electrode are connectedto the outer magnets. The two magnets in the upstream or the downstream regionis serially connected.
Figure 3.12 shows a picture of central space below the CT. At the center, thebeam dump of lead is placed. It is fixed with a holder and slides on a rail. It
is evacuated during alignment or intensity measurement in front of the detector.
There are also X-ray windows of polyimide with a thickness of 12.5 µm. The airof conversion regions is evacuated near these windows with a scroll pump. Behindthese components, a surface level balancer for liquid nitrogen is placed. It is composed of a brass pipe coated with an insulator and used to match the surface levelsof both containers.

3.3.4

Alignment

The magnets and the detector are aligned on the beam axis. Procedure of thisalignment is as follows. First, position of the X-ray beam is marked using a pieceof photosensitive paper. Two positions in EH1, the most upstream and the mostdownstream positions near the wall, are marked in this way. X-ray spot on these
papers is then pierced with a needle to create a pinhole.
To remember the beam axis, a laser diode with a center wavelength of 650 nm isused. The laser is placed at oﬀ-axis position near the most upstream of the hutch.
A retractable mirror is also placed on the axis before the first paper. The laser
is then directed to the mirror. The directions of the laser and of the mirror are
adjusted until the laser light goes through the two pinholes.
After this alignment of the laser axis, the laser works as a reference of the X-ray
beam and is hence referred to as a “reference laser”. Power of the laser is measured
with a laser power meter placed downstream of the hutch. The power meter is also
retractable. Magnets are then aligned onto the laser so that the center of its pipe
coincides with it. The alignment is carried out checking the power meter. Centerof the detector placed in EH2 is also aligned onto the reference laser. Finally, allretractable components are slid to oﬀ-axis positions, and X-ray intensity is checkedin front of the detector using a photodiode (PIN A), which will be described in afollowing section (Sec. 3.5.1).

3.3.5

Other devices and components

Liquid-nitrogen vessels
When data acquisition run is started, heat loss of the magnets (the total heating isabout 2.5 kW) consumes liquid nitrogen. In addition to this, natural evaporation
also lowers the surface level. Each container has a volume of 40 ℓ and they are filled
every 1–2 hours. Figure 3.13 shows a picture of the vessels placed at the outsideof EH1. The hose becomes frozen when the nitrogen is flowing. A pair of vessels istherefore used for a rapid switching. A 100-ℓ vessel is consumed every 1–2 hours,
and 12 vessels are repeatedly filled by a supplier.

3.3 Setup and devices

63

Figure 3.13: Vessels of liquid nitrogen placed at the outside of EH1. Left: a pairof vessels is used for a rapid switching. The hose goes through the duct. Right: 12
vessels are repeatedly filled by a supplier.

Figure 3.14: X-ray windows. Left: windows of the conversion region. X-ray beamof BL19LXU is so strong and there can be seen a burn spot on these center. Right:
windows of the re-conversion region.
X-ray windows
A polyimide foil with a thickness of 12.5 µm is used for windows of the conversion
and the re-conversion regions. Their pictures are shown in Fig. 3.14. The left figure
shows the upstream windows. Since X-ray beams of BL19LXU is so strong, there
can be seen a burn spot on the center of these windows. The beam is blocked at thecentral shield and therefore the spots do not appear on the downstream windows.
The other dielectric devices
Dielectric devices are used to control and monitor high-voltage environment of EH1.
Two of them, the CT and optical fibers, are described so far. In addition to these,
the other dielectric devices are explained below:• current transformer: Pearson Model 14239, reads out the magnet current.
• optical fiber: Sumitomo Electric CCV-HC-20/07, transmits a signal to thetrigger board.

64

3.4 Setup and devices• HV noise-cut transformer: Denkenseiki NCT-I4, 2 kV (DC) / 10 kV (impulse), provides AC100V to devices in EH1.
• isolation amplifier: NF Electronic Instruments 5325, amplifies the read-out
voltage of the photodiode in the shield (PIN B).
• insulation flange: Cosmotec N40ISL12KV, protects the vacuum pump.

3.4

EH2: detection system

Detection system consists of a germanium detector, its radiation shield, and DAQ
electronics. Performance of the detector is characterized by energy resolution,
detection eﬃciency, time resolution, and background count rate. This section firstsummarizes them, and then each item is described in detail. Alignment of thedetector on the beam axis is also explained.

3.4.1

Summary of detector performance

Table 3.2 shows a summary of the detector performance, which will be describedin the following sub-sections.
Parameter
Energy resolution
Detection eﬃciency
Time resolution
BG count rate (typ.)Value
93 eV (σ) at 9.5 keV
89±1% at 9.5 keV
20–30 ns at 14.4 keV
6 × 10−4 cps/0.5 keV at 9.5 keV

Table 3.2: Detector performance

3.4.2

Shield and alignment

Environmental radiation becomes background events of the signal. To reduce them,the detector is doubly shielded. The outer shield consists of lead blocks and isused to protect the detector from the environmental radiation. The inner shield
is attached to the end cap of the detector. It shields X rays from a decay chainof 210 Pb contained in the outer shield. By using a flange shield, it also works tonarrow its open angle and blocks X rays from the oﬀ-axis.
Figure 3.15 shows pictures and a schematic view of the inner shield. The left
figure shows the bare end cap (aluminum) of a germanium detector (Canberra
GL0210). The crystal has a diameter of 16 mm and a thickness of 10 mm. The
detector window is composed of beryllium and its thickness is 500 µm. The rightfigure shows the inner shield covering the end cap. The end cap is covered with abrass cylinder on its side and with a stainless-steel plate on its face. To avoid the

65

3.4 Setup and devices

8./%&0"--#-.""0#2%2":;/&5"#-3%"0'!

!+/--#-%'"#-3%"0'!
)"#*+,-./0!

10#"&'*/2!

!"#$%&'($!
</*==>!
8./%&0"--#-.""0#9+(&.#-3%"0'!

4%&%&56! 4%&%&57!

Figure 3.15: Germanium detector and its inner shield. Left: the bare end cap(aluminum) of a germanium detector (Canberra GL0210). Right: the inner shieldcovering the end cap. Bottom: the end cap is covered with a brass cylinder on its
side and with a stainless-steel plate on its face. A stainless-steel pipe-flange shield
is attached to the front shield to narrow the open angle.

direct contact of the plate on the detector window, two plastic linings are inserted
between them. A stainless-steel pipe-flange shield is attached to the front shield tonarrow the open angle.
Figure 3.16 shows pictures of the outer shield. As shown in the left figure, thedetector is aligned to the beam axis. Using the reference laser described in theprevious section. the alignment is first carried out without the pipe-flange shieldand is then checked with X rays using a photosensitive paper. This check is carriedout before and after the run to confirm that the detector has not moved. The rightfigure shows the outer shield. The solid angle other than the pipe-flange shield andthe Dewar is covered with lead blocks with a thickness of more than 50 mm.
Figure 3.17 shows measured background energy spectra. The energy thresholdis set around 3 keV. The black spectrum is obtained without the outer shield. The
background rate is 8 × 10−3 cps/0.5 keV at 9.5 keV, which is the photon energy ofthe experiment. The red spectrum is obtained using the outer shield, and its rate
is 6 × 10−4 cps/0.5 keV at 9.5 keV. The shield reduces the background rate by afactor of more than 10−1 .

