Beam Based Calibration of BPM Position
Sensitivity at SPring-8 Storage Ring
S. Sasaki*, K. Soutome* and H. Tanaka*
*SPring-8/JASRI, Kouto 1-1-1, Mikazuki, Sayo, Hyogo 679-5198, Japan
Abstract.
A method for beam based calibration of BPM position sensitivity is proposed, and preliminary
result at SPring-8 Storage Ring is presented.
Beam based alignments of the BPM offsets were performed in various accelerator facilities. We
extended this kind of beam based alignment techniques to calibrate the position sensitivity of the
BPM.
When the strength of one quadrupole magnet is changed slightly, a certain amount of extra COD
arises, depending how much the offset from the quadrupole center the COD has. The amplitude of
COD and the distance from the quadrupole center has a certain functional relation which is defined
by the quadrupole magnet field distribution and the storage ring optics parameters. By comparing
the COD amplitude and the BPM position reading, we can re-scale the position sensitivity of the
BPM.
Recently, a preliminary test of the method was performed. In this paper the obtained result are
presented.
INTRODUCTION
The beam based calibration of beam position monitor(BPM) offsets are applied in various accelerator facilities.[1-5] The common method is a minimum search of closed orbit
distortion(COD) occurred by a small change of the focusing strength of a quadrupole
magnet with scanning the orbit around the quadrupole axis. In performing this kind of
measurement, the amount of extra COD occurred by the quadrupole strength change has
a relationship to the offset from the quadrupole axis. This relationship can be used for
calibrating the position sensitivity of the BPM adjacent to the quadrupole magnet whose
strength is changed.
We describe the principle of the method first, the preliminary measurement performed
at the SPring-8 storage ring next
PRINCIPLE OF THE METHOD
First, we pose the following conditions for the method to be valid.
1. BPM are linear, which means the measured position (jt, y) of a BPM is expressed as
* = *o + F->
and
> y = yo +
>
CP648, Beam Instrumentation Workshop 2002: Tenth Workshop, edited by G. A. Smith and T. Russo
© 2002 American Institute of Physics 0-7354-0103-9/02/$19.00
425
C1)
where, *0 and j0 are offsets of horizontal and vertical directions, Sx and Sy are position
sensitivity coefficients, and u and v are defined as
u=
(A 1 +A 4 )-(A 2 +A 3 )
(A 1 +A 2 )-(A 4 +A 3 )
v=
AX+A2+A3+A4
AX+A2+A3+A4
or, in another definition, which is used for SPring-8 Storage Ring,
u=2Al+A2
A 4 +A 3
V
1 AI-\
=2
A2~A3
A2+A3'
where A 1? A2, A3, A4 are the signal amplitude of the electrodes from 1 to 4, shown as
figure 1
270mm
FIGURE 1. Cross section of the BPM part of the vacuum chamber. The coordinates(jc, y) and electrode
No. and its amplitudes^, • • •, A4) are defined as shown in the figure.
2. The optics of the storage ring is linear, which means the COD caused by a single
kick at s = s0 is expressed as
(2)
COD(s) =
where, COD(s): COD at position s along the storage ring, /3(i): beta function at s,
dsf
( rc dsf \
, v: tune ( = / nl A ) , where C is the circumference of the storage
=r
7o
ring. 0(^ 0 ) : kick angle at ^ = ^0.
3. The kick angle generated by changing the quadrupole strength is expressed as
B(SQ) = dK'L'
0 (SQ) = 6K - L -
o), for x direction, and
0 ) , for y direction,
(3)
(4)
where 0(s0): kick at s = s0, 6K: amount of the change of the quadrupole strength, L:
quadrupole length, 8X(sQ), 57(^0): offset of the orbit from the quadrupole axis.
If the *0 and j0 in the equations (1) coincide with the quadrupole axis, <5X(s0) = u/Sx
and8Y(xQ)=v/Sy.
Since we performed measurements for only y direction, because of the analysis
convenience, we describe only v-direction case hereafter. The equation (2) becomes
CODy(s) =
8K-L
2sm(jtvy)
(5)
426
The equation (5) suggests that the Sy can be calibrated if all the storage ring optics
parameters are accurate and the COD(s) are measured without any error. This means
that the COD generated by quadrupole strength change is used as a reference for the
BPM position reading to be calibrated.
The method is applicable for obtaining the deviation of the coefficients from the
common factor to all the BPM. If all the BPM has same amount of factor difference of
the position sensitivity coefficients from the true value, the exact value of the coefficients
cannot be obtained since the COD(s) themselves are measured with the BPM.
MEASUREMENT
SPring-8 storage ring and its BPM
Before proceeding to the experimental method, the SPring-8 storage ring and its BPM
are briefly described. The storage ring is a third generation synchrotron radiation source
with the stored electron energy of 8 GeV. It consists of 40-normal and 4-long-straight
cells. Normal cell is a double bend achromat type. Each normal cell has 6 BPM, and the
long straight cell has 8 BPM.
