Numerical Design Analysis of Energy-Spread
Monitor Using Multi-Stripline Electrodes
T. Suwada

Abstract—A new energy-spread monitor is under development
in order to control the transverse positions and energy spread ofa single-bunch positron beam with charges of 4 nC. This monitor
is to be installed at a dispersion section of the beam transportline (E = 1.1 GeV) for the positron beam transporting fromthe linac to a damping ring towards the Super KEK B-factory.
The author proposes the use of this new monitor consisting ofmulti-stripline electrodes in order to simultaneously measure not
only the transverse beam positions but also the energy spreadpulse-by-pulse. This report describes in detail the basic designof the energy-spread monitor, its detection sensitivity and its
characteristics depending on the transverse positions and energy
spread of the positron beam based on numerical simulations.

I. I NTRODUCTION
The Super KEK B-factory project (SKEKB) [1] is a nextgeneration B-factory that has been under construction at KEK
after the KEK B-factory project [2] was discontinued in 2010.
The SKEKB is an electron–positron collider with asymmetricenergies, and it comprises 4-GeV positron (LER) and 7-GeV
electron (HER) rings. The target luminosity of the SKEKB
is 40 times the peak luminosity of the KEKB. The SKEKB
is being commissioned based on the urgent need to perform
high-energy flavor particle physics experiments concerning theCP violation in B mesons [3].
The KEKB linac [4] is the injector linac for the SKEKBrings. The injector linac is also being concurrently upgraded
for the above-mentioned purpose [5]–[7]. The requirements of
the injector linac are to deliver low-emittance and high-current
electron and positron beams to the SKEKB rings. A lowemittance and high-current electron beam is to be generated
by using a new photo-cathode RF gun [8], [9]. On the other
hand, the low-emittance and high-current positron beam isto be generated by bombarding a tungsten target with highenergy primary electrons with an energy of 3.5 GeV andelectron charges of 10 nC. The positrons are to be efficiently
captured using a new flux concentrator and large aperture Sband accelerating structures [10], which are to be damped to
the level required for the low-emittance beam through a new
damping ring (DR) [11].
The new DR with a circumference length of 136 m is underconstruction alongside the end section of sector 2 in the linac,
and it is to be connected to the linac-to-DR transport line
(LTR) at the second beam switchyard (SY2) where the beamenergy is 1.1 GeV. Under actual operation, since the energy
spread of the positron beam is very large in comparison with
T. Suwada is with Accelerator Laboratory, High Energy Accelerator Research Organization (KEK) and the Graduate University for Advanced Studies
School of High Energy Accelerator Science, 1-1 Oho, Tsukuba, Ibaraki, 3050801 Japan and (e-mail: tsuyoshi.suwada@kek.jp).

the acceptance of the DR (±1.5%), particularly in its low
energy tail, the energy tail is planned to be cut with a seriesof collimators, and the energy spread is to be compressed
up to ±1.5% from ±5% by an energy compression system(ECS) comprising 41-MV S-band accelerating structures thatare to be installed in the LTR [11]. The positron beams shallbe extracted after 40 ms from the DR. After the positron
beams are delivered from the DR, the bunch length of thepositron beam is to be reduced by an order of magnitude with abunch compression system (BCS) installed at the DR-to-linac
transport line (RTL) in order to ensure that the energy spreadis reduced to as small a value as possible, which is generated
with the RF curvature of the downstream linac accelerating
sections. The positron beams shall subsequently be transported
back through the RTL to the SY2, and again accelerated up
to 4.0 GeV in the linac for injection into the SKEKB LER.
The specifications of the electron and positron injection
beams are summarized in Table I. Here, for purposes ofcomparison, the electron and positron beam specifications forthe previous KEKB are also listed.
TABLE IB EAM SPECIFICATIONS FOR THE INJECTOR LINAC
KEKB(e− /e+ )SKEKB(e− /e+ )Injection energy E [GeV]
Bunch charge Q [nC]
Number of bunches / pulse
Emittance γϵ [µm]Energy spread δ [%]Bunch length l [mm]8.0 / 3.5
1.0 / 1.0 (10∗ )2/2
300 / 2100
0.05 / 0.125
1.3 / 2.6

7.0 / 4.0
5.0 / 4.0 (10∗ )2/2
20 / 92[H] : 7[V ]0.08 / 0.07∗∗
1.3 / 0.7#(∗) for primary electrons(∗∗) with ECS(#) with BCS

