# PERFORMANCE ANALYSIS OF SPOKE RESONATORS, STATISTICS FROM CAVITY FABRICATION
TO CRYOMODULE Testing

A. Miyazaki<EMAIL_ADDRESS>P. Duchesne  D. Ledrean  D.
Longuevergne  and G. Olry
CNRS/IN2P3/IJCLab Université Paris-Saclay  91405 Orsay  France

###### Abstract

Irène Joliot-Curie Laboratory (IJCLab) has been leading the development of
spoke resonators in multiple international SRF projects, from fundamental R&D,
prototyping, to series production. The European Spallation Source (ESS)
superconducting linac is the first of its kind to put into operation the spoke
resonators. After three prototype cavities, 29 ESS production cavities have
been processed, tested, assembled into cryomodules at IJCLab, and then shipped
to Uppsala for the site acceptance test. Seven prototypes for two other major
projects, Multi-purpose hYbrid Research Reactor for High-tech Application
(MYRRHA) and Proton Improvement Plan II (PIP-II), designed in collaboration
with external institutions, have as well been processed and tested at IJCLab.
A new challenge is to fully process series cavities in industry, following the
successful implementation of 1.3 GHz elliptical cavities in the other
projects. This paper summarises main results obtained from fabrication to
final testing, including frequency tuning strategy, performance, limitation in
vertical cryostat, and identifies future direction of projects and R&D in the
field of spoke cavities.

##  1 INTRODUCTION

Superconducting spoke cavities are the choice in a medium-$\beta$ section of
proton drivers. Since the late 1980s [DELAYEN1989892], spoke cavities have
been developed and their technology is matured today [PhysRevSTAB.6.080101,
SHEPARD2006205, OLRY2006201, PhysRevSTAB.16.102001, Li_2014]. However,
practical challenges for the deployment of the these cavities in real machines
need to be identified and overcome. Unlike the 1.3 GHz TESLA-type cavities,
spoke cavities are not sufficiently standardised and there are many open
questions towards the successful operation of accelerators. Irène Joliot-Curie
Laboratory (IJCLab) plays a leading role in this crucial matter in
international projects.

IJCLab has been pioneering the development of spoke cavities technology from
fundamental studies [PhysRevAccelBeams.24.083101, LONGUEVERGNE201841] to
design and prototyping work [OLRY2006201, DUTHIL2016] and even deployment in
the machines. In this paper, we overview state-of-the-art technology in
developing spoke resonators at IJCLab with three international projects as
examples. The series production of European Spallation Source (ESS)
[Peggs:2013sgv] double-spoke cavities revealed delicate issues in frequency
tuning, including fabrication, chemical etching, and heat treatment. We
discuss how we overcame these issues with statistics obtained during the
production. These ESS cavities have been qualified in cold tests, integrated
in cryomodules, and all passed the site-acceptance tests at Uppsala
University. The next challenge of ESS is installation, commissioning, and of
course, operation in the machine.

We completed prototyping four single-spoke cavities for the Multi-purpose
hYbrid Research Reactor for High-tech Application (MYRRHA)
[0976c72ed89a41e6a8e2e1eb936af11c]. The next challenge is to industrialise the
surface treatment of spoke cavities, whose complicated shape may require
special attentions compared to conventional elliptical cavities. We also show
preliminary results on heat treatment in prototype MYRRHA cavities, which may
be a breakthrough towards 4 K operation of spoke resonators. Finally, we
started prototyping Single Spoke Resonator 2 (SSR2) for Proton Improvement
Plan II (PIP-II). We discuss preliminary results and trade-off of cavity
design between RF performance and cleaning process.

##  2 SUPRATECH

IJCLab hosts the SUPRATECH facilities, where one can perform chemical
treatments, high-pressure water rinsing (HPR), heat treatment, mechanical
frequency tuning, cold tests at 4 K and 2 K, assembly of cavity string and
cryomodules, and cryomodule testing. As shown in Fig. 1, two spoke cavities
can be tested at a time in a vertical cryostat ($\phi 800$) with a vacuum
insert which requires a helium tank welded around the cavity
[PhysRevAccelBeams.24.083101]. In SUPRATECH, we do not measure bare cavities
today because of the following strategic reasons. First, we can save a huge
amount of liquid helium for cold tests, because helium supply is a global
issue for the SRF community today. Secondly, the small heat capacitance of the
cryostat enables quick cool down and warm up. As a drawback, however, careful
frequency tuning is required in fabrication, surface processing, and even
cooling down because we skip the cold test of a bare cavity to check the
frequency before welding the helium tank. This unique tuning and testing
strategy has been successful in the ESS project and the same was adopted for
other similar projects (MYRRHA and PIP-II SSR2). Therefore, a global standard
of future projects can follow our strategy: accurate frequency tuning and only
one cold test in a vertical test-stand.

