Bunch length measurement and the beam signal observation through highpower RF waveguide system
T.Mimashi, H.Mizuno, KEK, Tsukuba Ibaraki Japan
B.Hong, IHEP, Beijing China
F.Tamura, Univ. of Tokyo, Tokyo JapanF(ω ) =Abstract
A bunched beam produces longitudinal electric field in
the RF cavity. The frequency spectrum of bunched beam
is observed through the beam-induced signal in the RFcavity at KEKB ring. [1] The signal propagates to theklystron gallery through the waveguide and is extracted
though the wide-band pick-up mounted on the wall ofwaveguide. The spectrum between 5 GHz and 20GHz istaken to calculate the bunch length. The strength ofsynchrotron oscillation and its frequency are alsomeasured.

∞
1f (t )⋅e j ⋅ω⋅t dt
∫
−∞
2 ⋅π
( t −n⋅∆T ) 2∞−a∞2⋅σ 2t=e∑∫2 ⋅ π n=−∞ −∞=a⋅ σ t −⋅e2⋅πω 2 ⋅ σ t22∞⋅ej⋅ ω⋅tdt-(2)∑e ωj⋅ ⋅n⋅∆Tn=−∞

The equation (2) indicates, the peaks appear every 1/∆T,
22and the envelop of these peaks gives exp(−ω ⋅ σ t / 2)
distribution.

1 INTRODUCTION

Bunch Length Measurement

The bunch length is expected to affect the KEKB
luminosity. The detail observation of the current
dependence of the bunch length and energy spread gives
the information of the strength of the impedance.
Accurate bunch length measurement [2] is also very
important to understand the intra-beam scattering effect inthe stored electron beam. Beam spectrum monitor isinstalled to measure the bunch length and to observe
longitudinal beam oscillation.

20Fundamental
Mode

Used data region(Bunch Length Measurement)

0HOM

dB-20

Calculation-40
Cut Off-60

2 BUNCH LENGTH MEASUREMENT
PRINCIPAL
The bunch length measurement is based on the spectral
analysis of the beam-induced signal in the RF cavity.
Suppose the Gaussian time profile is assumed, it producesa Gaussian frequency spectrum. When the Gaussianbunched beam pass through the RF cavity every ∆Τ sec,
they produce signal at the time t,∞f (t) = a ⋅ ∑ en=−∞−(t −n⋅∆T ) 2
2⋅σ t2- (1)Where σ t = σ z /C , σ z is the bunch length, C is thespeed of light and a is the function of bunch current.
Their frequency spectrum is given by the Fouriertransform of equation (1).

-800.1.

110GHzFigure. 1: Beam Spectrum measured at the KEKB Low
Energy Ring (LER) through high power RF waveguidesystem and the spectrum of the Gaussian beam.
Figure.1 shows the beam spectrum of the positron beamat KEKB LER. Below wave-guide cut off frequency, nofrequency component can be observed.
Then thefundamental mode appears at 508MHz. Between 508MHzand 5GHz, only higher order mode components of thefundamental frequency are observed. This is because thecavities absorb the signal of this region. Above 5GHz, thewavelength of the signal is much smaller than the size ofwave-guide, so that almost all components pass throughthe wave-guide. Using the signal spectrum in this region,
the bunch length is calculated.

There are two important advantages in this method. One isthis system can observe the wide-band beam spectrum
from 5GHz to 40GHz. The bare spectrum of the bunch isbrought to the final observation station with only a few
distortions above 5GHz, the distortion is much smaller
than that of button electrode and cable system. This makes
it possible to place the digitizer outside of tunnel, and tobe easy to modify the read out system without access tothe tunnel. Using this advantage, we can observe bunch
length directly by looking at major component of thelongitudinal beam spectrum. And it is also possible toobserve other beam oscillation such as synchrotron
oscillation or other beam instability.
Another advantage is no special hardware except for small
pickup is necessary to be installed. And this system can beused at any accelerators easily.

extracted. The induced signal in the RF cavity propagatesin the wave-guide to the klystron gallery and is extracted
through the wide-band pick-up. Then the spectrum
analyzer analyzes the signal. Several kinds of pickup thatthey should have flat frequency response at the region
between 5 GHz and 40GHz, was investigated [3] using
the MAFIA simulation code and Network-Analyzer test
bench. Finally a strip line type pickup was chosen. Inorder to avoid the coupling of the fundamental component,
the strip line is installed parallel to the microwave
propagating direction. In this installation, neither theelectric field nor the magnetic field of TE10 mode iscoupled.
Figure 3: A strip line type pickup mounted on the wall ofWaveguide

3 MEASUREMENTS AT KEKBThe KEKB, an asymmetric electron-positron collider is
now under operation. This collider consists of a 3.5 GeV
positron storage ring (LER) and an 8.0 GeV electron
storage ring (HER). The RF accelerating frequency is508.887MHz and approximately 5120 buckets of particles
are designed to be stored with 2nsec spacing. Theobservation of the beam spectra has been done with boththe positron and electron ring.

