DEVELOPMENT OF A NEW BEAM-ENERGY-SPREAD MONITOR
USING MULTI-STRIPLINE ELECTRODES
T. Suwada∗ , M. Satoh and K. Furukawa, KEK, Tsukuba, Ibaraki 305-0801, Japan
Abstract

scheme they are injected to the rings simultaneously.

A nondestructive beam-energy-spread monitor (BESM)
using multi-stripline electrodes has been newly developedin order to measure and control the energy spread of asingle-bunch electron beam at the 180-degree arc witha beam energy of 1.7 GeV in the KEKB injector linac.
A proof-of-principle experiment was performed to verifythe function of the BESM. The result shows that taking
into account the second-order moment derived from themultipole-moment analysis, the energy spreads are estimated to be 0.150±0.007% and 0.264±0.004% for theelectron beams with charges of 0.9 and 8 nC/bunch at therf phase of the energy-spread minimum, respectively.

1INTRODUCTION

The KEK B-Factory (KEKB) project [1] is in progress
for testing CP violation in the decay of B mesons. KEKB
is an asymmetric electron-positron collider comprising 3.5GeV positron and 8-GeV electron rings. Since KEKB is afactory machine, well-controlled operation of the KEKB
injector linac [2] is required for keeping the injection rate
as high as possible and for maintaining stable operation.
For this purpose, beam diagnostic and monitoring tools are
essential. The energy spread of the primary electron beamfor positron generation is often increased due to a longterm phase drift of high-power and booster klystrons. Thus,
beam diagnostic and monitoring tools are required to curethe beam energy spread; furthermore, those are expected
to control the longitudinal wakefields of the high-current
primary electron beam pulse-by-pulse, especially at large
energy dispersion sections.
The BESM with multi-stripline electrodes is one of very
useful monitoring tools for satisfying such requirements,
since it can measure the energy spread derived from aquadrupole moment of an electron beam. This monitor
was designed based on a numerical analysis by applying
the multipole moments of the electromagnetic field generated by a charged beam [3]. The BESM detects the spreadof transverse beam widths at a large energy dispersion section by measuring any variation of the electromagnetic field
distribution induced on the multi-stripline electrodes of themonitor. In this report the authors not only present a clear
experimental verification of this analyis based on the previous works [4, 5], but also demonstrate that the secondorder moment of an electron beam can be nondestructively
measured by the BESM, depending on the variation of theenergy spread. The BESM will enable to acquire beamcharacteristics of two beam bunches in an rf pulse in which∗ e-mail:tsuyoshi.suwada@kek.jp

2MULTIPOLE-MOMENT ANALYSIS OFA CHARGED BEAM

For a conducting round duct, the image charges induced
by a line charge can be solved as a boundary problem inwhich the electrostatic potential is equal on the duct [6](also see Ref. [7]). The formula for the image charge density j is given byj(r, φ, R, θ) =I(r, φ)
R2 − r 2, (1)2πR R2 + r2 − 2rR cos(θ − φ)where I is the line charge, (r,φ) and (R,θ) are the polar coordinates of the line charge and the pickup point on the duct,
respectively, and R is the duct radius. Assuming the transverse r-distribution ρ(r) of a traveling charged beam, thetotal image charge J is formulated by integrating the image
charge density with a weight of the transverse distribution
inside the duct area,R 2πJ(R, θ) =j(r, φ, R, θ)ρ(r)rdrdφ.
0(2)0It is easily expanded by a power series,
Ib
2
J(R, θ) ={1 +x cos θ + y sin θ2πRR2  2+ 2 x  − y 2  + x2 − y2 cos 2θ
R+2 (xy + xy) sin 2θ]+higher orders} ,(3)where Ib is the beam charge, x and y are the charge
center of gravity of the beam, x2  and y 2  are the horizontal and vertical mean square half widths of the beamin the x and y directions, and xy is the x-y couplingin the transverse plane, respectively. A transverse beamwidth measurement is performed to detect the secondorder (quadrupole) moment Jq at the least orders. The
quadrupole moment is described by using the following
eight-pickup amplitudes [Vi (i=1-8)] of the BESM:
2πJq≡

