First measurements of the vertical beam size with an X-ray beam size monitor in SuperKEKB rings

Accepted Manuscript First measurements of the vertical beam size with an X-ray beam size monitor in SuperKEKB rings Emy Mulyani, John Flanagan, Makoto Tobiyama, Hitoshi Fukuma, Hitomi Ikeda, Gaku Mitsuka

PII: DOI: Reference:

S0168-9002(18)31768-6 https://doi.org/10.1016/j.nima.2018.11.116 NIMA 61657

To appear in:

Nuclear Inst. and Methods in Physics Research, A

Received date : 27 March 2018 Revised date : 23 November 2018 Accepted date : 26 November 2018 Please cite this article as: E. Mulyani, J. Flanagan, M. Tobiyama et al., First measurements of the vertical beam size with an X-ray beam size monitor in SuperKEKB rings, Nuclear Inst. and Methods in Physics Research, A (2018), https://doi.org/10.1016/j.nima.2018.11.116 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

2

First Measurements of the Vertical Beam Size with an X-Ray Beam Size Monitor in SuperKEKB Rings

3

Emy Mulyani

1

4 5 6 7 8 9 10 11 12

13

a,b

, John Flanagan

a,c

, Makoto Tobiyama a,c , Hitoshi Fukuma c , Hitomi Ikeda Mitsuka a,c

a,c

, Gaku

a School

of High Energy Accelerator Science, The Graduate University for Advanced Studies (SOKENDAI) 1-1 Oho Tsukuba Ibaraki 305-0801 Japan b Center for Accelerator Science and Technology, National Nuclear Energy Agency (BATAN) Jl. Babarsari, Yogyakarta 55281, Indonesia c Accelerator Laboratory, High Energy Accelerator Research Organization (KEK) 1-1 Oho Tsukuba Ibaraki 305-0801 Japan [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]

Abstract This paper reports first measurements of the vertical beam size using an X-Ray Beam Size Monitor (XRM) for each of the SuperKEKB rings (Low Energy Ring, LER, and High Energy Ring, HER) during Phase 1 and 2 commissioning of SuperKEKB. The XRM device is dedicated to measuring the e− /e+ vertical beam size using X-ray synchrotron radiation, and will eventually have the capability for single-shot (single bunch, single turn) measurements. The preparation of a deep Si detector and high-speed readout electronics for single-shot measurements is underway. In the meantime for Phase 1 and 2, we used a scintillator screen and CCD camera for multi-bunch measurements. The XRM has been installed in each ring and images X-rays from a bending magnet that pass through optical elements (a single pinhole and coded apertures). Several studies (geometrical scale factors, emittance control knob, and beam lifetime study) were carried out during the commissioning. In Phase 1 (February - June 2016), the measured vertical emittances εy are ∼10 pm for LER (consistent with the optical estimation) and ∼ 35 pm for HER (3.5 × greater than the optical estimation). Analysis of the beam size and lifetime measurements suggests unexpectedly large point spread functions (PSF), particularly in the HER. The spatial resolution of the imaging system (defect of focus, diffraction, and spherical aberration) and scattering in the beamline (EGS5 simulation) contribute ∼ 6 µm of PSF, which does not adequately account for the observed PSF. The Phase 2 commissioning commenced in May - July 2018, with thinner Be filters, new optical elements, scintillator, and CCD camera with the purpose to reduce the PSF in HER. The Phase 2 study results suggest the PSF σs ∼ 6.6 µm in HER (corresponding to the spatial resolution of the imaging system and scattering in the beamline), which is ∼ 5 × smaller than in Phase 1. The overall performances of XRMs in LER and HER are accurate. The XRM in LER will be able to measure the design beam size at the zero current (14 µm). For the HER, the

PSF that we observed during the Phase 2 indicates that the minimum measured beam size corresponds to the emittance at the design current (12.9 pm) and the XRM will be able to measure the design beam size 1

at the zero current ( 7 µm). 14

Keywords: SuperKEKB, X-ray beam size monitor, vertical beam size, pinhole, coded aperture,

15

synchrotron radiation

16

1. Introduction

17

The SuperKEKB accelerator is a double-ring collider with asymmetric energy; the positron beam energy

18

(Low Energy Ring, LER) is 4 GeV, and the electron beam energy (High Energy Ring, HER) is 7 GeV.

19

The target for the SuperKEKB luminosity L is 8 × 1035 cm−2 s−1 , some 40 times larger than that of its

20

predecessor (KEKB), and the overarching mission is to support high-energy physics research programs.

21

The fundamental parameters of SuperKEKB were chosen based on the concept of the ’nano-beam scheme’

22

developed by P. Raimondi for the SuperB factory in Italy [1]. The basic idea of the nano-beam scheme is to

23

squeeze the vertical beta function at the interaction point (IP) and minimize the overlap region of the two

24

beams.

25

The nano-beam scheme uses a large crossing angle (2φ) and small beam spot size in both directions.

26

To achieve 40-times luminosity, SuperKEKB has 1/20 the vertical beta function and twice the beam current

27

of KEKB, with the same vertical beam–beam parameter of ∼ 0.09. Table 1 [2–5] lists the final machine

28

parameters of SuperKEKB.

29

In the SuperKEKB collider, the beam size must be precisely measured, as this plays an essential role

30

in determining the luminosity. Various techniques have been used to measure the beam size, such as a

31

Synchrotron Radiation (SR) interferometer using visible light [6, 7] and X-ray imaging with a pinhole

32

camera [8, 9].

33

When the LER and HER beams achieve their targeted emittances (see Table 1), the vertical beam sizes

34

at the monitor source points are less than 18 µm in both rings. The resolution of the SR interferometer is

35

fundamentally limited by the measurement wavelength λ and the opening angle between slits as seen from

36

the beam source point, as well as the maximum visibility (fringe modulation) that can be reliably measured.

37

The opening angle is in principle limited by the SR opening angle and by mechanical considerations, with the

38

latter being the dominant restriction at SuperKEKB; the mirrors are located in antechambers to minimize

39

Higher Order Mode (HOM) losses, with the height of the antechambers limited by the pole gap of upstream

40

quadrupole magnets to 24 mm in height. The mirrors are located at a distance of 24.5 (23.5) m downstream

41

of the source point in the LER (HER), so with a maximum effective slit separation of 20 mm at the mirror

42

location, the slits opening angle is 0.8 (0.9) mrad in the LER (HER).

43

For a 400 nm measurement wavelength, it would be necessary to be able to measure visibilities of

44

around 98% to measure the vertical beam sizes at the source points, which is extremely challenging. In

45

the horizontal direction, the beam sizes are 10 times (or more) larger than those in the vertical direction, Preprint submitted to Nucl. Instrum. Methods in Phys. Res., Sect. A

November 23, 2018

Table 1: Final machine parameters of SuperKEKB,

Parameter

∗

indicates values at the interaction point (IP).