Because the SKEKB is a B-factory machine, precise operation of the injector linac is required for minimizing the tuning
time and maximizing its stability in operation. Although stable
control of the beam positions and energies at several sectors
throughout the beam-position and energy-feedback systems are
essential even to the SKEKB operation, the energy spreadsof the injection beams are often enlarged due to the longterm phase drift induced by high-power and booster klystrons.
Thus, beam diagnostic and monitoring tools are required totune the beam-energy spreads; furthermore these tools are also
expected to control the longitudinal wakefields that are mainly
generated at the accelerating structures, particularly at the LTR
in SY2.
The energy-spread monitor (ESM) is a very useful monitoring tool to cater to such requirements. The ESM detects

35

25
5

#2

#3

#4

44

#1
10

1.5

2

6

15

76

22
R2

both the transverse beam positions and the energy spread atlarge dispersion sections by measuring any variations in theelectromagnetic field distribution induced in the multi-striplineelectrodes located in the monitor.
The ESM has been newly designed by numerical simulations based on the electrostatic analysis of a charged beam. It
is expected that with such ESMs, the energy spread could bemade as small as possible under real-time operation within aresolution of the order of 10−4 along with transverse position
control of the order of less than 0.1 mm with the use of suitabledetection electronics.

#6

#5

#7

#8

II. E NERGY- SPREAD MONITOR
5

A. Specifications of positron beam at SY2

25

The positrons are captured with a flux concentrator andaccelerated up to an energy of 120 MeV using large-aperture
S-band accelerating structures. The subsequently positioned
normal S-band accelerating structures accelerate the positrons
up to an energy of 1.1 GeV at SY2 and the positron beam
is injected into the DR through the LTR. The specificationsof the positron beam and the optics parameters at SY2 aresummarized in Table II [11].
TABLE IIS PECIFICATIONS AND OPTICS PARAMETERS FOR THE POSITRON BEAM AT
SY2Horizontal

Verticalβ [m]Dispersion η [m]R56 [m]Emittance ϵ [µm]Beam size σ [mm]
Energy E [GeV]
Energy spread δ [%]Bunch length l [mm]

6.26
0.639
-0.64
0.5
3.8∗

6.08
0
-1.0
0.5
1.7

(∗) average rms width(#) fwhm

1.1
2.3
5.0#

B. Basic design
A new multi-stripline-type ESM is under development inorder to measure the energy spread and beam positions of thepositron beam at a location of the quadrupole magnet (QLF1N)
installed immediately after the first bending magnet of the LTR
at SY2. The ESM is to be installed inside this quadrupole
magnet.
The ESM comprises eight stripline electrodes attached to theinner surface of a racetrack chamber along the beam axis asshown in Fig. 1. The lengths of the inner major and minor axesin the cross section of the chamber are 120 mm and 44 mm,
respectively. Each electrode comprises a 50-Ω parallel striplinewith a longitudinal length of 132.5 mm, width of 10 mm,
and thickness of 1.5 mm. An SMA vacuum feedthrough isconnected to the upstream side of each electrode, while thedownstream end is short-circuited to the chamber ground.
Although the electrodes are arranged at regular distances of
20 mm along the horizontal direction, the electrodes located on

15
35

Fig. 1. Cross-sectional view of the energy-spread monitor. The lengths are
specified in units of mm.

the upper and lower surfaces are asymmetrically configured.
This means that the four electrodes on the upper surface
are shifted from the center position by -5 mm while thoseon the lower surface are shifted from the center position
by 5 mm. By implementing such a nesting structure for theelectrode configuration, the transverse spatial spread of thebeam can be more precisely measured in comparison with theconventionally used symmetric electrode configuration. The
electrode width is selected mainly from the viewpoint of thesignal-to-noise ratio. The cross-sectional area of the chamberis chosen such that the positron beam can be completely passthrough even with a relatively large energy spread within theaperture of the chamber.
III. S IMULATION METHOD
Numerical analysis for the ESM design was carried out bymeans of the charge-simulation method [12], [13]. Here, onlya brief overview of this method is provided to discuss the ESM
analysis in the following section.
The electromagnetic field generated by a relativistic charged
beam inside a vacuum chamber is greatly boosted in thetransverse direction in terms of the beam axis due to Lorentz
contraction. This phenomenon implies that the electromagnetic
coupling of the electrodes to the beam can be treated as a twodimensional electrostatic potential problem when the bunch
structure of the beam in the longitudinal direction is not taken
into account. Thus, the electromagnetic analysis of the ESM
can be simply considered as an electrostatic potential problem
only in the transverse plane.
The charge-simulation method is based on one of the boundary element methods used for analyzing such electrostatic
potential problems. In this method, at certain boundary points,
imaginary and real charges are introduced in order to analyze
a given electrostatic field system. The boundary points arearranged on all the boundary surfaces of the conductors inthe system. An imaginary charge is placed in the immediate
vicinity of each boundary point in a one-to-one manner (seeFig. 2).