2πJ(R, θ) cos 2θdθ/0=J(R, θ)dθ,01(x2  − y 2  + x2 − y2 ),R28
Vi cos 2θi=1,8
Vii=1(4)Normalization by summing the eight-pickup amplitudes
needs to cancel out the beam charge fluctuations due
to any beam measurement jitter. It is understood thatthe quadrupole moment is related to the transverse beamwidths, while it also depends on the beam positions.

3

BEAM ENERGY-SPREAD MONITOR

Figure 1 show schematic cross-sectional drawings ofthe BESM. The mechanical design parameters are summarized in Table 1. The BESM is a conventional monitor with eight-stripline electrodes fabricated from stainless steel (SUS304) with π/8 rotational symmetry. Thestripline length L was determined to be as long as could
possibly be installed into the limited spaces in the beam line
so as to increase the signal-to-noise ratio. The inner andouter radii, R1 and R2 , and the angular width α of the electrode were chosen so as to comprise a 50-Ω-transmission
line. The eight pickups with a relatively narrow angularwidth of 15 degree are mounted with a tilt of π/8 rad at
the symmetrical polar coordinates in order to avoid any
direct impinging of synchrotron radiation and off-energy
electrons to the electrode surfaces at a large energy dispersion section.

aR2
R1

where the beam energy is 1.7 GeV. The layout of the beamline is described elsewhere [2]. The multipole moments ofthe electron beam were measured by the BESM while thetransverse spatial profiles of the beam were directly measured by a fluorescent screen monitor (SC) installed behind
the BESM with a beam-synchronous CCD camera and avideo-image frame grabber in order to calibrate the BESM
results at a rate of 1 Hz.
The transverse beam widths at the locations of thesemonitors were controlled by changing the rf phase of thebooster klystron at sector B. The BPMs located at sectors
A, B and the arc monitored the beam positions and chargesof the beam in order to control the beam positions and energy stably through the feedback systems without any beamloss during the experiment.
The beam experiments with the BESM were performedby measuring the quadrupole moment of the 0.9-nC electron beam, as a function of the horizontal (x) and vertical(y) beam positions. In this measurement the rf phase of
the booster klystron at sector B was fixed to reduce the energy spread to its minimum with the beam-orbit and energy
feedbacks at sector B off. The beam positions at the BESM
were controlled by the field strength of upstream x and ysteering magnets. The quadrupole moments of the 0.9-nC
and 8-nC electron beam depending on the rf phase of thebooster klystron were also measured while the beam positions of the electron beam were fixed at the center of theBESM with the beam-orbit and energy feedbacks on. One
data point of the BESM was obtained by averaging 200
successive data with the statistical errors after the position
dependence was corrected.

t5

Figure 1: Schematic cross-sectional drawing of the beamenergy-spread monitor.

Table 1: Mechanical design parameters of the BESM.
Mechanical parameter
Innner radius R1 (mm)Outer raidus R2 (mm)Electrode angular width α (deg)Electrode thickness t (mm)Electrode length l (mm)Total length L (mm)

420.6
23.4
15
1.5
132.5
283

BEAM TESTBeam experiments using single-bunch electron beams
of 0.9 and 8 nC/bunch were carried out under the nominal operation condition at the 180-degree arc after sector B