LER (e+ )

HER (e− )

Unit

Beam energy

E

4.000

7.007

GeV

Beam current

I

3.6

2.6

A

Bunches current

Ib

1.44

1.04

mA

Number of bunches/rings

nb

2,500

Circumference

C

3,016.315

m

Half crossing angle

φ

41.5

mrad

Horizontal emittance

εx

3.2 (1.9)

4.68 (4.4)

nm

():zero current >

Vertical emittance

εy

8.64 (2.8)

12.9 (1.5)

pm

():zero current >

32

25

mm

∗

Horizontal β function

βx

Vertical β function

βy ∗

0.27

0.30

mm

Horizontal beam size

σx

∗

10

11

µm

Vertical beam size

σy ∗

48

62

nm

Bunch length

σz

6 (4.7)

5 (4.9)

mm

Luminosity

L

Beam–beam parameter

ξy

cm−2 s−1

8 × 1035 0.088

():zero current

0.082

> zero current means the emittance value does not include enlargement of the emittance due to the intra-beam scattering which is significant at high bunch current.

46

so the required measurable maximum visibility is more reasonable than in the vertical direction (around

47

90%) [4]. Furthermore the SR interferometer will not be adequate for single-shot (bunch-by-bunch, turn-by-

48

turn) measurements, which are useful for studying beam instabilities, because of limited photon statistics

49

at short integration times.

50

An X-ray Beam Size Monitor (XRM) [10] based on a coded aperture (CA) [11] is being developed

51

for SuperKEKB. The longterm aim of XRM is to provide high-resolution bunch-by-bunch, turn-by-turn

52

measurements for low-emittance tuning, collision tuning, and instability measurements. The bunch-by-

53

bunch, turn-by-turn vertical beam size measurements using a coded aperture have been achieved at CESR

54

using the XBSM [12]. The preparations of a deep Si detector and high-speed readout electronics for single-

55

shot measurements using XRM are underway. In the meantime for Phase 1 and 2, we used a scintillator screen

56

and CCD camera for multi-shot measurements. CA imaging was initially developed by X-ray astronomers

57

using a pattern mask to modulate the incoming light. The projected image is then decoded using the known

58

mask pattern, allowing the original image to be reconstructed. The large open aperture provides much higher 3

59

photon throughput than a single pinhole, allowing better photon statistics in single-shot measurements.

60

Accordingly, there are two types of SR monitor on each SuperKEKB ring: visible SR interferometers,

61

primarily used for horizontal beam size measurements, and XRM, primarily used for the vertical beam size

62

measurements.

63

The Phase 1 commissioning of SuperKEKB operations commenced in February 2016 and lasted approx-

64

imately five months (until June 2016); the machine parameters are presented in Table 2 [2, 13]. An XRM

65

was installed in each of the SuperKEKB rings, and several studies were carried out during the commission-

66

ing process. This paper describes the XRM conceptual basis in Section 2, the apparatus for the Phase 1

67

commissioning of SuperKEKB in Section 3, Phase 1 commissioning in Section 4, and Phase 2 commissioning

68

in Section 5. A brief conclusion of the work to date is given in Section 6. Table 2: Machine parameters in Phase 1 commissioning of SuperKEKB.

Machine parameter

LER (e+ )

HER (e− )

Unit

Beam energy

E

4.000

7.007

GeV

Max. beam current

I

1.01

0.87

A

Max. number of bunches

nb

2363

2455

Horizontal emittance (optics estimation)

εx

1.8

4.6

nm

Vertical emittance (optics estimation)

εy

10

10

pm

Bunch length

σz

4.6

5.3

mm

βy,source

67.4

7.6

m

σy,source

∼ 25

∼9

µm

Vertical emittance/(bump-height) squared

∆εy

70.21 ± 0.03

42.19 ± 0.10

pm/mm2

Change in vertical dispersion/bump-height

ηy,source

0.056

0.017

m/mm

σp

7.7 × 10−4

6.3 × 10−4

σz (Ib )

4.58+0.59Ib

5.34+0.88Ib

nb

1576

1576

XRM parameter during measurements Beta function at XRM source point Vertical beam size at XRM source point (based on optics estimation)

Momentum spread Bunch length as a function of bunch current Number of bunches/ring

69

mm

2. Methods and tools

70

Each of the SuperKEKB rings has four straight-sections and four arc-sections. The X-ray sources are

71

the final arc-sections, located immediately upstream of the straight-sections in Fuji (LER) and Oho (HER).

72

The XRM installation images X-rays from a bending magnet through an optical element onto a detector. 4

73

A schematic and the parameters of the beamline are shown in Fig. 1 and Table 3, respectively. This section

74

reviews the conceptual design principles of the XRM.

Scintillator screen

Figure 1: Schematic of the XRM beamline at each ring (not to scale). Each XRM consists of a beryllium filter placed upstream of the optics to reduce the heat load, three sets of optical elements (a single pinhole and two sets of coded apertures), a beryllium window, and a 141-µm-thick scintillator with a CCD camera focused on the scintillator as an imaging system. The scintillator screen is tilted 45° in the horizontal plane, so that the camera and lens are out of the way beam.

Table 3: XRM beamline parameters,

†

indicate values at the Phase 1 commissioning.

Parameter

HER (e− )

Unit

Radius of source bend

ρ

31.85

105.98

m

Distance from source to optic

L

9.47

10.26

m

Distance from optic to Be window

L0

31.79

32.69

m

Thickness of Be filter

T

†

Thickness of Be window

T0

†

mm

0.2

0.2

mm

Thickness of Au

20

20

µm

Thickness of Diamond

600

600

Air gap

f

Effective thickness of scintillator (YAG:Ce † )

75

LER (e+ )

0.5

16

†

µm

100

mm

141

µm

2.1. X-ray spectrum of synchrotron radiation The design of the optical and detector elements in the XRM depends on the X-ray spectrum of SR produced by the bending magnet. The angular density of the spectral flux is defined as [14]      d2 Fσ    dθdψ     2      = α ∆ω I |Aσ,π (ω)|2 = 3α γ 2 ∆ω I ω (1 + X2 )2     2 ω e 4π ω e ωc     d2 Fπ   dθdψ

5

   .   2  2 X K (η) 2 1/3 1+X K2/3 2 (η)

(1)

where θ is the horizontal angle, ψ is the observation angle in the vertical plane, I is the accelerator beam current, ωc is the critical frequency, ω is the angular frequency of the photon, α is the fine-structure constant (α = e2 /4πε0 ~c = 1/137), Aσ,π are the components of the wavefront amplitude of the SR, and K is a modified Bessel function. The σ- and π- components are horizontal and vertical polarizations, respectively. The variables η, X, and ωc are defined as η=


3 1 ω 1 + X2 2 , 2 ωc X = γψ,

ωc =

3γ 3 c , 2ρ

(2)

76

where γ is the Lorentz factor for a particle, c is the speed of light, and ρ is the radius of instantaneous

77

curvature of the electron trajectory. In the plane of the bending magnet (ψ=0), the flux for the π-component

78

vanishes. In practical units (photons/s/mrad2 /0. 1%BW], the spectral flux becomes [14]

where

d2 F = 1.33 × 1013 Ee 2 [GeV]I[A]H2 (ω/ωc ), d2 Ω ψ=0 H2 (y) = y 2 K2/3 2 (y/2).

(3)

(4)

79

When normalized to 0.1% BW, the bending magnet radiation has a smooth spectral distribution with a

80

broad maximum near the critical frequency ωc . The critical photon energies corresponding to ωc , Ec = }ωc

81

(} = Planck’s constant), are 4.4 and 7.2 keV for LER and HER, respectively. The spectral distribution for

82

the SR from the bending magnet (at ψ = 0) for LER and HER are shown in Fig. 2.

