Proceedings of IBIC2012, Tsukuba, Japan

MOCB04VERTICAL EMITTANCE MEASUREMENTS
USING A VERTICAL UNDULATOR
K.P. Wootton∗ , M.J. Boland, G.N. Taylor, R.P. Rassool,
School of Physics, University of Melbourne, VIC, Australia
M.J. Boland, B.C.C. Cowie, R. Dowd, Y.-R.E. Tan, Australian Synchrotron, Clayton, VIC, Australia
Y. Papaphilippou, CERN, BE Department, Geneva, Switzerland

Photon Beam Brilliance

We have reported on initial work to measure verticalemittance using a vertical undulator. Using simulations, wemotivate the important experimental subtleties in the application of this technique. Preliminary measurements ofundulator spectra are presented that demonstrate the highsensitivity of vertical undulators to picometre vertical emittances. Finally, possible future applications of this technique are explored.

Modelled in SPECTRA [8], the sensitivity of horizontal
and vertical undulators to vertical emittance is illustrated inFigure 1 below.

THEORY
Undulators have been used as diagnostics of storage ringemittance. Horizontal undulators – undulators that deﬂect
the electron beam in the orbit plane of the ring – havebeen demonstrated to give excellent measurement of thehorizontal beam size and energy spread [3–7]. Where theelectron beam emittance is close to fully-coupled, the brilliance of horizontal undulators exhibits some sensitivity to
the vertical emittance [4]. Electron storage and rings typically design for transverse emittance ratios less than a few
percent, with damping ring designs aiming for minimum
vertical emittance. In this low vertical emittance limit horizontal undulators are identiﬁed as particularly insensitive
to vertical emittance, limited by the single-electron opening angle of undulator radiation [3].
∗ k.wootton@student.unimelb.edu.au

Brilliance, horizontal undulator Bx = 0.55 T

40.1 pm
0.2 pm
0.5 pm
1 pm
2 pm
5 pm
10 pm
20 pm
50 pm
100 pm32

1005001000
1500
Photon energy [eV]

2000

2500

Brilliance, vertical undulator By = 0.55 T

40.1 pm
0.2 pm
0.5 pm
1 pm
2 pm
5 pm
10 pm
20 pm
50 pm
100 pm32

1005001000
1500
Photon energy [eV]

2000

2500

Figure 1: Photon beam brilliance, for horizontal undulator
and vertical undulator of deﬂection parameter K = 3.85,
for ASLS user lattice with ηx = 0.1 m in the insertion [9].

ISBN 978-3-95450-119-9
Transverse & Longitudinal Emittance Measurements

1c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Electron storage ring light sources and damping rings
continue to produce beams of increasingly small verticalemittance. With the recent report of the minimum observed
vertical emittance of εy = 0.9 ± 0.4 pm rad at the SLS [1],we require techniques sensitive to sub-micrometre electron
beam sizes. At the Australian Synchrotron, we have developed a technique for measuring the vertical emittanceof electron beams that we call vertical undulator emittancemeasurement [2].
In these proceedings, we assess undulators as a beam diagnostic. In contrast to horizontal undulators being largely
insensitive to picometre vertical emittance, we highlightthe sensitivity of vertical undulators to the vertical emittance. We present preliminary results and simulations, aswell as ideas for future vertical emittance diagnostics.

Flux density [1016 ph mm−2 mrad−2 s−1 per 0.1% b.w.]

INTRODUCTION

Flux density [1016 ph mm−2 mrad−2 s−1 per 0.1% b.w.]

AbstractProceedings of IBIC2012, Tsukuba, Japan

Figure 1 illustrates the photon beam brilliance for horizontal and vertical undulators of equal deﬂection parameter. Over a range of operational vertical emittances there
is no measurable change in brilliance for a horizontal undulator. However we see that for a vertical undulator, athigh even undulator harmonics, the photon beam brilliancechanges by orders of magnitude. Hence, measurements ofthe photon beam brilliance at the even harmonics exhibit astrong dependence upon the electron beam emittance [10].
To measure the brilliance of these harmonics, we consider the angular distribution of undulator radiation. In Figure 2 we present simulations [8] of the vertical proﬁle of ahorizontal undulator, and a vertical undulator in Figure 3.

Photon count [ 1016 ph s−1 per 0.1% b.w.]

c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○3

Undulator radiation − horizontal undulator
12345678910
112.5
2Undulator radiation − vertical undulator
12345678910112.5
21.5
1
0.5
0−0.15−0.1 −0.05
00.05
0.1
Vertical opening angle [mrad]

0.15

Figure 3: Simulated vertical proﬁle of undulator harmonics, vertical undulator. Vertical emittance εy = 1 pm rad.
Around θy ≈ 0, the narrow interference peaks of the evenand odd harmonics are well-separated in amplitude.

1.5
1This idea has also been proposed for measurement of horizontal beam emittance in plasma wakeﬁeld accelerated
electron beams [6, 7].

