diffraction-limited storage rings
Journal of
Synchrotron
Radiation
The MAX IV storage ring project
ISSN 1600-5775
Pedro F. Tavares,* Simon C. Leemann, Magnus Sjöström and Åke Andersson
Received 28 February 2014
Accepted 19 May 2014
MAX IV Laboratory, Lund University, PO Box 118, SE-221 00 Lund, Sweden.
*E-mail: pedro.fernandes_tavares@maxlab.lu.se
The MAX IV facility, currently under construction in Lund, Sweden, features
two electron storage rings operated at 3 GeV and 1.5 GeV and optimized for the
hard X-ray and soft X-ray/VUV spectral ranges, respectively. A 3 GeV linear
accelerator serves as a full-energy injector into both rings as well as a driver for a
short-pulse facility, in which undulators produce X-ray pulses as short as 100 fs.
The 3 GeV ring employs a multibend achromat (MBA) lattice to achieve, in a
relatively short circumference of 528 m, a bare lattice emittance of 0.33 nm rad,
which reduces to 0.2 nm rad as insertion devices are added. The engineering
implementation of the MBA lattice raises several technological problems. The
large number of strong magnets per achromat calls for a compact design
featuring small-gap combined-function magnets grouped into cells and sharing
a common iron yoke. The small apertures lead to a low-conductance vacuum
chamber design that relies on the chamber itself as a distributed copper absorber
for the heat deposited by synchrotron radiation, while non-evaporable getter
(NEG) coating provides for reduced photodesorption yields and distributed
pumping. Finally, a low main frequency (100 MHz) is chosen for the RF system
yielding long bunches, which are further elongated by passively operated thirdharmonic Landau cavities, thus alleviating collective effects, both coherent (e.g.
resistive wall instabilities) and incoherent (intrabeam scattering). In this paper,
we focus on the MAX IV 3 GeV ring and present the lattice design as well as the
engineering solutions to the challenges inherent to such a design. As the first
realisation of a light source based on the MBA concept, the MAX IV 3 GeV
ring offers an opportunity for validation of concepts that are likely to be
essential ingredients of future diffraction-limited light sources.
Keywords: storage ring; synchrotron light source; multibend achromat.
1. Introduction
The MAX IV facility, currently under construction in Lund,
Sweden, is the first of a new generation of storage-ring-based
synchrotron light sources which employ a multibend achromat
lattice to reach emittances in the few hundred pm rad range in
a circumference of a few hundred metres, thus enabling the
realisation of a new class of experiments which are critically
dependent on source brightness and transverse coherence.
Central to the MAX IV design concept is the notion that
the diverse needs of the user community are difficult to satisfy
with a single source without compromising performance. In
fact, the scientific case for the MAX IV project (MAX IV,
2006) requires high average brightness over a wide spectral
range from infrared to hard X-rays as well as intense short
X-ray pulses in the fs range. An analysis (MAX IV, 2006) of
alternative solutions to meet those requirements led to the
conclusion that storage-ring-based sources are likely to
continue to be the workhorse of synchrotron-radiation-based
research for the foreseeable future and that recent advances in
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doi:10.1107/S1600577514011503
accelerator lattice design and engineering development in key
subsystems indicated the possibility of a substantial decrease
in storage ring emittance, bringing those sources closer to the
diffraction limit at X-ray wavelengths. Moreover, the growing
demand for temporally as well as spatially coherent radiation
pointed to the fact that free-electron lasers will also open new
research opportunities.
All of those considerations were included in a facility-wide
optimization procedure that led to a design (MAX IV, 2010)
based on three sources sharing a common site and infrastructure (Fig. 1):
(i) Two electron storage rings operating at different energies (1.5 GeV and 3 GeV) in order to cover a wide photon
energy range in an optimized way with short-period insertion
devices.
(ii) A linear accelerator which acts as a full-energy injector
into both rings and provides electron pulses with duration
below 100 fs to produce X-rays by spontaneous emission in the
undulators of a short-pulse facility (SPF) (Werin et al., 2009;
Thorin et al., 2011). The 3 GeV linear accelerator also allows a
J. Synchrotron Rad. (2014). 21, 862–877
diffraction-limited storage rings
Figure 1
Overview of the MAX IV facility.
future upgrade to a fully coherent free-electron laser source
based on seeding and/or cascading (Čutić et al., 2010; Curbis et
al., 2013).
The 3 GeV ring (Leemann et al., 2009; Eriksson et al., 2011)
is optimized for the production of high-brightness hard X-ray
beams and features a 20-fold seven-bend achromat lattice,
reaching a bare lattice emittance of 0.33 nm rad, which is
further reduced to 0.2 nm rad when insertion devices are
added. In order to reach such a low emittance in a circumference of only 528 m, a compact magnet design is mandatory.
This implies the use of small magnet gaps (Johansson et al.,
2011), which allows reaching larger integrated gradients in
shorter magnets and reduces the minimum required distance
between consecutive magnets. Moreover, these compact
magnets are built as integrated units in which the bending
magnet poles and quadrupole pole roots are machined out of a
pair of iron blocks, which are assembled together, each unit
holding all the magnets of a complete cell. This concept leads
to alignment accuracy within a cell being determined by
machining and assembly accuracy, rather than fiducialization
methods and also makes for high natural vibration frequencies
of the units, thus reducing the sensitivity of the magnets to
the environmental vibrational noise. Finally, the integrated
magnet concept allows for streamlined installation and system
testing.
The compact magnet design leads to narrow low-conductance vacuum chambers (Al-Dmour et al., 2011), which
necessitate distributed pumping and distributed absorption of
the heat load from synchrotron radiation. The heat load
problem is dealt with by choosing copper as the chamber
material and providing water cooling along the extended
region over which the synchrotron radiation heat is deposited,
whereas distributed pumping is provided by non-evaporable
getter (NEG) coating of the chamber’s inner surface. As a
result, the number of required lumped pumps and absorbers is
significantly reduced with a corresponding reduction in cost
and complexity.
J. Synchrotron Rad. (2014). 21, 862–877
The reduced chamber dimensions
lead to an increased risk of collective
instabilities (Tavares et al., 2011), such
as coupled bunch instabilities driven
by the resistive wall impedance. A key
ingredient in facing that problem is the
use of passively operated harmonic
cavities, which lengthen the bunches,
reduce the electron density, help keep
the heat load from beam-induced fields
on vacuum components down to
acceptable levels, and increase the
incoherent synchrotron frequency
spread that enhances Landau damping
of coherent instabilities.
The RF system (Andersson et al.,
2011) operates at 100 MHz and uses
capacitive-loaded normal conducting
cavities, of the same type as previously
developed for MAX II and MAX III.
The choice of RF frequency allows a large bucket height with
relatively low RF voltage and power to be achieved, which can
be obtained from standard high-efficiency RF transmitters
largely used in telecommunications, leading to low investment
and operation costs. Moreover, the cavity design pushes the
frequencies of the first higher-order modes (HOMs) of the
cavity to about four times the fundamental mode frequency, so
as to reduce the overlap of the cavity impedance spectrum
with the spectrum of the lengthened bunches.
The 1.5 GeV ring (MAX IV, 2010; Leemann, 2012c) will
replace the existing MAX II (Andersson et al., 1994) and
MAX III (Sjöström et al., 2009) rings in delivering UV, soft
X-ray and infrared radiation. With about the same circumference (96 m) as MAX II, the 1.5 GeV ring will deliver a
smaller emittance (6 nm rad) than its predecessor by applying
the same compact multipurpose magnet design concept
(Johansson, 2011) as in the 3 GeV ring to a 12-fold DBA
lattice. Here, two gradient dipole magnets, three combined
quadrupole/sextupole magnets as well as four pure sextupoles
and four combined trim sextupoles/orbit correctors are all
integrated into a single iron block pair comprising a full DBA
arc. An exact copy of the 1.5 GeV ring is being built at the
Polish laboratory Solaris (Bocchetta et al., 2012).