where w = 76 mm and h = 44 mm indicate the width of
the inner surface and the height between the top and bottom
sections of the inner surfaces, respectively. The coordinates(Xj ,Yj ) of the imaginary charges are given as:
(
)
j
1
−
(1 ≤ j ≤ n),(4)
Xj = w
2 nh
Yj = ± ± a,(5)2

Geometrical boundary
Imaginary chargebBoundary pointaFig. 2. Arrangement of boundary points on a conductor surface and theircorresponding imaginary charges.

If the length between a given boundary point and thecorresponding imaginary charge is a and the length between
alternating neighboring boundary points is b, we have thefollowing relationa = b × f,(1)

where f denotes a free parameter that is used to determine
the minimal spatial sizes for calculating the electrostatic fields
in the system. The parameter f requires to be determinedby numerical calculations for the electrostatic equipotential
line to stably reproduce the boundary of the conductor withinallowable calculation errors (generally chosen in the range of
0.2–1.5). The electrostatic potentials at the boundary points ofeach conductor and also at any spatial points can be calculated
so as to satisfy the boundary conditions of the system by using
the linear superposition principle of electrostatic fields contributed by all the imaginary charges. If there are real charges
in the system, they also contribute via linear superposition to
generate electrostatic fields along with the imaginary charges.
IV. A PPLICATION TO ESM
A. Segmentation of boundary surfaces
All the boundary surfaces of the chamber and electrodes
are segmented as shown in Fig. 2. The boundary points on
the inner surface of the chamber are arranged as n points
spaced at equal intervals. The outer surface of each electrodeis segmented by l × m points along the horizontal (x) andvertical (y) directions, respectively. The segmentation numbers(l, m, n) are decided based on the convergency study of theelectrostatic-field analysis. The electrostatic fields satisfying
all the boundary conditions in a given system are uniquely
found by the uniqueness theorem in electrostatic boundaryvalue problems.
The rectangular coordinates (xi ,yi ) of the boundary points
on the inner surface of the chamber in both the upper andlower straight sections are given as:
)
(
i
1
−
(1 ≤ i ≤ n),(2)
xi = w2 nhyi = ± ,(3)2

where the sign (±) is selected by the double sign correspondence so that the imaginary charges are adequately locatedjust along the positive and negative directions for the upper(+) and lower (−) surface boundaries, respectively. For thearc section of the chamber, the segmentation length between
the neighboring boundary points is set to be the same as thatdefined for the straight surface boundary.
For the electrodes, a similar segmentation method is applied
as follows:()
1 i
xi = we−(1 ≤ i ≤ l),
(6)
2 l
(
)
1
i
yi = te−(1 ≤ i ≤ m),(7)
2 m
where we = 10 mm and te = 1.5 mm indicate the width
and thickness of the electrode, respectively. The coordinates(Xj , Yj ) of the imaginary charges are similarly given as:()
1 j
Xj = we−(1 ≤ j ≤ l),
(8)
2
l
(
)
1
j
a
Yj = te−±(1 ≤ j ≤ m),(9)
2 m tewhere the sign (±) is again selected by the double sign
correspondence so that the imaginary charges are properly
located just inside the surface boundary.
B. Segmentation of asymmetrically spread beam
The transverse spatial distribution of the beam charges at
SY2 is complicated; however, here, for simplicity, the transverse charge distribution (Qb ) inside the chamber is assumed
to be expressed by asymmetric and symmetric Gaussian functions along the x and y directions, respectively. The transverse
charge distribution is assumed to be given by[](y − y0 )2
Qb (x, y) = Q0 exp −
2σy2
{
[
]
(x − x0 )2
× [1 − θ(x − x0 )]exp −
2
2σL
[
]}
(x − x0 )2+ θ(x − x0 )exp −
,
(10)
2
2σH
where (x0 , y0 ) denotes the peak coordinate position of theasymmetric charge distribution, Q0 denotes the peak charge
at x = x0 and y = y0 , σL (σH ) denotes the one-sigma
horizontal charge width in the region of x < x0 (x > x0 )in the asymmetric Gaussian distribution, and σy denotes theone-sigma vertical charge width in the symmetric Gaussian
distribution. Here, θ(u) denotes a step function defined as{
0 (u < 0),θ(u) =(11)
1 (u > 0).
The parameters of average rms charge width (σ) and asymmetry (A) are defined as
σ

