Chapter 6
RF system
6.1

RF System Overview

RF-related machine parameters for SuperKEKB main rings (LER and HER) are shownin Table 6.1. The beam currents in both rings of SuperKEKB (3.6 A and 2.6 A) areapproximately double those achieved in KEKB (2.0 A and 1.4 A). The most serious
issue we have to address to store these large beam currents is the excitation of fastgrowing longitudinal coupled-bunch instabilities (CBI) caused by the accelerating modeof detuned RF cavities which is needed to compensate for the reactive componentof beam-loading. The cavity higher-order mode (HOM) impedances also have to beminimized not to drive strong longitudinal and transverse CBI as well as to reduce theinduced HOM power. Another issue is the transient beam loading due to bunch gaps,
because it causes relative phase difference of colliding beams bunch-by-bunch, which
results in luminosity degradation and may deteriorate beam stability in the worst case.
To overcome these difficulties, two types of innovative heavily HOM-damped cavities, normal conducting cavities of the three-cavity system named ARES and single-cellsuperconducting cavities (SCC), were used in KEKB. An increase in the stored energy
in these cavities reduces the growth rate of the CBI and also mitigates the gap transient
effects. Since the ARES has a larger stored energy, this alone was used for the LER
that stored the higher beam current. The HER, where a higher RF voltage was required, was equipped with a combination of the SCC and ARES. They were operated
with a suitable relative phase angle to assign higher cavity voltage to the SCC andheavier beam loading to the ARES. The layout of the KEKB RF system is shown in
Fig. 6.1 (top). A set of typical RF-related parameters for the physics run is also shown.

149

Paramter
Beam Energy [GeV]
Beam current [A]Bunch gap length [%]Bunch length [mm] (rms)
RF frequency [MHz]Harmonic number
Revolution frequency [kHz]
Cavity type
Number of cavities
Total RF voltage [MV]RF voltage/cavity [MV]Wall loss/cavity [kW]Number of klystrons
Klystrons power [kW]Beam power [MW]

LER
4.0
3.6
2
6

HER
7.0
2.6
2
5
508.8765120
99.4
ARES SCC/ARES
22
8/8
10∼11
15∼16
0.5
1.5/0.5
150
-/150
18
8/8
∼600 ∼450/∼800∼8∼8.3

Table 6.1: RF-related machine parameters.
Each RF station consists of a klystron, the high-power RF (HPRF) and low-level RF
control (LLRF) systems, and either the ARES or SCC. The HPRF and LLRF systems
are accommodated in the RF buildings, and the ARES and SCC are located in thetunnel.
The KEKB RF system with the ARES and SCC showed excellent performance
during the physics run operation of KEKB. The LER beam current for the physics run
was limited up to about 1.8 A, which is lower than the design current of 2.6 A, due tobeam blow-up caused by the electron cloud effect. In order to check the performanceof the RF system with a higher beam current, the beam current was increased up to
2.0 A at an accelerator study with a bunch spacing of three buckets. The RF system
worked at this current without any problems. In order to increase the luminosity withthe limited LER beam current, the HER beam current was increased beyond the design
current of 1.1 A. The power delivered to the beam by each SC cavity was increased
from the design value of 250 kW to 350 kW (one cavity was operated at about 400 kW),and the HER beam current was successfully increased up to 1.4 A. The HOM damping
property of the ARES and the SCC was sufficient for the KEKB beam currents, andno CBI caused by the cavity HOMs was observed throughout the operation. The
frequency of beam aborts caused by any kind of RF trips at all ARES or SCC stations