2. Lattice and optics
The 3 GeV storage ring will serve as the main radiation source
of the MAX IV facility. In order to generate high-brightness
hard X-rays with state-of-the-art insertion devices (IDs), an
ultralow-emittance design was targeted. One simple and
robust method to achieve ultralow emittance is the use of a
multibend achromat (MBA) lattice (Einfeld & Plesko, 1993;
Joho et al., 1994; Einfeld et al., 1995; Kaltchev et al., 1995). The
MBA exploits the inverse cubic dependence of emittance on
the number of bending magnets.
By choosing a very small bending angle per dipole the
emittance can be dramatically reduced. By introducing a
Pedro F. Tavares et al.
The MAX IV storage ring project
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diffraction-limited storage rings
vertically focusing gradient in the
dipoles the emittance is further reduced
(the emittance scales inversely with the
horizontal damping partition Jx ) while
the dispersion is limited to small values
without requiring any extra space
Figure 2
for vertically focusing quadrupoles.
Schematic of one of the 20 achromats of the MAX IV 3 GeV storage ring. Magnets indicated are
Because of the resulting low dispersion,
gradient dipoles (blue), focusing quadrupoles (red), sextupoles (green) and octupoles (brown).
the MBA lattice allows the use of
narrow vacuum chambers without
limiting momentum acceptance. This in turn enables narrow
magnet gaps and hence magnets with strong gradients can
become very compact (additionally, the compact magnets
reduce the power consumption and hence the running cost).
The compact magnets allow for a shorter unit cell; thus
the number of unit cells for a given circumference can be
increased. This in turn allows to further reduce the bend angle
per unit cell which leads to even lower emittance (and in
addition reduces the radiation heat load on the vacuum
chamber). Thus, the MBA design approach closes a positive
feedback cycle.
Before the MBA concept was first applied to a light source
at MAX IV, this concept had been suggested for booster
Figure 3
synchrotrons (Mülhaupt, 1994) of which several operate
functions and dispersion for one achromat of the MAX IV 3 GeV
storage ring. Magnet positions are indicated at the bottom.
successfully today (Joho et al., 2006; Georgsson et al., 2004;
Benedetti et al., 2008). Distributing many sextupoles and/or
field drop-off towards the long straight reduces the amount of
making use of combined-function magnets throughout the
radiation hitting a downstream ID therefore facilitating the
MBA lattice allows the chromaticity to be corrected where it is
design of superconducting IDs.1 All dipoles contain a vertigenerated (Klotz & Mülhaupt, 1992) giving large dynamic
aperture and good off-energy performance. By introducing
cally focusing gradient. The matching cells contain dedicated
octupoles alongside the many sextupoles and carefully
quadrupole doublets in order to match the achromat optics to
balancing non-linear magnet families, the non-linear optics
the ID in the long straight. Each achromat also contains two
can be tuned for large momentum acceptance (MA) and
1.3 m short straights that separate the matching cells from the
dynamic aperture (DA) providing both long Touschek lifetime
unit cells. The short straights are used for RF cavities and
and high injection efficiency despite the very low emittance
diagnostics so that all long straights but the injection straight
(Leemann et al., 2009; Leemann & Streun, 2011).
are available for installation of IDs.
From its initial proposal in 2002 (Eriksson, 2002), the
Since the vertical focusing is performed by the gradient
MAX IV 3 GeV storage ring lattice went through several
dipoles, dedicated quadrupoles are, apart from ID matching
iterations (Tarawneh et al., 2003; Eriksson et al., 2007, 2008)
(cf. x2.3), only required for horizontal focusing. Horizontally
until a finalized version (Leemann et al., 2009; MAX IV, 2010)
focusing quadrupoles are installed between the cells of the
was funded in 2010. The optics were subsequently refined
achromat in pairs of two where the two quadrupoles are
(Leemann, 2011a,b) and a few minor modifications were made
installed on either side of a sextupole magnet. There are two
as a result of detailed magnet and vacuum systems engineering
families of focusing quadrupoles, one in the unit cells and one
(Leemann, 2011c, 2012d). Further optics optimization is
in the matching cells. Adjustment of the vertical focusing is
ongoing both in terms of choice of operational parameters
performed by exciting a current in the pole-face strips (PFSs)
(Leemann & Eriksson, 2013) as well as further modifications
that are installed in all dipoles. Such a lattice leads to very
to user optics (Leemann & Eriksson, 2014).
compact optics with strong focusing, low functions, and very
small peak dispersion. The optics for one achromat are
displayed in Fig. 3 and ring parameters are given in Table 1.
2.1. Linear optics
The working point was chosen away from systematic resonances so that both fractional tunes are just above the integer
The MAX IV 3 GeV storage ring consists of 20 seven-bend
achromats separated by 4.6 m long straight sections for IDs.
1
An overview of one MAX IV achromat is shown in Fig. 2.
Note that this slightly increases the bare lattice emittance. Longitudinal
Each of the achromats consists of five unit cells and two
gradients in bending magnets can be used to reduce the emittance (Nagaoka &
Wrulich, 2007; Guo & Raubenheimer, 2002; Streun, 2004; Leemann & Streun,
matching cells. The unit cells have a 3 bending magnet, while
2011), but this requires the bending radius to grow as the dispersion invariant
the matching cells at the ends of the achromat have a 1.5 softH increases. For the soft-end bending magnets in MAX IV the zero-dispersion
end bending magnet. In these soft-end dipoles, the magnetic
end of the bend is where the largest bending radii are.
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J. Synchrotron Rad. (2014). 21, 862–877
diffraction-limited storage rings
Table 1
Main parameters of the MAX IV 3 GeV storage ring.
Parameter
Value
Unit
Energy, E
Circumference, C
Maximum circulating current, I
Main radio frequency, fRF
Number of long straights
(available for IDs)
Betatron tunes, x,y
ð0Þ
Natural chromaticities, x;y
Corrected chromaticities, x;y
Momentum compaction, c, 2
Horizontal damping partition, Jx
Bare lattice emittance at zero
current, "0
Bare lattice natural energy
spread at zero current,
Bare lattice radiation losses
3.0
528
500
99.931
20 (19)
GeV
m
mA
MHz
42.200, 16.280
49.984, 50.198
+1.0, +1.0
3.06 104, 1.40 104
1.847
328
pm rad
0.769 103
363.8
keV per turn
and away from the most dangerous resonances. With the
working point held constant during operation (cf. x2.3), the
non-linear optics can be adjusted to minimize the chromatic
and amplitude-dependent tune shifts (ADTSs), therefore
keeping the tunes of most stored beam particles clear of
dangerous resonances. This shall be explained in the next
section.
2.2. Non-linear optics
Despite comparably relaxed linear optics, the non-linear
optics of such a MBA lattice are demanding. The strong
focusing gives rise to large negative natural chromaticities that
need to be corrected to prevent head–tail instability. This can
be performed with chromatic sextupoles. Because of the low
dispersion in the MBA these sextupoles tend to become very
strong. Although this is not a concern for the magnet design
(the 25 mm nominal magnet bore allows strong gradients), it
presents an optics design challenge as such strong sextupoles
give rise to pronounced non-linear amplitude-dependent
behaviour, which can limit both DA and MA. The most
common approach is to install several additional families of
sextupoles separated by appropriate phase advances in an
attempt to cancel resonance driving terms and limit chromatic
tune shifts (Bengtsson, 1988, 1997a; Streun, 2012).