66

3.4 Setup and devices

Count / s / 0.5 keV

Figure 3.16: Outer shield of the detector. Left: the detector is aligned to the beamaxis using a reference laser. Right: the outer shield. The solid angle other thanthe pipe-flange and the Dewar is covered with lead blocks with a thickness of morethan 50 mm.

10-2

-3

10

2

4

6

8

10

12

14

16

Energy [keV]

Figure 3.17: Measured background energy spectra. The energy threshold is set
around 3 keV. The black/red spectrum is obtained without/with the outer shield,
respectively. The shield reduces the background rate by a factor of more than 10−1 .

67

3.4 Setup and devices

Energy resolution"2 / ndf
10.46 / 8
p00.1094 ! 0.001435
p1
74.34 ! 0.318

160
150
140

! (eV)! (eV)

3.4.3"2 / ndf
10.46 / 8
p00.1094 ! 0.001435
p1
74.34 ! 0.318

125
120
115
110

130
120

105

110

100
95

100

%&'()!

90

!"#$!
**+$!

90

*,-.!

85

80
10

20

30

40

50

60

Energy (keV)

5

10

15

20

25

30

Energy (keV)

Figure 3.18: Measured resolution√ as a function of the energy. The data points are
fitted with a function of σ = F W E + σ02 (see the text). The energy resolution
at 9.5 keV is obtained as 93 eV.
In order to define energy region for the signal X rays, energy resolution of
the detector is measured using several checking sources. Figure 3.18 shows themeasured resolution expressed as the standard deviation. The data points are
fitted with a function of√(3.5)
σ = F W E + σ02 ,where F the Fano factor, W the W-value of the germanium of 2.95 eV, E theenergy in keV, and σ0 the constant oﬀset from the electric noise. The Fano factor
for the germanium detector is typically 0.05–0.13. The fitting is carried out by
setting F and σ0 as the fitting parameters. Their obtained values are shown in thebox of the figure. The energy resolution at 9.5 keV, which is the photon energy, isthus calculated as 93 eV.

3.4.4

Detection eﬃciency

Detection eﬃciency including attenuation in the detector window is also measured
with checking sources. Since the K-edge of germanium is 11 keV, thickness of deadlayer on surface of the crystal decides the eﬃciency at low energies. The thickness
is obtained with comparison of the data with GEANT4 simulation. A conventional
way is to measure the eﬃciency as a function of energy. It is then compared withsimulation, varying the thickness. The true thickness is estimated to be at theminimum of the χ2 distribution.
For low-energy X rays around 10 keV, on the other hand, scattering and absorption in the source window or in the air gives not a small correction to the data.
Moreover, each source (and each measurement) has a diﬀerent window thickness,
window material, and distance from the detector. To evaluate this precisely, simulations are carried out for each source and for each energy with corresponding
geometry. Thus the thickness is obtained for each measurement and is shown in
the left of Fig. 3.19. It is obtained to be 1.83 ± 0.48 µm, which is a reasonable68

3.4 Setup and devices

20

Efficiency

Thickness !m!2 / ndf
11.56 / 7
p0
1.834 " 0.4784
55

18
16

ID 1: Fe, 5.86 keV
55
ID 2: Fe, 6.45 keV
68
ID 3: Ge, 8.59 keV
68
ID 4: Ge, 9.20 keV
68
ID 5: Ge, 10.2 keV
57
ID 6: Co, 14.4 keV
ID 7: 241Am, 26.3 keV
241
ID 8: Am, 59.5 keV

14
12
10
8
6

0.8
t=1.83 µ m

0.7
0.6

t=1.83± 0.48 µ m

0.5
0.4

4
2
0

1
0.9

t=0 µ m

0.3
1

2

3

4

5

6

7

8

Measurement ID

0

10

20

30

40

50

60

Energy (keV)

Figure 3.19: Measurement of the detection eﬃciency. Left: comparison of the
thickness of the surface dead layer with data and simulation. Right: the detector
eﬃciency obtained by GEANT4 simulation with the thickness of 1.83 ± 0.48 µm,
including attenuation in the detector window. The dashed line shows the eﬃciency
without the dead layer. Eﬃciency at low energies below 5 keV steeply decreases
due to attenuation in the detector window.
value for this type of germanium detector. Using this value, the eﬃciency curveis finally obtained by a simulation. It is shown in the right figure and its value
is 0.89 ± 0.01 at 9.5 keV. The dashed line shows eﬃciency without the dead layer(t = 0). Eﬃciency at low energies below 5 keV steeply decreases due to attenuationin the detector window.

3.4.5

Time resolution

Signal events are synchronized with the pulsed field. To cut the other unsynchronized events, time resolution of the detector is also measured. Figure 3.20 shows apicture of the measurement. The measurement applies a decay chain of the 57 Co
source shown in the left of Fig. 3.21. First, a 5/2- state decays to a 3/2- state andemits a 122-keV γ ray. The state succeedingly decays to the ground state (1/2-)
with time constant of 141.8 ns and emits a 14.4-keV γ ray. The 122-keV γ ray
is detected with a LaBr3 scintillator mounted on a PMT, and it defines the start
time. The succeeding 14.4-keV γ ray is detected with the germanium detector.
As shown in the right of Fig. 3.21, the detector has a point-like back electrode.
Travel time of an electron hence becomes smaller when the photon hits the centerof the crystal. The photon from the outer edge, on the other hand, gives a large
travel time. The top of Fig. 3.22 shows a calculation of this travel time. The blueline shows the electron travel time and the red line is an expected time spectrum
obtained by decaying the blue line with a time constant of 141.8 ns. The middle
figure shows a measured time spectrum. The decay curve is fitted with an exponential function, and it gives a decay constant of 142.9±1.2 ns in agreement withthe expected time constant. The time resolution is red to be about 150 ns. The
bottom figure shows a time spectrum measured with the inner shield as shown in69

3.5 Setup and devices+,-.!

!"#$%$&'()*!

Figure 3.20: Measurement of time resolution.

./0$!

+154.),(-!
γ!

+00),(-!

+15),(-!
!#!

=>?@1!

+343),(-)
678+3+49):;<!
*(!

1/0$!

+343),(-!

+/0$!

2),(-!

"$%&'()*(!

$+),-!

!"!

Figure 3.21: 57 Co level diagram and geometry of the crystal electrodes. Left: a
5/2- state decays to a 3/2- state and emits a 122-keV γ ray. The state succeedingly
decays to the ground state (1/2-) with time constant of 141.8 ns and emits a 14.4keV γ ray. The 122-keV γ ray is detected with a LaBr3 scintillator mounted on
a PMT whereas the succeeding 14.4-keV γ ray is detected with the germanium
detector. Right: the detector has a point-like back electrode, and the electron
travel time becomes smaller when the photon hits the center of the crystal.
Fig. 3.20. The stainless-steel face shield collimates the incident X rays with anaperture of 5 mm. The fitting gives a decay constant of 140.5±3.3 ns and a better
time resolution of 20–30 ns is obtained.

3.5

Intensity measurement

This section describes measurements of beam intensity. Two PIN photodiodes,
PIN A and PIN B, are used at diﬀerent positions shown in Fig. 3.1. PIN A is used

70

Count / ns

3.5 Setup and devices

×103
140

!"#$%"&'"()*&
Beforedecay120+,"%&'"()*&
After
decay

100
80
60
40
20
0

-100

0

100

200

300

400

500

Count / 2 ns

Time (ns)!2 / ndf
p1
p2

600

224.4 / 228
1042 ! 6.6
142.9 ! 1.2

500
400
300
200

-./&01!