150

was typically only once per day. For details of the KEKB RF system, refer to [1, 2].
The SuperKEKB RF system design was investigated in the context of possibilityof using the existing RF system for KEKB with the ARES and SCC as much as
possible, by introducing necessary improvements and reinforcements. In particular,
following points are important, which all are related to the much higher beam currents
compared to those in KEKB.
• The RF system should deliver power to the stored beam up to approximately∼8 MW per ring, which is about double that in KEKB.
• Availability of present HOM dampers should be evaluated at the SuperKEKB
design parameters, and necessary measures need to be investigated.
• Beam-loading related issues and measures should be investigated: in particular
the CBI associated with the accelerating mode of cavities, gap transient effects,
stability and accuracy of the control performance with heavy beam-loading.
First, the twice beam current together with a larger radiation loss per turn in the LER
increases the beam power more than double that of KEKB. The beam power in the
HER also increases due to the higher beam current. On the other hand, the required RF
voltage is about the same as that of KEKB. Consequently, each cavity should provide
much higher power to the beam than the case of KEKB. To meet the requirement,
the RF stations with the ARES cavities need to be changed from the KEKB scheme,
where one klystron drives two cavities, to a new scheme where one klystron drives
one cavity. To change to the new scheme, reinforcement of the RF source, including
klystrons and other HPRF components, the LLRF system, as well as rearrangement of
ARES cavities are required. The RF parameters are chosen with the klystron output
power up to 850 kW in operation regardless of the maximum rated output power of
1.2 MW for the existing Toshiba tubes. This choice has advantages: (1) the existing
power supplies for the klystrons can be used without major modifications, (2) most of
the existing high power RF components can also be reused, and (3) the klystrons areoperated below saturation with a sufficient margin, which benefits stable control underheavy beam-loading. In consideration of such terms and conditions, the RF system
configuration and design parameters at its ultimate stage to store the design beam
currents were optimized as shown in Table 6.1 and Fig. 6.1 (bottom).
In order to increase the power delivered to beam by each ARES cavity, the input
couplers are needed to be replaced with new ones that have a stronger input coupling
factor of β = 6.0 (β = 2.7 for KEKB). The new input couplers are developed, and highpower performance with beam was demonstrated at the end of the KEKB operation
151

Figure 6.1: The layout of RF system, together with typical RF-related machine parameters. (top): The KEKB RF system with parameters (as of Nov. 15, 2006) for physics
run. (bottom): The SuperKEKB RF system at its ultimate stage to achieve the design
luminosity of 8 × 1035 cm−2 s−1 , together with parameters listed as an example.

152

in 2010. Two stations (D5-C and D5-E) were changed to the new scheme where one
klystron drives one cavity, and a prototype input coupler with a higher input coupling
factor was attached to the D5-C cavity. By changing the phase of this station relative toall other stations, beam loading to this station was increased. Finally, the beam power
provided by the cavity reached 610kW, which meets the requirement for SuperKEKB.
Following the success of the demonstration in beam operation, mass production of the
new input couplers started and is ongoing, as described in Section 6.2.6.
Second, the higher beam currents together with a shorter bunch length compared to
KEKB will increase the HOM power induced in the cavity region. Careful investigations
were conducted to check whether the present HOM dampers are usable or not at thedesign beam currents of SuperKEKB. Based on the evaluation of HOM power at the
ARES and related bench tests of the HOM dampers, it has been concluded that thepresent HOM dampers for the ARES cavities can be used without any modification,
as described in detail in Section 6.2.5. On the other hand, the capacity of the existing
HOM dampers for the SCC is not sufficient for the design beam current of the HER.
Several measures to reduce the HOM power or to improve the HOM damper with its
cooling system have been investigated. It was found that implementing an additional
damper made of SiC between the adjacent SCC reduces HOM power absorbed by theexisting HOM dampers made of ferrite, as described in Section 6.3.2. This measure
is considered to have a lower risk and in lower cost compared to the other measures
such as replacing the existing dampers with some new ones or changing configurationof beam pipes and tapers around the SCC to reduce the loss factor. Consequently,
an additional SiC damper will be implemented in one of the SCC before the phase 1
commissioning. After proving the performance with the beam, this measure will be
expanded to the other SCCs.
Third, the LLRF system is reexamined by taking higher beam currents into consideration. While the existing analog-based LLRF system, which had been operated
stably for KEKB, can also be used for SuperKEKB, a new digital LLRF system isbeing developed for higher accuracy and flexibility. The new digital LLRF systems
utilizes EPICS embedded FPGA board in the micro-TCA platform and also EPICS
embedded PLC. A prototype one has been tested successfully with an ARES cavity toverify the performance in high-power operation. After the successful test, mass production of new digital LLRF started. Nine existing LLRF systems located at the Ohobuilding, which suffered serious damage from the Great East Japan Earthquake, arebeing replaced with the new LLRF system. Since compatibility between the existingand new LLRF systems is taken into consideration in the design, the existing and new

153

D4
1

D5

OHO
2

C

2

1

C E

E

2

B

A

A

B

KEKB-RF

D7
D

C

B

D10 NIKKO D11

D8

FUJI

2

2

A

A

1

2

2

B

C

D

2

E

2

2

D C B A

1

2

A B C D

E

F

HER
LER
Crab cavity

SuperKEKB-RF (Phase 1)
5 klystrons, HP&LL added

3 power supplies added
D4
2

2

2

H G F E

2CA

1 power supply
upgraded

D5

OHO

2

2

A B C D E

2

2

E

F

B

A

1

2

2

A

B

NIKKO

D10

D8

2

C

D

FUJI

D7

4 old VP-klystrons replacedwith new T-klystrons

C

2

E

D

D11

2

2

D C B A2A B C D

HER
LER

2 cavities added
6 cavities relocated HER->LER
2

4 cavities removed

Type “A” power supply (for two klystrons)
Type “B” power supply (for one klystron)

