Journal of the Korean Physical Society, Vol. 54, No. 5, May 2009, pp. 20252030
Control and Measurement System for the Tuning of a PEFP Low-Beta
Superconducting RF Cavity
Zhang
Liping,
Sun
An, Yingmin Li, Tang Yazhe and Yong Sub Cho
Department of Electromechanical Engineering, Construction Machinery School, Chang'an University, Xi'an, 710064, China and
Proton Engineering Frontier Project, Korea Atomic Energy Research Institute, Daejeon 305-353
(Received 4 September 2008, in nal form 24 November 2008)
The superconducting RF (SRF) cavity is being considered to accelerate the proton beam in the
proton engineering frontier project (PEFP) linac and for its post-project. In order to correct for
the frequency shift and the eld atness variation of a TM010 mode in a raw PEFP multi-cell
(SRF) cavity caused by manufacturing errors and welding shrinkage during its production, a
eld atness tuning system has been developed. A new control and measurement system has
been successfully developed for the relevant tuning system. The system automatically controls
the bead's forward movement to a designated position and back to its original point and it also
drives the network analyzer to measure and acquire the data on the SRF cavity while the bead
is moving through the SRF cavity. After the bead has past through the cavity, the control and
measurement system provides the cavity's eld atness and the tuning frequencies of the individual
cells. The experiments in this study revealed that the control and measurement system is reliable.
By using this control and measurement system, the eld atness of a PEFP low-beta cavity can be
tuned from 75.62 % at 697.925 MHz to 1.43 % at 700 MHz, which can satisfy the control requirement.
PACS numbers: 28.65.+a, 29.20.Ej, 84.90.+a, 07.05.Dz
Keywords: PEFP, Superconducting RF, Field atness tuning, Control system
I. INTRODUCTION
Radio-frequency (RF) superconductivity is important
technology for particle accelerators. Many labs and institutes are participating in this eld and are trying to
develop and use superconducting RF technology for their
accelerators for dierent applications [1{3].
A superconducting radio-frequency (SRF) cavity is being considered to accelerate a proton beam after 100 MeV
operating at 700 MHz in the proton engineering frontier
project (PEFP) linac and its post-project [4{7]. The rst
section of the PEFP SRF linac is composed of low-beta
cryomodules. Each low-beta cryomodule has three 5-cell
cavities with a geometrical beta of 0.42.
The PEFP low-beta cavity is designed to be the lowest beta elliptical cavity operating at a pulse mode so
far. Generally, these lower beta cavities have a stronger
Lorentz force detuning than the higher beta cavities. In
order to control the Lorentz force detuning eects on
a low-beta cavity, a double-stiening ring is used for a
PEFP low-beta cavity [8]. For such a cavity with this
stiening structure, it is thought to be very dicult to
tune it.
E-mail:
lipizh221@163.com; Fax: +82-42-861-6950
The net accelerating voltage, the peak surface eld and
the Lorentz detuning coecient are the important physical parameters to evaluate a SRF cavity's performance.
These parameters are strongly aected by the eld atness in a multi-cell SRF cavity [9]. Due to manufacturing
errors and shrinkage during the welding process for the
stiening rings by an electron beam during cavity production, the cavity frequency is no longer the required
frequency; thus, the cavity eld atness becomes worse.
In order to correct for frequency shift and eld atness
variation, a raw cavity needs to be tuned by using a eld
atness tuning system before RF testing.
In order to tune a PEFP low-beta cavity with a doublestiening ring, a eld atness tuning system has been
developed. This tuning system includes a warm tuner
[10], a bead-puling system, a network analyzer and a
control and measurement system. Generally, the control
and measurement system is the most important part of
a tuning system. In this paper, we describe the development of the control and measurement system for the
PEFP tuning system. By using this system, a low-beta
cavity has been tuned to 1.43 % at 700 MHz. This control and measurement system can decrease the tuning
work and shorten the experiment time considerably.
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Journal of the Korean Physical Society, Vol. 54, No. 5, May 2009
II. FIELD FLATNESS TUNING PRINCIPLE
AND INSTRUMENT SETUP
Tuning a cavity is a process which sets a cavity's resonant frequency for an accelerating mode to the required
value while having the same eld amplitude in each cell.
