Doctorate Dissertation
博士論文

Study of Optical System of the Ultra-Cold Neutron
with High Intensity Pulsed-Beam at J-PARC for
Discovery of Neutron Electric Dipole Moment（中性子電気双極子能率の発見のための
J-PARC における大強度パルスビームを用いた
超冷中性子の光学系の研究）
A Dissertation Submitted for Degree of Doctor of Philosophy
December 2017
平成 29 年 12 月博士（理学）申請
Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科 物理学専攻

Ryo Katayama
片山 領

Abstract
The neutron electric dipole moment (EDM) is sensitive to new physics beyond the standard model(BSM). Currently, the best upper limit of neutron EDM, obtained at Institute Laue-Langevin (ILL),
is 3 × 10−26 e · cm (90% CL). Many BSM models, such as supersymmetric models, predict 1 to 2
orders of magnitude larger EDM that can be detected by experimental techniques that can be developed
today, which motivates a more precise measurement of neutron EDM. Generally, neutron EDM can bemeasured most precisely by confining ultracold neutrons (UCN) in a storage container to which electricand magnetic fields are applied. Today, the sensitivity of this measurement is mainly limited by statistics,
while it is expected to be drastically improved by the super-thermal method that can produce UCNs
eﬀectively. Therefore, new EDM experiments adopting the super-thermal method are being planned
all over the world. Recently, a new EDM experiment has been proposed at J-PARC (J-PARC P33
experiment). This experiment uses a unique experimental technique to make pulsed UCNs re-bunchedon the measurement cell, and is expected to be a strong candidate of next-generation experiment.
This thesis describes the first basic study for the neutron EDM experiment based on P33 concept. For
the J-PARC P33 experiment, there was a problem that the experimental capability was not evaluatedbecause it was particularly diﬃcult to understand eﬀects of the reflection loss and the non-specularreflection on the statistical sensitivity. Therefore, in this study, first of all, the dependence of thestatistical sensitivity on such reflection performances was tried to be quantitatively investigated by afull simulation that can deal with an experimental system and entire procedures based on J-PARC P33
concept. Neutron optical theory and micro-roughness model were used to represent the reflection loss
and the non-specular reflection. Total reflection energy, VF , and UCN loss probability coeﬃcient, η, wereused for controlling the reflection loss, which were chosen to be in the range from 91 neV ∼ 210 neV
and 8 × 10−5 ∼ 5 × 10−4 . On the other hand, RMS roughness b was used to handle the non-specularreflection, which was chosen to be in the range from 0 to 3 nm. As a result, it was shown that thestatistical sensitivity was changed by 8 times according to the diﬀerence of reflection performances.
Full simulation study showed that the development of reflection materials is the key to improving thesensitivity. Hence, high eﬃcient neutron mirrors, Nickel Molybdenum alloy (NiMo) and Diamond-Like
Carbon (DLC), were developed. NiMo was prepared by the binary vapor deposition, and DLC was
fabricated by methods of Filtered Arc Ion Plating Deposition (FAIPD) and Ionized Evaporation Method(IEM) and Plasma Based Implantation Deposition (PBIID). These reflectors were evaluated by surface
analyses; the neutron reflectometry showed that VF was 228 neV (NiMo), 243 neV (IEM), 264 neV(FAIPD), and 193 neV (PBIID); η was evaluated to be 3.6 × 10−4 (NiMo) and 3.4 × 10−4 (PBIID) by
the UCN storage experiment, and b was evaluated to be 0.3 nm (IEM) and 0.49 nm (FAIPD) by AFM.
Finally, with the above-evaluated reflection performances along with the systematic error evaluated ina similar manner as the ILL experiment, the experimental sensitivity for the measurement duration of 2.3
years was estimated to be (±1.6(stat)±2.5(syst))×10−27 e·cm. This is the first comprehensive evaluationof the experimental capability based on J-PARC P33 concept including the reflection performance, which
provides a reliable basis for future experiment design.

Contents
Chapter 1

Introduction

1

Chapter 2

Neutron Interaction and Basic Experimental Techniques

7

2.1

Interaction for UCN Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2

Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.3

Diﬀuse Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.4

UCN Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

Neutron EDM Experiment

25

3.1

The Principle of the Method to Determine Neutron EDM . . . . . . . . . . . . . .

25

3.2

ILL Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

3.3

Our Proposed Experiment: Neutron EDM Experiment at J-PARC . . . . . . . . .

33

3.4

Other Next Generation Experiments . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Chapter 4

Dependence Study of the Statistical Sensitivity on the Performance of the Reflection

Chapter 3

Material of UCN

39

4.1

Proton Beam Property at J-PARC Neutron EDM Experiment . . . . . . . . . . . .

40

4.2

UCN Source at J-PARC Neutron EDM Experiment . . . . . . . . . . . . . . . . . .

42

4.3

Rebuncher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

4.4

J-PARC P33 simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

4.5

Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

Development of Neutron Mirror for Neutron EDM Experiment

72

5.1

Fabrication method of Nickel Molybdenum Alloy . . . . . . . . . . . . . . . . . . .

72

5.2

Fabrication method of Diamond-Like Carbon . . . . . . . . . . . . . . . . . . . . .

73

5.3

The Method of Surface Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

5.4

Surface Analysis of Developed Material . . . . . . . . . . . . . . . . . . . . . . . . .

92

5.5

Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Chapter 5

Chapter 6

UCN Storage Experiment at J-PARC MLF

113

6.1

Material and Life Science Facility at J-PARC . . . . . . . . . . . . . . . . . . . . . 113

6.2

The Experimental Apparatus at BL05 . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.3

Determination of UCN velocity emitted from Doppler Shifter . . . . . . . . . . . . 134

i

6.4

UCN Storage Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.5

Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

Chapter 7

Evaluation of the Experimental Sensitivity

149

7.1

Evaluation of Statistical Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7.2

Evaluation of Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . 155

7.3

Final Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Chapter 8

Summary and Future Prospect

160

8.1

Sumarry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

8.2

Future Prospect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Appendix.A

Time-of-Flight Method

167

Appendix.B

Beam Fluctuation Suppression Using MNH10/4.2F

169

Appendix.C

Dependence of Detection Eﬃciency of DuNia-10 on Position and Time170

Appendix.D

Evaluation of UCN Density by Rebunch Storage Method

175

Appendix.E

Evaluation of Time Dependence of Rebunch Storage Number

176

Appendix.F

Details of Storage Experiment not to be Described in the Text

177

F.1

Wave height distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

F.2

Released Time Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

F.3

Import Time Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Appendix.G

Geometric phase eﬀect and crossing point analysis

180

Appendix.H

Dependence Study of the Instantaneous Intensity on Cut-Out Time Width183

Appendix.I

Source is of systematic errors of UCN EDM measurements

186

I.1

Local dipoles (Door cavity dipole and Other dipole fields) . . . . . . . . . . . . . . 186

I.2

Quadrupole diﬀerence and Earth Rotation . . . . . . . . . . . . . . . . . . . . . . . 186

I.3

Uncompensated B drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

I.4

v×E (Translation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

I.5

v×E (Rotation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

I.6

Light shift (indirect) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

I.7

Light shift (direct) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

I.8

Hg EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

I.9

Leakage current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

I.10

Electric force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

I.11

HV AC ripple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

ii

List of Tables
2.1

Details of ultracold neutron source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

4.1

Details of the beam condition of J-PARC P33 used in this study . . . . . . . . . . . . . .

41

4.2

Simulation condition of PHITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

4.3

Details of the geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

4.4

General assumptions in this simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

4.5

Reflection performance of the storage container considered in this study . . . . . . . . .

63

5.1

Details of apparatuses used for film formation of NiMo . . . . . . . . . . . . . . . . . . .

74

5.2

Apparatus used for DLC film formation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

5.3

Details of the film formation condition of IEM DLC . . . . . . . . . . . . . . . . . . . . .

78

5.4

Film formation condition of PBIID DLC . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

5.5

Measurement result of the Fermi potential . . . . . . . . . . . . . . . . . . . . . . . . . .

99

5.6

The composition ratio of DLC evaluated by RBS/ERDA . . . . . . . . . . . . . . . . . . 103

5.7

Example data of total electron density determined by X-ray reflectometry . . . . . . . . 104

5.8

Measurement result of surface roughness.

6.1

Details of storage experiment condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6.2

Details of the background measurement of the first storage experiment . . . . . . . . . . 142

6.3

Details of signal count for 1st storage experiment . . . . . . . . . . . . . . . . . . . . . . 142

6.4

Details of signal count for 2nd storage experiment . . . . . . . . . . . . . . . . . . . . . . 143

7.1

Summary of Experimental Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

C.1

Classification of low divergence beam measurement . . . . . . . . . . . . . . . . . . . . . 170

D.1

The UCN density in the storage container, calculated by the rebunch storage simulation. 175

H.1

The column to explain what means each cut-out time width . . . . . . . . . . . . . . . . 183

I.1

Non-parallelism condition of the electrode . . . . . . . . . . . . . . . . . . . . . . . . . . 189

iii. . . . . . . . . . . . . . . . . . . . . . . . . . 111

List of Figures
1.1

Feynman diagram of weak interaction for standard model that can break CP symmetry .

2

1.2

Feynman diagram of the interaction for supersymmetry model that can break CP symmetry2

1.3

The history in the precision of neutron EDM measurement . . . . . . . . . . . . . . . . .

3

2.1

Temperature dependence of up-scattering cross-section of solid deuterium. . . . . . . .

10

2.2

Phonon density of solid deuterium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.3

Phonon density of ice IV [24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.4

Temperature dependence of loss probability coeﬃcient of formula (2.17) . . . . . . . . .

13

2.5

Diﬀerence between Lambert’s cosine law and micro-roughness model . . . . . . . . . . .

14

2.6

Non-specular reflection probability distribution of micro-roughness model . . . . . . . . .

16

2.7

Correlation length dependence of non-specular reflection probability distribution . . . . .

17

2.8

The dependence of non-specular reflection probability on root mean square roughness/correlation length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

2.9

Time evolution of the UCN density accumulated in converters, the image is cited from [18] 21

2.10

Temperature dependence of superfluid helium τ due to up-scattering, the image is citedfrom [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

2.11

Schematic diagram of Doppler Shifter, taken from [38] . . . . . . . . . . . . . . . . . . .

24

3.1

Illustration of the principle to measure the neutron electric dipole moment, the image iscited from [40] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

3.2

Schematic illustration of Ramsey method . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

3.3

RF frequency dependence of count number in the neutron EDM measurement experiment, the image is cited from [42] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

3.4

Schematic view of setup used for the ILL experiment. the image is cited from [42]

29

3.5

Schematic diagram of the ultracold neutron source of the ILL experiment, the image is. . .

cited from [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

3.6

Example of the eﬀect of Hg co-magnetometer, the image is cited from [42] . . . . . . . .

31

3.7

Outline of J-PARC EDM experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

3.8

Apparatuses of J-PARC P33 experiment . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

3.9

UCN supply method assumed in J-PARC P33 . . . . . . . . . . . . . . . . . . . . . . . .

35

3.10

Illustration of the principle of the rebunch method, the image is cited from [44] . . . . .

35

iv

4.1

Schematic illustration of the beam distribution of J-PARC LINAC, the image is citedfrom [18, 19] and changed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

4.2

The arrangement of ultracold neutron source used in PHITS simulation . . . . . . . . . .

43

4.3

The energy spectrum of cold neutron flux passing through the solid deuterium converter,
the image is cited from [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

4.4

The cross-section view of the rebuncher prototype. The image is cited from [18].

. . . .

45

4.5

Linear gradient magnetic field used in rebuncher . . . . . . . . . . . . . . . . . . . . . . .

46

4.6

Relation of adiabatic parameter k and spin-flip probability

47

4.7

Schematic diagram of the setup used for the rebuncher demonstration experiment per-. . . . . . . . . . . . . . . .

formed at ILL, the image is cited from [44] . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8

48

The refocused TOF confirmed at the rebuncher demonstration experiment at ILL, theimage is cited from [44] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

4.9

Schematic diagram of the setup assuming in the J-PARC P33 simulation. . . . . . . .

51

4.10

Relation between RF magnetic field frequency and application time . . . . . . . . . . . .

52

4.11

Energy distribution of UCN in solid deuterium . . . . . . . . . . . . . . . . . . . . . . . .

54

4.12

Absolute velocity distribution of UCN in solid deuterium . . . . . . . . . . . . . . . . . .

54

4.13

Longitudinal velocity distribution of UCN beam . . . . . . . . . . . . . . . . . . . . . . .

55

4.14

Transverse velocity distribution of UCN beam . . . . . . . . . . . . . . . . . . . . . . . .

56

4.15

T0 distribution when UCNs generate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

4.16

Example of TOF distribution change due to non-specular reflection . . . . . . . . . . . .

61

4.17

Dependence of the rebunch eﬃciency on the surface roughness . . . . . . . . . . . . . . .

62

4.18

Examples of functions s(t) and S(t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

4.19

Example of the eﬀect of the potential on the rebunch storage number . . . . . . . . . . .

65

4.20

Dependence of the rebunch storage number on the non-specular reflection . . . . . . . .

66

4.21

Dependence of the rebunch storage number on the non-specular reflection . . . . . . . .

66

4.22

Example of time change of UCN storage number . . . . . . . . . . . . . . . . . . . . . . .

68

4.23

Dependence of the statistic precision on the non-specular reflection and UCN reflection
loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.24

69

Dependence of the statistic precision on the non-specular reflection and UCN reflection
loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

5.1

Schematic illustration of binary vapor deposition method . . . . . . . . . . . . . . . . . .

74

5.2

Classification diagram of DLC, the image is cited from [67] . . . . . . . . . . . . . . . . .

75

5.3

Schematic illustration of the ionized evaporation method, the image is cited from [67] . .

76

5.4

Schematic diagram of the PBIID method . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

5.5

Illustration of the flow of DLC film formation by PBIID method . . . . . . . . . . . . . .

81

5.6

Illustration of DLC film formation by FAIPD method . . . . . . . . . . . . . . . . . . . .

82

5.7

Fermi potential of the neutron mirror consisting of a substrate and a single layer . . . .

83

5.8

Example of reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

5.9

Relation of critical angle and the Fermi potential. . . . . . . . . . . . . . . . . . . . . . .

85

v

5.10

Outline of RBS/ERDA experiment, the image is cited from [67] . . . . . . . . . . . . . .

86

5.11

RBS/ERDA spectrum example, the image is cited from [67] . . . . . . . . . . . . . . . .

88

5.12

Schematic diagram of scattering of incident ions by target atoms, the image is cited from[67] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

5.13

Schematic diagram of recoil of target atoms by incident ions, the image is cited from [67] 89

5.14

Schematic diagram of X-ray reflection at material interface, the image is cited from [67] .

90

5.15

Example of X-ray reflectivity distribution . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

5.16

TOF distribution of beam supplied in J-PARC BL16 SOFIA . . . . . . . . . . . . . . . .

94

5.17

Schematic diagram of the setup in J-PARC BL16 SOFIA . . . . . . . . . . . . . . . . . .

94

5.18

Block diagram of experimental setup in J-PARC BL16 SOFIA . . . . . . . . . . . . . . .

95

5.19

Reflectivity of FAIPD DLC/SiO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

5.20

Reflectivity of FAIPD DLC/Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

5.21

Reflectivity of PBIID DLC/Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

5.22

Reflectivity of PBIID DLC/SUS304 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

5.23

Reflectivity of NiMo/Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

5.24

The reflectivity measurement result of IEM DLC/Si . . . . . . . . . . . . . . . . . . . . .

98

5.25

Fluctuation of incident angle due to beam divergence of J-PARC BL16 . . . . . . . . . . 100

5.26

Comparison of ERDA spectra of DLC/Si and DLC/SUS304 . . . . . . . . . . . . . . . . 102

5.27

Example of X-ray reflectivity distribution of IEM DLC . . . . . . . . . . . . . . . . . . . 105

5.28

X-ray reflectivity distribution of PBIID DLC

5.29

Comparison result of the Fermi potential determined by two methods . . . . . . . . . . . 108

5.30

Example of rf-GDOES spectrum of PBIID DLC/Si . . . . . . . . . . . . . . . . . . . . . 109

5.31

Example of lateral scanning of PBIID DLC/Si by transmission electron microscope . . . 109

6.1

Cross-sectional view of the non-polarized beam branch in J-PARC MLF BL05.the image. . . . . . . . . . . . . . . . . . . . . . . . 106

is cited from [38] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2

Overall view of UCN storage system in J-PARC MLF BL05 . . . . . . . . . . . . . . . . 116

6.3

Schematic illustration of the arrangement of the wideband monochromatic mirrors . . . 118

6.4

Overall figure of Doppler Shifter, the image is cited from [38] . . . . . . . . . . . . . . . . 119

6.5

Enlarged figure around the inlet of focus guide . . . . . . . . . . . . . . . . . . . . . . . . 120

6.6

Reflectivity of Doppler Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.7

Overall picture of UCN Storage System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.8

Photograph of the storage container with top cover opened . . . . . . . . . . . . . . . . . 121

6.9

Photograph of the inside of the storage container . . . . . . . . . . . . . . . . . . . . . . 122

6.10

Example of the test material used in the actual storage experiment . . . . . . . . . . . . 122

6.11

DUNia-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.12

Electric circuit of DUNia-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6.13

MNH10/4.2F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6.14

Schematic view of two-dimensional detector used for our experiment, the image is citedfrom [44] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

vi

6.15

RS-P4-0812-223 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.16

Setup used for the measurement of RS-P4-0812-223 . . . . . . . . . . . . . . . . . . . . . 128

6.17

The block diagram of the setup of the measurement using RS-P4-0812-223 in low divergence beam branch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.18

Setup used for the measurement of DUNia-10 detection eﬃciency . . . . . . . . . . . . . 129

6.19

The block diagram of the setup of the measurement using Dunia-10 in low divergence
beam branch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.20

Wavelength dependence of count rate ratio of DUNia-10 and RS-P4-0812-223 . . . . . . 130

6.21

The setup used for the R3292 detection eﬃciency . . . . . . . . . . . . . . . . . . . . . . 131

6.22

The block diagram of the setup of the measurement using two-dimensional detector inlow divergence beam branch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.23

Wavelength dependence of the ratio of two-dimensional detector to RS-P4-0812-223 . . . 132

6.24

Relative detection eﬃciency of two-dimensional detector . . . . . . . . . . . . . . . . . . 133

6.25

Setup used for neutron flux measurement of the focus guide . . . . . . . . . . . . . . . . 135

6.26

The schematic diagram of the setup used for measuring neutron flux of the focus guide . 136

6.27

The block diagram of the setup used for measuring neutron flux of the focus guide . . . 136

6.28

Cadmium slit and cadmium collimator used in experiment . . . . . . . . . . . . . . . . . 137

6.29

Velocity distribution of UCN emitted from Doppler Shifter side port . . . . . . . . . . . 137

6.30

The block diagram of the setup of the storage experiment.

6.31

Schematic diagram of the setup of our storage experiment . . . . . . . . . . . . . . . . . 140

6.32

Sequence of the UCN storage experiment ) . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.33

Dependence of the counting rate on storage time in the first storage experiment . . . . . 143

6.34

Dependence of the counting rate on storage time in the second storage experiment

6.35

The comparison plot of template samples having diﬀerent η . . . . . . . . . . . . . . . . 147

6.36

The dependency of the χ2 of SUS316 on the loss probability coeﬃcient . . . . . . . . . . 148

6.37

The dependency of the χ2 of NiMo/PBIID DLC on the loss probability coeﬃcient . . . . 148

7.1

Time of Flight when rebunched UCNs reach the shutter 1 position . . . . . . . . . . . . 153

7.2

Time evolution of the rebunch storage number . . . . . . . . . . . . . . . . . . . . . . . . 154

7.3

Time evolution of the number of UCNs confined in storage container . . . . . . . . . . . 154

B.1

J-PARC MLF beam stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

C.1

Time change of count rate of DUNia-10 found by low divergence beam measurement . . 171

C.2

Time change of pulse height of DUNia-10 found by low divergence beam measurement . 172

C.3

Surface position of DUNia-10 scanned in a low divergence beam branch . . . . . . . . . . 173

C.4

Pulse height distribution obtained by surface beam scan of DUNia-10. . . . . . . . . . . 174

E.1

Eﬀect of rebunch on the number of storage . . . . . . . . . . . . . . . . . . . . . . . . . . 176

F.1

Example of wave amplitude distribution at the storage experiment . . . . . . . . . . . . 177

vii. . . . . . . . . . . . . . . . 139. . . 144

F.2

Example of released time distribution of the second storage experiment . . . . . . . . . . 178

F.3

Dependence of the UCN detection number on the import time . . . . . . . . . . . . . . . 179

G.1

The relativistic magnetic field dependence on trajectories, the image is cited from [39]. . 180

G.2

Example of the crossing point analysis, the image is cited from [41][39] . . . . . . . . . . 182

H.1

Dependence of the rebunch eﬃciency on the shutter opening/closing operation along withthe surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

I.1

Dependence of the radial direction component of the electric field on the electrode size . 189

I.2

Two-dimensional distribution of electric field distortion due to non-parallelism of electrodes190

I.3

Analysis result of false EDM due to v×E (rotation) . . . . . . . . . . . . . . . . . . . . . 191

viii

Chapter 1

Introduction
This thesis deals with the first basic study of the proposed experiment for searching the neutron electric
dipole moment using ultracold neutrons produced by the J-PARC pulsed proton beams of the world’s
highest instantaneous luminosity.
The neutron electric dipole moment (EDM) is one of the most sensitive physical quantities to probe
the CP symmetry violation. In general, an intrinsic non-zero neutron EDM implies that time reversal
symmetry is violated, and the CPT theorem guarantees that the time reversal symmetry violation isequivalent to CP symmetry violation. Therefore, the source of CP violation can be eﬀectively searchedby the precise neutron EDM measurement. In the standard model, only second-order interaction fromthe weak interaction shown in Figure 1.1 contributes to CP symmetry violation, and thereby EDM about
10−31 e · cm appears. This is so small that it cannot be detected with current experimental techniques.
On the other hand, many of BSM models introduce first-order interaction as shown in Figure 1.2, andthereby the signal is possible to be detected even with current experimental techniques. Therefore, we cansearch for the existence of BSM eﬀectively by precise measurement of neutron EDM, which can be the key
to solving problems in elementary particle physics. For example, the hierarchy problem in the standard
model may be solved by the framework of a BSM model such as supersymmetric models (SUSY). In
addition, the violation of a large amount of CP symmetry supplied by BSM is also necessary to explain
the origin of the baryon asymmetry in the universe, which is an unsolved problem of elementary particle
physics [1]. Therefore, a new experiment to precisely measure the neutron EDM is well motivated as it
can probe two fundamental problems such as the existence of BSM physics and the baryon asymmetry
in the universe.
The current most tight experimental upper limit is 3×10−26 e · cm (90 % CL) [2], which was performedat Institute Laue-Langevin (ILL) in France. In this experiment, the statistical uncertainty was dominant
and its anticipated value was 1.34 × 10−26 e · cm [2]. In this thesis, the neutron EDM experiment
performed at Institute Laue-Langevin is referred to as the ILL experiment hereafter. The detail of theexperiment is described in chapter 3.2. Many of BSM models, such as SUSY, which is one of the mostpromising models of new physics, predict larger EDM values that can be detected by current experimental
techniques. For reference, a history about the precision of neutron EDM measurement is shown in Figure
1.3. The precision is improved year by year, and it comes to the stage reaching 10−26 e · cm which ispredicted by multi-Higgs models. Therefore, with the improvement of one or two orders of magnitude in
1

γ

s, b

s, b
W+
c, t

c, t
W−
d
d
u

d
d
u

Figure.1.1 Feynman diagram of weak interaction for standard model that can break CP symmetry

γ

d̃

d̃
χ0

d
d
u

d
d
u

Figure.1.2 Feynman diagram of the interaction for supersymmetry model that can break CP symmetry

the precision, many of BSM models can be eﬀectively searched by the precise neutron EDM measurement,
and there is a possibility that the neutron EDM experiment can prove BSM.
Today, the most precise neutron EDM measurement is possible by using low energy neutrons of 300
neV or less, which is referred to as Ultra Cold Neutron (UCN). In general, UCNs can reflect from thematerial surface, which makes the neutron EDM have the property of becoming parallel (or antiparallel)to the neutron spin and precess in the electric field. Therefore, the neutron EDM can be detected throughthe phase shift due to the spin precession occurring in UCNs confined in a container to which an electricfield is applied. In an actual measurement, a magnetic field is also used, and the electric field is applied
parallel/antiparallel to the magnetic field.
The current neutron EDM experiment is mainly limited by the statistical precision. Therefore, a more
intense UCN source is desired. Conventionally, the production method that neutrons emitted from a2

Figure.1.3 The history in the precision of neutron EDM measurement. History of precision ofneutron EDM measurement. The vertical axis is precision and the horizontal axis is the measurement year. At present, the precision of neutron EDM measurement reaches 10−26 e · cm.
[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

nuclear reactor are decelerated by reflection with a mirror has been used. This method is called the
Doppler Shift method. In recent years, a new production method that cools fast neutrons to ultracold
neutrons by inelastic scattering of quasiparticles in a substance has been developed and put into practice.
This method is called the super-thermal method [16]. Thanks to the super-thermal method, the statisticalprecision is expected to be improved. Accordingly, a lot of neutron EDM experiments adopting superthermal method are being planned all over the world. In particular, there is significant progress at PSI in
Switzerland and TRIUMF in Canada, and they announced that it has prospected to improve one or moreorder of magnitude from the ILL experiment. Both groups produce fast neutrons using an accelerator,
and it is cooled by liquid helium or solid deuterium.

3

At Japan Accelerator Research Complex (J-PARC), an experimental facility located in Tokai, Japan,
new neutron EDM experiment has been proposed which has the following quite unique characteristics[17, 18, 19]:
1. To produce fast neutron beams by nuclear spallation reaction with J-PARC pulsed proton beamwith the world’s highest instantaneous intensity.
2. To produce high intensity pulsed UCN beams by cooling via elastic scattering on heavy water andliquid deuterium and inelastic scattering on phonons in a solid deuterium converter.
3. To extract and transport the high-intensity pulsed UCN beams to the storage container for theneutron EDM experiment.
4. To refocus pulsed UCN to the shutter position in front of the storage container by deceleratinghigh velocity component with the magnetic field interaction to avoid the UCN bunches diﬀused in
the transportation.
5. To accumulate the refocused UCN in the storage container by the managing shutter opening/closing time to prevent back-flow.
6. To perform the EDM measurement when the UCN density is around the maximum.
This procedure was proposed in the 33rd proposal submitted to J-PARC. In this thesis, the experiment
adopting the above procedure is called as the J-PARC P33 experiment. In addition, the above techniqueto refocus pulsed UCNs is called “rebunch”, and the above method to take refocused UCNs into thecontainer with preventing back-flow is referred to as “rebunch storage” hereafter. For reference, a tableshowing the diﬀerence between the J-PARC P33 experiment and the ILL experiment is given below.
J-PARC P33

ILL Experiment

UCN Production

Super-Thermal Method

Doppler Shift Method

Fast Neutron Production

Nuclear Spallation

Nuclear Fission

Fast Neutron Beam Structure

Pulsed BeamContinuous Beam

UCN Beams Structure

Refocused BeamContinuous BeamWith the above J-PARC P33 experimental procedure, the world’s most intense pulsed beam at JPARC can be eﬃciently transmitted into the storage container, and the statistical precision is expected
to be significantly improved. Also, due to the pulsed beam characteristics, there is a merit that the heatload to the ultracold neutron source can be greatly reduced.
This thesis describes the first basic study for the neutron EDM experiment using the J-PARC facility
based on P33 concept. For J-PARC P33 concept, there was a problem that the experimental capability
had not been evaluated. Thereby, the experimental sensitivity expected at the present time could not be
evaluated, and any optimization studies to improve the sensitivity could not be done. In this experiment,
the sensitivity greatly depends on a lot of factors such as the experimental setup, the experimental
procedure, the magnetic field structure of the rebuncher, the performance of the ultracold neutron
source, the storage and transport eﬃciency of UCNs. In particular, it was diﬃcult to understand thestorage and transport eﬃciency that depend on the performance of the reflective material used in theneutron EDM experiment. Therefore, in this study, for solving this problem, the dependence of the4statistical sensitivity on such reflection performances was tried to be quantitatively investigated by afull simulation that can deal with an experimental system and entire procedures based on J-PARC P33
concept. Details of this content are described in chapter 4. The J-PARC P33 simulation results showedthat the experimental sensitivity greatly varied depending on all of the total reflection energy, the nonspecular reflection probability, and the loss probability of the reflector. Therefore, in this study, a highly
functional reflective material, which is the key to improving the experiment sensitivity, was developed.
The content of this study is described in chapter 5. In evaluating the reflection characteristics, various
surface analyses were needed. However, it was extremely diﬃcult to determine only the UCN loss
probability because its value is only about 10−4 for one bounce. Therefore, the author constructed
a dedicated experimental facility at J-PARC to perform the UCN storage experiment that enables us
to directly determine the UCN loss probability. Details of this experiment are described in chapter 6.
Finally, the sensitivity of the J-PARC P33 experiment expected at the present time was evaluated by
performing J-PARC P33 simulation with the information of the performance of the reflective material
along with the systematic error evaluated in a similar manner as the ILL experiment. As a result, theproblem that existed initially in the evaluation of J-PARC P33 experiment is solved, which gives a solid
basis on this experimental concept. This content is described in chapter 7.
In particular, the purposes of this study are as follows:
1. Numerical evaluation of the eﬀects of non-specular reflection along with UCN loss on the experimental sensitivity.
2. Development of reflective materials that are actually expected to be used for the experiment.
3. Performing the first UCN storage experiment at J-PARC, which establishes the solid basis for thefurther development.
4. Performance evaluation of reflective materials using various surface analysis methods related to 3.
5. Estimating final experimental sensitivity and feasibility by conducting full simulation using theresults obtained from the above 1-4.
The author’s contribution in this thesis is described below. Regarding the basic concept of this experiment, it was proposed as a J-PARC P33 experiment, and I am a co-researcher. In the J-PARC P33
experiment, we proposed a system called rebuncher to refocus high-intensity pulse neutrons, and thisconcept is also explained in this thesis. The author’s contribution to this study is following:
1. Development of dedicated tools to simulate the entire experimental system incorporated with
non-specular refection and the rebuncher system.
2. Performing first full simulation study of J-PARC P33 experiment.
3. Development of reflective materials expected to be used for the experiment.
4. Performing the first UCN storage experiment at J-PARC.
5. Estimating the final experimental sensitivity and its feasibility.
It is noted that although development of a highly precise magnetometer is an important subject in theneutron EDM experiment, this thesis does not deal with it.
This thesis is organized as follows. Chapter 1 is an introduction. In chapter 2, the basic neutron
5interaction and experimental techniques are explained. In chapter 3, an overview of the neutron EDM
experiments is presented, which deals with the sensitivity of the experiment and the details of theexperimental procedure. Chapter 4 deals with the evaluation of the dependence of the statistical precisionon the storage eﬃciency and transport eﬃciency. Chapter 5 deals with the development of reflective
materials that is key to the highly precise neutron EDM experiment. Chapter 6 explains the details of
the UCN storage experiment for directly measuring the loss probability coeﬃcient. In chapter 7, assuming
the performance of the reflector evaluated in chapters 5 and 6, the full simulation was performed in thesame manner as chapter 4 in order to evaluate the sensitivity of the J-PARC P33 experiment using thereflector developed in this study. Finally, this study is summarized in chapter 8.

6Chapter 2

Neutron Interaction and Basic Experimental
Techniques
2.1 Interaction for UCN Physics
2.1.1 Strong Interaction
Neutrons with kinetic energy less than 300 neV, whose velocity is less than ∼ 7.6 m/s, is called as
ultracold neutron (UCN). A material wavelength of UCN is longer than 50 nm. It is very long comparedto the atomic arrangement scale of 0.1 nm. Thus, when UCNs are incident on a substance, neutrons
feel at once the repulsive force from the nucleon near the surface. This potential is referred to the Fermi
potential and represented as a step function VF according to the following equation.
VF = 2πh̄2 /mn N b(2.1)

where mn is the mass of the neutron, N is the number of atoms per unit volume, and b is the coherent
forward scattering length, respectively.
UCNs have the property that can be confined in a material container, which can be used in experiments
to measure the fundamental neutron properties, such as lifetime and electric dipole moment. In general,
nickel is regarded as a standard material to evaluate the Fermi potential because of its excellent reflection
performance. The mirror which can reflect neutrons with a wavelength 1/N times the Fermi potentialof nickel is called mN mirror.
The Fermi potential of a substance consisting of n kinds of elements i(i = 0, 1, ..., n) is represented asfollows:

2πh̄2 ∑Ni bi
mN i=0
n

VF =

(2.2)

where Ni is the nuclear density of element i, bi is the scattering length of element i, and mN is theneutron mass.
Strong interactions not only lead to reflection between the UCN and the substance but also induce
loss and absorption. The eﬀect of absorption and loss is expressed as Fermi potential with an imaginary
part as follows:
VF = V − iW
7

(2.3)

It is possible to calculate the reflectivity / transmissivity of the substance by solving the Schrödinger
equation assuming the one dimension wall potential.
−h̄2▽2 ψ + [E − VF ]ψ = 0
2mn

(2.4)

We obtain the following neutron reflectivity |R|2 as the solution of the Schrödinger equation of 2.4.
|R|2 = 1 − µ(E, θ)()
E⊥ cos2 θ= 1 − 2ηV − E⊥ cos2 θ

(2.5)
(2.6)

where the second term is the UCN loss probability. If the second term of the right side of the formula(2.6) is zero, the reflectivity becomes unity.
In addition, the following relation is satisfied for the expression (2.6).
η=W
σloss mn v
=
V
4πh̄b

(2.7)

where σloss is the total sum of the cross-section due to interactions that lead to UCN loss and absorption,
mn represents the neutron mass, and v denotes the neutron velocity.
Although the reflectivity of UCN is expressed using the parameter η and can be theoretically calculated
like expression (2.6), in practice there is a large discrepancy between the theoretical prediction andexperimental result. In general, the theory predicts 10−5 to 10−6 , but 10−3 to 10−4 is observed in theexperiment.

2.1.2 Other Interaction
The scales of gravity potential and kinetic energy of UCN are the same for the neutron. Specifically, thecontribution of the gravity potential is given below.
Vg ∼ 1 (neV/cm)(2.8)

The neutron decays at ∼ 880 s through weak interaction [20].
n → p + e− + ν e(2.9)

The neutron lifetime is one of the fundamental parameters to test Big Bang nucleosynthesis and it is
an important physical quantity that aﬀects the ratio of the light element in the universe. However, theprecise value is not fixed because there is now a large discrepancy between two diﬀerent major methods.
In addition, the neutron lifetime is a parameter that determines the maximum time that UCN can be
stored in a container.
The neutron has a magnetic moment µ, so it interacts with magnetic fields. Under an external magnetic
field, neutrons cause spin precession. The main components of spin precession are represented as follows:ω = −γn B(2.10)

γn is the gyromagnetic ratio, which is related to γ = 2µ/h̄. For neutrons, γn ∼ 2π × 29.164702Hz/µT.
8Generally, time evolution of the spin precession of particles moving in an electric field follows the
Bargmann–Michel–Telegdi (BMT) equation [21][22].
[(
]
)
(
)
) γ
⃗
d⃗s
gn
1 ⃗ ( gngγEn⃗ β⃗ −= ⃗s ×−1+B−−1(β⃗ · B)
−
β⃗ ×
,
dt
2
γ
2
γ+1
2
γ+1
c

(2.11)⃗ and B
⃗ are electric and magnetic fields, gn is the neutron g factor, β iswhere ⃗s is the spin of UCN, E√
the ratio of the UCN speed to the speed of light, and γ is 1/ 1 − β 2 . The first term of the expression(2.11) represents a non-relativistic eﬀect, and the second and third terms represent relativistic eﬀects.
Assuming a typical UCN maximum speed 7 m/s, the contribution of the second term is negligibly small
compared to the third term. Therefore, in this study, the outer product vector of the third term can be
regarded as relativistic transverse magnetic field: Bv .
If UCNs rotate with the frequency ωr in a cylindrical container to which an electric field is applied, therelativistic fields also rotate. Then, the UCN spin rotation frequency changes as the following formula(2.12):
ωxy = ω0 +1 (ωrel )2,2 (ω0 ∓ |ωr |)(2.12)

where ω0 is the Larmor frequency of the neutron, and ∓|ωr | represents the angular velocity of counterclockwise/clockwise rotation. Further, ωrel is −γn Bv , where γn and Bv correspond to the gyromagnetic
ratio of neutrons and the third term of the equation (2.11), respectively.
For magnetic potential U , a contribution of a magnetic field is expressed as follows.
U = ±60 neV/T(2.13)

where ± sign represents whether the neutron spin is parallel/anti-parallel to magnetic fields.
Considering that the magnetized foil has an internal magnetic field, the neutrons passing through it
feels an additional potential as follows:
VF =

2πh̄2
N b ± µB
mn

(2.14)

where B is the magnetic field inside the material, and ± correspond to the two spin states. In general,a spin polarizer of UCN is realized by using a thin magnetized foil of ferromagnetic materials.

2.2 Inelastic Scattering
The reaction of the inelastic scattering that excites neutrons is called up-scattering, and the reverse iscalled down-scattering. In general, the up-scattering process causes a loss of UCN, while the downscattering can produce UCN. This section describes these two important interactions for UCN experiments.
In general, up-scattering occurs when phonons and angular momentum are exchanged between UCN
and a molecule. In the J-PARC P33 experiment, up-scattering process has a serious eﬀect on theperformance of UCN production, and its cross section is greatly diﬀerent between ortho-deuterium andpara-deuterium. The calculation result of the up-scattering cross section of the solid deuterium of 09and 1 phonon exchange is given in Figure 2.1, where the blue line corresponds to 1-phonon exchange
for ortho-deuterium, the red line corresponds to 1-phonon exchange for para-deuterium, and the green
line corresponds to angular momentum change. In this calculation, the up-scattering cross section of the
document [23] and the phonon density of Figure 2.2 are used. Obviously, it is found that there is a large
diﬀerence between ortho and para-deuterium. In this study, the up-scattering cross section of the Figure
2.1 and solid deuterium of ortho 95% of 5 K are assumed to indicate the performance of the ultracold
neutron source. It is noted that both the ortho-para ratio of 95 % and temperature of 5 K are enoughUp-scattering cross-section (barn)feasible.

101

1 phonon (Ortho D2)
1 phonon (Para D2)
0 phonon (J:1 → 0)
10-1

4

6

8

10

12

14

16

18

Temperature (K)Figure.2.1 Temperature dependence of up-scattering cross-section of solid deuterium. The verticalaxis represents the up-scattering cross section, and the horizontal axis represents the temperature ofsolid deuterium. The green line represents the process of up-scattering due to angular momentum
change and the blue and red line represent the cross section of the process where up-scattering
occurs due to the sum of inelastic scattering and angular momentum change.