=

A =

σL + σH,2
σL − σH,
σL + σH(12)(13)

for which the converse relations σL = σ(1 + A) and σH =σ(1 − A) are also satisfied. The asymmetric real charges aresegmented by similar segmentation numbers applied to theelectrodes within a region of three-sigma in the asymmetric
Gaussian distribution function.
C. Electrostatic field analysis
The electrostatic potential (Vik ) on the i-th boundary pointof the k-th electrode surface (for simplicity, k = 0 is assigned
to the chamber surface) can be calculated by linearly superb) contributed by all the
posing the potentials (Vijk and Vimkbimaginary (qj ) and real (qm ) charges, respectively, as follows:
Vik

=

∑
j

=

∑

Vijk +

∑

rij

(14)

m

Pij qjk +∑b
Pim qm
,

(15)

m

j

Pij

b
,
Vim

1
= −
ln rij + C,
2πϵ
√ 0
=
(Xj − xi )2 + (Yj − yi )2 ,

(16)
(17)

where Pij and rij denotes the potential coefficient uponassuming a line charge of infinite length and the length
between the i-th boundary point and the j-th imaginary (orreal) charge, respectively, ϵ0 denotes the dielectric constant invacuum, and C denotes the integration constant.
The boundary conditions in this analysis are given as
follows:
1 The electrostatic potential (Vi0 ) on the inner surface ofthe chamber is equal to zero (ground potential),
Vi0 = 0;(18)

2 The electrostatic potential (Vik (k ̸= 0)) on the surface of
the k-th electrode is equal to zero (short-circuited),
Vik = 0;

j

Qe

=

∑

Qke , Qke ==∑qjk (k ̸= 0),

(22)

j

k

Qb

∑

b
qm
,

(23)

m

where Qke (k ̸= 0) denotes the summation of all the imaginary
charges (qjk ) on the k-th electrode. Based on these threeboundary conditions, the imaginary charges on each electrodecan be calculated by solving the simultaneous linear equations (eq. (15)) obeying the boundary conditions (eqs. (18)(20)).
The imaginary charge (Qke ) induced on the k-th electrodeis proportional to the pick-up voltage of the electrode. Thus,
the electrostatic characteristics and sensitivity of the ESM depending on the spacial charge width and transverse positions of
the beam can be numerically simulated based on electrostatic
analysis within allowable calculation errors.
V. S IMULATION RESULTS
A. Convergency study
In order to ensure accurate simulation results, we performed
a convergency study by positioning a point charge at thecenter position of the ESM by changing the segmentation
numbers (l, m, n) for the boundary points and imaginary
charges induced on the chamber and electrode surfaces.
The segmentation numbers were simulated based on a seriesof refined computational boundary points until a steady stateof the induced charges was obtained. The typical results
are shown in Fig. 3. Fig. 3 (a) shows the variation in thesummation of all the imaginary charges (Qc ) induced on thechamber surface and Fig. 3 (b) shows the summation of theimaginary charges (Qe ) induced on all the electrode surfaces
as a function of b and the segmentation parameter f .
The convergency values are obtained to be approximately
0.4% and 1.4% for Qe and Qc at b = 0.5 mm, respectively, at segmentation numbers (l, m, n) = (6, 20, 76). These
convergence values are sufficiently small to obtain sufficient
resolution for simulating the imaginary charges induced on theelectrodes within a level of 0.4% upon taking into account theallowable computation time in simulation calculations.
The total number of segmentation parameters including thesegmentation of the spread beam charges has been fixed to be
675 in order to be efficiently solved to obtain precise valuesof the electrostatic physical parameters in the ESM analysis.

