JAERI-Conf 95-021

PA47
Refinement of Calibration Procedurefor Beam Position Monitors
Kazuhiro TAMURA, Shigeki SASAKI*, Masazurni SHOJI*and Shiro TAKANO*
Faculty of Science, Hiroshima University, Higashi-Hiroshima,Hiroshima 724, Japan* SPring-8, JASRJ-JAERI-RIKEN Project Team, Kamigori,
Ako-gun 678-12, Japan
Abstract

A. RF-Antenna

Experimental studies to examine calibration accuracyof beam position monitors (BPM's) with an RF-antenna
were conducted as an R & D for the BPM's of theSPring-8 storage ring. The antenna was optimized so as
to generate the electric field similar to that carried by anelectron beam. The accuracy was evaluated better than ±1 % for the position sensitivity after correction ofsystematic error due to the effect of the finite diameter of
the antenna, and within ± 56 J..Lm for the offset ofelectrical center.

The RF-antenna is made of a straight semi~rigid cablewith an inner conductor bared at the tip (Fig. 2). The
outer diameter of the cable is 3.6 mm and the length ofthe coaxial cable is chosen to be 295 mrn which is a half
wavelength of 508 MHz sinusoidal wave fed to theantenna. The frequency of 508 MHz is the RF frequencyof the SPring-8 storage ring and the BPM electronics ofthe storage ring detects the 508 MHz component of theelectric fields excited by an electron beam. The antenna is
supported by a long rod which is fixed to a threedimensional moving stage.

I. Introduction

SO IIITo measure the position of an electron beam with aBPM, it is necessary to calibrate precisely the offset ofelectrical center, and the relation between imbalances ofsignals from pickup electrodes and the deviation of theelectron beam from the electrical center. The imbalances
are expressed by position sensitivities U and V (Fig. 1).
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295

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720

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a stageSupporting Rod

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Semi·rigid Cable

Fig. 2 Structure of the RF-antenna.

V1

B. BPM Chamber

V3V4

Fig. 1 Conceptual drawing of a BPM and definition ofposition sensitivities U and V.
We studied the calibration procedure with an RFantenna as an R & D for the BPM's of the SPring-8
storage ring. Since the electric field around a relativisticelectron beam is contracted into a thin disk perpendicular
to the direction of motion, the electric field from theantenna has to be dominated by a transverse component
at the position of a BPM. We optimized the antenna togenerate a TEM field and examined the accuracy ofposition sensitivity and offset measurements with theantenna.

II. Equipment for BPM Calibration

Two BPM chambers have been prepared for thepresent study.
One has a circular cross section of 30 mrn in radius.
The chamber has been made to have symmetry ofrotation. Its dimensions have been measured with a
precise coordinate measuring machine. This chamber wasused to define the reference point for BPM calibration.
The other has an ideal elliptical cross section of thebeam chamber of the SPring-8 storage ring. Since theelectric field around a relativistic electron beam istransversal to the direction of motion, it can be modeled
as two-dimensional electrostatic field from a line chargeof infinite length located at the mass-center of theelectron beam. We can calculate it numerically by thetwo-dimensional boundary element method (BEM) [1]
imposing the boundary condition of the elliptical crosssection of the chamber, and calculate the dependence ofthe output voltages of individual pickup signals upon thebeam position. We measured the output voltages bymoving the antenna in this chamber, and investigated its
systematic difference from the calculation.

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III. Experiments and Results
A. Distribution ofTransverse Electric Field
Because uniformity of the coaxial structure, which iscomposed of the antenna and the elliptical BPM
chamber, is broken at the tip of the antenna, many
modes of electric field may exist there. However, only
the TEM mode can propagate through the coaxial
structure since the cutoff frequency is higher than 508
MHz.

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Longitudinal BPM Position (mm)Fig. 3 Distribution of transverse electric field measured
along the RF-antenna.

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To find 'the maximum point of the transverse electricfield, we investigated the longitudinal distribution oftransverse electric field along the antenna [2]. Changing
the longitudinal position of the BPM with respect to theantenna, we measured the voltage of a pickup signal
which is proportional to the transverse electric field. The
transverse electric field reaches a minimum at the tip of
the antenna and a maximum at about 130 mm (Fig. 3).
We decided to use the maximum point at 130 mm for
BPM calibration.
We measured the dependence of the output voltages ofindividual pickup signals upon the antenna position in
the transverse plane in order to verify if the distributionof the electric field around the antenna is consistent withthat of the TEM mode. The voltages measured with theantenna moving on the horizontal and vertical axes areshown as open circles in Fig. 4. They are normalized to
be unity at the electrical center. We can calculate theexpected voltages for the TEM mode by BEM, assuming
an indefinitely long charged metal rod of 3.6 mm indiameter (solid curves). The position dependence of themeasured voltages agrees with the calculation quite well.
The theoretical voltages for an electron beam arecalculated by assuming an infinitely long line charge(broken curves). Small systematic errors are found inmeasured voltages. We conclude that the electric fieldaround the antenna is consistent with that of the TEM
field, but is slightly different from that of an electron
beam because of the finite diameter of the antenna.