The MAX IV 3 GeV storage ring contains five sextupole
families, three focusing and two defocusing. The focusing
sextupoles are installed between the focusing quadrupoles
in the unit cells. This puts these sextupoles at locations with
comparably large horizontal function and dispersion. The
defocusing sextupoles are installed as close as possible to the
maximum of the product of dispersion and vertical : unit cell
dipoles are flanked on either side by a defocusing sextupole of
one family while the defocusing sextupoles in the matching
cells are installed in the short straights right next to the
matching cell soft-end dipole. In this way, sextupoles
compensate chromaticity where it is created thus limiting
chromatic beating (Mülhaupt, 1994). Because of the large
number of installed sextupoles and the small magnet gap, the
sextupoles can be kept short.
J. Synchrotron Rad. (2014). 21, 862–877
Sextupole optimization was performed with the codes OPA
(Streun, 2010) and Tracy-3 (Bengtsson, 1997b). The linear
chromaticities were corrected to +1.0 in both planes2 and the
first-order resonance driving terms along with second- and
third-order chromaticity were minimized as detailed by Streun
(2012). However, amplitude-dependent tune shifts are only
corrected as a second-order effect in sextupoles, therefore
requiring a lot of sextupole gradient strength and in turn
driving resonances and chromatic tune shifts. This can necessitate extra sextupoles and/or increased sextupole gradients in
order to keep first-order terms in check. Apart from leading to
a potential run-away problem, this is a delicate balance that
is easily disturbed by IDs, alignment errors and higher-order
multipoles, all of which exist in a real machine.
In an attempt to solve this fundamental challenge of nonlinear optimization in a MBA lattice, three achromatic octupole families were introduced into the matching cells of the
3 GeV achromat in locations with appropriate -function
ratios (Leemann et al., 2009; Leemann & Streun, 2011). These
octupoles correct the three terms for ADTS to first order.
Analogous to the linear system, which is solved to find
sextupole strengths that give a certain chromaticity, a linear
system can be set up to describe the ADTSs that result from
an octupole in the lattice. This system can be inverted to
calculate octupole strengths that give the desired ADTSs.
Rather than setting the linear ADTS to zero, the octupoles
in the MAX IV MBA were adjusted so the resulting overall
ADTS is minimized throughout the physical acceptance (cf.
Fig. 4).
Because the ADTSs are corrected with the octupoles, the
sextupoles are freed up for first-order corrections (linear
chromaticity, resonance driving terms). Some extra weight was
also added to minimize second- and third-order chromaticity
in an attempt to limit the chromatic tune footprint (cf. Fig. 5).
The result of this non-linear optimization is a very limited tune
footprint for particles with a range of amplitudes covering the
physically accessible aperture [roughly 9 mm/2 mm (H/V) at
the centre of the IDs] and energies covering the required
4.5% acceptance. This results in large DA and MA (cf. Fig. 6
and x3.1), which ensure high injection efficiency and good
Touschek lifetime. Frequency map analysis confirms the
‘wrap-up’ of tune shifts around the working point which
results in this compact tune footprint. This holds also for a
realistic machine, i.e. a storage ring with errors, misalignments
and IDs. This shall be discussed in the next section.
2.3. Optics matching and orbit correction
With the quadrupole doublets in the matching cells the
functions in the long straights can be tuned over a fairly wide
range. This allows matching of the linear optics to individual
IDs. The ID matching is performed both locally ( functions
are matched to minimize beat) and globally (phase advances
are corrected to restore the design working point). For the
2
An alternate optics has also been developed with linear chromaticity set to
+4.0 as a fallback solution in case of instability issues during commissioning
(Olsson & Leemann, 2013).
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diffraction-limited storage rings
Figure 6
Dynamic aperture at the centre of the long straight section in the bare
lattice of the MAX IV 3 GeV storage ring (Leemann, 2012d). Tracking
was performed with Tracy-3 in 6D for one synchrotron period. For
comparison, the vacuum chamber and physical aperture (projection of
vacuum chamber to the track point) are also indicated in the plot.
Figure 4
Amplitude-dependent tune shift in the MAX IV 3 GeV storage ring
(Leemann, 2012d). Note the very limited range of tune shifts that result
despite amplitudes extending to the edge of the physical acceptance.
global correction the PFSs in the dipoles can be used to adjust
the vertical focusing. Because this matching results in
restoring the design linear optics within the achromat, the
non-linear optics optimization is left almost undisturbed. If the
multipolar content of the IDs is limited to specified values
(Wallén & Leemann, 2011), neither sextupoles nor octupoles
have to be adjusted with ID gap movement. Tracking studies
with Tracy-3 using kick maps reveal that, in the storage ring
equipped with many strong in-vacuum undulators, the DA
is not substantially reduced if the ID matching is properly
performed. This can be recognized in Fig. 7 where ten typical
in-vacuum undulators (18.5 mm period, 3.7 m magnetic
length, 4.2 mm gap, 1.1 T effective magnetic field) have been
added to the ring and the lattice has been matched to the IDs.
The DA was calculated including various imperfections such as
misalignments (of individual magnets within the magnet block
as well as of the entire block), magnetic field errors and
multipole errors (upright and skew multipoles).
Each achromat also contains ten horizontal and nine
vertical dipole correctors as well as ten beam-position monitors (BPMs) that will be included in a slow orbit feedback.
Because of the vertical beam size in the user straights reaching
values as low as 2 mm r.m.s., beam stability is crucial. There are
Figure 7
Figure 5
Chromaticity in the MAX IV 3 GeV storage ring (Leemann, 2012d).
866
Pedro F. Tavares et al.
The MAX IV storage ring project
On-energy DA at the centre of the long straight section in the MAX IV
3 GeV storage ring where ten in-vacuum undulators have been added to
the ring (Leemann, 2011b). The plot shows the ideal lattice and results for
20 seeds with field and multipole errors as well as misalignments. Tracking
was performed with Tracy-3 in 6D for one synchrotron period.
J. Synchrotron Rad. (2014). 21, 862–877
diffraction-limited storage rings
four dedicated fast corrector pairs installed around each user
straight which, together with the BPM system, will allow
operation of a fast orbit feedback in order to cancel beam
motion effectively up to roughly 100 Hz (cf. x6.5).
Tracking studies have revealed that adequate DA remains
when expected misalignments are added to the lattice and the
orbit is corrected using the dipole correctors (Leemann,
2012d, 2013); this also holds if multipole errors are added to all
magnets (cf. Fig. 7). A crucial ingredient to achieving ample
DA is the magnetic shunting procedure (Leemann, 2012d).
Magnets can be shunted to a common gradient within their
respective families using a parallel circuit of resistor arrays. In
a first stage this shunting is performed after magnet manufacturing according to magnetic field measurement results.
Later this shunting can be revised according to the results of
beam-based calibration measurements [e.g. LOCO (Safranek,
1997)]. In this way a low spread of magnet gradients within
each family can be ensured while allowing for series connection of many magnets to one common power supply via a
single bus.
Finally, all octupoles and sextupoles are equipped with extra
windings that can be powered in various ways. This allows
adding dispersive and non-dispersive skew quadrupoles for
coupling control and removal of spurious vertical dispersion
as well as auxiliary sextupoles in order to restore the design
symmetry of the non-linear optics (Streun, 2012). These
windings can also be powered as upright quadrupoles, which
will be used to calibrate BPMs to the magnetic centres of the
adjacent sextupoles or octupoles.
3. Intrabeam scattering, Touschek scattering and
lifetime
The MAX IV 3 GeV storage ring’s MBA lattice makes use of
a large number of weak bending magnets which leads to low
radiation losses in the dipoles compared with power radiated
from insertion devices. Therefore, the ring’s zero-current
emittance depends strongly on the insertion devices and gap
settings (Leemann, 2014); this means the emittance during a
typical user run is not necessarily constant. In addition, the
large stored current along with the low emittance leads to
strong intrabeam scattering (IBS) which blows up the beam’s
six-dimensional emittance.