During such a tuning, according to the measurement and
calculation tuning frequencies of an individual cell, we
use a tuning system to tune the individual cells; then we
can obtain the required cavity operating frequency and
an equal eld amplitude in each cell. Here, we introduce
the tuning principles and the developed tuning system.
1. Field Flatness Denition and Measurement
Method
Normally, eld atness is used to express how at the
eld prole is in a N -cell cavity and is dened as [9]
f f =
Vcmax
PN VVcmin 100 %:
1
i=1
N
ci
Here, Vci is the accelerating voltage of the ith cell. Vcmax
and Vcmin are the maximum and the minimum Vci , respectively. Because the Vci can't be measured directly,
we used a small metal bead to perturb the axial electromagnetic eld and to obtain the cavity frequency change
f . Then, according to the Slater perturbation theorem
[11], we obtained the eld prole on the cavity axis and
the f f , which
expressed as
pf can bepf
max
f f =
PN pfmin 100 %:
1
i
i=1
N
0q
B
q
B
B
Bq
V~ = B
B
B
q
B
B
@q
2
5
sin(=10)
2
5
sin(3=10)
2
5
sin(5=10)
2
5
sin(7=10)
2
5
sin(9=10)
q
q
q
q
sin(=5)
2
2f=
5
2
(f2 f=
)
5
:
2
f [1 cos(=5)]
1
2
ff =
p
arg(S 21)cmax
1
N
PN p
i=1
2
5
sin(3=10)
(3)
Using Eqs. (2) and (3), a reduced transformation matrix
~ r and its inverse matrix H
~ r 1 of the TM010 mode can
H
be obtained by calculating its individual elements based
p
arg(S 21)cmin
100 %:
arg(S 21)ci
(1)
The eld atness of a PEFP low-beta cavity is specied
to be less than 8.0 %. If the eld atness of such a cavity
can't meet this specication, we need to tune the cavity's
eld atness.
2. Theory to Tune a Cavity's Field Flatness
According to the multi-cell eld atness tuning theory
described in \RF Superconductivity for Accelerators" [1],
the cell voltage matrix V~ of a 5-cell cavity with at elds
can be expressed as [12]
q
q sin(2=5)
p15
2
2
2
sin(3=5)
sin(9=10)
sin(=5) p15
5
5
5
q2
p15
q2 0
q2 5
q2 0
1
q 52 sin(2=5) q 25 sin(=10) q52sin(4=5) 1p5
sin(4=5) 5 sin(7=10)
sin(3=5) p5
5
5
2
5
According to the passband measurement data, the cellto-cell coupling factor k of a PEFP low cavity can be
obtained from
k=
Here, fi is the maximum frequency change perturbed
by a small bead in the ith cell. fmax and fmin are the
maximum and the minimum fi in a cavity, respectively.
In the experiment, we do not directly measure the frequency change fi ; instead, we measure the phase angle
of the scattering parameter of S21 by using a network analyzer. When a small bead on the pulling string moves
through a cavity's center axis, we measure the phase angle change of S21 [arg(S21)] in the time domain by using
a network analyzer. The couplings of the input and the
pickup antennas have to be so weak as not to perturb
the end-cell elds. Then, the f f can be approximated
by
2
5
1
CC
CC
CC :
CC
CA
on the following equation:
X vlj vkj vk5
Hlk
=
:
2k[cos(j=5) + 1]
j 6=5
(2)
(4)
Here, vij is the element of V~ . By using the bead-pulling
method, we can obtain the maximum frequency shift fi
in the ith cell. The measured
frequency shifts are averP
aged as < f > = 51 i fi .
Using the unperturbed eigenvector for the TM010 mode in Eq. (2), we can formulate an expression that
Control and Measurement System for the Tuning of a PEFP Low-Beta { Zhang Liping et
al.
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only involves the unperturbed
the measured
h fi modei vand
i
5
frequency shifts: vi = <f > 1 2 . Here, we use
V~() to express a column matrix composed of element
vi5 : V~() = p15 (1 1 1 1 1)T .