(19)

3 The summation of all the imaginary charges induced on
the chamber surface (Qc ) and on all the electrodes (Qe ),and all the real charges (Qb ) by the beam is conserved
to be zero as per the charge conservation law,
Qc + Qe + Qb = 0.

Here, the summation relations for the segmented charges aredefined as∑Qc =qj0 (k = 0),
(21)

(20)

B. Beam-position analysis for asymmetrically spread beam
Based on the beam dynamics in accelerator physics [14],the horizontal beam size (σx ) at a section with a horizontal
dispersion of ηx is represented as√2βx ϵx + (ηx δ) ,
(24)
σx =

Qy+
e
Qy−
e
Σ

≡
≡
≡

∆x

≡

∆y

≡

4
∑

Qke ,

(27)

Qke ,

(28)

Qke ,

(29)

k=1
x−
Qx+
e − Qe ,y−Qy+
e − Qe ,

(30)

k=1
8
∑
k=5
8
∑

(31)

for which the allocation of the electrode number is defined
as shown in Fig. 1. The beam positions are related to theparameters ∆x /Σ, and ∆y /Σ and the energy spread δ. The
horizontal (vertical) sensitivity for the beam position, Sx (Sy ),is defined at the center position by differentiating ∆x /Σ
(∆y /Σ) with respect to x (y) as a function of δ as follows:
(
)
d ∆x
.
(32)
Sx (δ) =dx ΣThe vertical sensitivity is defined by a similar formula. It
should be noted that the position sensitivities of the ESM
strongly depend on the energy spread.
The results based on a two-dimensional ∆/Σ analysis areshown in Fig. 4. Figs. 4 (a) and (b) show the variations in

Fig. 3. Variations in convergence on the imaginary charge summations, (a)Qc and (b) Qe as functions of b and the segmentation parameter f .

where βx , ϵx and δ denote the horizontal β-function, geometrical emittance, and energy spread at the dispersion section,
respectively. The vertical beam size is also similarly described.
It can be deduced that the beam size increases depending on
the energy spread along with increase in the emittance while
the intrinsic beam size is determined by the emittance valuethat depends on the beam optics at the dispersion section.
Since the dispersion functions are ηx = 0.639 m and ηy = 0 m
along the horizontal and vertical directions at the location of
the QLF1N, respectively, the vertical beam size is determined
only by the intrinsic emittance value. The transverse positionsof the beam with a given energy spread can be obtainedby analyzing the electrostatic field distribution generated byspatially spread charges in the transverse plane at the ESM.
Here, it is useful to introduce algebraic parameters related
to the signal intensities of the electrodes. These parameters
are defined as

Qx+
e
Qx−
e

≡
≡

4
∑
k=3
2
∑
k=1

Qke +
Qke +

8
∑
k=7
6
∑
k=5

Qke ,

(25)

Qke ,

(26)

Fig. 4. Variations in (a) ∆x /Σ and (b) ∆y /Σ depending on x (y = 0), andy (x = 0) and δ.

∆x /Σ and ∆y /Σ as functions of x (y = 0) and y (x = 0),
respectively, and δ. Since the nominal energy spread of thepositron beam is δ = 2.3% at SY2, the horizontal (vertical)
sensitivity is calculated to be Sx = 1.58 × 10−2 /mm (Sy =1.97 × 10−3 /mm) at the center position. The result indicatesthat the horizontal sensitivity is greater than the vertical one by
an order. This arises due to the difference in the electrostatic
field distributions generated in the racetrack-type ESM along
the horizontal and vertical axes. It can be also seen that when
the charge distribution of the beam is asymmetric with anenergy spread, ∆x /Σ ̸= 0 at x = 0 and ∆y /Σ ̸= 0 at y
= 0 while only for a symmetric charge distribution (or point
charge) ∆x /Σ = 0 and ∆y /Σ = 0 at the center position aresatisfied. This is because the ESM can measure the intensity
centroid of the spatial charge distribution, and the offsets inthe ∆/Σ curve result from the asymmetrically spread charges
depending on the energy spread. The results suggest that offset
calibrations should be carefully performed not only in the ESM
but also in the detection electronics with test pulses. Thus, it
should be noted that the beam positions can be calculated on
the basis of both the ∆/Σ analysis and energy-spread analysis.
If the energy spread is known, the beam positions can begenerally analyzed on the basis of a three-dimensional ∆/Σ
analysis by using polynomial functions as follows:
(
)i (
)j
k ∑
k
∑
∆x
∆y
x =
aij
,
(33)
Σ
Σ
i=0 j=0
)i (
)j
(
k ∑
k
∑
∆y
∆x
y =
,
(34)
bij
Σ
Σ
i=0 j=0
where aij and bij denote the calibration coefficients that can beobtained by a beam-based measurement. These formulas yieldcalibration curves with a higher-order polynomial (generallyk ≥ 3) in the beam position measurement. A typical result
for the horizontal position based on a three-dimensional ∆/Σ
analysis with δ = 2.3% is shown in Fig. 5. The vertical position∆x/Σ

