CHARACTERIZATION OF MICROPHONICS IN THE cERL MAIN LINAC
SUPERCONDUCTING CAVITIES
F. Qiu1,2,†, S. Michizono1,2, T. Miura1,2, T. Matsumoto1,2, D. Arakawa1, H. Katagiri1, E. Kako1,2,
H. Sakai1,2, K. Umemori1,2, T. Konomi1,2, M. Egi1,2
1High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
2
The Graduate Univiersity for Advanced Studies (Sokendai), Hayama, Kanagawa 240-0193, Japan
Abstract
In the main linac (ML) of the KEK-cERL, twosuperconducting cavities with high loaded Q (QL ≈ 1×107)
are operated in continuous wave (CW) mode. It is
important to control and suppress the microphonics
detuning owing to the low bandwidth of the cavities. We
evaluated the background microphonics detuning by thelow level radio frequency system during the beam
operation. Interestingly, a “field level dependence
microphonics” phenomenon was observed on one of thecavities in the ML. Several frequency components weresuddenly excited if the cavity field is above a thresholdfield (~3 MV/m). We found that this threshold field is
probably related with the cavity quench limits despite theunclear inherent physical mechanism. Furthermore, inorder to optimize the cavity resonance control system forbetter microphonics rejection, we have measured themechanical transfer function between the fast piezo tuner
and cavity detuning. Finally, we validated this model bycomparing the model response with actual system
response.

stability (left: ML1, right: ML2) in the past 5 years. After
2016, according to Fig. 1(b), the RF stabilities for ML1
cavity were, unfortunately, getting worse due to thedeteriorated microphonics conditions. Whereas thestabilities of ML2 cavity always performed well due to its
similar microphonics conditions in the past five years.
In view of this situation, we have investigated thebackground microphonics of these two cavities carefully.
Interestingly, a “field level dependence microphonics”
phenomenon was observed in cavity ML1 [3]. We foundthat if the cavity field in the ML1 is larger than a threshold
filed of 3 MV/m, several high frequency components weresuddenly excited. This threshold field is probably relatedwith quench limits according to the experimental results.
Furthermore, in order to optimize the current resonancecontrol, we measured the transfer function (TF) model
between the piezo tuner and the cavity detuning, and thendemonstrated the validation of the model in the beamcommissioning. This paper will present our studies in 2019.
890 Hz680 HzINTRODUCTION
At KEK, a compact energy recovery linac (cERL) wasconstructed to study the feasibility of the future 3 GeV ERL
based light source in 2009 [1]. It is a 1.3 GHz
superconducting (SC) facility that operated in continuouswave (CW) mode. In the main linac (ML) of the cERL, twonine-cell cavities (ML1 and ML2) were installed forenergy recovery [2]. These two cavities have a high loaded
Q (QL) of about 1×107, with the corresponding cavity halfbandwidth (ω0.5) of about 65 Hz. The lower bandwidth
makes the cavity phase very sensitive to the microphonics
detuning. A low level radio frequency (LLRF) system isusually required to reduce the microphonics effects.
Figure 1(a) compares the cumulative microphonics
detuning as a function of the vibration frequency of the MLcavities in the past 5 years (indicated by different colors).
In 2015, a 50 Hz component caused by scroll pumps wasobserved in both cavities (especially ML2). This
components were disappeared after inserting a rubber sheet
under the pumps. From 2016 to 2019, we have observedthat the microphonics conditions gradually deteriorated in
the ML1 cavity. Roughly, the RMS micrphonics detuning
in 2019 (blue) is 2.5 times of the detuning in 2016 (red).
On the other hand, such a phenomenon was not observedin the ML2 cavity. Figure 1(b) shows the corresponding RF___________________________________________†qiufeng@post.kek.jp

ML1

ML2(a)
6.0 MV
8.5 MV
7.0 MV
5.0 MV
5.0 MV

8.5 MV
7.0 MV
9.0 MV
7.5 MV
7.5 MV

After 2016

Before 2016

ML1

ML2(b)

Figure 1: Five years comparison of (a) cumulative RMS
detuning (in a function of vibration frequency) and (b)amplitude and phase stabilities (under feedback operation)of the ML1 (left) and ML2 (right). The cavity voltages ineach operation are also marked in Fig. 1(b).