100
0
-100

0

100

200

300

400

500

600

Count / 4 ns

Time (ns)!2 / ndf
p1
p2

160

122.4 / 127
726 ! 13.9
140.5 ! 3.3

140
120
100
80
60
40

2/34/&01!

20
0
-100

0

100

200

300

400

500

600

Time (ns)Figure 3.22: Calculation and measurements of the time spectra. Top:: calculated
time spectra. The blue line shows the electron travel time and the red line is an
expected time spectrum obtained by decaying the blue line with a time constant of
141.8 ns. Middle/bottom: measured time spectra without/with a face shield with
an aperture of 5 mm, respectively. The start time is defined by the 122-keV γ ray
detected by a LaBr3 scintillator.

3.5 Setup and devices

71

for intensity measurement in front of the germanium detector. The measurement
is carried out at the occasion of change from one data set to the next one (seeSec. 4.3.1). During the run, it is evacuated to oﬀ-axis position. PIN B, on theother hand, is always located on the beam axis at central space of the base plate.
It monitors the beam intensity during the run. When the beam intensity at thedetector is measured with PIN A, PIN B is evacuated to the oﬀ-axis.

3.5.1

Intensity measurement between data sets: PIN A

Intensity of the X rays is measured with a silicon PIN photodiode (Hamamatsu,
S3590-09). Figure 3.23 shows its picture. It has a depletion thickness of 300 µm.
For the light shielding, the bare chip is contained in an aluminum case coated withnickel plating. A beryllium foil with a thickness of 150 µm is used as its window.
Output current I of the photodiode is directly read out using a resistor of 50Ω. Beam intensity F is calculated from the current as
1
1
WSi I
× ×
,
(3.6)
F =
e
ω Rabs Rattwhere WSi the W-value of Si, which is 3.66 eV, e the elementary charge, ω the
X-ray energy, Rabs the absorption rate of the detector including its window, andRatt an attenuation rate of an aluminum plate. Figure 3.24 shows its absorption
rate as a function of energy. The black line shows the rate with the window and theblue line shows without it. Both are obtained with GEANT4 simulation. The redline is a calculation using NIST data, and agrees with the simulation. The X-ray
beam of BL19LXU is so strong to cause saturation of the output current of thephotodiode. An aluminum plate with a thickness of 301 ± 1 µm is therefore used
to attenuate the beam. Its attenuation rate Ratt is conservatively calculated witha plate thickness of 300 µm, and is 8.5% for 9.5-keV X rays. If the photodiode isinclined against the beam axis, eﬀective thickness of the attenuation plate becomeslarger, and X rays are more attenuated by a factor of cos θ−1 . A typical tilting
angle of, for example, θ = 3◦ changes the rate by 0.1%. Thus a measured value
becomes always conservative and is used in the analysis without this correction.

3.5.2

Intensity monitor during the run: PIN B

Another photodiode is also used to monitor the beam intensity at the shield. Figure 3.25 shows its picture. The same type of a bare chip is embedded in a leadcylinder with a diameter of 30 mm. This photodiode in lead also uses an attenuation plate of aluminum with the same thickness of 300 µm as a light-shielding
window. The edge of the plate is shielded with a tape. Another lead cylinder with
an aperture of 6 mm is fixed on it. The seam is also shielded with the shielding tapeand is wrapped around with lead sheet to avoid photon leakage. Electron beamof the storage ring is sometimes aborted due to machine troubles. Its intensity isthus always monitored to check whether the beam is on. The data taken during
the beam oﬀ is cut by oﬀ-line analysis.

72

3.5 Setup and devices!"#$$!

!"#$$!

!"#$$!

!"#$$!

!"#$$!
!"#$$!

%&'()!
*+,-'()#

absorption

Figure 3.23: Silicon PIN photodiode. Left: the bare chip (Hamamatsu, S3590-09).
Right: the bare chip is contained in an aluminum case coated with nickel plating
for the light shielding (PIN A).

1

normalwithout Be window (150 µm)

0.8
rough estimate (NIST)

0.6
0.4
0.2
0
0

5

10

15

20

25
30
energy (keV)

Figure 3.24: Absorption rate of the photodiode as a function of the X-ray energy.
The black line shows the rate with the window and the blue line shows without it.
Both are obtained with GEANT4 simulation. The red line is a calculation using
NIST data.

73

3.5 Setup and devices

4567,8975#+:5$6),&*#!

!"#$%&'($)*+&,#)-!+.),/01)223!

!*#<,%<#)-;=)223!

1/)22!

?/)22!
;1/)22!
><&**5$6)975#+:!

Figure 3.25: Another photodiode used to monitor the beam intensity at the shield(PIN B). The same type of a bare chip is embedded in a lead cylinder with adiameter of 30 mm. An aluminum plate with a thickness of 300 µm is used toattenuate the beam and to shield the light. Another lead cylinder with an apertureof 6 mm is fixed on it to avoid photon leakage.

74

3.5 Setup and devices

Chapter 4

Run and analysis
In this chapter, data acquisition and its analysis is described. First, beamtime andprocedure of the measurement is explained. Then the whole data is divided intosub-sets (data sets) and calculate the limit on gaγγ . Systematic uncertainties arealso discussed.

4.1

Beamtime

Data acquisition run has been carried out at BL19LXU in SPring-8. Beamtime isassigned for a week from November 18 to 25 in 2015. The first two days of the
beamtime are spent in preparation. It includes a setup of the magnets, the bank,and the detector, installing them into the hutch, and alignment of them on the beamaxis. There are consecutive holidays in the middle of the beamtime. Delivery of theliquid nitrogen stopped for these days, and the period became a deadtime of themeasurement. In order to release the hutch for the successive beamline user, ourbeamtime also includes a time for carry-out of the system from the hutch. After
subtracting these non-measurable times, net time of the data acquisition becomes
about two days.

4.2

Procedure of measurement

Procedure of the measurement is described as below.
• When surface level of liquid nitrogen becomes low, data acquisition and operation of the magnets are stopped.
• The hutch is opened and ventilated with large ventilators.
• The lead shield between the magnets (PIN B) is removed, and X-ray intensity
is measured with a photodiode (PIN A) set in front of the detector.
• The shield (PIN B) is returned to its original position, and liquid nitrogen
starts to be filled into the containers.
75

76

4.3 Run and analysis• When the surface level gets back to an operational level, operation of themagnets and data acquisition are started.
• When the surface level gets to the maximum height of the container, its fillingis sopped.

4.3

Summary of run

4.3.1

Data setBeam intensity is measured when the surface level of liquid nitrogen becomes lower.
Once the nitrogen is filled up, it takes about 1–2 hours for the surface level tobecome lower again. The whole data is thus divided into sub-sets (data sets) on
the occasion of the intensity measurement. A total of 35 data sets are obtained.
Table 4.1 shows their summary.
Due to some malfunction of the trigger board, four fifth of the data is taken witha low charged voltage of 3.50 kV. The rest of the data is acquired with 3.75–4.00 kV
operation. The Nshot is the number of shots during the data set. There are somedata sets having a small number of shots. This is due to beam abort of the electron
ring, which occasionally occurred during the measurement. The photon flux F
has been converted from the current of PIN A described in the previous chapter.
Intensity is measured between data sets. Thus each data set is sandwiched with two
intensity measurements (FA and FB ). The center value and its uncertainty during
the data set is calculated as (FA + FB )/2 ± (FA − FB )/2. There can be seen a slightdecrease fo the intensity over the whole measurements. The reason is considered to
be a detune of the monochromator due to the continuous irradiation on its crystals
for a week. The value of I 4 ttot F represents a contribution to the sensitivity on the
coupling constant gaγγ . It is again described in the following analysis. The value ofI 4 ttot /Nshot , on the other hand, represents its net contribution of the magnets per
shot. It clearly shows an eﬀectiveness of charging at a higher voltage. The total
number of shots in the measurement is 13,838.

