67th ICFA Adv. Beam Dyn. Workshop Future Light Sources
ISBN: 978-3-95450-224-0
ISSN: 2673-7035

FLS2023, Luzern, Switzerland

JACoW Publishingdoi:10.18429/JACoW-FLS2023-TU4P26

J. Kallestrup∗ , M. Aiba, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
Abstract

and

The SLS 2.0 storage ring will achieve low emittance andhigh brightness while maintaining large dynamic apertureand lifetime comparable to the present SLS. Special operational modes are investigated to further explore the potentialof the lattice. In this contribution, the first considerations
on such modes for the SLS 2.0 are outlined. A promisinghigh-brightness mode, increasing brightness by up to 25%
at insertion devices with minor deterioration to dynamic andmomentum aperture is presented. The use of round beams
and its impact on beam dynamics and the beamlines in theSLS 2.0 portfolio is discussed.

INTRODUCTION
One of the main goals of the SLS 2.0 is to minimize thenatural emittance of the machine, thereby generating significantly higher brightness than the existing SLS. This isachieved using a seven-bend achromat with longitudinal gradient bends and reverse bends [1, 2]. In this contribution we
explore two possible operational modes for SLS 2.0. We investigate the option of a high-brightness mode which lowers
the beta-functions at the insertion device (ID) source points.
Finally, we show a possible implementation of round beams
in SLS 2.0 in combination with one of the high-brightness
lattice options, and evaluate the impact on both machine andbeamline performance.

HIGH-BRIGHTNESS MODE
Motivation
The goal of the SLS 2.0 lattice design has been to create alattice that provides an order-of-magnitude higher brightnessand higher coherent flux than the existing SLS, withoutcompromising with the dynamic and momentum apertureof the machine [2]. This leads to an ambitious, but realistic
design. However, the brightness of IDs can be increased by
optimizing the beta-functions in the straight sections further.
We follow the definitions of brightness and spatial coherence as given in [3], defined as:

and

Φph
ℬ=,
2
4𝜋 𝜎T𝑥 𝜎T𝑥′ 𝜎T𝑦 𝜎T𝑦′ (𝑑𝜔/𝜔)

(1)

Φcoh
𝜆2=,
Φph
16𝜋2 𝜎T𝑥 𝜎T𝑥′ 𝜎T𝑦 𝜎T𝑦′(2)where Φph and Φcoh are the total and spatially coherent flux,
𝜆 is the photon wavelength, 𝜎Tu and 𝜎Tu’ are the effective
photon source size and divergence defined as𝜎T𝑢 = √𝛽𝑢 𝜖𝑢 +∗ jonas.kallestrup@psi.ch

𝜆𝐿,8𝜋(3)𝜎Tu’ = √(1 + 𝛼2𝑢 )𝜆𝜖𝑢 +,
𝛽𝑢2𝐿(4)

where 𝛽𝑢 and 𝛼𝑢 are the Twiss parameters at the ID source
point. The SLS 2.0 portfolio contains IDs of several differentlengths. The brightness and the coherence depends on theID length, 𝐿, and we compute them for a range of 1 ≤ 𝐿 ≤3 m, corresponding to the actual IDs to be installed.
In the following, first the possibilities for brightness improvement without physically modifying the storage ring areinvestigated. Next, the option of increasing the gradient ofquadrupoles will be considered.
The linear optics changes will be restricted to the straightsections to avoid modifying the optimized arc optics. This
also means that the equilibrium emittances will remain unchanged.
The baseline SLS 2.0 lattice is designed such that thebetatron phase advances along each straight section are
the same constant values. The super-periodicity for onmomentum particles is therefore as high as the number ofarcs: 12 (“pseudo symmetry”). To maintain good dynamic
and momentum aperture, it is beneficial to keep the pseudo
symmetry and, hence, the phase advance must be increased
equally in all straight sections.
For each proposed solution, a genetic algorithm is used
to optimize the nonlinear magnets in the lattice to maximize
Touschek lifetime, 𝜏𝑇 . Piwinski’s formula for the Touschek
lifetime is used [4], with the nominal “flat beam emittances”
𝜖𝑥 = 149 pm rad and 𝜖𝑦 = 10 pm rad. All tracking simulations are performed in Accelerator Toolbox [5, 6].
We are interested in the relative increase in brightness
and coherence between the baseline SLS 2.0 lattice and thenew high-brightness solutions. The denominators of Eqs.
(1) and (2) both scale as (𝜎Tx 𝜎Tx′ 𝜎Ty 𝜎Ty′ )−1 , meaning thatthe scaling of brightness and coherence will be the same,
and we will therefore only report impacts on brightness.