Figure 2: Spectral distribution of SR from bending magnet for LER and HER in linear scale (left) and log scale (right). The critical energies are 4.4 and 7.2 keV for LER and HER, respectively. The critical energy corresponds to critical frequency ωc , and divides the spectrum into two parts of equal radiated power: 50% of the total power is radiated at frequencies lower than ωc and 50% is radiated at frequencies higher than ωc (Colour on-line).

6

83

Photons from the bending magnet pass through the XRM beamline and interact with beamline materials

84

(beryllium, air, diamond, and gold) before reaching the detector. The optical element contains diamond

85

and gold; the reason for their use will be explained in Subsection 2.3. The interactions lead to absorption

86

or transmission through the materials; i.e., photons may give their energy to the material (absorption) or

87

may not interact with the material structure (transmission). Figure 3 shows the energy spectrum of photons

88

after passing through the XRM beamline for LER and HER.

Figure 3: Spectral distribution of SR after passing through all elements in the XRM beamline (beryllium, diamond, gold, and air) for LER (left) and HER (right). The gold (Au) has a larger attenuation coefficient than the other materials (Colour on-line).

89

2.2. Image simulation using the Point Spread Function After passing through an optical element, the X-rays from a point source form a diffraction pattern with peaks on the detector depending on the pattern of the optical element. This pattern is the point spread function (PSF), i.e., the expected X-ray intensity distribution at the observation plane for a given X-ray spectrum, beamline geometry, and optical elements due to a mathematical ’point source’. We use a Fresnel– Kirchhoff diffraction approximation to estimate propagation of the X-ray distribution from the SR source to the detector. For a one-dimensional mask as has been described in Fig. 1, the path integral in the vertical direction on the mask leads to Aσ,π( detector)

iAσ,π(source) = λ

Z

mask

t(ym ) i 2π (r1 +r2 ) e λ r1 r2



cosθ1 + cosθ2 2



dym ,

(5)

90

where Aσ,π(source) is the (angle-dependent) amplitude of the wave at the source point, λ is the wavelength,

91

and ym is the vertical coordinates at the mask. {r1 , θ1 } are the distance and angle from the source point

92

to the mask point at ym , and {r2 , θ2 } are the distance and angle from the mask point ym to the detector

93

point yd , respectively. t(ym ) is the complex transmission function at the mask point ym . The complex

94

transmission is represented as t(ym ) = T (ym )eiδ(ym ) , where T is the real transmission and δ is the phase

95

shift due to passing through the mask at ym . 7

96

For each pixel in the detector, the wavefront amplitude from each source point is calculated and converted

97

to the detected flux using Eqs. 1 and 5, respectively. The angular density of the spectral flux (number of

98

radiated photons per unit time) at the detector is then defined as 



2   Z ∆ω I iAσ,π(source) t(ym ) i 2π (r1 +r2 ) cosθ1 + cosθ2 λ e dy =α m . ω e λ 2  mask r1 r2

2 Fσ   ddθdψ  

 

d2 Fπ dθdψ

(6)

99

The synchrotron radiation field emission is incoherent, so the weighted flux contributions from all source

100

points are then summed over the source distribution. This process is repeated over the detectable spectral

101

range, taking into account the response properties of the detector. By varying the width of the Gaussian

102

distribution and comparing the resulting (measured) image against the data templates, the Gaussian source

103

profile can be reconstructed.

104

A large number of 1-dimensional templates corresponding to different values of the initial source param-

105

eters are pre-calculated, and the measured coded image is compared to each of the templates, searching for

106

a best-fit using a least-squares method. The variable parameters for the pre-calculated templates include

107

the beam size, normalization of the intensity, pedestal, offset of mask relative to the detector, and offset of

108

the source relative to the detector. It takes one day to calculate a full set of detector images (PSFs), from

109

which the template images are later constructed. Typically, some 1 million templates have been utilized for

110

fitting images obtained at XRM, taking less than 10 minutes to generate. In the fitting process, the number

111

of free parameters and their steps is generally limited to what we can process in 1 second.

112

At low intensities, the single-shot resolution of the system is limited by statistical fluctuations in the

113

number of detected photons. To estimate the resolution as a function of beam size, simulated images are

114

calculated for Gaussian beams of various sizes. The simulated detector images for different-sized beams are

115

then compared pair-wise against each other, with one image in a pair representing a measured image for

116

known beam size, and the other image representing a proposed model. The differences between the two

117

images in signal heights for each detector channel are used to evaluate the χ2 per degree of freedom v for

118

this fit [15] N

X [si 0 − si ] χ2 1 = , v N − n − 1 i=1 σi 2

119

120

121

2

(7)

where N is the number of detector channels (pixels), and n is the number of fit parameters. The residual weighting σi for a channel is taken to be proportional to the square root of the signal height (number of √ photons) in that channel si (σi = si ). For a 128-pixel linear detector, the number of degrees of freedom

122

v (N − n − 1) is then taken to be 126. The signal height in each channel is set to the number of expected

123

number of photons detected in that channel for a given bunch intensity. More explicitly, the average number 8

124

of photons per pixel at the detector is calculated, and the simulated image is normalized so that the average

125

signal height is equal to np . Finally, the value of χ2 /v that corresponds to a confidence interval of 68% is

126

chosen to represent the 1-σ confidence interval. The resolution is then defined as the change in the beam size, where the increment of χ2 /v = 1. An example of a χ2 /v map is shown in Fig. 4.

Figure 4: The resolution is defined where the increment of

χ2/v

= 1. The narrower

χ2/v

= 1 distribution around the y = x line,

the better statistical resolution that we achieve. The resolution chart can be calculated by comparing each beam size in x and y axes at

χ2/v

= 1, for example at 20 µm beam size, the resolution is a distance between O’ and O (Colour on-line).

127

128

2.3. Optical element design

129

Two types of optical elements were used during the Phase 1 commissioning: a single pinhole and CAs

130

(multi-slits and a Uniformly Redundant Array, URA [16]). Table 4 lists the parameters and specifications for

131

each of the optical elements. CAs offer a greater open aperture than a single pinhole and better statistical

132

resolution for single-shot measurements. The concept of CAs is for a pseudo-random array of pinholes

133

(apertures) to project a mosaic of pinhole images onto a detector. The detector image is then decoded

134

using the known mask pattern to reconstruct the original image. Image reconstruction to estimate the beam

135

size can be done by deconvolution (e.g., inverse Fourier transform or direct deconvolution), however the

136

deconvolution of the ’coded aperture’ to restore the original image is difficult. This difficulty is due to issues

137

of dealing with background and detector noise, diffraction effects, and also the non-uniform intensity profile

138

of the incident beam. These effects are not accounted for in the direct reconstruction methods.

139

An alternative method of analyzing the coded aperture image is used in order to extract the beam

140

parameters. Models/templates of the expected flux seen through the coded aperture are produced for several

141

initial beam parameters. The measured X-ray flux at the detector is then compared to those templates

142

(fitting method) as has been explained in Subsection 2.2. An example of a CA pattern is URA, which has

143

been successfully tested for beam size measurements at CesrTA [17] and DLS [18]. In this section, we discuss

144

the characteristics of each optical element and relevant design considerations. 9

Table 4: Parameters of the optical elements for Phase 1 commissioning.