EXPERIMENTAL RESULTS

Figure 2 shows the variations of the quadrupole moment
depending on the field strength of the upstream x steering
magnet for the 0.9-nC electron beam with and without thebeam-position corrections. It is clearly shown that after thecorrections of the beam position, the quadrupole moment
is constant over the measured range of the field strengthof the steering magnet within the estimated errors. Figure
3 shows the variations of the quadrupole moment for the0.9-nC and 8-nC electron beam depending on the rf phaseof the booster klystron after the beam-position correction.
For the 0.9-nC electron beam the beam-width data directly
measured by the screen monitor are also added in order tocompare the BESM data after the beam-profile correction
on the transverse distributions.
The BESM data are related to the SC data by,x2  − y 2  = f X 2 − Y 2 + g,
(5)where X and Y are the transverse beam widths measured
by the screen monitor in HWHM, g is a fitting parameter
caused by the gain imvalance and the geometrical errors of
the eight pickups of the BESM, and the parameter f is thebeam-profile correction factor depending upon the transverse distributions of the electron beam (see Ref. [7]). The

.,26XJquad4

position-corrected Jquad.,132J.

X [mm]

quad0.,1+0.,03

minimum, respectively. The resolution for the energyspread measurement is on the order of 10−3 , depending on
the beam charge. Figure 4 shows the time trend of the measured quadrupole moment and the rf phase of the booster
klystron during six hours, where the BESM data were obtained pulse-by-pulse and the rf phase data were taken every 1.5 minute. The good agreement between these twodata is a clear demonstration of the principal function ofthe BESM.

+22

1,3+4.,0PDφ1+6+2+1+0+/.

/011

20,3//,32Figure 2: Variations of the quadrupole moment depending on the field strength of the horizontal upstream steering
magnet for the 0.9-nC electron beam.

00.
/

result shows that the transverse beam profile is approximately well described not by a Gaussian function, but by
a parabolic function. The BESM data agree well with thecorrected SC data within the estimated errors over the measured region of the rf phase.
0.9-nC electron
QAa_jg`p_rgml
Gaussian distr.
Parabolic distr.

8-nC electron+/+0.

TimeFigure 4: Time trend of the quadrupole moment and the rf
phase of the booster klystron.

30.

6 hours.,3

RF Phase [degree]

Current of X Steering Magnet [A]<x >-<<y2> [mm ]+321/.
0<x2> - <y2> [mm2]<x2> - <y2> [mm2]

/33/.
53

6.

63

7.

73/..

.
/.3RF Phase φ [deg]Figure 3: Variations of the quadrupole moment dependingon the rf phase of the booster klystron.
Assuming that the vertical dispersion ηy is zero at theBESM, the energy spread ∆E of the electron beam canbe estimated from the transverse beam widths along withthe optics parameters (β functions and horizontal dispersion ηx ) and the transverse emittances as follows:x2  − y 2  βx x + (ηx ∆E/E)2 − βy y + g,(6)where g is the same parameter as defined in Eq.(5), and thetransverse emittances, x and y , were measured by wire
scanners at the end of sector B (see Ref. [7]). The resultshows that the obtained energy spreads are 0.150±0.007%
and 0.264±0.004% for the electron beams with charges of
0.9 and 8 nC/bunch at the rf phase of the energy-spread

6CONCLUSIONSThe second-order moments of single-bunch electron
beams were accurately measured by the nondestructive
beam-energy-spread monitor with multi-stripline electrodes at the injector linac.
The result shows thatthe analyzed energy spreads were 0.150±0.007% and0.264±0.004% for electron beams with charges of 0.9 and
8 nC/bunch at the rf phase of the energy-spread minimum,
respectively. The authors have a plan to investigate beamcharacteristics of two beam bunches in the two beam bunch
injection scheme in the nominal operation mode.

7

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pp.167-190.
[3] T. Suwada, LINAC2000, Monterey, California, U.S.A., 2000,pp.199-201.
[4] R. H. Miller, J. E. Clendenin, M. B. James and J. C. Sheppard,
HEAC’83, Fermilab, U.S.A., 1983, pp.602-605.
[5] T. Suwada, Jpn. J. Appl. Phys. 40 (2001) pp.890-897.
[6] J. D. Jackson, Classical Electrodynamics (John Wiley &Sons, New York, 1975) 2nd ed., p.54.
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Beams 6 032801 (2003).