Generally, the UCN loss probability that the neutron optical theory predicts is 1 to 2 orders of magnitude higher than the actual observation. This discrepancy is suspected to be caused by hydrogen having

10

Phonon Density

0.3

0.25
0.2

0.15
0.1
0.05
0

2

4

6

8

10
12
14
Phonon Energy (meV)

Figure.2.2 Phonon density of solid deuterium. The density of phonon contained in 5 K solid
deuterium calculated by using Debye model. The total sum of the spectrum of phonon density isnormalized to 1. The vertical axis represents phonon density, and the horizontal axis represents
phonon energy.

a large up-scattering cross section. Golub and his colleagues have derived the up-scattering cross section
caused by hydrogen film forming on the material surface as follows [24]:√∫ωσie (E) = 4πb2 e−2W (T ) G(ω)n(ω, T )dωE∫ ωmax2W (T ) =0ω′G(ω ′ )
coth( )dω ′′ω
2T

ηfilm = 2σie (E)AH(2.15)(2.16)(2.17)

where W (T ) is Debye-Waller factor, b is incoherent length of hydrogen, n(ω, T ) is 1/[exp (ω/T )−1], G(ω)
is the phonon density of Ice IV of Figure 2.3, n is the density of hydrogen film, ω is the frequency ofphonon, ωmax is the maximum frequency of phonon, E0 is the kinetic energy of neutron in the hydrogenfilm, and AH is the area density of hydrogen.
It was confirmed that the numerical calculation of formula (2.17) tended to be somewhat lower but
consistent [24][25]. Figure 2.4 shows the calculation result of the temperature dependence of UCN loss
probability using the phonon density from Figure 2.3, where the density of hydrogen and the incident
energy of neutron are assumed to be 7.2 × 1023 (atoms/cm3 ) and 100 neV, respectively. This calculation
result is consistent with the result of the original paper [24].
11G(ω)(1/meV)

0.02
0.015
0.01
0.005
0

0

20

40

60

80

100

120

meV
Figure.2.3 Phonon density of ice IV [24]. The total sum of the spectrum of phonon density of ice
IV is normalized to 1. The vertical axis is the phonon density of ice IV and the horizontal axis is
the energy of the phonon.

12

Loss Probability per Collision

Graph

×10-3

0.25
0.2
0.15
0.1
0.05
0

0

100

200

300

Temperature (K)Figure.2.4 Temperature dependence of loss probability coeﬃcient of formula (2.17). The verticalaxis shows loss rate of formula (2.17) and the horizontal axis shows temperature. Temperaturedependence of loss probability coeﬃcient of formula (2.17) is calculated using phonon density in
Figure 2.3.

13

2.3 Diﬀuse Scattering
In this study, the ratio of the pulsed beam intensity when using the rebunch method to that when
not using the rebunch method is referred to as the rebunch eﬃciency. In the experiment of J-PARC
P33, the rebunch eﬃciency is significant to assure the experimental capability. However, the rebuncheﬃciency decreases if the non-specular reflection occurs on the inner surface of the transport guide. On
the other hand, if UCNs collectively rotate along the sidewall of the cylindrical measurement cell, thesystematic errors due to the relativistic magnetic field and the distortion of the electric/magnetic field
become enhanced. In this case, the systematic errors increase if the non-specular reflection does notoccur on the inner surface of the storage container. Therefore, it is important for the neutron EDM
experiment to control the degree of the non-specular reflection and incorporate these eﬀects into thesimulation study. Conventionally, Lambert’s cosine law was used to model the non-specular reflection.
The scattering intensity of non-specular reflection which Lambert’s cosine law predicts is expressed asfollows:
dIlambert = I0 cos θdΩ(2.18)

where dIlambert is the intensity of reflection beam incident on a diﬀerential solid angle dΩ, I0 is theintensity of incident beam, and θ is the polar angle.
However, in recent years, it is reported that this model does not match experimental result for a wellpolished surface, while the micro-roughness model showed a good agreement with an actual measurement[26, 27]. For reference, Figure 2.5 shows the schematic diagram for the non-specular reflection predicted
by Lambert’s cosine law and that of the micro-roughness model. The micro-roughness model is one of the

Figure.2.5 Diﬀerence between Lambert’s cosine law and micro-roughness model

models of DWBA theoretical model [28]. In DWBA theoretical model, the contribution of non-specularreflection is calculated by using the distorted wave Born approximation (DWBA). The specular reflection
is regarded as a plane wave reflected from a perfect surface, and the non-specular reflection is regarded
14

to be caused by the deviation between the perfect plane and the undulated plane. The diﬀerence inpotential corresponding to the substance between the perfect plane and the undulated plane cause theperturbation Hamiltonian of the distorted wave Born approximation. In this section, the x-axis is definedas the direction that an incident beam travels, and the z-axis is defined as the surface normal of theperfect plane, and the direction orthogonal to x and z is defined as the y-axis. In the DWBA theorem,
the non-specular reflection due to the sample roughness is derived by perturbation calculation. Hence,
the modeling of the surface state is needed. Shinha shows that the non-specular reflection distributionof X-rays can be reproduced very well by using the following diﬀerential scattering cross section andautocorrelation function [28]:
(

dσ
dΩ

)
= Lx Ly Nb2 |T (k⃗1 )|2 |T (k⃗2 )|2 S(⃗
qt )(2.19)

dif f

2k1z
t
k1z + k1z∫t 2
exp[−[(qzt )2 + (qzt∗ )2 ]b2 /2] ∞dRR(e|qz | C(R) − 1)J0 (qr R)
S(⃗qt ) = 2π|qzt |20

T (k⃗1 ) =C(R) = e−(R/w)

2h(2.20)(2.21)(2.22)

where Lx Ly is the irradiation area of beams (x-ray or neutron etc.), k1 is the wave number vector of
the incident beam, k1 r is the wave number vector of the reflection beam, k1t is the wave number vectorof the transient beam, q⃗t = k⃗t − k⃗t is the transfer wave number vector of the transmit beam, and
2

1J0 (x) is the Bessel function of the first kind of order zero, R is the distance between two points on
the surface, and b, w, h, and C(R) are RMS surface roughness, correlation length, hurst-exponent, andauto-correlation function, respectively. Regarding roughness parameters, b corresponds to the averagevalue of the diﬀerence from the height of the surface roughness, w represents the roughness in the lateral
direction of the surface, h represents information on irregularities on the local surface, and C(R) models
the surface roughness that causes the non-specular reflection. Therefore, C(R) strongly depends on thesurface profile of the sample.
Although Shinha’s model is consistent with actual measurement, it becomes a problem that a large
amount of CPU power is required to calculate the numerical integration of S parameter included in the√expression (2.21). If we take h → 1, w → 2w in the expression (2.22), then the integral of S parametercan be replaced for the analytic solution. Therefore, it is possible to greatly reduce the calculation time.
Such a parameter fixed DWBA theoretical model is called “micro-roughness model” and is widely usedin UCN physics [29, 30]. In the micro-roughness model, the non-specular reflection probability density
P (θf , ϕf ) is given as follows (note that the incident azimuthal angle ϕi is assumed to be zero) [26]:P (θf , ϕf ) =[]kc4 (bw)2(wk)2|F (θi )|2 |F (θf )|2 × exp −(sin θi 2 + sin θf 2 − 2 sin θi sin θf cos Φf ) (2.23)
8π cos θi2
F (θ) = 2 cos θ/(cos θ + (cos θ2 − kc 2 /k 2 )1/2 )15(2.24)

where k is the wave number vector of UCN, θi is the incident polar angle to the normal of a surface,θf is the scattering angle to the normal of a surface, ϕf is the scattering azimuthal angle, b is the RMS
roughness of a surface, w is correlation length of a surface, and kc is√the critical wave number vector for
total reflection. In addition, it is also noted that kc is defined as

2mn VF, where mn is neutron massh̄2

and VF is the Fermi potential. Using formula (2.23), the non-specular probability of the micro-roughness
model can be calculated as P (θ, ϕ)dθdϕ.

Figure.2.6 Non-specular reflection probability distribution of micro-roughness model. Distributionof non-specular reflection probability when neutron of 100 neV is incident with 45 degree. The
horizontal axis corresponds to polar angle after scattering, and the vertical axis corresponds to theazimuthal angle. The white circle means an incident point. In addition, the white cross indicatesthe point having the maximum value. the image is cited from [31]Figure 2.6 shows a typical non-specular reflection probability distribution of the micro-roughness model.
As for the condition of Figure 2.6, w = 33 nm and V = 200 neV are used. It is noted that the total sumof non-specular reflection probability is normalized to unity. It is found that the distribution is localized
depending on the incidence angle and is symmetric to ϕ.
Also, the θ − ϕ distribution of the non-specular reflection where w are 5 nm, 50 nm and 100 nm, and λ =250 nm are given in Figure 2.7. It is found that the distribution is narrowing as w becomes large. This
corresponds to the fact that the surface becomes flat as w becomes large. Generally, the mean squareradius of roughness, b, has a strong eﬀect on non-specular reflection probability but does not aﬀect
distribution. For reference, a plot of roughness and the non-specular reflection probability are given in
the left side of 2.8. Also, w is proportional to the non-specular reflection probability. For reference, a
relation between the correlation length versus non-specular reflection probability is given in the rightside of Figure 2.8. The vertical axis is the non-specular reflection probability, and the horizontal axis is16

θi:7.85e-01 rad, b:1 nm, w:50 nm, V:220 neV

Scatter Angle: φ (rad)Scatter Angle: φ (rad)θi:7.85e-01 rad, b:1 nm, w:1 nm, V:220 neV

3
2
1
0

3
2
1
0

-1

-1

-2

-2

-3
0

-3
0

0.2 0.4 0.6 0.8 1 1.2 1.4
Scatter Angle: θ (rad)θi:7.85e-01 rad, b:1 nm, w:150 nm, V:220 neV

Scatter Angle: φ (rad)Scatter Angle: φ (rad)θi:7.85e-01 rad, b:1 nm, w:100 nm, V:220 neV

3
2
1
0

3
2
1
0

-1

-1

-2

-2

-3
0

0.2 0.4 0.6 0.8 1 1.2 1.4
Scatter Angle: θ (rad)-30

0.2 0.4 0.6 0.8 1 1.2 1.4
Scatter Angle: θ (rad)0.2 0.4 0.6 0.8 1 1.2 1.4
Scatter Angle: θ (rad)Figure.2.7 Correlation length dependence of non-specular reflection probability distribution. Nonspecular reflection probability distribution is calculated assuming neutron having kinetic energy 100
neV incident on material surface with correlation length of 1 nm, 5 nm, 50 nm, 100 nm at 45 deg.
The horizontal axis shows the polar angle after scattering, the vertical axis shows the azimuth
angle after scattering, and a white star shows the incident point. Each square pads corresponds toa non-specular reflection distribution with correlation lengths of 1 nm, 5 nm, 100 nm and 50 nm
from the upper left in a clockwise direction. Here, b and VF are chosen to 2 nm and 200 neV.

the correlation length. It is noted that b and V are chosen to be 1 nm and 200 neV, respectively.
Since the perturbation calculation is used in the DWBA theorem, the micro-roughness model has thefollowing application limit for surface roughness:
qz b ≪ 1(2.25)√

U CN
where qz is defined as 4π/λ sin θ = 2 2mE
sin θ.
h̄The condition of qz b < 1 for 10 m/s neutrons correspond to b < 30 nm. In fact, a more severe roughness
is required as a condition when using the micro-roughness model because qz b ≪ 1 is the applicable limit.
In this study, it is considered that the application limit condition of qz b ≪ 1 is satisfied if b < 3 nm.

17

θi:7.85e-01 rad, b:3 nm, V:220 neV

Diffuse Probability

Diffuse Probability

θi:7.85e-01 rad, w:33 nm, V:220 neV

0.12

0.1

0.08

0.06

0.07

0.06

0.05

0.04

0.03

0.04

0.02

0.02

0.01

0

0

1

2

3

4

0

5
b (nm)

0

20

40

60

80

100
w (nm)

Figure.2.8 The dependence of non-specular reflection probability on root means square roughness/correlation length. (Left) The root mean square roughness dependence of non-specular reflection probability when neutron having kinetic energy 100 neV incident on the material surface
at 45 degree. The horizontal axis represents the mean square roughness, and the vertical axis
represents the non-specular reflection probability. Correlation length and potential are chosen to
33 nm and 200 neV. (Right) Correlation length dependence of non-specular reflection probability
when neutron having kinetic energy 100 neV incident on the material surface at 45 degree. Here,b and VF are chosen to 2 nm and 200 neV.

18

2.4 UCN SourceThis section explains the details of two UCN production method: the super-thermal method and the
Doppler shift method.

2.4.1 super thermal UCN production
In general, fast neutrons produced by nuclear reactions can be cooled down to several meV with deceleration due to the elastic scattering with nucleons, but further cooling requires inelastic scatteringof the quasiparticles such as phonons and magnons. In this thesis, the technique to generate ultracold
neutrons in this way is called the super-thermal method. There are three candidate materials used for
UCN source: liquid helium, solid deuterium, and solid oxygen. At the present time, liquid helium andsolid deuterium are in practical use.
When the cold neutron flux Φ is irradiated to the substance having the cooling cross section σ forcertain interval ∆t, the density of generated UCN ρ and UCN production rate is expressed by thefollowing equations [32][33].
ρ = P τ (1 − exp (−∆t/τ ))(2.26)

P = N σΦ(2.27)

where N is the number of nuclei, P is the production rate of UCN source, and τ is the decay time
determined by absorption and up-scattering in UCN source.
In this study, The UCN density produced when the UCN source is irradiated by DC beam for a longtime denotes ρDC . On the other hand, the UCN density produced when a UCN source is irradiated bypulsed beam for ∆t denotes ρpulse . In general, ρDC can be calculated by taking t → ∞ in the expression(2.26), which results in ρDC = P τ = N στ . ρpulse can be calculated by taking t → ∆t in the expression(2.26). It is noted that the flux for pulsed beam is changed as Φ → Φ/∆t. Therefore, ρDC and ρpulse arerepresented as follows:ρDC = N σΦτ(2.28)= Pτρpulse = N σΦ/∆tτ (1 − exp(−∆t/τ ))(2.29)∼ N σΦ
=P
From the above, it is understood that τ represents the DC beam characteristic and P represents thepulsed beam characteristic, respectively. As an example, the calculation below shows the UCN density
produced in 5 K solid deuterium source. Hereafter, the cold neutron flux of a Maxwell distribution of
30 K is assumed. In the case of the DC beam irradiation, the following relation holds between the UCN
density ρDC,sD2 and the cold neutron flux Φ (see Table 4 of document [34]).
19

ρDC,sD2 = 1.5 × 10−11 Φ(2.30)On the other hand, the UCN density produced when a pulsed beam is irradiated can be calculated fromρ

the relation that ρpulse = ρDC ρpulse= ρDC /τ and τ = 146 ms for solid deuterium. As a result, theDCfollowing relationship is satisfied between ρpulse,sD2 and Φ.
()ρpulse,sD2 = 1.5 × 10−11 /146 × 10−3 Φ ∼ 10−8 Φ(2.31)

The characteristics of various ultracold neutron sources are given in Table 2.1 [20][23][34][35]. Generally,liquid helium has a low production rate but P τ is high, whereas solid deuterium is the opposite. In otherwords, liquid helium is suitable for DC proton beam experimental system because of its poor timing
structure, but solid deuterium is suitable for the experiment using pulsed proton beam because of its
good timing structure. For reference, The time evolution of P τ is shown in Figure 2.9, where it isassumed that the cold neutrons flux follow Maxwell distribution of 30 K and the amount of flux isΦ0 = 2 × 1012 [n/cm2 /s], respectively.
Converter Material

Superfluid 4 He

Solid ortho-D2

αO2

Interaction

PhononPhononPhonon, Magnon

Ideal Temperature of Material

0.7 K

5K

2K

Ideal Neutron Flux Temperature

9K

Production rate with 30 K neutrons−10

9.3 × 1029 K
3

Φ0 /cm /s−8

1.0 × 1012 K
3

Φ0 /cm /s

2.4 × 10−9 Φ0 /cm3 /s

Ideal storage time

886 s

146 ms489 msUCN density with 30 K DC neutrons

8.2 × 10−7 Φ0 /cm3

1.5 × 10−9 Φ0 /cm3

1.2 × 10−9 Φ0 /cm3

Table.2.1 Details of ultracold neutron source

Because τ value of liquid helium is very sensitive to temperature, temperature management is needed
to maximize its performance. It gives the temperature dependence of helium τ in Figure 2.10. The
temperature dependence of τ depends on the up-scattering cross section and absorption cross section.
In general, the temperature dependence of the cross section of solid deuterium is not tight compared toliquid helium. Such an easy temperature control is an advantage of ultracold neutron source of solid
deuterium.
Solid deuterium has two states: ortho and para. In the present work, a technique for aligning purity of
95% or more with ortho D2 has been established. The absorption cross section of ortho solid deuteriumis 520 microbarn against thermal neutron, and this contribution is smaller than the up-scattering crosssection of Figure 2.1. The elastic scattering cross section and mean-free path of solid deuterium are 2.04
barn and 8.2 cm [36]. If elastic scattering occurs, the timing structure will be distorted somewhat when
it is taken outside from the solid deuterium.
In general, the up-scattering cross section of solid deuterium depends greatly on how it is produced.
It is believed that the crystalline state and residual stress of solid deuterium are influencing [37]. For
example, when a solid deuterium is produced directly from deuterium gas, it becomes a solid with a very
20

Figure.2.9 Time evolution of the UCN density accumulated in converters, the image is cited from[18]. For details see the text.

good crystalline state, and as a result, the residual stress decreases. In addition, because the proton
beam radiation aﬀects the crystallinity of solid deuterium, it degrades the UCN production performance.
Thus, the UCN production method with pulsed beams can suppress the performance deterioration more
eﬀectively than with DC beams.

21

Figure.2.10 Temperature dependence of superfluid helium τ due to up-scattering, the image is cited from [18].

222.4.2 Doppler Shift
In general, particles are decelerated when reflected from a mirror moving in the same direction as follows[38]:⃗vr = ⃗v + 2|(⃗v − ⃗vm )·⃗n|⃗n(2.32)

where ⃗vr is the velocity of the reflection neutron, ⃗v is the velocity of the incident neutron, ⃗vm is thevelocity of the mirror, and ⃗n is the normal vector of the reflection point.
A machine that decelerates neutrons by using the relation of formula (2.32) is referred to as Doppler
Shifter. If ⃗vm is chosen to have a ⃗v /2, the reflected neutron becomes decelerated to nearly at rest. Thisis the principle to produce UCN with Doppler Shift method. By using multilayer mirror used for thereflector of Doppler Shifter, it is possible to decelerate neutron with an energy higher than the Fermi
potential. In general, such a multilayer mirror is called a super mirror. The super mirror can be used
for the Doppler Shifter to eﬀectively produce ultracold neutrons. The super mirror of Doppler Shifter isreferred to as a Doppler mirror hereafter.
Following the document [38], the three-dimensional velocity when the neutron reflected by a Doppler
mirror are illustrated as in the Figure 2.11. The situation of Figure 2.11 is an analogy of the actual
operation of the Doppler Shifter of J-PARC MLF BL05. Hereafter, the z-axis is defined as the beam
direction, the rotation axis is defined as the x-axis, and the direction orthogonal to x and z is definedas the y-axis. In this thesis, the intersection point of the center of the mirror surface and the z-axis isreferred to as a pseudo source point. In addition, it is assumed that the Doppler mirror rotates at the
speed vm ∼v/2 and the plane of the mirror is parallel to the x-axis. At this time, the velocity componentsv ′ x , v ′ y , v ′ z of reflection neutrons can be written as follows:vx′⃗ =  vy′ 
V
vz′



(2.33)

2vm δx
2vm (δy + θ(t))=22vm − v + 3vm θ(t)(2.34)

where δx is the incident angle of the neutron in the x plane, δy is the incident angle of y plane, v and vm
are the magnitudes of ⃗v and ⃗vm , and θ(t) is the rotation angle of the mirror with respect to y axis at a
certain time t. Also, when deriving the expression (2.34), we neglected terms which are higher than thethird order in |vm − v/2|, δx , δy and θ.
The UCN velocity can be calculated assuming an incident neutron velocity and formula (2.32). In thisstudy, such a simulation is called the Doppler Shifter Simulation. Indeed, by substituting the typicalneutron velocity and divergence to the expression (2.34), we can confirm that√the UCN production by
the Doppler Shifter. Specifically, using speed v = 136 m/s, vm = 68 m/s, δ =δx 2 + δy 2 =30 mrad andθ = 0, we can get the speed of reflected neutron as v ′ = (vδx , vδy , 0) → |v ′ | = vδ < 7 m/s. This result
satisfies the definition of UCN.
23

Figure.2.11 Schematic diagram of Doppler Shifter, taken from [38]24Chapter 3

Neutron EDM Experiment
3.1 The Principle of the Method to Determine Neutron EDM
The intrinsic non-zero neutron EDM (dn ) becomes parallel or antiparallel to the spin vector [39]. This
fact assures that the neutron EDM has the same transformation rule as spin. The hamiltonian H
of non-zero neutron EDM in an electric fields E is represented as H = −dn ·E. In general, after atime reversal transformation, neutron spin change its plus/minus sign and the electric field E does notchange sign. Therefore, the hamiltonian changes its sign as Hbefore = −dn ·E → Hafter = dn ·E, where
Hbefore and Hafter are hamiltonian before and after the time reversal transformation, respectively. If
the physics does not change before and after the time reversal transformation, following relation holds:
Hbefore = Hafter ⇒ dn = 0. From the contraposition, it is concluded that following logic becomes true:
if an intrinsic non-zero neutron EDM is observed, time reversal symmetry is violated.
Neutrons precess in a magnetic field due to its magnetic moment µn . Similarly, if neutrons have EDM
dn , neutrons precess in an electric field. Assuming that neutrons have µn and dn , a magnetic field
is applied upward, and an electric field is applied parallel/anti-parallel to the magnetic field, and theneutron spin vector will precess with the following frequency ω:ω↑↑/↑↓ =2µn B↑↑/↑↓ ± 2dn E
h̄

(3.1)

where ω↑↑ represents the case where the magnetic field is upward and the electric field is upward, andω↑↓ is the case where the magnetic field is upward and the electric field is downward.
In the formula (3.1), the contribution of the neutron EDM can be derived by taking the diﬀerence ofthe precession frequencies of the two cases. Using ∆ω = ω↑↑ − ω↑↓ , the neutron EDM can be written as
follows:dn =h̄∆ω − 2µn (B↑↑ − B↑↓ )
4E

(3.2)

Normally, the contribution due to the term of B↑↑ − B↑↓ can be regarded as zero. In this case, theamount of the neutron EDM can be derived using the precession frequency change as dn = h̄∆ω
4E . For
reference, a schematic illustration of the principle of neutron EDM measurement is given in Figure 3.1.
If B↑↑ − B↑↓ is non-zero in expression (3.2), this term becomes a systematic error.
25

Figure.3.1 Illustration of the principle to measure the neutron electric dipole moment, the image
is cited from [40]In an actual neutron EDM experiment, a method called “the Ramsey separated-oscillatory-field magnetic resonance method” is used to detect the precession frequency change [41]. The schematic illustrationof the sequence of the Ramsey separated-oscillatory-field magnetic resonance method is shown in Figure
3.2. At the beginning of the measurement cycle, polarized neutrons are filled in a storage container towhich a static magnetic field B0 and a static electric field E are applied. Next, the resonant oscillating
field Brf is applied in the direction orthogonal to B0 in order to turn the spin of neutrons into parallelto the ground. Next, UCNs are made to precess for a long time. Finally, Brf is applied again so thatthe spin turns in the opposite direction to that of the first neutron polarization. This is the procedureof Ramsey’s method of separated oscillating fields.
After the Ramsey’s method, UCNs are extracted from the storage container and then counted by adetector behind the spin filter. The oscillation in the detected counts corresponding to RF frequency
as shown in Figure 3.3 [42] can be observed. Specifically, the count number measured after Ramsey’s
method follows as formula (3.3):
Ndown/up (ω) = Ndown/up [1 ± α cos ((ωrf − γn B0 )(T + 4tπ/2 /π))]N=

Nmax + Nmin
2

(3.3)
(3.4)

where Ndown/up is the number of counted neutrons for each spin state, ωrf is the precession frequency
by an oscillating magnetic field, T is the free precession time, Nmax and Nmin are the maximum andminimum values of the count number, and N is defined as the average of Nmax and Nmin , α is thequantity called visibility and it is typically represented as (Nmax − Nmin )/(Nmax + Nmin ), and tπ/2 is theperiod of the π/2 spin-flip pulse.
Diﬀerentiating the formula (3.3) with respect to the frequency of the RF magnetic field, we obtain thefollowing equation:dN (ω)= Ndown/up αT sin ((ωrf − γn B0 )(T + 4tπ/2 /π))dωrf
∼ Ndown/up αT sin ((ωrf − γn B0 )T )

26

(3.5)

Figure.3.2 Schematic illustration of Ramsey method

The expression (3.5) becomes maximal when (ωrf − γn B0 )T = π/2. Therefore, we can experimentally
determine ω = (ωrf − γn B0 ) most eﬃciently by fitting two points near π/2 of the measurement data withthe expression (3.3). If the neutron EDM is present, an additional shift contributed from the neutron
EDM will occur in ωT . In this study, the total count number in the data with (ωrf − γn B0 )T = π/2
is referred to as N hereafter. On the other hand, as mentioned in 3.2, neutrons for each spin state arecounted in every measurement cycle. Therefore, N can be represented as N = Nup + Ndown . In this way,
the sensitivity of the measurement can be derived as follows:σωrf =

dωrf
1
√
dN =
dN
(αT N )

(3.6)

In an actual neutron EDM measurement, the dataset with the electric field upward and downward
are subtracted from one another to eliminate the contribution of the magnetic field (see formula (3.1)
and (3.2)). Therefore, the statistics of the formula (3.6) must be regarded as one-half and the error√
propagation factor 2 must be multiplied. In such a way, the following formula can be obtained as thesensitivity of the neutron EDM experiment:27

Figure.3.3 RF frequency dependence of count number in the neutron EDM measurement experiment, the image is cited from [42]. The vertical axis represents the number of detected UCNs, thehorizontal axis represents the frequency of RF, and T in the figure represents free precession timeof neutrons in Ramsey’s method. The counted number after Ramsey’s method vibrates according1
to the RF frequency. The count number changes most largely at the point 4T
.

σdn =

√
1
h̄σωrf1√∼ h̄ 2
4E
4E(αT N/2)h̄√(2αET N )h̄√=(2αET nN1meas )
=

(3.7)
(3.8)

where N represents the number of UCNs counted in the whole experiment, N1meas represents the numberof UCNs counted in one EDM measurement cycle, and n represents the number of repetition for themeasurement cycle used in the whole experiment.

√
The sensitivity of the neutron EDM experiment is scaled by 1/ N . In addition, the sensitivity ofthe experiment is improved the most when the denominator becomes maximum. Assuming the time
evolution of UCN number N follows N = N0 exp (−T /τ ), we obtain the following condition as the best
statistical sensitivity:)d ( √T exp (−T /τ ) = 0
dT→ T = 2τ

(3.9)

In this study, the condition of formula (3.9) is used to estimate the statistical precision of J-PARC P33.
28

3.2 ILL ExperimentThis section explains the procedure of the neutron EDM measurement experiment of the ILL experiment.
Figure 3.4 shows the setup of the ILL experiment [42]. In the ILL experiment, the following apparatuses
are used: ultracold neutron source, transport guide, polarizer, storage cell, polarized Hg cell, door system,
electrode, magnetic shield, and 3 He detector. Following the document [42], give an explanation of themain apparatuses below.

Figure.3.4 Schematic view of setup used for the ILL experiment. the image is cited from [42]Ultracold neutron source
The schematic diagram of UCN source of ILL is shown in Figure 3.5 [20]. Nuclear fission neutrons
emitted from the reactor of ILL are moderated with 20 K by heavy water and then transported

29

upward with a 12 m long guide pipe with a curve. Since high-speed neutrons cannot curve, only
cold neutron less than 50 m/s reaches the tip of transport guide. Finally, UCN production is done
by Doppler shifter.
Storage Container
The storage container used in the ILL experiment consists of quartz glass cylinder and discs coatedwith DLC film. DLC film was deposited on 30 mm aluminum substrate with 1 µm. The inner
shape of the container was 47 cm in diameter and 12 cm in length (21 L). In general, the potentialof quartz glass is 91 neV, and the potential of DLC is 210 neV. The reason why quartz is used on
the side of the container is that current flows occurs unless it is an insulator. Two holes are drilledin the lower disk, and its opening and closing can be controlled with two doors, called UCN doorand Hg door. There are small windows on both sides of the sidewall of the storage cell, where thelaser can be incident from the outside on one side of the window and its intensity can be monitoredwith a photomultiplier tube outside the windows.

Figure.3.5 Schematic diagram of the ultracold neutron source of the ILL experiment, the image
is cited from [20].

Polarized Hg chamber
When polarized 199 Hg is irradiated with right-handed circularly polarized light of a wavelength of30

Figure.3.6 Example of the eﬀect of Hg co-magnetometer, the image is cited from [42]. The verticalaxis shows the fluctuation of the precession frequency, the horizontal axis shows the measurement
time, the blue and red shows the data before and after correction by Hg co-magnetometer. Before
the correction, ∼ 5 × 10−11 T errors occurred due to the fluctuation of the magnetic field, but it issuﬃciently suppressed after the correction.

254 nm, its intensity is attenuated according to the spin component of 199 Hg. Hence, it becomes
possible to monitor the state of precession of the 199 Hg gas confined in the storage container towhich a magnetic field is applied. In the ILL experiment, the fluctuation due to environmental
magnetic field was corrected by monitoring the precession frequency of polarized 199 Hg cohabiting
with UCNs in the chamber. Such a tool of correcting the magnetic field drift by Hg atoms iscalled Hg co-magnetometer. In the ILL experiment, 204 Hg lamp was used as the light source usedfor Hg co-magnetometer. The eﬀect to compensate an environmental magnetic field fluctuation isshown in Figure 3.6. The blue and red points represent the drift of magnetic field in the neutron
EDM measurement before and after correction of the environmental magnetic field. Before thecorrection, the magnetic field change amount to 10−25 e·cm, but it is suppressed to a much smaller
magnetic field change after correction.
Door system
The storage container has two holes. One hole is 67 mm in diameter at the center and 4 cm
deep, which serves to connect the storage container to the UCN detector. The other is a holewith a diameter of 10 mm, which serves to connect the storage container to the Hg chamber. The
function of opening and closing of the door was implemented by moving the UCN door consistingof beryllium-copper coated by DLC, and its opening and closing was controlled by the compressed
air. The gap of the door and hole was less than 100 µ m. All the device consist of nonmagnetic

31

materials. In the ILL experiment, a survey at a distance of 2 cm from the inner wall of the surface
was carried out with a flux gate magnetometer with an accuracy of 1 nT, and it was confirmedthat there was no residual magnetic field. In other words, in the ILL experiment, the possibility
that a magnetic field of less than 1 nT existed cannot be excluded. This caused systematic errors,so that this issue must be discussed in detail later in the section of systematic errors.
ElectrodeIn the ILL experiments, a DLC/Aluminum disk was used as the electrode. The HV feedthroughwas connected to the upper disk and the lower disk was grounded. In the ILL experiment, themagnitude of the voltage applying in the upper and lower disks was 7 kV/cm. In the ILL experiment, it was found that there was a dipole magnetic field synchronized with the direction of theelectric field applying in the HV feedthrough. This will cause systematic errors, so that this issue
must be touched in detail later in the section of the systematic error.
Polarizer
The Fermi potential of iron with saturation magnetization depends on the polarization of neutron
and it becomes 90 neV or 300 neV. In the ILL experiment, the transport path was blocked witha Si/Fe filter that becomes magnetization saturation with 0.1 T permanent magnet. As a result,since the UCNs on one polarization cannot pass through the filter, it is operated as a polarizer.
Magnetic shield
The time change of the environmental magnetic field has a huge eﬀect on the neutron EDM
measurement. Therefore, a magnetic shield was constructed by disposing four layers of mu-metalaround the measurement container. However, it was diﬃcult to make the arrangement of the
mu-metal perfectly symmetrical. Non-uniformity of the magnetic field caused systematic errors,so that this issue must be discussed in the section of the systematic error.
3

He gas proportional counterIn the ILL experiment, 3 He gas proportional counter was used as UCN detector. Helium 3 cause thefollowing nuclear reaction with neutrons: 3 He + n →3 H + p. The interaction cross section is verylarge as great as 5333 barn. Thus, ultracold neutrons are detected through the above-mentioned
reaction.
In the ILL experiment, the neutron EDM measurement was performed by the following procedure.

1.Production of ultracold neutrons
The nuclear fission neutrons emitted from the reactor of ILL are cooled with heavy water, transported upward by a nickel guide pipe with a curve, and finally converted into ultracold neutrons
by Doppler Shift method.
2.Transport of UCNs
UCNs are transported from turbine house to the storage container.
3.Polarizing UCNs
The degree of polarization of neutrons is increased by passing through the above-mentioned polarizer on the way of transport.
4.Start of storage sequence32

UCNs are filled inside the storage container with the UCN door open for 20 s. Then the UCN
door is closed, and the Hg door is opened instead and the container is filled with polarized Hg.
Finally. the Hg door is closed again.
5.Applying RF1
RF is applied and the UCN spin is turned parallel to the ground.
6.Applying static electric field and magnetic field
The electrostatic field is made apply parallel/antiparallel to the static magnetic field for 140 s.
7.Applying RF2
RF is applied and the spin is turned in the direction perpendicular to the ground.
8.End of storage sequence
The central door is opened and the UCN from the container is evacuated.
9.Detecting polarized UCNs
UCNs are counted with the detector installed on the underside of the storage container. At thistime, the number of UCNs is evaluated while applying RF to the coil by a certain time interval.
10.Repeat of process1
Repeat procedures 1 to 9 while using diﬀerent RF adopted in procedures 5 and 7.
11.Repeat of process2
Repeat procedures 1 ∼ 10.

3.3 Our Proposed Experiment: Neutron EDM Experiment at J-PARC
This section explains the experimental procedure of J-PARCP 33. In the J-PARC P33 experiment, fastneutrons are produced by the nuclear spallation reaction between a lead target and J-PARC pulsed protonbeam. Then, fast neutrons are cooled to few meV by the elastic scattering of nuclei, and further cooledto O(100 neV) by the inelastic scattering from a solid deuterium. At present, such a low energy neutrons
are extracted from the ultracold neutron source as UCN beam and are transported with refocused in
front of the storage container by the rebuhch method and taken in the storage container. This procedure
repeats until UCN density becomes nearly maximum, and thereby statistical precision and heat load canbe improved eﬃciently compare to other experiments.
For reference, schematic diagrams of J-PARC P33 experiment are given in Figure 3.7, and an enlarged
figure around the storage container is given in Figure 3.8. In addition, a schematic diagram of UCN
transportation with UCN rebunch method is given in Figure 3.9 and 3.10.
For J-PARC P33, the neutron EDM measurement is assumed to be performed at room temperature.
Therefore, many main apparatuses are common with the ILL experiment. Specifically, the polarized
Hg cell, the door system, the electrode and the magnetic shield are common. On the other hand, theultracold neutron source, the transport guide, the polarizer, the storage container, and the detector are
diﬀerent from ILL. Also, the rebuncher is an apparatus that does not exist in ILL.
Only six main apparatuses diﬀerent from the ILL experiment are explained in the following.
Ultracold neutron source
33

Figure.3.7 Outline of J-PARC EDM experiment. (1) A lead target is irradiated with J-PARC
proton beam and fast neutrons is produced by nuclear spallation reaction. (2) Fast neutrons arecooled down to several meV (referred to as cold neutrons) by elastic scattering by liquid deuterium
and heavy water. (3) Cold neutrons are further cooled to ultracold neutrons by inelastic scatteringof solid deuterium phonon. (4) To extract the high intensity pulse UCN produced by transport
guide. (5) The high-speed component of UCN is decelerated with rebunch method and refocus itin front of the storage container. (6) To open the shutter and take the UCN in the container, andthen immediately close the shutter to minimize backflow. (7) Repeat 1∼6 until reaching almost
maximum density. (8) Start measurement of precession. The image is cited from [18].

Figure.3.8 Apparatuses of J-PARC P33 experiment. Schematic diagram of apparatuses of J-PARC
P33. The front UCN shutter is used for cutting out the rebunch pulse, and the rear shutter is used
for preventing backflow during measurement. The image is cited from [18].

The ultracold neutron source consists of a lead target, heavy water of 300 K, liquid deuterium of
20 k and solid deuterium of 5 K. When J-PARC proton beam is incident on the lead target, fastneutrons are generated by nuclear spallation reaction. By cooling it from O(MeV) to several meV
through collisions of deuterium molecules in heavy water and liquid deuterium, cold neutrons canbe obtained. Then, ultracold neutrons are produced by further cooling from meV to O(100 neV)34

Figure.3.9 UCN supply method assumed in J-PARC P33. The flow from 1 to 1′ represents thetime evolution. At the time of 1, a large amount of UCN is generated instantaneously by J-PARC
pulse proton beam which has the world’s highest instantaneous intensity, but it becomes diﬀused
according to the speed as time grows from 1 to 4. So, decelerate the high-speed component using
the rebuncher, and refocus it as 4′ → 1′ to restore the UCN density in front of the storage container.
The image is cited from [43] and partially changed.

Figure.3.10 Illustration of the principle of the rebunch method, the image is cited from [44]. Pulse
neutrons emitted from the neutron source at time t0 undergo deceleration of diﬀerent magnitude
for each velocity at time t1 , and as a result, it is focused to the detector point at time t2 .

or less due to inelastic scattering of phonon in solid deuterium. The solid deuterium is surrounded
by a nickel mirror to prevent leaking the ultracold neutron flux. Because the solid deuterium
reacts immediately, the incident timing of the pulse proton beam is well conserved. Note that thereason why deuterium is used for cold neutron production is that the absorption is lower than thatof hydrogen, and as a result, the intensity of cold neutrons can be increased more.
Transportation guideHigh intensity pulse UCN is transported to the storage container. The inner surface of the transport guide is made of high reflectivity material, such as NiP or NiMo or DLC.

35

Rebuncher
Rebuncher is a neutron accelerator instrument combining gradient static magnetic field and RF
magnetic field. Both magnetic fields are orthogonal one another. In this study, it is assumed
that gradient magnetic field region is set at a point 5 m from the tip of the transport guide andRF magnetic field region is extended to its center to 20 cm. In addition, -3.2 T/m for magnetic
field gradient, and 6 ∼ 30 MHz for RF frequency are assumed, respectively. If RF is applied
while changing RF frequency, the resonant spin reversal will occur only where the spin resonantcondition is satisfied. When the spin reversal occurs in the stronger magnetic field region in thegradient magnetic field, the more the energy increases (decreases). Therefore, if the application
timing of RF magnetic field is adjusted to decelerate UCNs having high-speed component, it ispossible to refocus the pulse UCN in front of the storage container. In this study, spin reversal
probability of 100% is assumed for simplicity.
Storage container
The storage container consists of a cylindrical container coated with a highly reflective material
having high insulation properties and two disks coated with a non-magnetic material. It is assumed
that the inner shape of the storage container and the door system of UCN and Hg are the same
specifications as the ILL experiment, but it is undecided whether UCN intake port is set on theside or bottom of the container.
Polarizer
A magnetic field area of 5 T is applied between UCN source and the transport guide. This willautomatically polarize all the UCNs going to the storage container.
Detector
In the ILL experiment, Helium-3 proportional counter was used. However, the dead time is toolong to use for next generation neutron EDM experiments such as PSI or TRIUMF. Therefore, weare planning to use a more rapid detector. For example, a lithium glass scintillator or similar is acandidate.
The experimental result of J-PARC is directly aﬀected by the performance of the main apparatuses.
For example, the repetition frequency of the pulsed beam, the proton beam current, the initial time distribution when ultracold neutrons are produced, the UCN extraction eﬃciency from the solid deuterium
ultracold neutron converter, the rebunch eﬃciency of the transport guide, and the ability to be stored,
and so on. The eﬀect of these performances is considered in chapter 4. In addition, the above performance is sensitive to the performance of the developed reflector. The current status of development ofreflective materials is described in chapter 5.
The procedure of J-PARC P33 experiment is as follows:
1.Production of nuclear spallation neutrons
A lead target is irradiated with J-PARC LINAC pulsed proton beam to generate nuclear spallation
neutrons.
2.Production of ultracold neutrons
Nuclear spallation neutrons are made cooled to ultracold neutrons by using elastic scattering in36

the heavy water and liquid deuterium and the inelastic scattering in solid deuterium.
3.Conversion to fully polarized UCNs
A magnetic field of 5 T is applied near the outlet of UCN source and only the upward spincomponent is taken out.
4.Transportation of UCNs
Polarized neutrons are transported to the storage container. UCN with high-speed component isdecelerated by rebuncher during transportation and refocused in the front of the storage container.
5.Start of UCN storage
The UCN door is opened to take in only the refocused UCN beam. This procedure is repeateduntil the number of UCNs in the storage container becomes almost maximum. After that, UCN
door is closed, Hg door is opened instead and the container is filled with polarized Hg. Finally,
the Hg door is closed again.
6.Applying of the second RF magnetic field
RF magnetic field is applied for a certain time to align the spins of UCN in a direction parallel tothe ground.
7.Duration of UCNs freely precessing for a long time
The electrostatic field of 10 kV/cm is applied parallel/antiparallel to the static magnetic field fora long time.
8.Applying of the second RF magnetic field
RF is applied and spin is turned in a direction perpendicular to the ground.
9.End of UCN storage duration
UCNs are released from the storage container.
10.Duration of detection of polarized UCNs
The number of UCNs is counted with a detector. At this time, measurements are performed byalternately applying RF to the coil installed in front of the detector, and the number of bothpolarized UCNs can be evaluated.
11.Repetition
Repeat steps 1∼10 with diﬀerent RF used in procedures 5 and 7.