Optical element

Parameter

Value

PH (pinhole)

width

33 µm

Multi-slits

Diamond thickness

600 µm

Au thickness

20 µm

Number of slits

17

Pattern, S=slit, M=Au mask (µm) 33S-22M-33S-66M-33S-22M-33S-110M-33S-22M-33S-44M-33S-22M-33S-198M33S-22M-33S-44M-33S-22M-33S-66M-33S-22M-33S-44M-33S-22M-33S-110M-33S

URA

Diamond thickness

600 µm

Au thickness

20 µm

Number of slits

12

Pattern, S=slit, M=Au mask (µm) 66S-33M-66S-99M-33S-33M-33S-33M-66S-132M-33S-165M-132S-33M-132S-66M -33S-33M-33S-33M-99S-66M-33S

145

The optical elements in the XRM consist of 20-µm-thick gold masking material on 600-µm-thick diamond

146

substrates. The diamond substrate mask is more robust than silicon because of better heat conduction

147

providing better tolerance to the LER and HER power densities [19]. Subsections 2.3.1 and 2.3.2 explain

148

the pinhole and CA design procedures.

149

2.3.1. Optimizing the pinhole (single slit) size

150

The pinhole size is optimized by simulating detector images for a point source in both rings using various

151

pinhole (slit) sizes with a trade-off between diffraction effects and geometric smearing to achieve the best

152

resolution. Then a Gaussian distribution was fitted to the simulated detector image to obtain the standard

153

deviation. The minimum standard deviation of the resulting detector images was found to be 33 µm for

154

LER and 30 µm for HER, as shown in Fig. 5. Eventually, we prefer to use an identical system with 33 µm

155

as the optimum pinhole size for both rings.

156

2.3.2. Design of CA multi-slits

157

Pairs of 33 µm slits were simulated with different separations between the pairs. For each separation, we

158

calculated the resolution curves for different beam sizes using Eq. 7, as in Fig. 6, to determine the resolution

159

of each range of beam sizes. We optimized the resolution at the smallest beam sizes, then used a large 10

Figure 5: Standard deviation of images for various slit widths for LER and HER. The 33 µm slit size was taken as the optimum slit and basic size for both rings (Colour on-line).

160

spacing to cover larger beam sizes. The 22 µm slit separation size was optimal for small beam sizes, so we

161

used this for the design.

Figure 6: Pairs of 33 µm slits were simulated with different separations between the pairs (16, 20, 21, 22, 25, 33, and 50 µm). The 22 µm slit separation size is optimal for small beam sizes (Colour on-line).

162

A series of multi-slit patterns were devised, using a suitable range of slit separations to cover the dynamics

163

of interest. Figure 7 shows some examples of the multi-slit patterns along with their resolutions, which were

164

quantized into 0.5 µm step sizes. The resolution is defined as the change in beam size, where ∆(χ /v)=1

165

(see Eq. 7), for a given number of photons. In general, more slits are better for photon statistics, but large

166

beam sizes require large slit separations to maintain the resolution. For aperture reasons, the mask pattern

167

width in our XRM system should be less than 2 mm. Thus, the best resolution was found to have 17 slits

168

with the pattern listed in Table 4. Additionally, the 12-slit URA pattern was calculated using 33 µm as the

169

basic size. Figures 8 and 9 show the final patterns and a 1000× magnification under a Scanning Electron

170

Microscope of all three optical elements.

2

171

For the optical element design, a PSF image simulation was applied without noise using 128 channels 11

Figure 7: Series of multi-slit patterns with their resolutions. The spacing size for 15-, 16-, 17.ver1-,and 17.ver2-slits was 13151911319151, 131517191315171, 1213151272151311, and 1315121912131215, respectively. A spacing size of 1 means 22 µm, 2 means 44 µm, 3 means 66 µm, and so on. The 17.ver2-slits achieve better resolution than the others with the small beam sizes that we are interested in (<30 µm) (Colour on-line).

(a) Pinhole

(b) Multi-slits

(c) URA

Figure 8: Mask pattern (a) pinhole, (b) 17 multi-slits, and (c) 12-slits URA for both rings. The mask consists of 20-µm-thick gold masking material on 600-µm-thick diamond substrates.

Figure 9: Three types of optical elements imaged using a 1000× Scanning Electron Microscope: (left) pinhole, (middle) multi-slits, and (right) URA.

172

(pixels) of silicon with 2 mm sensing depth and a pixel pitch of 50 µm (as a detector system that will be

173

used for single-shot measurements). Figures 10 and 11 show simulated detector images for all mask patterns

174

under ideal conditions from LER and HER where the number of photons in LER and HER detectors are

175

1943 and 3342 photons/turn/mA/bunch, respectively. Equation 7 defines the resolution as the change in

176

beam size where the increment of χ2 per degree of freedom (χ /v) = 1, and Figs. 12, 13 show the contours of

177

χ2/v

178

we can achieve. Fig. 14 shows the statistical resolution for all optical elements in both rings, calculated by

2

for both rings. The narrower the distribution around the y = x line, the better statistical resolution that

12

2

179

comparing each beam size along the x- and the y-axes of Figs. 12, 13 at ∆(χ /v) = 1. As expected the coded

180

apertures show the superiority in resolution compare to the pinhole. The multi-slit elements are estimated

181

to provide 2 – 3 µm resolution for 10 – 25 µm vertical beam sizes in both rings at 1 mA bunch current, as

182

shown in Fig. 14. For larger beam sizes (> 30 µm), the 12-slits URA mask has better resolution than the

183

17 multi-slits.

2000 1500 1000

2000 1500 1000

500

500

0

0

0

20

40

60

80

100

120

140

3000

1µm 10µm 25µm 50µm 100µm 150µm 200µm 300µm 450µm

2500 photon/pixel

photon/pixel

3000

1µm 10µm 25µm 50µm 100µm 150µm 200µm 300µm 450µm

2500

1µm 10µm 25µm 50µm 100µm 150µm 200µm 300µm 450µm

2500 photon/pixel

3000

2000 1500 1000 500

0

20

40

60

pixel

80

100

120

0

140

0

20

40

60

pixel

(a) Pinhole

80

100

120

140

pixel

(b) Multi-slits

(c) URA

Figure 10: Simulated detector images showing the number of photons/pixel for single-pass 1 mA bunches for different beam sizes in LER. A series of detector image templates are generated for a range of beam sizes, and these are then compared with the data to find the closest match. (a) Pinhole mask, (b) multi-slits mask consisting of 17 peaks, and (c) URA mask consisting of 12 peaks. The number of peaks represents the number of slits that allow light to pass through (Colour on-line).

3000 2500 2000 1500 1000

3500

0

3000 2500 2000 1500 1000

500

4500

1µm 10µm 25µm 50µm 100µm 150µm 200µm 300µm 450µm

4000

photon/pixel

3500 photon/pixel

4500

1µm 10µm 25µm 50µm 100µm 150µm 200µm 300µm 450µm

4000

3500

20

40

60

80 pixel

(a) Pinhole

100

120

140

0

3000 2500 2000 1500 1000

500 0

1µm 10µm 25µm 50µm 100µm 150µm 200µm 300µm 450µm

4000

photon/pixel

4500

500 0

20

40

60

80 pixel

(b) Multi-slits

100

120

140

0

0

20

40

60

80

100

120

140

pixel

(c) URA

Figure 11: Simulated detector images showing the number of photons/pixel for single-pass 1 mA bunches for different beam sizes in HER. A series of detector image templates are generated for a range of beam sizes, and these are then compared with the data to find the closest match. (a) Pinhole mask, (b) multi-slits mask consisting of 17 peaks, and (c) URA mask consisting of 12 peaks. The number of peaks represents the number of slits that allow light to pass through (Colour on-line).