0.5
0−0.15

3Photon count [ 1016 ph s−1 per 0.1% b.w.]

MOCB04

METHOD−0.1 −0.05
00.05
0.1
Vertical opening angle [mrad]

0.15

Figure 2: Simulated vertical proﬁle of undulator harmonics, horizontal undulator. Vertical emittance εy = 1 pm rad.
For a ﬁxed, low vertical emittance of εy = 1 pm radand horizontal emittance εx = 10 nm rad, Figures 2–3 exemplify the difference between the horizontal and verticaldirection of undulation. With undulations in the horizontal direction in Figure 2, we see the incoherent superposition of spontaneous undulator radiation from a beam witha comparatively large horizontal emittance.
In Figure 3 however, the small simulated vertical emittance of εy = 1 pm rad is indicative of the single-electrondistribution of undulator radiation. The narrow spatial distribution of the interference pattern created at each undulator harmonic is of sin2 θ distribution for odd harmonics,
and cos2 θ distribution for even harmonics. Hence an onaxis pinhole aperture passing a narrow angular distribution
above and below the orbit plane of the undulator passes amaximum ﬂux for odd undulator harmonics, and minimum
for even harmonics, as illustrated in Figure 1.
The beam emittance is evaluated as a ratio of peak ﬂux
in the even harmonic to that of the adjacent odd harmonic.

We measure the undulator ﬂux passing an on-axis pinhole. The pinhole is formed by closing white-beam slits on
the beamline. As a spectrometer, we utilise the soft x-rayuser beamline [11, 12].

Vertical EmittanceA calibrated model of the storage ring lattice was measured using orbit response matrix analysis, and ﬁtted using
the LOCO technique [13]. The electron beam vertical emittance was adjusted by optimising skew quadrupole magnets
in the lattice model [14].

PhotodiodeThe preliminary measurements presented in Figures 4 –5 were made using a Hamamatsu G1963 GaP/Au Schottky photodiode. The diode was selected as it is installedon the beamline as a standard diagnostic of photon ﬂux.
The responsivity of the photodiode was calculated over therelevant range of photon energies [15]. Over the desired
photon energy range, the responsivity for this type of diodeexhibits large discontinuities at absorption edges. To avoid
this, use of a doped silicon photodiode should be considered.

ISBN 978-3-95450-119-9
2Transverse & Longitudinal Emittance Measurements

Photon count [ 1011 ph s−1 per 0.1% b.w.]

Proceedings of IBIC2012, Tsukuba, Japan

MOCB04

Measured undulator spectrum

1

2.5 ± 1.0 pm
5.5 ± 1.7 pm
9.2 ± 2.5 pm
84 ± 13 pm
EPU gap 100 mm

0.8
0.6
0.4
0.20800

1000

1200

1400
Photon energy [eV]

1600

1800

2000

Figure 4: Measured vertical undulator ﬂux passing an on-axis pinhole.

Measured Undulator Spectra
The measured undulator spectra are plotted in Figure 4above. Four vertical emittance lattice conﬁgurations wereconsidered, with the undulator closed to a gap of 17.1 mm,
close to the minimum gap. This corresponds to an undulator deﬂection parameter of K = 3.85. The sensitivity ofthis technique to small vertical emittances is illustrated inFigure 5 below. The even undulator harmonics 6 – 14 areshown on an expanded vertical scale, to highlight the measurable separation in intensity of undulator spectra between
beams of several picometre vertical emittance.

Table 1: Measured Flux Ratio F10 /F11εy [pm rad]F10 /F1184 ± 139.2 ± 2.5
5.5 ± 1.7
2.6 ± 1.0

0.204 ± 0.006
0.083 ± 0.005
0.078 ± 0.005
0.074 ± 0.005

DISCUSSION
Future diagnostics and applications of vertical undulators to synchrotron light source storage rings are summarised.

Background Flux
The background was estimated by measuring the photonﬂux with the undulator open to 100 mm, close to the maximum gap. This is shown in black on Figures 4 – 5. Withthe undulator open to 100 mm, the ﬁrst undulator harmonicis shown in the measured spectrum at 1140 eV, and is not abackground feature.

Measured Flux Ratio
The ratio of ﬂuxes of adjacent harmonics is evaluated for
10 and 11. The results are summarised in Table 1 below.
The vertical emittance and corresponding uncertainty wasevaluated using orbit response matrix analysis. Uncertainty
in the corresponding ratio of ﬂuxes is estimated from systematics in measurement of the background ﬂux, as well asstatistical uncertainties. This measured ratio can be compared with simulation of the apparatus, however to extract
a meaningful measurement of the emittance, the vertical dimension of the pinhole must be known. It can be seen thatfor this unknown pinhole dimension, that picometre beamemittances are resolvable at the level of a factor of two.