3.4 Other Next Generation Experiments
Other next generation neutron EDM experiments are proceeding, all of which employ the super-thermal
method for UCN production. These experiments are explained in the following.
PSI is already ready for next generation neutron EDM experiment and the measurement is started.
In this experiment, using 1.2 MW Proton Cyclotron, the beam of 590 MeV and 2 mA are incident on
Pb target for 6 sec to produce nuclear spallation neutrons and then cooled it with 30 liters of solid
D2 and D2 O moderator. PSI group is aiming to achieve 5 × 10−27 e · cm in the first stage and finally
5 × 10−28 e · cm EDM measurement. Details of the neutron EDM experiment at PSI can be found in[45, 46, 47, 48].

37

TRIUMF also plans a next generation neutron EDM experiment using liquid He-II as a spallation
UCN source. The spallation source using He-II has already been demonstrated at RCNP, where Pb
target is irradiated with 400 W (400 MeV, 1 µA) proton beam accelerated by Cyclotron (DC) for about
100 seconds to produce nuclear spallation neutrons and cooled it with 8 liters of 0.7 K by He-II and D2 O
moderator. It was confirmed that 15 UCN/cm3 (E < 90 neV) can be achieved. Even at TRIUMF, inthe first stage 10−27 e · cm, in the second stage 5 × 10−28 e · cm or less. For details of the neutron EDM
experiment of TRIUMF, please refer to the document [49].
ILL is planning a new neutron EDM experiment called CryoEDM that cold neutrons emitted fromthe nuclear reactor are cooled with He-II. In CryoEDM, cold neutrons are incident on a container filledwith liquid Helium to produce UCNs, and it is transported to a cell filled also with liquid Helium.
In this experiment, the distortion of the magnetic field is corrected using the only SQUID without
using co-magnetometer. In the CryoEDM experiment, a strength of electric field can make twice higher
because of insulation of liquid He, which results in improving the precision by two digits as comparedto the conventional ILL experiment. However, in order to carry out this experiment, it is necessary
to redevelop the experimental apparatuses as a whole. For details of CryoEDM, please refer to the
document [50].
SNS is planning next generation neutron EDM experiment. In this experiment, as well as CryoEDM,
a cold neutron is incident on a container filled with He-II to produce UCNs for experiments. On theother hand, unlike CryoEDM, a small amount of 3 He doped in liquid helium is used as co-magnetometer.
Specifically, the precession of 3 He is monitored from the modulation of detection of the scintillation light
due to the absorption of polarized 3 He. For the details of SNS experiment, please refer to the document[51, 52, 53].
In addition, WWR-M is planning a new neutron EDM experiment using a method that the 15 MW
neutron flux emitted from the nuclear reactor is cooled with He-II. They are aiming at measuring neutron
EDM with less than 5 × 10−28 e · cm. For the details of the experiment of WWR-M experiment, pleaserefer to the documents [54, 55].

38

Chapter 4

Dependence Study of the Statistical
Sensitivity on the Performance of theReflection Material of UCN
This chapter describes the study to evaluate the dependence of the statistical sensitivity on the reflection
performance of J-PARC P33 experiment. For the J-PARC P33 concept, there was a problem that theexperimental capability had not been evaluated. Due to it, the experimental sensitivity expected at thepresent time could not be evaluated, and any optimization studies to improve the sensitivity could not
be done. In general, although the statistical sensitivity of the J-PARC P33 experiment depends on a
lot of factors, it was particularly diﬃcult to understand how much the storage eﬃciency and transport
eﬃciency aﬀect the statistical sensitivity through the reflection loss and the non-specular reflection fromthe material surface. In this study, for solving this problem, the dependence of the statistical sensitivity
on such reflection performances was evaluated by a full simulation that can deal with an experimental
system and entire procedures based on J-PARC P33 concept. Using PHITS [56], Geant4UCN [57]and an original program that was developed by the author, all of J-PARC P33 procedures and thenecessary interactions for UCN were incorporated into the simulation. The magnetic field structure of
the prototype of the rebuncher was used to represent the rebunch method, and the neutron optical theory
and the micro-roughness model were used to handle the above-mentioned reflection interactions. In sucha way, the J-PARC P33 experiment was totally simulated from the upstream to the downstream in orderto quantitatively investigate the dependence of the statistical sensitivity on the reflection performance.
Details of this study are described below.
This chapter is organized as follows. First, the detail of the pulsed beam property of J-PARC LINAC,
which is the basis of the J-PARC P33 experiment, is explained in 4.1. In 4.2, the UCN density producedin the solid deuterium ultracold neutron source is evaluated. This information is necessary to relate theintensity of UCN beams that must be assumed in the Monte Carlo simulation to that of UCN beams
expected in the actual J-PARC P33 experiment. In 4.3, details of the rebuncher are explained, whichis the key device for J-PARC P33 experiment. In 4.4, details of J-PARC P33 simulation are described.
Specifically, in 4.4.1, the phase space density of UCNs is evaluated, which is used for the transport andstorage simulation. In 4.4.2, it is described how essential points aﬀecting the results of the simulation
39

were chosen. In 4.4.3, the transportation simulation is performed to evaluate the dependency of therebunch eﬃciency, especially on non-specular reflection. In 4.4.4, the storage simulation is performed toevaluate the expected number of UCNs that can be stored with the rebunch storage method and thedependence of it on reflection performances. In 4.4.5, the statistical sensitivity of the J-PARC P33 andthe dependence of it on reflection performances are evaluated. Finally, a short summary of this chapter
is given in 4.5.

4.1 Proton Beam Property at J-PARC Neutron EDM Experiment
In this section, the property of J-PARC LINAC proton beam is described. The schematic illustration of
the J-PARC LINAC proton beam is shown in Figure 4.1. In the future plan of J-PARC, the proton beam
will be supplied at LINAC with 50 Hz, of which 25 Hz goes to RCS and the remaining 25 Hz is used in
LINAC. The beam energy is 181 MeV so far, and it is going to be 400 MeV in the future. This study
assumes a part of the beam of LINAC is used for the neutron EDM experiment. The J-PARC LINAC
proton beams consist of 25 macropulses, which further consist of many micropulses (see Figure 4.1).
The pulse width of a macropulse is 500 µ s, the pulse width of a micropulse is 560 ns, and the interval
between two adjacent micropulses is 1065 ns (181 MeV) or 815 ns (400 MeV). Therefore, a macropulse
consists of 500 micropulses that can be calculated from (500 × 10−6 ) / (1065 ns). In addition, the pulse
width of a macropulse tmacro can be changed continuously by the factor of 1/10 to 1, the pulse width ofa micropulse tmicro can be changed continuously by the factor of 1/5 to 1, and the interval between two
adjacent micropulses Tmicro can be discretely changed to 1, 1/2, and 1/4.
If all of two pulse width factors and the interval factor of a micropulse are chosen to be 1, the average
current of the macropulse of the J-PARC LINAC is Iavg = 375 µA(181 MeV) or 625 µA(400 MeV). On
the other hand, the instantaneous current of the J-PARC macropulse can be derived from Iavg × 1/(25Hz)
500 µs ,which result in 30 mA (181 MeV) or 50 mA (400 MeV). Because the average beam power of J-PARC
LINAC is 67.9 kW (181 MeV) or 250 kW (400 MeV), the instantaneous beam power of J-PARC LINAC
is 5.4 MW (181 MeV) or 20 MW (400 MeV ).
In this study, the repetition rate and the peak power of the J-PARC LINAC beam are chosen to be
0.5 Hz and 20 MW, respectively. The characteristics of the beam condition used into this study aresummarized in Table 4.1.

40

Figure.4.1 Schematic illustration of beam distribution of J-PARC LINAC. Although macro pulseof 50 Hz will be supplied to J-PARC LINAC, only half of macropulses can be used in the experiment
which will be conducted in LINAC. In this study, it was assumed that only 0.5 Hz out of 25 Hz
was used for the neutron EDM measurement. In addition, it was also assumed that tmacro was
Tmicro= 1 where (Tmicro )std is the standard value of the interval
500 µs, tmicro was 560 ns, and (Tmicro)std
between two adjacent micropulses. The image is cited from [18, 19] and partially changed.

Proton Energy

400 MeV

Pulse width

0.5 msRepetition used in Experiment

0.5 HzRepetition Rate of J-PARC LINAC

25 Hz

Peak Proton Current

50 mA

Average Proton Current

0.625 mA

Peak Power

20 MW

Average Power250 kW

Table.4.1 Details of the beam condition of J-PARC P33 used in this study41

4.2 UCN Source at J-PARC Neutron EDM Experiment
In this section, the density of UCN produced in the solid deuterium converter is evaluated. In J-PARC
P33, the ultracold neutron source is assumed to consist of cylindrical solid deuterium having a diameterof 10 cm and a length of 20 cm, liquid deuterium of 20 K, heavy water of 300 K, lead target and graphite.
The geometry conditions and schematic diagram used in PHITS simulation are shown in the Table 4.2
and Figure 4.2.
Generally, the density of UCNs produced in the ultracold neutron source is proportional to the intensityof cold neutron flux passing through it. In J-PARC P33, cold neutron flux was simulated with the heavy
ion transport calculation code PHITS. Regarding the accuracy of the PHITS calculation, there is anactual comparison between the actual measurement result of J-PARC MLF BL10 and the simulation
result. It has been confirmed that both results agree with the accuracy of 10% ∼ 20% [58]. In thiscomparison, a proton beam of 3 GeV and a mercury target were used for producing nuclear spallation
neutrons, and cold neutrons were produced by decelerating it with liquid hydrogen, which corresponds
to the case of J-PARC MLF. On the other hand, for J-PARC P33 concept, as shown in Table 4.1 andTable 4.2, the proton beam of 400 MeV and the lead target are used for producing nuclear spallation
neutrons, and cold neutrons are produced by decelerating it with heavy water and liquid deuterium.
The cold neutron flux distribution passing through solid deuterium converter calculated by PHITS isgiven in Figure 4.3. The horizontal axis is the energy of incident neutron, the vertical axis is the neutron
flux passing through the solid deuterium converter, the black line is calculation result, and the red line is
the fitting result with Maxwell distribution. Note that the phonon interaction of the PHITS simulation
creates the peak structure of the flux energy distribution of Figure 4.3.
In Figure 4.3, the cold neutron flux Φ can be calculated by integrating of 10 meV or less, resultingin Φ = 5.8 × 1011 cm−2 s−1 . On the other hand, the fitting result of Figure 4.3 showed that the mostprobable energy of cold neutron flux is approximately 2.6 meV. In other words, the cold neutron fluxof Figure 4.3 can be approximated to be Maxwell distribution of 30 K. Because the expression (2.31) ispossible to be used for Maxwell distribution of 30 K, UCN production can be estimated by substituting
Φ = 5.8×1011 cm−2 s−1 into the expression (2.31). In such a way, ρ = 5, 800 UCN/cm3 was obtained as thedensity of UCN produced in solid deuterium converter. This is evaluation result for UCN production of
J-PARC P33 experiment. It is noted that the maximum energy of UCNs produced in the solid deuteriumis assumed to be 252 neV in the expression (2.31).

42

Proton Charge

25 µC

TargetLead (Φ10 cm× 20 cm)

ShieldLead (Φ30 cm× 30 cm × 15 cm)

Converter

Solid D2 (Φ10 cm× 20 cm)

20 K Moderator

Liquid D2 (Φ20 cm× 30 cm)

300 K Moderator

Heavy Water (Φ50 cm× 50 cm)

Reflector

Graphite (Φ 100 cm × 100 cm)

Distance from target to converter

22.5 cm

sD2 density

0.196 g/cm3

sD2 atom density

0.0590 atoms/barn/cm

sD2 atom density

0.0295 molecule/barn/cm

Table.4.2 Simulation condition of PHITS

Figure.4.2 The arrangement of the ultracold neutron source used in PHITS simulation. Fastneutrons due to nuclear spallation reactions caused by pulse proton beams with the Lead Target(pink) were decelerated by the elastic scattering by Heavy Water (Blue) and Liquid Deuterium(Purple), and by the inelastic scattering by solid deuterium placed in the center (light blue). As aresult, it is converted into ultracold neutrons. Ultracold neutrons are extracted from the transport
guide (red) and transported to the EDM measurement apparatus.

43

Figure.4.3 The energy spectrum of cold neutron flux passing through the solid deuterium converter, the image is cited from [18]. The horizontal axis is the energy of the incident neutron, thevertical axis is the neutron flux passing through the solid deuterium converter. The calculation
was performed by PHITS. See the text for details.

444.3 Rebuncher
In this section, the design concept and the operation principle of the optical equipment rebuncher are
explained. In addition, the demonstration experiment of the rebuncher conducted in ILL is explained.
The rebuncher is designed to make pulsed UCN beams refocused at a certain point by changing theamount of the velocity of UCNs as described in chapter 3.3. The rebuncher operation is based on theexperimental technique to control the spin resonant reversal in a gradient static magnetic field. In general,
if neutron is in a static magnetic field of B, the neutron spin reversal can be induced by applying therotating magnetic field with the spin reversal resonant frequency ω orthogonal to B. The spin resonant
reversal condition is given as follows:h̄ω = 2µB

(4.1)

where µ is neutron magnetic moment.
If neutron spin is reversed in a static magnetic field with a certain gradient B(z), the potential energychange of 2µB(z) occurs according to each position z. Therefore, a desired kinetic energy change can berealized by controlling the spin reversal point in the static gradient magnetic field. This is the operational
principle of the rebuncher. For this reason, the rebuncher consists of an electromagnet to supply a static
gradient magnetic field and a spin flipper to supply a rotating magnetic field. For reference, the schematic
illustration of the magnetic field generator of the rebuncher prototype is given in Figure 4.4 [18]. In thissystem, by combining a normal conducting electromagnet and anisotropic intermediate magnetic poles,
the linear gradient magnetic field of -3.2 T/m is realized. The measurement result of the linear gradientmagnetic field of the rebuncher prototype is shown in Figure 4.5.

Figure.4.4

The cross-section view of the rebuncher prototype. The image is cited from [18].

If neutron travels in the static magnetic field of the gradient dB
dz and the rotating magnetic field Brf is45

Magnetic Field [T]

1
0.8
0.6
0.4
0.2
0

-600 -400 -2000
200 400 600
Rebuncher Position [mm]Figure.4.5 Linear gradient magnetic field used in rebuncher

applied to this region, the neutron spin is reversed in the following probability p [44]:
)
( √
1
2 π
2
1
+
k
sin
1 + k222
ωLγn Brf
k=
=
ωB
vn dB
dz
p=1−

(4.2)
(4.3)

where k is the adiabatic parameter, vn is the component of the neutron velocity in the direction of
travel, ωL is the frequency of the applied rotating magnetic field, and ωB is the resonant frequency. For
reference, a plot of the spin reversal probability is given in the Figure 4.6.
Regarding the rebuncher prototype, the magnetic field gradient in the accelerating region is -3.2 T/m.
In this case, we need k > 1.4 to achieve a spin reversal rate of 90% or more from the formula (4.2). Thus,
it is estimated that a rotating magnetic field intensity of Brf = 0.35 mT is required. Actually, because
the RF magnetic field is a combination of clockwise and counterclockwise rotating magnetic fields, theexperiment requires twice the magnetic field intensity. Therefore, by using RF with a magnetic field
intensity of more than 0.7 mT, experiments with spin reversal probability more than 90% can be easily
achieved.
In 2012, the demonstration experiment of the rebuncher was performed at the ILL/PF 2 TES port (seedocument [59] for details). In this experiment, by a shutter coated with gadolinium oxide to make pulsed
UCN beams from DC UCN beams supplied at ILL, the change of time of flight due to rebunch eﬀect waschecked. If the rebunch eﬀect appears, time-of-flight should be changed when UCNs are detected at a
certain point. A schematic diagram of the experimental setup and the time of flight spectrum obtained
are shown in Figure 4.7 and 4.8, respectively [44]. It was actually confirmed that UCN of 5 m/s was46

Spin-flip probability

1

0.8

0.6

0.4

0.2

0
0

1

2

3

4

5

6

7
8
9
Adiabaticity parameter,kFigure.4.6 Relation of adiabatic parameter k and spin-flip probability

decelerated to 4 m/s by the rebuch method, and that the instantaneous intensity of the UCN beamincreased by about 1.4 times. On the other hand, the spin reversal probability at the demonstration
experiment was confirmed to be 0.5. It is thought to be due to the incomplete impedance matching of
the RF resonator. Currently, an improved machine is being developed, and the test at J-PARC MaterialLife Science Research Facility Beam Line No.5 is being prepared.

47

Figure.4.7 Schematic diagram of the setup used for the rebuncher demonstration experiment performed at ILL, the image is cited from [44]. (1) UCN beam supplied in ILL is transported to thefront of the shutter through ϕ 67 mm stainless steel pipe. (2) UCN beam is collimated with a 100
mm long bellows whose inside wall is covered with cadmium plate. (3) The UCN beam is pulsed
by cutting out with opening/closing the shutter and is supplied to the rebuncher guide consistingof a square pipe of 60 mm (H) × 30 mm (W) × 5.6 m. Here, the longitudinal-gradient magnet
with anisotropic interpole and an RF coil are installed in the middle part, and a UCN detector isinstalled in the endpoint. (4) RF magnetic field of intensity 0.5 mT with a frequency of 17.5 MHz
to 28.6 MHz was applied to the rebuncher for 80 ms from the chopped timing.

48

Neutrons/25ms

10 8

Velocity (m/s)
4

6w Rebuncher

10-1

w/o Rebuncher

10-2

0.5

1

1.5
2
TOF from shutter (s)Figure.4.8 The refocused TOF confirmed at the rebuncher demonstration experiment at ILL, theimage is cited from [44]. The horizontal axis is TOF, the vertical axis is the counting rate, thewhite point marker is the spectrum when the spin flipper is not used, and the black dot marker isthe spectrum when used.

49

4.4 J-PARC P33 simulation
In this section, the phase space distribution, the rebunch eﬃciency, the number of UCNs that can beaccumulated in the storage container by the rebunch storage method, the statistical sensitivity of J-PARC
P33 experiment, and the dependence of these quantities on the performance of reflection materials were
evaluated. The schematic representation of the simulation setup in this study is shown in Figure 4.9.
Furthermore, details of the simulation setup assumed in this study is summarized in Table 4.3. In thisstudy, it was assumed that the rebuncher equipment is installed at 5 m from the tip of the transport
guide. Regarding the magnetic field generator, the static gradient magnetic field of -3.2 T/m and theRF magnetic field of the frequency changing from 6 MHz to 30 MHz were assumed. Furthermore, thespin reversal probability of 100% was assumed. In this simulation, Geant4UCN [57] and an original
program developed by the author were used. The total experimental duration of EDM measurement
was assumed to be 3 years, while the amount of the time used for the measurement was assumed to be
18 hours/day. In addition, the ratio of ortho-deuterium to para deuterium and elastic scattering crosssection for solid deuterium converter, which have a large eﬀect on the statistical precision of the J-PARC
P33 experiment, were assumed as below. Regarding the ortho-para ratio, although it has been reported
that other institutes such as PSI have achieved 98%, this study adopted 95% for conservative evaluation.
With respect to the elastic scattering cross section of solid deuterium, only the incoherent cross section
was taken into account. These general assumptions are summarized in Table 4.4.
sD2 Converter

Φ100×L200 mm2Transport Guide

100×100 mm2 ×10 m

Rebuncher Position

5 m (from the tip of the transport guide)

Storage Container

Φ470×L120 mm2

Focus Guide (cross section)

35×35 mm2 (at the exit)

Focus Guide (Length)

15 mmTable.4.3

Details of the geometry

Total EDM Experimental Duration

Assuming 3 years

Measurement time

Assuming 18 hours/day

Simulation Framework

Using Geant4UCN and original program

Ortho-Para Ratio of sD2

95:5

Elastic Scattering Cross Section of sD2

Assuming only the incoherent cross section

Static Gradient Magnetic Field of Rebuncher

Using the magnetic field of Figure 4.5

RF Magnetic Field of Rebuncher

Using the magnetic field of Figure 4.10

Spin reversal probability

100 %Table.4.4

General assumptions in this simulation

50

Figure.4.9

Schematic diagram of the setup assuming in the J-PARC P33 simulation

51

RF Frequency [MHz]

30

25

20

15

10
0.8

0.85

0.9

0.95

1

1.05

RF Timing [s]Figure.4.10 Relation between RF magnetic field frequency and application time. The vertical axis
shows the RF frequency used in the simulation, the horizontal axis shows the RF magnetic field
application time52

4.4.1 Phase Space of J-PARCP33 setup
In this section, the phase space distribution of the J-PARC P33 experiment, necessary to simulate thetransport and storage of UCNs, is evaluated. The conditions used in the simulation to evaluate the phasespace distribution are described below.
1. A solid deuterium cylinder of Φ100 mm × L200 mm laid out horizontally, which is surrounded bynickel reflector.
2. UCNs are uniformly produced for space in solid deuterium and the direction of initial velocity isisotropic.
3. An initial energy E is assigned according to the probability density distribution of√E, which is

known to be valid for low energy neutrons produced by the super-thermal method.
4. Considering the reaction cross section of neutron absorption and up-scattering of solid deuterium.
5. Considering the eﬀect of acceleration due to the diﬀerence in the Fermi potential between thevacuum space and the solid deuterium.
In the simulation, the position and velocity distribution of UCNs reaching the boundary between
the solid deuterium converter and the inlet of transport guide were recorded. The obtained energy
distribution, absolute velocity distribution, longitudinal velocity distribution, and transverse velocity
distribution are given in the Figure 4.11, 4.12, 4.13, and 4.14. The phase space distribution includes the
position distribution, but it is not given here because it is obvious. In this study, the time at which the
UCN is generated since the J-PARC proton beam is injected to Pb target is called T0 hereafter. The T0
distribution calculated by PHITS is given in Figure 4.15. It is understood that T0 is suppressed to beless than 5 ms.

53Normalized Events/neV

0.01

0.008

0.006

0.004

0.002

0

0

20

40

60

80

100

120

140

160

Kinetic Energy (neV)Normalized Events/(0.1 m/s)

Figure.4.11 Energy distribution of UCN in solid deuterium. The vertical axis is the numberof Monte-Carlo events, and the horizontal axis is the kinetic energy of UCN generated in solid
deuterium. The total sum of the number of events is normalized to 1.

0.05

0.04

0.03

0.02

0.01

0
0

1

2

3

4

5

6

7

8

9

10

Velocity Length (m/s)

Figure.4.12 Absolute velocity distribution of UCN in solid deuterium. The vertical axis is thenumber of Monte-Carlo events, and the horizontal axis is the absolute velocity of UCN generated
in solid deuterium. The total sum of the number of events is normalized to 1.

54

Normalized Counts/(0.1 m/s)

0.05

0.04

0.03

0.02

0.01

0
0

1

2

3

4

5

6

7
vz (m/s)

Figure.4.13 Longitudinal velocity distribution of UCN beam. The vertical axis is the number ofMonte-Carlo events, and the horizontal axis is the longitudinal velocity length of UCN reaching
the boundary between the transport guide and the solid deuterium converter. The total sum of
the number of events is normalized to 1.

55

vy (m/s)

60.0025
4
0.002
2

0

0.0015

-2

0.001

-4
0.0005
-6
-6

-4

-2

0

2

4

6
vx (m/s)

0

Figure.4.14 Transverse velocity distribution of UCN beam. The vertical and horizontal axis denotecomponents of the transverse velocity of UCN reaching the boundary between the transport guideand the solid deuterium converter, and the color represents the number of Monte-Carlo events.
The total sum of the number of events is normalized to 1.

56

×10

FLUX [neutrons/cm2]

9

25

20

15

10

5

0
0

5

10

15

20

25

30
35
40
JPARCP33_T0 (ms)Figure.4.15 T0 distribution when UCNs generate in the solid deuterium converter. The verticalaxis is the neutron flux calculated by PHITS, the horizontal axis is the time at which the UCN isgenerated since the J-PARC proton beam is injected to Pb target, T0 .

57

4.4.2 Essential Point of Simulation
In this section, it is explained what kind of criteria is adopted for the simulation study. Simulation
results are aﬀected by the following factors:
1. Rebunch Eﬃciency
2. Storage Performance
3. Rebunch Storage Performance
4. Guide Size
5. Bottle Size
6. Electric field strength
The performance of the rebunch eﬃciency is determined by the non-specular reflection, the application
timing of the RF magnetic field, the gradient magnetic field, and the spin reversal resonance probability.
Regarding the non-specular reflection, the micro roughness model is used in this study. In this model,
because the surface roughness is a significant principal parameter, these parameters are changed withinrealistic conditions. Regarding the RF magnetic field, it is adjusting within the realistic range expected
to be feasible from the development of the rebuncher. Regarding the gradient magnetic field, the samevalue as the prototype of the actual rebuncher system is adopted in this study. Regarding the probabilityof spin reversal resonance, in order to evaluate the upper limit of the experimental ability, it is chosen
as 1 which is the ideal condition.
The storage performance is determined by Fermi potential and UCN loss probability coeﬃcient. Regarding Fermi potential, ILL and PSI values are assumed in this study. Regarding the loss probability
coeﬃcient (η), it is aﬀected by temperature and the surface condition. η typically amounts to ∼ O(10−4 )at room temperature, but it also amounts to several 10−5 by cooling it. It is found that η has large
variation depending on conditions (refer [85][86][82]). Therefore, in this study, η is changed in the range
from several 10−5 to several 10−4 according to these references.
The rebunch storage performance is determined by the distance from UCN source to the shutter
position, the beam repetition of J-PARC pulse proton beam, the shutter opening/closing timing, therebunch eﬃciency, and the storage performance. In this study, the distance from UCN source to the
shutter position is chosen to 10 m, based on the specification value of J-PARC P33 experiment. Then,it takes 1.4 s ∼ 2.4 s to detect UCNs from the time when UCN is produced by nuclear spallation. In
this study, for simplicity, the beam repetition of J-PARC pulse proton beam is chosen to 0.5 Hz = 2 s
to exclude the eﬀect of pulse pile up. Therefore, in this study, it is estimated how much the following
three factors contribute to the changes in the rebunch storage performance: the timing adjustment of
opening/closing of shutter, the rebunch eﬃciency, and the storage performance.
Regarding the size of the transport guide, it is modeled by the specification of the J-PARC P33
experiment. Regarding the magnitude of the electric field, it is determined by the discharge limit.
Regarding the bottle size, it is chosen to be the same size as ILL and PSI.

58

4.4.3 Rebunch Eﬃciency
In this study, the transportation simulation assuming J-PARC P33 experiment was performed and theeﬀect of the rebunch method was evaluated by analyzing the time of flight at the shutter point. In
addition, the experimental setup of Figure 4.9, the general assumptions of Table 4.4, and the initial
position and initial velocity distribution described in chapter 4.4 are assumed, respectively. Therefore,
the rebuncher is assumed to be at 5 m, and a gradient magnetic field of Figure 4.5 and an RF magnetic
field of Figure 4.10 are assumed to be applied. The time of zero in this simulation is regarded as that of the
proton beam injection. In this situation, UCNs are generated in the solid deuterium and transported tothe measurement cell through the rebuncher. Both rebuncher magnetic fields make UCNs concentrating
on shutter 1 point of Figure 4.9 at the time of 2.15 s to 2.2 s (see later Figure 4.16 for details).
In this study, the period that shutter opens after the J-PARC proton beam injection is referred toas “cut-out time”. Thanks to the rebunch method, the UCN density in the measurement cell becomes
improved most eﬀectively by adjusting the cut-out time width to the time for which the pulsed UCN
beams refocus on a shutter point. Hence, the cut-out time width used in this section is chosen to be 2.15
s to 2.2 s for which pulsed UCN beams refocus on shutter 1 point of Figure 4.9.
In general, the rebunch eﬃciency decreases when non-specular reflection occurs during transport of
UCN. Therefore, this study evaluated the eﬀect of non-specular reflection by using the micro-roughness
model, confirmed to be well matched with the actual measurement. In this study, it was assumed thatthe non-specular reflection occurs only on transport guide according to micro-roughness model. The
following benchmark points were considered for three free parameters of the micro-roughness model.
Surface roughness of guideThis simulation study considered the cases of b = 0 nm, 0.5 nm, 1 nm, 1.5 nm, 2 nm, 2.5 nm,
3 nm RMS. It is decided to estimate the eﬀect of roughness more precisely within the practicalrange on the application limit of micro roughness model (see chapter 2.3).
Correlation length of guideThis simulation study considered the cases of w = 22 nm, 33 nm, 45 nm. It is estimated by theactual measurement of neutron mirrors such as NiC and DLC, which were evaluated to be 22 nm
and 45 nm with AFM (DI-3100, Veeco Instruments Inc.) [31].
Surface potential of guideThis simulation study considered VF = 210 neV. It corresponds to the mirror made by NiP plating
method. The plating method can coat large area, and NiP is inexpensive and nonmagnetic. That
is why NiP mirrors are chosen as a benchmark in this study.
Based on the above-shown assumptions, the transport simulation is performed as below. First, UCNs
are generated uniformly in the solid deuterium converter according to the phase space distribution
as described in chapter 4.4.1, and then UCNs are transported from UCN source to the shutter 1 of
Figure 4.9. In this way, if UCN reaches shutter 1 point, the time of flight of UCN is recorded. The
same procedure repeats 100,000 times, which generates the time-of-flight distribution of J-PARC P33

59

experiment. Finally, by analyzing obtained result, the number of Monte Carlo events recorded on 2.15
to 2.2 s and the dependence of it on the non-specular reflection are evaluated. The larger the number ofMonte Carlo events is, the higher the rebunch eﬃciency becomes.
For reference, Time of Flight distribution obtained by the transport simulation is shown in Figure 4.16.
The horizontal axis shows Time of Flight when UCNs reach the shutter 1 of Figure 4.9, the vertical axis
shows the number of Monte Carlo Events, the line color denotes the roughness of the transport guideor whether the rebunch method is used or not. When assuming specular reflection, 6896 events wereobtained as the Monte Carlo Events of UCNs which can reach at the shutter 1 position. On the other
hand, the number of trials is 100,000 Events. Therefore, the extraction eﬃciency from UCN source wasestimated as 6.896±0.08 % in this simulation condition.
The intensity of UCN flux varies depending on the rebuncher and shutter operation, which can be
estimated from Figure 4.16. If using neither the rebunch nor the shutter operation, the intensity is
calculated as 6896±80 Events/2 s = 3448±40 Events/s. Similarly, if using both the rebunch method
and the shutter opening/closing operation with the cut-out time width 2.15 s to 2.2 s, the intensity is
calculated as ∼ 2,020±40 MC Events/50 ms = 40,400±800 Events/s. The diﬀerence corresponds to 11.7
times. This fact indicates that the intensity of the UCN flux varies greatly according to the cut-out time
width and the time focusing eﬀect by the rebuncher.
The analysis results of dependence on the non-specular reflection is shown in Figure 4.17. Obviously,
the intensity within the time window 2.15 s to 2.2 s becomes drastically attenuated as the surface
roughness increase, which is reduced to be 1/5 as the surface roughness increases from b = 0 to 3 nm.
Therefore, it is found that the non-specular reflection has a serious eﬀect on the intensity of UCN beams.
In Figure 4.17, the eﬀect of correlation length, w, is very small. Hence, in this study, the parameter w
is fixed to 33 nm for simplification hereafter.
This study chose the cut-out time width to be 2.15 s to 2.2 s at which pulsed UCN beams refocus
on shutter 1 point so that the rebunch eﬃciency becomes maximal. However, in general, eﬀectiveness of rebunch method changes depending on how the cut-time out width is synchronized with UCN
beams because it has eﬀect on the instantaneous intensity. For reference, the dependency study of theinstantaneous intensity on the cut-out time in some extremely cases is given in the Appendix H.

60

MC Events/50 ms

2000
1800

No Rebunch

1600

No Roughness

1400

b=1.0 nm, w= 33 nm

1200

b=2.0 nm, w= 33 nm

1000

b=3.0 nm, w= 33 nm

800
600
400
200
0
0

0.5

1

1.5

2

2.5

3

3.5

Time of Flight (s)Figure.4.16 Example of TOF distribution change due to the non-specular reflection. TOF change
at the shutter 1 point was evaluated in the case that UCN passes through a transport guide with
diﬀerent surface roughness. The horizontal axis is TOF, and the vertical axis is the number of
UCNs which can reach shutter.

61

Normalized Intensity

shutter opens for 2.15 s to 2.2 s
45000

w = 22 nm

40000

w = 33 nm

35000

w = 45 nm

30000
25000
20000
15000
10000
5000

0

0.5

1

1.5

2

2.5

3

RMS roughness (nm)Figure.4.17 Dependence of the rebunch eﬃciency on the surface roughness. The vertical axis is
the number of Monte Carlo events normalized to 1 s, the horizontal axis is the RMS value of thesurface roughness of transport guide, and the line color denotes the correlation length.

62

4.4.4 Rebunch Storage
In this section, it is confirmed how much UCN number will increase when refocused UCN beams areaccumulated in a storage container with the rebunch storage method. And also, it is confirmed how
the number of the storable UCN depends on the reflection performance of the storage container and thenon-specular reflection.
In this study, it was assumed that pulse UCNs are supplied from the ultracold neutron source every
two-seconds cycle. Therefore, the time evolution of the number of UCNs in the storage container can be
represented by accumulating that of one pulse. In addition, the time dependence of total storage number
is expressed as S(t), and the time dependence of storage number due to one pulse is expressed as s(t)hereafter. In this way, S(t) was derived by evaluating s(t) and piling it up. This relation is represented
clearly as follows:

S(t) =i∑max

s(t + 2i)

(4.4)

i=0

where imax indicates the upper limit of the number of pulses piled up. In this study, imax = 50 was used
so that the storage time becomes long enough. In other words, it means that the accumulation up to
100 s was considered in this simulation.
The number of UCN achieved by the rebunch storage method changes depending on the accumulation
period and the reflection performance of the storage container and non-specular reflection. In this study,
the accumulation period was defined as the elapsed time until S(t) becomes the maximum value of 90 %since the start of accumulation of UCNs. Furthermore, benchmark points of reflection performance werechosen to be the following 8 points shown in Table 4.5. As mentioned in section 4.4.2, Fermi potential
assumed in this study is chosen to be that of ILL and PSI experiment. And also, η values are chosen
to be from 8×10−5 to 5×10−4 because η value is typically changed from ∼ O(10−4 ) to several 10−5
depending on conditions. In addition, in this study, micro-roughness model assuming parameters used in
the previous section was adopted to represent the non-specular reflection on the transport guide surface.
potential ID

potential (bottom and top)potential (side)

η

1

210

91

(8 × 10−5 , 1 × 10−4 , 3 × 10−4 , 5 × 10−4 )

2

210

160

(8 × 10−5 , 1 × 10−4 , 3 × 10−4 , 5 × 10−4 )Table.4.5

Reflection performance of the storage container considered in this study

Simulation assumption and procedure are described below. First, the experimental setup of Table
4.3 and the general assumptions of Table 4.4 are assumed. Second, the cut-out time width of 2.15 s to
2.2 s is assumed. Third, regarding parameters having eﬀects on the non-specular reflection of the innersurface of the transport guide, the RMS roughness of b = 0 ∼ 3 nm, the correlation length of w = 33 nm,
and VF of 210 neV are assumed. Fourth, it is assumed that only specular reflection occurs at the innersurface of the storage container. Fifth, it is assumed that the inner wall of the storage container has
63the reflection performance of Table 4.5. Sixth, it is assumed that pulsed UCN beams are generated by
one proton beam injection and emitted from the ultracold neutron source in J-PARC P33 environment.
Under such six assumptions, the transport simulation repeats 100,000 times to evaluate s(t), and thenS(t) is derived by piling up s(t) by every two-second cycle. Finally, the number of UCNs that can be
stored with the rebunch storage method is evaluated as the maximum value of 90 % of S(t).
An example of a function of s(t) and S(t) are given in Figure 4.18. The vertical axis is the numberof UCNs in the storage container, the horizontal axis is the elapsed time since the start of accumulationof UCN, red is s(t), and black is S(t). The potential ID1 corresponds to a container having the samepotential as the ILL experiment, and the potential ID2 corresponds to a container having the samepotential as the deuterated polystyrene that PSI developed. In other words, in the former it is assumed
that DLC coated on aluminum on the top and bottom and SiO2 on the side are used, and in the latter itstorage number

is assumed that DLC coated on aluminum on the top and deuterated polystyrene on the side are used.

45000
40000
35000
30000
25000
20000
15000
10000
5000
0

0

10

20

30

40

50

60

70

80

90

100

storage time (sec)S(t):pileup spectrum w/ rebunchs(t):first pulse spectrum w/ rebunch
Figure.4.18

Examples of functions s(t) and S(t)For reference, the time evolution of the rebunch storage number for potential ID1 and 2 and a loss
probability coeﬃcient of 3 × 10−4 is given in Figure 4.19. The vertical axis corresponds to the number ofstored UCNs, and the horizontal axis corresponds to the storage time. The maximum value of the stored
UCN varies depending on the potential diﬀerence. In general, the UCN loss probability coeﬃcient also
has a similar eﬀect.
The analysis result obtained from this study is given in Figure 4.20 and 4.21. The vertical axis is
the number of the rebunch storage, and the horizontal axis is the surface roughness. The number ofthe rebunch storage strongly depends on the non-specular reflection, which decreases 1/2.5 to 1/3 as b
increases from 0 nm to 3 nm RMS. Regarding the Fermi potential, the number of the rebunch storage inthe case of using the potential lD1 becomes 1/1.7 to 1/2.1 compared to the case of using potential ID2.
64

Also, the number of UCNs that can be achieved with the rebunch storage method decreased about 1/1.5
as η varied from 8 × 10−5 to 5 × 10−4 . From the above, it is understood that the non-specular reflection
has the most serious eﬀect on the performance of the rebunch storage method.
Figure 4.20 shows that the best case achieves 35,000, while the worst case achieves 5,000. There was adiﬀerence of 7 times between two cases; it is thought that such a large diﬀerence was due to the change
in the rebunch eﬃciency and the storage eﬃciency. Because the number of trials of simulation for thetransportation of one-pulse UCN is 100,000 times, it is found that the number of UCNs that can be storedby the rebunch storage method amounts to 5% to 35% compared to the number of UCNs generated instorage number

the solid deuterium converter by one proton beam injection.