184

3. Apparatus

185

Two XRM diagnostic beamlines have been installed at SuperKEKB for electrons (HER) and for positrons

186

(LER). They are identical, differing only in the distance from the source to the optics and from the optics

187

to the detectors, and the thickness of the beryllium filters (L, L0 , and T , respectively, in Fig. 1), with the

188

values given in Table 3. Each apparatus consists of three primary components: beamline, optical elements,

189

and detector. 13

(a) Pinhole Figure 12: Calculated

χ2/v

(b) Multi-slits

(c) URA

contours for each mask in LER at single-pass 1 mA bunch current. The resolution was calculated

by comparing the x- and y-axes (beam sizes) at the point where ∆(χ2/v) = 1. The narrower

χ2/v

= 1 distribution around the

y = x line (blue area), the better statistical resolution that we achieve. The coded apertures show the superiority in statistical resolution compare to the pinhole (Colour on-line).

(a) Pinhole Figure 13: Calculated

χ2/v

(b) Multi-slits

(c) URA

contours for each mask in HER at single-pass 1 mA bunch current. The resolution was calculated

by comparing the x- and y-axes (beam sizes) at the point where ∆(χ2/v) = 1. The narrower

χ2/v

= 1 distribution around the

y = x line (blue area), the better statistical resolution that we achieve. The coded apertures show the superiority in statistical resolution compare to the pinhole (Colour on-line).

190

3.1. Beamline

191

Figures 15, 16 [20], and Table 3 show the layout and parameters for each of the beamlines, respectively.

192

In each case, the distance from the source point to the detector is ∼ 40 m. The optical elements are placed

193

in optics boxes ∼ 9 – 10 meter from the source point, so that the geometrical magnification factor is ∼ 3×

194

for both lines. The beamlines are connected directly to the ring vacuum system. A gate valve is located

195

upstream of the optics boxes for isolation during vacuum work downstream of the beamlines, or in the

196

event of vacuum leaks. The X-rays from the upstream bending magnet go through the beryllium filter and

197

optical elements, then propagate down the beamline toward the detector. Screen monitors are installed

198

on the downstream ends of the beamlines, midway between the optic boxes and detector for beam-based

199

alignment.

14

HER HER

single-slit URA multi-slits

Resolution [µm]

10 200 single-slit 180 160 8 20 URA 20 140 multi-slits single-slit single-slit 15 120 6 15 URA URA 100 multi-slits 10 multi-slits 80 4 10 60 5 40 2 5 20 0 5 10 00 0 00 5 50 10 100

20 25 30 20 Beam 200 25 250 30 size [µm]

35 30035

LER LER

15 15

20 25 30 20 Beam25 30 size [µm]

40 35040

45 400 45

50 450 50

single-slit URA multi-slits

Resolution [µm]

20 single-slit 18 URA 16 20 15 20 multi-slits single-slit single-slit 14 15 15 URA URA 12 10 multi-slits 10 10 multi-slits 10 8 5 5 6 5 4 0 0 5 10 2 0 0 5 10

15 15 150

35 35

40 40

45 45

50 50

Figure 14: Single-bunch, single-turn vertical beam size resolutions for 1 mA bunch current in LER and HER for each optical element (pinhole, multi-slits, and URA) calculated by comparing each beam size in x- and y-axes of Figs. 12, 13 at ∆(χ2/v) = 1. The 17 multi-slits is estimated to provide 2 – 3 µm resolution for 10 – 25 µm vertical beam sizes at 1 mA bunches. For larger beam sizes (> 30 µm), the 12-slit URA mask has better resolution than the 17 multi-slits (Colour on-line).

Figure 15: Location of XRM beamline for the LER in Fuji straight-section.

Figure 16: Location of XRM beamline for the HER in Oho straight-section.

200

3.2. Optical elements

201

A photograph of the coded aperture masks taken with a 1000× Scanning Electron Microscope is shown

202

in Fig. 9. Figure 17 shows the enclosed chamber for the optics, 31.79 (32.69) m upstream of the detector

203

box and 9.47 (10.26) m downstream of the source point in LER (HER).

15

Figure 17: Optical system at Fuji straight-section (LER). The X-ray beam goes through the optical elements via a beryllium filter that is placed between the source point and optic box to reduce the heat load. The optical element is mounted on a stage controlled by a stepper motor that allows vertical motion.

204

3.3. Detector system

205

The longterm aim of XRM is for single-shot vertical beam size measurement using a Si detector and

206

high-speed readout electronics, but the aim of Phase 1 was to benchmark the performance of the XRM for

207

multi-shot setup measurements using scintillator screens. The detector systems are placed in lead boxes, and

208

incoming X-rays reach the scintillator through the beryllium window with the layout as shown in Fig. 18. For

209

the Phase 1 commissioning of SuperKEKB, a cerium-doped yttrium-aluminum-garnet (YAG:Ce) scintillator

210

was combined with a CCD camera for the X-ray imaging system, as shown in Fig. 19. The YAG:Ce has the

211

maximum emission wavelength 550 nm, decay time 70 ns, and 4.55 g/cm of density. The CCD ROX-40

212

was selected because of its high sensitivity (0.0005 lx) with peak around 500 nm, and 8.4 µm× 9.8 µm pixel

213

size.

3

Figure 18: Detector system at Fuji straight-section (LER) for Phase 1 commissioning of SuperKEKB operation. The incoming X-rays go through to the scintillator via the Be window.

16

Figure 19: Detector system at Fuji straight-section (LER) for Phase 1 commissioning of SuperKEKB. Inside the detector box: Be extraction window and a 141-µm-thick YAG:Ce scintillator with CCD camera. The scintillator is tilted 45° in the horizontal plane, so that the camera and lens are out of the way beam. The camera and lens are also tilted 45°, so that they view the scintillator face-on. This does not effect the image in the vertical direction.

214

215

4. Phase 1 Commissioning The SuperKEKB rings were commissioned from February–June 2016. Several studies were carried out

216

to investigate the geometrical scale factors, emittance control knobs, and beam lifetime.

217

4.1. Geometrical scale factor checks

218

Using beam-based measurements (see schematic in Fig. 20), the geometrical scale factors were measured

219

by moving either the beam or the optical elements and observing how the peak features change. The ratio of

220

geometric magnification from source-to-scintillator M and camera scale m was then calculated. The camera

221

scale m consisted of the detector system (camera) magnification from scintillator-to-camera and the pixel

222

size (µm/pixel).

223

When the beam is moved, the position (in pixels) of a peak feature from X-rays that passed through

224

a slit onto the scintillator P1 is defined as P1 = − M m y with y the source point position. The correlation

225

of y, vertical BPM value y1 , y2 and distance between them based on the schematic in Fig. 20 is defined as

226

y = y1 +

ds1 ds (y2

− y1 ).