4.3.2

Field distribution

As a summary of the measurement, Fig. 4.1 shows field distribution of the mostdownstream magnet (magnet5) for the total 13,838 shots. The field is represented
by a value at the center of the magnet. The first pulse is ranging from 8.1 T to
9.6 T, and the second pulse is from 5.5 T to 6.9 T. Due to heat loss of the first
pulse, the second pulse is generated with a relatively smaller energy. This results
in a decrease of the peak field of the second pulse.
As the field increase, the number of shots decreases for both the first and thesecond pulses. One reason for this is that 21% of the total shots is generated witha little higher voltage of 3.75–4.00 kV than 3.50 kV. This contribution is clearlyseen as the gap of the first pulse around 8.5 T. On the other hand, both of the

77

4.3 Run and analysis

Data set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Total

Vc
[kV]

Nshot

3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.75–4.00
3.75
3.75
3.75
3.75
3.75
3.75

239
73
330
431
505
305
506
562
526
390
456
336
523
398
481
36
249
356
397
504
325
184
381
592
464
368
317
705
298
418
471
483
428
444
357

13

[10

F
photon/s]

I 4 ttot F[10 kA4 photon]

I 4 ttot /N shot[101 kA4 s]

1.35
0.40
1.80
2.31
2.67
1.61
2.69
2.91
2.65
1.99
2.28
1.73
2.63
1.98
2.28
0.15
1.25
1.77
1.96
2.46
1.58
0.91
1.94
3.09
2.38
1.88
1.68
3.51
1.70
2.34
2.26
2.11
2.29
2.37
1.90

1.62
1.63
1.64
1.62
1.62
1.60
1.62
1.63
1.62
1.63
1.62
1.67
1.64
1.63
1.66
1.67
1.65
1.63
1.62
1.61
1.61
1.62
1.63
1.66
1.70
1.71
1.71
1.90
2.09
2.04
1.86
1.86
1.87
1.89
1.88

3.48±0.16
3.32±0.00
3.33±0.01
3.29±0.04
3.27±0.02
3.29±0.01
3.28±0.03
3.18±0.07
3.10±0.02
3.14±0.03
3.08±0.03
3.07±0.02
3.08±0.02
3.04±0.02
2.85±0.17
2.54±0.15
3.04±0.01
3.05±0.01
3.05±0.01
3.04±0.01
3.02±0.01
3.06±0.05
3.13±0.02
3.14±0.00
3.02±0.12
2.98±0.08
3.10±0.04
2.62±0.01
2.72±0.09
2.75±0.06
2.58±0.11
2.35±0.12
2.86±0.01
2.84±0.01
2.83±0.00

13,8381770.8±0.3

Table 4.1: Data sets

78

Count / 0.1 T

4.4 Run and analysis

104

Second pulse

First pulse

3

10

102
10
1
5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

Bcenter [T]Figure 4.1: Field distribution of the most downstream magnet for the total 13,838
shots. The field is represented by a value at the center of the magnet. The first
pulse is ranging from 8.1 T to 9.6 T, and the second pulse is from 5.5 T to 6.9 T.
Due to heat loss of the first pulse, the second pulse is generated with a relatively
smaller energy. This results in a decrease of the peak field of the second pulse.
separated distributions of the first pulse still show the falling behavior with respect
to an increase of the field. This is due to a transient phenomenon, which lasts until
the coil temperature reaches a thermal equilibrium. As an example, Fig. 4.2 showschange of the field measured at the beginning of the 29th data set. The first shot
generates 9.4 T, and then the field decays exponentially. The decay lasts until itreaches a thermal equilibrium around 8.7 T. Fitting of the data points other than
the first shot gives its time constant to be 2.3 shots. Since the shot repetition ofthis data set is about 0.09 Hz, it corresponds to a time constant of 26 s. This seems
to be contrary to the time constant shown in Chapter 2. The reason is, however,clear since most of the temperature increase is completed at the first shot. Thiscan also be seen as an isolated structure in Fig. 4.1 around 9.5 T for the first pulse
and around 7 T for the second pulse.

4.4

Event timing

Timing information of an event at the detector is recorded and expressed as anelapsed time from the latest shot. Figure 4.3 shows the time spectrum of all events.
The top figure shows its long time view. The counts decrease rapidly at about 10
s. This is consistent with the fact that most of the data sets are operated witha shot repetition of about 0.1 Hz. The first several data sets are operated with arelatively slow shot repetition of ∼0.07 Hz for conditioning. These data give the

79

Bpeak, center [T]

4.5 Run and analysis

χ2 / ndf
p0
p1
p2
p3

9.6
9.4

2.047e-05 / 118.722 ± 0.0005752
0.6619 ± 0.5002-0.8172 ± 1.775
2.334 ± 0.03466

9.2
9
8.8
8.6

0

2

4

6

8

10

12

14 16
# of shots

Figure 4.2: Change of field of the most downstream magnet, measured at the
beginning of the 29th data set. The field is represented by a value at the center ofthe magnet. The first shot generates 9.4 T, and then, the field decays exponentially.
The decay lasts until it reaches a thermal equilibrium around 8.7 T.
counts around 13±3 s. Events hitting the detector during the field can be signal
candidates, and the rest of unsynchronized events are cut oﬀ. The bottom figure
shows a magnified view around the first 100 ms. The duration of a shot is about
2 ms. This corresponds to the leftmost bin in the figure. It contains one event,which hit the detector at 1.8 ms, the end of the second pulse. The other events
spread uniformly and do not show any peculiar structure.

4.5

Energy spectrum

Figure 4.4 shows a measured energy spectrum of all events. Energy threshold is set
around 3 keV. The black spectrum shows unsynchronized events which occurredin 8 s from the latest shot. The red one shows the synchronized event, and its
energy is 4.8 keV. Since these two spectra are normalized with time, the large
time diﬀerence between the signal (∼2 ms) and the background (8 s) makes any
synchronized event out of the figure. Therefore, signal strength of synchronized
events is taken to be 1/100 for visibility. The second event hits the detector at 8.3
ms and the total number of unsynchronized events are 1,521 from 0 keV to 16 keV.
These give an estimated count to be observed from 1.8 ms to 8.3 ms. The count is
0.96 ± 0.62 and is self-consistent with the observed one event.
Energy resolution of the detector is 93 eV (σ) at the beam energy of 9.5 keV

80Count / 0.4 s

4.5 Run and analysis

100

50

Count / 2 ms

0
0

2

4

6

8

10

12

14

16

18 20
Time [s]0.080.1Time [s]

3
2
1
0
0

0.02

0.04

0.06

Figure 4.3: Time spectrum of all events. The origin of the time is defined by thelatest shot. Top: the long time view. The counts decrease rapidly at about 10 ssince most of the data sets are acquired with a shot repetition of about 0.1 Hz.
Bottom: the magnified view around the first 100 ms. The duration of a shot isabout 2 ms. This corresponds to the leftmost bin in the figure. It contains one
event, which hit the detector at 1.8 ms, the end of the second pulse.