~ r 1 and v1 4 , we
Using the reduced inverse matrixes H
~ r 1 V~r .
can express the reduced error vector ~er as ~er = H
Using this, we can obtain a corrected vector ~ec
0 < er >
B < er >
~ec = B
B
@ << eerr >>
er1
er2
er 3
er 4
< er >
1
C
C
C
A:
(5)
where < er > = 51 (er1 + er2 + er3 + er4 ). Note we have
divided (er1 + er2 + er3 + er4 ) by 5, not 4. We can
convert these to -mode frequency corrections for each
)
~ec to make sure all the cells are
cell via f~c = f(measured
10
tuned without changing f .
In addition to the cells being out of tune with respect to each other, if f is not equal to the desired value f (desired) , each cell can be altered by the
same amount so that f is altered, but the eld atness is unaected. For a \at" cavity, each cell has
an equal contribution for determining the -mode frequency. The frequency correction for each cell should be
f
f
f = (desired) 5 (measured) . The nal frequency, which
needs to be tuned for an individual cell, is
df~ =
f(measured)
10
er1
er 2
er 3
er 4
< er >
1
C
C
C
A
f(measured)
:
(6)
5
According to this result, each cell in succession needs
to be stretched or squeezed to meet the tuning requirements: a cavity's eld atness is less than 8.0 % at 700
MHz.
+
f(desired)
0 < er >
< er >
B
B
B
@ << eerr >>
Fig. 1. PEFP cavity eld atness tuning system.
shift by a moving metal bead, which is driven by a stepping motor. The stepping motor is driven directly by
its driver, which is controlled through a USB port using
the LabVIEW program. We do not use the stepping motor controller in a normal manner. This can help us to
simplify the experimental setup and to reduce the beadpulling system's cost.
A network analyzer is used to measure the frequency
shift (or the phase angle of the scattering parameter of
S21) due to the bead perturbation for a cavity and it
is connected to a computer through a GPIB card. The
bead, which acts as a disturber, moves through the cavity
along a shing line at a constant velocity as soon as it
enters the cavity and the network analyzer begins to scan
the cavity frequency and obtain a series of the phase
shifts. According to the phase shift curve, we can obtain
the eld atness.
The control and measurement system is written by using LabView. It controls the stepping motor to drive the
bead with a planned route. It initializes the network analyzer parameters, controls the analyzer to measure the
cavity phase shifts and acquires the measurement data
from the network analyzer. Then, it calculates the cavity
eld atness and the individual cells' tuning frequency
according to the eld-atness-tuning principles described
in Section II.1 and II.2.
III. SOFTWARE DESIGN AND ERROR
3. Instrument Setup
Figure 1 shows the eld atness tuning system for a
PEFP cavity. This system includes a warm tuner, a
bead-puling system, a network analyze and a control and
measurement system. The warm tuner is used to support
the cavity and to change an individual cell's frequency
by stretching or squeezing an individual cell. A PEFP
warm tuner has already been designed and fabricated for
tuning all PEFP SRF cavities (low, medium and high )
[10].
The bead-pulling system is used to perturb a cavity
axial eld distribution and to induce a cavity frequency
CONTROL
Based on the eld atness tuning principles and instruments described in Section II, we designed a control ow
chart for the PEFP cavity eld atness tuning, as shown
in Figure 2. We used the LabView code to construct this
chart.
1. Software Design and Realization
In the process, synchronous operation of the beadpulling system and the network analyzer is very important. In order to maintain a good synchronism between
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Journal of the Korean Physical Society, Vol. 54, No. 5, May 2009
Fig. 3. Front panel of the control and measurement system.
ning the program, the image of the eld prole on the
cavity axis, the eld atness, the Ezmax and the tuning
frequencies of the individual cells are displayed on the
front panel.
2. Error Control
In order to obtain precise and accurate measurement
results and to maintain the control and measurement
system stable, we used the corresponding methods to
reduce the following measurement errors:
Fig. 2. Control ow chart for the PEFP cavity eld atness
tuning.
these two components, we tested the exact step-numbers
of the stepping motor when the bead was passing the
active tailstock and the tailstock of the warm tuner and
the cavity and we set the scanning time of the network
analyzer according to the resultant values. The LabView
Program controls the stepping motor's step-numbers and
direction and sets the scanning time of the analyzer.