SOLEIL DiagOn
Recently, direct of projections of undulator harmonics
have been measured at SOLEIL [16]. Designed as a beamdiagnostic for APPLE-II insertion devices, the reported
DiagOn device measures the distribution of horizontallypolarised undulator radiation at a ﬁxed photon energy. By
rotating the device around the beam axis to pass photons ofvertical polarisation, the inteference pattern at ﬁxed energy
could be measured to observe the vertical emittance.

Vertical Undulator
As an aside to emittance measurement, vertical undulators may be used with existing storage rings to provide amore brilliant photon source. As shown in Figure 1 thebrilliance of high, odd undulator harmonics is a factor of
two greater for the undulator in the vertical rather thanhorizontal conﬁguration, at vertical emittances of several
pm rad. These small vertical emittances are achievable atmany storage ring light sources.

ISBN 978-3-95450-119-9
Transverse & Longitudinal Emittance Measurements

3c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○RESULTSc 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○

0.6
0.4
0.2
0760

0.8

800840
Photon energy [eV]0.8

Harmonic 120.60.40.2
00.8

1600
1640
Photon energy [eV]Harmonic 80.60.40.2010401080
1120
Photon energy [eV]0.8

Harmonic 100.6
0.40.2013201360
Photon energy [eV]Harmonic 14
84 ± 13 pm

0.6

9.2 ± 2.5 pm
5.5 ± 1.7 pm

0.4

2.6 ± 1.0 pm

0.201840[1010 ph s−1 per 0.1% b.w.]

Harmonic 6[1010 ph s−1 per 0.1% b.w.]

0.8

Proceedings of IBIC2012, Tsukuba, Japan[1010 ph s−1 per 0.1% b.w.][1010 ph s−1 per 0.1% b.w.][1010 ph s−1 per 0.1% b.w.]

MOCB04

EPU gap 100 mm
1880
1920
Photon energy [eV]Figure 5: Even harmonics shown on expanded vertical scale, with background subtracted. The even harmonics 6 – 14 areillustrated for vertical emittances of 2.5, 5.2, 9.2 and 84 pm rad. Also shown in black is the undulator spectrum measured
with the EPU open to 100 mm, for which the photon energy of the ﬁrst harmonic is Eph = 1140 eV.

CONCLUSION
We have reported on initial work to measure verticalemittance using a vertical undulator. Using simulations, wedemonstrate the usefulness of vertical undulators as a diagnostic for vertical emittance. Preliminary measurements ofundulator spectra are presented that demonstrate the highsensitivity of vertical undulators to picometre vertical emittances. Future applications of this technique are explored,
notably the possibility of imaging the interference pattern
at a ﬁxed photon energy.

ACKNOWLEDGEMENTS
This research was undertaken on the soft x-ray beamlineon the storage ring at the Australian Synchrotron, Victoria,Australia.

REFERENCES[4] Å. Andersson, et al., Proceedings of EPAC 1998, Stockholm, Sweden, WEP05J, June (1998)[5] B.X. Yang and J.J. Xu, Proceedings of PAC 2001, Chicago,USA, WPAH108, June (2001)[6] M. Bakeman, et al., Proceedings of PAC 2009, Vancouver,Canada, WE6RFP074, May (2009)[7] M. Bakeman, et al., Proceedings of PAC 2011, New York,USA, MOP161, March (2011)[8] T. Tanaka and H. Kitamura, J. Synch. Rad. 8, 1221 (2001)[9] G.S. LeBlanc, M.J. Boland and Y.-R.E. Tan, Proceedings ofEPAC 2004, Lucerne, Switzerland, THPKF005, July (2004)[10] G. Dattoli and G. Voykov, Il Nuovo Cimento B 111, 743(1996)[11] B. C. Cowie, A. Tadich, and L. Thomsen, AIP Conf. Proc.
1234, 307 (2010)[12] C. Ostenfeld, et al., Proceedings of PAC 2007, Albuquerque,USA, TUPMN006, June (2007)[13] J. Safranek, Nucl. Instrum. Methods A 388, 27 (1997)[1] M. Aiba, M. Böge, N. Milas, and A. Streun, Nucl. Instrum.
Methods A 694, 133 (2012)[14] R. Dowd, et al., Phys. Rev. ST Accel. Beams 14, 012804(2011)[2] K.P. Wootton, M.J. Boland, R. Dowd, Y.-R.E. Tan, B.C.C.
Cowie, Y. Papaphilippou, G.N. Taylor, and R.P. Rassool.
Manuscript submitted for publication.

[15] M. Krumrey and E. Tegeler, Rev. Sci. Instrum., 63 (1), 797(1992)[3] E. Tarazona and P. Elleaume, Rev. Sci. Instrum. 67 (9),3368-3368 (1996)[16] T. Moreno, E. Otero, and P. Ohresser, J. Synch. Rad. 19, 179(2012)

ISBN 978-3-95450-119-9
4Transverse & Longitudinal Emittance Measurements