Proceedings of IBIC2012, Tsukuba, JapanTUPB74

DIAMOND MIRRORS FOR THE SUPERKEKB SYNCHROTRONRADIATION MONITOR
J.W. Flanagan, M. Arinaga, H. Fukuma, H. Ikeda, KEK, Tsukuba, JapanThe SuperKEKB accelerator, a 40x luminosity upgrade
to the KEKB accelerator, will be a high-current, lowemittance double ring collider[1]. The beryllium primary
extraction mirrors used for the synchrotron radiation
monitors at KEKB suffered from heat distortion due toincident synchrotron radiation, leading to systematicchanges in magnification with beam current andnecessitating continuous monitoring and compensation ofsuch distortions in order to correctly measure the beam
sizes[2]. The heat loads on the extraction mirrors will behigher at SuperKEKB, with heat-induced magnification
changes up to 40% expected if the same mirrors wereused as at KEKB. We are working on a design based on
mirrors made of quasi-monocrystalline diamond, which
has much higher heat conductance and a lower thermal
expansion coefficient than beryllium. With such mirrors
it is targeted to reduce the beam current-dependent
magnification effects to the level of a few percent at
SuperKEKB. The design of the mirror and its heatsink/holder will be presented, along with numericalsimulations of the expected heat-induced mirror surface
deformations will be presented.

INTRODUCTION
The synchrotron radiation monitors at SuperKEKB will
use source bends in the same locations as at KEKB,
which are the 5 mrad “weak bends” heading into the Fuji(LER) and Oho (HER) straight sections. The source bend
parameters are shown in Table 1. The source bend for theLER will be replaced with one with a longer core andlarger bending radius (a re-used LER regular arc bendmagnet) in order to reduce the SR power intensity.
Despite the reduced bending radius, the increase in beamenergy and beam current means that the incident angularpower density will be higher (72 W/mrad) than that of theKEKB LER (48 W/mrad). The source bend will remain
the same at the HER, and the effect of the increased
current of the beam is almost cancelled out by the reduced
beam energy, so that the angular power density is only alittle bit higher than at KEKB.
It is planned to move the chambers a bit further
downstream from the source bends than they were at
KEKB, which will help reduce the SR power intensity
hitting the primary extraction mirrors. However, the heat
deformation of the KEKB mirrors was already a verysignificant problem, requiring complicated measures tomeasure and compensate for the distortion in real time inorder to correct the beam-current dependence on themeasured beam size. For this reason, we are pursuing thedesign of mirrors made of diamond, which has a higher
heat conductivity and lower thermal expansion coefficientthan beryllium. The design of the mirror will be
described in the next section.
Table 1: SR Source bend parameters
Parameter

KEKB

SuperKEKBLERHERLER

HER

Energy (GeV)

3.5

8

4

7

Current (A)

2

1.4

3.6

2.6

Bending radius
(m)

85.7

580

177.4

580

SR Power(W/mrad)

48

136

72

149

DESIGNThe design of the mirror is based on CVD diamond,made by Cornes Technology (formerly Seki Technotron)and EDP Corporation. For best thermal conductivity, theidea mirror material would be a pure monoctystalline
diamond, rather than a polycrystalline one.
The
monocrystalline diamond also gives good surface
smoothness after polishing, with an Ra from 2-10 nm
expected. For optical reflectivity, a metallic surface isneeded.

Figure 1: 10 mm x 20 mm x 0.65 mm prototype diamondmirror, consisting of two 10 mm x 10 mm monocrystals,with 3 m Au reflective coating.

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Copyright ○Abstract

TUPB74

Proceedings of IBIC2012, Tsukuba, JapanThe size of mirror we currently expect to need is ~1020 mm wide x 30 mm tall; the prototypes manufactured
for us so far consist of 10 mm x 10 mm monocrystalline
sections fused together, with a reflective surface made of
3 um of gold. A 10 mm x 20 mm x 0.65 mm prototype isshown in Fig. 1.

placing any extraneous strain on the surface of the mirror
due to heat deformation of the copper. Each half of thecopper cylinder is cooled with symmetrically-locatedwater pipes brazed in place. A prototype of theholder/heat sink made by Cornes Technology is shown inFig. 2, and a prototype mirror mounted in the holder isshown in Fig. 3.

SIMULATIONS

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Copyright ○ANSYS simulations were carried out to investigate theeffect of a line heat source (such as from an SR fan) on
the surface of a diamond mirror. The mirror wassimulated as a 20 mm x 20 mm x 1 mm monocrystalline
diamond with a 3 m gold coating. The diamond istreated as having a heat transfer coefficient of 2000
W/k/m, and a thermal expansion coefficient of 2.6
m/m/K. The mirror is mounted in a copper heatsink/holder of the same design as the prototype, and withthe water in the cooling channels being treated as aconstant-temperature heat sink.

Figure 2: Copper mirror mount.

Figure 4: ANSYS simulation of temperature distributionof diamond mirror in copper holder, heated in a 2-mm
horizontal ribbon on the mirror’s face.