Figure 1: Vacuum insert of the vertical cryostat at SUPRATECH. Two cavities
are mounted in the same insert and share the same beam vacuum.

##  3 ESS SERIES CAVITIES

ESS is a proton driver in Sweden for neutron science via nuclear spallation.
In the spoke section from 90 MeV to 216 MeV, it deploys 13 cryomodules, each
of which accommodates two double-spoke cavities with 352 MHz. The target
gradient is $E_{\rm acc}=9$ MV/m with an unloaded quality factor
$Q_{0}=1.5\times 10^{9}$ at 2 K. Since the geometry factor is $G=133$ $\Omega$
and the peak field ratio is $6.9\,{\rm mT(MV/m)^{-1}}$, the target surface
resistance and peak magnetic field are 89 n$\Omega$ and 69 mT, respectively.
Compared to state-of-the-art elliptical cavities, the target performance is
more conservative partially because the field level is somewhat limited by
beam dynamics in the spoke section. However, we achieved performance beyond
the specification by one order of magnitude. Typical $Q_{0}$ achieved was
above $2\times 10^{10}$ at 9 MV/m and maximum gradient was above 15 MV/m.

A particular challenge of these cavities was frequency tuning without a bare
cavity testing at cold. The behavior of spoke cavities, with intrinsically
complicated shape compared to the conventional elliptical cavities, must be
fully understood and controlled in such a very delicate process. We describe
the strategy in fabrication, heat treatment, and chemical etching in the
following subsections.

###  3.1 TUNING AT FABRICATION

The goal of fabrication is to keep the frequency tolerance within $\pm 150$
kHz. The body of the cavity has 5 mm margin for both sides before welding the
end-caps there, as indicated by red arrows in Fig. 2. Depending on the
frequency, preliminary measured by clamping these parts, and based on
frequency shifts by the electron-beam welding (EBW), the trimming lengths were
decided by IJCLab. The first leak check was performed after this final EBW and
frequency was permanently shifted due to vacuum pumping inside of the
cavities.

Figure 2: Configuration of the frequency measurement before the trimming and
final electron-beam welding. The red arrows indicate the trimming margins and
the end-caps are temporarily clamped for the RF measurement at warm.

After the first leak check, a helium jacket was manually welded to the cavity
body by Gas tungsten arc (TIG) welding. In the beginning of the series
production, frequency shifts by different welders were evaluated by four pre-
series cavities in order to estimate the influence of this manual welding on
the helium jacket. The jacket welding of series cavities were performed by the
selected welder and further statistics were recorded. After the welding,
careful machining was performed in order to form the parts, which are
dedicated to mounting cold tuners on the cavity during the module assembly
process. The cavities frequency was further shifted due to a strong supporting
force that holds the cavity during machining because of the required high
mechanical tolerance for the tuner. As summarized in Fig. 3, although a few
exceptions were observed, the frequency tuning during the manufacturing
process was under control.

Figure 3: Statistical distributions of frequency shifts due to the final EB
welding, TIG welding of the helium jacket, and final machining.

###  3.2 CHEMICAL TREATMENT

The chemical treatment is the major mean to fine-tune the cavity frequency
after the manufacturing process. Ports originally prepared for HPR, enabled
Buffer Chemical Polishing (BCP) in two orientations. Horizontal BCP decreases
the frequency by $-0.62$ kHz/$\mu$m while vertical one increases it by $+0.34$
kHz/$\mu$m as shown in Fig. 4. Depending on the frequency at the reception, we
optimised the periods of horizontal and vertical BCPs, in order to meet the
frequency tolerance within $\pm 40$ kHz. After heat treatment, light BCP was
performed to remove surface contamination generated during annealing. This
light BCP is mainly in the vertical orientation; however, fine-tuning by
additional horizontal BCP was sometimes necessary due to unexpected frequency
detuning caused by the heat treatment as described in the next subsection.

Figure 4: Statistics of frequency detuning by BCP. The Gaussian fits show mean
values of $-0.62\,{\rm kHz/\mu m}$ and $+0.34\,{\rm kHz/\mu m}$ for horizontal
and vertical BCPs, respectively.