1

Klystron, HP&LLRF system

SC cavity

ARES cavity

The RF system with reinforcement done for Phase 1 can support 70% design beam current.

add 2 more klystrons, HP&LL,
add 1 more power supply
OHO

D4
2

2

2

2

H G F E D C B A

A B C

2

2

2
D E

FUJI

D7

D5
2

optionadd 2 more klystrons, HP&LL,
add 1 more power supply

F

F

2
E

D

B

D10

D8

2

C

A

B

C

2

2

2

2

A

add 2 SC cavities
add 2 klystrons, HP&LL

D

E

F

NIKKO

2

D C B A

D11

2
A B C

2

2
D

E

F

More RF reinforcement plan to further increase beam current after Phase 2

Figure 6.2: (top): The layout of KEKB RF system, (middle): the layout of SuperKEKB
RF system for phase 1 commissioning, and (bottom): the layout of SuperKEKB RF
system at the ultimate phase.

154systems coexist in different RF stations for beam operation without problems. Afterthe beam commissioning, the other analog LLRF systems will be replaced with new
digital ones step by step, according to available budget.
In the context of LLRF, two issues need more careful investigation for the higher
beam currents: one is the CBI associated with the accelerating mode, and the otheris the gap transient effects. In the KEKB operation, the µ = −1 mode instability wasobserved at around 1 A, even with the ARES and the SCC, and a damper system forthe µ = −1 mode was used to suppress the instability. For SuperKEKB with higher
beam currents, an improved damper system is needed to have higher damping rate
for the µ = −1 mode. In addition, we need to pay attention to the µ = −2 (maybe
also µ = −3) modes. A new damper is being developed for a higher damping rate,
which will replace the present µ = −1 mode damper used in KEKB. The new damper
will be extended for the µ = −2 mode after the beam commissioning. As for the gap
transient effects, a new simulation method was developed, where three cavity systemof the ARES is taken into account, to evaluate the gap transient-related issues andpossible cures. Details of the new digital LLRF system, the CBI damper, and the gap
transient evaluation are described in Section 6.4.
Based on these investigations, we have concluded that the SuperKEKB RF system
can be constituted by reusing the existing RF system with the ARES and SCC as muchas possible with necessary reinforcement and improvements. This strategy passes on
the reliability of the KEKB RF system, proven in the long-term operation, and also
reduces the construction cost. The reinforcement of the RF system will be performedin phases, as shown in Fig. 6.2, to meet the available budget as well as beam commissioning scenario. During construction period from 2010 to 2014 the RF system will
be reinforced from the KEKB RF system (top of Fig. 6.2) to the system matched tothe phase 1 commissioning (middle of Fig. 6.2). In the construction phase, five RF
stations are added in D4 and D5 of the Oho straight section. And the ARES cavities
are rearranged as follows: six cavities in D5 are converted from the HER beam line to
the LER, two cavities are added in D4 for the HER, and four cavities in D7 and D8
for the LER are removed. With the new configuration, 14 RF stations are operated
with the new scheme where one klystron drives one ARES cavity. Up to about seventy
percent of the design beam current can be supported with this configuration. After thecommissioning starts, more RF reinforcement will be conducted to increase the beam
currents to the design values, as shown in (bottom of Fig. 6.2), depending on machine
performance and available budget.

155

6.2

Normal Conducting Cavity

6.2.1

PrefaceThrough design investigation on the normal conducting RF cavity system for the SuperKEKB collider based on the nano-beam scheme, we have concluded that the existing
ARES cavities developed for KEKB can be reused without modification. It seems to
be a conservative solution, however, reliable and consequently economical. In addition,
the results of high power tests on the two types of existing HOM loads for the ARES
cavity have shown that either type can be reused within each performance limit. On
the other hand, the input coupler needs to be upgraded in accordance with the increase
in beam loading per cavity.