30000
25000
20000
15000
10000
5000
0

0

10

20

30

40

50

60

70

80

90

100

storage time (sec)bottom & top=210 neV, side=91 neV, η=3e-4
bottom & top=210 neV, side=160 neV, η=3e-4
Figure.4.19 Example of the eﬀect of the potential on the rebunch storage number. The verticalaxis shows the rebunch storage number and the horizontal axis shows the storage time. See thetext for details.

65

The 90 % Maximum Storage Number

25000
20000
15000
10000
5000
0

0.5

1

1.5

2

2.5

3

RMS roughness (nm)bottom & top=210 neV, side=91 neV,η=8e-5
bottom & top=210 neV, side=91 neV,η=1e-4
bottom & top=210 neV, side=91 neV,η=3e-4
bottom & top=210 neV, side=91 neV,η=5e-4

The 90 % Maximum Storage Number

Figure.4.20 Dependence of the rebunch storage number on the non-specular reflection. The vertical axis shows the number of storage and the horizontal axis shows the surface roughness. See
the text for details.

45000
40000
35000
30000
25000
20000
15000
10000
5000
0

0.5

1

1.5

2

2.5

3

RMS roughness (nm)bottom & top=210 neV, side=160 neV, η=8e-5
bottom & top=210 neV, side=160 neV, η=1e-4
bottom & top=210 neV, side=160 neV, η=3e-4
bottom & top=210 neV, side=160 neV, η=5e-4
Figure.4.21 Dependence of the rebunch storage number on the non-specular reflection. The vertical axis shows the number of storages and the horizontal axis shows the surface roughness. See
the text for details.

664.4.5 Statistical Sensitivity
In this section, the dependence of the statistical precision on the performance of the reflection material
are evaluated. The evaluation flow is explained as below. In general, in order to evaluate the statisticalsensitivity, following five variables must be determined: E, α, T , n, and N1meas (refer formula (3.8)
for details). Of these variables, the electric field strength (E) and the visibility (α) can be fixed using
the reference values based on the ILL and PSI experiment. In this study, 10 kV/cm and 0.86 areused as E and α, respectively. The detection number of UCNs expected in one measurement (N1meas )and the time needed for one measurement (T ) can be determined by the UCN storage simulation andthe maximum statistical sensitivity condition of expression (3.9). This study uses the rebunch storage
number evaluated in previous section as the number of UCNs stored in the container at the beginningof the storage duration. The repetition number of measurements (n) can be determined by dividing
the total measurement duration (Ttot ) by the time necessary for one measurement cycle (T1meas ). Ttot
is determined by the assumption of Table 4.4. T1meas can be determined by the following formula:
T1meas = Tacc + T + Trel , where Tacc denotes the time needed for accumulation of UCN, and Trel denotes
the time needed for release of UCNs. Tacc can be determined by the rebunch storage simulation. On
the other hand, in this study, Trel is assumed to be 100 s, for which UCNs in the storage container of 21
Litter can be evacuated enough (refer Appendix.F.2 for the case of the storage container of 98 Litter).
In such a way, all E, α, T , n, and N1meas can be determined. Thereby, the statistical precision is derived
and its dependence on the reflection performances is analyzed.
Simulation assumptions and procedure are described below. First, the electric field strength is chosen
to be 10 kV/cm. Second, the total experimental duration and the measurement time per one day are
assumed to be 3 years and 18 hours/day, respectively. Third, visibility α is assumed to be 0.86, whichis the evaluation value of the document [63] assuming time invariance of α during storage. Fourth, it isassumed that UCNs are released from the measurement cell for 100 s after UCN storage period. Fifth,
it is assumed that the rebunch storage number, evaluated in previous section, is used as the numberof stored UCNs in the measurement cell at the beginning of UCN storage period. Sixth, it is assumed
this study inherits all of the reflection performance used in the rebunch storage simulation adopted inprevious section. Under such six assumptions, UCN storage simulation is performed 500 times to search
the storage time and the storable number of UCNs satisfying the maximum sensitivity condition of
expression (3.9). As a result, E, α, T , N1meas , and n are determined. Finally, by substituting thesevalues for five variables of formula (3.8), the statistical sensitivity is evaluated.
For reference, an example of the time evolution of the number of UCNs obtained from the storage
simulation is given in the Figure 4.22. The vertical axis corresponds to the number of stored UCNs,
and the horizontal axis corresponds to the storage time. It represents the storage time dependence ofthe number of UCNs in the storage containers whose potential ID are 1 or 2 in Table 4.5 and UCN loss
coeﬃcient η is 3 × 10−4 .
The statistical precision obtained in this simulation is given in Figure 4.23 and 4.24. Each figure corresponds to the result assuming diﬀerent potential ID 1 or 2, respectively. The horizontal axis represents

67the surface roughness, the vertical axis represents the statistical precision that can be achieved whenthe experiment continued for 3 years, and color denotes η diﬀerences. The best statistical precisionobtained by the simulation was (7.2 ± 0.2) × 10−28 e·cm, whereas the worst statistical precision was(5.9 ± 0.2) × 10−27 e·cm. There was a diﬀerence of 8 times between two cases; such a large diﬀerence
was due to the change in the rebunch eﬃciency and the storage eﬃciency. The statistical precision wasdeteriorated by the non-specular reflection, and it was changed by about 1.6 times with b varied from 0
nm to 3 nm. In addition, the statistical precision changed by about 3 times as η varies from 8 × 10−5 to
5×10−4 , while it improved by 1.5 ∼ 1.7 times with the potential of sidewall increased 91 neV to 160 neV.
In this way, the dependence of the statistical sensitivity on the performance of the reflective materialof UCN of J-PARC P33 was numerically clarified. It is concluded that accurate evaluation of reflection
performance is needed for reliable estimation of the statistical sensitivity of J-PARC P33. In particular,
it is important to evaluate the UCN loss probability having the largest eﬀect on the sensitivity. In otherwords, it is understood that development of highly functional reflective materials is extremely eﬀective
for improving the statistical sensitivity of J-PARC P33.

storage number

Example:Compare Storage Lifetime

102

10

1
0

100

200

300

400

500

600

700

800

900

1000

storage time (sec)bottom & top=210 neV, side=91 neV, η=3e-4
bottom & top=210 neV, side=160 neV, η=3e-4
2τ crosssing line
Figure.4.22 Example of time change of UCN storage number. The time evolution of stored UCNs
is simulated. The vertical axis is the number of UCNs in the container, and the horizontal axis
is the storage time. η = 3 × 10−4 and potential ID = 1 (red) or 2 (blue) were selected as thereflection performance of the container. The number of trials of Monte Carlo was chosen to be 500.
The black line (2τ crossing point) corresponds to the number of UCNs satisfying the maximum
sensitivity condition of expression (3.9).

68statistical error (e•cm)

×10-27
6
5
4
3
2
1
0

0.5

1

1.5

2

2.5

3

RMS surface roughness (nm)bottom & top=210 neV, side=91 neV,η=8e-5
bottom & top=210 neV, side=91 neV,η=1e-4
bottom & top=210 neV, side=91 neV,η=3e-4
bottom & top=210 neV, side=91 neV,η=5e-4
Figure.4.23 Dependence of the statistic precision on the non-specular reflection and UCN reflection loss. Simulation was used to estimate the statistical precision of the J-PARC neutron EDM
experiment. The horizontal axis represents surface roughness, the vertical axis represents the statistical precision, and the line color represents potential and η. Note that the use of a container
with Potential ID = 1 is assumed here.

69

4 ×10statistical error (e•cm)

-27

3.5
3
2.5
2
1.5
1
0.5
0

0.5

1

1.5

2

2.5

3

RMS surface roughness (nm)bottom & top=210 neV, side=160 neV, η=8e-5
bottom & top=210 neV, side=160 neV, η=1e-4
bottom & top=210 neV, side=160 neV, η=3e-4
bottom & top=210 neV, side=160 neV, η=5e-4
Figure.4.24 Dependence of the statistic precision on the non-specular reflection and UCN reflection loss. Simulation was used to estimate the statistical precision of the J-PARC neutron EDM
experiment. The horizontal axis represents surface roughness, the vertical axis represents the statistical precision, and the line color represents potential and η. Note that the use of a container
with Potential ID = 2 is assumed here.

704.5 Short Summary
1. Using PHITS simulation, the energy distribution of the neutron flux passing through the solid
deuterium converter of J-PARC P33 ultracold neutron source was evaluated. As a result, anenergy distribution in Figure 4.3 was obtained, which can approximate to Maxwell distribution
with a peak at 30 K. By normalizing the flux distribution with the beam current of one pulse of
J-PARC LINAC proton beam, 5.8 × 1011 cm−2 s−1 was obtained as the evaluation of total neutron
flux sum.
2. Assuming Maxwell distribution with a peak at 30 K, the UCN density generated in the solid
deuterium was estimated. As a result, 5,800 UCN/cm3 was found to be produced in the solid
deuterium when injecting one pulse of J-PARC LINAC proton beam to the ultracold neutron
source.
3. Transportation of J-PARC P33 was simulated. As a result, the TOF distribution and its nonspecular reflection dependence were evaluated as Figure 4.16 and Figure 4.17. It was confirmedthat the rebunch method makes the intensity gained by 11.7 times if not taking account nonspecular eﬀect, and that the non-specular reflection makes the intensity attenuated by 1/5 times
as b increased 0 nm to 3 nm RMS.
4. Rebunch storage simulation was performed. As a result, the time dependency of the number ofthe rebunch storage was evaluated as Figure 4.20 and 4.21. This result indicated that the numberof UCNs decreased by 1/2 or less due to non-specular reflection, by 1/1.7 or less due to the Fermi
potential diﬀerence, and by 1/1.5 due to loss probability coeﬃcient diﬀerence.
5. The simulation to evaluate the statistical precision of J-PARC P33 neutron EDM experiment was
performed. As a result, the statistical precision as Figure 4.23 and Figure 4.24 were obtained. 3
years is assumed for an experimental period and its duty is 3/4. This result indicated that statistical precision becomes deteriorated by about 1.6 times due to non-specular reflection diﬀerence,by about 1.5 times due to the Fermi potential diﬀerence, and by about 3 times due to the loss
probability coeﬃcient diﬀerence, respectively.

71

Chapter 5

Development of Neutron Mirror for Neutron
EDM Experiment
In this chapter, the details of the development of the neutron reflective material are summarized. In
the previous chapter, it became clear that the development of reflective materials is key to high precise
neutron EDM measurement. The performance of the reflector can be indicated by the Fermi potential,
the non-specular reflection probability, and the UCN loss probability coeﬃcient as described in theprevious chapter. In addition to those indexes, a nonmagnetic property is desirable because a low
spin reversal probability is achieved. Furthermore, a high insulating property is desirable for a sidewall
material of the storage container because it suppresses leakage current flowing in the sidewall. Therefore,
NiMo (nonmagnetic, high Fermi potential) and Diamond Like Carbon (nonmagnetic, high insulation,
low non-specular reflection probability) have been developed in this study.
The performance of the reflector was evaluated by surface analysis such as neutron reflectometry,
Rutherford backscattering spectroscopy/elastic recoil detection analysis (RBS/ERDA), X-ray reflectometry, electron microscope, glow discharge optical emission spectrometry (GDOES), and so on. As for the
UCN loss probability coeﬃcient, two evaluation ways are possible: one is the method using RBS/ERDA
and the other is the method using UCN storage experiment. In this chapter, only evaluation method
using RBS/ERDA is taken. The method using UCN storage is described in the next chapter.
This chapter is organized as below. First, the reflective material about NiMo is described. Specifically,
the feature as neutron mirrors and the manufacturing method are explained. In next section, similar
explanations for Diamond Like Carbon are given. This section consists of three subsection dealing
with manufacturing methods, plasma based ion implantation deposition method, ionized evaporation
deposition method, and filtered arc ion plating deposition method. Next, the details of the surface
analysis methods are described. Next, the performance of all the developed materials evaluated by thesurface analysis is summarized. Finally, the short summary of this chapter is given.

5.1 Fabrication method of Nickel Molybdenum Alloy
Nickel is an excellent material with high Fermi potential of 252 neV. However, Nickel does not become an
excellent neutron mirror because its polycrystalline structure causes poor surface roughness. Generally,72

amorphous structure tends to have better surface roughness. Therefore, nickel alloys doped with anelement such as C, Mo, V are used for neutron mirrors. In particular, the alloy doped with Mo ata weight ratio of 15% is a promising material that has been confirmed to achieve high transportationeﬃciency [64, 65].
Normally, the sputtering method is used for the preparation of the alloy film, but it cannot deal withthe formation of large area substrate. In this study, vapor deposition method was tried to prepare NiMo
alloy. In order to obtain an alloy film by vapor, it was necessary to use a special method in which Ni andMo are separately evaporated and mixed on a substrate. Hereafter, such method is called binary vapor
deposition. A schematic illustration of binary vapor deposition method is shown in Figure 5.1. In thisstudy, with the technical cooperation of Kanagawa Institute of Industrial Science and Technology [66],development of NiMo mirrors became possible. The equipment used in this study is summarized in the
Table 5.1.
In the film formation process, the chamber was evacuated to 10−5 Pa, and Ni and Mo were evaporated
by electron beams, and it was exposed to the substrate. In this study, 10 kV and 320 mA were used aselectric power and current of the electron beam. The substrate was rotated to prevent non-uniformity
while binary vapor deposition proceeding. The film thickness was evaluated by measuring the step
between silicon masking region and the other. In step measurement, laser microscope with the precisionof ∼ 1 nm was used.
The NiMo alloy preparation flow is illustrated as follows.
1. Ni and Mo are evaporated alone to confirm the deposition rate.
2. The time of irradiating an electron beam to each target is determined.
3. NiMo is deposited on 10 mm square silicon by using the film deposition condition of 2.
4. The composition ratio of the sample made at 3 is evaluated.
5. The work of 2 – 4 repeats to search for optimum film formation condition.
The composition ratio of NiMo was evaluated by X-ray Photoelectron Spectroscopy (XPS) and a crystal
oscillator, and the result was feedback to adapt film formation condition. The depth profile measurement
using XPS showed that there was no dependence of depth direction and there was little contaminationof oxygen and nitrogen. Although the composition ratio of Mo measured by XPS systematically tended
to be higher than that of a crystal oscillator, the results of XPS measurement and the result of thecrystal oscillator measurement had a strong correlation. For example, in a certain case, Ni:Mo ratio was
86.8%:13.2% in the result of XPS, 88.6%:11.4% in the result of the crystal oscillator. Finally, by quartz
oscillator evaluation, it was confirmed that NiMo film with the weight ratio of 13.6 % was achieved.

5.2 Fabrication method of Diamond-Like Carbon
Diamond has a potential of 304 neV, which exceeds Nickel, and it has high insulation and nonmagnetic
property. However, its polycrystalline structure causes poor surface roughness (and also it is expensive).
From this point of view, in recent years, Diamond-Like Carbon (DLC) is paid attention. DLC is referred
to as a carbon film having the properties of graphite (planar structure) and diamond (three-dimensional73

Figure.5.1 Schematic illustration of binary vapor deposition method. An alloy film of a desired
composition ratio can be obtained by giving diﬀerent amounts of heat to each ingot to evaporate
them separately and mix them on the substrate. Please see the text for details.

Equipment

PurposeManufacturer

Ion plating apparatus (SIP-700)

Film formation

SHOWA SHINKU Co., Ltd.

VersaProbe2XPS

ULVAC-PHI, Inc.

CRTM-9000

Crystal Oscillator

ULVAC, Inc.

JEBG-303UA

Electron Beam

JEOL Ltd.

ST-10F

Power Source

JEOL Ltd.

Dektak 3030ST

Stepmeter

Sloan Co., Ltd

Table.5.1 Details of apparatuses used for film formation of NiMo

structure). DLC generally has an amorphous structure, so that this surface is smooth and it is possible
to be an excellent mirror for a transport guide. In addition, DLC has high insulation for diamondcharacteristics, which is desirable for a side material of the neutron EDM experiment to prevent electric
current flow.
In general, a carbon film whose hydrogen ratio is about 20 to 30% is also included in the definition of
DLC. For this reason, the characteristics of DLC can be represented as a triangle plot having vertexes.
The triangle plot of the nature of DLC is given in Figure 5.2. The vertex of sp3 indicates the diamondstructure ratio, the vertex of sp2 indicates the graphite structure ratio, and the vertex of H indicatesthe hydrogen content ratio [67]. It can be seen from Figure 5.2 that DLC can be classified into various
types depending on the ratio of sp3, sp2, and H. ta-C DLC is categorized to the group having the highest
sp3 ratio, which indicates the strongest diamond property. Thus, both of high Fermi potential and highinsulation can be expected. Graphite is used as the source material in a ta-C DLC film formation process.
74

Figure.5.2 Classification diagram of DLC, the image is cited from [67]. A triangle diagram shows
the classification of properties of DLC film. See the text for the details.

On the other hand, ta-C:H DLC is categorized to the group having both of a hydrogen content and adiamond-like property. In general, the source material of ta-C:H DLC is organic gas such as benzene.
Although ta-C:H DLC has a diamond-like property, it is inferior to that of ta-C DLC. However, ta-C:H
DLC has engineering merits such that large area coating and three-dimensional coating can be performed,
which ta-C DLC does not have.
In this study, ta-C DLC and ta-C:H DLC have been examined. The reason why ta-C DLC was adopted
is that it shows both of high Fermi potential and high insulation. On the other hand, the reason why
ta-C:H DLC was adopted is as below. (1) By using deuterated substitution technique, it can achieve theFermi potential of 200 neV or more. (2) Large-area three-dimensional coating is possible. In general,hydrogen deteriorates both of the Fermi potential and UCN loss probability per one bounce, whereas
deuterium improves them. Therefore, ta-C:H DLC after deuterated substitution is possible to apply tothe sidewall material of a neutron EDM measurement cell. In fact, the Fermi potential of the sidewall
material of ILL experiment and PSI experiment are 91 neV (quartz glass) and 160 neV (deuterated
polyethylene). This fact implies the possibility that ta-C:H DLC after deuterated substitution becomes
an excellent sidewall material. Deuterated DLC has already been evaluated in documents [68][69], butthey have not prepared mirrors from which hydrogen was completely eliminated. In this study, deuterated
benzene of a deuteration rate of 99.5% was used as source gas.
In the following section, the details of DLC film formation will be described. Three types of DLC
deposition method tried in this study are shown in Table 5.2.

5.2.1 Ionization Evaporation Method
A schematic diagram of the ionized evaporation method is shown in the Figure 5.3. In ionized evaporation
method, a hydrocarbon gas is ionized by using thermal electrons emitted from a filament, and it sprayed
on a substrate with a bias voltage. In this way, ionized gas is attracted to the substrate and DLC film

75

DLC formation method

Type

Corp

Apparatus

IEM

ta-C:HNANOTEC Co.,Ltd. [70]ICF-330

PBIID

ta-C:HKURITA SEISAKUSHO Co.,Ltd. [71]PBII-R1000

FAIPD

ta-C

ONWARD CERAMIC COATING Co., Ltd. [72]AC-X

Table.5.2 Apparatus used for DLC film formation. Details of IEM DLC, PBIID DLC, and FAIPD
DLC are described in chapter 5.2.1, 5.2.2, and 5.2.3, respectively.

Figure.5.3 Schematic illustration of the ionized evaporation method, the image is cited from [67].
See the text for details.

deposition proceeds.
In this study, DLC produced by the ionized evaporation method is referred to as IEM DLC. The flowof film formation for ionized evaporation method is shown below:
1. The silicon substrate is fixed to the film-forming table.
2. The pressure is evacuated to 10−2 Pa with a turbo molecular pump.
3. The heater keeps operated for about 3 hours to realize the thermal equilibrium state.
4. Substrate is bombarded with argon gas to remove the oxide film on the substrate surface.
5. Deuterated benzene is made filled into the chamber.
6. Gas is made ionized with thermal electrons emitted from tungsten filament.
7. Bias voltage is applied to the film-forming table.
8. The silicon substrate is exposed to ionized gas, which is attracted by an electric field of the filmforming table.
769. DLC film growth proceeds.
In this study, ICF-330 (Nanotec corporation) was used for DLC film formation [70]. Inside ICF-330, an
ionization vacuum gauge, a baratron vacuum gauge, and a thermometer are installed. The temperature
can be controlled 300 to 500 degrees by a heater, the flow rate of the deposition gas can be controlled
0.1 to 9.9 sccm, and the bias voltage on a substrate can be adjusted to 0 to 3 kV.
Since it has been confirmed that there is a correlation between the gas flow rate and the pressure, it
is possible to control the pressure by the gas flow. Therefore, in this study, pressure, bias voltage andtemperature were adopted as the parameter to control DLC film state.
From the formula (2.2), the Fermi potential of a sample is determined by its composition ratio anddensity, which greatly changes depending on the film formation conditions of DLC. Namely, the reflection
performance of DLC is determined by the film forming conditions. In this study, temperature, pressure
and substrate voltage are adopted as conditions. As for temperature, “Low” is defined as 200 degrees,“Middle” is defined as 300 degrees, “High” is defined as 450 degrees. With regard to the flow rate, “LowPressure” is defined as 0.6 sccm, “Middle Pressure” as 3.1 sccm, and “High Pressure” as 6.2 sccm. In
this study, a lot of number sample were tested. Film formation conditions used are shown in Table 5.3.

5.2.2 Plasma Based Ion Implantation Deposition
Plasma Based Ion Implantation Deposition (PBIID) is the method of applying an RF and a pulsed
negative high voltage to the substrate installed in the process chamber filled with a source gas. Schematic
illustration of PBIID film formation process is given in Figure 5.4 and 5.5. DLC film is formed by plasma
and afterglow generated around the substrate. For brevity, DLC fabricated by PBIID is referred to as
PBIID DLC in this thesis hereafter.
Generally, in PBIID film formation, both RF plasma and afterglow contributes to DLC film formation.
The afterglow mainly contributes film formation. Thanks to afterglow, film formation can be performed
at a temperature as low as 300 degrees, which is far lower than plasma CVD using only RF plasma.
As a result, the residual stress of the DLC film is relaxed. In addition, the substrate and DLC film areconnected by ion implantation, resulting in enhancement of the adhesion of film. Furthermore, because
the film is formed by afterglow around the substrate, uniform three-dimensional coating is possible.
The PBIID deposition procedure is described as follows:(a) Gas Fill
Process gas is flowed into vacuum chamber.
(b) Plasma CVD
A high frequency voltage (RF) is applied to a substrate, and plasma is generated around thesubstrate. When RF is applied, electrons with high mobility are absorbed by the substrate, but
the ions tend to remain, and as a result, the substrate is negatively biased on average.
(c) Plasma Left Behind
When stopping applying RF field, the plasma is left behind around the substrate.
(d) Ion Implantation

77

No

kV

sccm

Temp

No

kV

sccm

Temp

12

3

3.1

middle

79

0.5

3.1

middle

14

0.5

3.1

middle

80

0.5

3.1

middle

17

1.5

3.1

middle

81

0.5

3.1

middle

31

0.5

3.1

middle

82

0.5

3.1

high

32

0.5

3.1

middle

83

0.75

3.1

high

33

1.5

3.1

middle

84

1

3.1

high

34

3

3.1

middle

87

1.25

3.1

high

35

0.1

3.1

middle

88

0.75

3.1

high

36

0

3.1

middle

89

1.25

3.1

middle

37

0.1

3.1

middle

90

1.25

3.1

middle38

0

3.1

middle

93

0.75

0.6

middle

40

0.05

3.1

middle

94

0.75

3.1

middle

41

0.05

3.1

middle

95

0.75

0.6

middle421

3.1

middle96

1

0.6

middle431

3.1

middle

97

0.5

0.6

middle

44

0.3

3.1

middle

98

0.25

0.6

middle

45

0.3

3.1

middle

103

0.38

0.6

middle

46

0.75

3.1

middle

104

1

0.6

middle

47

0.75

3.1

middle

105

0.25

0.6

middle

65

0.5

6.2

middle

106

0.5

0.6

middle

66

1.5

6.2

middle

107

0.75

0.6

middle

68

0.5

6.2

middle

111

0.5

0.6

middle

71

0.5

3.1

low

112

0.63

0.6

middle

72

0.5

3.1

low

114

0.5

3.1

middle

73

0.5

3.1

middle

115

0.75

3.1

middle

74

0.5

3.1

middle

117

0.75

3.1

middle

76

1.5

3.4

middle

118

0.75

3.1

middle

77

1.5

3.1

middle

119

0.75

3.1

middle78

1

3.1

middle

120

0 .75

3.1

middleTable.5.3

Details of the film formation condition of IEM DLC

78

When a high pulse voltage of about -10 kV is applied, ions are drawn into the substrate. As aresult, ion implantation between the DLC film and the substrate occurs.
(e) Afterglow
Ions is drawn by high voltage pulse to collide with the source gas and cause ionization. As a result,around the substrate, high-density radicals (= afterglow Plasma) is increased, and film formation
proceeds further.
(d) Restart
Afterglow plasma is lost. Return to (a) and start film formation process again.
In this study, with the technical cooperation of KURITA SEISAKUSHO CO., LTD, developmentof PBIID DLC mirrors became possible. KURITA SEISAKUSHO CO., LTD is one of the leading
companies to fabricate PBIID. In general, film formation parameters for PBIID DLC are the pressurein the chamber, the pulse voltage value, and the repetition frequency of the pulse voltage. In this study,
the pulse voltage value and the repetition frequency are chosen as film formation conditions, and thepressure in the chamber is fixed at 4 Pa. Film formation conditions are shown in Table 5.4.

79

Name

Pulse Voltage

Pulse Width

Repetition

sample1-10 kV

20 µs

1000 pps

sample2-15 kV

5 µs

4000 pps

sample3

-5 kV

5 µs

4000 pps

sample4-10 kV

10 µs

2000 pps

sample5-10 kV

5 µs

4000 pps

Table.5.4 Film formation condition of PBIID DLC

Figure.5.4 Schematic diagram of the PBIID method. See the text for details.

80

Figure.5.5 Illustration of the flow of DLC film formation by PBIID method. By turning on andoﬀ the RF and high voltage pulse power supply alternatively, the state transits along following
arrow direction: (a) → (b) → (c) → (d) → (e) → (a) ... etc. Please refer to the text for details.

815.2.3 Filtered Arc Ion Plating Deposition
Arc discharge on graphite surface cause carbon ions vapor, and ta-C DLC film can be obtained byexposing the carbon ions flux to a negative biased substrate. Such film formation method is called arc
ion plating deposition method (AIPD). AIPD has two advantages. First, it is possible to obtain the most
diamond-like carbon film. Second, it is possible to obtain diamond-like carbon film having no hydrogen
which deteriorates neutron reflection performance. On the other hand, AIPD has a disadvantage thatneutral macroscopic particles, called droplets, mix in carbon ions vapor and it deteriorates the film
surface state. Therefore, the method to filter droplets by using magnetic field was proposed to solve thedisadvantage. Such method is called filtered arc ion plating deposition (FAIPD). Schematic diagram of
FAIPD is given in Figure 5.6. By using FAIPD, we can achieve ta-C DLC film having polished surface,high carbon density, and a high insulator property.
For brevity, DLC fabricated by FAIPD is referred to as FAIPD DLC in this thesis hereafter. In thisstudy, AC-X (Onward Ceramic Coating Corporation) was used for DLC film formation. The reason
why AC-X was chosen as the apparatus used in deposition is that according to the catalog, it is able
to fabricate the hardest film, which is equivalent to high carbon density. In this study, W26 mm×L50
mm×T1 mm synthetic quartz glass and Φ76 mm×T2 mm silicon were used as substrates.

Figure.5.6 Illustration of DLC film formation by FAIPD method. When arc discharge occurs
on the surface of graphite, carbon vapor ions are generated. DLC film formation proceeds bydepositing ions vapor on the substrate to which a negative bias voltage is applied. Thereby, thehighest dense DLC film can be obtained. FAIPD method improves surface roughness by removing
neutral particles (called droplets) emitted together with carbon ions.

82

Figure.5.7 Fermi potential of the neutron mirror consisting of a substrate and a single layer. The
vertical axis represents the potential, and the horizontal axis represents the depth direction. Fromthe left: air: 0, neutron mirror material: 1, substrate: 2.

5.3 The Method of Surface Analysis
5.3.1 Neutron Reflectometry
This section introduces the principle of neutron reflectometry. By using neutron reflectometry, we canevaluate the reflectivity distribution of sample consisting of a substrate and a single layer. For brevity,
a sample consisting a film of X and a substrate of Y is expressed as X/Y hereafter. The reflectivity ofthe sample as shown in Figure 5.7 can be derived by solving a one-dimensional Schrödinger equation as
follows [73]:R = DWT(qz , σ)(k0 − k1 )(k1 + k2 ) + (k0 + k1 )(k1 − k2 ) exp (ik1 d)(k0 + k1 )(k1 + k2 ) + (k0 − k1 )(k1 − k2 ) exp (ik1 d)

DWT(qz , σ) = exp (−qz2 σ 2 )

(5.1)
(5.2)

where R is the reflectivity of sample, qz is the transfer wave number during reflection, σ is the RMS
surface roughness, and d is the thickness of the film material. ki for i = 0, 1, 2 represent that the wave
number of neutrons in each region, DWT is Debye-Waller factor which express the surface spreads dueto thermal vibration.√It is noted that the incident region is 0, the film region is 1, and the substrateregion is 2, and ki =i
k0 2 − 2mV
for i = 1, 2. In addition, it is also noted that Debye-Waller factor ish̄2

obtained separately from the Schrödinger equation [74].
At specular reflection, the incident wave number and the reflected wave number are same, and qz isrepresented as 2k0 . Therefore, the expression (5.1) is a function of qz , and its Fermi potential can beextracted directly by fitting the neutron reflectivity distribution with the expression (5.1).
83

Reflectivity

DPS/Si1

Ni/Si
Quartz Bulk

0.8

Diamond Bulk

0.6
0.4
0.2
0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35
0.4
Qz(nm-1)

Figure.5.8 Example of reflectivity. Theoretical values of the neutron reflectivity distribution of
deuterated polystyrene/Si (red line), Ni/Si (blue line), Quartz bulk (green line), Diamond bulk
(black line). The vertical axis shows reflectivity, the horizontal axis shows the transfer wave number
Qz on specular reflection.

An example of reflectivity distribution is given in Figure 5.8. Figure 5.8 is the case that single layer
film has 100 nm thickness, and surface roughness is zero. In general, the rougher the surface is, the fasterthe attenuation is in the wide-angle side. In addition, the thicker the film is, the lower the frequency is.
Further, the higher the potential is, the larger the critical angle becomes.
For reference, the relationship between the critical angle and the potential are given in Figure 5.9.
This relation of Figure 5.9 is used to evaluate the systematic error of the reflectivity measurement at
J-PARC MLF BL16.

84

potential [neV]

250

200

150

100

50
0.1

0.12

0.14

0.16
0.18
0.2
0.22
Q_z for critical angle [nm-1]

Figure.5.9 Relation of critical angle and the Fermi potential.

85

Figure.5.10 Outline of RBS/ERDA experiment, the image is cited from [67]. An acceleratedalpha particles of 2.5 MeV hit a sample tilted by 15 degree with respect to the beam axis, and theoccurrence events were observed by silicon detectors fixed at 150 degree and 30 degree.

5.3.2 Rutherford Backscattering Analysis and Elastic Recoil Detection Analysis
In this study, RBS (Rutherford Backscattering Spectroscopy) and ERDA (Elastic Recoil Detection Analysis) are used for sample composition analysis. In the RBS/ERDA analysis, when an accelerated ion
beam is irradiated to the sample, ions scattered in the forward and backward directions are detected andthe element composition ratio is derived. Divalent helium ions were used as incident ions in this study.
A schematic diagram of measurement setup is shown in Figure 5.10.
For reference, the schematic illustration of the reaction used in RBS and ERDA analysis are shownin Figure 5.12 and Figure 5.13. In this section, the initial energy and the mass of the incident alphaparticle are represented as E0 and M1 , and the mass of target atom is represented as M2 .
Regarding RBS analysis, the energy and the cross section of the backscattering are calculated as thefollowing formula (5.3) and (5.4) [67].
√ERBS = M1 cos θ +()2σ(E, θ)RBS =Z1 Z2 e22E

(M22 − M12 sin2 θ)

M1 + M2


E0 

√
(
)2
1 2
cos θ + 1 − ( M) sin2 θM
2√sin−4 θ22
1
1 − (M
M2 ) sin θ

(5.3)

(5.4)

where σRBS is the elastic backscattering cross section and ERBS is energy of the back scattered particle
and θ is the angle between the beam axis and the back-scattered direction.
Regarding ERDA analysis, the energy and the diﬀerential cross section of the recoiled reaction arecalculated as the following expression (5.5) and (5.6) [67].

864M1 M2 cos2 ϕ
E0(M1 + M2 )2()
Z1 Z2 e2 (M1 + M2 )cos−3 ϕσ(E, ϕ)ERDA =2M2 E
EERDA =

(5.5)
(5.6)

where σERDA is the elastic recoil scattering cross section and EERDA is the energy of the recoiled scatteredparticle and ϕ is the angle between the beam axis and the recoil scattered direction.
In RBS/ERDA measurement, the following relational expression (5.7) holds regarding the detected
counts.
Yi = I0Ni σiΩRBS/ERDA
A(5.7)

where Yi is the count of the element i obtained by RBS/ERDA, Ni is the number of nuclei, σi is the crosssection of the element i, I0 is the incident intensity, A is the irradiation area, and ΩRBS/ERDA represents
the solid angle cut by the detector.
By dividing Yi of the element i for the RBS side by Yj of ERDA side for the element j, following
expression can be obtained:Yi
Ni σ i Ω i=
Yj
Nj σj Ωj

(5.8)
N

In formula (5.8), by transforming YYji to the composition ratio Nji and setting i → ERDA, j → RBS, we
obtain the following relational expression.
NERDA
YERDA σRBS ΩRBS=NRBS
YRBS σERDA ΩERDA(5.9)

Therefore, the element composition ratio in the sample can be determined by using the counting ratio,
the cross section ratio, and the solid angle ratio. In general, the counting ratio is obtained by themeasurement, and the cross section ratio is picked up from the reference value or is determined byan actual measurement with a standard sample, and the solid angle ratio is obtained from the actual
measurement with a standard sample. In this study, the solid angle ratio was evaluated by the fittingwith analysis software SIMNRA [75].

87Figure.5.11 RBS/ERDA spectrum example, the image is cited from [67]. This is the case that
deuterated DLC/Si with DLC film thickness of ∼ 100 nm is measured by RBS/ERDA. The left is
RBS and the right is ERDA spectrum. The vertical axis is the count number, and the horizontal
axis is the A/D converted value of the detector signal. In RBS, the carbon spectrum piles up on
the silicon spectrum. In ERDA, separation of hydrogen and deuterium spectrum is realized.

Figure.5.12 Schematic diagram of scattering of incident ions by target atoms, the image is cited from [67]88Figure.5.13 Schematic diagram of recoil of target atoms by incident ions, the image is cited from [67]89

5.3.3 X-ray reflectometry
This section introduces the principle of X-ray reflectometry. In general, the refractive index of a material
has an information of the electron density ρe , and X-ray reflectivity show an intrinsic pattern according
to it. Therefore, we can extract the electron density from X-ray reflectivity distribution. Such surface
analysis method is called X-ray reflectometry. The following relationship holds for electron density ρeand refractive index n:n = 1 − λ2 ρe re /2π(5.10)

where λ is the incident wavelength, ρe is the electron density, re is the electron classical radius.
For conciseness, the incident region is denoted as 0, the film region is denoted as 1, and the substrateregion is denoted as 2, and the refractive index in each region is denoted as ni hereafter. When X-rays
F
at the interface between istrike diﬀerent layers i, j as shown in Figure 5.14, the reflection amplitude rij

and j is given by the following equation (5.11).

Figure.5.14 Schematic diagram of X-ray reflection at material interface, the image is cited from[67]. Reflection and refraction are illustrated when X-rays are incident on a sample on which a filmof thickness d is formed on a substrate. Note that multiple reflections are not depicted here.

F
rij
=

ni sin αi − nj sin αjni sin αi + nj sin αj(5.11)

Expression (5.11) represents only a single reflection. When taking into account the eﬀect of multiple
reflections, the generalized theoretical X-ray reflectivity R can be obtained as follows:90R = exp (−qz2 σ 2 )

F
F
r01
+ r12
exp (i2k1 d)
FF
1 + r01 r12 exp (i2k1 d)(5.12)

The formula (5.12) is a theoretical expression giving the X-ray reflectivity distribution that can becompared with the actual measurement.
As is clear from the expression (5.11), each term of the expression (5.12) depends on the incident angle.
Therefore, by measuring the reflectivity of incident monochromatic X-rays while changing the incident
angle θ, we can obtain an intrinsic distribution depending on the electron density of the sample. The
value of the electron density ρe is analytically extracted by fitting the X-ray reflectivity distribution.
This is the principle for X-ray reflectometry.
For reference, an example of X-ray reflectivity distribution is shown in Figure 5.15. In this figure, a
Example of X-ray Reflectivity Distribution (Enlarged Figure)

Reflectivity

Reflectivity

Example of X-ray Reflectivity Distribution
ρ=1.5g/cm ,ND/Ntot =0.2
31

ρ=2.0g/cm ,ND/Ntot =0.2
3

-1

10

ρ=2.5g/cm ,ND/Ntot =0.2
3

ρ=1.5g/cm ,ND/Ntot =0.23

ρ=2.0g/cm ,ND/Ntot =0.23

ρ=2.5g/cm ,ND/Ntot =0.2
3

1

10-2
10-3
10-4

10-1

10-5
10-6
0

0.2 0.4 0.6 0.8

1

10-2 0.3

1.2 1.4
2θ

0.35

0.4

0.45

0.5

0.55
2θ

Figure.5.15 Example of X-ray reflectivity distribution. It is assumed that a sample consists a
single layer of deuterated organic compound film and a silicon substrate. The film properties are:film thickness 100 nm, surface roughness 1 nm, deuterium ratio ND /Ntot = 0.2, and density 1.5
g/cm3 (red) or 2 g/cm3 (blue) or 2.5 g/cm3 (green).

sample is assumed to consist of a single layer of a deuterated organic compound and a silicon substrate(see Figure 5.15 for details). In Figure 5.15, the reflectivity becomes maximum up to a certain incident
angle. This total reflection angle is called critical angle. Generally, the critical angle has an eﬀect on film
density, and film thickness has an eﬀect on the oscillation period, and surface roughness has an influenceon the attenuation on wide angle side. It is noted that an extra beat appears and node size does not
become constant in the sample with the multilayer film.

915.4 Surface Analysis of Developed Material
This section reports on details of the results obtained from surface analyses of Neutron Reflectometry,
RBS/ERDA, X-ray Reflectometry, GDOES, an electron microscope measurement, and surface roughness
measurements.