Touschek lifetime relies strongly on the six-dimensional
emittance: it grows with increasing longitudinal emittance
which makes bunch lengthening cavities attractive. On the
other hand, in the ultralow-emittance regime (where transverse momenta are small compared with the large momentum
acceptance), reducing the transverse emittance actually
increases the Touschek lifetime (Leemann et al., 2009;
Leemann, 2014). This unusual behaviour in the ultralowemittance regime is depicted in Fig. 8. Damping wigglers and
insertion devices reduce the transverse emittance, but because
their added losses reduce the available cavity overvoltage,
they also lengthen the bunches which can increase the
Touschek lifetime. Overall, Touschek lifetime will vary as a
J. Synchrotron Rad. (2014). 21, 862–877
Figure 8
Touschek lifetime as a function of equilibrium emittance assuming the
bare lattice emittance could be adjusted freely while keeping the energy
spread constant (Leemann, 2012d). The overall MA has been set to 4.5%
while the vertical emittance is adjusted to 8 pm rad. The effect of Landau
cavities (LCs) is included. The equilibrium emittance of the MAX IV
3 GeV storage ring bare lattice "0 = 328 pm rad is indicated.
function of the resulting emittance including IBS as well as
bunch lengthening.
The bare lattice has a zero-current emittance of 328 pm rad,
but, at the shortest bunch length (i.e. at maximum cavity
voltage and without Landau cavities) of 9 mm, IBS blows up
the emittance by 45% for 500 mA of stored current (calculated with ZAP and Tracy-3)3 (Leemann, 2014). However,
once the Landau cavities have been tuned in and the bunches
lengthened to 54 mm (cf. x5.1) as expected during user
operation, the IBS blow-up results in an emittance of
372 pm rad at 500 mA, i.e. only 13% above the zero-current
emittance. For a moderately ID-equipped ring with cavities
running at maximum voltage (giving an RF acceptance of
6.05%), the emittance including the effect of IBS at 500 mA
and Landau cavities is expected to lie around 272 pm rad
corresponding to an IBS blow-up of 16% compared with the
zero-current emittance. The lowest emittance that can be
expected in the 3 GeV ring should result from a ring fully
equipped with IDs. In such a situation the zero-current emittance is expected to be about 187 pm rad which increases to
221 pm rad at 500 mA stored current assuming proper bunch
lengthening from the Landau cavities.
3.1. Momentum acceptance and Touschek lifetime
The 3 GeV storage ring optics have been optimized to
ensure that the MA exceeds 4.5% throughout the entire lattice
in order to allow for roughly 25 h of Touschek lifetime
corresponding to 10 h overall lifetime (see below). In addition
to adequate off-momentum performance, this MA target
requires appropriate dimensioning of the vacuum (cf. x6.2)
and RF systems (cf. x6.3). The underlying assumptions for the
3
The emittance blow-up from IBS is calculated assuming the vertical
emittance is adjusted to the 1 Å diffraction limit, i.e. 8 pm rad. If, however,
a lower emittance coupling is chosen in order to improve ID brightness
(Leemann & Eriksson, 2013), this blow-up becomes even more severe. For
example, if skew quadrupoles are used to adjust the vertical emittance to
2 pm rad, the IBS blow-up for 500 mA becomes 69%, or 24% if bunch
lengthening from Landau cavities is included.
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diffraction-limited storage rings
Figure 9
Lattice momentum acceptance for one achromat of the MAX IV 3 GeV
storage ring (Leemann, 2012d). A bare lattice with actual vacuum
chamber apertures has been used. The solid blue line shows lattice MA
from 6D tracking with Tracy-3. For comparison, the RF acceptance
is shown as well: cavities at maximum voltage 1.8 MV (7.1% RF
acceptance) and at 1.0 MV (4.5% RF acceptance).
MA and lifetime calculations are 500 mA stored current in an
even fill (i.e. all buckets equally populated with no ion-clearing
gap) resulting in 5 nC charge per bunch. The 3 GeV storage
ring has six main RF cavities for a maximum overall accelerating voltage of 1.8 MV. For a bare lattice (Eloss = 364 keV
per turn) this corresponds to an RF acceptance of RF = 7.1%.
The nominal inside diameter of the cylindrical vacuum
chamber is 22 mm; the aperture model, however, includes
additional aperture restrictions from, for example, septum and
tapers. Momentum acceptance tracking in 6D with Tracy-3
was used to verify that the resulting overall MA fulfilled
design specifications (cf. Fig. 9). Landau cavities are expected
to be tuned in during user operation. In order to include the
effects of such bunch lengthening, the Touschek lifetime,
however, cannot simply be scaled with the bunch length. The
reason for this is IBS. When the Landau cavities are tuned in,
the bunches are stretched leading not only to an increased
Touschek lifetime but also to a decrease of IBS emittance
blow-up. Since the resulting emittance is lowered, the
Touschek lifetime is further increased (cf. Fig. 8) compared
with the result from charge density reduction alone. Therefore, a fully self-consistent approach using 6D tracking is
required (Leemann, 2014). Such studies show that even for a
fully ID-equipped ring operated with Landau cavities a
Touschek lifetime beyond 25 h (including the effect of
imperfections and reduced vertical aperture from in-vacuum
undulators) can be expected. Combined with the gas scattering lifetimes (MAX IV, 2010) this leads to an overall lifetime beyond 10 h compatible with the foreseen top-up
injection scheme with one top-up injection every few minutes
to ensure a top-up deadband of about 0.5%.
4. Injection dynamics
The MAX IV 3 GeV storage ring will be operated in top-up
mode with an overall lifetime of about 10 h. This requires topup injections every couple of minutes. Top-up injection shots
868
Pedro F. Tavares et al.
The MAX IV storage ring project
will be delivered to the storage ring from the MAX IV linac
(Thorin et al., 2011) serving as a full-energy injector. The
maximum injection repetition rate of 10 Hz is matched to
leave about seven storage ring damping times between each
injection shot. A maximum of roughly 3 nC can be injected
in one shot which corresponds to 0.34% of the total stored
charge at 500 mA current. Assuming 10 h overall lifetime and
that capture in the storage ring is highly efficient, this corresponds to a single top-up injection every other minute. If a
larger top-up deadband can be tolerated, the quiet period
between injection shots can be lengthened followed by several
top-up shots injected at 10 Hz. Capture in the storage ring is
expected to be highly efficient as a result of the low emittance
of the linac combined with the comparably large acceptance of
the storage ring. Bunches from the thermionic RF gun (Elafifi
et al., 2012) are expected to have a normalized emittance of
10 mm mrad (corresponding to horizontal and vertical emittances of 1.7 nm rad at 3 GeV) and an energy spread of the
order of 0.1% r.m.s. when they are injected into the storage
rings.
The original injection scheme (MAX IV, 2010) foresaw use
of a closed four-kicker bump around the DC Lambertson
septum in the injection straight of the storage ring. In light
of the very tight beam stability requirements in the 3 GeV
storage ring there was considerable doubt that four injection
kickers could be aligned, balanced and synchronized well
enough to prevent perturbation of the stored beam beyond
the limits of these stability requirements. Furthermore, since
the injection bump would have contained several strong
sextupoles and octupoles, the bump could not be closed
properly for all amplitudes and all particles in the bunch. This
led to the development of a new injection scheme for the
MAX IV storage rings.
4.1. Pulsed multipole injection
Intrigued by KEK’s pioneering work on pulsed quadrupole
(Harada et al., 2007) and pulsed sextupole injection (Takaki et
al., 2010), it was recognized that a pulsed multipole had the
potential to make top-up injection shots into the MAX IV
storage rings transparent to users while allowing for a
substantial reduction of complexity. Instead of four dipole
kickers and their pulsers, only a single magnet and its pulser
were required; the pulsed magnet could be aligned to the
stored beam through beam-based measurements.