45mma7mm

b50ohmPort 1terminatorhigh power RF wave-guide system

3.2

Bunch Length measurement

At KEKB, the bunch length is controlled by themomentum compaction factor α and RF cavity voltage
Vc. The designed natural bunch length in 2000 year
operation is around 4-8mm.

All data from spectrum analyser
20

Bunch Length Measurement-20-10-40-20-60-80-100
5101520GHzFigure 2: Observed beam spectrum of the KEKB HighEnergy Ring (HER) between 5GHz and 20GHz.

Beam Spectrum (dB)Beam Spectrum (dB)0-30-40-50-60-70

3.1

Set upA wide-band pickups are mounted on the wall of waveguide between klystron and the RF cavity both in KEKB
Low Energy Ring (LER) and High Energy Ring (HER) tomeasure the spectrum of the stored beam. From obtained
beam spectra, several important information such as
bunch length, synchrotron oscillation frequency, is

7mm (Calculation)
9mm (Calculation)
Measurement (HER 516mA)Bunch Length = 8.04mm
68101214161820GHzFigure 4: Frequency component picked up every 127MHz.
And expected spectrum of several bunches length of thebeam.

The positron and electron beam are filled in every 3 or 4buckets in 2000 year luminosity run. More than 1000

bunches are stored in the ring. The monitor measures anaverage bunch length of these bunches. As we mentioned
in the section 2.2, when the positron beam is filled inevery 4 buckets, peaks are observed every 127.22 MHz(=508.887/4 MHz) on the spectrum analyzer. Peaks
between 5GHz and 20GHz are picked up and used tocalculate the bunch length. The system is designed to beable to observe the signal up to 40 GHz so that it canmeasure the shorter bunch length in future. Figure 2
shows beam spectrum between 5 and 20GHz. Figure. 4
shows picked up peaks and expected beam spectrum ofthe several bunch length.
HER Bunch Length and Beam current
HER current

Bunch Length

600

8.5
8.4
8.3

400
8.23008.1

200

8Bunch Length (mm)Beam Current (mA)

500

7.91007.800246810Time (Hours)

show in Figure. 4, it seems enough sensitivity todetermine the bunch length. Although it is very difficult tomeasure transfer function of the cavity and waveguidesystem, once the bunch length measurement is calibrated
by the other measurement, such as streak camera, we candetermine the transfer function.
Figure.5 shows bunch length and total beam current of theKEKB HER. The resolution of the bunch length
measurement is about +-0.25 %.

3.3

Synchrotron frequency measurement

The longitudinal coherent oscillation of the beam alsoobserved from the spectrum. The synchrotron oscillation
is observed as the side band of revolution peak. One ofthe peaks around 6GHz was picked up and zoomed up.
Figure. 6 shows the 2kHz synchrotron oscillation sideband. And it also shows unknown beam oscillation as the15 kHz side band. Thus when the instability occurs, thismonitor would be very useful to observe the strength andfrequency of the instability.

4 CONCLUSIONSThe longitudinal coherent motion of stored electron(positron) beam was observed through high power RFwave-guide system in KEKB. Strip line type of wide band
pick-up is mounted on the wall of wave-guide between theklystron and the RF cavity. The frequency spectrum ofbunched beam was measured. Using the 5GHz to 20GHz
beam spectrum, the average bunch length was calculated.
Synchrotron oscillation frequency also measured frombeam spectrum.

Figure 5: Total beam current and bunch length of theKEKB High Energy Ring.

REFERENCES[1] S.Kurokawa et al, “KEKB B-Factory Design Report”,
KEK Report 95-7, August 1995
[2] T.Ieiri, “Measurement of Bunch Length Based on
Beam Spectrum in the KEKB”, EPAC2000, Viena,Austria, June 2000
[3] B.Hong et al, “A Wide-Band pick-up for measuring
beam spectra in KEKB”, It will be submitted toAPAC2001, Beijing, China, September 2001

Synchrotron Oscillation Side Band
0Beam Spectrum (dB)-20-40

-60

-80

-100
-20-15-10-505101520

kHzFigure. 6: Synchrotron oscillation Side-band at KEKB
LER
Assuming Gaussian time profile of the beam, picked up
data is fitted with two parameters, bunch length and bunch
current. More than 100 points are used for fitting. As