Solutions-A: Unaltered Machine Layout
Two options are investigated for an unaltered machinelayout: increasing the horizontal tune by a full integer (“solution A-1”) or increasing the vertical tune by 0.56 (“solutionA-2”). A comparison between the baseline and new Twiss
parameters in the straight sections is shown in Table 1, andthe relative brightness increases for IDs of the three lengths
are shown in Fig. 1 for solution A-1 and A-2 as solid anddashed lines, respectively. Qualitatively, short IDs have thelargest gain in brightness. Solution A-1 provides the biggest
increase around the soft x-ray region of 1 keV photon energies, while solution A-2 is most beneficial around hard
x-rays at 10 keV. Long straight sections benefit in a broader
spectral range; for high photon energies this stems from thesmaller values of 𝛼𝑥 and 𝛼𝑦 at the source points.
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SPECIAL OPERATIONAL MODES FOR SLS 2.0

B-1

𝑄𝑥
𝑄𝑦

SSMS
LS#1
LS#2
SSMS
LS#1
LS#2
SSMS
LS#1
LS#2
SS
MS
LS#1
LS#2-39.37
15.22
2.5
3.4
9.3
7.8
1.3
2.4
6.5
5.8
0.0
−0.1
−0.4
0.4
0.0
−0.1
−0.9
0.7
5.4

40.37
15.22
1.4
2.0
7.2
5.0
1.3
2.3
6.4
5.7
0.0
0.0
0.0
0.0
0.0
−0.1
−0.8
0.6
4.7

39.37
15.78
2.5
3.5
9.5
8.0
0.6
1.2
5.4
3.3
0.0
−0.1
−0.7
0.5
0.0
0.2
0.1
−0.1
4.8

40.37
15.78
1.5
2.0
7.0
5.3
0.5
1.0
5.9
3.0
0.0
0.0
−0.1
0.1
0.0
0.2
0.2
−0.2
<1

𝛽𝑥 [m]

𝛽𝑦 [m]𝛼𝑥𝛼𝑦
𝜏T [h]The results for the on- and off-momentum dynamic apertures without errors are shown in Fig. 2. The physical aperture restriction is 5.0 mm, i.e., the dynamic aperture is stilloutside the physical aperture of the chamber. The Touschek
lifetime (with physical aperture but without third harmoniccavity) is found to be 4.7 h and 4.8 h for solutions A-1 and A2, respectively, corresponding to a 13% and 11% reduction
compared to the nominal lattice lifetime of 5.4 h.

Solutions-B: Modified Machine Layout
The potential phase advance increase is limited in the shortstraight sections due to the limited strength of quadrupolesin the matching sections. An option of installing stronger
quadrupoles is evaluated as a hypothetical future upgrade
option. We investigated a working point of [40.37, 19.78],
i.e., combining the features of solutions A-1 and A-2, that requires the stronger, but still achievable, quadrupole strength
118 T m−1 .
The relative increase in brightness is shown as the dottedlines in Fig. 1. This solution exceeds the previous two withsignificant gains particularly in the tender and hard x-ray
range. For one of the flagship beamlines, I-TOMCAT, ahard x-ray beamline based on a 1 m high-temperature superconducting undulator in a short straight section [1, 7], theexpected increase in brightness at 10 keV is around 50%.
The nonlinear optimization of this solution has yet to yieldsatisfying Touschek lifetime; the working point is close tothe 𝑄𝑥 + 2𝑄𝑦 = 72 resonance, which is systematic for a
twelve-fold symmetric machine, and is suspected to be thelimitation for this lattice solution. Other modified lattices

B low- /B 0A-2

1.5

L undu = 1 m

1.4
1.3
1.2
1.1

1.5
1.4
1.3
1.2
1.1

1102

103

104

105

Photon energy [eV]101610 2

10 3

10 4

10 5

Photon energy [eV](a) Short straight

10 6(b) Medium straight

1.7

1.7

1.6

1.6

1.5

1.5

B low- /B 0A-1

1.6

L undu = 2 m

1.4
1.3
1.2
1.1

1.4
1.3
1.2
1.1

1

102

103

104

105

Photon energy [eV]101610 2

10 3

10 410 5

Photon energy [eV](c) Long straight #1

10 6(d) Long straight #2Figure 1: Ratio of brightness between the nominal SLS 2.0
lattice and high-brightness options A-1 (solid lines), A-2(dashed lines) and B-1 (dotted lines) in each straight section
for various undulator lengths.
6644

y [mm]

Baseline

1.7

L undu = 3 m

1.6

B low- /B 0Source

1.7

B low- /B 0

Lattice

JACoW Publishingdoi:10.18429/JACoW-FLS2023-TU4P26

y [mm]

Table 1: Optics of baseline and high-brightness lattice solutions. Twiss parameters refer to the source points ofshort (SS), medium (MS), long straight #1 (LS#1) and longstraight #2 (LS#2), respectively.

FLS2023, Luzern, Switzerland

20-10-5(a)0x [mm]510𝛿𝑝
𝑝 = 0%StandardA-1A-2

20-10-5(b)0x [mm]510𝛿𝑝𝑝 = −3%6y [mm]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

67th ICFA Adv. Beam Dyn. Workshop Future Light Sources
ISBN: 978-3-95450-224-0
ISSN: 2673-7035

420-10-5(c)0x [mm]510

Figure 2: Dynamic apertures
for the baseline SLS 2.0 latticeand high-brightness solutions
A-1 and A-2 at the injection
septum.