5.4.1 Result of Neutron Reflectometry
In this study, neutron reflectivity was measured at J-PARC MLF BL16 Soft Interface Analyzer (SOFIA).
Time-of-Flight method was used to calculate the reflectivity of incident neutrons (see Appendix.A for
details). For reference, the actual Time-of-Flight distribution obtained in SOFIA is given in Figure 5.16.
Schematic illustration and block diagram of the experimental setup of BL16 are given in Figure 5.17
and 5.18. The BL16 setup consists of three 5 mm thick B4 C slits, the stand for sample mounting, a
two-dimensional detector, an A/D converter, and a PC network. The incident angle and irradiation area
can be adjusted by controlling the relative position of the B4 C slit and the stand for sample mounting
as shown in Figure 5.17 and 5.18. In this way, reflected beam or direct beam can be measured, andneutron reflectivity can be calculated by the ratio of reflection beam intensity (Iref to direct beam
intensity (I0 ). R3292 (HAMAMATSU Co.Ltd) and ZnS/LiF scintillator (AST Co.Ltd) were used as
the two-dimensional detector, and NeuNET, developed by KEK-KENS DAQ group, was used for A/D
converter. NeuNET records wave height and Time-of-Flight (TOF) on receiving the signal transmitted
from R3292&ZnS/LiF, and TOF gives us to information of neutron wavelength, λ.
The analysis procedure of BL16 measurement is as follows:
1. To measure the wavelength of direct beam intensity so that the sample is avoided from the beam
injection.
2. To measure the wavelength of reflected beam intensity so that the sample is intersected to theincident beam.
3. The dependence of neutron reflectivity on wavelength is derived by dividing reflection beam intensity by direct beam intensity.
4. Assuming only the specular reflection, the wavelength is converted to the transfer wave number,
Q = 4πλ sin (θ), where λ is a wavelength of neutron and θ is a glancing angle of incident beam.
5. To fit the obtained neutron reflectivity, |R(Q)|2exp , with the formula (5.1).
6. To extract the Fermi potential from fitting result.
The fitting results of the neutron reflectivity are shown in from Figure 5.19 to Figure 5.24. Regarding
IEM DLC sample, only the result of sample 97 in Table 5.5 is given because the number of IEM DLC
samples is too many.
The analyzed result of the Fermi potential is listed in Table 5.5. In this study, measurement was
conducted in two ways. one was with incident angle 0.5 degree and irradiation area 15 × 15 mm2 ,another was with incident angle 0.3 degree and irradiation area 30 × 30 mm2 . Note that only 7 samples

92

for IEM DLC were summarized because the number of IEM DLC samples is too many. It is also notedthat the IEM DLC sample 97, which achieved the best performance, was measured twice, as shown in
Figure 5.24. The second measurement was performed two years after the initial measurement. In thismeasurement, three kinds of substrates, silicon, SUS304 and synthetic quartz were used, and it was
guaranteed that the flatness was 20 µm or less even for the worst case.
In this measurement, a systematic error of Q exists due to the beam incident angle divergence. Suchsystematic error can be expressed as |ππ(sin ((θi +dθi )× 180)−sin (θi × 180))|, where dθi is deviation of incidentπsin (θi × 180)

angle. In this study, such error was evaluated from beam divergence measurement of direct beam. The
result of direct beam divergence measurement is given to Figure 5.25. In the case of the incident angle of
0.5 degree & irradiation area 15×15 mm2 , the systematic error of Q was found to be 1.8%. On the other
hand, in the case of the incident angle of 0.3 degree & the irradiation area of 30 × 30 mm2 , the systematic
error of Q was turned out to be 2.8%. As a result, errors of the Fermi potential can be calculated bysubstituting errors of Q for the plot showed in Figure 5.9. Systematic errors of the Fermi potential are
listed in Table 5.5.
The highest potential values obtained in neutron reflectivity measurement were 228 ± 13 neV for
NiMo, 243 ± 8 neV for IEM DLC, 264 ± 14 neV for FAIPD DLC, and about 190 ± 11 neV for PBIID
DLC, respectively. PSI succeed in fabricating NiMo of weight ratio 15 % and its Fermi potential was
210 ± 10 neV [64]. The result was consistent in that of our samples. The best Fermi potential of IEM
DLC was comparable to that of nickel. The best Fermi potential of PBIID DLC was 193 neV, which wasinferior to IEM DLC. But it is noted that PBIID DLC is possible to apply to the sidewall of a storage
container. The value of 193 neV is quite high for the side wall materials. The best Fermi potential of
FAIPD DLC was 264 neV, which is one of the highest values. This value is close to the result of laser
ablation which PSI group fabricated.
According to Table 5.5, it was found that the Fermi potential of IEM DLC gets higher as the substratevoltage and the gas flow rate gets smaller, and does not depend on the temperature of the substrate. In
addition, it was also found that PBIID DLC samples have almost same Fermi potential. The considerationon this phenomenon is given in chapter 5.4.5.

93

Normalized Events

0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
time-of-flight [ms]Figure.5.16 TOF distribution of beam supplied in J-PARC BL16 SOFIA. The horizontal axis isTOF (ms), and the vertical axis is count rate. Here, the TOF of direct beam measurement is given.
Note that the total sum of the histogram is normalized to 1. The distance from the spallation point
to the detector is ∼ 17.9 m

Figure.5.17 Schematic diagram of the setup in J-PARC BL16 SOFIA used for the reflection beammeasurement (Left) and the direct beam measurement (right). Incident angle and beam irradiation
area (called footprint) were determined by the arrangement of the slit1 and slit2. In the reflection
beam measurement, only beam reflected at sample and passing through an angle of slit2 and slit3
was measured. On the other hand, In direct beam measurement, beam coming from slit2 wasdirectly measured. Reflectivity of the sample was estimated from the count ratio obtained in two
measurements.

94

Figure.5.18 Block diagram of experimental setup in J-PARC BL16 SOFIA. PC can remotely
control the relative positions of the slits 1 to 3, the sample and the detector. Detector signal is
carried to NEUNET, it is A/D converted together with the kicker pulse signal, and it is saved in
the PC.

95

Reflectivity

FAIPD DLC coated on SiO2
1

χ2 / ndf

10-1

640.5 / 61Prob0260.5 ± 0.1589

potential:DLC(ta-C)

94 ±potential:Quartz
10-2

0

0

thickness

106.4 ± 0.3108

DW factor

1.695e-06 ± 0.7134

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Qz(nm-1)

Figure.5.19 Reflectivity of FAIPD DLC/SiO2 . The incident angle is 0.3 degree. The vertical axis
is the reflectivity of FAIPD DLC/SiO2 , and the horizontal axis is Qz = 4π.
λReflectivity

FAIPD DLC coated on Si
1χ2 / ndf-1

286.9 / 59

Prob

10

1.13e-31

potential:DLC(ta-C)

10-2

0

264.3 ± 0.1841

potential:Si

54 ±thickness

118.9 ± 0.5622

DW factor

1.717e-10 ± 18.06

0.05

0.1

0.15

0

0.2

0.25

0.3

0.35
Qz[1/nm]

Figure.5.20 Reflectivity of FAIPD DLC/Si. The incident angle is 0.3 degree. The vertical axis is
the reflectivity of FAIPD DLC/Si, and the horizontal axis is Qz = 4π.
λ96Reflectivity

PBIID DLC coated on Si

1

10-1

χ2 / ndf
Prob
potential:DDLC
potential:Si
thickness
DW factor

739.9 / 87
0194.7 ± 0.2849
54 ± 087.48 ± 0.1715
1.482 ± 0.06491

0.35

0.45
-1
Qz(nm )

10-2

10-3

10-4
0.05

0.1

0.15

0.2

0.25

0.3

0.4

Figure.5.21 Reflectivity of PBIID DLC/Si. The incident angle is 0.3 degree. The vertical axis is.
the reflectivity of PBIID DLC/Si, and the horizontal axis is Qz = 4π
λReflectivity

PBIID DLC coated on SUS304
χ2 / ndf
Prob
potential:DDLC
potential:SUS304
thickness
DW factor

1

10-1

270.9 / 87
9.274e-21
192.6 ± 0.3697
185 ± 0110.9 ± 1.854
0.9402 ± 0.1187

10-2

10-3

10-4
0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45
-1
Qz(nm )

Figure.5.22 Reflectivity of PBIID DLC/SUS304. The incident angle is 0.3 degree. The verticalaxis is the reflectance of PBIID DLC/SUS304, and the horizontal axis is Qz = 4π.
λ97Reflectivity

NiMo coated on Si no1
χ2 / ndf
Prob
potential:NiMo
potential:Si
thickness
DW factor

11158 / 1130
228 ± 0.1949
54 ± 095.52 ± 0.14
1.144 ± 0.05528

10-1

10-2

10-3
0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45
Qz(nm-1)

Figure.5.23 Reflectivity of NiMo/Si. The incident angle is 0.3 degree. The vertical axis is thereflectivity of NiMo/Si, and the horizontal axis is Qz = 4π.
λReflectivity

χ2 / ndf

Neutron Reflectivity for DDLC coated on Si
1729 / 52
0

Prob

1

potential:DDLC

242.9 ± 0.2054
54 ±potential:Si

10-1

0

thickness

75.35 ± 0.07913

DW factor

1.44 ± 0.02389

Reflectivity

Neutron Reflectivity for DDLC coated on Si

χ2 / ndf

2745 / 95
0

Prob

1

potential:DDLC

253.2 ± 0.1083

potential:Si

54 ±thickness

104.8 ± 0.1215

DW factor

0.5812 ± 0.0589

-1

10
10-2

10-2
10-3
10-3
-4

10

0

0.1

0.2

0.3

0.4

0.5

0.05

Qz[1/nm]

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Qz[1/nm]

Figure.5.24 (Left) The first measurement result of IEM DLC/Si (incident angle 0.5 deg)(right)
The second measurement result of ionized evaporation DLC/Si (incident angle 0.3 deg). The.
vertical axis is the reflectivity, and the horizontal axis is Qz = 4π
λ

98

0

Method

Substrate

Potential

Condition

OthersIEM (sample12)

silicon

190 ± 7 neV

θi =0.5 deg(3.0 kV ,3.1 sccm, middle)

IEM (sample17)

silicon210 ± 8 neV

θi =0.5 deg(1.5 kV ,3.1 sccm, middle)

IEM (sample31)

silicon226 ± 8 neV

θi =0.5 deg(0.5 kV ,3.1 sccm, middle)

IEM (sample65)

silicon

227 ± 9 neV

θi =0.5 deg(0.5 kV ,6.2 sccm, middle)

IEM (sample97)

silicon243 ± 8 neV

θi =0.5 deg(0.5 kV ,0.6 sccm, middle)

IEM (sample72)

silicon228 ± 9 neV

θi =0.5 deg(0.5 kV ,3.1 sccm, low)

IEM (sample82)

silicon219 ± 8 neV

θi =0.5 deg(0.5 kV ,3.1 sccm, high)

IEM (sample97)

silicon

253 ± 13 neV

θi =0.3 deg

remeasure two years later

NiMosilicon228 ± 13 neV

θi =0.3 deg

average of three samples

FAIPD

synthetic quartz

260 ± 14 neV

θi =0.3 deg

–

FAIPD

silicon

264 ± 14 neV

θi =0.3 deg–

PBIID (sample1)

silicon

193 ± 11 neV

θi =0.3 deg–

PBIID (sample2)

silicon

192 ± 11 neV

θi =0.3 deg–

PBIID (sample3)

silicon

195 ± 11 neV

θi =0.3 deg–

PBIID (sample4)

silicon

190 ± 11 neV

θi =0.3 deg–

PBIID (sample5)

silicon

190 ± 11 neV

θi =0.3 deg–

PBIID (sample1)

SUS304193 ± 11 neV

θi =0.3 deg–

PBIID (sample2)

SUS304

192 ± 11 neV

θi =0.3 deg–

PBIID (sample3)

SUS304193 ± 11 neV

θi =0.3 deg–

PBIID (sample4)

SUS304194 ± 11 neV

θi =0.3 deg–

PBIID (sample5)

SUS304194 ± 11 neV

θi =0.3 deg–

Table.5.5 Measurement result of the Fermi potential

99

0.09
0.08

Entries

948366Mean-0.003762

RMS
χ2 / ndf

Direct beam measurement for 30x30 footprint

Normalized Events/2e-3 degree

Normalized Events/2e-3 degree

Direct beam measurement for 15x15 footprint

0.011850.0486 / 97

0.07

p0

0.08144 ± 0.11629

p1-0.003791 ± 0.009582

0.06

p2

0.009319 ± 0.009248

0.05
0.04
0.03
0.02
0.01
0
-0.1

-0.05
0
0.05
0.1
dΘi corresponding to beam divergence

0.1

Entries473378Mean

0.001449

RMS

0.08

χ2 / ndf

0.011
0.04745 / 97

p0

0.08922 ± 0.12887

p1

0.001582 ± 0.008743

p2

0.008518 ± 0.008659

0.06
0.04
0.02
0
-0.1

-0.05
0
0.05
0.1
dΘi corresponding to beam divergence

Figure.5.25 Fluctuation of incident angle due to beam divergence of J-PARC BL16. The horizontal
axis represents the fluctuation of the incident angle of the direct beam, and the vertical axis
represents the count. Since the distance between slit2 and detector is 2170 mm, we can convert
the amount of the beam spread into the fluctuation of the incident angle. Note that total sum of
the histogram is normalized to 1. The result fitted with Gaussian function is the red line, and p2
in the figure means standard deviation. From this, we can extract the standard deviation of thefluctuation of the incident angle, dθi .

100

5.4.2 The Result of RBS/ERDAIn this section, the result of RBS/ERDA measurement is described. In this study, IEM DLC and PBIID
DLC that coat on silicon or SUS304 substrate were used for samples. RBS/ERDA measurement was
performed at accelerator facility of Applied Accelerator Division, University of Tsukuba [76] in orderto determine the composition ratio of DLC films. A schematic illustration of the experiment has beenshown in Figure 5.10). In this measurement, Alpha particle was accelerated to 2.5 MeV by Tandetron
accelerator system and was irradiated to the sample of ∼ 10×10 mm2 . A sample was installed in thechamber of 10−4 Pa and was tilted at 15 degree relative to the beam axis at the center. In this way,
the number of particles scattered around was counted with two detectors. Regarding two detectors, one
was silicon detector BU 014 050 100 of ORTEC ULTRA SERIES, and the other was the silicon detector
PD 50 12 100 AM of CANBERRA PIPS. The former was installed in 150 degree for RBS measurement,
while the other was installed in 30 degree for ERDA measurement. In addition, the Mylar film wasinstalled before PD 50 12 100 AM to collimate the recoil particles except for hydrogen and deuterium.
For data conversion, Wilkinson type ADC of 2201A of Labo Co. Ltd. was used. In this measurement,
the counting rate of this measurement was ∼ 1,000 counts per second and dead time was less than ∼ 2%.
In this study, the number of nuclei of hydrogen, deuterium, carbon and all elements are denoted as
NH , ND , ND , and Ntot .An outline of the analysis is given below:
1. Extract the quantities YH , YD and YC from measured data in the same manner as described in
Figure 5.11
2. Substituting YH , YD and YC into the expression (5.9), the ratio of an element to carbon is calculated
as NH /NC , ND /NC , Ntot /NC = NC /NC + NH /NC + ND /NC
3. From the above, the composition ratio is easily derived as NH /Ntot , ND /Ntot , NC /Ntot
In this analysis, the value in document [77] was used as the cross section of hydrogen and the value in
document [78] was used as the cross section of deuterium. In addition, the solid angle ratio of RBS to
ERDA was chosen to 2.7 (for IEM DLC measurement) or 6.1 (for PBIID DLC measurement), whichcorrespond to the calibration data in such a way as described in chapter 5.3.2.
The composition ratio obtained by this analysis is shown in the Table 5.6. It was found that Hydrogenamount ratio of DLC/SUS304 was less than that of DLC/Si in the Table 5.6. For reference, the actual
ERDA spectrum of sample 1 of PBIID DLC/Si and PBIID DLC/SUS304 are shown in Figure 5.26. In
Figure 5.26, it was confirmed that there was the bump of hydrogen in the spectrum of DLC/Si, while it
did not exist in the spectrum of DLC/SUS304. The reason why such diﬀerence appears is considered asfollows:
1. In general, surface oxide causes hydrogen occlusion. In this study, a longer sputtering period isadopted in the case of DLC/SUS304 than in the case of DLC/Si. Thus, a surface oxidation of
SUS304 was eﬀectively removed than silicon, resulting in a reduction of hydrogen.

101

2. A large amount of hydrogen was contained in the silicon substrate. Indeed, the GDOES analysis
shows hydrogen content in the silicon substrate (see chapter 5.4.5 for details).
UCN loss probability coeﬃcient can be estimated by using an area density of hydrogen, AH , as shownin formula (2.17). Generally, the area density of the number of atoms can be extracted from energy loss
rate in the matter, dEdx. RBS/ERDA spectrum also has information of AH because it consists of dEdx
spectrum. So, in this study, the UCN loss probability coeﬃcient of PBIID DLC/SUS304 (sample1) was
evaluated from ERDA spectrum in the following procedure:
1. To regard PBIID DLC/SUS304 as containing no hydrogen because dEdx of hydrogen is too small.
2. To extract the area density of the total number of atoms, Atot , from ERDA spectrum by using afunction implemented in analysis software SIMNRA.
3. To multiply Atot with actual hydrogen composition ratio 1.4 % and derive the area density of thenumber of hydrogen atoms as AH = 1.4 %×Atot .
4. To calculate the UCN loss probability coeﬃcient by assigning AH with formula (2.17).
In this way, AH and the UCN loss probability coeﬃcient can be evaluated as 2.7 × 1016 atoms/cm2

Normalized Events [Counts/20 keV]and 1.5 × 10−4 , respectively.

0.16
0.14

PBIID DLC/Si

0.12
PBIID DLC/SUS304

0.1
0.08
0.06
0.04
0.02
0
0

200

400

600

800

1000 1200 1400
ERDA Energy [keV]

Figure.5.26 Comparison of ERDA spectra of DLC/Si and DLC/SUS304. The vertical axis iscount and the horizontal axis is energy. Total sum is normalized to 1. The energy on the horizontal
axis is derived by energy calibration of the value of A/D conversion.

102

No

methodsubstrate

NH /Ntot

ND /Ntot

NC /Ntot

12

IEM

silicon (W10 mm×L10 mm× T2 mm)

0.035 ± 0.002

0.31 ± 0.02

0.66 ± 0.02

17

IEM

silicon (W10 mm×L10 mm×T2 mm)

0.024 ± 0.002

0.29 ± 0.01

0.69 ± 0.01

31

IEM

silicon (W10 mm×L10 mm×T2 mm)

0.027 ± 0.002

0.33 ± 0.01

0.65 ± 0.01

65

IEM

silicon (W10 mm×L10 mm×T2 mm)

0.015 ± 0.001

0.35 ± 0.01

0.64 ± 0.01

72

IEM

silicon (W10 mm×L10 mm×T2 mm)

0.024 ± 0.002

0.39 ± 0.02

0.59 ± 0.02

82

IEM

silicon (W10 mm×L10 mm×T2 mm)

–

–

–

97

IEM

silicon (W10 mm×L10 mm×T2 mm)

0.038 ± 0.005

0.31 ± 0.02

0.65 ± 0.02

1

PBIID

silicon (W10 mm×L10 mm×T2 mm)

0.037 ± 0.002

0.23 ± 0.01

0.73 ± 0.01

2

PBIID

silicon (W10 mm×L10 mm×T2 mm)

0.028 ± 0.001

0.22 ± 0.01

0.75 ± 0.01

3

PBIID

silicon (W10 mm×L10 mm×T2 mm)

0.037 ± 0.003

0.29 ± 0.02

0.68 ± 0.01

4

PBIID

silicon (W10 mm×L10 mm×T2 mm)

0.033 ± 0.002

0.22 ± 0.01

0.74 ± 0.01

5

PBIID

silicon (W10 mm×L10 mm×T2 mm)

0.026 ± 0.001

0.25 ± 0.01

0.72 ± 0.01

1

PBIID

silicon (W10 mm×L10 mm×T0.7 mm)

0.035 ± 0.002

0.22 ± 0.01

0.75 ± 0.01

2

PBIID

silicon (W10 mm×L10 mm×T0.7 mm)

0.031 ± 0.002

0.23 ± 0.01

0.74 ± 0.01

3

PBIID

silicon (W10 mm×L10 mm×T0.7 mm)

0.034 ± 0.003

0.26 ± 0.02

0.70 ± 0.01

4

PBIID

silicon (W10 mm×L10 mm×T0.7 mm)

0.034 ± 0.002

0.22 ± 0.01

0.74 ± 0.01

1

PBIID

SUS304 (W10 mm×L10 mm×T1 mm)

0.014 ± 0.001

0.23 ± 0.02

0.75 ± 0.02

2

PBIID

SUS304 (W10 mm×L10 mm×T1 mm)

0.013 ± 0.001

0.21 ± 0.02

0.77 ± 0.02

3

PBIID

SUS304 (W10 mm×L10 mm×T1 mm)

0.016 ± 0.003

0.23 ± 0.04

0.75 ± 0.03

4

PBIID

SUS304 (W10 mm×L10 mm×T1 mm)

0.012 ± 0.001

0.21 ± 0.02

0.77 ± 0.01

5

PBIID

SUS304 (W10 mm×L10 mm×T1 mm)

0.015 ± 0.002

0.18 ± 0.02

0.80 ± 0.01

Table.5.6 The composition ratio of DLC evaluated by RBS/ERDA

103

No

methodsubstrate

ρe

12

IEM

silicon(W10 mm×L10 mm×T2 mm)(5.73 ± 0.02)×1023

17

IEM

silicon(W10 mm×L10 mm×T2 mm)(6.05 ± 0.02)×1023

31

IEM

silicon(W10 mm×L10 mm×T2 mm)(6.25 ± 0.03)×1023

65

IEM

silicon(W10 mm×L10 mm×T2 mm)(6.13 ± 0.02)×1023

72

IEM

silicon(W10 mm×L10 mm×T2 mm)(6.11 ± 0.02)×1023

82

IEM

silicon(W10 mm×L10 mm×T2 mm)

–

97

IEM

silicon(W10 mm×L10 mm×T2 mm)(6.48 ± 0.03)×1023

Table.5.7 Example data of total electron density determined by X-ray reflectometry

5.4.3 The Result of X-ray Reflectometry
In this section, the result of X-ray Reflectometry is described. X-ray Reflectometry enables us to get
the information about electron density from X-ray reflectivity distribution. In this study, IEM DLC
and PBIID DLC were used for samples. In this study, smart Lab (Rigaku Co. Ltd.) [79] was used
for X-ray reflectometry, which is a machine that can automatically conduct all functions necessary for
X-ray reflectometry such as X-ray emission, adjustment of angle, inclination of sample, and so on. In
this measurement, Cu Kα radiation was chosen as an incident X-ray beam. The beam intensity wasmeasured with a photomultiplier, and the beam divergence was reduced with Ge(220) single crystal anda slit. X-ray was irradiated to sample of Φ 76 mm while changing an incident angle to obtain X-ray
reflectivity spectrum.
The reflectivity distribution of IEM DLC is given in Figure 5.27. The horizontal axis is the incident
angle of the X-ray, and the vertical axis is the X-ray reflectivity. In each panel, the measurement datafor other bias voltage conditions from 0.1 kV to 3 kV used in the IEM DLC film formation is plotted.
On the other hand, the X-ray reflectivity distribution of PBIID DLC is shown in Figure 5.28. In eachpanel, the measurement data for other film formation conditions listed in Table 5.4 is plotted.
For IEM DLC, the critical angle and the period of vibration were clearly shown, and the X-ray reflectivity distribution can be easily fitted by the theoretical expression (5.12). On the other hand, for
PBIID DLC, not only short-period vibrations but also long-period vibrations were mixed. The spectrum
was quite diﬀerent from the distribution as shown in Figure 5.15 predicted from the theoretical formula(5.12). Therefore, it was not possible to fit the X-ray reflectivity distribution of PBIID DLC successfully.
Such a strange behavior that PBIID DLC show is discussed in chapter 5.4.5.
In this measurement, carbon was considered to be especially dominant for X-ray reflection. In thisanalysis, DLC was therefore regarded as composed of only carbon, and the total electron density was
extracted by fitting with the theoretical expression (5.12). The obtained electron density is summarizedin Table 5.7.

104

Reflectivity

Reflectivity

1
10-1
10-2

10-1

10-2

-3

-3

10

10

10-4

10-4

-5

-5

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

10 0

2

2θ [deg]

Reflectivity

10 0

Reflectivity

1

1
-1

10

10-2

0.4

0.6

0.8

1

1.2

1.4

1.6

2θ [deg]

1.8

2

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

2θ [deg]

1.8

2

1
10-1

10-2

-3

-3

10

10

10-4

10-4

-5

10 0

0.2

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-5

10 0

2

2θ [deg]

1

0.1 kV, 3.1 sccm, middle Temperature

10-1

0.5 kV, 3.1 sccm, middle Temperature
10-20.75 kV, 3.1 sccm, middle Temperature-310

1.5 kV, 3.1 sccm, middle Temperature

10-4
-5

10 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

3.0 kV, 3.1 sccm, middle Temperature

2

Figure.5.27 Example of X-ray reflectivity distribution of IEM DLC

105

Reflectivity

Reflectivity

1
10-1
10-2

-3

10

10

10-4

10-4

-5

-5

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

10 0

2

2θ [deg]

Reflectivity

10 0

Reflectivity

10-1

10-2

-3

1
10-1

0.6

0.8

1

1.2

1.4

1.6

2θ [deg]

1.8

2

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

2θ [deg]

1.8

2

10-1

-3

10

10-4

10-4
-5

-5

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

10 0

2

2θ [deg]1

pbiid sample1
pbiid sample2
pbiid sample3
pbiid sample4
pbiid sample5

10-1
10-2
-3

10

10-4
-5

10 0

0.4

1

10

10 0

0.2

10-2

10-2
-3

Reflectivity

1

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2θ [deg]

Figure.5.28 X-ray reflectivity distribution of PBIID DLC

106

5.4.4 Reflectivity consistency
In this section, the analysis result of the Fermi potential calculated by the result of X-ray reflectometry and RBS/ERDA is described, and the result obtained in this way is compared to that of neutronreflectometry. For deuterated DLC, the Fermi potential is expressed as follows:
VF = bC NC + bD ND + bH NH(5.13)

where b is coherent length and N is the density of atomic nucleus.
In addition, the density of atomic nucleus for each element can be derived using following equation:
Z i Niρe
Zi Ni = ∑kmax
k=0 Zk Nk(5.14)

where i is the identifier of each element, and Ni is the nuclear density of the element i, Zi is the atomic
number, and kmax is the number of elements, and ρe is the electron density.
The Fermi potential of formula (5.13) can be calculated by ρe obtained from X-ray reflectometry and
NH /NC and ND /NC obtained from the RBS/ERDA. The comparison result of the Fermi potential obtained from two diﬀerent ways was given in Figure 5.29. The vertical axis is the Fermi potential obtained
from the neutron Reflectometry, the horizontal axis is the potential calculated with the expression (5.13)
and (5.14). Although the error is fairly large, it can be seen that both results are consistent in therange of about 8%. The error is thought to be caused from the uncertainty of the cross section used in
RBS/ERDA measurement.

5.4.5 Consideration of Unnaturalness of PBIID DLC
Regarding IEM DLC, it is confirmed that the film formation condition has a strong eﬀect on DLC film
density and composition ratio, resulting in variation of the Fermi potential (see Table 5.5 and Table
5.6 ). However, regarding PBIID DLC, all of PBIID DLC show the same potential irrespective of theirfilm formation condition. Such an unnaturalness is thought to be due to the film formation process of
PBIID. In PBIID, a mixing layer occurs between DLC film and a substrate due to the ion implantation
process illustrated in Figure 5.5, which gives PBIID sample a property looks like DLC/SiC/Si rather
than DLC/Si. Actually, X-ray reflectivity spectra of Figure 5.28 shows the anticipated behavior for a
multilayered sample such that short-period and long-period oscillations mix. In addition, it is confirmedthat the following two measurements indicate a mixing layer.
GODES
GODES measurement was performed with an instrument manufactured by Horiba corporation inorder to investigate the depth profile. GDOES is one of the methods to determine the composition
ratio in the depth direction. It is possible to evaluate the composition ratio by sputtering sample
while monitoring the light intensity emitted from the scattered particles. It is noted that hydrogenand deuterium cannot be distinguished because of the same emission spectra. The actual obtained107Determined by Neutron Reflectometry [neV]

300
280
260
240
220
200
180
160
140
120
100
100

150

200
250
300
Calculated by XRR and RBS/ERDA [neV]

Figure.5.29 Comparison result of the Fermi potential determined by two methods. The verticalaxis shows the value of the Fermi potential obtained from the neutron reflectivity measurement,
and the horizontal axis shows the value of the potential calculated by the measured value of the
RBS/ERDA and XRR. Both of them agreed with relative accuracy of about 8%.

spectrum is shown in Figure 5.30. Signal intensity of H and C continue even after sputteringreaches the silicon substrate. This fact indicates that a non-negligible amount of deuterium ismixed in the silicon substrate.
Transmission Electron Microscope
Transmission electron microscope measurement was conducted with JEM-4010 (JEOL Ltd.). The
specimen was cut out from the original sample and the vicinity of the surface was polished well.
In this way, the intensity distribution of transmitted electrons was investigated when scanning
the side with an electron beam. The element composition and the nuclear density are reflectedin the contrast of the obtained image. The result is shown in Figure 5.31. It is noted that, in
this measurement, tungsten was deposited on the top layer to avoid radiation eﬀect from gallium
beams used on cutting out the specimen. In Figure 5.31, it is confirmed that there is a mixing
layer between the silicon substrate and the DLC film layer. Further, it seems that DLC layer isdivided into two layers. This indicates that film formation growth may be diﬀerent in the process.

5.4.6 The Result of Measurement of Surface Roughness
In this section, the result of the surface roughness measurement is described. Because the surface
roughness has a crucial eﬀect on non-specular reflection probability, it was evaluated in this study. In
the measurement, two diﬀerent apparatuses were used. One is an atomic force microscope L-trace IIA

108

Figure.5.30 Example of rf-GDOES spectrum of PBIID DLC/Si

Figure.5.31 Example of lateral scanning of PBIID DLC/Si by transmission electron microscope

109

(Hitachi High-Technologies Corporation), and the other is a surface topography measurement instrument
P-7 Stylus Profiler, serial number 7300163,(KLA Tencor Corporation). L-trace IIA and P-7 Stylus
Profiler use techniques based on Scanning probe microscope (SPM). In general, SPM refers a technique
to obtain surface profiles by scanning a specimen with a physical probe.
L-trace IIA uses Dynamic Force Mode (DFM) technique to determine the surface shape profile. In
general, the probe feels the force depending on the distance from the sample surface to it due to intermolecular force and air attenuation. Thereby, if the probe is vibrated while approaching to the sample
surface, the vibration amplitude changes according to the distance. Therefore, the sample surface profile
can be determined by scanning with the probe so that the vibration amplitude is maintained constant.
According to the catalog, the vertical resolution of L-trace IIA is 0.05 nm. In this study, SI-DF 40P withwidth of 30 nm was used for the probe.
In P-7 Stylus Profiler system, surface roughness is determined by LVDC sensor. LVDC sensor cantransform linear displacement into diﬀerential capacitive change. Therefore, the probe movement up anddown according to surface roughness can be estimated by capacitance change of LVDC sensor. According
to the catalog, the vertical resolution of P-7 Stylus Profiler is 0.4 nm for 1 σ. In this study, a diamondchip with a curvature of about 2 µm was used as the probe.
The results of surface roughness measurement of IEM DLC, FAIPD DLC, and PBIID DLC are given
in Table 5.8. In this study, Φ 76 mm and 2 mm thick silicon (Furuuchi Chemistry Corporation) wasused for the silicon substrate, of which surface roughness was evaluated to be 0.3 nm RMS by AFM(DI-3100, Veeco Instruments Inc.) [31]. In addition, 25.4 mm × 76.2 mm and 1 mm thick synthetic
quartz (VIOSIL-SQ (W grade), Shin-Etsu Chemical Co., Ltd) was used for the quartz substrate. The
surface roughness of synthetic quartz was measured by L-trace IIA, which was found to be 0.3 nm RMS.
Furthermore, 50 mm × 80 mm and 5 mm thick SUS304 substrate made by Sanko Seiki Manufacturing
Corporation was used. The surface roughness of SUS304 was measured by P-7 Stylus Profiler, which was
found to be 1.8 nm RMS. Regarding samples, the surface roughness of DLC has been actually measured.
As a result, it was confirmed that ∼ 3 angstrom for IEM DLC, ∼ 4.9 angstrom RMS for FAIPD DLC
and 1 ∼ 2 nm RMS for PBIID DLC. The surface roughness of PBIID DLC was not good compared tothe other. This is probably because PBIID DLC was inherited from the surface roughness of the SUS304
substrate.

5.5 Short Summary
1. NiMo of molybdenum weight ratio of 15% was fabricated with binary vapor deposition method.
As a result, a film with the weight ratio of 13.6% can be obtained so far, which was evaluated by
the crystal oscillator. By the neutron reflectivity measurement of J-PARC MLF BL16, 228 neV ±13 neV was obtained as the Fermi potential (see Table 5.5 and Figure 5.23). The potential value
was consistent with that fabricated by the conventional sputter method by PSI.
2. DLC was fabricated with ionization evaporation deposition method. More than hundred types of110method

substrate

instrument

conditionroughness [nm]No Film

silicon——0.30 ± 0.01 RMS [31]

IEM (sample97)

silicon

L-TraceIIA

measure 10µm×10µm

0.30 ± 0.01 RMS

FAIPDquartz

L-TraceIIA

measure 10µm×10µm

0.36 ± 0.01 RMS

FAIPDquartz

L-TraceIIA

measure 10µm×10µm

0.62 ± 0.01 RMS

No Film

quartz

L-TraceIIA

measure 10µm×10µm

0.32 ± 0.01 RMS

No Film

quartz

L-TraceIIA

measure 10µm×10µm

0.28 ± 0.01 RMS

PBIID (sample1)

siliconP-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.1 ± 0.4 RMS

PBIID (sample2)

siliconP-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.2 ± 0.4 RMS

PBIID (sample3)

siliconP-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.8 ± 0.4 RMS

PBIID (sample4)

siliconP-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.9 ± 0.4 RMS

PBIID (sample5)

siliconP-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.0 ± 0.4 RMS

PBIID (sample1)

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.8 ± 0.4 RMS

PBIID (sample2)

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.5 ± 0.4 RMS

PBIID (sample3)

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.4 ± 0.4 RMS

PBIID (sample4)

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.4 ± 0.4 RMS

PBIID (sample5)

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

2.5 ± 0.4 RMS

No Film

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.7 ± 0.4 RMS

No Film

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

2.2 ± 0.4 RMS

No Film

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.5 ± 0.4 RMS

No Film

SUS304P-7 Stylus Profiler

Force: 2mg, scan: 0.2 mm

1.8 ± 0.4 RMS

Table.5.8 Measurement result of surface roughness.

DLC mirrors such as listed in Table 5.3 have been tested so far. Neutron reflectivity measurementof J-PARC MLF BL16 revealed that the sample having highest Fermi potential was 243 ± 8 neV,
which is as high as the Fermi potential of nickel (Table 5.5 and Figure 5.24). On the other hand,by combining the results of X-ray reflectivity and RBS/ERDA measurements, the Fermi potential
was evaluated to be systematically higher by ∼ 8% as shown in Figure 5.29. In addition, thesurface roughness measured by AFM was evaluated to be 0.30 ± 0.01 nm RMS as listed in Table
5.8.
3. DLC was fabricated with Plasma Based Ion Implantation Deposition (PBIID) method. PBIID is
known as a film formation method suitable for three-dimensional coating on the inner surface andfor large area coating. Five samples listed in Table 5.4 have been tested so far. Neutron reflectivity
measurement at J-PARC MLF BL16 showed that the potentials of PBIID DLC were aligned to∼ 193 ± 11 neV irrespective of film formation conditions (Table 5.5 and Figure 5.21). Surface
roughness was evaluated to be 1 ∼ 2 nm RMS using a high precision step meter as listed in Table
5.8. Surface roughness was not so good. That is probably because it inherited the roughness of
SUS304 substrate of 1 ∼ 2 nm RMS.

111

4. DLC was fabricated with FAIPD method. In this study, the AC-X apparatus of Onward Co. Ltd
was used for fabrication of FAIPD DLC. Neutron reflectivity measurement at J-PARC MLF BL16
indicated that the potential of 264 ± 14 neV was achieved (Table 5.5 and Figure 5.19) and Figure
5.20. In addition, the average value of the surface roughness measured by AFM was evaluated tobe 0.49 ± 1 nm RMS as listed in Table 5.8.

112

Chapter 6

UCN Storage Experiment at J-PARC MLF
In this chapter, the result of UCN storage experiment enables us to directly determine UCN loss probability coeﬃcient are described. UCN loss probability is one of the important parameters having a strong
eﬀect on the statistical precision of the neutron EDM measurement. For example, assuming gravity andnon-specular reflection are negligible, the number of UCNs with the speed ⃗v = (v, 0, 0) confined in thebox of one side length L will change in time according to the following expression (6.1).
tt) = exp (− )
τ
µ(v)
v

N (t) = exp (− L

(6.1)

where µ(v) denotes the UCN loss probability depending on velocity.
Because the best statistical precision becomes inversely proportional to 2τ (the expressions (6.1) and(3.7) and 3.9), UCN loss probability µ has a serious eﬀect on the neutron EDM measurement. Therefore,
it is so much important to directly measure UCN loss probability by UCN storage experiment.
Generally, the UCN loss probability can be indicated by the loss probability coeﬃcient, η (see theexpression (2.6) and the expression (2.7)). In this study, η of NiMo or PBIID DLC were determined bymeasuring how the number of UCNs change when stored in the SUS316 storage bottle covered partiallywith NiMo or DLC. This experiment was performed at J-PARC MLF BL05 May and June 2016. In
J-PARC MLF BL05, ultracold neutron can be used by using Doppler Shifter.
This chapter is organized as follows. In the first section, the experimental environment of J-PARC
MLF BL05 is described. Next, the velocity distribution of UCNs emitted from Doppler Shifter in JPARC MLF BL05 is explained. Next, the UCN storage experiment performed in J-PARC MLF BL05
are summarized. Finally, the results of UCN storage experiment and details of the analysis are described.

6.1 Material and Life Science Facility at J-PARC
Japan Proton Accelerator Research Complex (J-PARC) is an experimental facility located in Tokai,
Ibaraki, Japan. It consists of three diﬀerent accelerators LINAC, Rapid Cycling Synchrotron (RCS),
and Main Ring (MR). The world’s highest intensity pulsed proton beam of kW class is supplied to thebeam line for experiments. In J-PARC, The protons emitted from the ion source are first accelerated
to 181 MeV with LINAC of ∼330 m. Although the beam of LINAC has not been used for experiments

113

yet at the present time, it will be used in the future for the test of Accelerator Driven Reactor System(ADSR) and J-PARC P33 experiment. Beams that are not used in LINAC are sent to RCS with adiameter of 350 m and accelerated to 3 GeV, and then sent to the Material Life Science Laboratory(MLF) or sent to MR with a diameter of 1.6 km to be accelerated to 30 GeV.
The proton beams of RCS produce a nuclear spallation reaction in the liquid mercury target at thecenter of the Materials and Life Science Experimental Facility (MLF) and produce fast neutrons. The
current beam supply period in RCS is almost 25 Hz. The H2 moderator (20 K, 1.5 Pa) is arranged
around the mercury target, and the fast neutrons are cooled to the room temperature while colliding
with H2 , and then is emitted from the moderator surface. These are delivered to 23 beam lines for users
of MLF.
In an experiment at MLF, users always receive two signals from facility, kicker pulse (kp) and timing
pulse (tp). Both kp and tp are synchronized with the timing of proton beam incidence. By using theinformation on the timing of the proton beam incidence, the neutron velocity can be determined by thetime-of-flight (TOF) method (see Appendix.A for details). Because only the signal of kp is interrupted
when the proton beam delivery stops, users can know whether the entire MLF beam delivery system isdown or when the beam is directed to MR.

6.2 The Experimental Apparatus at BL05
In this section, the experimental environment of J-PARC MLF BL05 is described. In BL05, neutron
beam coming from the mercury target is divided into three branches: low divergence beam branch, a
non-polarized beam branch, and a polarized beam branch. Neither branch has the ability to supply
UCNs. Thus, UCNs are produced by decelerating neutrons emitted from a non-polarized beam branch
by using Doppler Shifter. Apparatuses related to UCN storage experiment are transportation, m3.5
monochromatic mirror, focus guide, Doppler Shifter, UCN Storage System. All the equipments except
UCN Storage System are arranged on the line of the unpolarized beam branch, while UCN Storage
System is arranged perpendicular to unpolarized beam branch. For understanding the relative positionof experimental setup, a cross-section diagram of the unpolarized beam branch of J-PARC MLF BL05
is given in Figure 6.1, and the schematic diagram of the UCN Storage System is given in Figure 6.2.
The five main apparatuses mentioned above are described below.

