12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

EFFECT OF INCOHERENT DEPTH OF FIELD FOR BEAM HALO
MEASUREMENT WITH THE CORONAGRAPH IN SuperKEKB
T. Mitsuhashi†, H. Ikeda and G. Mitsuka, KEK
Abstract
In the case of beam profile measurement by imaging system, observed apparent beam profile will change by the incoherent depth of field. This apparent change of beam profile, especially extra beam tail in one side has certain influence for beam halo measurement using the coronagraph,because it has a large dynamic range of 6-digit contrast.
Since the magnitude of asymmetric tail is depending on
bending radius, this effect is larger in large high energy
physics machine which has a long bending radius. This effect is studied with geometrical optics and coronagraphmeasurement of beam halo in the SuperKEKB. As a conclusion, the IDF effect has significant effect in the beam
halo observation with coronagraph at SuperKEKB.

INTRODUCTION
For the measurement of beam image, the incoherent
depth of field (IDF) due to horizontal instantaneous opening of the Synchrotron Radiation will apparently modify
the horizontal profile of beam image in asymmetric manner.
We have presented this IDF effect for horizontal beam size
measurement with interferometry in IBIC2017 [1]. In theinterferometry, The IDF effect deduces spatial coherencein horizontal direction, and correction is necessary for thehorizontal beam size measurement with interferometry [1].
The IDF effect has not only reducing the spatial coherence,but also modify the apparent horizontal beam profile withasymmetric manner. As a result, observed beam image
with focusing system will be deformed. Especially, tis
asymmetric deformation of beam profile can introduce extra asymmetric distribution in beam tail (or halo) which isexisting surrounding of beam core. We studied this effectusing the geometrical optics in the case of beam halo measurement with coronagraph in the SuperKEKB. And compare the measurement result s of beam halo with the coronagraph [2].

EFFECT OF INCOHERENT DEPTH OF
FILED FOR APPARENT DEFORMATION
OF BEAM PROFILE
In the horizontal plane, the profile of beam is modified
apparently by IDF with the instantaneous opening of theSR in the horizontal plane as shown in Fig. 1.

Figure 1: Apparent beam profile with the IDOF effect by
the instantaneous opening of the SR in the horizontal planein the SuperKEKB HER case.
In the geometrical Optics, the intensity distribution in theentrance aperture has no effect for imaging as shown inFig. 2. Also, due to small emittance of the source beam,opening angle and source size is very smaller than openingof SR in the visible light region, this effect will be negligible small for IODF.

Figure 2: Point to point transfer of source point into imaging point in the geometrical optics.
Denote the total intensity of SR inside of the entrance
aperture in horizontal plane by I(as a function of horizontal observation angle the apparent beam shape a(x)is given by,
𝜎 𝑥 =___________________________________________†email address: toshiyuki.mitsuhashi@kek.jp

03 Transverse Profile and Emittance Monitors

I(θ) ⋅𝑒𝑥𝑝− x − 𝜌 1 − 𝑐𝑜𝑠(𝜃)2𝜎𝜎 ⋅ √2𝜋dθ ,(1)where the original beam profile is assumed to be a Gaussian distribution.
For the discussion of horizontal IODF, we needknowledge of instantaneous intensity distribution of SR inhorizontal plane to evaluate I().
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Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 0 5

The SR from circular trajectory is written by Schwinger
in 1945 [3, 4]. He only gave his theory for the case of horizontal observation angle=0.
For the case in the horizontal observation angle 0, is
discussed by one of author [1]. The intensity radiated perunit frequency interval per unit solid angle is given by𝑑 𝐼𝑒𝜔𝜌=𝑑𝜔𝑑𝛺 3𝜋 𝑐 𝑐

1+𝜓 +𝜉
𝛾𝐾 / (𝜁)(2)+𝜓1+𝜓 +𝜉𝛾

𝐾 / (𝜁) ,where,32  1
 2   2   2  3c  

(3)

The result given by Eq. (2) indicates both of vertical intensity distribution and horizontal instantaneous intensity
distribution have same angular dependence. This result issame as in the result from qualitative discussion in K.J.
Kim [5]. The total intensity of SR in entrance aperture isgiven by integrating instantaneous intensity distribution ininside of the aperture. The horizontal total intensity inside
the aperture is given by integrating the Eq. (2) in horizontal
direction inside the entrance aperture,

I()=+ (𝜓 + θ)

(4)

𝐾 / (𝜁) 𝑑𝜓 ,where,

𝜁=𝐾 ( 𝜁) +Figure 3: Simulation result of horizontal beam profile image for HER. (a)leaner scale, (b) log scale. Red line: beamprofile image with IDF, blue line without IDF.

+𝜓SIMULATION OF HORIZONTAL BEAM
PROFILE WITH IOD EFFECTA simulation of horizontal beam profile using the Eq. (1)is performed for Super KEKB HER and LER.
The parameter of source bend and horizontal beam size ofthe HER and LER are summarized in Table 1.
Table 1: Parameter of Bending Source
HER
LER
Beanding radius
580.0 m177.4 mBeam Energy
7 GeV
4 GeVHorizontal beam177 m
226 msizeThe result of beam profile with and without IDF effectin linear scale and log scale for HER an LER is shown inFigs. 3 and 4 respectively.
As shown in Fig. 3 (a), a slight asymmetry is seen in horizontal beam profile due to a long bending radius in HER.
R=580 m in HER. This asymmetry in profile is clearer inlog plot as shown in Fig. 3 (b).