81

4.6 Run and analysis(Fig. 3.18). This gives a signal region of ±2σ to be 9.5 ± 0.2 keV, which is also
shown in the figure. Any candidate is not observed in the region.

Count / s / 0.4 keV-3

0.8 ×10

0.6

0.4

0.2

0

0

0'12133!
2

4

6

8

!"#$%&'()#"*$'+,-./!
10

12

14

16

Energy [keV]
Figure 4.4: Measured energy spectrum of all events. Energy threshold is set around3 keV. The black spectrum shows unsynchronized events which occurred in 8 s fromthe latest shot. The red one shows the synchronized event, and its energy is 4.8
keV. The two spectra are normalized with time, and signal strength of synchronized
events is taken to be 1/100 for visibility.

4.6

Constraining the coupling constant

Since the field (and its current) changes with time (Fig. 4.5), the conversion probability also depends on time. Equation (1.11) is thus rewritten as∫ ttotN =η

Pγ→a (t) Pa→γ (t) F dt,

(4.1)

0

where Pγ→a (t) the conversion probability of upstream region, Pa→γ (t) that of downstream region, F the photon flux in s−1 , and ttot the total pulse duration summed
up over all shots. Correspondingly, the conversion probability of Eq. (1.12) isrewritten as
∫
2
2
gaγγ
ω
iqz
√
(4.2)
Pγ→a (t) = Pa→γ (t) =B(z, t) e dz
4
ω 2 − m2awith B(z, t) as a function of space and time.
Here the beam energy is 9.5 keV. Detection eﬃciency at the energy is obtained
to be 89 ± 1% from Fig. 3.19. The photon flux and total pulse duration are listed
in Tab. 4.1. The air in the beam pipe is evacuated, and the pressure is monitored

82

4.7 Run and analysis

during the run. It is better than 10 Pa. From Eq. (1.14), this gives an eﬀective
photon mass of 7 meV. The null observation gives the number of signal events to be
2.96 at 95% confidence level (N95CL ). Both conversion probabilities depend on thefield maps. They are scaled from Fig. 2.11 using field-current ratio at high voltages
shown in Fig. 2.7. The resulting maps are shown in Fig. 4.6 with the pictures.
Their spacing is 417 ± 1 mm. These values are listed in Tab. 4.2.
Although these magnets have slightly diﬀerent maps with each other, their
input current is common since they are serially connected with cables. The current
transformer reads the sum of the upstream and the downstream currents (Isum =Iu + Id ). The ratio of the two currents (Iu and Id ) are measured by passing eachcable through the hole. Figure 4.7 shows the measured currents and their diﬀerencewith respect to a charged voltage. Each current is almost exactly half of the total
current and their diﬀerence is less than 1%.
Parameter

Value

Photon energy ω
Detection eﬃciency ηEﬀective photon mass mγ
Signal events at 95% C.L. N95CL
Photon flux F
Total pulse duration ttot
Field B(z, t)

9.5 keV
0.89 ± 0.1
7 meV
2.96
see Tab. 4.1
see Tab. 4.1
see Fig. 4.6 and Fig. 4.5

Table 4.2: Parameters used to calculate the limit
Since the t and z are integrated independently, right side of Eq. (4.1) can be
rewritten as
4
gaγγ
ω2
η
16 ω 2 − m2a∫ ttot (0

Isum (t)
2

)4

∫
F dt

2
iqz

(B/I)u (z) e

dz

∫

2

(B/I)d (z) eiqz dz .

(4.3)
The first integral is calculated by using a sum of the two currents (Isum (t)) recordedby each shot. It has already been listed as I 4 ttot F for each data set in Tab. 4.1.
The second and the third integral are calculated from the maps of the upstream
and downstream region ((B/I)u (z) and (B/I)d (z), Fig. 4.6).

4.7

Systematic uncertainties

Before the limit is calculated, various sources of systematic uncertainties are studied
here. They are calculated as the change of gaγγ in its flat region below ≃0.1 eV.
They are summarized in Tab. 4.4

83

I [kA]

4.7 Run and analysis

10
8
6
4
2
0
-2
-4
-6
0

1

2

3

4

5
time [ms]!"#$%&"'()!

!"#$%&"'()!

Figure 4.5: Current shape of a shot with four magnets (Isum (t)) operated with acharged voltage of 3.75 kV. NOTE that the vertical value has been attenuated withan attenuator of -10 dB.

Figure 4.6: Field maps of the upstream (Iu , left) and the downstream (Id , right)
regions. The spacing between the two magnets is 417 ± 1 mm. The maps are scaled
from Fig. 2.11 using field-current ratio at high voltages shown in Fig. 2.7.

84

Ipeak [kA]

4.7 Run and analysis

16
15
14

∆ Ipeak/I peak [%]

13
3

3.2

3.4

3.6

3.8

4

3

3.2

3.4

3.6

3.8

4

-0.4
-0.6
-0.8
-1
Vc [kV]

Figure 4.7: Ratio of the two currents (Iu /Id ) as a function of charged voltage.
Top: the measured currents of the upstream (triangle) and the downstream (box)magnets. Bottom: the diﬀerence of the two currents. Their diﬀerence is less than
1%.

4.7.1

Small uncertainties

Uncertainty of the photon flux is estimated from the diﬀerent two measurements
between before and after the data set, and is shown in Tab. 4.1. Its contribution
is included in the calculation of I 4 ttot F . Since measurements of each data set
are independent, their quadrature sum gives (70.8 ± 0.3 ) × 1017 kA4 photon. gaγγ
depends on the fourth root of I 4 ttot F , and its uncertainty becomes 0.1%.
Another systematic error comes from the detection eﬃciency. It arises fromuncertainty of the thickness of the surface dead layer shown in Fig. 3.19. The
detection eﬃciency is found to be 89 ± 1%. Since gaγγ depends on the fourth rootof the eﬃciency, its uncertainty becomes 0.4%.
The field-current ratio slightly changes with its charged voltage. The uncertainty of each magnet is shown in Fig. 2.7. Since gaγγ linearly depends on this,their quadrature sum gives the second largest uncertainty of 1.2%.
Accuracy of map measurements also aﬀects gaγγ . Since the flat region of gaγγ
linearly depends on the field-length product, a value obtained by the space integralof the map is concerned. Integrals of two measured maps in Fig. 2.9 give theirdiﬀerence to be ±0.9%.
Contributions from the magnet spacing (Fig. 4.6, 417±1 mm) and current ratio(<1%) are evaluated by changing the parameters of the gaγγ calculation. Althoughphase of the conversion probability changes with respect to the magnet spacing,
contribution from that appears at extremely high mass region of gaγγ . Any changes
are thus not observed for the low mass region. Significant contribution from a slightchange of the current ratio is also not confirmed. The reason for this is that if thecurrent of one side increases, that of the other side decreases. gaγγ depends on the4.7 Run and analysis

85

product of both probabilities, and the resulting changes becomes so small.