x [mm]∆y/Σ
Fig. 5. Variations in the horizontal position depending on ∆x /Σ and ∆y /Σ(δ = 2.3%). The solid points indicate calculated data points.

can be similarly analyzed.
C. Energy-spread analysis for asymmetrically spread beam
The energy spread can be analyzed by measuring thehorizontal spatial spread of the induced charge distribution
because the energy spread is related to the spatial spread, as
seen from eq. (24). Fig. 6 shows a typical example of thehorizontal spatial spread of the induced charges for a positron
beam with a nominal energy spread of δ = 2.3% at y = 0.
The curve is a fitting of the calculated data of the charge
distribution induced on the eight electrodes assuming that the
charge distribution is along the horizontal direction with anasymmetric Gaussian function as described by eq. (10) whilethe vertical spatial spread is fitted with a Gaussian function. It

Fig. 6. Horizontal imaginary charge distribution induced on the electrodes
along with the beam charge distribution with δ = 2.3% at y = 0. The solid line
(black) denotes the fitting curve of the horizontal induced charge distribution
with an asymmetric Gaussian function. The solid curve (red) indicates thespatial charge distribution of the beam with an asymmetric Gaussian function
along the horizontal direction.

can be clearly seen that the peak position of the fitting curve isshifted along the negative direction in the horizontal axis dueto the asymmetric structure of the induced charge distribution
while the peak position of the beam charge distribution is set
to the center position.
Fig. 7 shows the variations in the peak position (XC ) of
the fitting curve as a function of the energy spread where an
asymmetric Gaussian function for the horizontal beam charge
distribution with a fixed asymmetry (A = 0.56) is assumed,
and the peak position of the charge distribution is fixed tothe center position. The dependence of the curve in termsof the energy spread becomes nonlinear with increase in theenergy spread. This is because the electrostatic fields inducedby the beam charges exist considerably outside the region of
the electrodes in the negative direction of the horizontal axis.
The differential of the fitted peak position with respect to δ at
δ = 2.3% isdXCdδ= −2.7 mm/%.

(35)

Fig. 8 shows the variations in the width of the fitting
curve on the induced charge distribution depending on theenergy spread. It can be deduced that the curve becomes
nonlinear with decrease in the energy spread. This is because
the width varies approximately linearly in the larger energy
spread region where the spatial charge spread is dominant
over the energy spread in comparison with the intrinsic charge
spread. At δ = 2.3%, the differential of the width with respectFig. 7. Variations in the peak position of the fitting curve on the induced
charge distribution depending on the energy spread. The solid line is a guideto the eye only.

Fig. 9. Variations in (a) Sx and (b) ∆x /Σ depending on the energy spread.
Both the solid lines indicate fitting curves with a fourth-order polynomial
function.
Fig. 8. Variations in the width of the fitting curve on the induced charge
distribution depending on the energy spread. The solid line is a guide to theeye only.

to δ isd(2σ)= 2.5 mm/%.
(36)dδ
Figs. 9 (a) and (b) show the variations in (a) the horizontal
position sensitivity and (b) ∆x /Σ depending on the energy
spread. Both Sx and ∆x /Σ monotonically reduce with increase in the energy spread. At δ = 2.3%, Sx and ∆x /Σ arecalculated to beSx (δ) =∆x /Σ(δ) =0.016/mm,(37)−0.25.