###  3.3 HEAT TREATMENT

After bulk BCP, heat treatment was performed in order to degas hydrogen and
avoid Q-disease. The annealing parameters were optimised to 650∘C for 10 hours
because higher temperature was not necessary due to little gain by flux
expulsion as described in Ref. [PhysRevAccelBeams.24.083101]. Since the
annealing temperature is marginal, some flanges were even copper-brazed in
advance.

The frequency shift by heat treatment showed an unexpected behavior as seen in
Fig. 5. It statistically distributes around $+10$ kHz with a substantially
large standard deviation at $32$ kHz. The heat treatment either increases or
decreases the resonant frequency of cavities unpredictably. This may be due to
the helium jacket (made of titanium) annealed together with the niobium
cavity, releasing mechanical stress in its material history. We did not know
the stress level of this titanium jacket at the stage of heat treatment. In
the series production of the ESS cavities, we made use of horizontal and
vertical BCPs to compensate the unexpected frequency shift. In a few cases, we
performed mechanical tuning by pressurising the helium circuit. For more
details, see Ref. [duchesne:ipac2021-mopab392].

Figure 5: Statistics of frequency detuning by annealing at 650∘C for 10 h. The
Gaussian fit shows the mean at $9.8\,{\rm kHz}$ with standard deviation of
$32\,{\rm kHz}$.

###  3.4 COLD TESTS

In order to qualify the RF performance of the cavities, cold tests were
performed after HPR. All 29 cavities passed the tests although a few of them
required several iterations with HPR and sometimes even light BCP to remove
contaminants causing field emission. We obtained excellent performance in all
the cavities as shown in Fig. 6, with low-field surface resistance ranging
from 2 to 7 n$\Omega$. In order to evaluate the trapped flux sensitivity for
the series cavities, two cavities (DSPK07 and 17) were measured without active
compensation of the ambient magnetic field and still met the project
specification. This is consistent to the dedicated studies with prototype
cavities [PhysRevAccelBeams.24.083101]. Another concern was the fact that the
cavity mounted at the lower side might capture more contamination than the
upper one, because the lower one got cold even when the upper was still at
room temperature. Nevertheless, as shown in Fig. 6, we did not find
significant systematic differences in the cavities tested at upper or lower
positions of the vacuum insert.

Figure 6: RF performance of the ESS series cavities mounted at higher (upper
figure) and lower (lower figure) position in the vacuum insert.

Note that no HPR was performed between the cold test and module assembly111HPR
was performed for two cavities DSPK06 and 13 exceptionally after the cold test
and field emission in DSPK23 observed in the test was successfully removed in
the cryomodule. Although the pick-up antennas were carefully re-mounted after
the HPR, the field calibration could be potentially uncertain. However, no
major impact was observed in the site acceptance test.. Therefore, the pick-up
antenna was not touched until the site acceptance tests so that the calibrated
field to power values were preserved. This may provoke a concern about
degradation of field emission onset in the cryomodule, but we did not observe
any substantial increase of X-rays in the site acceptance test at Uppsala
University [FREIA_SRF2023_poster]. This evidences that ICJLab’s strategy was
successful.

##  4 MYRRHA PROTOTYPE CAVITIES

A proton driver in MYRRHA will provide a high-power proton beam to an
accelerator-driven subcritical nuclear reactor. The first stage of the
accelerator is composed of 60 single spoke cavities to provide protons at 100
MeV. IJCLab developed four prototype single spoke cavities in collaboration
with SCK-CEN. The cavities will be operated at 352 MHz and its target gradient
is at 9 MV/m including fault tolerance during the reactor operation. The peak
field ratio of MYRRHA’s single spoke cavities is slightly higher than that of
ESS, $7.3\,{\rm mT/(MV/m)^{-1}}$ while the geometrical factor is slightly
lower $G=109\,{\rm\Omega}$.

The RF performance is shown in Fig. 7 plotted on top of all the ESS series
cavity results in a gray scale. MYRRHA prototype cavities showed as excellent
performance as ESS and therefore the future series production looks promising.
Note that the peak magnetic field and surface resistance are slightly
different in ESS and MYRRHA due to geometrical factors, but this does not have
any impact in this conclusion.

Figure 7: RF performance of MYRRHA prototype cavities projected onto the ESS
series cavities. The difference in the geometrical factors are disregarded in
this comparison.

