The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

Measurement of Longitudinal Coupling Impedance at KEKB
Takao IEIRI*, Kazunori AKAI and Nobumasa AKASAKA
KEK, High Energy Accelerator Research Organization
Oho 1-1, Tsukuba, Ibaraki 305-0801, Japan

Abstract
We have measured current dependence of thesynchronous phase and the bunch length in order toevaluate the longitudinal coupling impedance at KEKB.
A real part of the impedance can be estimated from avariation of the synchronous phase. An imaginary partof the impedance is derived from bunch lengthening.
Measured loss factor indicated from two to three times aslarge as a design value. Measured impedance exceeded adesign value by a factor of five.

1 Introduction
The coupling impedance is one of the most important
issues forB-factories, such as KEKB [1,2], to achieve
high beam current and a high luminosity. Problems ofbunch lengthening and parasitic wall loss give us a severe
KEKB is ancondition to perform design values.
asymmetric electron and positron collider with twoAbout 5000
storage rings, named LER and HER.
bunches will be stored with a 2 ns spacing in each ring.
The total current is designed to be 2.6 A in LER and 1.1
A in HER. Basic parameters are listed in Table 1.
Table 1
Basic parameters of KEKB used in this measurement
HER LER
Parameter
3.5 (Gev)
8.0
E Beam Energy508.886 (MHz)frt RF Frequency
99.39 (kHz)fo Revolution Frequency
5120
h Harmonic Number
4.0 (MV)vc RF Cavity Voltage 8.0
fs Synchrotron Frequency 1.17 1.14-1.18 (kHz)a Momentum Compaction 1.88 1.41 -1.53 xw- 4
6.67 7.31 x w- 4
oe Energy Spread
3.49 0.85 (MeV)U o Energy Loss/Turnmomentum compaction, when total cavity voltage is
The cavity voltage in a storage ring gives afixed.
circulating bunch electric energy to compensate for theradiation loss. The synchronous phase is determined by
the energy balance between the rf voltage and the radiation
A bunch loses more energy due to resistiveloss.
impedance of a vacuum chamber. This additional energy
loss represented by the loss factor, k(a) depending on thebunch length, is compensated by an appropriate shift inthe synchronous phase, which is given by(2)Vcsin(IPso+L1cps)= Uo +k(a)Tolb.
eHere, IPso is the synchronous phase for a very small beam
current and I b is beam current when a single bunch isassumed. Assuming L1cp s is small enough, the loss
factor is obtained byk(a) = Vc COS IPsO L1cps.

2
1 00
k(a) = - fZr(w)e-(wa) dw,

where Zr ( w) is a real part of the impedance and a is rms
bunch length. The natural rms bunch length is given bycaoe 1(5)aLO = - - - ,2n fs
where c is the velocity of light. The natural bunch
length is inversely proportional to the synchrotron
The coefficient is determined by thefrequency.
momentum compaction and the energy spread.
As the beam current increases, an effect of thecoupling impedance appears. An inductive or capacitive
impedance changes the bunch length due to the potentialwell distortion. When a purely inductive impedance isassumed, the bunch lengthening for a Gaussian bunch isanalytically derived [3] and given byaLO

aLO(_.B.__)3(Z;(W))-JlTibn2hVc cos cps aLO

2 Longitudinal Beam Parameters

ealb2

afrte vc icos (/) s 1
(1)
2nET0
where IPs is the synchronous phase and T0 is revolution
period. The synchrotron frequency is proportional tofs =~aVcjcosqJsl in a storage ring and a measure of the(4)no(--~-} -(~) =Longitudinal beam parameters represented by thesynchrotron frequency, the synchronous phase and thebunch length of a bunch are coupled with each other.
The synchrotron frequency is given by(3)

IbToThe loss factor is also related to the resistive impedance
and it is given for a Gaussian bunch by(_.B.__)3(Zi(w))

4-JlTrs E aLO

r= 4-JlT.

n(6)Here, R is average radius of a ring, n is integer given by
n=(J)/ Wo and Ys is the synchrotron tune and r is adimensionless parameter introduced by K. Bane [4]. An
inductance is given by w 0L = jz; I nj, where w0 is theangular revolution frequency. The bunch lengthening
using Eq. (6) agrees with a numerical calculation using
the Haissinski equation within 1% up to r=40 [5].