4.7.2

Temperature increase at thermal equilibrium

During repetitive operation, temperature of the coil becomes higher than a liquidnitrogen temperature of 77 K and reaches an equilibrium temperature. Temperature dependence of parameters are described here.
Temperature increase of the coil causes i) an increase of field length along thebeam axis, ii) an increase of the inductance, and iii) an increase of the resistance ofthe coil. i) and ii) are caused by the geometrical deformation of the coil due to thethermal expansion. iii) is caused by the temperature dependence of the resistivityof copper.
Expansion of the field length
The temperature increase of the coil is estimated from the current shape. The resistance component of the magnet changes a sinusoidal shape of ideal LC oscillation
into a LCR dumpling oscillation. Its shape is written as
(
)
R
ω0
exp −
t sin ω t,
I(t) = I0
ω
2L

(4.4)

√
√
√
√
where I0 = V0 C/L, ω0 = 1/ LC, and ω = ω0 1 − γ 2 (γ = R/2 C/L). Fitting
is carried out for a current shape at thermal equilibrium of 3.75 kV and 0.12 Hz
operation, which gives a heating of about 0.5 kW. The resistance of one magnet is
obtained to be 25 mΩ. Coil temperature at the thermal equilibrium is calculated
from the temperature dependence of resistivity of copper
ρ(T ) = −3.14 × 10−9 + 7.2 × 10−11 × (T [K]).

(4.5)

The resistance corresponds to T ≡ T0 + ∆T = (77 + 115) K.
Although thermal expansion of the coil is suppressed by its backup metals,
expansion of a free coil (i.e. without backup metals) is assumed here. Expansion ofa free coil is calculated from the coeﬃcient of thermal expansion of copper, whichis 16.8 × 10−6 K−1 . This increases the longitudinal length of the coil (200 mm)
by 0.2%. The increase of the field volume causes an increase of the inductanceand therefore decreases the current. Its contribution to gaγγ is included in thecalculation of measured current shapes at thermal equilibrium and is described in
the next sub-section. The field-current ratio, on the other hand, does not changewith this longitudinal expansion. The product of the field-current ratio and the coillength, which linearly aﬀects gaγγ , thus increases by 2%. The extreme assumptionof a free coil gives better result on gaγγ and here this contribution is conservatively
neglected.

86

4.7 Run and analysis

Diﬀerence of the two currents
The two cases of (ii) and (iii) are the change of circuit parameters, R and L.
If these values at thermal equilibrium are diﬀerent between upstream and downstream magnets, they give diﬀerent shapes of current (Iu (t) ̸= Id(t) ). Here twochanges are conceivable; current ratio and time scale. The ratio of the two currents
becomes unbalanced when there is abnormal temperature rise in either upstream or
downstream magnets. This is caused by the diﬀerence between the two resistancecomponents (Ru and Rd ). Change of the time scale between the two currents, on
the other hand, is caused by the diﬀerence between the two inductance components(Lu and Ld ).
Since only the sum of the two currents are read out and used in the analysis, additional measurements are carried out to measure Iu (t) and Id (t) separately. Eachof them at thermal equilibrium are read out one by one with the same setup of therun. The magnets are operated with 3.75 kV and 0.12 Hz, which gives the largest
heating among all the data sets and therefore would give the largest changes. Iu (t)and Id (t) are compared with a half of Isum (t)/2, which has been measured during
the run. The results are summarized in Tab. 4.3. Circuit parameters obtained fromthe fitting of current shapes using Eq. (4.4) show good agreements other than aslight diﬀerence of resistance component of the downstream (Rd ).
Both contributions from the changes of magnitude and time scale of the twocurrents are directly calculated with an integral of Iu and Id . The contribution fromthe diﬀerence between the two currents, which linearly aﬀects gaγγ , is obtained as


1/4

∫ t1

Iu (t)2 Id (t)2 dt 

1 −  ∫0 ()4t1
Isum (t)dt2
0= 0.3%,(4.6)

where t1 a period of one shot.
Current

R [mΩ]

L [µH]

Imax [kA]

Isum /2
Iu
Id

51.2
51.4
49.8

69.9
69.8
69.9

14.6
14.6
14.7

+0.3%
−2.8%

−0.1%
0.0%

0.0%
+0.4%

(Iu − Isum /2)/(Isum /2)(Id − Isum /2)/(Isum /2)

Table 4.3: Circuit parameters obtained by fitting the current shapes (Eq. (4.4)).

4.7.3

Alignment of the magnets

The largest systematic error comes from the uncertainty of beam path. Although
it has been assumed until now that the beam path coincides with the center path,87

4.8 Run and analysis

the beam path can be diﬀerent from the center path. In this case, the field at thebeam also becomes diﬀerent. This contribution is estimated with the worst case,in which the path gives the lowest field-length product. The inner diameter ofthe 1/4-inch-pipe is 5.35 mm. On the other hand, during the run, the margin ofalignment has been checked by shifting the height or the translation of the four
magnets until the beam intensity starts to decrease. In this way, the beam margin
is measured to be ±0.45 mm. Taking the beam size of ∼1.0 mm (Fig. 3.7) into
account, conceivable deviation of the beam center from the pipe center is 1.7 mm.
Since most of the photons are contained in ±0.3 mm region from the beam center(see again Fig. 3.7), estimation of the largest deviation is taken as 2.0 mm. The
field map of the transverse direction along the X-ray polarization is calculated with
3D finite element simulation and is shown in Fig. 4.8 at the central cross section of
the magnet. The 30 boxes are the cross section of the Cu wire with its height of 3.0
mm. The bottom of the figure shows the field along the x direction. Its horizontal
scale corresponds to the actual length of the top figure. The central region of−4 mm < x < +4 mm is the field volume between the innermost wires. The field
at x = 0 is the lowest since this point is the farthest from the innermost wires.
Deviation in this direction thus receives the stronger field. On the other hand,
deviation in the y direction contributes to decrease of the field when it goes beyond
the uniform region (yellow). The worst path can be found on the symmetricalplane, which divides the left and the right of the figure, since the farthest points
from the innermost wires are located on this plane. The path goes into the pipewith a deviation of +2.0 mm from the pipe center along the y direction, passes
through the center, and goes out with a deviation of −2.0 mm. Figure 4.9 shows
maps of the path through the pipe center (red) and the above worst path (blue).
These two integrals (i.e. the field-length products) give their diﬀerence of 6.4%.

Parameter
Photon flux (Tab. 4.1)
Detection eﬃciency (Tab. 3.19)
Field-current ratio vs Vc (Fig. 2.7)
Map measurement (Fig. 2.9)
Magnet spacing (Fig. 4.6)
Current ratio vs Vc (Fig. 4.7)
Thermal expansion of coils
Diﬀerence between Iu and Id at Teq (Eq. (4.6))
Deviation of beam path (Fig. 4.9)

Value
±0.1%
±0.4%
±1.2%
±0.9%
< ±0.1%< ±0.1%< ±0.1%
±0.3%
+6.4%
+6.5%
−1.6%

Total

Table 4.4: Systematic uncertainties

88

4.8 Run and analysis"!

B/I [T/kA]

!!

0.8
0.6
0.4
0.2
0
!0.2
!0.4
!0.6
!0.03

!0.02

!0.01

0

0.01

0.02

0.03

x [m]
Figure 4.8: Top: the field map of the transverse direction along the X-ray polarization at the central cross section of the magnet (simulation). The 30 boxes are thecross section of the Cu wire. The height of the wire is 3.0 mm, and the center region(yellow) has a good uniformity of the field. Bottom: field along the x direction.
Its horizontal scale corresponds to the actual length of the top figure. The central
region of −4 mm < x < +4 mm is the field volume between the innermost wires.