Because of the low emittance of the injected bunches,
sampling the gradient of a multipole at injection was not
considered to be a problem. The strong non-linearity of
betatron motion in the 3 GeV storage ring, however, required
optimization of the pulsed multipole injection (PMI) scheme
with tracking studies in order to determine the best location
and kick amplitude for the pulsed multipole (Leemann,
2012b). A scheme was developed for a pulsed sextupole
magnet (PSM) using both single-turn and two-turn injection as
well as different kick strengths (cf. Fig. 10). It was shown that
such an injection scheme did indeed allow for very high
capture efficiency of the injected bunch with only minute
J. Synchrotron Rad. (2014). 21, 862–877
diffraction-limited storage rings
Figure 11
Upper half geometry (top) and resulting field profile in the midplane
(bottom) of a BESSY-type non-linear injection kicker adapted to the
MAX IV 3 GeV storage ring (Leemann & Dallin, 2013). Note that the
resulting field around the centre is similar to an octupole.
Figure 10
Top: trajectory of the injected bunches in the MAX IV 3 GeV storage
ring starting at the septum (Leemann, 2012b). The PSM is installed in
the second long straight and kicks the injected bunch into the ring
acceptance. Bottom: tracking of injection and capture of 1000 particles at
the septum in the 3 GeV storage ring. The first five turns are indicated in
blue. For comparison, the stored beam is indicated in red.
perturbation of the stored beam. Following the KEK PSM, a
solid-iron sextupole was designed for injection in MAX IV.
Despite the smaller magnet apertures in MAX IV and the
corresponding reduction of the magnet inductance compared
with the KEK PSM, the required voltages remained very high
as a consequence of the short pulse duration (Leemann &
Dallin, 2013).
A novel non-linear injection kicker developed for
BESSY II (Atkinson et al., 2011) appeared to solve these
issues. Its stripline-like design generates a non-linear magnetic
field with limited inductance. The non-linear field profile
crosses zero at the centre, is flat around this area, and achieves
a highly localized maximum several millimetres from the
centre. In this way a large kick can be supplied to the injected
bunch while minimizing any residual kick to the stored beam.
In the vicinity of the stored beam the field is octupolar which
leads to an even lower perturbation than a PSM. At BESSY II
this kicker delivers roughly 1 mrad of kick at 12 mm distance
from the stored beam. The separation of the injected bunch
from the stored beam in MAX IV is, however, only about
5 mm (Leemann, 2012b). In order to apply the BESSY kicker
design to MAX IV the vertical separation of the inner rods
would have to be reduced to levels that are no longer
J. Synchrotron Rad. (2014). 21, 862–877
compatible with the vertical acceptance requirements.
However, because the injected beam at MAX IV has such a
low emittance, bunches can be injected on the slope of the
kicker field. Fig. 11 shows the geometry of a BESSY-type nonlinear injection kicker adapted to MAX IV along with the
generated field profile. Tracking of injection and capture of
bunches in MAX IV using a BESSY-type kicker is displayed in
Fig. 12. For comparison, the effect of a PSM and a pure dipole
are included. The latter clearly disperses the injected beam
less than the two multipole kickers; however, since it also kicks
Figure 12
Tracking of 1000 particles of an injected bunch during the first five turns
in the MAX IV 3 GeV storage ring using single-turn injection (Leemann
& Dallin, 2013). Injection with the BESSY-type kicker (blue) is compared
with a PSM (red). For reference, a pure dipole kick (green) has also been
included.
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The MAX IV storage ring project
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diffraction-limited storage rings
the stored beam it is not compatible with the requirement of
transparent top-up injection. Tracking studies have also shown
that the perturbation of the stored beam by a BESSY-type
kicker including a vacuum chamber with a thin metallic
coating remains negligible if the kicker is aligned properly to
the stored beam. A collaboration between MAX IV, SOLEIL
and BESSY has been launched with the goal of developing
and manufacturing BESSY-type kickers for both MAX IV
storage rings and SOLEIL.
4.2. Injection with a single dipole kicker
Commissioning an entirely new storage ring relying only on
PMI is demanding. The kick received by the injected bunch
depends heavily on the bunch position and angle at the
injection septum as well as the optics between the septum and
the injection kicker. In a new storage ring these parameters
are not known to high accuracy and optics deviations from
design are to be expected as a consequence of misalignments,
calibration uncertainties and/or cabling errors. Such errors
can be diagnosed and resolved; however, usually beam-based
measurements are employed. Hence, a minimum amount of
injection and capture have to be ensured so commissioning
can progress.
Figure 14
Tracking of 1000 particles of a stored bunch (red) and 1000 particles of an
injected bunch (blue) in the MAX IV 3 GeV storage ring (Leemann,
2012a). The dipole kick strength has been reduced to allow for stacking:
the injected bunch is captured while already stored charge in the same
bucket is not ejected out of the machine acceptance. The first five turns
after injection are indicated.
In order to provide a simple and robust injection into the
storage ring to allow for early commissioning activities, an
alternative to PMI was desired. Injection with a single dipole
kicker presented a solution (Leemann, 2012a). Although a
dipole kicker does not allow for transparent top-up injection,
it offers an injection with little dependence on initial parameters and optics. In the MAX IV 3 GeV storage ring, a
horizontal dipole kicker installed in the first short straight
after the injection septum allows for both on- and off-axis
injection (cf. Fig. 13).4 In fact, if the kick strength of the dipole
kicker is reduced, the injection kick can be divided between
the injected bunch and any stored charge already in the bucket
so as to allow for some stacking (cf. Fig. 14).
Once small amounts of beam are injected and stored in the
storage ring, beam-based measurements will allow the optics
to be adjusted to its design values. At this point commissioning
of the pulsed multipole magnet can begin. Pulsed multipole
injection will then allow accumulation of large amounts of
charge in the storage ring without perturbation of already
stored beam thus enabling transparent top-up operation for
users. The single dipole kicker will from then on serve as a
horizontal pinger magnet for machine studies.
5. Coherent collective instabilities
Figure 13
The MAX IV design concept leads to several challenges in
reaching stable operation of the machine at high currents.
These challenges arise from the compact magnet design, which
calls for a small vacuum chamber aperture leading to an
increased interaction of the beam with its environment; in
particular, the resistive wall impedance, which scales inversely
as the third power of the beam pipe aperture, may lead to the
excitation of transverse coupled-bunch modes. Moreover, the
Top: off-axis injection with a single dipole kicker (KI) in the MAX IV
3 GeV storage ring starting at the septum (Leemann, 2012a). Bottom:
phase space plot showing tracking of injection and capture (first five turns
are indicated) of 1000 particles at the septum.
4
On-axis injection requires injecting at a slight angle in the septum. The
transfer line has been designed to include dipole correctors and diagnostics
allowing adjustment of position and angle of the injected bunch in the septum.
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The MAX IV storage ring project
J. Synchrotron Rad. (2014). 21, 862–877
diffraction-limited storage rings
low-emittance lattice design leads to a small dispersion function in the arcs (8 cm maximum), which, coupled with the large
bending radius, results in a small momentum compaction
factor, and consequently small values for single-bunch
instability thresholds, particularly for the microwave
instability and transverse mode coupling instability.
In order to face the issues described above, the MAX IV
facility design relies on the fact that short light pulses will be
produced by a linac source (the 3 GeV injector linac and
corresponding short-pulse facility), which relieves the storage
rings from the need to achieve short-bunch and single-bunch
high-current operation. This allows us to:
(i) Choose a relatively low RF frequency for the accelerating cavities, which leads to longer bunches for a given RF
momentum acceptance.