A BPM consists of 4 button pickups as shown in figure 1. The electrodes are welded
directly on a long vacuum chamber with the lengths up to over 5 m. The chamber is
a ante-chamber type one, as shown in figure 1. The tuning frequency for detection of
electrode signals is same as RF acceleration frequency, which is 508.58 MHz.
Experiment
We adopted the following procedure for the measurement of the beam based calibration of the BPM position sensitivity.
1. Make a bump across one of the quadrupole magnet and its adjacent BPM. This
BPM is the target for calibration.
2. Change the quadrupole strength slightly.
3. Measure COD all around the storage ring before and after the change of the
quadrupole strength.
4. Repeat the step from 1 to 3 for the predefined set of bump heights.
We adopt the amplitude of the tune component of the COD fourier spectrum for the
indicator of the amount of the extra COD caused by the single kick generated with
quadrupole strength change.
After transformation from (y (.?.•), s*) to the normalized coordinate (
fourier-cosine and -sine components were calculated, where y - is the position reading
value of j— th BPM. The definition of the cosine (Cy(n)) and sine(Sy(ri)) components of
427
the n-th fourier harmonics are
Cy(n) = '
cosHyJdfc , Sy(n) =
- sin(^)<%,
(6)
where (f>y(s) = ——— , and the amplitude is Ay(ri) =
Vy
We approximated the fourier components by the summations of measured values as,
-*y,),
(?)
The sign to the amplitude was applied as Ay(ri) <— sgn(Cy(ra)) -Ay(ri) , for the analysis
convenience, where sgn(jt) = < _ 1
~~ .
Further modification to the Ay(ri) was made for normalization to the kick angle as
\ /,^\
Mn) = ——.
Taking the n as the integer part of the vertical tune(ra =18), the position reading
values of the target BPM were plotted against the normalized fourier amplitude of the
extra COD-difference occurred by change of quadrupole strength for each bump height.
The plot is expected to be on a straight line, and the slope has the information about the
BPM position sensitivity.
preliminary result
We made measurements on 8 BPM-quadrupole sets for vertical direction. They are
listed in table 1.
The quadrupole strength was changed by changing the current applied to the magnet.
The change of the current(<57) were the same for all the measured quadrupoles, which
was 10 A. The amount of strength change 6K was obtained as 6K = K • (5///0), for the
magnets operated in the linear range of excitation curve, where K is the nominal value of
strength, /0 is the nominal current applied in usual operations. Corrections were applied
for the magnets whose nominal current were non-linear range of the excitation curve.
Relative changes of the strength(6^T/^T) are also listed in table 1.
In figure 2(left), an example of the extra COD caused by 10-A change of the
quadrupole current is shown. The calculated value from the designed optics parameter and the unit kick angle at the same quadrupole was plotted on the same graph. The
428
TABLE 1. Measured set of BPM and quadrupole magnet and relative variation of quadrupole
strength
£ Jf
set No.
BPM(serial No. / cell-No.in the cell)
Q magnet(cell-No. in the cell)
23/4-5
87 /15-3
119/20-5
122/21-2
144 / 24-6
192 / 32-6
227 / 38-5
266/45-2
4-8
15-4
20-8
21-3
24-10
32-10
38-8
45-3
1
2
3
4
5
6
7
8
48
96
144
192
240
288
10
20
30
—(
K
2.6
2.0
2.6
2.6
4.5
4.5
2.6
2.6
40
50
harmonics order
BPM No
FIGURE 2. Calculated(open circles) and measured(closed diamonds) COD(left) and their fourier spectra(right) for the 7-th set of BPM-quadrupole(serial No. 227 BPM) in Table 1. Calculation was made using
the linear part of the designed optics parameters. Fourier components were calculated up to 50-th order
harmonics.
agreements of the COD pattern were quite good for all the measured set of quadrupole
and BPM. It shows that the nonlinearity of the optics parameter was small enough so
that the condition 2 was fulfilled.
An example of fourier spectrum of the extra COD is shown in figure 2(right) with the
spectrum of the calculated COD. The spectrum also agrees well. The n = 18 component
of the fourier spectrum was used for the estimation of the sensitivity coefficient, since
the integer part of the vertical tune is 18 for normal operation condition of the SPring-8
storage ring.
The BPM reading values are plotted against the normalized amplitude A^(18) as
shown in figure 3. The graph shows a linear dependency, and the data were fitted with
a straight line. The slope, which we express as a here, is related to the sensitivity
coefficient.
To compare the sensitivity obtained with the designed optics parameters, the COD
was calculated in the case of the 1-mm offset of the target quadrupole, and the fourier
amplitude of n = 18 component was obtained for the calculated COD, which we express
429
(18) here. Since the calculated data make a line connecting the origin (0,0) and
the point (A^calc (18), 1 mm), the slope of this line is
- i^tilc
y
2
1.5
1
0.5
D)
0
I
-0.5
0
-1
0_
-1.5
CO
E
E
"y = -0.35947 + 2.5447A (18)
-2
-1
-0.5
0
A y (18)
0.5
N
FIGURE 3. BPM reading values of serial No. 227 BPM vs. 18-th order harmonics of normalized fourier
amplitude for each bump height (open circles). The line indicates the fitted straight line.