4.8 Run and analysis

4.8

89

Limit

The limit on gaγγ obtained from this experiment is shown in Fig. 4.10 as a red line.
The black lines are limits from previous searches. For the high mass region, twostructures are observed; oscillation and dumping. The oscillation of the sensitivity
is caused by a short oscillation length (= q −1 ) compared with the field length(∼20 cm). The dumping of the sensitivity comes from the momentum mismatch
between an incident or an outgoing photon and ALP. Although they give diﬀerent
structures, they have the same origin; a large ma . Such oscillation or momentum
mismatch, on the other hand, do not occur for the low mass region below 0.1 eV.
Therefore, the sensitivity for this region becomes flat.
The result is represented for the flat region below ≃0.1 eV as−4gaγγ < (2.36 +0.15
GeV−1−0.04 (sys.)) × 10

(4.7)

In Eq. (4.7), taking 2.96 events from the null result is already quite conservative.
Therefore, a value one-standard-deviation-smaller than the central value is used as
the 95% C.L. result including the systematic uncertainties,
gaγγ < 2.51 × 10−4 GeV−1 , 95% C.L.

(4.8)

90

B/I [T/kA]

4.8 Run and analysis

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.15

−0.1 −0.05

0

0.05

0.1

0.15

z [m]

Figure 4.9: Uncertainty from the deviation of the beam path. Maps of the paththrough the pipe center (red) and the worst path (blue), which deviates from thepath through the pipe center by 2.0 mm. These two integrals give their diﬀerenceof 6.4%.

91

gαγ γ [GeV-1]

4.8 Run and analysis

10-1
10-2
ESRF (2010)
-3

10

10-4
OSQAR (2015)
ALPS (2010)

-5

10

10-2

10-1

1
mα [eV]

Figure 4.10: Limit on gaγγ at 95% C.L. obtained by this search (red). The blacklines are limits from previous searches. ALPS and OSQAR are LSW experiments
using an optical laser and long dipole magnets. ESRF is a search carried out at
an European Synchrotron Radiation Facility using two superconducting solenoids
with their maximum field of 3 T.

92

4.8 Run and analysis

Chapter 5

Discussion and prospect
In the first section of this chapter, the limit obtained in the previous chapter iscompared with the other limits. The physical significance of the result is thendescribed. In the third section, upgrades of the magnets and of the LSW limit aredescribed.

5.1

Comparison with previous LSW limits

The previous limits are shown in Fig. 4.10 as black lines. They are compared withthe limit obtained in the previous chapter.

5.1.1

Laser LSW limits

ALPS [37] and OSQAR [38] are LSW experiments using an optical laser as theirlight source. The OSQAR limit was recently published in 2015. It is more stringent
by ∼2 times than that of the ALPS for the flat region below 0.2 meV. Since theyused two long dipoles with each length of 14.3 m, their sensitivity for higher mass
is surpassed by that of ALPS using one dipole of 8.8 m with a shield placed in
the middle. The ALPS experiment builds up the laser intensity of the γ → aconversion region by using a Fabry Perot cavity. The build-up factor is 300. Thus
using a relatively shorter magnet than those of the OSQAR, they achieved a highsensitivity.
On the other hand, their laser wavelength gives the photon energy of 2.3 eV.
From Eq. (1.13), ALP mass searched by the LSW experiment is proportional to thesquare root of the photon energy. Since the photon energy is 9.5 keV, the search
has sensitivity for the 64 times heavier mass region from only this energy relation.
Although the world’s strongest X-ray beam is used in this experiment, the photon
flux itself is smaller by many orders of magnitude than those laser search. This is
one of the reasons which make the sensitivity to gaγγ relatively weaker.
The present limit crosses these laser limits around 30 meV. This region corresponds to an extremely high mass region for the two limits, and dumping oscilla93

94

5.2 Discussion and prospecttion makes unsure about the validity of their sensitivities for this region. Thus thepresent limit is also considered to hold a significance below ∼0.03 eV.

5.1.2

An X-ray LSW limit

In addition to these optical searches, experiments with other light sources haverecently been carried out to cover the wider range of the ALP mass. A pioneering
search using X-ray beams has been carried by Battesti et al. [40] as the BMV
project. They used 50.2 keV and 90.7 keV X-ray beams of synchrotron radiation at
ESRF (European Synchrotron Radiation Facility). Two superconducting solenoids
are used at their maximum field of 3 T. It is the first LSW search using X rays as
a light source.
As a comparison with the same X-ray LSW search, our result improves theirlimit by factor 5.2 at the masses below ∼0.1 eV. Most of the gain comes from thefield-length product of the magnets.

5.1.3

Another terrestrial search

As an ALP search, the NOMAD collaboration also published a similar result below∼0.1 eV in 2000 [74]. The main target of the NOMAD experiment is to detect tau
neutrino appearance. They re-analyzed the data collected in 1996 and obtained thelimit. This is a pioneering work to search for ALPs using a high energy accelerator.
However, some uncertainties seem not to be taken into the consideration. Theyare:
• uncertainties of the γ-ray flux, which come from i) the measurement of theabsolute flux, ii) eﬀect of the energy spectrum at the low energies, and iii)
direction of the ALP flux,• background estimation at low energies and signal excess of 1.6σ,• material eﬀect of γ → a conversion region in the target drift chamber.
Thus the direct comparison of limits is restricted only to the dedicated LSW experiments to avoid confusion.

5.2

Physical significance of the result

This section describes the physical significance of the present result with respect
to the each motivation shown in the introduction (Chapter 1).

5.2.1

Significance to the general motivation

Since the mass and the coupling of ALPs are not bound, a search for new parameter
space in the mass-coupling place has importance. The present result newly excludes
the possibility of gaγγ stronger than 2.5×10−4 GeV−1 below ∼0.1 eV for the firsttime as an LSW search. It confirms that there are no new physics with 95% C.L.

95

5.3 Discussion and prospect

5.2.2

Significance to the interests of X-ray terrestrial experiments

Powerful X-ray sources can be found in the Sun or in a synchrotron radiation
facility. Thus the two have a good complementary relation. In terms of the possible
solutions to some solar problems with ALP mass of 10–20 meV, the region has been
covered with spikes of oscillations of the optical limits before the present result. The
present limit excludes this possibility up to gaγγ = 2.4 × 10−4 GeV−1 at 95% C.L.
Astrophysical bounds are valid only if the ALPs escape from the Sun without
any further interaction. Their mean free path λa of the Primakoﬀ conversion is
given by [75]λa = Γ−1γ→a
Γγ→a =

2 T κ2 [(
gaγγ
s

32π

κ2
1 + s2
4E

)

(
)
]
4E 2
ln 1 + 2 − 1 ,
κs

(5.1)
(5.2)

where T the temperature, κs the screening scale [75], and E the photon energy.
For 4 keV ALPs with T ≈ 1.3 keV and κs ≈ 9 keV at the solar center, it becomes−2 8 × 10−7 R⊙ [65]. This corresponds to
λa ≈ gaγγ
0.9 × 10−3 GeV−1 < gaγγ < 1.3 × 10−3 GeV−1(5.3)

for R⊙ /2 < λa < R⊙ . This assumes the environment of the solar center forthe entire volume of the Sun, and thus Eq. (5.3) is relatively conservative. The
region has not been ruled out by the previous X-ray LSW search. The present
limit experimentally excludes this possibility up to ∼0.1 eV. This would provide agood cornerstone for the previous astrophysical bounds.