LLRF SYSTEM
Figure 2 shows the digital LLRF systems (indicated byred block) and frequency tuner system (indicated by blueblock) of the ML cavities. The detailed information ofthese two systems can be found in [4-5] and [6],respectively. The phase differences ( Δφ ) between cavity
pick-up and cavity incident (Pf) are calculated in both twosystems. In LLRF system, this Δφ will be further filteredby a first order low-pass filter with 2.5 kHz bandwidth toreduce the background noise. The microphonics detuningΔω is then calibrated based on the Δφ by the equation    0.5  tan     ,(1)where ω0.5 represents the half-bandwidth of the cavity. Inthe tuner system, the Δφ is first regulated by an integral (I)controller and then combined with a feedforward model(FF2 in Fig.2). This combined signal will finally drives apiezo tuner which tune the cavity resonance frequency.
CavityCavityPick UpADCADC

PfIΔφLOPfIFADC

DAC

Low-pass
FilterI/QModulator

FF2
LLRF (field ctrl.)
Time

SETI/QDAC

PIEternetRF

FF1Fil2.5 kHzΔφI/Q Fil

Communication

SSA
1.3 GHz

Tuner(freq. ctrl.)

VcIFADC

Pf“field dependence microphonics” phenomenon did notappeared.
We scanned this field-detuning maps by several times
under different LLRF conditions (switching on/off theLLRF FB control loops or the frequency tuner feedbackloop). The threshold voltage was reproduced almost on thesame value for all of these cases. We therefore ruled out thepossibility of the FB loops that caused the “fielddependency microphonics” phenomenon. On the otherhand, we found the value of the threshold voltage isprobably related with quench limits. The cavity quench
limit field of ML1 was increased from 5.9 MV/m to 6.3
MV/m by the pulse (PS) aging processing. It is interesting
to see that the threshold field was also increased from 3.0
MV/m to about 3.2 MV/m. After one week beam operation,
we observed that the quench limits level was reduced
slightly, as well as the corresponding threshold field.
Table 1 has summarized the quench limits field and thecorresponding threshold field under different stage [3].

IQDAC
Power PCEPICSPCFigure 2: Schematic of the digital LLRF system (indicatedby red block) and frequency tuner system (indicated byblue block) of the cERL ML cavity.

MICROPHONICS OF ML CAVITIESIn 2019, the operational field of ML1 was limited to6 MV/m due to the degradation of the cavity performance[2]. We found that some high frequency components suchas 680 Hz and 890 Hz were excited under 6 MV/m
operation (see the accumulative RMS detuning plot atFig.1). However, these components were disappeared
when we operate the ML1 with lower field (e.g. 2 MV/m).
It seems that the microphonics detuning is related with thefield level in the ML1. To evaluate whether there is a fielddependence of the microphonics detuning, we graduallyincreased the cavity voltage (Vc) by changing the set valueof the LLRF system under feedback (FB) operation (seeFig. 2). The field-detuning map was then obtained byperforming Fourier analysis of Δω under different cavityfield.
Figure 3 shows the measured field-detuning maps ofML1 (upper) and ML2 (lower) cavities. The color code
here represents the detuning spectrum power. Interestingly,
an unexpected boundary, corresponding to a threshold Vcof approximately 3.1 MV, was observed in the map of theML1. Noted that the relationship between Vc and the cavity
field (Eacc) is expressed as Vc [MV] = 1.038 [m]×Eacc[MV/m], i.e. the value of Vc and Eacc is almost same in ourcavity [7]. In the field-detuning maps of the ML2, such aFigure 3: Field-detuning maps of ML1 (upper) and ML2(lower) cavity. The color in the figure presents the intensityof the microphonics detuning. A threshold voltage of 3.1MV appeared on the map of the ML1.
Table 1: Threshold Field versus Quench Limit Field
Cavity Conditions