(ii) Use harmonic (also called Landau) cavities (HCs)
operating in passive mode in order to further elongate the
bunches, reducing the charge density thus alleviating intrabeam scattering, which is not only essential to reach the target
equilibrium emittances at high current but also increases the
average current thresholds for longitudinal single-bunch fast
instabilities and reduces the beam-induced heat load on
vacuum chamber components. In addition, the Landau
cavities provide increased tune spread that helps prevent
instabilities and makes up for the relatively long radiation
damping times that result from the large bending radius.
(iii) Require only multibunch operation with relatively low
current per bunch.
5.1. Harmonic cavities and bunch lengthening
As noted above, long bunches and HCs are an essential
ingredient in the MAX IV design concept. Practical experience (Georgsson et al., 1998) has demonstrated the possibility
of operating such cavities passively, so that the beam itself
provides the excitation of the HC. If one chooses the HC
parameters (Hofmann & Myers, 1980) such that the first and
second derivatives of the total voltage seen by the beam are
zero at the synchronous phase, the longitudinal potential well
that holds the bunches becomes approximately quartic and
the incoherent synchrotron frequency grows approximately
linearly with amplitude for small amplitudes, being exactly
zero at the centre of the bunches. For the MAX IV 3 GeV ring
at 500 mA nominal beam current, with an accelerating voltage
of 1.6 MV and 856 keV energy loss to synchrotron radiation
per turn, such flat potential conditions correspond to a HC
shunt impedance of Rs = 2.017 M and a HC detuning f =
28.43 kHz, which leads to an r.m.s. bunch length of 54.1 mm,
whereas the natural bunch length without HCs is 10.1 mm.
This bunch lengthening is accompanied by a widening of the
synchrotron frequency distribution and a corresponding
increase of the Landau damping rate of coherent modes.
Even though this choice of parameters for the HC system
leads to flat symmetric bunch shapes, one must keep in mind
that passive operation of HCs always implies operation on the
Robinson unstable slope of the fundamental mode of the HCs;
in other words, one must rely on other damping mechanisms
J. Synchrotron Rad. (2014). 21, 862–877
Figure 15
Equilibrium longitudinal bunch density distribution for two different
settings of the HC system in the MAX IV 3 GeV ring.
such as synchrotron radiation damping and Robinson
damping from the fundamental mode of the main (100 MHz)
RF cavities to keep the beam stable. In fact, for the MAX IV
3 GeV ring parameters mentioned above, the Robinson
growth rate from the fundamental mode of the HC at flat
potential conditions is too large (67 s1) to be compensated by
radiation damping alone (39 s1).
However, calculations for the MAX IV parameters
(Tavares et al., 2013, 2014) indicate that lengthening similar to
the flat potential case can also be achieved with a passively
operated HC with higher detuning and correspondingly lower
Robinson anti-damping, as long as the HC shunt impedance
can be raised significantly above the flat potential conditions.
By choosing, for example, a shunt impedance Rs = 4.2 M
and f = 60.36 kHz (Fig. 15), we can reach an r.m.s. bunch
length of 54.2 mm and the Robinson growth rate due to the
HC fundamental mode is then reduced by more than a factor
of four to 15.3 s1, well within the range of radiation damping.
The incoherent synchrotron tune spread can also be made
similar to or even larger than the spread corresponding to the
flat potential case, as long as there is enough margin in HC
shunt impedance, even though the bunches become somewhat
asymmetric and show a slightly larger peak current. This is in
fact the approach adopted for the MAX IV 3 GeV ring, where
a significant margin in shunt impedance above the flat
potential condition is provided by installing three identical
HCs, each with a shunt impedance of 2.5 M . Having the total
shunt impedance split among three different cavities allows
tailoring the actual shunt impedance seen by the beam by
tuning each cavity independently and additionally also permits
the power dissipated in each cavity to be kept within acceptable levels.
5.2. Multibunch instabilities
Transverse coupled-bunch modes driven by the long-range
resistive wall wakefields are a potential concern given the
small pipe radius (11 mm) in the MAX IV 3 GeV ring.
Lengthening of the bunches provides us, however, with a very
efficient means of enhancing the effectiveness of positive
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The MAX IV storage ring project
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diffraction-limited storage rings
impedance for all modes trapped in the chamber is quite large
for the vast majority of components, going down to about 3 for
a resonance at the double flanges around the BPM bodies.
Finally, the power deposited on vacuum chambers by beaminduced fields is found to be negligible as long as the bunches
are lengthened by the HCs.
5.3. Single-bunch instabilities
Figure 16
Threshold current at which the growth rate of the fastest growing coupled
bunch mode (and lowest synchrotron mode number, i.e. the rigid bunch
mode) driven by the resistive-wall impedance equals the transverse
synchrotron radiation damping rate as a function of chromaticity for two
different bunch lengths corresponding to the situations with and without
HCs.
chromaticity in fighting these unstable modes. In fact, the long
bunches imply a narrow frequency span of the head–tail
modes, which leads to a small overlap of the chromaticityshifted eigenmode spectra with the resistive wall impedance
spectrum, which is concentrated at low frequencies leading to
lower growth rates. This expectation is confirmed by applying
the standard Sacherer formalism as implemented in the
computer code ZAP (Zisman et al., 1986) to calculate the
corresponding growth rates as shown in Fig. 16. The same
trend is also confirmed by a more direct frequency domain
calculation with the code rwmbi, in which actual eigenvectors
(instead of the approximate Hermitian modes adequate for
Gaussian bunches) are used (Tavares et al., 2011).
Even though these results are reassuring, the direct use of
the Sacherer formalism for the situation with HCs might be
questioned, as the very concept of synchrotron modes seems
to lose its validity in that limit since, for flat potential conditions, the phase focusing at the very centre of the bunches
vanishes. However, particle tracking simulations (Klein et al.,
2014) give indications that the lengthened bunches are indeed
safe from resistive-wall-driven instabilities at nominal current
levels.
Longitudinal multibunch instabilities are driven by high-Q
trapped modes in vacuum chamber components as well as by
the HOMs in RF cavities. While the growth rates of unstable
modes can be calculated from the standard Sacherer formalism when no HCs are present, a modified version of the
theory (Bosch et al., 2001) is required to predict the growth
rates when the HCs flatten out the longitudinal potential well.
An analysis based on this formalism has been carried out for
MAX IV making use of a detailed longitudinal impedance
budget (Günzel, 2009) and led to the conclusion that the ratio
between the allowed shunt impedance (i.e. the one below
which the beam is stable) and the actual estimated shunt
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The MAX IV storage ring project
In the MAX IV 3 GeV ring, longitudinal single-bunch
instabilities are a source of concern not because of the associated increase in bunch length (since by design we lengthen
the bunches anyway) but rather due to the potential increase
in energy spread associated with the microwave instability and
the resulting degradation of the undulator spectra.
Longitudinal single-bunch instabilities have been studied by
multi-particle tracking (Klein et al., 2013). In those studies, a
longitudinal impedance model composed of seven resonators
as well as purely resistive and inductive components was fitted
to the numerically determined impedance of the vacuum
chamber components (Günzel, 2009). The effects of the
passively operated HC were included in the code mbtrack and
the results indicate (Klein & Nagaoka, 2013) that the beam
remains stable without significant increase of the energy
spread at the nominal beam current of 2.84 mA per bunch.
These studies have also allowed the identification of a few
components, in particular bellows and BPMs, as the main
items responsible for determining the instability thresholds.