The next challenge in the MYRRHA project is full industrialization of all the
production process including chemical, heat treatments, and HPR. This is one
of the major objectives of the pre-series cavity development led by SCK-CEN.
IJCLab contributes to vertical tests of the pre-series cavities as well as
giving practical advice based on our long experience in spoke cavity
development for ESS. Note that such industrialization has been successful in
1.3 GHz TESLA-type elliptical cavities but its application to spoke cavities
is highly non-trivial due to its fundamentally complicated shape intrinsically
required by the RF performance at low-$\beta$.

##  5 BAKING OF SPOKE CAVITIES

During the series production of ESS double-spoke cavities, IJCLab did not
perform conventional baking after HPR except for very mild heating (120∘C, 3
h) for just drying water from the surface and reducing multipacting (MP).
Baking at 120∘C for 48 h is known as low temperature (low-T) baking
[10.1063/1.1767295] and can improve the accelerating gradient and $Q_{0}$ in
elliptical cavities at 1.3 GHz. The former is thanks to removing the high-
field Q-slope so that the peak magnetic field exceeds 100 mT (around 25 MV/m
for typical elliptical cavities). The latter is mainly thanks to lowering loss
contributions from thermally excited quasi-particles on dirtier surface, so-
called BCS resistance $R_{\rm BCS}$. Consequently, low-T baking has been
included in the standard procedure of other projects such as the International
Linear Collider. However, as a byproduct, a temperature-insensitive component,
so-called residual resistance $R_{\rm res}$ usually increases. Because of this
issue, the spoke cavities do not necessarily benefit from this standard
process.

The field levels of low-$\beta$ cavities are limited by beam dynamics even if
the ultimate field is improved. Typically, for the spoke cavities, around 9
MV/m or maximum 12 MV/m is the field level required by the projects. Clearly,
one does not need to remove the high-field Q-slope with low-T baking.
Moreover, at 2 K, the low frequency (below 400 MHz) leads to $R_{\rm
BCS}<1\,{\rm n\Omega}$ at 2 K because $R_{\rm BCS}$ has approximately a
parabolic dependence on the RF frequency. In this case, $R_{\rm res}$
dominates the loss, so that low-T baking may even deteriorate the unloaded
quality factor at low field.

When one takes into account the 4 K operation, the benefit of baking should be
re-evaluated. Since $R_{\rm BCS}$ is higher than $50\,{\rm n\Omega}$ at 4 K
with 352 MHz, the unloaded quality factor can be significantly improved by
baking. Figure. 8 shows the substantial improvement of cavity performance at 4
K after low-T baking. Although the MYRRHA project is primarily designed for
the 2 K operation, even the 4 K cavity performance after low-T baking met the
specification of the machine. This is a potential breakthrough in the future
spoke cavity technology [Longuevergne:2018ykg].

Figure 8: Influence of low temperature baking for a prototype MYRRHA cavity at
4 K.

Considering the recent progress in various baking methods beyond the
conventional low-T baking, we suppose that the medium temperature baking
(mid-T baking; 200-400∘C) may be the most promising as the new research
direction. IJCLab developed an excellent vacuum furnace [Fouaidy2021RecentRO]
and we plan to perform fundamental studies in baking spoke cavities in coming
years by using a spare ESS series cavity and prototype MYRRHA cavities.

##  6 PIP-II PROTOTYPE CAVITIES

The Proton Improvement Plan II (PIPII) is an international project to build a
proton driver, hosted by Fermilab, for answering questions of fundamental
physics, such as Dirac CP phase in neutrino, muon physics, and dark sector
[Lebedev:2017vnu]. This project includes two types of spokes cavities, SSR1
($\beta=0.22$) and SSR2 ($\beta=0.47$), in which IJCLab is strongly involved
on SSR2 section since the design phase [Parise:2019eod] and has agreed an in
kind contribution for the production phase of SSR2 [PIPII_SRF2023_poster].

One objective of PIPII SSR2 is the same as MYRRHA, i.e., industrialization
including fabrication and surface processing. IJCLab performs the vertical
tests of cavities fully prepared by the manufacturer and evaluate their
quality of surface preparation. When field emission is observed, we perform
our own surface treatment, fully qualified by ESS series cavities, and provide
feedback to the manufacturer.

