Chapter 10
Beam Transport Lines andInjection System
10.1

Beam Transport Lines

The beam parameters of the beam transport lines for SuperKEKB and KEKB
are shown in Table 10.1. The most significant diﬀerence from the KEKB
is that the energy of the positron line increases to 4 GeV from 3.5 GeV.
Almost all components of the beam transfer lines, which convey electronsand positrons to the HER and LER of KEKB, are planned to be reused forthe corresponding beam lines in the SuperKEKB . Several modifications in
the positron line are required in accordance with the energy change:• Reconstruction of the ECS layout in the SY3.
• The BH2P-type and BH3P-type bends are modified in the air gap toincrease the magnetic field without changing current.
• Maximum current of the power supplies is increased for bends B3P,
BH1CP, BH1P, and BV2P.
For both lines sextupole magnets are installed in the dispersive section inorder to correct high-order dispersion, Because of low emittance it emerges
370

Table 10.1: Beam parameters in comparison with the KEKBSuperKEKB
ee+
Beam energy
7†1
Emittance
1.46 / 4.77†2
Energy spread
0.1
Charge/bunch4
No. of bunch/pulse
Rep. rate†1 at the end of Linac.

KEKB
ee+

4
8
12.8
23
0.125 0.125
4
1
2
50

3.5
200
0.125
0.5

unit

GeV
nm
%
nC
Hz

†2 at the end of the beam line.

as one of major sources of the emittance degradation.

10.1.1

Changes in the layout of ECS in the SY3

The ECS system for the positron beam is composed of a chicane and two
S-band accelerating structures. Since the design energy is changed from 3.5
GeV to 4.0 GeV magnetic field of bends that are used to make the chicane
orbit also has to be increased by a ratio of 4/3.5=1.143 in order to obtain thesame R56 component. Because the first bend BC1P.1, which has a very widepoles, is not accessible with a crane it is diﬃcult as well as expensive to replacewith a new magnet. We have adopted another option: we use the BC1P withthe magnetic field unchanged while the other four bends are replaced withnew magnets. The last bend BC1P.2 is also reused for symmetry. Figure 10.1
shows layout of ECS in the SY3. Accelerating structures ACC.1 and ACC.2
are moved to downstream while preserving the position of B1P. Specificationsof ECS bends are shown in the Table 10.2. Since the energy of electrons isdecreased from 8 GeV to 7 GeV the bend angle of BC1P.1 for electrons getlarger. To preserve the positions of magnets at downstream of B0E theincreased angle is compensated by exciting BHD0.1, which has been set zero371

in the KEKB and energized only in the operation of the beam-dump mode.

ACC.1

QLF1P.L
QLD1P.L

BC1P.2

BC2P.2

BC3P.2

BC3P.1

BC2P.1Figure 10.1: Layout of the ECS in the SY3. (a) for the old KEKB, (b) for
the SuperKEKB

10.1.2

Changes of the magnet system in the positronline

Magnets of the positron line are classified into four categories according to
its degree of modification in application to the upgraded beam line: (A)372