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When the bunch lengthening is small enough at a very
low current, the bunch length is given byecLib
a= aLO+c2•bunch length agrees with an absolute value within ± 1mm considering a gain error of the detector.
12~~~~~~-.. .- .. .- .. .~(7)

8"1/1ra8eE
It is noted that the second term is independent of thebunch length and the synchrotron tune.
3 Measuement
Measurement was performed with a single bunch atboth LER and HER, where wiggler magnets at LER werenot excited. A longitudinal position was detected using a
tum-by-tum monitor [6] which can detect a beam phasefrom a ratio of orthogonal components of a beam at 509
MHz. An averaging method improves a resolution ofmeasurement. Measurement reproducibility of less than
0.3 deg. was achieved in a short term. The synchronous
phase was measured as a function of the cavity voltage
when the bunch current was around 0.3 rnA and 0.4 rnA.
When the cavity voltage is changed under a constantbeam current, the AqJ 8 in Eq.(3) would be almost
constant, because the cavity voltage and the loss factor
similarly varies for a change in the bunch length. TheAqJ s was actually 1.1 ± 0.1 de g. using measured data
described later. Thus we can evaluate the cavity voltage
from measurement of the synchronous phase. Measured
phase was shifted so as to match it with a calculated
synchronous phase. The best agreement was achieved byshifting the phase by 147 deg. and by multiplying the Vc
by 1.05 at LER. This result means that the mesured Vc
is lower than that in calculation by 5% at LER. An error
in the Vc was only 2% at HER.
The synchrotron
oscillation was excited and its frequency was measured asa function of the Vc on a spectrum analyzer. The best fitof the f,. with a calculation including the error of the Vc
was a condition of using the a = 1.50 x 10-4 at LER.
On the other hand, the bunch length can be obtained
from the beam spectrum. When we detect two frequency
components, w1 and w2 , in the beam spectrum under thecondition of wa < 1, an amplitude ratio of thesecomponents gives an rms value of a bunch shape. Thismethod is applicable to even an asymmetric distributionof a bunch.
Thus, amplitudes of two frequency
components at 0.5 GHz and at 2.5 GHz were detectedusing a beam signal from a button electrode. A common
electronics circuit was used for detecting both beams of
LER and HER. Since it is difficult for this method todetermine an absolute value of the bunch length, thecalculated natural bunch length at zero beam current isused as a reference value. In order to calibrate themonitor, the bunch length was plotted as an inverse
function of the fs as shown in Fig. 1. The slope ofmeasured bunch length was 5.95 ± 0.1 mmkHz at HER,
which agrees with a calculation with 5.97 mmkHz. The
measured bunch length has an offset of about 0.8 mm forthe calculated natural bunch length, which may be due tothe potential-well effect shown in Eq.(7). The measuredokzr

2
1l!fsFig. 1 Measured bunch length shown in dots vs. 1/fs.
Solid line is the calculated natural bunch length.
The loss factor can be obtained from a slope of asynchronous phase as a function of the beam current
using Eq.(3). The bunch length was also measured as afunction of the lb as described in the next paragraph.
Figure 2 shows the loss factor for HER and Fig. 3 for
LER as a function of the bunch length . The loss factor
at the design bunch length of 4 mm was not measured
because the natural bunch length was longer than 4 mm.
The loss f actor ofb oth ..
nngs are ch ange d as a -1.6±0.2 at
29HER and a- · ±0.3 at LER as a function of the bunch
length. When we extrapolate the loss factor at the bunch
length of 4 mm from measured data, the loss factor would
be 67 ± 16 V/pC at HER 87 ± 30 V/pC at LER. The
measured data suggest that the resistive impedance at LER
has a little stronger frequency dependence than that at
HER.
,.....,

uc..

~60£g 40~"'"'020....:l106
78Bunch Length (mm)Fig.2 Loss factor vs. bunch length at HER. The error
bars are due to ambiguity of the bunch length
depending on the beam current.