(38)

These values also yield the corresponding calibration coefficients to estimate the energy spread.
D. Expected resolution for position and energy-spread measurements
The position resolution (σx ) of the ESM can be approximately obtained by modifying eq. (32) as
)
(
∆x
−1
,
(39)
σx ≈ dx = Sx dΣwhere d(∆x /Σ) is related to the resolution of the detection
electronics. This parameter can be estimated by the numberof bits (nb or n10 in the decimal system) of an analog-todigital circuit (ADC) embedded in the detection electronics.
Here, for simplicity, assuming that the dynamic range of thedetection electronics is set to the induced charge intensity at
maximum (Qm ) at a certain channel, the detection resolution
can be determined as 1/n10 . Furthermore, it is assumed
that the detection resolution is identical for all the detection
channels without taking into account any noise. Thus, basedon standard error analysis, the detection resolution of ∆x /Σ
can be described as
√∑
8
(
)
k
2
∆x
k=1 (dQe /Qm )
d
≈
,
∑8
k
Σ
k=1 Qe /Qm
√
8
≈
.
(40)
∑8
n10 k=1 Qke /Qm
The position resolution can be calculated by combining
eqs. (39) and (40) as a function of the energy spread.
The resolution of the energy spread (σδ ) can be approximately written as
)(
)−1
(
∆x
dg(δ)
,
(41)
σδ ≈ dδ = dΣdδwhere g(δ) denotes the fitting function in the ∆x /Σ curvewith a fourth-order polynomial, as shown in Fig. 9 (b). The
resolution of the energy spread can be calculated by combining
eqs. (40) and (41) as functions of the energy spread.

have been successfully carried out by numerical simulations
based on electrostatic-field analysis. The results show that
detection resolutions of σx ≃ 80 µm (traverse position) andσδ ≃ 2 × 10−4 (energy spread) can be attained at the nominal
energy spread with a nine-bit ADC embedded in the detection
electronics. The new ESM can be used as a beam monitoring
tool in the pulse-by-pulse beam-position and energy-spreadmeasurements at large dispersion sections.
R EFERENCES

Fig. 10. Variations in the expected resolutions of (a) the position and (b)the energy spread as functions of the energy-spread value and the number ofbits. The solid line is a guide to the eye only.

Figs. 10 (a) and (b) show the variations in the horizontal
position and energy-spread resolution as functions of theenergy-spread value and the number of bits, respectively.
The typical results show that the resolutions of the positionand energy spread are expected to be σx ≃ 80 µm andσδ ≃ 2 × 10−4 at a nominal energy spread of δ =2.3% for an ADC with a nine-bit resolution embedded in thedetection electronics. It should be noted that the transverse
spatial distribution of the beam charges at SY2 is complicated;
however, similar analyses can be applicable without assuming
any asymmetric and symmetric Gaussian functions for the
beam charge distribution in the transverse direction because
all the physical parameters discussed here can be describedby using measurable values.
VI. C ONCLUSIONSThe basic design and systematic investigations of the detection sensitivity and characteristics of a new energy-spreadmonitor, which can simultaneously measure both the transverse positions and energy spread of the positron beam at SY2,