B. Position Sensitivity
Moving the antenna by 1 mm step in a central squareof 10 mm by 10 mm within the elliptical BPM chamber,
we measured the position sensitivities U and V (opencircles in Fig. 5).

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Fig. 4 Normalized voltages of individual pickup signals.
Open circles show the measurement with the antenna.
The broken curves and solid curves show the voltages by
BEM calculated for an electron beam and the TEM mode,
respectively.

Fig. 5 The position sensitivities U and V measured withthe antenna (open circles) and calculated theoretically(crosses).
Crosses represent the sensitivities calculated for theelectron beam by BEM at the same points. We foundsmall systematic errors in measured sensitivities. They
are caused by the finite diameter of the antenna. In order-160-JAERI-Conf 95-021

to evaluate the systematic errors !1 U and !1 V
quantitatively, they are plotted as a function of thetheoretical sensitivity, respectively (Fig. 6). According
to least squares fit to a straight line, the systematic errors
are evaluated to be + 2.8 % in horizontal sensitivity U
and - 2.2 % in vertical sensitivity V. After correction of
the errors, residual systematic errors are ± 0.3 % for U
and± 0.6% for V. Taking account of the random errorof 0.2 % caused by the repeatability of measurement, weconclude that the total accuracy of position sensitivity
measurement is± 0.5% for U and± 0.8% for V.

center (an open circle) from the position measured in caseof the setup in Fig. 7 (a). Since the rotational center is at
the midpoint of the electrical centers thus measured, wecan identify the location of the rotational center, i.e., thereference point.

0.01
(a)

0.005

Fig. 7 Measurement of the distances between therotational center and the electrical center of the circular
BPM chamber. The midpoint between tow electricalcenters in setups (a) and (b) corresponds to the rotationalcenter.

0-0.005
L1U = +0.028 X ucal

-0.01

-0.4 -0.3 -0.2 -0.1

0After setting the antenna at the reference point withthe circular BPM chamber, we slide the antenna awayfrom the chamber and replace it with a BPM chamber
which should be calibrated. Then the antenna is slid into
the chamber, and the offset of the electrical center ismeasured.
The precision of the reference point and that of theelectrical center of the elliptical BPM chamber were± 24
Jlm (full error) and ± 15 Jlm (full error), respectively.
The total accuracy of offset measurement is evaluated tobe ± 54 Jlm (full error), which is the sum of the
precision of the reference point, the precision of theelectrical center and the residual errors of thecharacterization of the signal processing circuits.

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ucal

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L1V = -0.022 XVcal

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(b)

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0.2

IV. Conclusion
0.3

Fig. 6 Systematic errors of the position sensitivities
measured with the RF-antenna.

C. Offset of Electrical Center
To measure the offset of the electrical center of aBPM, we have to locate the antenna at the reference
point whose location is definitively identified. We
defined it as the rotational center of the circular BPMchamber.
Owing to the measurement of its dimensions,location of the rotational center of the circular BPM
chamber is known (crosses in Fig. 7). The position
where we can set the antenna directly, however, is not
the rotational center, but the electrical center (a solid
circle in Fig. 7 (a)). If we know the distances between
the rotational center and the electrical center, we canidentify the location of the rotational center through theelectrical center. In order to find out the distances, werotated the chamber to the configuration shown in Fig. 7(b), and measured the displacements of the electrical

We studied the calibration procedure for BPM's andevaluated the calibration accuracy. An RF-antenna wasoptimized so that the distribution of electric field aroundit was consistent with that of TEM mode. The position
sensitivities were calibrated with accuracy of within ± 1% after correction of systematic errors due to the finite
diameter of the antenna, and the total accuracy of offset
measurement was evaluated to be within± 54 Jlm.

References[1] T. Shintake, M. Tejima, H. Ishii and J. Kishiro,
Nucl. Instr. and Meth. A 254 (1987) 146.
[2] M. Tejima, H. Ishii, T. Shintake, J. Kishiro, A.
Ogata, T. leiri and Y. Mizumachi, IEEE Trans. Nucl.
Sci. 32 (1985) 1947.

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