580~~~-.-,-,-,-,-,-,-,,

6040

2004678Bunch Length (mm)Fig.3 Loss factor vs. bunch length at LER.

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The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

Figure 4 shows bunch lengthening as a function of thebunch current at HER. The natural bunch length is 5.5
mm. The bunch length measured using a streak camera
is also plotted [7]. The streak measured fwhm/2.354 of abunch. There seems to be a disparity in the measured
bunch length between the streak and the spectrum at
higher current above 1 rnA. The streak indicated aparabolic distribution [7] rather than a Gaussian at thehigher current. The deformation was remarkable as thebeam current increased. The disparity should be causedby the deformation of a bunch shape. A fitting curveusing Eq. (6) agrees with the measured rms bunch length,
where jzi I nj = 0.076 Q is used. On the other hand,bunch lengthening at LER is shown in Fig. 5. A fitting
curve ia also shown, where jzi I nj = 0.075 Q is used.
However, the fitting is not so good as that in HER. One
possible reason for the poor fitting at LER may be a limit
of using a purely inductive impedance model. It wasobserved that the synchronous phase shifted to more than
one standard deviation of the natural bunch length as thebunch current increased up to 1 rnA at LER.
12,--..,

Ei 10Ei'--'
8.sCiO~Q)____________!__ _---->--o __ Q ___~-------<P

6u4------------------~;::la:!

2-------------~---------We have measured the loss factor and the imaginary
part of the longitudinal impedance at both rings. The
results are listed in Table 2, where design values are also
shown for comparison. Measured loss factors are fromtwo to three times as large as the design values of about
28 VlpC at aL =4.0 mm. On the other hand, measured
impedance is about 5 times as large as the design value inboth rings.
We notice a big disparity between theactual machine and the designed values.
Vacuumchambers have been modified especially in the interaction
region and unexpected components added since the designnote was published in 1995. A remaining issue is toevaluate those components.
The authors are grateful to the KEKB commissioning
term led by Prof. K.Oide.
Discussions with Dr.
Y.Ogawa are very helpful.
Table 2
Measured impedance together with designed values.
The loss factor is a value at the bunch length ofa=4mm.
measurement
HER
designedk (VIpC)
67± 1628
jzi I nj (Q) 0.076 ± 0.006 0.015
measurement
LER
k (VIpC)
87±30
jzi I nj (Q) 0.072 ± 0.011....l,.04 Summary---------0 02
Bunch Current (rnA)
Fig. 4 Bunch length vs. bunch current at HER. Dots arebunch length by a spectrum method and circles are
by a streak camera. Solid line is calculated bunch
length.
10,,-,-,~,,-,-,,-,,-,-,,--..,

Ei

8

§

-5bll 6~.3

4,.0u

~

::l

2

----r--------- -------------r-------r ------------------

a:!

00

designed25
0.015

2Bunch Current (rnA)
Fig.5 Bunch length vs. bunch current at LER, where thenatural bunch length is 4.3 mm. Solid line iscalculated bunch length.

References[1] KEKB B-Factory Design Report, KEK Report 95-7.
[2] Y.H. Chin and K.Oide, "Collective Effects andImpedance in the KEKB", Proc. oflnt. Workshop on
Collective Effects and Impedance for B-Factory,
CEIBA95, KEK Proceedings 96-6.
[3] B. Zotter, "Collective Effects", CERN 85-19 (1985)
415. L. Palumbo and V. Vaccaro, "Wake Fields
Measurements", Lecture Notes in Physics 343,
Springer-Verlag (1989) 312. J. Laclare, "Bunched
Beam Coherent Instabilities", CERN 87-03 (1987)
264.
[4] K. Bane and D. Ruth, "Bunch Lengthening
Calculations for the SLC Damping Rings", IEEETrans. on Nucl. Sci., (1989) 789.
[5] Y. Shobuda, Private communication.
[6] T. Ieiri and T. Kawamoto, "A Four-Dimensional
Beam-Position Monitor", to be published in Nucl.
Instrum. Methods A.
[7] J. Flanagan and T. Mitsuhashi, P1ivatecommunication.
*e-mail: takao.ieiri@kek.jp-411-