[1] Y. Ohnishi, et al.. Theor. Exp. Phys. (2013) 03A011.
[2] T. Abe, et al., Prog. Theor. Exp. Phys. (2013) 03A001.
[3] T. Abe, et al., KEK Report 2010-1, edited by Z. Doležal and S. Uno.
[4] M. Akemoto, et al., Prog. Theor. Exp. Phys. (2013) 03A002.
[5] T. Kamitani, M.Akemoto, D. Arakawa, M. Ikeda, A. Enomoto, S. Ohsawa,Y. Ogawa, K. Kakihara, H. Katagiri, E. Kadokura, M. Kurashina,
M. Satoh, T. Shidara, A. Shirakawa, T. Sugimura, T. Suwada, T.
Takenaka, K. Nakao, H. Nakajima, T. Higo, S. Fukuda, K. Furukawa,
H. Honma, H. Matsushita, T. Miura, K. Mikawa, S. Matsumoto, T.
Matsumoto, S. Michizono, Y. Yano, K. Yokoyama, M. Yoshida, N.
Iida, M. Kikuchi, M. Tawada, T. Mimashi, Y. Kojima, K. Nakanishi, K.
Hosoyama, T. Sanami, Proceedings of the XXVth International Linac
Conference (LINAC10), Tsukuba, Japan, 2010, pp. 70-72.
[6] T. Higo, M. Akemoto, D. Arakawa, Y. Arakida, A. Enomoto, S.
Fukuda, K. Furukawa, Y. Higashi, H. Honma, N. Iida, M. Ikeda, E.
Kadokura, K. Kakihara, T. Kamitani, H. Katagiri, M. Kurashina, H.
Matsushita, S. Matsumoto, T. Matsumoto, S. Michizono, K. Mikawa,T. Miura, F. Miyahara, T. Mori, H. Nakajima, K. Nakao, T. Natsui, S.
Ohsawa, Y. Ogawa, M. Satoh, T. Shidara, A. Shirakawa, T. Suwada,
H. Sugimoto, T. Takatomi, T. Takenaka, Y. Yano, K. Yokoyama, M.
Yoshida, L. Zang, and X. Zhou (KEK, Tsukuba), D. Satoh (TIT,
Tokyo), Proceedings of the 3rd International Particle Accelerator Conference (IPAC12), New Orleans, U.S.A., 2012, pp.1819-1821.
[7] K. Furukawa, M. Akemoto, D. Arakawa, Y. Arakida, A. Enomoto, S.
Fukuda, H. Honma, R. Ichimiya, N. Iida, M. Ikeda, E. Kadokura, K.
Kakihara, T. Kamitani, H. Katagiri, M. Kurashina, S. Matsumoto, T.
Matsumoto, H. Matsushita, S. Michizono, K. Mikawa, T. Miura, F.
Miyahara, T. Mori, H. Nakajima, K. Nakao, T. Natsui, Y. Ogawa, S.
Ohsawa, F. Qiu, M. Satoh, T. Shidara, A. Shirakawa, H. Sugimoto, T.
Suwada, T. Takatomi, T. Takenaka, M. Tanaka, Y. Yano, K. Yokoyama,
M. Yoshida, L. Zang, X. Zhou (KEK, Tsukuba), D. Satoh (TIT, Tokyo),
Proceedings of the 3rd International Particle Accelerator Conference(IPAC13), Shanghai, China, 2013, pp. 1583-1585.
[8] T. Natsui, M. Yoshida, X. Zhou, and Y. Ogawa, Proceedings of the
3rd International Particle Accelerator Conference (IPAC13), Shanghai,
China, 2013, pp. 1117-1119.
[9] X.Zhou, T. Natsui, M. Yoshida, and Y. Ogawa, Proceedings of the
3rd International Particle Accelerator Conference (IPAC13), Shanghai,
China, 2013, pp. 2965-2967.
[10] T. Kamitani, M. Akemoto, Y. Arakida, D. Arakawa, A. Enomoto,S. Fukuda, K. Furukawa, Y. Higashi, T. Higo, H. Honma, N. Iida,
M. Ikeda, E. Kadokura, K. Kakihara, H. Katagiri, M. Kurashina, H.
Matsushita, S. Matsumoto, T. Matsumoto, S. Michizono, K. Mikawa,T. Miura, F. Miyahara, T. Mori, H. Nakajima, K. Nakao, T. Natsui, S.
Ohsawa, Y. Ogawa, M. Satoh, T. Shidara, A. Shirakawa, T. Suwada,
H. Sugimoto, T. Takatomi, T. Takenaka, Y. Yano, K. Yokoyama,
M. Yoshida, L. Zang, X. Zhou (KEK, Tsukuba), D. Satoh (TIT,
Tokyo), Proceedings of the XXVIth International Linac Conference(LINAC12), Tel-Aviv, Israel, 2012, pp. 177-179.
[11] N. Iida, H. Ikeda, T. Kamitani, M. Kikuchi, and K. Oide, and D. Zhou,
Proceedings of the 2nd International Particle Accelerator Conference(IPAC11), San Sebastian, Spain, 2011, pp. 532-534.
[12] H. Singer, H. Steinbigler, and P. Weiss, IEEE Trans. on Power
Apparatus and Systems, Vol. PAS-93, No. 5, pp. 1660-1668, 1974.
[13] N. H. Malik, IEEE Trans. on Electrical Insulation, Vol. 24, No. 1,
pp. 3-20, 1989.
[14] A. W. Chao and M. Tigner (eds.), Handbook of Accelerator Physics
and Engineering (World Scientific, Singapore, 1999), p. 559.