Figure 3: Copper mirror mount, with prototype mirror
mounted in it.
The design of the holder presented some issues.
ANSYS simulations (see below) showed that for anyholder design which touches the mirror on all edges oralong the back side, the deformation of the holder would
be large enough to cause unacceptable deformations inthe surface of the diamond mirror, much larger than thedeformations caused by the heat distribution pattern in thediamond mirror itself. The solution that was finallysettled on was a split cylinder of soft copper, which grips
the mirror near one edge only. The soft copper permits agood heat-sinking contact with the portion of the mirror
surface gripped within the split (about 6 mm), without

Figure 5: Shape deformation of simulated mirror andholder under heating. (Colors represent deformation in zdirection, perpendicular to mirror surface.)
The temperature distribution for 400 W applied over a2-mm high ribbon across the 20-mm width of thediamond mirror is shown in Fig. 4. The resulting shape
distortion is shown in Fig. 5, with the z-direction(perpendicular to mirror surface) distortions highlighted

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Proceedings of IBIC2012, Tsukuba, Japanin color. A cross-section of the surface of the mirror isshown in Fig. 6. As can be seen, the surface of the mirror
essentially “folds” back at the point of heating, with thepart of the face above the heat ribbon (to the right in Fig.
6) is tilted away from the part below the ribbon (to the leftin Fig. 6).

TUPB74

PROTOTYPE SIMULATIONS
The first prototype received is a 10 mm x 20 mm x 0.65
mm quasi-monocrystal, comprising two 10 mm x 10 mm
sections fused together, which was polished on both sides
but only coated with gold on the front side. The backsideof the prototype mirror was uncoated. In planned
measurements, an infrared line heater will be applied tothe back side in order to leave the front side free from
obstruction, so that the surface flatness can be measured.
Simulations were made of the 10 mm x 20 mm x 0.65 mm
diamond mirror prototype, for different amounts ofabsorbed heat. The heat source was treated as occurringin a 2 mm high by 10 mm wide (full width of prototype
mirror) region, with 100 W, 200 W and 400 W being
simulated. The resulting cross-sections of the surface
across the heat source are shown in Fig. 8.

Figure 8: ANSYS simulation of the surface deformationof 10 mm x 20 mm x 0.65-mm monocrystalline diamondmirror at different absorbed heat loads.

Figure 7: Surface deformation for Be mirror of type usedat KEKB for 200 W applied over 35 mm width of mirror.
For comparison, the same surface distortion is shown
for a Be mirror of the type used at KEKB (a 35 mm wideby 35 mm deep block of beryllium, mounted to a watercooled copper heat sink on the back). While simulated
power intensity is much lower for the beryllium block, itcan be seen that the resulting surface deformation is muchhigher.
The mirror surface deformation has been found to scaleroughly linearly with applied heat (see below). Scaling
the results above to the power intensity expected atSuperKEKB, and accounting for the effect of mirror
deformations on the effective slit separation for aninterferometer, the deformation in the beryllium mirror isprojected to cause a change of 43% in the measured beam
size at full current in the HER. The diamond mirror, incomparison, would only change the apparent beam sizeby about 3%, which would represent a great improvement.

Figure 9: Differences in surface slope on either side of
the heating line from ANSYS simulations in Fig. 8. The
best fit slope difference is 4x10-5 m/mm/W.
Figure 9 shows the differences in left-hand versus righthand slope for different incident heat levels. The best-fit
slope difference across the heat source line is 4x10-5
m/mm/W, which is about half of the level seen in thesimulation for the 20 mm x 20 mm x 1 mm mirror.
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3c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Figure 6:
Surface deformation of 1-mm thickmonocrystalline diamond mirror due to 400 W applied
over 20 mm width of mirror.

TUPB74

Proceedings of IBIC2012, Tsukuba, Japan

Preliminary measurements were attempted on the
prototype mirror using a Shack-Hartmann wavefront
sensor (Thorlabs WFS-K2), a He-Ne laser, and using an
infrared line heater (Fintech LHW-30) to provide a heatsource for the mirror. Unfortunately, the precision of themeasurement setup at present is not sufficient to measurechanges in mirror surface of the order required to verify
the simulation. Modifications will be made to improve
the precision of the measurement setup, including awider-field wavefront measurement system and a more
powerful heat source, and be reported in a future paper.

SUMMARY AND FUTURE DIRECTIONS

c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○We have designed a diamond extraction mirror andholder that, according to simulations, should suffer muchless heat-induced surface deformation than the beryllium
mirrors used at KEKB. The eventual size of mirror weneed will be 10-20 mm wide by 30 mm tall by 1 mm thick.

Initial prototypes have been made of monocrystalline
fused tiles, which are undergoing testing to verify theirperformance. If necessary it is expected that tiled quasimonocrystalline mirrors can be used at SuperKEKB, andeventually it is hoped that a single monocrystalline
structure will become feasible. Current prototypes arecoated with gold, but it is planned to try a nickel coatingin the future.

ACKNOWLEDGMENT
We would like to thank T. Mitsuhashi for helpfuladvice on possible improvements to the design andmeasurement of the extraction mirror.

REFERENCES[1] H. Koiso, Proceedings of IPAC'11, 1931(2011).
[2] M. Arinaga et al., NIM, A499, p. 100 (2003).

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