The slope of the line consists of the measured data should be equal to I/Ay (18), if
the sensitivity derived from the measured COD is accurate. Here we introduce the ratio
of the slope of measured data(a)to the slope of the calculated line as r ;
r=
The obtained values of a, 1' /A^
(18), and r are summarized in table 2.
Jcalc
x
/
TABLE 2. Summary of fitted slope, the inverse of the calculated fourier amplitude, and the ratio of them, for the measured set of BPM and quadrupoles
1
Set No. BPM (serial No. / cell-No, in the cell) | a\
1-1
1-2*
2
3
4
5
6
7
8
23/4-5
23/4-5
87 / 15-3
119/20-5
122/21-2
144 / 24-6
192/32-6
227 / 38-5
266/45-2
2.43
2.42
2.74
2.28
2.55
2.29
2.31
2.54
2.57
2.31
2.31
2.32
2.24
2.34
2.20
2.18
2.33
2.36
1.05
1.05
1.18
1.01
1.09
1.04
1.06
1.09
1.09
* The measurement for BPM 4-5 was made twice with the interval of about 1 month,
from which the reproducibility of the measurement is estimated to be 0.4%
430
DISCUSSION
The reproducibility of the measurement was estimated to be less than 1% from the
difference of two measurements on the same BPM (BPM 4-5), as noted in the table 2.
The slope fitted with the measured data agree withe calculated values within 10% except
one BPM(serial No. 87: 15-cell No.3 BPM). The values of r are different from unity
above the reproducibility level. Suppose the accuracy of r is the level of reproducibility,
corrections to the sensitivity coefficients^) must be applied, and the serial No. 87 BPM
has the correction as large as 18%.
0.2
0.0001
-0.2
48
96
144
192
240
10
288
20
30
40
50
harmonics order
BPM No
FIGURE 4. Calculated(open circles) and measured(closed diamonds) COD(left) and their fourier spectra(right) for the serial No. 87 BPM. Calculation was made using the linear part of the designed optics
parameters. Fourier components were calculated up to 50-th order harmonics.
2
1.5
E
1
0.5
D)
C
0
-0.5
0
-1
Q_
-1.5
CO
"y = -0.1074 - 2.7403A" (18)
-2
-1
-0.5
0
A N y (18)
0.5
FIGURE 5. BPM reading values of serial No. 87 BPM vs. 18-th order harmonics of normalized fourier
amplitude for each bump height (open circles). The line indicates the fitted straight line.
In figure 4, the COD and its spectrum are shown for the serial No. 87 BPM. The
COD and the fourier spectrum have the similar patterns of the calculated ones. The plot
of BPM reading valued vs. fourier amplitude is shown in figure 5. The data are on a
straight line. From these figures, we can judge that the cause of 18% difference from the
unity of the r value is not the non-linearity effect.
431
For the SPring-8 Storage Ring BPM, the sensitivity coefficients were obtained by
scanning an RF antenna. The antenna was supported by the single end and attached to
an x — y stage for scanning purpose. The antenna consisted of a supporting rod and a
semi-rigid coaxial cable with center conductor disclosed at the tip of the cable. The total
length of the antenna (rod, cable) from the top end to the supporting end was about 2 m.
The measurement was done for all the 288 BPM of the storage ring before installing
the vacuum chambers. The sensitivity values obtained the RF antenna scanning method
varied from BPM to BPM by several %. If this variation of the values of Sy came from
the measurement accuracy of the RF antenna method, the several % of correction to Sy is
plausible. However, the 18-% correction, as in the case of serial No. 87 BPM, exceeded
our expectation. Thus, the estimation of the accuracy of this method must be investigated
to decide whether the 18-% correction should be applied or not.
SUMMARY
We propose a method for beam based calibration of BPM position sensitivity, and
made preliminary measurements for some of the BPM in the SPring-8 storage ring.
The reproducibility of the measurement of this method is better than 1%. The level of
accuracy of the measurement should be investigated further.
REFERENCES
Peter Rqjsel, "A beam position measurement system using quadrupole magnets magnetic centra as the
position reference", Nuclear Instruments and Methods in Physics Research A343 (1994) 374-382
A. Jankowiak, C. Stenger, T. Weis, K. Wille, "The DELTA Beam-Based BPM Calibration System",
Proceedings of The 8th Beam Instrumentation Workshop(BIW98), SLAC, 1998
B. Dehning, G.-P. Ferri, P. Galbraith, G. Mugnai, M. Placidi, F. Sonnemann, F. Tecker, J. Wenninger,
"Dynamic Beam Based Calibration of Beam Position Monitors", Proceedings of the Sixth European
Particle Accelerator Conference, Stockholm, 22-26 June 1998, p430-432
K. Soutome, H. Tanaka, M. Takao, H. Ohkuma, N. Kumagai, "Estimation and measurement of
effective beam position monitor offsets by using a stored beam", Nuclear Instruments and Methods
in Physics Research A459 (2001) 66-77
Mitsuhiro Masaki and Storage Ring Commissioning Group, "A Method of Beam-based Calibration
for Beam Position Monitor", Proceedings of The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, Hyogo, Japan 1997, pp83-85
432