QXF2E.M

QXF2P.AQXD2P.A(b) SuperKEKB

QXD2E.M

QXF1E.M

BV1E.4

QXF1P.AQXD1P.A
BV1E.3
BHD0.3QXD1E.M

QLF2P.K

B1P
B1E.1
BHD0.2

QX5E.S

QX4E.SQLD2P.K

ACC.2

QLD2P.K
BV1E.2
ACC.2

ACC.1

QLF1P.L
QLD1P.L
BV1E.1

QX3E.S

BC2P.2

BC1P.2B0E

QX2E.M

QX1E.M

BC3P.2

BC3P.1
BHD0.1

BC2P.1

BC1P.1(a) KEKBTable 10.2: Specifications of ECS bends

Bend angle
Magnetic field
Air gap
Pole widthCore length

BC1P BC2P

BC3P

unit

.1648
1.427
25
320
1.0

-.3764
1.510
20
150
3.210

rad
T
mm
mm
m

.2116
1.501
20
150
1.771

both the aperture and the maximum current of the power supply must be
upgraded, (B) the aperture must be modified while the power supply can beused without modification, (C) the aperture need not be changed but thepower supply must be upgraded, (D) usable without any changes. No magnet, fortunately, falls to A. All quadrupoles, steering magnets, and roughly
half of the bends go to category D, while rest of bends falls under B or C:(B) Seven BH2P-type bends and eleven BH3P-type bends used in the Arc-2
and Arc-3, respectively, are modified in there aperture from 40 mm
to 34 mm by inserting a flat silicon-steel plate with thickness of 6
mm between the pole-block and the return yoke. A simulation of themagnetic field shows no significant degradation in the field profile.
(C) Maximum current of the power supplies for bends B3P, BH1CP, BH1P,
and BV2P is increased. Maximum voltage of these power supplies neednot be upgraded because the regulator voltage has enough margin.

10.1.3

Stability of power supplies

Since the beam emittance from the Linac is very small, about 4 % of thatin KEKB, stability of power supplies, which is expected to be reused, might
be a concern. If deviations from the design values (errors) is static, they canbe corrected with ordinary orbit/optics correction technique using orbit/wire373

measurements. For an error that varies with higher frequency, it will produce
an orbit jitter or a jitter in beta-functions at the injection point, dependingon whether the error be dipole or quadrupole.
First, in the quadrupole case, jitter in beta-functions generates larger
eﬀective-emittance. It can be quantified by so called Beta mismatch Bm ,
√ )2
( √
(
)
β
β∗
1 β∗
β
1
Bm =
+ ∗ +
α∗
−
α
,
(10.1)2 ββ
2β∗β
where, α∗ and β ∗ are changed values of α and β due to quadrupole errors.
The beta-mismatch due to a single quadrupole error ∆kj in the beam line
is calculated from Eq. (10.1), assuming the thin lens model, as ∆Bm =1 + (βj ∆kj )2 /2, where βj is the beta-function at the error source. Taking
summation over all the quadrupoles we obtain the beta-mismatch at the endof the beam line,
∏[
∑
]
Bm =
1 + (βj ∆kj )2 /2 ≃ 1 +(βj ∆kj )2 /2 ,(10.2)jj

where we assumed no correlation exists between errors. In correlated casethe beta-mismatch would be less than Eq. (10.2). The second term can be∑∑
estimated using j (βj kj )2 /2 = 2405, j (βj kj )2 /2 = 2770 for horizontal andvertical plane of the positron line, respectively. Assuming ∆kj /kj = 5 × 10−4
the eﬀective emittance increases by a negligible amount, ∆ϵ/ϵ = Bm − 1 =6 × 10−4 , and 6.9 × 10−4 . The similar estimation holds for the electron line.
Secondly we investigate the eﬀect of a random dipole kick on the eﬀective
emittance due to a strength error of power supplies for bending magnets.
The beam ellipses overlaid in the phase space, with its centroid randomly
shifted by pulse to pulse, would have larger emittance compared to that of asingle bunch. Denoting the centroid shift (X, X ′ ), sizes of the overlaid beam
can be expressed by⟨⟩ ⟨ ⟩ ⟨ ⟩⟨ ⟩β̂ϵ̂ ≡ (x + X)2 = x2 + X 2 = βϵ + X 2 ,(10.3)−α̂ϵ̂ ≡ ⟨(x + X)(x′ + X ′ )⟩ = ⟨xx′ ⟩ + ⟨XX ′ ⟩ = −αϵ + ⟨XX ′ ⟩ ,(10.4)⟨ ⟩⟩ ⟨ ⟩ ⟨ ⟩⟨γ̂ϵ̂ ≡ (x′ + X ′ )2 = x′2 + X ′2 = γϵ + X ′2 .
(10.5)
374

From Eqs. (10.3)-(10.5) the eﬀective emittance is written as⟨ ⟩⟨ ⟩ϵˆ2 = (βϵ + X 2 )(γϵ + X ′2 ) − (−αϵ + ⟨XX ′ ⟩)2⟨ ⟩⟨ ⟩( ⟨ ⟩⟨ ⟩)2= ϵ2 + X 2 X ′2 − ⟨XX ′ ⟩ + β X ′2 + 2α ⟨XX ′ ⟩ + γ X 2 (10.6)
ϵ.
The centroid shift is expressed by a summation of shift due to each error-kick
θi :∑(10.7)
X=
M12 (i)θi ,
i