5.3

UpgradesFeasibility of using pulsed magnets for an X-ray LSW experiment has been demonstrated in this thesis. This section describes the original goal of this experiment,
which uses pulsed beam from SACLA. Some improvements of magnet operation are
explained from the experience of the present experiment. The expected sensitivity
is then calculated.

5.3.1

Improvements of magnet operation

The number of magnets
The current capacity of the present bank is designed to operate eight magnets. As
shown in Tab. 2.1, each magnet has a body length of 350 mm, and the total lengthof eight magnets becomes 2.8 m. An experimental hutch in SACLA has an inner
width of about 4 m. Thus it is possible to place eight magnets in a hutch.
The present experiment uses four magnets. Since gaγγ linearly depends on field
length, eight magnets give a gain on gaγγ by a factor of two.

96

5.3 Discussion and prospect

Charged voltage
Repetition field is confirmed to be safe up to 9.5 T as described in Sec. 2.3.6. The
durability test has been carried out with a charged voltage of 4.0 kV. On the other
hand, most of the present magnets have been operated with a field around 8.3 T for
the first pulse as shown in Fig. 4.1. This is because most of the data set have been
operated with a lower charged voltage of 3.5 kV (Tab. 4.1), due to malfunction of
the trigger board, which appeared at 3.75–4.0 kV. This trouble is considered tooriginate from a diﬀerent noise environment between the durability test and thepresent experiment at SPring-8. If the trouble is fixed, magnets are operated with
4.0 kV as planned. The field gain thus becomes a factor of 1.14. Since gaγγ linearly
depends on field, it gives a gain on gaγγ by the same factor.
Connection of magnets
Left of Fig. 5.1 shows the present serial connection of two magnet. The total
inductancebecomes double, and the pulse width becomes larger by a factor of√
2 when it is compared with one magnet. Since the heat loss scales to the pulse
width, this results in a smaller repetition by the same factor. Instead, the serial
connection reduces the voltage on each magnet by half and hence does not requirea high withstand voltage to the magnets.
If two magnets are connected in parallel, the opposite results are obtained(right of the Fig. 5.1); the total inductance becomes half and the heat loss decreases
whereas the withstand voltage of each magnet is required to be double. The present
magnets are designed to have a withstand voltage of 4.9 kV, and can be operated
with parallel connection at 4 kV. It results in an increase of repetition by a factorof two when it is compared with the present serial connection. Since gaγγ depends
on the fourth root of repetition, it gives a gain on gaγγ by a factor of 1.19.

5.3.2

XFEL SACLA

The present LSW setup uses pulsed magnets and DC X rays at SPring-8. If pulsed
X rays from SACLA is used, a better sensitivity on gaγγ is obtained. Light source
performance of SACLA is summarized in Tab. 5.1. If the same run time as thepresent experiment of two days is assumed, the gain factor on gaγγ from using
SACLA is expressed as()1/4
NSACLA= 2.05,(5.4)
3
8 FBL19 ∆t
where 3/8 a DC factor, which comes from the time integral of fourth power ofthe sinusoidal field shape, FBL19 = 3 × 1013 photon/s the X-ray flux at BL19LXU(Tab. 4.1), ∆t = 2 ms the pulse width of the field, and NSACLA = 4 × 1011 photon/pulse the number of photons contained in a pulse.

97

5.3 Discussion and prospect

I!

I!
L!

+V! C!

2L!

+V! C!

L! L!

L/2!

L!

I =V

C
2L

I =V

T = π 2LC

2C
I
C
→ =V
L
2
2L

T = π LC / 2

Figure 5.1: Diﬀerence of the connection between series and parallel. Left: thepresent serial connection of two magnets. Right: parallel connection of two magnets. Both connections give the same current for each magnet. The withstandvoltage of the parallel magents is required to be double than that of the serial
magnets. Instead, the pulse width T is smaller by a factor of two, reducing theheat loss and increase the repetition by the same factor.
Parameter
EnergyIntensity (max)Beam size
Pulse width
Repetitionvalue∼10 keV (variable)
4 × 1011 photon/pulse∼100 µm< 10 fs
30 Hz

Table 5.1: Light source parameter of SACLA.

5.3.3

Expected total gain on gaγγ

Gain factors of the future experiment at SACLA is summarized in Tab. 5.2. The
total gain on gaγγ is expected to be the product of them. This gives an improvement
by a factor of 5.57 from the present limit of Eq. (4.8).
Parameter

gain on gaγγ

Total field length
Repetition field
Repetition
SACLA

2.00
1.14
1.19
2.05

Total

5.57

Table 5.2: Expected gain factors of the future experiment at SACLA

98

5.3 Discussion and prospectChapter 6

Conclusion
The first X-ray LSW search for axion-like particles (ALPs) using strong pulsed
magnets has been reported in this thesis. A transportable magnet system for highrepetition use has dedicatedly been developed. The experiment has been carriedout at the BL19LXU beamline of SPring-8, which produces the world’s strongest
DC X-ray beams. During two days of net run time, four magnets are operated ata mean peak field of 8.3 T and 5.7 T (the first and the second pulse, respectively)
with a pulse repetition of about 0.2 Hz. After a total of 27,676 pulses, no signal
events are observed. A new limit on ALP-two-photon coupling constant gaγγ is
obtained as
gaγγ < 2.51 × 10−4 GeV−1
below∼ 0.1 eV at 95% C.L. This is the most stringent LSW limit around 0.1 eV.
This experiment also demonstrates the feasibility of using pulsed magnets for X-ray
LSW search. With the combination of strong pulsed beam from XFEL SACLA,
the sensitivity on gaγγ will be further improved in the future experiment.

99

100

6.0 Conclusion

Acknowledgements
First, I would like to express my sincere gratitude to my supervisor Prof. Shoji
Asai (The University of Tokyo) and my former supervisor Prof. Tomio Kobayashi(KEK) for providing me with opportunity of this work. I was supported by theircontinuous encouragement.
I also wish to express my great appreciation to Prof. Toshio Namba (ICEPP,The University of Tokyo) for guiding this work in the right direction with his
experience. His outstanding suggestions and technical advice supported me andthis work from the beginning.
My special thanks go to Dr Takayuki Yamazaki (ICEPP, The University ofTokyo). It would not have been possible to perform this work without his support.
Most of this work has been carried out with his excellent cooperation.
I would also like to thank Mr. Tomohiro Yamaji for his support at the experiment.
The range of this work spreads to many regions other than particle physics. We
would like to express our gratitude to Prof. Koichi Kindo, Dr. Akira Matsuo, andDr. Takashi Kawaguchi (ISSP, The University of Tokyo) for providing technicaladvice on the fabrication of magnets. We also wish to express our great appreciation
to Prof. Hiroyuki Nojiri and Prof. Yasuo Narumi (IMR, Tohoku University) for
guiding the design of the capacitor bank.
Our special thanks go to the BL19LXU beamline manager Prof. Kenji Tamasaku(RIKEN, SPring-8) and the former beamline manager Prof. Yoshihito Tanaka (University of Hyogo) for their technical support. We would also like to express our
gratitude to Prof. Yuichi Inubushi, Prof. Kei Sawada, Prof. Makina Yabashi, andProf. Tetsuya Ishikawa for their useful discussions.
At this point, I would like to thank all the staﬀs and students of International
Center for Elementary Particle Physics (ICEPP) at The University of Tokyo.
Finally, I would like to thank my family, who always support me behind thescenes.

101

102

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105