The eld atness is calculated with the LabView Program by using Eq. (1), but the tuning frequency calculation is completed with the MatLab program by using
the equations in Section II.2. The MatLab program operates within LabView as a module. The ordered control
approach of Figure 2 is completed by using a sequence
structures in the LabView program.
Figure 3 shows the front panel of the control and measurement system. On the front panel, we can input the
parameters: the measured f and f =5 , the output le's
path and name and the desired frequency. After run-
A. Error caused by the initial bead position: Wrong
bead position could cause the bead-pulling system and the network analyzer not to work synchronously. This could cause the LabView program
to produce a wrong eld atness and wrong tuning
frequencies. In order to avoid this measurement
error, we checked and corrected the initial position
of the bead before each measurements.
B. Error induced by the bead size: Large-sized beads
could induce a magnetic eld perturbation and a
wrong phase measurement result from the network
analyzer, as shown in Figure 4(a), but too small
a bead could induce a much stronger noise that
would produce incorrect calculation results and the
frequency measurement error of the TM010 mode
will cause the phase curve to decline, as shown in
Figure 4(b). This tilt of the phase curve will induce calculation errors. In order to obtain correct results, we chose a bead, which produced a
maximum phase shift of 20 , because the tilt was
about 0.25 .
C. Error caused by the frequency measurement of the
TM010 mode: As mentioned in B, this error will
Control and Measurement System for the Tuning of a PEFP Low-Beta { Zhang Liping et
al.
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Fig. 5. Cavity's eld atness tuning. (A) is the original
eld atness; (B) is the middle process; (C) is the nal tuning
result.
IV. EXPERIMENT RESULTS
Fig. 4. Network analyzer measurement errors induced by
bead size. (a) Error induced by a big bead (b) Tilt error
induced by a small bead.
induce a tilt of the phase shift curve. After testing,
we found that if we increased the tested frequency
of the TM010 mode by 100 Hz, the tilt disappeared.
D. Error induced by the network analyzer: The network analyzer could introduce a background phase
shift, which could induce measurement and calculation result errors. To remove this error, we used a
dierence method to correct this error in the LabView program.
E. Error caused by the measurement of the cell-tocell coupling factor k: The k is not a constant
value during tuning and will take on various values
for dierent cell pairs. The k measurement error
will induce tuning frequency errors. In order to reduce the error introduced by the k measurement,
we measured the frequencies of the TM010 and
/5 modes; then, we used Eq. (3) to calculate the
value of k in the LabView program. At the same
time, we tuned the cavities by using the results
attained in the last step.
The mechanical setup for the control and measurement
system is shown in Figure 1. Figure 5 shows the tuning
process and the tuning results for the copper cavity A.
The initial situation of cavity A was that the TM010 mode frequency was 697.6 MHz and the eld atness was
75.62 %. In order to avoid a subsequent adjustment of
a cavity before obtaining an ideal value, we introduced
a middle process. In the middle process, the desired
frequency was given as 699.5 MHz. Its purpose was to
adjust the cavity frequency to near 700 MHz and to result in a 0.5 MHz error. For the last tuning process, we
introduced the desired frequency of 700 MHz and slightly
adjusted the cavity. Finally, the eld atness was tuned
from 75.62 % to 1.43 %, which satises the control requirements for eld atness.
V. CONCLUSIONS
In a SRF cavity-eld-atness-tuning system, the control and measurement system is very important and necessary. Based on cavity tuning theory, a PEFP control
and measurement system has been successfully developed. With this system, a cavity without tuning any
cell has been measured over ten times and each time we
could obtain almost the same results for the eld atness, the tuning frequencies and the Ezmax of each cell.
At the same time, the resultant values agreed well with
the analyzed results. Thus, we can say that the system
is stable. In the tuning process, according to the running
results of the control and measurement system, the eld
atness of PEFP cavity A was tuned to 1.43 %, which is
much lower than the specication. This proved that the
PEFP control and measurement system had been developed successfully and that it could be used for tuning a
cavity properly.
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Journal of the Korean Physical Society, Vol. 54, No. 5, May 2009
ACKNOWLEDGMENTS
This work was supported by the Ministry of Education, Science and Technology of the Korean government.
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