While one may expect that the use of HCs can improve the
situation for fast longitudinal instabilities, since the lengthening of the bunches reduces the bunch peak current for a
given stored average current, this may not necessarily happen
for fast transverse single-bunch instabilities. Preliminary
calculations (Tavares et al., 2011) with the computer code
MOSES (Chin, 1988) based on a simplified single-resonator
impedance model indicated that a relatively low chromaticity
of 0.5 was enough to keep the beam stable against fast
transverse instabilities at the nominal beam current. More
detailed tracking studies based on a numerically determined
transverse impedance budget and subsequent impedance
modelling studies for the transverse plane are ongoing (Klein
et al., 2014) and have so far confirmed the same trends
observed in the simplified models.
6. Engineering and instrumentation
6.1. Magnets
The main requirement for the 3 GeV ring magnets5 is to
produce the large integrated focusing strengths needed to
achieve ultralow emittance with relatively short magnets so as
to minimize the total machine circumference and associated
costs. Additional objectives include tight alignment tolerances,
5
The magnet system for the 3 GeV ring is described in detail in a companion
paper in this issue (Johansson et al., 2014). Early development and prototype
work on these magnets are reported by Tarawneh et al. (2003, 2005). Here we
briefly highlight the major aspects of the magnet design.
J. Synchrotron Rad. (2014). 21, 862–877
diffraction-limited storage rings
low sensitivity to vibrations and an integrated design concept
that allows for streamlined installation and system tests.
The key ingredient to achieve these goals is a reduced
magnet gap: 25 mm bore diameter in quadrupoles and sextupoles and 28 mm pole gap at the transverse centre of the
gradient dipoles. A small pole aperture allows realisation of a
compact lattice for several reasons: first, the lengths of the
elements can be made shorter for a given integrated strength
while keeping the pole-tip fields below saturation levels;
second, the distance between consecutive magnetic elements
is constrained to about one pole gap by the need to limit field
quality deterioration caused by fringe-field effects, and, third,
a reduced pole gap allows for smaller coil cross-sections which
makes it easier to fit the coil ends between magnets.
The requirements on low sensitivity to vibrations and tight
alignment tolerances are achieved by having all magnets in
each cell built as a single unit, i.e. the magnet block. The dipole
poles and quadrupole pole roots are machined out of two yoke
halves that serve also as a girder in which all magnets in the
cell are assembled. The magnet blocks are then supported by
massive concrete stands. With this concept the relatively small
and light magnet blocks have high natural vibration frequencies, which makes them insensitive to typical floor vibrations.
Moreover, the relative alignment of the various magnets
within a block is defined by the combination of machining
accuracy of the yokes and poles and the corresponding
assembly errors, which can be performed to tighter accuracies
( 20 mm) than optical alignment of the whole block. In this
way, resulting misalignments of individual magnets tend to
be correlated throughout a magnet block leading to partial
compensation among the resulting kicks. Last but not least,
the integrated magnet design concept assumes that the
magnetic field quality is determined by mechanical tolerances
so that no further adjustment based on magnetic measurements (such as, for example, shimming for alignment to
magnetic centres) is planned, except for possible shunting for
the strength of the main components. This simplifies considerably the installation and system tests procedure as well as
contributes to cost reduction.
6.2. Vacuum
The vacuum design6 is defined by the small magnet apertures which lead to narrow low-conductance vacuum chambers (22 mm inner diameter). The major challenges of the
design are therefore the need to reduce photodesorption and
provide adequate pumping all along the chambers as well as
the safe extraction of the heat load from synchrotron radiation
on the chamber walls. In order to face these issues, the
chamber consists of a cylindrical copper tube which is coated
with non-evaporable getter (NEG) alloy. Even though the
NEG coating technology, originally developed at CERN
(Benvenuti et al., 2001), has already been applied on a large
scale to insertion device chambers (Kersevan & Hahn, 2006)
6
The vacuum system for the 3 GeV ring is described in detail in a companion
paper in this issue (Al-Dmour et al., 2014). Here we briefly highlight the major
aspects of the vacuum design.
J. Synchrotron Rad. (2014). 21, 862–877
as well as to straight vessels in synchrotron radiation sources
[about 56% of the SOLEIL chambers are NEG coated
(Herbeaux et al., 1998)], the MAX IV 3 GeV storage ring will
be the first light-source storage ring to be close to 100% NEG
coated, including straight sections as well as dipole (bent)
chambers. The coating of such narrow tubes, particularly the
chambers which are used for extraction of the insertion device
radiation, presents a significant engineering challenge. Some
of the issues that were faced during the development phase of
NEG coating procedures for the MAX IV chambers (Calatroni et al., 2013) include the coating of bent chambers, already
demonstrated for larger diameters at MAX II (Hansson et al.,
2010), the coating of wire-cut parts and of chambers made of
different materials such as copper and stainless steel brazed
together.
Cooling of the chambers is realised by means of electronbeam welded cooling channels along the chambers, which act
as distributed heat absorbers. Finite-element analysis has been
extensively used (Al-Dmour et al., 2011) to understand the
effects of the deposited heat and ensuing stresses on the
mechanical integrity of the cambers as well as on the positional stability of the BPM blocks, a critical issue due to the
tight requirements on beam position stability that result from
the machine’s ultralow emittance.
As a result of the small clearance between magnets and
chambers, the chamber assembly and activation of full
achromats (approximately 22 m length) will not be performed
in situ, but rather in a bakeout oven assembled on a table over
the lower yoke halves. The fully assembled and activated
achromat chamber will then be lowered onto the magnet
halves and the upper yoke halves assembled on top.
6.3. RF system
A main RF system of relatively low frequency, 100 MHz,
has been chosen. The main cavities are made entirely of
copper and are of normal-conducting capacity-loaded type,
where the present cavities of the MAX II and MAX III
storage rings have served as prototypes (Andersson et al.,
2002, 2011; MAX IV, 2010). The shunt impedance amounts to
1.6 M . It is not possible to reach as high a shunt impedance
per metre cavity length as for higher-frequency systems.
However, a low-frequency system requires a lower overvoltage (peak voltage to synchronous voltage ratio) for a given
RF energy acceptance. In the end, for the MAX IV case, a
low-frequency system turns out to be advantageous considering power consumption. As can be seen from Table 2, for a
fully ID-equipped MAX IV 3 GeV ring with 4.5% RF energy
acceptance the total copper losses will amount to 185 kW. A
500 MHz system occupying the same accelerator length and
providing the same RF energy acceptance would generate
roughly 400 kW in copper losses. High-efficiency (60–70%)
RF transmitters available at 100 MHz additionally help in
power saving.
From a beam dynamics point of view, it may not be obvious
at first sight why a low-frequency choice should be preferred.
In fact, the resulting lower RF voltage leading to the same RF
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diffraction-limited storage rings
Table 2
Main parameters of the MAX IV 3 GeV ring RF system.
Parameter
Commissioning
Final
Energy loss
Current
Total SR power
Total RF voltage
Number of main cavities
Main cavity shunt impedance (V 2/2P)
Main cavity total copper losses
Main cavity coupling
Number of RF stations
Minimum RF station power
Total HC voltage
Number of HCs
HC shunt impedance
Total HC copper losses
360 keV
200 mA
72 kW
1.0 MV
4
1.6 M
78 kW
1.9
4
39 kW
308 kV
3
2.5 M
6.3 kW
1000 keV
500 mA
500 kW
1.8 MV
6
1.6 M
169 kW
4.0
6
114 kW
478 kV
3
2.5 M
16 kW
energy acceptance for the low-frequency choice still results in
a higher bunch peak current for the same total stored beam
current, even though the bunches are longer. Again
comparing with a 500 MHz system, the bunch peak current
would be roughly 35% higher. However, when HCs are used
to lengthen the bunches, as described in x5, the impact of
frequency choice on the bunch peak current is reduced. In
fact, if we excite the HCs so that the flat potential case is
reached, the bunch peak currents for 100 MHz and 500 MHz
RF systems differ by only about 15%.