′

X =

∑

M22 (i)θi ,(10.8)iwhere M (i) is a transfer matrix from the error source to the observation
point. Given the transfer matrix we can estimate the eﬀective emittanceunder appropriate assumptions on the error kicks. For the electron line, forexample, it is evaluated asϵ̂2h = ϵ2h + 117.5 δ 4 + 28.5 ϵh δ 2 ,(10.9)

ϵ̂2v = ϵ2v − 4 × 10−7 δ 4 + 0.12 ϵv δ 2 ,(10.10)where δ is the current jitter of power supplies. We have assumed ⟨θi θj ⟩ =Θi Θj δ 2 if i and j belongs to the common power supply, otherwise ⟨θi θj ⟩ = 0,
where Θi and Θj are the design bend-angle of the magnet. In the verticalplane the emittance is insensitive to the current jitter of the power supplies
because in almost cases the optics is designed such that the dispersion function is closed at the end of a region subtended by vertical bends that areconnected to a common power-supply. Using the measured current-ripple ofδ = 4.5 ppm , whose dominant frequency is 300 Hz, and ϵh = 1.46 nm, weestimate that ϵ̂/ϵ = 1.2. Taking into account of an eﬀect of eddy current in
the vacuum chamber, which is made of aluminum with thickness of 3 mm,
magnetic field in the chamber will be suppressed by an order of magnitude.
Thus the eﬀect of the current-ripple on the emittance is expected to be negligibly small. The same conclusion holds for the power supplies of the positron
line.
375

10.1.4

Emittance growth due to synchrotron radiation

The quantum nature of synchrotron radiation induces a transverse emittance.
The beam transport lines to the main rings comprise of four major arcs andthey have many dipole magnets with the bend-angle surpassing 5 radian in
total, which was a consequence of complicated geometry bypassing the PFAR[2]. Since the emittance growth scales as E 5 /ρ3 and and linearly depends
on the total bend angle the higher energy (electron) line is expected to havelarger eﬀects. The emittance including the quantum excitation is expressedas the same form as the Eq. (10.6), where X and X ′ are interpreted as thequantum excitation due to synchrotron radiation at bends. Figure 10.2
shows a simulation results of the horizontal emittance at the end of theelectron line as a function of the input emittance, which was obtained with aparticle tracking using SAD. The emittance fits well the following equation,√
ϵ20 + ϵp ϵ0 + ϵ2q(10.11)ϵ =with ϵq = 2.98 nm,
ϵp = 8.03 nm,
where, ϵ0 is the input emittance. For the design emittance of ϵ0 = 1.46 nm,
the actual emittance at the end of beam line increases to 4.77 nm. The
beam size at the injection septum is 0.31 mm, assuming βx = 20 m. The
required injection aperture is still dominated by the septum width of 2.5 mm.
Although the emittance growth due to synchrotron radiation is very big, it
plays only a minor role on the injection aperture itself. For the vertical plane,
the eﬀect of synchrotron radiation on emittance is negligible: ϵq = 0.0073 nm,
and ϵp = 0.022 nm.

10.1.5

Instrumentation

Wire scanners
The wire scanners have been used for the beam size measurement in the
beam transport lines from Linac to to the KEKB main rings [1]. The diameter
376

Emittance ✏ (nm)

Input emittance ✏0 (nm)Figure 10.2: Simulation results of the horizontal emittance at the end of
the electron line including a synchrotron radiation as a function of inputemittance.
of the wires has been 200 µm, which was suﬃciently small compared to theinjected beam. In the SuperKEKB, however, the size of the injected beam
will be comparable to the wire diameter. In such cases the beam size cannot
be measured correctly without corrections of the wire-size eﬀect. Therefore,
the wire with a diameter of 60 µm will be used.