114

Concrete shields
16.2 mSupermirror benderSupermirror guides

1m

Unpolarized branch exit
VCN mirrors
Focus guide
PMT holder

235 mmBeam monitor
Doppler Shifter

12 m

16 m

17.1 mFigure.6.1 Cross-sectional view of the non-polarized beam branch in J-PARC MLF BL05. theimage is cited from [38]. The neutron flux emitted from the moderator surface is transported to 7.8
m by the initial guide which is not shown in the figure, and then it is passed to the bender guide andis divided into three diﬀerent super mirror guides at 12 m point. One of three branches in the centeris called a non-polarized beam branch. Neutrons that have reached the exit of the unpolarized beam
branch intersect the m3.5 monochromatic mirror. At this time, only the component of ∼ 136 m/s
is kicked out obliquely downward, it enters the focus guide tube, and only such neutrons finallyreach the Doppler Shifter and is converted into ultracold neutron.

115

Installed sample
GateValve1

Storage Chamber

25-micron aluminum foil

Doppler
MirrorDoppler
Shifter

GateValve2

DUNia-10

Figure.6.2

Overall view of UCN storage system in J-PARC MLF BL05116

6.2.1 Transportation
Three guides are used to transport neutrons from the mercury target to the point of 16.2 m. Each guideis called as the initial guide, the bending guide, and the super mirror guides.
First, fast neutrons emitted from the moderator surface are transported to the point 7.8 m through the
m2 initial guide. The neutron of J-PARC MLF BL05 is divided into three branches at the exit of the m2
initial guide. Guides having diﬀerent characteristics are installed in the three branches. In low divergence
branch, the beam having less transverse velocity is supplied. In non-polarized branch, the large output
divergent beam is supplied. In polarized branch, the polarized beam is supplied. B4 C sintered bodies are
installed near the entrance ports of the three branches in order to adjust neutron flux supplied from eachbranch. Neutrons incident on the unpolarized branch are transported to 12 m point along m3 bending
guide with a slope of 2.6 degree upward, and fast neutrons are lost due to the curve. After this section,neutrons enter the entrance of the m3 mirror guide and transport to the exit of the unpolarized branch
at 16.2 m point. The velocity distribution of neutrons emitted from the moderator surface follows theMaxwell distribution. Referring to the document [38], and the total flux of the unpolarized beam line isΦ = 2 × 109 [n/cm2 /s].

6.2.2 VCN transportation
Immediately behind the exit of the unpolarized beam branch, wideband multilayer monochromatic mirrors of m = 3.5 are installed as shown in Figure 6.3. Wideband multilayer monochromatic mirrors consistof 65 mm square 0.5 mm thick m3.5 mirrors stacked in 6 layers every 11 mm, fabricated at Kyoto University Research Reactor Institute (KURRI). The wideband multilayer monochromatic mirrors can kickneutrons only with ∼ 136 m/s into the direction almost parallel to the center axis of focus guide (tilted
18.6 degree to the ground). The setup related to wide-band monochromatic mirrors is shown in Figure
6.3. The kicked neutrons will be transported to Doppler Shifter along focus guide.

6.2.3 Focus guide section
Neutrons bounced by the wideband monochromatic mirrors go to Doppler Shifter through a focus guide.
The inner surface of the focus guide is made of glass coated with Nickel. The focus guide consists of twoof 515 mm and 230 mm guide, which are a square of 60 mm at the entrance and a rectangle of 40 mm
× 26 mm at the exit. See Figure 6.3 for the detail.

6.2.4 Doppler Shifter
The whole figure of Doppler Shifter is shown in Figure 6.4, and an enlarged figure of the connection partwith the focus guide is shown in Figure 6.5. In Doppler Shifter, a neutron of about 136 m/s is injected
every 40 ms from the focus guide. The chamber of Doppler Shifter is evacuated to several Pa, and an

117

Figure.6.3 Schematic illustration of the arrangement of the wideband monochromatic mirrors.
m3.5 mirrors are placed tilting 8.2 degree to the ground. Neutrons reflected by m3.5 mirrors are
kicked and incident horizontally on the focus guide. See the text for details.

arm with a radius of 325 mm with a mirror (Doppler Mirror) attached at the tip rotating with 68 m/s.
Doppler Mirror and incident beam intersect with a beam once in every 120 ms, which produces UCN
at 8.33 Hz. As well as wide-band monochromatic mirrors, Doppler Mirror is also fabricated in KURRI,
which consists of four NiC/Ti mirrors stacked on 0.3 mm thick silicon. The reflectivity of each mirror
is given in Figure 6.6. The index of Figure 6.6 represents the order when counting the mirrors from thebottom. Regarding neutrons incident at 136 m/s against the Doppler Mirror rotated with 68 m/s, theQ = 4π/λ and the reflectivity amount to 2.16/nm and 22.9 ± 0.4 %. Therefore, UCNs are produced
according to formula 2.32 at the pseudo source point as described in chapter 2.4.2.
UCNs produced by Doppler Shifter can be taken from three ports above and beside the pseudo source
point. In addition, the cold neutron beam which is not converted to UCN is monitored with MNH10/4.2F
to correct the fluctuation of the neutron beam of J-PARC MLF (described in chapter 6.2.6 ). The
Doppler shifter control device makes Doppler Mirror synchronized with the proton beam incident timing
and produces the timing pulse when the mirror and the neutron beam are intersected. Although there
is a slight rotation instability, this eﬀect amounts to about 0.01 m/s in terms of speed conversion, which
is negligible level in this experiment.

6.2.5 UCN Storage System
The whole figure of the UCN Storage System is given in Figure 6.2. UCNs emitted from the pseudo
source point are transported through NiC/SiO2 square guide and SUS316 cylinder pipe and are stored
in SUS316 container of Φ498 mm × L500 mm. The interior of the chamber is polished to a surface
roughness of 10 nm Ra or less by composite electrolytic polishing treatment. There are two ports on the

118

74.3

65.0

0.6kg

SMSB6.5-20

0.4kg

GLMK-95-5
GLFCJ95
FRN1A1-A95-V80

GLMK-95-5
GLFCJ95
FRN1A1-A95-V65

TG-550C/NW25

4.65
1kg

3kg

SCPW55-19-20#6004

F1B-020-CAWN

1.5kg

MLHS202.7kg

1664.72

44.5kg

133kg

1.2kg

27kg

14kg

PETPS40-95-F80-G35-SC40-M20-N20

1.3kg

50.0

9kg

30kg

1kg

HFSU12-80

1kg

0.9kg

300.0

180.0

35kg

4kg

4kg

50kg

65.0

65.0

6.0

MRBR16

1.6kg

STRS12CKZJ65-H
5000N

FJFNV16-100
3.5～12.0kN

Figure.6.4 Overall figure of Doppler Shifter, the image is cited from [38]. The angle of the armof Doppler Shifter can be variable and viewport is 100 mm away from Doppler Mirror center. In
this experiment, The arm angle was fixed to 18.6 deg and the left viewport was used for UCN
extraction.

sidewall and the bottom plate, of which diameters are Φ73 mm and Φ100 mm. Two gate valves (VATinc.) are installed to control open/close two ports. The gate valves are made of SUS304 and its surface
are coated with NiP after the electrolytic polishing treatment. The proportional counter (DUNia-10) is
installed under ∼ 900 mm to count UCNs. In this experiment, NiMo and PBIID DLC films deposited
on a SUS304 substrate were used as test materials. The test material can be installed by replacing the
SUS316 disk on the top of the storage container. The surface roughness of the SUS304 substrate was
evaluated to be 1 nm Ra or less by measuring small test piece with a step meter (P-7 Stylus Profiler,
KLA Tencor Corp).
For reference, the whole configuration of UCN storage system is given in Figure 6.7. The right is
the Doppler Shifter and the left is the storage container. UCNs produced by the Doppler Shifter aretransported from right to left. For further reference, the image taken when opening the upper lid isshown in Figure 6.8. In addition, the photograph of the inside of the specularly polished chamber isshown in Figure 6.9. In Figure 6.8, the inner surface of the test material faces inside Figure 6.9. In
the storage experiment, diﬀerent test materials are set by replacing as shown in these photographs. A
gap between the container and the test material is several 100 µm, and the eﬀect on the experimentis negligibly small. For reference, the photograph of PBIID DLC sample is shown in Figure 6.10. In
storage experiment, the DLC coated green side is made facing the inside of Figure 6.9.

119

Wide-band
monochromatic
mirrors

515 mm
8.2°
230 mm

10.7°

Side
viewport
18.6°

60 mm W × 60 mm H

40 mm W × 26 mm H

182 mmPseudo source point

Figure.6.5 Enlarged figure around the inlet of focus guide. Neutrons kicked out by monochromatic
mirrors go to Doppler Shifter through the focus guide. Ni/SiO2 is aﬃxed inside the focus guidetube, and its beam axis is inclined at 18.6 degree with respect to the ground. the image is citedfrom [38].

Figure.6.6 Reflectivity of Doppler Mirrors. The vertical axis is the reflectivity of Doppler Mirror,
and the horizontal axis is Q = 4π
. the image is cited from [38]. This Doppler Mirror is m10
λsuper mirror having world’s highest reflectivity and can reflect 136 m/s neutrons coming from the
upstream of the unpolaized beam branch at J-PARC MLF BL05.

120

Figure.6.7 Overall picture of UCN Storage System. The storage container is on the left, theDoppler Shifter is on the right, the transport guide is in between.

Figure.6.8 Photograph of the storage container with top cover opened. The upper lid of thestorage container was opened and the picture was taken from above. The white disc on the top of
the cylindrical container is the test material.

121

Figure.6.9 Photograph of the inside of the storage container. The upper lid of the storage container
was opened, the test material was removed, and the picture was taken from above. The inner surface
is subjected to the composite electrolytic polishing treatment and the inner surface is lustered likea mirror.

Figure.6.10 Example of the test material used in the actual storage experiment. The PBIID
DLC/SUS304 actually used for the experiment was photographed. The green luster is due to DLC.
Before the storage experiment, this shiny side was placed against the inner surface of Figure 6.9,
the upper lid of the storage container of Figure 6.8 was closed, and the vacuum was drawn.

1226.2.6 Detectors and DAQ system used in measurements
This section describes the detector and DAQ system used in the storage experiment.
DUNia-10
As a detector for the storage experiment, a 3 He gas proportional counter DUNia-10 (FLNP,JINR) wasused. The real front view of this detector is given in the left of Figure 6.11 and the schematic diagramof the chamber cross section in the right of Figure 6.11. The dimension of the schematic diagram has
an error of about 1 mm. The entrance window of DUNia-10 with a diameter of 90 mm is covered
with a pure 100 µm thick aluminum sheet, which is supported by 2 mm thick aluminum bar placed atintervals of 10 mm. The mixed gas of 1858 Pa 3 He and 1.1 atms Ar 99% and CH4 1% was filled in thechamber. A tungsten wire of ∼ Φ 100 µm is tensioned across the chamber, which was being appliedwith an electric potential in measurements. Neutrons entering in chamber interact 3 He gas elementswith 3 He + n→p +3 H and the avalanche multiplication occurring around the wire causes the signal. In
this study, +1 kV potential was applied, resulting in the amplification factor of the wire of DUNia-10∼100 times. The electronic circuit of DUNia-10 used in this study is shown in Figure 6.12. An electronic
circuit is installed in the back of DUNia-10, and the signal passes through this circuit before outputting.
The secondary low-pass filter provided in the circuit does not only reduce noise but also amplify thesignal.

Figure.6.11 (Left) Front view of the actual product of DUNia-10 (right) Schematic diagram of thecross section of the chamber of DUNia-10. The 90 mm entrance window on the front of the chamberis covered with an aluminum sheet of 100 µm thick. Also, the Aluminum sheet is supported by 2
mm thick Aluminum bars from the outside.

123

Figure.6.12

Electric circuit of DUNia-10

124

MNH10/4.2F
In this study, the neutron beam that is not converted to UCNs by the Doppler Shifter was monitored
using MNH10/4.2F (CANBERRA) in order to correct the fluctuation of the intensity of UCN beamemitted from the Doppler Shifter (see Figure 6.13) [80]. The setup used for the measurement is shownin Figure 6.1. The current of J-PARC MLF proton beam fluctuates by about 3%, while it is suppressed
to 1.4% or less. Thus, accurate storage experiment can be carried out. MNH10/4.2F is a proportionalcounter in which a mixed gas of argon and CH4 of 1.3 Pa and a small amount of 3 He is filled. In thismeasurement, a voltage of +1 kV was applied to the wire of MNH10/4.2F. In addition, the output of
MNH10/4.2F was amplified using CANBERRA 2006E and ORTEC 572. Please see the Appendix.B for
the detail of suppression of beam fluctuation by using MNH10/4.2F.

Figure.6.13 MNH10/4.2F. (right) A photograph that MNH10/4.2F installed at the neutron flux
outlet of Doppler Shifter.

R3292-02(ZnS/LiF)
In this study, the two-dimensional sensitive detector consisting of R3292-02 (HAMAMATSU) and
ZnS/LiF scintillator were used to evaluate divergence of neutron flux emitted from the focus guidedescribed in chapter 6.3. ZnS/LiF scintillator containing natural lithium was used for the focus guidemeasurement. A schematic view of two-dimensional detector used in our study is shown in Figure 6.14.
When neutrons are incident on ZnS/LiF adhered to the front of R3292-02, a lot of scintillation photon
are yielded through the nuclear reaction of 6 Li + n → 3 H + α, and the photocathode convert theminto photoelectrons. As a result, a photocurrent is generated by the electric field amplification throughthe mesh diode of R3292-02. In this study, a voltage of +1 kV was applied to the mesh diode. The
photocurrent flows into the resistance dividing circuit of x and y, and signal wave heights are read fromboth end point of lines of x and y. If the four of signal wave heights are defined as X1, X2, Y1 and Y2,
then the position X and Y can be calculated by X=X1/(X1 + X2) and Y=Y1/(Y1 + Y2). For R3292,

125the position resolution has been evaluated to be 1 mm. In this study, the signal wave height was further
amplified with a spectroscopic amplifier 4066-4A (CLEAR-PULSE Co., Ltd.) with shaping time 1 µs.
Although the composition ratio and density of this scintillator cannot be disclosed because of confidential corporate information, the mean-free path of 136 m/s in the ZnS/LiF scintillator is suﬃciently
longer than the scintillator thickness 100 µm. This fact guarantees that the wavelength dependence ofthe detection eﬃciency is proportional to be 1/v even if very cold neutrons are detected as described inchapter 6.3.

Figure.6.14 Two-dimensional detector used for our experiment, the image is cited from [44]. Detector consists of R3292-02 and ZnS/LiF scintillator. Actually, ZnS/LiF is aﬃxed on the front of
R3292-02.

DAQ System
In this study, 16 ch Peak Hold ADC A3400 VME Module (NIKIGLASS Co., Ltd.) was used as an
Analog to Digital converter. When inputting a voltage wave with a peak value of 0 to 10 kV to theA3400, it will be automatically peak-held and A/D converted to 0 to 8192 digital value. Data conversion
is performed when the voltage intersects to the ground level, and the time at the point is also recordedwith accuracy 1 µ s. The data list is converted into a text file and stored in the PC. The data conversion
time is 400 ns for each channel. Moreover, it does not hold the peak below the discriminator level thatusers can set through online. In this study, the peak value was less than 2000 ch. And the counting rate
was 3000 counts per second at most. Using the rectangular wave emitted from a function generator, it
was confirmed that there was not drop count to 100 kHz and the linearity of A/D conversion was kept
up to 4000 ch.
Detector Calibration
Generally, by comparing with another detector whose feature is well known, it is possible to evaluate
the detection eﬃciency. In this study, the detection eﬃciency was evaluated by comparing a proportionalcounter filled with 1 MPa 3 He gas, RS-P4-0812-223. The layout of RS-P4-0812-223 is given in the right of
Figure 6.15. The signal of RS-P4-0812-223 is amplified by CANBERA Model 2006 Proportional Counter
Preamplifier and ORTEC 572. Measurements were conducted at the low divergence beam branch at
J-PARC MLF BL05. In this measurement, thermal/cold neutron beam was irradiated to the center of a126

detector. At this time, the beam was narrowed down to ϕ 1 mm due to cadmium collimator. A schematic
diagram of the measurement setup and the block diagram of RS-P4-0812-223 is shown in Figure 6.16
and 6.17.

Figure.6.15 RS-P4-0812-223. (Left) Overall image of RS-P4-0812-223 (right) Drawing of RS-P40812-223. The chamber of RS-P4-0812-223 is made of SUS304. There is no leakage gas because
the joint part is welded.

The detection eﬃciency ratio r (λ) of a test detector (DUNia10 or R3292) to RS-P4-0812-223 is givenin the following equation:r(λ) =(1 − exp (−p1 λ))(1 − exp (−p2 λ))(6.2)

where p1 is the reaction coeﬃcient of 3 He gas of DUNia-10 or 6 Li of ZnS/LiF scintillator, p2 is thereaction coeﬃcient of RS-P4-0812-223.
Actually, the eﬀects of absorption of materials such as aluminum and SUS304, and attenuation from thewave height cut and the counting loss were included in the obtained result. Thus, in order to compare
measured data with expression (6.2), it was necessary to correct these eﬀects. In this study, the countobtained after absorption and attenuation eﬀects are corrected is referred to as “the corrected count”
hereafter.
The evaluation of the detection eﬃciency of DUNia10 is described as below. A schematic diagramof the measurement setup and the block diagram of DUNia-10 are shown in Figure 6.18 and 6.19.
Figure 6.20 shows the result of fitting with expression 6.2 the corrected count ratio between DUNia-10
and RS-P4-0812-223. From the comparison between Figure 6.20 and expression (6.2), we got ε(λ) =1 − exp (−0.0708λ) as the detection eﬃciency of DUNia-10. It is noted that the unit of λ is nanometers.
The value of p1 predicted from the gas pressure of 3 He at 1858 Pa is 0.071, which was consistent withthe fitting result within the error range. It was confirmed that the detection eﬃciency of DUNia-10 was
position dependent and time dependent. However, the eﬀect of time dependence can be compensated by
the measurement procedure of the storage experiment (described later). The position dependence was
evaluated in the low divergence beam branch by the position scanning of DUNia-10 surface. Please refer
to Appendix.C for details of position dependency evaluation.
127

The evaluation of the detection eﬃciency of R3292 & ZnS/LiF scintillator is described a below. The
schematic illustration of the setup used for the measurement and its block diagram are shown in Figure
6.21 and Figure 6.22. The corrected count rate ratio of R3292 (ZnS/LiF) to RS-P4-0812-223 when the
beam is irradiated to the center position of R3292 (ZnS/LiF) is given in Figure 6.23. By fitting the
wavelength region 0.5 to 1.04 nm with the expression (6.2), ε(λ) = 1 − exp (−0.104λ) can be obtained.
The detection eﬃciency of R3292 (ZnS/LiF) has the position dependency. In this study, in order tocorrect the eﬀect, surface scan using the low divergence beam have been performed. The two-dimension
map for relative detection counts obtained from the measurement is given in Figure 6.24.

Figure.6.16 Setup used for the measurement of RS-P4-0812-223. RS-P4-0812-223 was set in a
distance of ∼ 100 mm from the exit of the low divergence beam branch. Cadmium slit of ϕ2 mm
was aﬃxed in the exit to narrow the beam. It is aligned so that the center of the neutron beamhits the detector center with an accuracy of 1 mm.

128Figure.6.17 The block diagram of the setup of the measurement using RS-P4-0812-223 in low
divergence beam branch.

Figure.6.18 Setup used for the measurement of DUNia-10 detection eﬃciency. DUNia-10 was set
at a distance of ∼ 100 mm from the exit of the low divergence beam branch. Cadmium slit of ϕ2mm was aﬃxed to the exit to narrow the beam. It is aligned so that the center of the neutron
beam hits the detector center with an accuracy of 1 mm.

129

Figure.6.19 The block diagram of the setup of the measurement using Dunia-10 in low divergence
beam branch.

Figure.6.20 Wavelength dependence of count rate ratio of DUNia-10 and RS-P4-0812-223. Wavelength dependence of count rate ratio of DUNia-10 and RS-P4-0812-223. The red line is a fit by
the expression (6.2). The vertical axis represents the count rate ratio, and the horizontal axis
represents the wavelength (nm).

130

Figure.6.21 The setup used for the R3292 detection eﬃciency. Attaching cadmium slit to the exitof low divergence beam branch at J-PARC MLF BL05, the beam was irradiated to the detector
installed at a distance of 270 mm from the exit point. In this situation, surface scanning was
performed so that the detector was moved to the direction orthogonal to beam axis.

Figure.6.22 The block diagram of the setup of the measurement using two-dimensional detector
in low divergence beam branch.

131

RatioResult of RPMT Efficiency Fitting
0.1

Fitting Result
Entries427

Mean

0.4459RMS

0.11070

Underflow

0.09

Overflow0

Integral

1.899

χ2 / ndf

0.08

55.02 / 33

p00.1041 ± 0.0084

p1

6.296 ± 1.911

0.07
0.06
0.05
0.04
0.03
0.02
0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

wave length[nm]Figure.6.23 Wavelength dependence of the ratio of two-dimensional detector to RS-P4-0812-223.
The red line is the fit result by the expression (6.2). The vertical axis represents the count rate
ratio, and the horizontal axis represents the wavelength (nm).

132

Y1/(Y1+Y2)

Relative Efficiency Map
1

1

0.9
0.8

0.8

0.7
0.6

0.6

0.5
0.4

0.4

0.3
0.2

0.2

0.1
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 0.9
1
X1/(X1+X2)

0

Figure.6.24 Relative detection eﬃciency of two-dimensional detector. Two-dimensional distribution of the intensity ratio obtained when scanning R3292-02 (ZnS/LiF) with a low divergence beam.
The vertical axis is the relative position of Y, and the horizontal axis is the relative position of X.

133

6.3 Determination of UCN velocity emitted from Doppler Shifter
In this section, it is described how to determine the velocity of UCN beams emitted from the side portof the Doppler Shifter. As mentioned in chapter 2.4.2, the velocity distribution of UCN beams generated
by the Doppler Shift method can be calculated by a simulation assuming the velocity distribution ofneutrons incident to the Doppler Shifter. For J-PARC MLF BL05, such incident neutrons correspond tothe very cold neutrons (VCNs) emitted from the focus guide (see chapter 6.2.3). The velocity of VCNs
can be calculated from the beam divergence and TOF. For this reason, the author actually measured
the beam divergence and TOF of VCNs emitted from the focus guide in June 2017.
The experimental setup used in this study is shown in Figure 6.25. In addition, the schematic illustration of this experimental setup is given in Figure 6.26, and the block diagram of the experimental setup
is given in Figure 6.27. This setup consists of the focus guide, X-Y stage, two-dimensional detector, andhelium flow tube. In this setup, a cadmium slit with 36 pinholes of ϕ 1 mm was pasted to the tip offocus guide (see the right of Figure 6.28), and a cadmium collimator of ϕ 4 mm (see the left of Figure6.28) was aﬃxed to the front end of the helium tube. In addition, the two-dimensional detector was
mounted on the X-Y stage so that the center of the two-dimensional detector could be adjusted to oneof 36 pinholes one by one. The distance between the slit and the collimator was about 2 mm. Whenthe center of the two-dimensional detector is aligned with the center of one of pinholes of Cadmiumslit, it is guaranteed that only the neutron flux emitted from the pinhole can reach the two-dimensional
detector. The purpose of the helium flow guide was to suppress air scattering between the focus guideand the two-dimensional detector. In this way, using this experimental setup, VCN flux emitted fromone of pinholes was measured one by one while aligning the center of the two-dimensional detector to thepinhole. The VCN beam divergence could be obtained from the beam spread on the two-dimensional
detector surface, and the TOF could be obtained from the time at which UCNs are detected since theproton beams are injected at J-PARC MLF. Finally, VCN velocity can be calculated with the beam
divergence, the TOF, the distance from the cadmium slit to the detector (482 mm), and the distancefrom the J-PARC mercury target to the detector (17.6 m).
As mentioned in the above, the UCN velocity can be calculated by the Doppler Shifter simulation
assuming the VCN velocity distribution. The velocity of UCN beams obtained in this way is shown in
Figure 6.29.

134

Figure.6.25 Experimental setup used for neutron flux measurement of the focus guide. A cadmium
slit with 36 pinholes of ϕ 1 mm was pasted to the aluminum cover of the focus guide (see the rightof Figure 6.28). A cadmium collimator of ϕ 4 mm in the left of Figure 6.28 was aﬃxed to the front
end of the helium flow tube. The both end of the helium flow guide is covered with an aluminum
sheet of 200 µm thickness, the surface of the two-dimensional detector is covered with a foil of
100 µm thickness, and the tip of the focus guide is covered with an aluminum cap of thickness
200 µm. The distance between the slit and the collimator was about 2 mm. When the center of
the two-dimensional detector was aligned with the center of the pinhole of Cadmium slit, only theneutron flux emitted from the pinhole reaches the two-dimensional detector surface.

135

Figure.6.26 The schematic diagram of the setup used for measuring neutron flux of the focus
guide. The distance from the moderator to the detector surface was ∼ 17.6 m, and the distancefrom the tip of focus guide to the detector was 482 mm. The signals of two-dimensional detector,
timing pulse, and kicker pulse were Analog to Digital converted and recorded on the PC.

Figure.6.27 The block diagram of the setup used for measuring neutron flux of the focus guide136Normalized Simulated Events/(0.1 m/s)

Figure.6.28 Cadmium slit and cadmium collimator used in experiment

0.02

0.015

0.01

0.005

0

0

2

4

6

8

10 12 14 16 18 20
velocity (m/s)

Figure.6.29 Velocity distribution of UCN emitted from Doppler Shifter side port. The horizontal
axis shows UCN velocity calculated by Doppler Shifter simulation, and the vertical axis shows thenumber of Monte Carlo Events. Total sum is normalized to 1.

137

6.4 UCN Storage Experiment
In this section, details of UCN storage experiment are described. This section is divided into three parts.
In the first part, the background of this experiment is introduced. In the second part, the obtained resultis explained. In the final part, the details of the analysis to determine UCN loss probability coeﬃcientare described.

6.4.1 Introduction of UCN Storage Experiment
UCN storage experiment was performed twice in May 2016 and June 2016. In the first storage experiment, SUS316 and DLC/SUS304 were used as a test material, and in the second storage experiment,
NiMo/SUS304 and SUS316 were used. A block diagram of setup in which storage experiments were
performed is shown in Figure 6.30, and a schematic diagram is shown in Figure 6.31. Features of thissetup are as follows:
1. The UCN produced by Doppler Shifter was picked up by NiC transport guide installed in the
viewport.
2. An aluminum foil, 25 µm, was attached to the tip of the NiC transport guide.
3. UCNs importation and storage and release were controlled by the opening/closing gate valves in
Figure 6.31.
In the storage experiment, the measurement procedure consists of the following four parts: (1) monitoring of UCN (2) accumulation of UCN (3) storage of UCN (4) release and detection of UCN. Each statetransition was controlled by managing two valves opening/closing. For reference, the sequence of thestorage experiment is given in Figure 6.32. The details of the sequence are described as follows (Pleasealso refer Figure 6.32):
UCN monitoring: (gate valve1 open, gate valve2 open):In this period, it is possible to count the number of raw UCNs coming from the Doppler Shifterand going to the detector. Its procedure is set for the purpose of correcting the fluctuation of the
UCN beam. It is noted that its procedure is not used in the current analysis.
Accumulation of UCN (gate valve1 open, gate valve2 close):In this period, UCN coming from Doppler Shifter is accumulated in the storage container. In thisway, the number of UCNs is increased to be nearly maximum.
Storage of UCN (gate valve1 close, gate valve2 close):In this period, UCN is kept stored for a certain time. In this way, the inner surfaces of the storage
container and the test material are reacted with UCN.
Releasing UCN: (gate valve1 close, gate valve2 open):
During this period UCN in the container is released. The released UCN is counted by DUNia-10
installed under the container.

138

Figure.6.30 The block diagram of the setup of the storage experiment.

In this experiment, storage time was repeatedly changed for each run like 0 s → 100 s → 200 s → 300 s→ 400 s → 0 s → ... .
In this experiment, substances in upstream emit gamma radiation and it is picked up by detectors. In
general, the energy that the gamma radiation deposits on the detector is smaller than that neutrons do.
And also, the gamma radiation instantaneously increases at the timing of J-PARC pulsed proton beam
injection. In this study, the following two cuts were applied for improving the signal to noise ratio.
Gamma cut
The wave height value recorded on A3400 should be 400 or more.
T0 cut
The events recorded on A3400 after 0.4 ms from J-PARC pulsed beam injection are used.

6.4.2 Result of UCN Storage Experiment
The result of UCN storage experiment is described below. Regarding the first storage experiment, dataacquisition and analysis were conducted as follows:
Setup
PBIID DLC/SUS304 or SUS316 is installed at the top of the container.
Data acquisition
Repeat following procedure: (1). To accumulate UCNs for 50 s (2). To choose the storage period
from one of 0 to 400 s cyclically (3). To store UCNs for the storage period. (3). To release UCNs
139

Figure.6.31 Schematic diagram of the setup of our storage experiment. When opening both gate
valves, UCN coming from Doppler Shifter pass through the storage container and go to DUNia-10.
When only the valve on the Doppler Shifter side is opened, UCN is accumulated inside the storage
container. When both valves are closed, UCN is stored inside the storage container. When only
the shutter on the DUNia-10 side is opened, UCN inside the container is released and counted by
DUNia-10.

for 100 s.
Data process
The foreground was determined by DUNia-10 counts in the duration of release. On the other hand,the background was determined from the average counts of data acquired in the conditions shownin Table 6.2. Finally, signals were determined by subtracting the background from the foreground.
Signal Data
Statistics of the signal count are shown in Table 6.3.
In the second storage experiment, data acquisition and analysis were carried out as follows:
Setup
NiMo/SUS304 or SUS316 is installed at the top of the storage container.
Data acquisition
Repeat following procedure: (1). To accumulate UCNs for 50 s (2). To choose the storage period
from one of 0 to 400 s cyclically (3). To store UCNs for the storage period (4). To release UCNs
for 150 s or more.
Data process
The foreground was determined by DUNia-10 counts obtained from the UCN release period from140

Figure.6.32 Sequence of the UCN storage experiment )0 s to 100 s. On the other hand, the background was determined from DUNia-10 counts obtained
from the UCN release period from 100 s to 150 s or more. Finally, the signal was determined bysubtracting the background from the foreground.
Signal Data
Statistics of the signal count are shown in Table 6.4.
In the above data process, events were adopted when beam loss is suppressed to be 1 % or less during
the accumulation period in J-PARC MLF. In this study, such events to satisfy the above condition iscalled “kp-ok events”.
The obtained results are shown in Figure 6.33 and Figure 6.34. The horizontal axis is storage time,
and the vertical axis is the average signal counts of DUNia-10 for one measurement cycle, and the blackline is the result when SUS316 is used (both cases), and the red line is the result when DLC or NiMo is
used.
Obviously, there is a significant diﬀerence in the count rate of Figure 6.33 and Figure 6.34. This isthought to be due to a detection eﬃciency deterioration between the first storage experiment in 2016 May
and the second storage experiment in 2016 June (see Appendix.C for details). Although Appendix.C
show such deterioration amounts to 10% for a month, it is noted that this diﬀerence does not aﬀect theresult of our storage experiment. That is because data taking was performed from 0 to 400 s cyclicallyfor each runs and time change of detection eﬃciency was averaged over. As an example, assuming sucheﬃciency deterioration changes in time linearly, the deviation corresponding for the period of 2000 s can
2000s= 0.05%. It is therefore too much less than a statistical precision for eachbe evaluated as 10% × 1month

data points.

141

Data id

Exp idSampleHow to evaluate Background1

1st storage

SUS316

Evaluated from the average of Table 6.2

2

1st storage

DLC/SUS304

Evaluated from the average of Table 6.23

2nd storage

NiMo/SUS304

Extracted from 150 s released time distribution

4

2nd storage

SUS316Extracted from 200 s released time distribution

Table.6.1

Details of storage experiment condition

data idcounts per 100 s

situation

1605150907

3.0 ± 0.6

Extracted from 200 s released time distribution

1605151018

2.4 ± 0.4

Same the above

1605160804

2.3 ± 0.4

Same the above

1605151325

2.7 ± 0.4

Extracted from the data measured with mirror avoided from beam

1605180536

3.3 ± 0.4

Extracted from the data measured with GV1 and GV2 closed

combine data

2.7 ± 0.2

Average the above

Table.6.2

Details of the background measurement of the first storage experiment

Name

time

Number of Signal Events

Number of kp-ok Events

sus316 1st

02530 ± 51

49

sus316 1st100

1281 ± 37

48

sus316 1st

200

688 ± 2947

sus316 1st

300

366 ± 2243

sus316 1st

400

249 ± 2045

dlc 1st01987 ± 45

39

dlc 1st1001129 ± 35

41

dlc 1st200

593 ± 2637

dlc 1st300

379 ± 2236

dlc 1st400

198 ± 17

33

Table.6.3 Details of signal count for 1st storage experiment

142

Name

time

Number of Signal Events

Number of kp-ok Events

sus316 2nd01459 ± 42

34

sus316 2nd100

873 ± 3336

sus316 2nd200

459 ± 2635

sus316 2nd300

276 ± 2335

sus316 2nd400

164 ± 2033

nimo 2nd

03809 ± 64

87

nimo 2nd100

1975 ± 48

82

nimo 2nd200

1184 ± 40

84

nimo 2nd300

670 ± 33

84

nimo 2nd400

492 ± 30

87

Table.6.4 Details of signal count for 2nd storage experiment

waku
Entries
Mean
RMS

Counts/100 sec/cycle

compare_dlc_to_sus316 (FG-BG)
70

SUS316

0
0
0

60

DLC

50
40
30
20
10
0

0

50

100

150

200

250

300 350 400
Storage Time (sec)Figure.6.33 Dependence of the counting rate on storage time in the first storage experiment. The
horizontal axis is the storage time, and the vertical axis is the averaged counts per run. Black is
the result of SUS316, red is the result of DLC/SUS304.

143

waku
Entries
Mean
RMS

Counts/100 sec/cycle

compare_nimo_to_sus316 (FG-BG)

SUS316

70

0
0
0

60

NiMo

50
40
30
20
10
0

0

50

100

150

200

250

300
350
400
Storage Time (sec)Figure.6.34 Dependence of the counting rate on storage time in the second storage experiment.
The horizontal axis is the storage time, and the vertical axis is the averaged count per run. Blackis the result of SUS316 and red is the result of NiMo/SUS304.

144

6.4.3 Analysis of UCN Storage Experiment
The analysis result of UCN storage experiment is described below. In this study, the chi-squared analysis
was used to determine the loss probability coeﬃcient from the time change of UCNs of Figure 6.33 and
6.34.
The definition of the chi-square value χ2 adopted in this study is shown as follows:

χ2 =

4
∑
(Nexp,i − Ntmp,i )2δtot,ii=0√δtot,i =δexp,i =√2(δexp,i ) + (δsyst,i )2Nexp,iδsyst,i = 0.014×Ntmp,0

(6.3)
(6.4)
(6.5)
(6.6)

where Nexp,i is the number of UCNs actually measured after the storage time of i×100 s, Ntmp,i isthe count number after storage time of i×100 s created by Monte Carlo simulation (template samples),and δsyst,i is the systematic error of an uncertainty of initial storage number due to the J-PARC beam
fluctuation (see Appendix.B for details), respectively. In this study, the reduced chi-squared value of theexpression (6.3) was used for analysis.
The conditions to prepare the template sample used in the chi-square analysis are given as follows:
Preparation of Template Samples
Template samples, necessary to be compared with experimental data, were generated by the storage
simulation assuming the velocity distribution of Figure 6.29, the storage container configurationof Figure 6.2 and the theory of neutron optics. In this study, the velocity region from 3 m/s to 7
m/s was used for comparison. In addition, the number of Monte Carlo Events was chosen to be
100,000.
Non-specular Reflection
In this study, Lambert’s cosine law was used to represent the non-specular reflection occurringin the storage container, and 5 % was assumed for its non-specular reflection probability. Thisvalue is chosen to be consistent with the evaluation value of 5.7 ± 2.1 % described in the document[81] for evaluation of the non-specular reflection probability of SUS316 subjected to composite
electrolytic polishing.
Reflection on Gate Valve Surface
Only gate valves of Figure 6.2 were subjected to NiP coating and (merely) electrolytic polishing(see chapter 6.2.5 for details). In this analysis, the UCN loss probability coeﬃcient, the Fermi
potential and the non-specular reflection probability of the gate valves were chosen to be 0, 210
neV, and 0%, respectively. These assumptions are thought to be appropriate for following reasons:
1. The ratio of collision to gate valves is only 1 %.
2. Non-specular reflection probability is typically 10 % or less for an electrolytic polishing surface.
3. UCN loss probability coeﬃcient is typically O(10−4 ) for a well-polished surface.
145For reference to the experimental ability, the comparison plot of η dependency of the template sample
prepared by the above procedure is shown in Figure 6.35. This plot shows the η dependency of thenumber of UCNs confined in the storage container whose NiMo is used for test material. Please refer
the figure caption for detailed simulation conditions. In fact, it can be found that a significant diﬀerence
occurs according to the η diﬀerence. The η dependence of the chi-squared value for SUS316 is shown in
Figure 6.36. According to Figure 6.36, the loss probability coeﬃcient η of SUS316 can be evaluated to be−4−4(2.4+0.31(the first storage experiment) and (2.2+0.32(the second storage experiment).
−0.21 ) × 10
−0.24 ) × 10

In this study, 2.3 × 10−4 was adopted as the evaluation value of the UCN loss probability coeﬃcient of
SUS316, which is the average value for the first storage experiment and the second storage experiment.
The η dependency of the chi-squared value for NiMo/PBIID DLC is shown in Figure 6.37. In Figure
6.37, the chi-square value becomes minimized for η < 1 × 10−4 , while it drastically increases in the otherregion. This means that although it is impossible to identify the loss probability coeﬃcient of the test
material, it can be guaranteed that the reflection performance is superior to a certain level. In this study,
a point of 1 σ away from the reduced chi-square value of η < 1 × 10−4 is adopted as the upper limit of
the UCN loss probability coeﬃcient for NiMo and PBIID DLC.
From the above, it is concluded that the upper limit values of the loss probability coeﬃcient of NiMo
and PBIID DLC were evaluated to be 3.6 × 10−4 and 3.4 × 10−4 , respectively, which are the point
corresponding to 1 σ in Figure 6.37.

6.5 Short Summary
The results obtained in the storage experiment are summarized below.
1. The author succeeded in constructing a system that can store UCNs for the first time in thehistory of J-PARC. In this system, it is possible to control accumulation, storage and release of
UCNs by management of opening/closing of two types of gate valve like Figure 6.31. The storage
container is a cylindrical configuration of SUS316 with Φ498 mm × L500 mm, and its inner surface
is subjected to the method of composite electrolytic polishing like Figure 6.9. The upper surfaceof the storage container can be replaced for a test material as shown in Figure 6.8 and Figure 6.10.
By storing UCNs in the container and observing the time change for the number of UCNs, UCN
loss probability coeﬃcient for test material can be evaluated.
2. In unpolarized beam branch of J-PARC MLF BL05, the storage experiment using SUS316,
NiMo/SUS304 and DLC/SUS304 were performed. As a result, the loss probability coeﬃcient of−4−4
SUS316 was evaluated to be (2.4+0.31(the first storage experiment) and (2.2+0.32−0.21 ) × 10
−0.24 ) × 10

(the second storage experiment).