Threshold Eacc

Quench Limits

Before PS aging

3.0 MV/m

5.9 MV/m

After PS aging

3.2 MV/m

6.3 MV/m

After one weekoperation

3.1 MV/m

6.1 MV/m

TRANSFER FUNCTION MEASUREMENT
In the current frequency tuner system based on Icontroller, the bandwidth of the closed system is less thanseveral Hz. However, as shown in Fig. 3, the microphonics
components are distributed from DC to several hundred Hz.
That is to say, the current I controller is not capable of
suppressing the microphonics detuning. To achieve a better
performance of the tuner FB system, advanced control
method such as active compensation method with adaptive
finite impulse response filter or active noise control
method are candidate approaches [8-9]. In such methods,prior measurement of the tuner TF model is necessary (orhelpful) for the controller design.
The TF model of piezo tuner system with N modes isgiven by [8]N M0  Td s
 k2 M k 2.
H s  e2   s  1 k 1 s  2 k  k s   k Figure 5(a) has compared the response of the type-A signalof the actual system (indicated by blue color) and the TF
model (indicated by red color). Similarly, Figure 5(b)compared the responses of the type-B signal. The results
are in good agreement in both of these two cases.

(2)

The parameter M0 is the steady state gain and τ a time
constant of a low-pass filter. The parameter Td represents
the group delay of the system. The parameters ωk, Mk andξk represent the frequency, magnitude, and damping
constant of the kth mode, respectively.
In cERL, inspired by the successful experience of a
disturbance observer (DOB)-based method in the LLRF
field control system [5], we also estimated the possibilityof extending this method to the tuner control system in2016 [6]. A tuner system model is also required in thedesign of the DOB-based controller. However, due to thetime limitation in the beam commissioning, we did nothave enough time to measure the complete TF model of thetuner system at that time. We only considered that the tuner
system is a simple first-order model [see the first ordermodel in (2)] with a group delay, and then used thissimplified model for controller design. The experiment is
not fully successful due to the oscillation of a 340 Hz
mechanical mode [6].
In 2019, we have measured the tuner TF by exciting thetuner system with the sinusoidal signal from FF2 (see theyellow block in Fig. 3). The response of the cavity detuningwas then calculated by LLRF system. We recorded theresponse of the tuner system from 5 Hz to about 340 Hz
which covers the main vibration components. Thefrequency step is set to 1 Hz, and for each frequency point,
up to 5 seconds measurements was conducted to achieve asteady state response.
The amplitude and phase response of the tuner system ofML1 (blue) and ML2 (red) are shown Fig. 4. From theamplitude response of ML1, a 340 Hz mechanical mode iseasily found. This mode is in good consistence with theresult in Ref. [6]. In addition, for ML1 tuner system, thesteady state gain M0 is approximately 2.6 according toFig. 4. This result is also in good agreement with the result
in Ref. [6], which has a M0 of 2.7. By fitting a linear curveto the phase response plot, we can identified the systemgroup delay of 0.11 ms by the slope of the linear curve. The
other parameters in each mechanical mode can beidentified by modern system identification method.
To validate the identified TF model, we have compared
the response of the TF model and actual tuner system in theML1 cavity. Firstly, we operated the tuner system andLLRF system with the open-loop. In the next step, weexcited the tuner system with two types of signals, type-A
and type-B. In the case of the type-A, the excited signal isa 50 Hz square wave signal with amplitude a1. In the caseof the type-B, the excited signal is a 20 Hz square-wave
with the amplitude 4∙a1. Finally, we measured thecorresponding cavity detuning response of this two cases.

Figure 4: Tuner amplitude (upper) and phase (lower)
response as a function of exciting frequency of ML1 (blue)
and ML2 (red).

Figure 5: Comparison of the square-wave response of thetransfer function model (red) and actual tuner system(blue). We have applied two types of square wave. (a)Type-A, 50 Hz and amplitude = a1, (b) Type-B, 20 Hz andamplitude = 4∙a1.

SUMMARY
The microphonics detuning is increased in the past five
years in one of the ML cavities. After investigating thecavity back-ground microphonics carefully, a “field level
dependency microphonics” phenomenon was observed.
Several components were suddenly appeared if the cavity
field is above a threshold field of 3 MV/m. This thresholdfield is probably related with the quench limits although
the internal mechanism is still not well understood.
Furthermore, we have measured the TF model of the tuner
system, and then validate the model by comparing themodel response with the measured system response. For
the future work, we will optimize our tuner control with theidentified TF model.

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