10.2

Injection System

In the KEKB [1], the beam injection had been performed with the betatron
injection scheme, which inevitably induces betatron oscillation of the injected
beam[2]. Since the dynamic aperture of the SuperKEKB is considerably narrower than the KEKB, the injection amplitude has to be much smaller toallow the injected beam stably circulate within the dynamic aperture. It has
been pointed out that a transient beam-blowup might occur during injection because of the beam-beam eﬀect[3]. Since the beta-function is strongly
377

squeezed in the vertical plane at the interaction point, a particle that has afinite vertical amplitude experiences a very strong beam-beam eﬀect during
the horizontal oscillation, which is specific in the betatron injection in the
nano-beam scheme without using club-waist that has been adopted in the
SuperKEKB. To cure the beam loss due to the transient blowup, which depends on the dynamic aperture, we adopt the so called synchrotron injection
scheme as a backup option for the injection method. In the synchrotron
injection, incoming beam that has an energy oﬀset is injected on the closed
orbit with the corresponding energy-oﬀset in the ring, thus inducing no betatron oscillation but in turn the oscillation in the synchrotron phase space.
Denoting ∆x the distance between the stored beam and the incoming beam,
ηR the dispersion function at the injection point of the ring, and δ the energy
oﬀset, an equation∆x = ηR δ
has to be satisfied. For the HER we found a design that satisfies above equation. For the LER, however, it is diﬃcult to create the dispersion function
at the injection point because of a requirement that the dispersion function at the RF cavities, which are located nearby the injection region, must
disappear.
In the SuperKEKB project the old KEKB systems are to be reused as
many as possible. Regarding the injection system, half of injection septum
magnets that are located near to the main rings are totally reconstructed tomake the septum width as thin as possible, thereby reducing the injection
amplitude as small as possible. New septum magnets have been designed
and constructed based on the careful study of the injection orbit.

10.2.1

Injection Orbit

For the betatron injection, the horizontal dispersion of the ring around theinjection region is set to be ηR = 0; on the other hand, for the synchrotron
injection, larger |ηR | eases demand for the energy-spread of the incoming378

beam. The beam separation ∆x between the injected beam and the stored
beam is the sum of the eﬀective septum width ws and the beam size of thetwo beams:(10.12)∆x = ws + nR σR + ni σi ,where nR and ni are eﬀective beam sizes of the stored and the injected beam,
respectively, in unit of their rms sizes, σR and σi . Hereafter we employ nR = 3
and ni = 2.5.
Betatron Injection scheme
Optical parameters at the injection point and the emittance of the ring,as well as the injected beam are given in Table 10.3. The required injection
Table 10.3: Beam parameters for the betatron injection.
Parameter HER
αR
βR
εR
εi
∆x
∆x′

LER

unit

-7.93 -13.36
100
100
m
4.6
3.2 nm4.77 12.78 nm
7.8
8.4 mm-0.62-1.1 mrad

aperture of the ring axR as a function of the beta-function, βR , of the injectedbeam is shown in Figure 10.3a. The eﬀective thickness of the septum has been
assumed to be 2.5 mm. Assuming the beta-function of the ring βR = 100 m,
for example, an optimum value of the beta-function of the injected beam thatmakes the injection aperture minimum is found to be βR = 15.3 m and 28.7 m
for HER and LER, respectively. Though the larger βR than 100 m gives thesmaller injection aperture, its gain is not so significant considering an adverse
eﬀect of the larger chromaticity and the necessary larger physical-aperture.
379

(a) HER(b) LER

Figure 10.3: Injection aperture in the case of betatron injection.
We have adopted βR = 100 m as the design value. The orbit around theinjection point is shown in Figure 10.4. Passing through a long slit openedat the one side the ring chamber, the injected beam enters the ring. The
beam position and angle at the injection point, which is defined as the exitof the septum magnet, is given in Table 10.3, where ∆x and ∆x′ are relative
position and angle of the injected beam to the stored beam at the injection
point.

(a) HER(b) LER

Figure 10.4: Orbits of the injected beam for the betatron injection.