Moreover, while the peak bunch current is relevant for
single-bunch instabilities, the growth rate of coupled-bunch
instabilities depends on the total circulating current and on the
overlap of the impedance with the bunch spectrum. As a
result, choosing a low RF frequency while keeping the total
current constant reduces the growth rates of coupled-bunch
instabilities due to the longer bunches.
The HCs are chosen to be of similar type as the main
cavities, primarily because the capacity loaded type has the
advantage of pushing higher-order modes to relatively high
frequencies compared with pillbox cavities. The fundamental
mode shunt impedance per cavity stays at the moderate value
of 2.5 M . Table 2 shows the relevant numbers for the RF
parameters for a plausible commissioning case and for a fully
ID equipped MAX IV 3 GeV ring, both with 4.5% RF energy
acceptance. The final design value for the RF station power
has consequently been set at 120 kW. To reach this power, two
60 kW transmitters are combined.
6.4. Diagnostics
6.4.1. General. Both storage rings will be equipped with a
set of standard diagnostic equipment. This includes scraper
sets to allow measurement of vacuum lifetimes, stripline
antennas for tune excitation and a fluorescent screen profile
monitor directly after the injection septum to better diagnose
the injection process. The latter will be complemented with an
extra BPM.
6.4.2. BPMs. The MAX IV storage rings will use standard
capacitive button BPMs. In the 3 GeV ring the standard BPM
housing will have a circular aperture of d = 25 mm. A few non-
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The MAX IV storage ring project
standards exist in regions where a larger horizontal aperture is
required for injection.
The capacitive buttons are based on the ALBA design
(Olmos et al., 2006) for both rings but with somewhat reduced
dimensions. Altogether the BPM designs have sensitivities, i.e.
changes in the U=U signal due to beam movement, of Sx =
Sy = 11% mm1 for the 3 GeV ring standard units.
All BPMs will be equipped with Libera1 Brilliance+ electronics. Apart from allowing the now standard applications of
fast orbit feedback and LOCO response matrix analysis
(Safranek, 1997) to calibrate the linear optics, the BPMs will
also have single-turn and turn-by-turn data acquisition
capability. The former will assist in first-turn beam threading
while the latter will provide, amongst others, the possibility of
investigating the resonance driving terms using frequency map
analysis (Robin et al., 2000). Pinger magnets will be installed
for both planes in order to induce transient betatron oscillations. The eventual aim of such analysis is of course correcting
errors in the non-linear optics (Bartolini & Schmidt, 2005).
The 3 GeV storage ring will be equipped with 200 BPMs.
Given the betatron tunes of x = 42.2, y = 16.28, the betatron
period is thus well sampled. It should be noted that the large
number of BPMs in the 3 GeV storage ring was motivated
primarily by the need to restrict orbit excursions inside the
strong sextupoles, which can otherwise result in an increased
emittance coupling between the transverse planes.
6.4.3. Transverse emittance diagnostics. Each ring in the
MAX IV project will be equipped with two diagnostic beamlines based on imaging of the electron beam using visible to
ultraviolet synchrotron radiation. The design will be similar to
that given by Andersson et al. (2008) and Saá Hernández et al.
(2013), where -polarized light plays an important role in
determining the vertical emittance (Andersson et al., 1996).
The method relies on an accurate determination of the
transverse beam sizes, utilizing the wave properties of the
emitted synchrotron radiation (Chubar & Elleaume, 1998),
both in the vertical and horizontal directions (MAX IV, 2010).
The beamlines are placed so that both a low and a high
dispersion point in the lattice are observed. In this way it
becomes possible to determine both horizontal and vertical
beam emittance as well as energy spread. Also, the horizontal
and vertical dispersion will be directly measured at the source
point. Only the betatron values need to be determined from
lattice fits to the orbit response matrix, which should be
accurate to within a few percent. The most demanding beam
size measurements are at the 3 GeV ring, where we expect to
be able to determine vertical/horizontal beam sizes of 6 mm/
18 mm with an r.m.s. uncertainty of 0.3/1.0 mm. The derived
vertical/horizontal emittance in the vicinity of 2 pm rad/
200 pm rad will have a relative r.m.s. uncertainty of roughly
10%/15%.
6.5. Orbit feedback
The orbit feedback systems in both storage rings share the
same conceptual design (Sjöström et al., 2011) and differ
mainly in two areas: number of sensors and actuators, as well
J. Synchrotron Rad. (2014). 21, 862–877
diffraction-limited storage rings
as the physical design of the BPMs and dipole corrector
magnets. Electronics, power supplies, algorithms, software and
general topology will be identical. In terms of required orbit
stability the 3 GeV ring is the more demanding with vertical
beam sizes of 2–4 mm on the long straights, which results in
orbit stability requirements of the order of 200 nm. The orbit
feedback system uses two separate global feedback loops,
which use the same set of BPM sensors but two different sets
of actuators.
The ‘slow’ loop will handle corrections for slow drifts.
Update frequencies are expected to be in the 0–10 Hz region.
Actuators will be dipole corrector magnets with solid iron
yokes, which in the 3 GeV ring are located around Cu vacuum
chambers. Their expected bandwidth will be around 30 Hz
(6 dB point) and have a kick strength of 0.35–0.42 mrad,
depending on location. Given the long time period between
updates it is possible to rely on the main control system for
data gathering, calculations and transmission of new set points
to the actuators. The loop bandwidth, i.e. the region in which
there is noise attenuation, is expected to be roughly 100 times
lower than the loop update frequency.
The ‘fast’ loop will handle orbit noise and transient disturbances. The update frequency of both sensor data and
actuator set values will be 10 kHz. While the dipole corrector
magnets that will be used as fast actuators are still being
designed, space for the actuators was reserved around stainless steel vacuum details during vacuum design. This was in
order to not limit the actuator bandwidth due to chamber wall
eddy currents, which persist significantly longer in a lowresistivity Cu chamber. The final actuator bandwidth is
expected to be limited primarily by the power supply regulation loop. With some exceptions due to engineering
constraints there will be four fast actuators available per
achromat and plane in the 3 GeV ring, all located around a
stainless steel chamber detail with circular cross section, 1 mm
wall thickness and 25 mm inner diameter. The feedback loop
logic itself will be implemented entirely in the Libera1 Brilliance+ system. Global exchange of BPM data will be carried
out via the Global Data eXchange (GDX) modules in each
Libera1 Brilliance+ unit, using a single optical fibre chain.
Orbit correction calculations will then run in the Brilliance+
units on the field-programmable gate array (FPGA) available
in the GDX module. The calculations will use a weighted
response matrix to prioritize stability in the ID straights.
Owing to the response matrix size the horizontal and vertical
planes will be treated independently of one another. Once
actuator set points have been calculated they will then be
transmitted via RS485 links from the Brilliance+ units directly
to the local actuator power supplies.
Both loops will communicate with one another in a manner
similar to that in use at SOLEIL (Hubert et al., 2005) in order
to prevent the feedback loops fighting one another. The ‘slow’
loop will include a correction for each iteration to reduce the
fast actuator strengths, while the ‘fast’ loop will use the most
recent target orbit of the ‘slow’ loop as its reference. Further
details are available from Sjöström et al. (2011).
J. Synchrotron Rad. (2014). 21, 862–877
7. Conclusions
The MAX IV 3 GeV storage ring will be the first of a new
breed of storage-ring-based light sources which make use of a
multibend achromat lattice to reach unprecedented brightness and coherence. Commissioning of MAX IV will thus
provide an opportunity for the validation of concepts that are
likely to be essential ingredients of future diffraction-limited
storage rings. Moreover, several future development possibilities aiming at further performance improvements are
already under consideration (Leemann & Eriksson, 2013,
2014).
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