𝛿𝑝
𝑝 = +3%

with, e.g., working points [40.37, 16.22] are currently underdevelopment.

Further Considerations
For the high-brightness lattices with increased horizontal
tune, the smaller 𝛽𝑥 at the source points comes with theincreased horizontal phase advance. Due to the twelve-foldpseudo symmetry it becomes more challenging to maintaina large value of 𝛽𝑥 at the injection point, which is used toincrease the dynamic aperture for off-axis injection. Nevertheless, the nonlinear optimization provides on-momentum
dynamic apertures exceeding the physical apertures.

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JACoW Publishing

L undu = 1 m

11L undu = 2 m

0.8

L undu = 3 m

0.6
0.4
0.2
0

ROUND BEAM MODE

0.8
0.6
0.4
0.2

102

103

104105Photon energy [eV]0106(a) Short straight

Motivation𝐽𝑥
𝜖𝑥 = 𝜖𝑦 = 𝜖0 (),𝐽𝑥 + 𝐽 𝑦(5)where 𝜖0 is the natural emittance, 𝐽𝑥 and 𝐽𝑦 are the horizontal and vertical damping partition numbers, respectively. For SLS 2.0, with a natural emittance of 149 pm rad,𝐽𝑥 = 1.85 and 𝐽𝑦 = 1, the emittances will become 𝜖𝑥 = 𝜖𝑦 =96 pm rad.
The “A-1” high-brightness lattice setting has the attractive
feature that the horizontal and vertical beta-functions at theID source points in all sections are approximately equal. Thismeans that, by coupling the beam transversely, it is possible
to create photon beams with approximately identical sizes
and divergences in both transverse planes.

Optics Options
For this purpose, a special version of the “A-1” solution isdeveloped, henceforth called “A-1R”, with the working point[40.37, 15.37]. Optical functions do not differ significantly
from the values in Table 1. A coupling coefficient of |𝐶 − | =0.01 is introduced using 72 non-dispersive skew quadrupoles.
This value is selected to ensure that all particles within theequilibrium bunch experience resonant coupling [13].
To quantify the effect of the coupling sources on the lattice performance, we calculate the Touschek lifetime forboth the uncoupled and coupled lattices using the flat beamemittances including the physical apertures. The lifetimes
become 4.3 h for the uncoupled and coupled lattice. Next,
the Touschek lifetime is evaluated using the round beamemittances (Eq. (5)). This leads to 𝜏𝑇 = 10.6 h, around afactor two larger than for the baseline SLS 2.0 lattice.

Beamline Perspective
The denominators of Eqs. (1) and (2) contain the electron
beam sizes and divergences and, hence, the emittances. The
larger vertical emittances will thereby lead to lowering thebrightness and spatial coherent flux for the round beam mode.

104105106

Bround/B 010.8
0.6
0.40.20103(b) Medium straight

1Bround/B 0

The use of round beams means redistributing the equilibrium emittance between the two transverse planes. Twobenefits arise from this: the horizontal emittance is lowered,
while the Touschek lifetime is increased and intrabeam scattering is reduced. Round beam operation is being considered
and tested at several light source including SLS 2.0 [8–13].
The simplest way to generate the round beam is by operating the storage ring on the linear difference resonance𝑄𝑥 − 𝑄𝑦 = 𝑝, where 𝑝 is an integer. On the resonance theemittances will become [14]:102

Photon energy [eV]0.80.60.40.2

102103104105Photon energy [eV](c) Long straight #1

106

0102

103

104105Photon energy [eV]106(d) Long straight #2

Figure 3: Ratio of brightness between the nominal SLS 2.0
lattice and round beam lattice solution A-1R with working
point [40.37, 19.37] in various straight sections for different
undulator lengths.
Figure 3 shows the brightness of the round beam lattice
relative to the baseline lattice as a function of photon beamenergy. Not all beamlines may benefit from the round beammode, but it can be enabled upon request and by agreementwith the users.

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doi:10.18429/JACoW-FLS2023-TU4P26

Bround/B 0Increasing the focusing gradient of the quadrupoles is technologically challenging, and it might therefore be simpler
to install additional quadrupoles within the straight sections.
This would, however, limit the available length for IDs. The
trade-off between ID length and stronger focusing at thesource points must be thoroughly evaluated.

FLS2023, Luzern, SwitzerlandBround/B 0

67th ICFA Adv. Beam Dyn. Workshop Future Light Sources
ISBN: 978-3-95450-224-0
ISSN: 2673-7035

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

67th ICFA Adv. Beam Dyn. Workshop Future Light Sources
ISBN: 978-3-95450-224-0
ISSN: 2673-7035[9] Y. Hidaka, W. X. Cheng, Y. Li, T. V. Shaftan, and G. M.
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doi:10.18429/JACoW-IPAC2018-THPMF036

FLS2023, Luzern, Switzerland

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[14] A. W. Chao and M. J. Lee, “Particle distribution parametersin an electron storage ring”, J. Appl. Phys., vol. 47, pp. 44534456, 1976. doi:10.1063/1.322412

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