In addition, the upper limit value of the loss probability

coeﬃcient of NiMo and PBIID DLC were evaluated to be 3.6 × 10−4 and 3.4 × 10−4 , respectively,
which are the point corresponding to 1 σ in Figure 6.37.

146

Monte-Carlo Number

Monte-Carlo Number

Experiment45

Eta=1.0e-0340

Eta=7.0e-04

35

Eta=3.0e-04
Eta=1.0e-06

30

Experiment
Eta=1.0e-03
Eta=7.0e-04
Eta=3.0e-04
Eta=1.0e-06

10

25
20

15
10
5
0

50 100 150 200 250 300 350 400

storage time [s]0

50 100 150 200 250 300 350 400

storage time [s]Figure.6.35 The comparison plot of template samples having diﬀerent η. (Left) Linear scale(Right) Log Scale. The vertical axis is Monte-Carlo number, the horizontal axis is storage time,color lines are results of the template samples prepared assuming diﬀerent η values. For reference,
the obtained result of UCN storage experiment is also plotted in the Figure (square point). Eacherror bar of the square point corresponds to the statistic error of (6.5), while each error bar in
the color line corresponds to the systematic error of (6.6). In this plot, it is assumed that NiMo
is used for test material and the UCN loss probability coeﬃcient of SUS316 is 2.3 × 10−4 . The
plot of η = 1 × 10−6 corresponds to the case that the UCN loss is determined only by the SUS316
contribution. The value of each template sample at the time of zero is scaled to that of the actual
measurement data.

147

Reduced Chi2 of SUS316 for 2nd storage
χ2/NDF

χ2/NDF

Reduced Chi2 of SUS316 for 1st storage
3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5

0
0.18

0.2

0.22

0.24

× 10
0.26
0.28
0.3
0.32
Loss Probability Constant: η

-3

0
0.18

0.2

0.22

0.24

× 10
0.26
0.28
0.3
0.32
Loss Probability Constant: η-3

Figure.6.36 The dependency of the χ2 of SUS316 on the loss probability coeﬃcient. (Left) The
case for first storage experiment (right) The case for second storage experiment. The vertical axis
is reduced chi-square, and the horizontal axis is loss probability coeﬃcient.

Reduced Chi2 for DLC

χ2/NDF

χ2/NDF

Reduced Chi2 for NiMo
3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5

0

0.1

0.2

0.3

0.4

0.5

× 10

-3

0

Loss Probability Constant: η

0.1

0.2

0.3

0.4

0.5

× 10

Loss Probability Constant: ηFigure.6.37 The dependency of the χ2 of NiMo/PBIID DLC on the loss probability coeﬃcient.
(Left) The case for NiMo (right) The case for PBIID DLC. The vertical axis is reduced chi-square,
and the horizontal axis is the loss probability coeﬃcient η.

148

-3

Chapter 7

Evaluation of the Experimental Sensitivity
In this chapter, the experimental precision of J-PARC P33 experiment was evaluated assuming thereflective materials described in chapter 5 and 6 are used. In this study, the statistical precision was
evaluated by simulation, and the systematic error was derived through comparison with the preceding
study. The details of the final evaluation of statistical precision and systematic error are described below.

7.1 Evaluation of Statistical Sensitivity
In this study, the statistical precision was evaluated using the procedure described in chapter 4 under
the following simulation conditions:
UCN Production
Referring to the J-PARC Proposal 33, it was assumed that the pulsed proton beams with 400
MeV, 50 mA described in Figure 4.1 and Table 4.1 are supplied to a Pb target every 0.5 Hz for
generating nuclear spallation neutrons. It was also assumed that spallation neutrons are cooled andconverted into UCNs using the ultracold neutron source of Table 4.2 and Figure 4.2. Ultracold
neutron source was assumed to consist of heavy water, liquid deuterium, and solid deuterium(sD2 ). Furthermore, the density of UCN produced in sD2 was assumed to be 5,800 UCN/cm3 as
evaluated in chapter 4.2.
Upscattering Cross Setion of sD2 Converter
Although it is reported that other institutes such as PSI have achieved 98% for the ratio of orthoD2 to para-D2 , this study adopted 95% for conservative evaluation, and the up-scattering crosssection was calculated with the relation in Figure 2.1.
Elastic Scattering of sD2 Converter
In this study, referring to document [36], the elastic cross section and the mean-free path of 2.04
barn and 8.2 cm were assumed.
Experimental Setup
It was assumed that the experimental setup of Figure 4.9 consists of a solid deuterium converterof 100 mm diameter and 200 mm length, a transport guide of about 10 m long with 100×100
mm2 cross section, a storage container of 470 mm diameter and 120 mm length, a focus guide, a149

rebuncher and shutters.
Simulation Framework
This study used PHITS for the evaluation of the UCN yield, Geant4-UCN and an original simulation tool developed by the author for evaluation of UCN transportation and refocusing UCN
and UCN storage simulations and systematic error. For the original simulation, the author implemented new functions in the Geant4 simulation framework. As a result, the refocusing of UCN,
the opening and closing of shutters, the interaction during UCN reflection predicted by the theoryof neutron optics, the non-specular reflection of UCN predicted by the micro-roughness model,
and spin precession due to relativistic magnetic field are realized in our simulation study.
Storage Performance
The storage performance was determined by two factors: (1) the energy that incident neutron
can be totally reflected from a material surface (2) the UCN loss probability less than 0.01 % percollision. The total reflection energy is the Fermi potential of the expression (2.2). On the other
hand, the UCN loss probability is indicated by η of the expression (2.6). In this study, it was
assumed to use reflective materials whose potential and η were measured by actual measurement
for a reliable evaluation. NiMo (see chapter 5.1) and PBIID DLC (see chapter 5.2.2) can be usedas such material. In this study, NiMo was assumed to be used for the electrode, and PBIID DLC
was assumed to be used for the side surface of the storage container.
The measurement result for the Fermi potential and η are listed as follows:
Fermi potential(VF )Regarding VF , 228 neV (NiMo) and 193 neV (PBIID DLC) were evaluated by the neutronreflectivity measurement described in chapter 5.4.1. The fermi potential for PBIID DLC wasevaluated by X-ray reflectometry and RBS/ERDA. It was confirmed to be 8% higher than theneutron reflectivity measurement.
UCN loss probability (η)η was evaluated by the UCN storage experiment described in chapter 6. It was confirmed thatthese upper limits of NiMo and PBIID DLC were evaluated be 3.6 × 10−4 and 3.4 × 10−4 ,respectively, which are the point corresponding to 1 σ in Figure 6.37. On the other hand, ηof PBIID DLC was evaluated by RBS/ERDA described in chapter 5.4.2. It was evaluated tobe 1.5 × 10−4 .
In this study, for conservative estimation, 228 neV/3.6 × 10−4 (NiMo) and 193 neV/3.4 × 10−4
(PBIID DLC) were adopted as the result of VF and η.
Transport Performance
Transport eﬃciency was determined by two factors, the Fermi potential, and non-specular reflection. In this study, ionized vapor deposition DLC (see chapter 5.2.1) and FAIPD DLC (seechapter 5.2.3) were assumed to be used on the inner surface of the transport guide. The potential of the two materials has been evaluated by the neutron reflectivity measurement described inchapter 5.4.1 and it was evaluated as 264 neV (IEM DLC) and 243 neV (FAIPD DLC). Regarding150

non-specular reflection, it was handled using the micro-roughness model described in chapter 2.3.
Regarding the parameters necessary to calculate the micro-roughness model, the root-mean-squareroughness were evaluated to be 0.30 nm (IEM DLC) and 0.49 nm (FAIPD DLC) by a atomic force
microscope, and the correlation length was chosen to be 33 nm (the averaged value of measured
data of IEM DLC and NiC).
Implementation of Rebuncher
The rebuncher was assumed to be an apparatus shown in Figure 4.4 where the gradient static
magnetic field of Figure 4.5 and the RF magnetic field of Figure 4.10 are applied. In the simulation,
it is assumed that the rebuncher is installed at 5 m of the experimental setup with a spin reversal
probability of 100 %. As a result, it was confirmed that UCNs refocus on the shutter 1 point of
Figure 4.9 from 2.15 s to 2.2 s, as described in chapter 4.4.3.
Shutter Opening/Closing TimeIt assumed that shutter 1 of Figure 4.9 is open from nuclear spallation between 2.15 s and 2.20 s.
The Condition of Best Statistical Sensitivity
For the evaluation of the statistical precision, the best statistical precision condition of the formula(3.9) was imposed, which is a reasonable assumption.
Experimental Period
Experiment period and the time assigned for the EDM measurement were assumed to be 3 years
and 18 hours/day, respectively.
Measurement Time of UCN
It assumed that the UCN measurement time is 100 s.
Determination Strategy for Statistical Sensitivity
Under the following conditions, five variables of the expression (3.7) were determined to obtainthe statistical precision of the neutron EDM measurement:
Electric Field Strength (E)E is determined to be 10 kV/cm taking into account the discharge limit and past experimental
results.
Visibility (α)α is the amount determined by the spin polarization rate, the performance of the systemcounting polarized spins, and the eﬀect of spin polarization relaxation time during storage.
However, the J-PARC P33 experiment is not at the stage where the UCN spin can be measured. Therefore, in this study, the evaluation value 0.86 of the document [63] assuming timeinvariance of α during storage was adopted.
Storage Time (T)The value of T was determined from the time which satisfies the condition of best statisticalprecision (expression (3.9)) by storage simulation.
Number of Measurement Repetition (n)The value of n was derived from the experimental period, the UCN measurement time, andthe T value.
Detected Counts (N)151

The value of N was determined by evaluating the initial storage UCN number using the rebunchstorage simulation described in chapter 4.4.4.
Rebunch Storage Number
In this study, the storage number was evaluated by the rebunch storage method for 100 s, and
90% of it was adopted.
As mentioned in “Transport Performance”, the result of listed in Table 5.8 was used for the surface
roughness of the transport guide assumed in this simulation study. Actually, in the measurement described in chapter 5, surface roughness was evaluated at several microscopic points but were not becompared with diﬀerent samples. In addition, the sample size used in Table 5.8 was thought to be sosmall compared to the area of the transport guide of J-PARC P33. Thus, there is an uncertainty ofsurfaces roughness due to sample qualities or macroscopic positions. However, it is noted that substrates
listed in Table 5.8 are typical semiconductor materials such as silicon and synthetic quartz. For thosematerials, surface flatness and zero defects are required. Hence, large area uniform polishing method
is generally established for those materials. Furthermore, it is generally considered that film formation
process used in this study is uniform on the substrate surface because films are created with continuous
gas-like materials such as plasma and vapors. In the following, it is discussed how much a macroscopic
surface roughness aﬀects the evaluation result. According to the catalog of Shinetsu Corporation thatdelivers the synthesize quartz substrates used in this study, it is assured that the surface roughness isbetter than 0.3 nm Ra even if the size of the synthetic quartz is Φ 300 mm. On the other hand, Furuuchi
Chemistry Corporation that delivers the silicon substrate used in this study ensured that the surface
roughness of the silicon substrate is better than 0.6 nm Ra even if the size of silicon wafer is Φ 300 mm.
Table 5.8 showed that the surface roughness of the neutron mirror was mainly determined by the surface
roughness of the substrate. And also, for a gaussian distribution of unevenness of a surface, the RMS
roughness RRMS and the Ra roughness Ra satisfies following relation: Ra = 1.25RRMS . So, assuming
the surface roughness of a neutron mirror is 0.6 Ra ×1.25 = 0.75 nm RMS in Figure 4.23 and 4.24, it
is concluded that the deterioration of the statistical precision is suppressed to 10% or less. Hence, thesurface roughness of each neutron mirror developed in chapter 5 is expected to be smooth enough for
applying to an actual neutron EDM experiment.
Under the above assumption, the Time-of-Flight (TOF) distribution at the time when UCNs reach the
shutter 1 position of Figure 4.9 was evaluated by the same procedure as described in chapter 4.4.3. The
result is shown in Figure 7.1. The vertical axis is the number of UCNs transported, the horizontal axis
is TOF, and the bin width is 50 ms. The blue line is the TOF distribution assumed to use IEM DLC,
and the red line is the TOF distribution assumed to use FAIPD DLC. From the result, it is found that
non-specular reflection is not critical for both cases and the large peak occurs from 2.15 s to 2.20 s.
Under the above assumption, the number of UCNs achieved by the rebunch storage method wasevaluated by the same procedure as chapter 4.4.4. The result is shown in Figure 7.2. In this study, thestorage simulation for one pulse was performed 100,000 times, and then the rebunch storage spectrum
was created by piling them up. From Figure 7.2, 27,739 ± 146 (for IEM DLC) and 25,627 ± 141 (for
FAIPD DLC) were obtained as the Monte Carlo Events. By using the formula (D.1) in Appendix.D,

152

MC Events/50 ms

2000
1800
1600
1400
1200
1000
800
600
400
200
0
0

0.5

1

1.5

2
2.5
Time of Flight (s)Rebunch TOF For FAIPD DLC
Rebunch TOF For IEM DLC

Figure.7.1 Time of Flight when refocused UCNs reach the shutter 1 position of Figure 4.9. (Left)
The case for IEM DLC. (Right) The case for FAIPD DLC. The vertical axis is the number oftransported UCNs, the horizontal axis is time when UCNs reach at shutter 1 position. The blueline is the TOF distribution assumed to use IEM DLC, and the red line is the TOF distribution
assumed to use FAIPD DLC. It is noted that the number of Monte Carlo simulation is chosen to
be 100,000.

the expected number of J-PARC P33 experiment was calculated. As a result, N = 78,533 ± 415 (forIEM DLC) and 72,554 ± 401 (for FAIPD DLC) were obtained as the expectation value of the rebunchstorage number.
Under the above assumptions, the time evolution of the number of stored UCNs was estimated by thesame procedure as chapter 4.4.5. The result is shown in Figure 7.3. The spectrum is created by thestorage simulation for 500 trials. The vertical axis is the number of stored UCNs, the horizontal axis is
the storage time, the red line is the time evolution of the number of stored UCNs, and the black line is
the number corresponding to 2τ . Finally, the 2τ value was evaluated to be 197+10−10 s (for IEM DLC) and198+10−10 s (for FAIPD).
From the above, substituting five statistical variables, E = 10 kV/cm, α = 0.86, T = 2τ = 197+10−10 s(for IEM DLC) and 198+10−10 s (for FAIPD), N = 78,533 ± 415 (for IEM DLC) and 72,554 ± 401 (for
FAIPD DLC), n = 197,100 ± 9,954 experiments (IEM DLC) and 196,554 ± 9,977 experiments (FAIPD),
into formula (3.7), (±1.6 ± 0.2) × 10−27 e · cm can be obtained as the statistical precision of an averaged
value of IEM DLC and FAIPD DLC. This is the evaluation value for the statistical precision of the
J-PARC P33 derived under the above conditions.

153

storage number

35000
30000
25000
20000
15000
10000
5000
0
0

10

20

30

40

50

60

70

80

90

100

storage time (sec)
Rebunch Storage For FAIPD DLC
Rebunch Storage For IEM DLC

600

storage number

storage number

Figure.7.2 Time evolution of the rebunch storage number. (Left) The rebunch storage number
when passing through the transport guide coated with IEM DLC. (Right) The rebunch storage
number when passing through the transport guide coated with FAIPD DLC. The vertical axis is
the rebunch storage number, the horizontal axis is the elapsed time during the rebunch storage.
The red line is the spectrum considering only one pulse UCN, the blue line is the spectrum madewith one pulse spectrum piled up. It is noted that one pulse spectrum is made with the number ofMonte Carlo simulation 100,000.

500
400
300

600
500
400
300

200

200

100

100

0

50

100

150

200

250

300

storage time (sec)

0

50

100

150

200

250

300

storage time (sec)Time Evolution For FAIPD

Time Evolution For IEM DLC

2τ crosssing line2τ crosssing line

Figure.7.3 Time evolution of the number of UCNs confined in the storage container. (Left) Timeevolution of UCNs supplied from the transport guide with IEM DLC. (Right) Time evolution of
UCNs supplied from the transport guide with FAIPD DLC. The vertical axis is storage number,the horizontal axis is the elapsed time used in storage. Red and blue lines are time evolution of
UCNs to be stored, the black line is the value corresponding two τ . It is noted that the number ofMonte Carlo simulation is chosen to be 500.

154

7.2 Evaluation of Systematic Uncertainty
The systematic error depends strongly on the experimental procedure. In this study, the systematic errorof the neutron EDM experiment was evaluated under the following assumption:• The neutron EDM is measured from the time change of the polarization state when a magnetic
field is applied to the polarized UCN filled in a storage container in one direction and an electricfield is applied parallel/antiparallel to the magnetic field (see formula (3.1) in chapter 3.1).
• The neutron EDM is measured in the two cases of the magnetic field upward/downward, anda crossing point analysis is performed to eliminate the systematic error (GPE) due to the nonuniformity of the magnetic field inside the storage container (see Figure G.2 in Appendix.G).
• As described in chapter 3.2, the magnetic field fluctuation can be corrected by monitoring theintensity of the probe light emitted from 204 Hg passing through 199 Hg gas filled in the storage
container (see Figure 3.6).
Generally, the systematic error arises from the subtraction of the two spin precession frequencies
corresponding to when applying the electric field and magnetic field parallel/antiparallel. In this chapter,the systematic errors due to such procedure is called direct systematic error.
In this study, direct systematic error was evaluated as follows:
GPE
In this study, the contribution of GPE was assumed to be eliminated by using the crossing point
analysis described in Appendix.G.
v×E (Translation)
When UCNs are collectively translated and the electrostatic field is curved in the storage container,a relativistic magnetic field occurs which is oriented parallel/antiparallel to the static magnetic
field. The ILL experiment estimated it to be 1×10−29 e · cm (see document [2]). This thesis
adopted it as evaluation of the systematic error of v×E (Translation). (see Appendix.I.4 fordetails).
v×E (Rotation)
In this study, a simulation similar to the document [82] was used to evaluate the systematic
error which is caused by the coupling of the electric field distortion inside the container and therelativistic magnetic field due to the collective rotational motion of UCNs (see chapter I.5). As aresult, it was confirmed that even when the non-specular reflection probability caused by collision
is 1%, the systematic error is suppressed to be 1 × 10−28 e · cm or less. In fact, the inner surfaceof the sidewall of the storage container is diﬃcult to be polished to achieve a diﬀuse probability
less than 1 %. Therefore, its systematic error is evaluated to be 1 × 10−28 e · cm or less (seeAppendix.I.5 for details).
Leakage Current
Regarding the systematic error induced by the magnetic field due to the application of electric field155

(called Leakage Current), the evaluation using an actual experimental apparatus is important.
However, because our group does not yet have an experimental facility for an evaluation, thissystematic error was evaluated by scaling the evaluation value of the ILL experiment to the electricfield strength of this experiment. As a result, 2 × 10−28 e · cm was obtained as the evaluation value(see Appendix.I.9 for details).
Electric force
With respect to the systematic error caused by the container being squeezed by the electric force(called electric force), it was evaluated to be 3 × 10−35 e · cm. This result corresponds to themeasurement result of the distortion of the container at the time of the electric field application
described in [83] (see Appendix.I.10 for details).
AC HV Ripple
With respect to the systematic error caused by the magnetic field generated when switching thedirection of applied the electric field (called AC HV Ripple), the evaluation using an actual experimental apparatus is important. However, because our group does not yet have an experimental
facility for evaluation, its systematic error was evaluated by scaling this evaluation value of the
ILL experiment to the electric field strength of this experiment. As a result, 2 × 10−29 e · cm was
obtained as the evaluation value (see Appendix.I.11 for details).
Uncompensated B drift
Regarding the systematic error caused by the magnetic field emitted from the mu-metal magnetizedin the direction of application of the electric field (called uncompensated field drift), the evaluation
using an actual experimental apparatus is important. However, because our group does not yet
have an experimental facility for an evaluation, in this study, the source of this error is regarded
as the same of ILL experiment. In the ILL experiment, the magnitude of the systematic error was
evaluated as 3.4 × 10−27 e · cm [2] (see Appendix.I.3 for details).
For evaluation of this systematic error, it is also important to take into account the eﬀect that isinversely proportional to the distance from mu-metal surface. ILL experiment used the mu-metalof the diameter of 1.5 m. On the other hand, this study assumes the use of mu-metal of diameter 3
m, and the systematic error 1.7 × 10−27 e · cm is adopted as evaluation of uncompensated B drift.
Hg EDM
Regarding the systematic error caused by EDM of 199 Hg, an EDM value (2 ± 6) × 10−29 e · cm wasadopted in this study, which is the theoretical value of the Hg EDM described in the document[2] (see Appendix.I.8 for details).
Direct Light shift
Regarding the systematic error caused by the change of the intensity of the probe light of 204 Hg
depending on the direction of the applied electric field (Direct Light Shft), it is important to evaluate it using the actual apparatus. However, because our group does not yet have an experimental
facility for evaluation, its systematic error was evaluated in the same manner as the ILL experiment described in the document [2]. As a result, 2 × 10−28 e·cm was adopted as the systematic
error of Direct Light Shift in this study (see Appendix.I.7 for details).

156

In this study, it was assumed that GPE, which is a particularly large source, is removed by using
the crossing point analysis. However, in that case, it becomes necessary to evaluate as new systematic
sources due to the shift of the crossing point (Figure G.2 in Appendix.G) depending on the directionof the applied magnetic field. In this chapter, this kind of systematic error is called indirect systematic
error.
In this study, the indirect systematic error was evaluated as follows:
Dipole Eﬀect
The dipole magnetic field emitted from the magnetized part near the experiment apparatus change
the crossing point and produces an indirect systematic error. In the ILL experiment, two sources ofthe dipole magnetic field were confirmed. In the literature [41], one is called “Door Cavity Dipole”
and the other is called “Other dipole fields”. For the evaluation of such dipole eﬀect, it is necessary
to perform comprehensive evaluation including the eﬀect of the dipole magnetic field itself and thecorrection by using a high accuracy magnetometer. However, because the experimental setup is
not available, it was not possible to study how systematic sources exist in apparatus. Therefore,
in this study, it was assumed that the systematic error source is the same as the one actuallyconfirmed in the ILL experiment.
Regarding Door Cavity Dipole, the eﬀect can be suppressed to (0.71 ± 0.07) × 10−26 e · cm by the
analysis in the ILL experiment [2]. Therefore, this value was adopted as the evaluation value of
the Door Cavity Dipole in this study. It is noted that 0.71×10−26 e·cm is not the term regarded as
an error, but a correction term. Only the term of 0.07 × 10−26 e·cm should be regarded as an error
for the Door Cavity Dipole. In this thesis, this evaluation value is adopted as one of Door Cavity
dipole eﬀect. Regarding Other dipole fields, the ILL experiment evaluated to be 6 × 10−28 e·cm
[41][2]. The systematic eﬀect of Other dipole fields was caused by the accuracy of the fluxgate
magnetometer. Therefore, it is possible to improve the error by newly conducting a magnetic
field survey using a high precision magnetometer. For example, PSI has successfully developed a
Cs magnetometer that can measure at 10 pT accuracy with a distance of 4 cm from the wall at
the present time. If residual magnetic fields are measured at a distance of 2 cm from the wall,
its accuracy corresponds to 80 pT and Other dipole eﬀect can be reduced to be 1/12 from theevaluation value of the error of ILL. Our group does not yet have a highly precise magnetometer.
Hence, assuming that the Cs magnetometer is used, it is concluded that the eﬀect of Other dipole
fields is reduced to be 5 × 10−28 e·cm. In this thesis, this evaluation value is adopted as Other
dipole fields eﬀect.
From the above, in this study, 0.07×10−26 e·cm and 5×10−28 e·cm were adopted as the evaluation
value of Other dipole eﬀect.
Quadrupole Diﬀerence
If there is incompleteness in the symmetry of the mu-metal, the magnetic field distribution in thelateral direction inside the container changes slightly depending on the direction of the appliedmagnetic field. This appears to change the precession cycle of UCN according to the directionof the magnetic field, resulting in a change of the crossing point. This systematic error is called

157

Quadrupole Diﬀerence. This was evaluated with the spin precession change due to the rotation of the earth. For the evaluation of the Quadrupole Diﬀerence, it is important to check the
distribution of the transverse magnetic field distortion components present in the actual experimental apparatus, but there is no setup yet for this experiment. Therefore, in this study, for the
Quadrupole Diﬀerence, the same value as in the ILL experiment described in the document [2], 1.4 ± 0.1×10−27 e · cm was adopted (see Appendix.I.2 for details).
Indirect Light shift
The probe light emitted from 204 Hg causes an eﬀective magnetic field as in formula (I.2), whichaﬀects the spin state of 199 Hg. Because the spin state of 199 Hg is used for correcting the magnetic
field drift, the crossing point shifts through the Hg co-magnetometer. Such a systematic error iscalled the Indirect Light Shift. For the evaluation of the Indirect Light Shift, it is important tocheck the correspondence relation between the eﬀective magnetic field and the probe light intensity
using an actual setup, but there is no setup yet for this experiment. Therefore, in this study, for
the Indirect Light shift, the same value of the ILL experiment described in the document [2],0.8 × 10−27 e · cm was adopted (see Appendix.I.6 for details).
If these systematic errors are considered to be independent and propagated as a sum of squares,
2.5 × 10−27 e · cm is obtained as the total systematic error. This is an outline of the evaluation of thesystematic error in this study.

7.3 Final Evaluation
By combining the statistical error derived from the above condition with the systematic error, theprecision of the neutron EDM experiment is calculated to be (±1.6 ± 0.2(stat) ± 2.5(syst)) × 10−27 (e·cm)(see Table 7.1 for details). This is the final evaluation value of the experimental precision of the J-PARC
P33 experiment.

158

Error Source

Error Value (e·cm)

Statistical Precision

1.6 × 10−27

Door Cavity Dipole

7 × 10−28

Other Dipole Fields

5 × 10−28

Quadrupole

1.4 × 10−27

Uncompensated B drift

1.7 × 10−27

v×E (Translation)

1 × 10−29

v×E (Rotation)

1 × 10−28

Light shift (indirect)

8 × 10−28

Light shift (direct)

2 × 10−28

Hg EDM

6 × 10−29

Leakage current

2 × 10−28

Electric force

3 × 10−35

HV AC ripple

2 × 10−29

Total Sum of Systematic Errors

2.5 × 10−27

Experimental precision(±1.6(stat) ± 2.5(syst)) × 10−27

Table.7.1 Summary of Experimental Precision

159

Chapter 8

Summary and Future Prospect
8.1 SumarryThis thesis deals with the first basic study of the proposed experiment for searching the neutron electric
dipole moment using ultracold neutrons produced by the J-PARC pulsed proton beams of the world’s
highest instantaneous luminosity.
The neutron electric dipole moment (EDM) is one of the most sensitive physical quantity to BSM.
Currently, the best upper limit of the neutron EDM, obtained by the ILL experiment, is 3 × 10−26 e · cm
(90% CL). Many BSM models such as SUSY predict 1 to 2 orders of magnitude larger EDM that canbe detected by improving the current experimental techniques. The neutron EDM can be most precisely
measured by confining UCNs in a storage container to which an electric field is applied and detecting
the spin change when polarized UCNs interact with the electric field. Because the current neutron EDM
measurement is mainly limited by the statistical error, a more intense UCN source is key to improving
the experimental sensitivity. In recent years, a new production method that cools fast neutrons toultracold neutrons by inelastic scattering of phonons in materials such as solid deuterium or He-II has
been developed and put into practice, which is expected to achieve UCN production much higher thanthe ILL experiment. Therefore, new neutron EDM experiments adopting the super-thermal method arebeing planned all over the world. In particular, there is significant progress at PSI in Switzerland andTRIUMF in Canada, and they have announced that it has prospected to improve one or more order ofmagnitude from the ILL experiment. Both groups produce fast neutrons using an accelerator and cool
it using the converter material such as liquid helium or solid deuterium.
At J-PARC, a new experimental concept is proposed for searching the neutron electric dipole moment(J-PARC P33 experiment). This proposal consists of the following three basic ideas:
1. To generate fast neutrons by using the J-PARC LINAC pulsed proton beams of the world’s highest
instantaneous luminosity.
2. To produce pulsed UCNs by using the super-thermal method and the solid deuterium converter.
3. To transport UCN eﬀectively by using the newly proposed rebuncher system.
Actually, the phase space density of UCNs in the solid deuterium converter produced by J-PARC
LINAC pulsed proton beams is estimated to be ∼ 4.1 UCN(cm)−3 (m/s)−3 , while the phase space density160

of UCNs for the ILL experiment is estimated to be ∼ 0.084 UCN(cm)−3 (m/s)−3 at its transport guide
exit. When the generated UCNs are utilized eﬃciently by using transport with keeping the density, thestatistical sensitivity of J-PARC P33 experiment should be expected to be drastically improved similarly
to PSI and TRIUMF. However, despite the high experimental potential of the J-PARC P33 experiment,a reliable evaluation was yet to be performed so far.
In this thesis, fundamental properties of UCN and conceptual design of the J-PARC P33 experimentare discussed. The result of such a basic study which the author mainly performed are listed as follows:(α): Development of a dedicated simulation for the J-PARC P33 experiment
For J-PARC P33 concept, there was a problem that the experimental capability had not been evaluated. Thereby, the experimental sensitivity expected at the present time could not be evaluated,
and any optimization studies to improve the sensitivity could not be done. In this experiment, thesensitivity greatly depends on a lot of factors such as the experimental setup, the experimental
procedure, the magnetic field structure of the rebuncher, the performance of the ultracold neutron
source, the storage and transport eﬃciency of UCNs. Therefore, the author developed the full
simulation that can deal with not only an experimental system and its entire procedures based on
J-PARC P33 concept but also the storage and transport eﬃciency that depend on the performanceof the reflective material. Specifically, PHITS and Geant4UCN, together with an original programthat is developed by the author, were used. With these tools, J-PARC P33 experiment can betotally simulated from the upstream to the downstream, by which the statistical sensitivity of the
J-PARC P33 experiment can be numerically evaluated.
(β): Evaluation of the eﬀects of reflection performances
Regarding evaluation of the experimental sensitivity of J-PARC P33, it was particularly diﬃcult
to understand the eﬀects of the non-specular reflection and reflection loss which depend on theperformance of the reflective material used in the neutron EDM experiment; the non-specular reflection has the eﬀect of deteriorating the rebunch eﬃciency and the reflection loss at the reflection
has the eﬀect of decreasing the number of UCNs that can be stored and transported. Regarding
the non-specular reflection, in recent years, it turned out that Lambert’s cosine law, which was
believed to be able to handle non-specular reflection well, did not match actual measurement, andits eﬀect could not be accurately evaluated. In this study, micro-roughness model, a theoreticalmodel confirmed to be in good agreement with the actual measurement, was used for properly evaluating the eﬀect of non-specular reflection. Regarding the reflection loss, neutron optical theory
was used to represent it. The total reflection energy, VF , and the UCN loss probability coeﬃcient,η, were used for controlling the degree of the reflection loss, while RMS roughness b was used forcontrolling the behavior of the non-specular reflection. These reflection interactions were incorporated into the above-described simulation. Finally, by performing the simulation while changing
values of VF , η, and b within a realistic condition, the dependence of the statistical sensitivity on
the performance of the reflective material of UCN of J-PARC P33 could be numerically clarified.
(γ): Development and Evaluation of highly eﬃcient neutron mirrors
The precision of the neutron EDM experiment was seriously aﬀected by the performance of the161reflective material used in the experiment. Therefore, high eﬃcient neutron mirrors, Nickel Molybdenum alloy (NiMo) and Diamond-Like Carbon (DLC), were developed. NiMo was prepared by thebinary vapor deposition, and DLC was fabricated by methods of Filtered Arc Ion Plating Deposition (FAIPD) and Ionized Evaporation Method (IEM) and Plasma Based Implantation Deposition(PBIID). These reflection performances were evaluated by surface analyses such as neutron reflectometry, Rutherford backscattering spectroscopy/elastic recoil detection analysis (RBS/ERDA),
X-ray reflectometry, electron microscope, glow discharge optical emission spectrometry (GDOES),
and so on.
(δ): Performing UCN storage experiment at J-PARC
UCN storage experiment was performed to directly measure η value at J-PARC Materials andLife Science Experimental Facility (MLF). In particular, the author has succeeded in performing
the storage experiment at first in J-PARC history, and thereby established the solid basis for thefurther development.
(σ): Evaluating experimental sensitivity and feasibility
The sensitivity was evaluated by full simulation with the above-evaluated reflection performancesalong with the systematic error evaluated in a similar manner as the ILL experiment. Comparedwith the sensitivity of the ILL experiment, the feasibility evaluation at J-PARC P33 has been
performed.
As for topics of (α) and (β). the simulation study assuming the J-PARC P33 was performed experiment
as follows:(1) the J-PARC pulsed beams of 20 MW/pulse (400 MeV, 50 mA) of 0.5 Hz (2) the rebunch method (3)the UCN production in solid deuterium (sD2 ) of 5,800 UCN/cm3 (4) the UCN loss at reflection (5) theexperiment setup based on the J-PARC P33 (6) the ortho-para ratio of sD2 of 95:5 (7) the elastic crosssection of sD2 of 2.04 barn (8) the gradient magnetic field of the rebuncher of -3.2 T/m (9) the total
experiment period of 3 years (10) the time assigned to EDM measurement of 18 hours/day.
In this study, the Fermi potential of the transport guide was chosen to be 210 neV, that of the containerside was chosen to be 91 neV or 160 neV, and that of the top-bottom side was chosen to be 210 neV,
respectively. The UCN loss probability coeﬃcient of the storage container was chosen to vary from8 × 10−5 ∼ 5 × 10−4 , and that of the transport guide was chosen to be 0. The RMS roughness of thetransport guide was chosen to vary from 0 to 3 nm, and that of the other parts was chosen to be 0.
From this simulation study, it was found that the statistical precision was evaluated as (7.2 ± 0.2) ×
10−28 e·cm (best case) to (5.9 ± 0.2) × 10−27 e·cm (worst case). There was a diﬀerence of 8 times between
two cases; such a large diﬀerence was due to the change in the rebunch eﬃciency and the storage
eﬃciency. The statistical precision was deteriorated by the non-specular reflection, and it was changed
by about 1.6 times with b varied from 0 nm to 3 nm. In addition, the statistical precision changed
by about 3 times as η varies from 8 × 10−5 to 5 × 10−4 , while it improved by 1.5 ∼ 1.7 times with thepotential of sidewall increased 91 neV to 160 neV. In this way, the dependence of the statistical sensitivity
on the performance of the reflective material of UCN of J-PARC P33 was numerically clarified, whichshowed that development of highly functional reflective materials is extremely eﬀective for improving the162statistical sensitivity of J-PARC P33.
As for topics of (γ) and (δ), Nickel Molybdenum Alloy (weight ratio Ni:Mo = 85:15) and Diamond-Like
Carbon (DLC) have been developed. NiMo and DLC were fabricated using a quite unique film formation
techniques such as binary vapor deposition method, Ionized Evaporation Method (IEM), Plasma BasedIon Implantation Deposition (PBIID) and Filtered Arc Ion Plating Deposition method (FAIPD). These
reflection performance have been evaluated using various surface analysis methods as follows:
Total reflection energy
The total reflection energy, the Fermi potential VF , was evaluated by neutron reflectivity measurement in J-PARC Material Life science Facility Beam Line16. As a result, 228 ± 13 neV for NiMo
and 190 ± 7 neV ∼ 243 ± 8 neV for IEM DLC and about 193 ± 11 neV for PBIID DLC and
264 ±14 neV for FAIPD were obtained. In the case of IEM DLC, the same value as nickel wasachieved, which is a highly functional reflective material. In the case of PBIID DLC, the quite
high Fermi potential was achieved as candidates possible to use as the sidewall material of thestorage container. In the case of FAIPD DLC, it was confirmed that the value was achieved, whichis comparable to highest total reflection energy as mirrors developed for neutron EDM measurement. In the case of IEM DLC, X-ray reflectivity and RBS/ERDA were also used for evaluation,
and as a result, it was found that its evaluated value amount to ∼ 8% higher than the case ofneutron reflectivity measurement.
The UCN loss probability coeﬃcient
The UCN loss probability coeﬃcient, η, was evaluated by UCN storage experiment performed
at J-PARC, which is the first case in J-PARC history. It was confirmed that these upper limitsof NiMo and PBIID DLC were evaluated be 3.6 × 10−4 and 3.4 × 10−4 , respectively, which are
the point corresponding to 1 σ in Figure 6.37. In general, it is also possible to evaluate η fromthe surface hydrogen amount. Therefore, for PBIID DLC, the indirect measurement has been
performed. As a result, it was confirmed that its evaluation value corresponded to 1.5 × 10−4 .
RMS surface roughness
Atomic force microscope and a profilometer were used for evaluation. As a result, 0.30 ± 0.01
nm for IEM DLC and 1.7 ± 0.4 nm for PBIID DLC and 0.49 ± 0.01 nm for FAIPD DLC wereobtained.
Finally, as for topics of (σ), assuming the reflection performance obtained as above and the experimental
setup used in the full simulation study, the statistical precision of J-PARC P33 experiment was estimated.
In this study, for conservative evaluation, the results of neutron reflectivity measurement and UCN
storage experiment were adopted as reflection performance. Assuming that IEM DLC or FAIPD DLC is
used for the transport guide and NiMo and PBIID DLC are used for the storage container, the statisticalprecision of an averaged value of both cases was estimated to be (1.6 ± 0.2) × 10−27 e·cm. Therefore, by
combining it with the systematic error 2.5 × 10−27 e·cm, it is concluded that the experimental precision is(±1.6±0.2(stat)±2.5(syst))×10−27 e·cm. This is the first comprehensive evaluation of the experimental
capability based on J-PARC P33 concept including the reflection performance, which provides a reliablebasis for future experiment design.
1638.2 Future Prospect
The result of this simulation showed that the sensitivity of the J-PARC P33 experiment exceeds the ILL
experiment which is the current world’s highest precision. However, it turned out that neutron EDM
measurement of O( 10−28 e·cm), which PSI and TRIUMF are aiming for, has not been reached. In
the following, it is discussed what is necessary to perform the neutron EDM verification of the world’s
most precision. For improving statistical precision, following two experimental techniques are thought
to be eﬀective. First, by increasing the diameter of the solid deuterium converter and the cross-sectionof transport guide, the total UCN flux can be increased more according to the area, which enables us
to perform the neutron EDM experiment using multiple measurement cells. Second, with the current
rebuncher system, by adjusting applying the RF magnetic field and controlling the velocity distributionof the multiple UCN pulses, 3∼4 pulses can be focused at the same time, and the UCN density can beincreased more. For the systematic error, total systematic uncertainty can be improved eﬀectively bysuppressing GPE with the measurement cell size smaller. In such a way, by increasing the number of
UCNs that can be used in the experiment and making the measurement cell size smaller simultaneously,both the statistical error and systematic errors are expected to be improved eﬀectively. Thereby, it isconsidered that the experiment based on the J-PARC P33 concept not only easily achieves 10−27 e·cm,
but also can verify several 10−28 e·cm by making full use of experimental techniques. From the above, it
is concluded that this study has succeeded in providing a solid basis for future experiment design aiming
for the neutron EDM verification with world’s highest precision.