380

Synchrotron Injection scheme
The condition that the incoming beam is injected onto the closed orbit withthe energy oﬀset δi is given by= ∆x(10.13)

η ′ δi = ∆x′ ,(10.14)η δiwhere η and η ′ are dispersion and its slope in the ring at the injection point,
while ∆x and ∆x′ are relative position and angle of the injected beam to thestored beam, i.e., closed orbit bump by injection kickers. Above conditions
ensures that no coherent betatron-motion is induced. However, an incoherent
betatron oscillation is induced if beta functions of the injected beam does notmatch that of the ring. A condition to minimize the beta-mismatch isβi = βR ,αi = αR .

(10.15)

From Eqs. (10.12)(10.13)(10.15), the energy oﬀset of injected beams required for the synchrotron injections is given by()√√
δi = η −1 ws + nR εR βR + (ησε )2 + ni εi βR ,(10.16)
where, we assumed dispersion of the injected beam disappears at the injection
point: ηi = 0. Figure 10.5 shows the energy-oﬀset as a function of thedispersion, where the curves correspond to diﬀerent value of beta functions
at the injection point. Here we have assumed ws = 2.5 mm, εR = 4.6 nm,
and εi = 4.77 nm. The maximum energy deviation of the injected beam, i.e.,required energy-acceptance, is given by
εmax = δi + nε σεi ,(10.17)

where, σεi is the energy spread of the injected beam. Hereafter we employ
nε = 2.5. Figure 10.6 shows the εmax as a function of η for the case ofβR = 20 m. The required energy-acceptance is strongly dependent on theenergy-spread of the injected beam. For the assumed energy-acceptance of381

i (%)R :⌘ (m)Figure 10.5: Dependence of the energy-oﬀset on the dispersion at the injection point.
0.65 m, which is the design value of the main rings, parameters (εmax , |η|) of(0.1 %, 1.5 m) or (0.125 %, 2 m), for example, are required.
The beam parameters for the synchrotron injection scheme are shownin Table 10.4. Beam orbit in the synchrotron injection scheme is shown in
Fig. 10.7. Because the eﬀective septum thickness of the septum magnets used
for the KEKB is ws = 4.0 mm, it is unusable for the SuperKEKB injection
system for both of LER and HER. It is thus necessary to reconstruct septum
magnets nearest to the ring: one septum magnet in LER and two septa in
HER.

10.2.2

Design of Septum Magnet

The eﬀective thickness of 4 mm in the old septum magnet breaks down into
the conductor with 1.5 mm thickness, two 0.5 mm-thick silicon steel sheet formagnetic shielding against the leakage field, and tiny spacings between themthat amounts to 1.5 mm in total. In order to reduce eﬀective thickness down
to 2.5 mm, we use a conductor with thickness of 1.0 mm instead of 1.5 mm
in the old system, and a single 0.5 mm-thick silicon steel for shielding. The
larger tensile stress generated by the thinner conductor can be recovered by
reducing the gap height to 8 mm from 11 mm. Utilizing a chamber made382

"max (%)

"i :

⌘ (m)

Figure 10.6: Energy acceptance as a function of the dispersion at the injection
point for the case of βR =20 m.
Table 10.4: Beam parameters for the synchrotron injection scheme.
Parameter
Beta-function of the ringBeta-function of injected beam
Emittance of the ring
Emittance of the injected beam
Dispersion of the ring
Energy spread of the stored beam
Energy spread of the injected beam(nR , ni , nε )Eﬀective septum-width
Energy oﬀset
Orbit diﬀerence at injection
Energy acceptance†1 Ref. [4]

βR
βi
εR
εi
ηR
σε
σεi
ws
δi
∆x
εmax

Value

unit

20
20
4.6
4.77
-1.4
0.059
0.1 †1(3.0, 2.5, 2.5)
2.5
0.41
4.1
0.65

m
m
nm
nm
m
%
%
mm
%
mm
%
.

of iron for the ring, enough shield-eﬀect can be obtained even for a single
silicon-steel sheet. Considering the beam impedance, inner surface of the iron383

Figure 10.7: Orbits at the injection region in the case of synchrotron injection
scheme.
chamber is plated with copper of 0.3 mm in thickness. A schematic view ofthe proposed design of the new septum magnet is shown in Fig. 10.8.