Then the P1 is derived as P1 =



−

M m



1−

ds1 ds



y1 −

M ds1 y2 , m ds

(8)

227

where ds is the distance between downstream and upstream beam position monitors (BPMs), ds1 is the

228

distance from the upstream BPM to the source point, ds2 is the distance from the downstream BPM to the

229

source point, and y1 , y2 are the readouts from the upstream and downstream BPMs, respectively. 17

Figure 20: Schematic for the geometrical scale factors check, consisting of a source point with two beam position monitors (upstream s1 and downstream s2 ), optical elements, and a scintillator. P1 is the position (in pixels) of a peak feature from X-rays that passed through a slit onto the scintillator and P2 is the peak feature from X-rays transmitted through the Au mask.

When the optical element is moved, the ratio (M + 1)/m is defined as P1 = 230

M +1 ymask . m

(9)

where ymask is the position of the optical element in µm.

231

P1 and P2 were recorded during this study, and the ratio between M and m (geometrical scale factors)

232

were calculated using Eqs. 8 and 9. We also evaluated the geometry scale through physical tape measure; the results are presented in Table 5. The geometrical magnification factors given by the tape- and beam-based Table 5: Evaluation of geometry scale by tape measurement.

Parameter

LER

HER

Unit

Distance from source to optics

9.468 ± 0.005

10.261 ± 0.010

m

Distance from optics to scintillator

31.789 ± 0.005

32.689 ± 0.010

m

Magnification (M )

3.358 ± 0.002

3.186 ± 0.003

51.8

52.4

Scintillator camera scale (m)

µm/pixel

233 234

measurements agreed within a few percent at both beam lines (see Table 6).

235

4.2. Emittance control knob method

236

In SuperKEKB there is a tool to enlarge the vertical beam size intentionally by making an asymmetric

237

bump, called an ”iSize” bump, at one of the strongest non-interleaved sextupole magnets in each ring. A

238

screen shot of emittance control knob ’ECK’ measurement technique is shown in Fig. 21. The ECK method [21] enlarges the beam size and measures an overall consistency factor between the reported beam size measurements and Structured Accelerator Design (SAD) simulation. The variation in 18

Table 6: Geometrical scale factors check for LER and HER using the ratio of geometrical magnification M and scintillator camera scale m. The ratios given by tape- and beam-based measurements are agreed within a few percent at both beam lines.

M/m

(M+1)/m

Tape measurement (pixels/mm) LER

66.27 ± 0.10

85.58 ± 0.10

HER

61.51 ± 0.10

80.59 ± 0.10

Beam-based measurement (pixels/mm) LER

69.50 ± 0.50

86.00 ± 0.60

HER

59.20 ± 0.50

79.30 ± 0.10

Figure 21: The emittance control knob ’ECK’ measurement technique for HER, enlarging the vertical beam size by making an asymmetric bump (Colour on-line).

the vertical beam size with respect to the bump height is defined as σy meas


2

2

2

2

= (con σy0 ) + (con R) (h − h0 ) ,

(10)

where σy0 and σy meas are the minimum vertical beam size and measured beam size, respectively. The relation between the vertical beam size σy , vertical emittance εy , and a vertical beta function βy is given by σy =

p

εy βy .

(11)

The parameters h and h0 are the bump height and its offset, con is the consistency factor, and R is a linear coefficient defined as 2

R2 = ∆εy βy,source + (ηy,source σp ) ,

(12)

239

where ∆εy is the change in vertical emittance for a unit of bump-height squared as shown in Fig. 22,

240

ηy,source is the change in vertical dispersion for a unit of bump-height, and σp is the momentum spread. 19

241

The beam parameters ∆εy , βy,source , ηy,source , and σp are given by the optics model (as shown in Table 2).

Figure 22: The ∆εy knob parameter as a change in vertical emittance for a unit of bump-height squared. 242

243

The results of this study for both beam lines are shown in Figs. 23, 24, and Table 7. The minimum

244

measured beam size σy0 and vertical emittance εy for LER (HER) were ∼ 30 µm (∼ 35 µm) and ∼13 pm (∼

245

160 pm), respectively. The value of εy for LER is close to the design value given by the optical estimation

246

∼10 pm. The measured value for HER is an order of magnitude higher than the design value during the

247

Phase 1 tests. The PSF was studied using beam lifetime data to further investigate the discrepancy in both

248

rings, as described in Subsection 4.3.

Figure 23: LER emittance control knob data for all optical elements at 200 mA beam current. Data points are fitted using the function in Eq. 10 with consistency factor (con) and minimum vertical beam size (σy0 ) as free parameters. Phase 1 design value εy = 10 pm, measured value εy = 13 pm (Colour on-line).

249

4.3. Beam lifetime technique

250

The beam lifetime, which was recorded during the emittance control knob studies, was used to study the

251

PSF [22]. A bunch of charged particles (electrons/positrons) in a ring decays due to the quantum lifetime

252

(emission of SR), Coulomb scattering (elastic and inelastic scattering on residual gas atoms), bremsstrahlung

253

(photon emission induced by residual gas atoms), and the Touschek effect (electron–electron scattering).

254

During the phase 1 commissioning, the lifetime was dominated by Touschek scattering [23]. Touschek

255

collisions transfer momentum from transverse to longitudinal motion, and both electrons can slip outside the 20

Figure 24: HER emittance control knob data for all optical elements at 190∼195 mA beam current. Data points are fitted using the function in Eq. 10 with consistency factor (con) and minimum vertical beam size (σy0 ) as free parameters. Phase 1 design value εy = 10 pm, measured value εy = 160pm (Colour on-line). Table 7: Results of the emittance control knob method. From this data, the value of εy for LER (HER) is found to be ∼13 pm (∼160 pm). This is close to the design value for LER, but much higher for HER. The PSF was studied using beam lifetime data and the calibration factor con to investigate this discrepancy.

Mask

σy0 (µm)

Consistency factor (con) LER

pinhole

28.80 ± 1.01

0.92 ± 0.02

multi-slits

32.50 ± 1.51

0.86 ± 0.02

URA

30.07 ± 0.98

0.94 ± 0.01 HER

pinhole

33.60 ± 0.78

1.01 ± 0.02

multi-slits

37.06 ± 0.83

1.12 ± 0.02

URA

36.83 ± 0.72

1.02 ± 0.01

256

range of longitudinal acceptance, in which case they are lost. Piwinski [24], Khan [25], and Carmignani [26]

257

express the loss rate as 1 = τ

*

+ cre 2 np q F (ξ) , 8πγ 2 σz (∆p/p)3 σx 2 σy 2 − σp 4 Dx 2 Dy 2

(13)

258

where τ is the Touschek lifetime, np is the number of particles, D is dispersion, σp is the relative mo-

259

mentum spread, ∆p/p is the momentum acceptance, F (ξ) is the Touschek factor, and h i denotes an average

260

over the whole circumference of the storage ring. For a flat beam with a very small vertical oscillations

261

(Dy = 0), the loss rate becomes [25] 1 = τ

262

263



 cre 2 np F (ξ) . 8πγ 2 σz σx σy (∆p/p)3

(14)

In our analysis, we considered the beam parameters σx , ∆p/p, and F (ξ) to be constant, which implies that the Touschek lifetime is proportional to

σz/Ib

and the vertical beam size σy . The bunch current Ib 21

Figure 25: Relation between lifetime and measured beam size for LER with bunch length correction for each bump height, fitted using Eq. 15 to obtain the PSF σs (Colour on-line).

Figure 26: Relation between lifetime and measured beam size for HER with bunch length correction for each bump height, fitted using Eq. 15 to obtain the PSF σs (Colour on-line).