164

Acknowledgement
First of all, I am deeply grateful to my supervisor, Prof. Satoru Yamashita, for helpful advice on thisstudy. I express my appreciation to Hirohiko Shimizu of Nagoya University for giving me the opportunity
to conduct this basic study on J-PARC P33 experiment. I would like to thank Kenji Mishima of HighEnergy Accelerator Research Organization and Tamaki Yoshioka of Kyushu University for the significant
contribution on the evaluation of cold neutron flux passing through the solid deuterium converter. I
would like to thank Masaaki Kitaguchi and Shohei Imajo of Nagoya University for the collaborationof development of algorithms of the transport simulation using the rebunch method. I would like toexpress my appreciation to Dai Sakurai of Tokyo University of Science and Shinji Kakusho of J-NOP
for the significant contribution on development of ionized-evaporated deuterated DLC. I would like toexpress my gratitude to Dai Sakurai of Tokyo University of Science and Yoshichika Seki of JAEA for thecollaboration of the development of algorithms for non-specular reflection calculation. I would like toshow my gratitude to Masahiko Mitsuhashi of Kanagawa Institute of Industrial Science and Technology
for fabrication of binary vapor deposition NiMo. Also, I would like to show my gratitude to Masahiko
Sugihara of Kurita Seisakusho Co., Ltd for fabrication of deuterated PBIID DLC. I would like to oﬀer
my appreciation to Daiju Tsuya of National Institute for Materials Science and Eiichiro Watanabe ofTechnical Service Oﬃce for Pure and Applied Sciences, University of Tsukuba for measuring surface
state of a lot of samples with Atomic Force Microscope. Furthermore, I am grateful to Mikiko Saito of
National Institute for Materials Science, Waseda University for measuring our DLC sample using GDOES.
Similarly, I am grateful to Professor Shigeru Otsuka and Hideo Tsunagawa of the Faculty of Engineering
at the University of Tokyo who measured our DLC sample by using SEM and TEM. I am grateful to
Daiichiro Sekiba, Isao Harayama, Yumi Watahiki, of Institute of Applied Physics, University of Tsukuba,
and Hiroshi Naramoto and Satoshi Ishii of Tandem Accelerator Complex, University of Tsukuba for
helpful advice and technical assistance with measuring RBS/ERDA. I am grateful to Masahiro Hino
and Tatsuro Oda of Kyoto University Research Reactor Institute for fabrication of NiC mirror to use
the transport guide of UCN storage system. Also, the author thanks N.L. Yamada of High Energy
Accelerator Research Organization for helpful advice and technical assistance with neutron reflectometryat J-PARC MLF BL16. I am grateful to Sohei Imajo of Nagoya University and Yosihisa Iwashita of Kyoto
University for the collaboration on measuring very cold neutron flux emitted from the unpolarized beam
branch at J-PARC MLF BL05. Furthermore, special thanks to Hisaya Kurashige of Kobe University
for discussion to improve Geant4 code to reduce the rounding error. This work was partially supported
by JSPS KAKENHI Grant Number JP26247035 and JP23244047, and Grant-in-Aid for JSPS Fellows

165

Grand Number 14J01295. In addition, a part of this work was supported by the University of Tokyo,
NIMS and Waseda University Nanofabrication/Microstructural Characterization Platform as a programof “Nanotechnology Platform” of the Ministry of Education, Culture, Sports, Science and Technology(MEXT), Japan. And also, the neutron experiment at the Materials and Life Science Experimental
Facility of the J-PARC was performed under a user program (Proposal No. 2015A0246, No. 2014B0263,
No. 2013B0161. This thesis did not hold without cooperation from many people. I would like to express
my heartfelt gratitude to the people concerned. Finally, I deeply appreciate my late mother Keiko, myfather Hisao, and my brother Yuusuke, who gave me so many supports and opportunities and always
encourage me. I would like to dedicate this thesis to my late mother Keiko.

166

Appendix.A

Time-of-Flight Method
In following, explain the time-of-flight(TOF) method to measure the wavelength spectrum of low-speed
neutrons. Since low-speed neutron has no charge, its detection is performed by measuring secondary
particles derived from nuclear reaction with helium 3 or lithium 6 having a large neutron capture crosssection. Neutron absorption reactions of helium 3 and lithium 6 are given byn +3 He →3 H + p + 0.76MeV(A.1)

n + Li → H + α + 4.79MeV

(A.2)

6

3

Express t0 as the time when the neutron is emitted from the neutron source, L as the distance between
the pulsed neutron source and the detector, and t as the time when the detector measures the secondary
particle. In general, using L, t, and t0 , the velocity (wavelength) component of the neutron can beobtained as follows.

Lt − t0
h
λ=
mv
v=

(A.3)
(A.4)

where h is Plank’s constant, and m is the mass of neutron. ∆t = t − t0 is called the time of flight (TOF)of neutron. The method of determining the velocity (wavelength) of neutron by using the equation of(A.4) is called the TOF method.
Generally, the reaction cross section of slow neutron with velocity v has the following rate dependence.

σ(v)v = σ(v0 )v0(A.5)

where v0 represents the thermal neutron velocity 2200 m/s.
In general, the probability P causing nuclear reaction with atoms when slow neutrons penetrate until x
cm in the material can be written as follows.
P (x, λ) = 1 − exp(−ρσ(v0 )v0v0x) = exp(−ρσ(v0 ) h x) = 1 − exp(−peﬀ λ)
v
mλ
167

(A.6)

where ρ is the density of atoms per cubic cm constituting the material.
The parameter peﬀ of the equation (A.6) is an important parameter indicating the detector performance,from which it is possible to evaluate the velocity dependence of the detection eﬃciency. Although peﬀ canbe extracted by fitting the measured velocity distribution with the equation (A.6), actual measurement
data includes eﬀects such as attenuation on the detector surface, attenuation due to cut eﬃciency to
the wave height distribution, counting loss, and so on. Therefore, by fitting with the equation (A.6) the
distribution corrected for these eﬀects, it is possible to evaluate the detection eﬃciency using peﬀ .
The gamma ray background, which is a problem in J-PARC MLF, is synchronized with the time atwhich proton beam spallation reaction occurs. Therefore, SN ratio can be eﬀectively improved by using
TOF method.

168

Appendix.B

Beam Fluctuation Suppression Using
MNH10/4.2F
In this section, the method to correct beam fluctuation using MNH10/4.2F is described. March 2015,
both UCN flux and neutron flux not converted to UCN was measured for 40,000 seconds continuously at
J-PARC MLF BL05 unpolarization beam branch. In this measurement, DUNia-10 had been fixed at the
viewport of Doppler Shifter and MNH10/4.2F had been fixed at beam emission port. The count ratio
of DUNia-10 to MNH10/4.2F is shown in Figure B.1. The standard deviation of Figure B.1 was 1.4%,
which was smaller than J-PARC proton beam current fluctuation 3%. The fact indicated that the countof MNH10/4.2F was correlated 1.4 % with the intensity of UCN beam. Thus, it can be understood that
the UCN beam fluctuation can be suppressed to 1.4% by comparing the count of MNH10/4.2F.

Figure.B.1 J-PARC MLF beam stability. The horizontal axis is DAQ time, the vertical axis is theratio of UCN to cold neutron count. The red line is the fitting result by the zeroth order equation.
Bin width was 100 s.

169Appendix.C

Dependence of Detection Eﬃciency of
DuNia-10 on Position and TimeIn this section, the time dependence of the count rate of DUNia-10 is described. Such dependency wasevaluated with a cold neutron beam irradiated at the center of DUNia-10 at a low divergence beam
branch of J-PARC MLF BL05. These measurements were performed 4 times, before and after the firststorage experiment and before and after the second storage experiment (see Table C.1)). In this section,
each of measurements is classified as Event 1, 2, 3, 4.
ID

Situation

1

before the first storage experiment2

after the first storage experiment3

before the second storage experiment4

after the second storage experiment

Table.C.1 Classification of low divergence beam measurement

The count rate and wave height distribution obtained from the measurement at low divergence beam
branch are given in Figure C.1 and Figure C.2. It is found that the count rate decreases with time byabout 10 %, and the pulse height distribution becomes closer to the low channel side.
It has confirmed that there is a position dependency in the counting rate of DUNia-10. The resultof investigating the position dependence of the pulse height distribution by the on-plane scan using the
low divergence beam is summarized in the Figure C.4. It can be seen that the wave height distribution
greatly varies depending on the position.
The counting rate of the storage experiment has already been summarized into the Figure 6.33 andFigure 6.34. Between the beginning of the first storage experiment and at the end of the second storage
experiment, the count rate has varied by 15%. It is larger than the time change obtained by measurementof the low divergence beam. Therefore, an explanation is required.
The reasons for this discrepancy can be considered as the following two points.
1. In the low divergence measurement, only the center of DUNia-10 was used to count the number
170

of UCNs, while in the storage experiment UCNs were detected using the whole surface. Thereby,
the diﬀerence of the counting rate due to position dependency appeared strongly.
2. If the wave height distribution becomes closer to low channel, the cut eﬃciency of the wave height
deteriorated with time growth. In this way, the counting rate further is thought to be decreased.

Counts(e>400)/kp{×}25

Counts(e>400)/kp{×}25
114
112
110
108
106
104
102
1

1.5

2

2.5

3
3.5
4
Measurement ID

Figure.C.1 Time change of count rate of DUNia-10 found by low divergence beam measurement.
The horizontal axis is measurement id and the vertical axis is count rate. It turns out that thecount rate becomes lower as the time spend.

171

SG0

Counts(e>400)/kp{×}25/ch

SG02539198
BeforeEntries
1stStorage
Mean

1026

RMS

157.3

After 1stStorage

1
Before 2ndStorage

0.8

After 2ndStorage

0.6
0.4
0.2
0
0

200 400 600 800 100012001400160018002000
chFigure.C.2 Time change of pulse height of DUNia-10 found by low divergence beam measurement.
The horizontal axis is the pulse height value A/D converted, and the vertical axis is the count rate.
We use neutrons of several meV to 25 meV for the measurement. It turns out that the distribution
is shifting to the low channel side as time grow172

Figure.C.3 Surface position of DUNia-10 scanned in a low divergence beam branch. Since the electric field structure of DUNia-10 must be circularly symmetric, a low divergent beam was irradiatedonly to the lower right quadrant by 12.5 mm.

173

coutnts/25 kp/40 ch

20
18
16
14
12

point A:x_y=0.0_0.0
point B:x_y=12.5_0.0
point C:x_y=25.0_0.0
point D:x_y=37.5_0.0
point E:x_y=0.0_-12.5
point F:x_y=0.0_-25.0
point G:x_y=0.0_-37.5
point H:x_y=12.5_-12.5
point I:x_y=25.0_-12.5
point J:x_y=37.5_-12.5
point K:x_y=0.0_-25.0
point L:x_y=12.5_-25.0
point M:x_y=25.0_25.0

10
8
6
4
2
0

200

400

600

800

1000

1200

1400

1600

1800

2000
ch

Figure.C.4 Pulse height distribution obtained by surface beam scan of DUNia-10. Pulse height
distribution obtained by scanning of Figure C.3. The horizontal axis represents the A/D converted
value of the wave height, and the vertical axis represents the count. The correspondence of eachposition is explained in the legend of the figure.

174

Appendix.D

Evaluation of UCN Density by Rebunch
Storage Method
In general, UCN density can be calculated by using the following expression (D.1).
ρchamber Vchamber =ρsD2 ×VsD2
× NSurvive ×ϵϕ
NTry

(D.1)

where ρsD2 is the UCN density in solid deuterium converter, ρchamber is the UCN density in thecontainer, NTry is the total trial number of transportation Monte Carlo simulation, NSurvive is thenumber of Monte Carlo events of UCN reaching in the container, VsD2 is the volume of solid deuterium,
and Vchamber is the volume of the storage container. Finally, ϵϕ represents the ratio of the phase spacevolume of UCNs produced in solid deuterium converter to the phase space volume of UCNs that can beextracted outside.
It is noted that, in this study, ρsD2 is evaluated to be 5,800 UCN/cm3 and ϵϕ correspond to (150neV)3/2 /(252 neV)3/2 . For reference, the UCN density in the storage container calculated by the expression (D.1) is summarized in Table D.1. It is noted that the eﬀect of non-specular reflection is not taken
account in Table D.1.
potential ID

η = 8 × 10−5

η = 1 × 10−4

η = 3 × 10−4

η = 5 × 10−4

1

16.8 UCN/cm3

16.5 UCN/cm3

13.3 UCN/cm3

11.3 UCN/cm3

2

35.2 UCN/cm3

34.5 UCN/cm3

27.5 UCN/cm3

22.8 UCN/cm3

Table.D.1

The UCN density in the storage container, calculated by the rebunch storage simulation.

175

Appendix.E

Evaluation of Time Dependence of Rebunch
Storage Number
In the case of potential ID 0 of loss probability 3 × 10−4 , the time change of the number of UCNs in thecontainer using the rebunch storage method and that of not using rebunch storage method are given instorage number

Figure E.1.

40000
35000
30000
25000
20000
15000
10000
5000
0

0

10

20

30

40

50

60

70

80

90

100

storage time (sec)pileup spectrum w/ rebunch and shutter operation

pileup spectrum w/o rebunch and shutter operation

Figure.E.1 Eﬀect of rebunch on the number of storage

Thanks to rebunch storage, the density increase about 4 times.

176

Appendix.F

Details of Storage Experiment not to be
Described in the Text
In this section, what was too detailed to explain in the text is described.

F.1 Wave height distribution
An example of the wave height distribution obtained during the storage experiment is shown in Figure
F.1.

Events/4-ch

Typical Wave Amplitude Distribution
1600
Entries
Real Data Entries
Mean
Mean

1400

RMS
RMS

E2
E
6686
37254
870.1
386.9
293.9
321.6

Data With Typicel BG Cut

1200
1000
800
600
400
200
0

0

200

400

600

800

1000 1200 1400 1600
Nikiglass Channel

Figure.F.1 Example of wave amplitude distribution at the storage experiment.

F.2 Released Time Distribution
A typical released time distribution of the storage experiment is shown in Figure F.2. Horizontal axis isreleased time and vertical axis is counting rate. This result indicates the time evolution of the number of
UCNs in the storage container of 98 Litter. It can be found that 100 s is enough long for evacuating UCNs
177

stored in the storage container. In this analysis, the integration value of the released time distribution 0
to 100 s was used as the UCN detection number, i.e. foreground. Because the count rate converges to a
fixed value at 100 s or more, the background as the 2nd storage experiment was evaluated by using the
integration value of 100 to 200 s. For the first storage experiment, it is note that the average of the run
described in Table 6.2 was taken as the background.

Detected Counts/sec

gvt/1e6 {(gvid==3)&&(ch==15)&&(e>300)&&(tof%4e4>400)}
TOF
Entries
9375
Mean
31.37
RMS
34.01

450
400
350
300
250
200
150
100
50
0
0

20

40

60

80

100
120
140
Export Time (sec)Figure.F.2 Example of released time distribution of the second storage experiment. The verticalaxis shows detected counts, and the horizontal axis shows the released time. Because the countmore than 100 s converges to constant, the time range can be regarded as the background.

F.3 Import Time Distribution
In order to check import time dependency, the following sequence was adopted as follows:
1.import Accumulate UCNs in storage container with either of time between 10 s to 45 s.
2.storage Storage UCNs for 25 s.
3.release Release UCNs for 100 s and detect the number of UCNs.
4.cycle again Repeat procedure of 1 to 3 two times.
The dependency of the detected counts on the import time is shown in Figure F.3. In this study, thedistribution of Figure F.3 is referred to as “Import Time Distribution” hereafter. Note that the statisticalerror was large because measurement cycles was performed only two times, and also the background has
not been subtracted. The detected counts of Figure F.3 indicates that the storage number has reachedmaximum at 35 s. On the other hand, the import time in the storage experiment was 50 s (see chapter 6
for details). Therefore, it is considered that UCN was accumulated to the maximum during the storage
experiment.
178

Counts/100 s/cycle for 25 s Storage

70
60
50
40
30
20
10
0
5

10

15

20

25

30

35

40
45
50
Import Time (s)Figure.F.3 Dependence of the UCN detection number on the import time179

Appendix.G

Geometric phase eﬀect and crossing point
analysis
This section describes the mechanism of systematic error called geometric phase eﬀect (GPE). In theexperimental environment, there is a magnetic field gradient dB
dz = ∼ 10 nT/m and the associatedcurvature of the magnetic field. Generally, a transverse magnetic field proportional to dB
dz is generated
in the radial direction inside the storage container. In this case, the magnitude is about the same as therelativistic magnetic field which UCNs feel in the neutron EDM experiment [84]. When the relativistic
magnetic field combines with the distortion of the magnetic field, it becomes a resultant magnetic field
whose contribution changes according to the direction and trajectory of the electric field.
For example, if UCN is rotating, the resultant magnetic field also rotates. In order to understandthis mechanism, the time evolution (orbital dependence) of the resultant magnetic field of UCN which
is translating or rotating in a cylindrical container is shown in Figure G.1 [84]. Obviously, the resultant
magnetic field rotates in both cases. Therefore, the rotation period of the spin precession changes via
the expression (2.12).

Figure.G.1 The relativistic magnetic field dependence on trajectories, the image is cited from[39]. (Left) the case of translation (Right) the case of rotational motion. The synthetic magnetic
field vector is made of relativistic magnetic field and environmental magnetic field. It rotates withtime and its magnitude depends on the direction of application of the electric field, which cannot
be canceled by subtraction between the upper and lower electric field. Therefore, it becomes asystematic error via the expression (2.12).

180

The systematic error due to the distortion of a magnetic field and the relativistic magnetic field
has a characteristic that it accumulates as the particle takes a specific orbit. Therefore, it is possible
to statistical suppression by diﬀusing the trajectory of particles. However, even if the trajectory iscompletely diﬀused, systematic errors cannot be canceled as a whole. This systematic error whichcannot be completely canceled is called Geometric Phase Eﬀect (GPE).
The false neutron EDM due to GPE caused from UCNs and Hg atoms confined in a cylindrical vesselof diameter R to which uniform gradient magnetic field applies are represented as follows [84]:
[
]−1
z
2
h̄ dB
ωr 2
dz vxydn,f = −1− 2
4 Bz 2 c2
ω0[]−1h̄ dBz γHg γn R2
ω0 2
dHg,f =
1
−
8 dz
c2
ωr 2

(G.1)
(G.2)

where dn,f is false neutron EDM caused by UCNs, dHg,f is false neutron EDM caused from Hg atoms,
B0z is the static magnetic fields used in the neutron EDM experiment, vxy is the average neutron velocity
on the orthogonal direction to the magnetic field, ωr is the angular velocity, ω0 is the Larmor precession
0z
frequency, dB
dz is the longitudinal magnetic field gradient in the storage container.

If assuming B0z = 1 µT and dB
dz = 1 nT/m and vxy = 2.67 m/s and the same condition of the ILL
experiment, we can get −1.1 × 10−27 e·cm (UCNs) and 5 × 10−26 e·cm (Hg atoms) as false EDM due to
GPE (see [84] for details). Hg GPE is not only 50 times larger than neutron GPE, but also cause thelargest systematic error.
In the ILL experiment, GPE is eﬀectively eliminated by using the characteristic that the expression(G.2) is linearly proportional to the vertical gradient of the magnetic field. This technique is calledcrossing point analysis. Specifically, the following function of Ra can be defined with vertical gradient[84].
ωn γHgωHg γn
∆h dB
=1±
B0 dz

Ra =

(G.3)

where ∆h is the diﬀerence of the center of gravity between Hg and UCN, and ± sign denotes the direction
to which the static magnetic field B0 is applied (upward or downward).
In general, using formula (G.2) and (G.3), the false EDM caused by Hg GPE dn,f is written as follows[84]:h̄
R2 B0zdHg,f = ± |γn γHg |(Ra − 1)8∆hc2
= ±k(Ra − 1)

(G.4)
(G.5)

The plot of Ra − 1 obtained in the ILL experiment is shown in Figure G.2. The horizontal axis is Ra − 1
and the vertical axis is the actual measured EDM value. On the crossing point, the contribution of GPE
can be regarded as 0 (see formula (G.5) and (G.3)). Therefore, by analytically extracting neutron EDM
from the crossing point, it is possible to eliminate the contribution of GPE.
This is an outline of crossing point analysis. In this study, the crossing point analysis was used toevaluate the experiment of J-PARC P33.
181

Figure.G.2 Example of the crossing point analysis, the image is cited from [41][39]. The horizontal
axis is Ra − 1, the vertical axis is measured EDM dn,meas as a function of Ra − 1. The measured
EDM at the cross point can be regarded as the value whose GPE is removed. For details see the
text.

182

Appendix.H

Dependence Study of the Instantaneous
Intensity on Cut-Out Time Width
In this thesis, the period that shutter is open after the J-PARC proton beam injection is referred toas “cut-out time”. By comparing the cut-out time, we can investigate the eﬀect of the shutter opening/closing on the instantaneous intensity of the refocused pulse UCN beams entering to the measurement
cell. The higher the instantaneous intensity is, the more the rebunch eﬃciency improves. The aim of thisappendix to show the dependence of the refocused pulsed UCN beams intensity on such a cut-out time
width. In general, eﬀectiveness of rebunch method changes depending on how the cut-time out width issynchronized with. In this study, the following extremely cases are considered as listed in Table H.1.
case/operation

What the cut-time out width is synchronized with.

case1

Not Synchronize (Shutter Always Open)

case2

Synchronize Average Beam Arrival Time

case3

Synchronize Refocused Beam Peak Arrival Time

Table.H.1 The column to explain what means each cut-out time width

The case listed of Table H.1 corresponds to the following cut-out time width:
1. the case that the shutter is always open
This cut-out time width corresponds to the proton beam repetition period, and it is chosen to 2 s
as seen in 4.1.
2. the synchronization with average beamThis cut-out time width corresponds to the full width of time of flight of UCN beams, and it
corresponds to from 1.4 s to 2.4 s as seen in Figure 4.16.
3. the synchronization with refocused beamThis cut-out time width corresponds to the time of flight of refocused UCN beam, and it corresponds to 2.15 to 2.2 s as seen in Figure 4.16.
In this study, both eﬀects of the shutter opening/closing and the non-specular reflection are tested.
For evaluating it, transport simulation is performed in the same manner as described in chapter 4.4.3.
183

In this transport simulation, it was recorded the time when UCNs can reach the shutter 1 position of
Figure 4.3. The transport simulation repeats 100,000 times to make the time of flight distribution. In
the analysis, the number of Monte Carlo assigned in the period within the above-shown cut-out time
width is compared. The obtained comparison result is shown in Figure H.1. The vertical axis is thenumber of Monte Carlo events normalized to 1 s, the horizontal axis is the RMS value of the surface
roughness of transport guide, and the line color denotes the correlation length. Each frame corresponds
to the cut-out time width, the upper left is the case that cut-out time width 0 s ∼ 2 s, the upper rightis that the case the cut-out time width 1.4 s ∼ 2.4 s, and the lower left is that the case that the cut-out
time width is 2.15 s ∼ 2.2 s. The high the instantaneous intensity is, the more eﬀectively the UCN
density in the measurement cell improves. Comparing the result of the cut-out time width 0 s ∼ 2 s andthat of the cut-time width 1.4 s ∼ 2.4 s, there is two times diﬀerence in the normalized beam intensity.
Comparing the result of the cut-out time width 0 s ∼ 2 s and that of the cut-time width 2.15 s ∼ 2.2 s,there is about eleven times diﬀerence in the normalized beam intensity. These result indicate that theway of synchronizing the shutter operation with UCN beams have a serious eﬀect on the UCN density
to be achieved in the experiment.

184

shutter opens for 1.4 s to 2.4 s
Normalized Intensity

Normalized Intensity

shutter always opens
4000
3500
3000
2500

9000
8000
7000
6000
5000

2000

4000

1500

3000

1000

2000

500

0

0.5

1

1.5

2

2.5

1000

3

0

RMS roughness (nm)

0.5

1

1.5

2

2.5

3

RMS roughness (nm)Normalized Intensity

shutter opens for 2.15 s to 2.2 s
45000

w = 22 nm

40000
35000
30000

w = 33 nm

25000
20000
15000

w = 45 nm

10000
5000

0

0.5

1

1.5

2

2.5

3

RMS roughness (nm)Figure.H.1 Dependence of the rebunch eﬃciency on the shutter opening/closing operation alongwith the surface roughness. The vertical axis is the number of Monte Carlo events normalized to
1 s, the horizontal axis is the RMS value of the surface roughness of transport guide, and the line
color denotes the correlation length. Each frame corresponds to the cut-out time width, the upper
left is the case that cut-out time width 0 s ∼ 2 s, the upper right is the case that the cut-out time
width 1.4 s ∼ 2.4 s, and the lower left is the case that the cut-out time width is 2.15 s ∼ 2.2 s.

185

Appendix.I

Source is of systematic errors of UCN EDM
measurements
This Appendix summarizes the source is of systematic errors of the experiments for neutron EDM
measurements. Following lists are taken from the latest analysis of the ILL experiment.

I.1 Local dipoles (Door cavity dipole and Other dipole fields)
The systematic error generated by external magnetic field is called as Local dipole. In the ILL experiment,
experimental setup had been surveyed from 2 cm distance by using fluxgate magnetometer with accuracy
1 nT to eliminate external magnetic fields. However, after the ILL experiment, two local dipole were
found in the setup. One is called ”Door cavity dipole” and the other is called ”Other dipole fields” [41]. It
was estimated that Local dipole existed 1.3 cm behind UCN door and its intensity was −4.2 × 10−7 A·m2 .
ILL group succeed in reducing it by analytical technique, and finally, the door cavity dipole contribution
decreased to be (0.71 ± 0.07) × 10−26 e·cm[2]. It is noted that 0.71 × 10−26 e·cm is not the term regarded
as an error, but correction term. On the other hand, a source of Other dipole fields was found by
the magnetic field survey performed at PSI after the ILL experiment. In the ILL experiment, it wasestimated that the error amount to 6 × 10−27 e · cm, which corresponded to the accuracy of the fluxgate
magnetometer used in the ILL experiment [41][2].

I.2 Quadrupole diﬀerence and Earth RotationdBdB
If magnetic field gradient is 0, GPE and Local dipole do not occur. But if dB
dz = 0, dy ̸= 0 and dx ̸= 0 is

satisfied, the magnetic field is twisted in the xy plane, causing another systematic error. Such a twisting
magnetic field Bq is called quadrupole field and Bq is expressed as Bq = (−qx, qy, 0) [84][85] .
Indeed, by the magnetic field survey performed at PSI after the end of the ILL experiment [2], it waspresent in the EDM experiment setup used for the ILL experiment.
Because of Hg moving at high speed, the quadrupole field is averaged and does not contribute. On theother hand, because of UCN moving at slow speed, such a small distortion cannot be ignored and the
local distortion magnetic field results in the phase shift of UCNs. As a result, the frequency ratio of Hg

186

to UCN changes, and Ra −1 used in crossing point analysis is changed by ∆RQ . If ∆RQ does not dependon the direction of the static magnetic field, the crossing point does not move and can be neglected as asystematic error. However, it is actually confirmed that such quadrupole field has asymmetry dependingon the applied direction of the static magnetic field, which causes the systematic uncertainty.
In general, Earth Rotation also behaves like the quadrupole eﬀect and aﬀects the frequency ratio of
Hg to UCN. The ILL experiment estimated the systematic error caused by the sum of earth rotationand quadrupole eﬀect as 0.33 ± 0.14 × 10−26 e · cm [2]. It is noted that 0.33 × 10−26 e·cm is not the term
regarded as an error, but correction term. This thesis adopted it as evaluation of the systematic error ofquadrupole eﬀect and earth rotation.

I.3 Uncompensated B drift
The ILL experiment confirmed that the existence of a magnetic field changing according to the directionof the electric field. This is thought to be due to the hysteresis of the mu-metal according to the positiveor negative of the voltage. This magnetic field has a R−3 dependence, while the center of gravity of
Hg and UCN in the storage container diﬀers by 0.3 cm. This generates a systematic error via Hg comagnetometer. In the ILL experiment, this systematic error is called uncompensated B drift. Thissystematic error is inversely proportional to the distance from mu-metal surface [41][42][2]. In the ILL
experiment, mu-metal of diameter was 1.5 m. Therefore, its systematic error can be suppressed if thediameter of mu-metal is increased.
The strength of this dipole field was estimated to be ∼ 30 fT [83], and the magnitude of the systematic
error was evaluated as 3.4 × 10−27 e · cm [2]. If the error is suppressed by using the magnetometer, a
new fluxgate meter that can achieve accuracy 10 fT or better is needed.

I.4 v×E (Translation)
When UCNs collectively translate and an electrostatic field is curved in the storage container, a relativistic
magnetic field occurs oriented parallel/antiparallel to the static magnetic field. It depends on the directionof electric field application, so that mimic EDM signal occurs. The ILL experiment estimated it as
1×10−29 e · cm at most even if large [2].

I.5 v×E (Rotation)
When UCNs collectively rotate inside the storage container to which the curving electrostatic field
is applied, a relativistic magnetic field occurs behaving as mimic EDM signal. The evaluation valueof this systematic error have not been determined because the magnitude of this error diﬀers from2 × 10−27 e · cm ∼ 5 × 10−28 e·cm depending on the reference such as [41], [83] and [85]. Therefore, thisstudy evaluates the degree of this systematic error as below.
The systematic error due to rotational motion of UCNs and distortion of the electric field can beevaluated by the phase shift of the UCN spin precession using the following expression (I.1):

187

dv×E =

h̄Φ
4Et

(I.1)

where E is the strength of electric field, t is the measurement time, and Φ is the phase diﬀerence causedby the systematic error.

I.5.1 [Evaluation Condition]
Generally, this systematic error was determined by the degree of rotational motion of UCN and the degreeof distortion of the electric field. In addition, a non-specular reflection diﬀuses the collective rotationalmotion inside the container and suppress systematic errors. In this study, to determine systematic errors,
the degree of rotational motion, that of distortion of the electric field, and that of non-specular reflection
were assumed as follows:
Rotational motion
The rotational motion is thought to be caused by the setup misalignment. In this thesis, therotational collective motion was created assuming that the transport guide was moved by 10 mmlaterally relative to the center of ultracold neutron source.
Non-specular reflection
In this thesis, this systematic error suppression eﬀect was expressed by using Lambert’s cosine lawof formula (2.18) assuming probabilities of 0%, 1%, 5% and 10%.
Electric field distortion
Electric field distortion can be estimated by using Finite Element Calculation (FEM). In thisstudy, ANSYS simulation framework version 17 was used [86]. The electric field distortion wasdetermined by the position of the edge of the electrode and the misalignment of electrodes. In thisstudy, the degree of distortion was created as follows:(Edge position)
The container having three size electrodes of Φ 470 mm, Φ 600 mm and Φ 800 mm wereassumed on the finite element calculation. The result is shown in Figure I.1. As the electrodebecomes bigger, the electric field distortion decreases more.
(Misalignment of electrodes)
In this study, the condition of misalignment of electrodes was assumed in as shown Table I.1.
The degree of misalignment corresponds to three times of σ. which is the accuracy of thecommercially available leveling unit, 0.1 mm/m. For reference, the electric field obtained fromfinite element calculation is shown in the Figure I.2. It can be found that the electric fielddistortion occurs due to the misalignment of electrodes.

I.5.2 [Simulation Study]
In this study, the non-specular reflection occurring only in the storage duration, Φ 800 mm for theelectrode size, the cut-out time width from 2.15 s to 2.2 s are assumed, respectively. In addition, the188

tilt ID

top lidbottom lid

0

0

0

1

(3×0.1 mm/m×470 mm, 0)02(3×0.1 mm/m×470 mm/2, 0)(-3×0.1 mm/m×470 mm/2, 0)

3(3×0.1 mm/m×470 mm, 0)(0, 3×0.1 mm/m×470 mm)

Table.I.1 Non-parallelism condition of the electrodeR235xL120_ER300

1
200

10-1

150
100

10-2

50

10-3

0
-50

10-4

-100

10-5

-150
-200

Y (mm)Y (mm)

R235xL120_ER235

1
200

10-1

150
100

10-2

50

10-3

0
-50

10-4

-100

10-5

-150
-200

-200

-150

-100

-50

0

50

100

150

200
X (mm)

10-6

-200

-150

-100

-50

0

50

100

150

200
X (mm)

10-6

Y (mm)

R235xL120_ER400

1
200

10-1

150
100

10-2

50

10-3

0
-50

10-4

-100

10-5

-150
-200
-200

-150

-100

-50

0

50

100

150

200
X (mm)

10-6

Figure.I.1 Dependence of the radial direction component of the electric field, er , on the electroderadius, ER , was calculated by ANSYS. The graph corresponds to the cross-sectional view of thestorage container, and the color represents the magnitude of er . In this FEM calculation, the sizeof measurement cell is assumed to be the cylinder of 235 mm radius and 120 mm length, whereas
ER is assumed to be one of 235 mm (upper left), 300 mm(upper right), and 400 mm (lower left).

non-specular reflection probability is chosen to be one of 0%, 1%, 5% and 10%, while the degree of themisalignment of the storage container is chosen from Table I.1. In this way, the simulation to evaluate
the systematic error is performed as below. First, polarized UCNs are accumulated in the container for
50 s using the rebunch storage method in same manner as chapter 4.4.4. Second, the spin precession
continues to be calculated for 200 s assuming the storage region is the cylindrical configuration of Φ470
mm×L120 mm. Third, the additional spin phase shift, caused by the rotational motion and the distorted

189

R235xL120_ER400_tiltid1

1
200

10-1

150
100

Y (mm)Y (mm)

R235xL120_ER400_tiltid0

100

10-4

-100

10-5

-150
-200

10-2

50

10-3

0
-50

10-1

150

10-2

50

1
200

10-3

0
-50

10-4

-100

10-5

-150
-200

-200

-150

-100

-50

0

50

100

150

200
X (mm)

10-6

-200

-150

-50

0

50

100

150

200
X (mm)

10-6

R235xL120_ER400_tiltid3

1
200

10-1

150
100

10-2

50

10-3

0
-50

10-4

-100

10-5

-150
-200

Y (mm)Y (mm)

R235xL120_ER400_tiltid2

-100

1
200

10-1

150
100

10-2

50

10-3

0
-50

10-4

-100

10-5

-150
-200

-200

-150

-100

-50

0

50

100

150

200
X (mm)

10-6

-200

-150

-100

-50

0

50

100

150

200
X (mm)

10-6

Figure.I.2 The dependence of the radial direction component of the electric field, er , on nonparallelism of electrodes was calculated by ANSYS. The graph corresponds to the cross-sectionalview of the storage container, and the color represents the magnitude of the radial direction component of the electric field, er . The degree of non-parallelism is assumed to be one of ID in Table
I.1. Specifically, the upper left is tilt ID0, the upper right is tilt ID1, the lower left is tilt ID2, andthe lower right is tilt ID3. The size of measurement cell is assumed to be the cylinder of 235 mm
radius and 120 mm length, whereas the electrode radius ER is assumed to be 400 mm.

electric field, is evaluated at the end of 200 s storage duration. Finally, the systematic error is evaluatedwith the expression (I.1) by using the same method as described in the document [21][82].
The obtained result is shown in Figure I.3. The vertical axis is the systematic error evaluated, thehorizontal axis is the index of the non-specular reflection probability, the black line is the average valueof false EDM, and the red line is the error of the average value of false EDM. For the case that thenon-specular reflection probability is 0, the systematic error amounts to O(1 × 10−26 e · cm). On theother hand, for the other cases, it was suppressed to 1 × 10−28 e · cm or less. Therefore, systematic
uncertainty due to v×E (Rotation) can be suppressed if the non-specular reflection probability of morethan 1%. Figure 2.8 shows that the non-specular reflection probability can be 1% or more if surface
roughness is several nm. Obviously, it is easy to satisfy this requirement. Hence, it is concluded thatthe systematic error of v×E (Rotation) can easily be reduced to 1 × 10−28 e · cm or less in J-PARC P33
experiment. Therefore, in this study, the magnitude of the systematic error due to v×E (Rotation) was

190

evaluated as 1 × 10−28 e · cm for conservative evaluation.
R235xL120_ER400_tiltid1

false EDM (e•cm)

false EDM (e•cm)

R235xL120_ER400_tiltid0

-26

10

-26

10

10-27

10-27

-28

10

-28

-29

10

10

-29

10

0

0.02

0.04

0.06

0.08

0.1

0.12

0

0.02

0.04

0.06

diffuse probability

0.1

0.12

R235xL120_ER400_tiltid3

false EDM (e•cm)

R235xL120_ER400_tiltid2

false EDM (e•cm)

0.08

diffuse probability

-26

10

-26

10

10-27

10-27

-28

10

-28

-29

10

10

-29

10

0

0.02

0.04

0.06

0.08

0.1

0.12

0

0.02

diffuse probability

0.04

0.06

0.08

0.1

0.12

diffuse probability

Figure.I.3 Analysis result of false EDM due to v×E (rotation). The horizontal axis represents theidentification number of the surface roughness, and the vertical axis represents the magnitude of
the systematic error, the black circle point is the calculated systematic errors, and the red squarepoint is the error of the calculated systematic errors. Each pad corresponds to one of the degree of
non-parallelism specified in Table I.1. Specifically, the upper left corresponds to tilt ID0, the upper
right corresponds to tilt ID1, the lower left corresponds to tilt ID2, and the lower right corresponds
to tilt ID3. The size of measurement cell is assumed to be the cylinder of 235 mm radius and 120
mm length, whereas the electrode radius is assumed to be 400 mm.

I.6 Light shift (indirect)
When precessing 199 Hg is illuminated by non-resonant light, the atomic energy level shift becomes
broader, which results in changing the Larmor precession frequency [87].
Generally, the above-mentioned change of the precession frequency is caused by the following fictitious
magnetic field, Beﬀ [87][83].
B⃗eﬀ ∝ Beﬀ (I, ω)⃗k(I.2)

where, ⃗k is a unit vector of the propagation direction for incident light, and I and ω are the intensity andthe frequency of incident circularly polarized light, respectively. In general, the incident light angle in thevertical plane, α, used for monitoring Hg co-magnetometer has misalignment, dα. Therefore, at EDM
measurement, 199 Hg atoms feel the extra magnetic field Badd = Beﬀ sin (dα) applied along the vertical191

direction. As a result, the magnitude of the magnetic field becomes diﬀerent by Badd in crossing point
analysis, which results in a systematic error. In the ILL experiment, this systematic error is referred toas indirect light shift. The magnitude of indirect light shift depends on the intensity of incident light.
In the ILL experiment, an indirect light shift was corrected by run-by-run by using the correspondence
relation between incident light intensity and Ra − 1 of crossing point analysis. As a result, the systematic
error can be reduced to 0.8 × 10−27 e · cm after the correction [41][2].

I.7 Light shift (direct)
In the ILL experiment, it was confirmed that there was a correlation between the incident light intensityof the 204 Hg lamp and the direction of the applied electric field. Obviously, a systematic error occurs dueto the mechanism through the second term of the equation (3.2). In the ILL experiment, this systematic
error is referred as to direct light shift and it was estimated to be 2 × 10−28 e · cm [41][2].

I.8 Hg EDM
There is room for Hg to produce EDM. If there is EDM in Hg, the precession cycle of co-magnetometer has
dependence on the direction of the electric field, resulting in a systematic error. In the ILL experiment,
the magnitude of this systematic error was estimated as (2 ± 6) × 10−29 e · cm [41][2]. It is noted that2 × 10−29 e·cm is not the term regarded as an error, but correction term.

I.9 Leakage current
When a voltage is applied between the top and bottom lids of the storage container, a systematic error
occurs due to the magnetic field that a leakage current causes. In the ILL experiment, the magnitude of
the systematic error was estimated to be less than to 1 × 10−28 e · cm [41][2].

I.10 Electric force
Because the storage container becomes squeezed by applying the electric field, the perfect parallelism of
the electric field and the magnetic field lose, which result in a systematic error. In the ILL experiment,
the degree of the systematic error was estimated to be 4 × 10−28 e · cm [41]. Actually, the magnitude ofthis systematic error was confirmed to be less than 3 × 10−35 e · cm by actual measurement using thephoto detector [83].

I.11 HV AC ripple
During measurement of the neutron EDM, it is necessary to turn on and oﬀ HV. At that time alternative
current by ripple generates a magnetic field and systematic error is caused. In the ILL experiment, its
contribution was estimated to be 1 × 10−29 e·cm [41][2]. The magnitude of this error is proportional tothe applied voltage.
192

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