Figure 10.8: Cross-sectional view of the septum magnet in the design concept.
The width of the Si-steel sheet is 0.5mm.

384

10.2.3

Field measurement of the prototype for the septum magnet

We have constructed a prototype for the septum magnet. Figure 10.9 shows
the photos of the prototype magnet in the setup for the field measurement,
where a mock-up beam pipe, which is made of ferromagnetic SUS430 stainless steel, was attached on the septum conductor. In the measurement, aFigure 10.9: Photos of a prototype of the septum magnet. A mockup of thebeam pipe made of ferromagnetic SUS430 stainless steel is attached on the
septum conductor for the field measurement.
field mapping was performed in the median plane using a 10-turn pickup coilthat has an area of 20 × 0.5 mm2 . The result is summarized in Fig. 10.10.
The vertical axes are magnetic flux density and the horizontal axes indicate
the transverse position in the line perpendicular to the beam direction in the
median plane, where the origin of x is on the inner (gap-side) surface of the
septum conductor, and the region of x < −1 mm corresponds to the outsideof the septum while the x > 0 represents inside of the gap. The left inset ofthe figure shows the field in the gap as well as the leakage field in outside of
the septum conductor, while the right inset shows the enlarged data for theoutside of the septum, exhibiting the dependence of the leakage field on theshield materials and their combinations. A single shield of the Si-steel sheetof 0.5 mm thickness is not suﬃcient to suppress the leakage nor is the SUS430
chamber. Coexistence of the SUS430 chamber and Si-steel sheet are necessary for the leakage field to be suppressed less than a few Gauss. In the field385

Figure 10.10: Results of the magnetic field measurement along the lateralposition. Data-set for various shield conditions are shown; SUS430 duct only
(green open-circle); No shielding (blue open-circle); Si-steel sheet only (redopen-circle); and both of Si-steel sheet and SUS430 duct (black open-circle).
measurement we found a non-uniformity in the gap field of the septum magnet, which might aﬀect the quality of the incoming beam. We have checked
the eﬀect using the field data by a beam tracking simulation. Traversing the
gap field, the change of the bend angle is obtained as a function of the relative transverse position to the beam center. In Fig. 10.11 plotted is the angle
diﬀerence from that of the beam-center. The horizontal axis is the relative
position to the beam center at the entrance of the septum, in unit of thebeam size. The thick (red) line represents the result of a fit to a straight line,
slope of which manifests the existence of a quadrupole component. Subtracting the quadrupole component, a higher-order field component still remains,
as shown in Fig. 10.12. The quadrupole component can be compensated byadjusting the quadrupoles in the upstream transport line, while the eﬀect ofhigher-order component cannot be recovered. The maximum angle diﬀerenceis 1.2 µrad, which is negligibly small compared with the natural divergence√angle of the injected beam of ni εi /βi = 24.4 µrad, thus the rate of unrecoverable distortion is only about 5%. Similarly evaluation of high-order
position deviation with respect to the beam center shows that it is negligibly386

Figure 10.11: Angle diﬀerence from that of the beam-center. The horizontal
axis is the relative position to the beam center at the entrance of the septum,in unit of the beam size. Thick (red) line represents the result of a least-square
fit to a straight line.
small compared to the angle deviations.

10.2.4

Remedies for the vacuum degradation of MR due
to outgas from septum magnets

In KEKB operation, it has been pointed out that the vacuum of the beamducts of main ring in the vicinity of septum magnets abruptly degraded ata certain beam current[2]. This phenomenon had frequently interrupted thebeam accumulation after the beam-abort. Outgassing from the core of the
septum magnets has been strongly doubted as a possible source, consideringa situation that the vacuum baking of the septum core had been insuﬃcient;
the vacuum of the the septum chamber had been rather poor and it hadconnected to the ring chamber through openings like a beam channel for theincoming beam as well as the spacings between bellows finger of the ringchamber.
Several mitigation for the issue are adopted.
• Enforce the baking system of the septum chamber.
387