The design of SSR2 is based on lessons learned from SSR1 and ESS cavities. As
is well known, substantial MP is one of the major challenges of spoke
cavities. Figure. 9 shows the MP bands of ESS cavities before being
conditioned. Clearly, the MP bands even cover the nominal accelerating
gradient, which is a typical field level for the spoke cavities. This
differentiates spoke cavities from the elliptical cavities whose MP bands are
usually sufficiently lower than the operational gradient. The potential
concern is any unexpected influence in stability during accelerator operation
even if the MP bands are conditioned in advance during machine commissioning.

Figure 9: Q vs E curves of ESS cavities with multipacting bands.

In the prototype SSR2, the cavity structure was designed to avoid MP bands at
the nominal field level at the expense of a slight degradation of peak field
ratios [Berrutti:2019tge], being inspired by the balloon spoke cavities
developed in TRIUMF [ZYYao2013StudyOB]. IJCLab has tested three prototypes of
this design with preliminary results shown in Fig. 10 [PIPII_SRF2023_poster].
Surprisingly, we observed a deterministic field emission whose onset has been
systematically around 4-5 MV/m in all the prototype cavities. Moreover, MP
bands at the low fields are substantially more difficult to condition compared
to the ones in ESS and MYRRHA cavities.

Figure 10: Preliminary results of PIPII prototype
cavities[PIPII_SRF2023_poster].

The cause of the field emission is traced back to the fact that the designed
SSR2 shape, optimized to avoid MP in the nominal fields, is so different from
previous cavities that existing HPR tooling cannot cover the whole surface of
the cavity. During the design phase, a better RF performance was prioritized.
Fermilab and IJCLab are currently optimizing the HPR tooling to completely
clean the complex surface of this spoke cavity. We are forced to spend a
factor of three times longer to pass the MP bands at low field. Although the
MP bands were well predicted at low field during design phase, the strength
and conditioning dynamic of MP is not predictable with the today code.
Moreover, we are starting R&D of preventive plasma processing during surface
preparation that will definitely improve and speed up MP conditioning.

These preliminary results and discussions may imply important trade-offs among
RF performance, surface cleaning, cold tests and operation for successful
implementation of new cavities of complicated shape. For example, as mentioned
in this paper, the ESS series cavities are equipped with additional ports for
HPR. These ports enable horizontal and vertical BCP and therefore they offer
thorough surface cleaning as well as fine tuning of the cavity frequency.
However, the ultimate reach of RF performance is slightly degraded by such
ports, influencing the geometrical factors slightly. The MP bands around the
operational gradient are certainly of great concern but they have been easily
conditioned (within 30 minutes) in the cold tests at IJCLab. On the contrary,
lower field MP needs several hours to overcome, even by experts of cavity
measurement. We could optimise RF performance but we might lose something else
as a side effect. These are important research subjects in the next years
about global optimization in the spoke cavity technology.

##  7 CONCLUSION

IJCLab successfully tuned the frequency shifts of 29 series double-spoke
cavties for the ESS project. All the challenges in fabrication and processing
were identified and were all solved so that the final frequency tolerance met
the specification. The ESS cavity performance was sufficiently beyond the
project’s specification. All the ESS series cavities were assembled into
cryomodules and passed the site acceptance test at Uppsala University and are
being installed in the ESS tunnel. The prototype single-spoke cavities for the
MYRRHA project also showed very promising performance and the pre-series
cavities are being fabricated by industry. The new challenge is to
industrialize chemical processing, heat treatment and HPR, following the
recent success in the LCLS-II project for 1.3 GHz elliptical cavities. The
PIP-II SSR2 cavities are still in the prototyping phase. Similar to the MYRRHA
cavities, IJCLab plays a leading role in industrializing all the processes of
cavity preparation. One major difference from ESS and MYRRHA is its optimised
RF design to avoid the MP bands at the nominal fields. The MP bands is known
to be problematic in spoke cavities. Although this design challenge revealed
another issue concerning surface cleaning, we are optimising the cleaning
process for this new geometry and will give feedback to the industry. Another
research subject is on baking spoke cavities and we pave the way to their
operation at 4 K.

##  8 acknowledgment

We greatly appreciate the invaluable contributions from the FREIA laboratory
during the series production of ESS spoke-cavity cryomodules. We would like to
acknowledge with appreciation the crucial role of colleagues from ESS. We are
deeply grateful to SCK-SEN and Fermilab for their leadership and cooperation
in the MYRRHA and PIPII projects, respectively. Last but not least, we thank
all the technical staff, administrative colleagues, and in particular
students, without whom the project and R&D would have not and would not be
feasible at all.

## References

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