Figure 4: Simulation result of beam profile image for LER.
(a): leaner scale, (b): log scale. Red line: beam profile image with IDF, blue line without IDF, but both curvatures
are almost same and overlapped in each other.

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03 Transverse Profile and Emittance Monitors

IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 0 5

On the other hand, due to rather short bending radius(177.4 m in LER), the same result for LER has almost noasymmetry in beam profile as shown in Fig. 4. From Fig 4,
the effect of IDF in LER is very small and beam profiles
with IDF and without IDF is almost same.
As a result, beam profile change in the outside aria from5  of the beam size will be very small, and no significant
effect of IDF for beam halo observation in 6-digit in theSuperKEKB with the coronagraph. We expect some beam
halo will exist in this aria.

The intensity of beam halo (note this intensity is not peakintensity in Fig. 6) is 2 x 10-6 to the peak intensity of thebeam core. We observed no significant effect of IDF in horizontal halo profile.

OBSERVATION OF BEAM CORE AND
HALO WITH CORONAGRAPH
The effect of IODF for beam core image and beam halo
image are observed experimentally using the coronagraph [4] for both of HEL and LER in the SuperKEKB.
The result of observed beam profile on the direct focal
plane of objective system of coronagraph at HER is shownin Fig. 5. A plot of horizontal profile of distribution is also
shown in Fig. 5. From this figure, a slight asymmetry inhorizontal distribution of beam core image is observed. On
other hand, profile of beam tail is very symmetry in thisobservation result. Since this extent of asymmetry in theimage is sometimes appear due to residual aberration of
objective system, but the wavefront error in coronagraphsystem including the extraction polycrystal-diamond mirror is smaller than /5 [6], so beam image in Fig. 5 is diffraction limited one. The extent of horizontal profile ofbeam image in HER with this observation result is good
agreement with the simulation result in Fig. 3 (a). The outside aria from 5  of the beam size seems having no significant IODF effect.
The beam halo is observed with the coronagraph in 6digit contrast. The result of halo observation in HER isshown in Fig. 6 [2]. An intensity distribution along the horizontal plane is also shown in this figure. The beam core
image and opaque square image for blocking the glare ofbeam core are superimposed in this figure for reference.

Figure 6: Result of beam halo observation with the coronagraph in 6-digit contrast in HER. Upper: beam halo image,lower: horizontal profile of the halo image.
The result of halo observation in LER is shown in Fig. 7.
An intensity distribution along the horizontal plane is also
shown in this figure. As same manner, in Fig. 6, the beamcore image and opaque square image for blocking the glareof beam core are superimposed in this figure for reference.
Different from HER, an interesting beam halo is observedin LER. As same as in HER, we observed no significant
effect of IDF in horizontal halo.

Figure 7: Result of beam halo observation with the coronagraph in 6-digit contrast in LER.

CONCLUSION

Figure 5: Result of observed beam core profile in HER.
Upper: beam core image, lower horizontal profile of theimage.

The effect of IDF for beam core image and beam halo
image by using the coronagraph are studied with geometrical optics and experimentally observation for both ofHEL and LER in the SuperKEKB. From the observation
result, we detect no significant effect of IDF in horizontal
halo profile of both of HER and LER. We can conclude
IDF effect is enough smaller in the halo observation withthe coronagraph in SuperKEKB.
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337

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12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 0 5

Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

REFERENCES[1] T.M. Mitsuhashi, M. J. Boland, and W. J. Corbett,“Horizontal Opening of the Synchrotron Radiation andEffect of Incoherent Depth of Field for Horizontal Beam
Size Measurement”, in Proc. IBIC'17, Grand Rapids, MI,USA, Aug. 2017, pp. 364-368.
doi:10.18429/JACoW-IBIC2017-WEPCC09[2] G. Mitsuka, H. Ikeda, and T. M. Mitsuhashi, “Design andConstruction of Optical System of the Coronagraph for
Beam Halo Observation in the SuperKEKB”, in Proc.
IPAC'22, Bangkok, Thailand, Jun. 2022, pp. 769-771.
doi:10.18429/JACoW-IPAC2022-TUOXGD1[3] J. Schwinger “On Radiation by Electron in a Betatron” in A
Quantum Legacy: Seminal paper of J. Schwinger, B.G.
Englert, Ed., Singapore, World Scientific, 2000, pp. 307-331.
[4] J. Schwinger “On the Classical Radiation of AcceleratedElectrons”, Phys. Rev. vol. 75, p.1912, 1949.
doi.org/10.1103/PhysRev.75.1912[5] K.J. Kim, “Characteristics of Synchrotron Radiation”, in AIP
conference proceedings 184, p. 364, 1989.
[6] G. Mitsuka, H. Ikeda, and T. M. Mitsuhashi, “Renovation ofthe SR Beam Profile Monitors with Novel Polycrystalline
Diamond Mirrors at the SuperKEKB Accelerator”, in Proc.
IPAC'22, Bangkok, Thailand, Jun. 2022, pp. 313-315.
doi:10.18429/JACoW-IPAC2022-MOPOPT031

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