Figure 10.12: Residual in the angle diﬀerence after subtracting the first ordercomponent. Three data set corresponding to diﬀerent shim type are shown;(blue) open circles for shim height of 0.08 mm and shim-width of 1.0 mm;(green) open circles for shim height of 0.1 mm and shim-width of 0.5 mm;(red) open circles for shim-height of 0.06 mm and shim-width of 1.0 mm.
• The vacuum chamber of the ring that is installed inside the septum
chamber is replaced with a new one that has no opening to the septum
chamber except for the beam channel for the injected beam.
• To prevent the outgas flowing through the beam channel to the ringchamber, a diﬀerential pumping system is installed between the septum
chamber and the ring chamber, by introducing a narrow beam channel
between them: 8 mmH × 12 mmW × 0.5 mL for LER, and 5 mmH ×
12 mmW × 0.5 mL for HER.
With these improvements vacuum of the ring chamber is estimated to bewithin 10−6 Pa even vacuum in the septum chamber get worse to 10−4 Pa.

388

10.2.5

Power supplies for septum magnets

Figure 10.13 shows the schematic diagram of septum power supplies for the
injection septum of HER and LER. The same power supply is used for the
injection- and extraction-septum magnet of the damping ring(DR). The main

Figure 10.13: Schematic diagram of power supplies for the septum magnets.
capacitors (C1) are discharged by making the thyristors switches (THY3)
turn on. The regenerative power is recharged to the main capacitors throughdiodes (D0) which are connected to the thyristors switches (THY3) in parallel. This gives the full sine pulse shape of about 250 µs. The leakage fields
at the circulating beam are expected to be reduced in its slow component
by using the full-sine pulse shape. Actual pulse shape is not perfectly symmetrical between positive and negative swing due to a resistive componentof the main circuit. Figure 10.14 shows the current waveform at the magnet
coil.
After the voltage of C1 is regenerated up to 86 % of the initial voltage,
the main capacitors are re-charged up to the 99 % of the target voltage,389

Figure 10.14: Current waveform for the DR injection septum.
which is determined by a de-Qing circuit, with a resonant charging throughC0 and L0. The start timing of resonant charging is controlled by the thyristors switches (THY2). Finally, the power supply using the transistor dropper(FET) precisely controls the voltage at the main capacitor C1. The main
parameters for these septum magnets are summarized in Table 10.5. The
voltage stability of 0.01 % is required at any repetition rate. Figure 10.15
and Fig. 10.16 show the voltage stability at the start of operation and thatafter 1 hr, respectively.

390

Table 10.5: The main parameters of the septum magnets for the DR injection,
DR extraction, HER and LER.
DRinj DRext HER1,2 HER3,4 LER1 LER2 unit
Deflection angle
78.8
103
37.5
No. of magnets
1
1
2
Aperture (h,v)(70,24) (70,30) (44,9)†
Inductance
5.77
4.7
9.6
Charging voltage 1.2
1.8
1.44
Peak current
7.0
11.4
5.5
Stability
0.1
0.01
0.01

37.5
50
50
mrad
2
1
1
(44,11) (44,9) (44,11) mm
7.6
7.6
6.0
µH
1.58
1.29
1.43
kV
7.6
5.4
7.4
kA
0.01
0.01
0.01
%

† at 3.3kHz

Figure 10.15: Voltage stability of the main capacitor of the power supply forthe injection septum at the start of operation.

391

Figure 10.16: Voltage stability of the main capacitor of the power supply forthe injection septum observed after 1 hr operation with a repetition frequencyof 20 Hz.

392

Bibliography[1] “KEKB Design Report”,
http://www-acc.kek.jp/kekb/publication/KEKB_design_report/[2] M. Kikuchi, et al.,“Beam-transport system of KEKB”, Nucl. Instr. Meth.
A 499 (2003) pp. 8-32
[3] T. Mori et al., “Design Study of Beam Injection for SuperKEKB MainRing”, IPAC’12, New Orleans Luisiana, USA, May 2012, TUPPR089(2012),
http://accelconf.web.cern.ch/AccelConf/IPAC2012/papers/
tuppr089.pdf[4] K. Furukawa et al., “High-Intensity and Low-Emittance Upgrade of 7
GeV Injector Linac toward SuperKEKB”, IPAC’13, Shanghai, China,
TUPME010 (2013).

393