264

decreased during the measurements (see Table 2) and as the bunch length σz is a function of Ib [27], we

265

should consider this correction in the analysis. The measured value σy meas will be larger than the actual

266

beam size σy because of the PSF. If σy is convolved with a Gaussian smearing function of size σs , then

267

σy 2meas = (σy 2 + σs 2 ) con2 , where con is the consistency factor from the emittance control knob method.

268

The Touschek lifetime can then be represented as

τ= 269

270



σz k σy Ib



=

*

σz k Ib

r

σy 2meas − σs 2 con2

+

.

(15)

Fitting the lifetime using the bunch length correction, i.e., τ Ib /σz vs σy meas data using Eq. 15 with k and σs as free parameters, gives results shown in Figs. 25 and 26.

271

Using the correlation between the vertical beam size σy , beta function βy , and emittance εy given by

272

Eq. 11 and the parameters in Table 2, we can calculate a minimum vertical beam size σy0 from the smallest

273

measured beam size σy meas , which corresponds to the minimum vertical emittance εy0 . The averaged values

274

of σs , σy0 , and εy0 over all measurements made with the three optical elements are given in Table 8.

275

The LER vertical emittance εy is consistent with the optics estimation (∼ 10 pm), but for HER, the

276

emittance is 3.5× the optics estimation (∼ 35 pm for Phase 1 tests). These results indicate unknown sources

277

that made the measurement in the HER bigger than optics estimation.

22

Table 8: Average of PSF σs , minimum vertical beam size σy0 as fitting results of Figures 25 and 26, and vertical emittance εy0 measured with all three optical elements.

278

LER

HER

Unit

σs

15.63 ± 2.90

31.58 ± 0.72

µm

σy0

21.56 ± 2.91

16.93 ± 0.74

µm

εy0

∼ 10

∼ 35

pm

4.4. Spatial resolution of the detector system Regarding the detector, several parameters affect the spatial resolution: focus defects, diffraction effects, and spherical aberrations [28]. The relationships between the spatial resolution Rf and the scintillator depth dz (141 µm), numerical aperture of the camera N A (0.03132), XRM magnification M (3.2), and wavelength of visible light from the scintillator λ (550 nm) are Rf ∼

dzN A , defect of focus ∼ 1.4 µm, M

(16)

Rf ∼

λ , diffraction effect ∼ 5.5 µm, MNA

(17)

Rf ∼

dz(N A)2 , spherical aberration ∼ 1 µm. M

(18)

279

The effects contribute ∼ 5.8 µm of smearing at the source point. Additionally, the resolution of the

280

detector can be limited by the spatial distribution of the deposited energy imparted from ionizing radiation.

281

This distribution is affected by scattered X-rays or secondary electrons that may deposit energy far away

282

from the primary photon interaction site. The EGS5 (Electron-Gamma-Shower) code [29] is a general-

283

purpose package for conducting Monte Carlo simulations of the coupled transport of electrons and photons

284

in an arbitrary geometry for particles with energy from a few keV to several hundred GeV. In our case,

285

EGS5 calculated the absorbed dose of an X-ray pencil beam passing through the Be filter, optical elements,

286

Be window, and onto the flat surface of the 141-µm-thick YAG:Ce scintillator. The EGS5 analysis attempted

287

to determine the effect of scattering along in the beamline or detector of the imaging system.

288

We calculated the absorbed dose of 6 – 50 keV X-ray pencil beams from the source point to the YAG:Ce

289

scintillator. The parameters applied in the EGS5 simulation were: sampling of angular distributions of

290

photoelectrons, explicit treatment of K- and L-edge fluorescent photons, explicit treatment of K and L

291

Auger electrons, coherent (Rayleigh) scattering, linearly polarized photon scatterings, incoherent scattering

292

function for Compton scattering angles, and Doppler broadening of Compton scattering energies. The EGS5

293

calculation results in Fig. 27 show that the scattered background falls off by an order of magnitude within

294

1 µm. 23

6 keV 7 keV 8 keV 9 keV 10 keV 20 keV 30 keV 40 keV 50 keV

101

Deposition [keV]

100 10-1 10-2 10-3

101

10-1

10-4

10-2 10-3 10-4 10-5 10-6

10-5 10-6

8 keV 10 keV 15 keV 18 keV 20 keV 30 keV 40 keV 50 keV

100

Deposition [keV]

102

10-7 -30

-20

-10

0

10

20

10-8

30

Position [µm]

-30

-20

-10

0

10

20

30

Position [µm]

(a) LER

(b) HER

Figure 27: Deposited energy in YAG:Ce for given X-ray energy: (a) LER and (b) HER. The peak spectrum energy for LER and HER is estimated to be 11 keV and 18 keV, respectively. The scattering range is <1 µm with a background/peak ratio of ∼ 10−4 (Colour on-line).

295

Altogether, the contribution from focus defects, diffraction effects, spherical aberrations, and scattering

296

effects is ∼ 6 µm at the source point. This cannot account for the smearing observed in the lifetime studies.

297

Other possible sources of PSF or resolution loss include beam tilt or motion, camera misfocus, or some

298

sources of scattering not simulated by EGS5, such as impurities or inhomogeneities in the Be filters. During

299

Phase 2 commissioning, new optical elements were installed for XRM, and we have replaced the Be filters

300

with thinner ones.

301

5. Phase 2 Commissioning

302

Continuing studies were made during Phase 2 (May – July 2018) with the purpose to understand and

303

reduce the PSF found in Phase 1.

304

5.1. New equipments in the Phase 2

305

Several new types of equipment have been installed in the HER beamline: thinner Be filters, optical

306

elements that have been re-optimized, LUAG:Ce scintillator screen, and a CCD camera.

307

5.1.1. Thinner Be filter

308

The function of the Be filter is to separate the vacuum between the X-ray extraction chamber and XRM

309

beamline and reduce the X-ray power density. In Phase 1, a 16 mm of Be was used in the HER system

310

to increase the margin of safety regarding the heat load [19]. The Phase 1 XRM study suggested the PSF

311

made the measured beam size bigger than the optic estimation. The Be filter was considered one of the

312

sources because of the possibility of X-ray diffraction on it, e.g., a small-angle scattering mainly due to

24

313

density fluctuation or poly-crystal structure [30]. For that reason, we replaced the Be filter in HER with a

314

thinner filter, from 16 mm to 0.2 mm or the same thickness as the Be window.

315

5.1.2. Optimizing the pinhole size

316

The pinhole size was re-optimized by simulating the detector image for a point source in both rings

317

using various pinhole (slit) sizes. The procedure was as same as the Phase 1, differing only in the diamond

318

thickness (800 µm) and Be filter thickness. The minimum standard deviations of the resulting PSFs were found to be 33 µm for LER and 31 µm for HER as shown in Fig. 28. We took 31 µm as the new minimum

Figure 28: Standard deviation of images for various slit widths for LER and HER in Phase 2. The 33 µm (31 µm) slit size was taken as the optimum slit and basic size for LER (HER) ring (Colour on-line). 319 320

slit size for HER and kept 33 µm as the minimum slit sizes for LER. The same optical element patterns as

321

in Phase 1 are then rescaled with 31 µm as the minimum slit size. The detail parameters and pattern of the

322

optical elements for Phase 2 commissioning in HER are listed in Table. 9.

323

5.1.3. Scintillator, lens, and camera system

324

We then replaced the YAG:Ce with LuAG:Ce to improve the spatial resolution. A comparison between

325

YAG:Ce and LuAG:Ce for X-ray imaging was observed [31]. The LuAG:Ce single crystal is denser compared

326

to YAG:Ce (6.76 and 4.55 gram/cm , respectively), and the X-rays are absorbed stronger by LuAG. 1.7 times

327

more X-ray radiation is absorbed in the range between 1 and 40 keV, as calculated using X-ray radiation

328

attenuation coefficients. The LuAG:Ce screen has higher conversion efficiency than YAG:Ce screen, so that

329

the signal-to-noise ratio of the image is better for use in the imaging system. Another X-ray imaging system

330

with a YAG:Ce screen has been demonstrated successfully for vertical beam size measurement in Diamond

331

Light Source, DLC [18].

3

332

Pentax C1614A lenses [32] were used for both rings with 16.0 mm of focal length, 1:1.4 maximum aperture

333

ratio, 0.3 m minimum object distance, and 58 gram weight. The distance between lens and scintillator is 5

334

cm, so the extension tube set (macro ring) [32] was inserted between the lens and camera to shift the focal

335

point further than the mechanical limit of the lens for the close-up application. We also used an acA2440-

336

20gm-Basler ace CCD camera [33] with 2448 × 2048 pixel grayscale resolution, 3.45 µm × 3.45 µm pixel 25

Table 9: Parameters of the optical elements for Phase 2 commissioning for HER ring.

Optical element

Parameter

Value

PH (pinhole)

width

31 µm

Multi-slits

Diamond thickness

800 µm

Au thickness

20 µm

Number of slits

17

Pattern, S=slit, M=Au mask (µm) 31S-21M-31S-62M-31S-21M-31S-103M-31S-21M-31S-41M-31S-21M-31S-186M-31S-21M-31S-41M -31S-21M-31S-62M-31S-21M-31S-41M-31S-21M-31S-103M-31S URA

Diamond thickness

800 µm

Au thickness

20 µm

Number of slits

12

Pattern, S=slit, M=Au mask (µm) 62S-31M-62S-93M-31S-31M-31S-31M-62S-124M-31S-155M-124S-31M-124S-62M-31S-31M-31S -31M-93S-62M-31S

337

size and 23 fps of frame rate. The exposure time was set to 800 µs to not saturate the white balance at ∼

338

700 mA beam current.

339

5.2. Phase 2 results

340

A primary goal in Phase 2 was to reduce the PSF found in the HER during the Phase 1. The emittance

341

control knob method used in Phase 1 was repeated to check the consistency between the measured beam size

342

and SAD simulation. The beam parameters and the ECK results during Phase 2 are shown in Table 10 and Fig. 29, respectively. The lifetime study was repeated, fitting the lifetime with the bunch length correction Table 10: XRM beam parameters in HER during Phase 2 commissioning of SuperKEKB Operation.

Parameter Beta function at XRM source point

βy,source

Vertical emittance/(bump-height)squared

∆εy

Change in vertical dispersion/bump-height

ηy,source

HER

Unit

7.64

m

41.978 ± 0.020 pm/mm2 0.019

m/mm −4

6.304 × 10

Momentum spread

σp

Beam current

I

60 – 100

Number of bunches/ring

nb

788

343

26

mA

Figure 29: HER emittance control knob study for URA mask, taken with slow (left) and quick (right) knob scans. We did a quick scan after slow scan to avoid the change of beam condition during the measurements. The consistency factors between measured and SAD simulation beam sizes are 0.996 ± 0.007 and 1.002 ± 0.003 for slow and quick scans, respectively.

344

in Eq. 15 with k and σs as free parameters, leading to results as shown in Fig. 30. The average of PSF

345

factor σs was found to be 6.60 ± 0.73 µm.

Figure 30: Relation between lifetime and measured beam size with bunch length correction for each bump height: (top) slow scan, (bottom) quick scan. Fitted using Eq. 15 to obtain the PSF factor σs . The average of σs was found to be 6.60 ± 0.73 µm, which is about 5 times smaller than Phase 1 (Colour on-line).

346

The results suggest a PSF σs ∼ 6.6 µm for the HER, which is ∼ 5 × smaller than in Phase 1. The PSF

347

indicates that the minimum beam size corresponds to the design emittance of 12.9 pm at the 2.6 A design

348

current (see Table 1). With the reduced σs , it is not a limiting factor for σy measurements and we should

349

be able to measure the design beam size at the zero current, σy ∼ 7 µm. 27

350

6. Conclusion

351

We have described the installation, operation, and calibration of X-ray beam size monitors (XRMs)

352

during the Phase 1 and 2 commissioning of SuperKEKB. In the XRM, the X-rays from a mathematical

353

point source in a bending magnet pass through optical elements and form a diffraction pattern with an

354

array of peaks depending on the pattern of the optical element.

355

For Phase 1 commissioning, the overall performance at the low energy ring (LER) were consistent with

356

expectations based on the optics estimation εy ∼ 10 pm and will be able to measure the design beam size

357

358

at zero current (∼ 14 µm). The high energy ring (HER) measurement predicted εy ∼ 35 pm, which is 3.5 × larger than the optics estimation and suggested a large point spread function (PSF) σs ∼ 31 µm.

359

Studies were made during Phase 2 commissioning with several new equipment improvements in the HER:

360

thinner Be filters, updated optical elements, a new scintillator screen, and CCD camera with the purpose to

361

reduce the PSF. The results show a PSF σs ∼ 6.6 µm, which is 5 × smaller than in Phase 1. This revised σs

362

indicates that the minimum measured beam size corresponds to the emittance at the design current (12.9

363

pm). The σs is also small enough to measure the design beam size at zero current, σy ∼ 7 µm. The resulting

364

vertical beam size measurements in Phase 1 and 2 are summarized in Table 11. Table 11: Vertical beam size measurements in Phase 1 and 2.

Parameter σy optics estimation

Phase 1

Phase 2

LER

HER

HER

∼ 25

∼9

∼9

σy measured

21.56 ± 2.90

16.93 ± 0.75

12.35 ± 0.39

σs (inferred PSF)

15.63 ± 2.90

31.58 ± 0.72

6.60 ± 0.73

Unit µm µm µm

365

In the next phase, the detector will be supplemented by 128 channels of silicon with 2-mm sensing

366

depth and a pixel pitch of 50 µm which is enough to absorb 90% of the incident spectrum expected. The

367

high collection efficiency will improve the statistical resolution for single-shot measurements. This detector

368

system will have a capability for the single-shot measurement which is useful for studying beam instabilities.

369

Acknowledgment

370

We would like to thank the SuperKEKB commissioning team for providing beams and allowing us to

371

conduct calibration studies. J.F. would like to thank Jonathan (Josh) Grindlay of the Harvard-Smithsonian

372

Center for Astrophysics for introducing us to the idea of coded aperture imaging many years ago, which

373

eventually led J.F. to apply it to accelerator beam profile imaging. E.M. was supported by Research

374

and Innovation in Science and Technology Project (RISET-Pro) Kemenristekdikti, Ministry of Research, 28

375

Technology, and Higher Education of Indonesia. We also would like to thank anonymous reviewers for the

376

thoughtful comments and constructive suggestions, which help to improve the quality of this manuscript.

377

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