6.2.2

Introductory Review on ARES scheme

The ARES cavity is a normal-conducting three-cavity system [3] developed for KEKB
in order to suppress the longitudinal coupled-bunch instabilities (CBIs) due to large
detuning of the accelerating mode from the RF frequency for beam-loading compensation. The acronym “ARES” stands for Accelerator Resonantly coupled with Energy
Storage, just representing its RF schematics based on the π/2-mode operation where an
accelerating cavity is resonantly coupled with an energy storage cavity via a coupling
cavity in between. Figure 6.3 shows an equivalent kinematic model of three coupledpendulums, where the π/2 normal mode is used as the accelerating mode. The energy
storage cavity, which corresponds to the left-side pendulum with a relatively huge mass,functions as an electromagnetic flywheel to stabilize the accelerating mode by increasing its total stored energy against the beam loading onto the accelerating cavity (theright-side pendulum). By the way, this scheme is inevitably accompanied with two parasitic modes other than the π/2 mode, namely, the 0 and π normal modes. Moreover,these parasitic 0 and π modes interact with the beam as strongly as the accelerating
mode, and would drive severe longitudinal CBIs. In order to avoid this difficulty, thecoupling cavity (the middle pendulum) is equipped with a damper selectively acting
on the 0 and π modes.
Key features of the ARES scheme based on the π/2-mode resonant coupling aresummarized as follows.
• The stored energy ratio for the π/2 mode is given by Us /Ua = ka2 /ks2 , where Ua
is the stored energy in the accelerating cavity and Us the energy in the storage
156

Figure 6.3: Coupled pendulum model showing the ARES scheme.
cavity, ks the coupling factor between the accelerating and coupling cavities andks the coupling factor between the storage and coupling cavities.
• The π/2 mode shows extraordinary field stability, which assures that the stored
energy ratio Us /Ua can be kept almost constant in the presence of detuning by∆fa for the accelerating cavity loaded with beam. Therefore, the detuning of theπ/2 mode will be reduced as ∆fπ/2 = ∆fa /(1 + Us /Ua ).
• The parasitic 0 and π modes can be selectively damped by equipping the coupling
cavity with a damper.
• Moreover, the damped 0 and π modes are nearly symmetrically located withrespect to the RF frequency. Therefore, the impedance contributions from these
two modes to CBIs cancel each other out to some extent.

6.2.3

ARES cavity

Figure 6.4 shows the front, side, and top views of the ARES cavity for KEKB, thedesign of which is based on a concept demonstrator named ARES96 [4]. For a better
understanding of this RF structure, a 3D transparent view is also shown in Fig. 6.5,
where the half-cell coupling cavity (HCC in Fig. 6.4) is intentionally omitted for simplicity.
The energy storage cavity is a large cylindrical steel structure with dimensions of1070 mm in diameter and 1190 mm in axial length, whose inner surfaces are electro157

fRF
Us /Ua
R/Q0
Q0
Vc
Pc

508.9 MHz915 Ω
1.1 × 105
0.5 MV150 kWfor the π/2 accelerating mode

60 kW (acc. cav.) + 90 kW (str. cav.)

Table 6.2: RF parameters of the ARES cavity.
copper plated. The Q value of the TE013 mode is 1.65 × 105 , which is 85% of thetheoretical value assuming a copper electrical conductivity of 5.81 × 107 S/m (100%
IACS conductivity). The storage and coupling cavities are electromagnetically coupled through a rectangular aperture of 120 mm wide by 180 mm high, and mechanically connected with rectangular stainless-steel flanges. Then, the flange connection is
vacuum-sealed by welding thin stainless-steel lips along the perimeter. RF power is fed
through an input coupler [5] attached to a drive port of the storage cavity (Fig. 6.5).
Details of the input coupler for the ARES cavity are described later, together with its
upgraded parts.
The accelerating cavity is a HOM-damped structure in itself, which was carefully
designed to be smoothly embedded into the whole ARES scheme without any structural
or electromagnetic incompatibilities. The accelerating cavity was fabricated by brazing
oxygen-free copper (OFC) parts in a vacuum furnace. Details of HOM damping in the
ARES cavity, together with its RF absorbers, are described in a later section. The
coupling cavity, also made of OFC parts, is brazed to one side of the accelerating
cavity in the horizontal direction. The accelerating and coupling cavities are coupledthrough a rectangular aperture of 120 mm wide by 160 mm high. On the other side,a half-cell coupling cavity is brazed (front view in Fig. 6.4) in order to restore mirror
symmetry with respect to the vertical mid-plane including the beam axis.
A coaxial antenna-type coupler [6] is attached to the central port of the coupling
cavity in order to damp the parasitic 0 and π modes (C-damper in Fig. 6.4 or Fig. 6.5).
The coupler consists of two coaxial lines crossing at a right angle, where the end of thehorizontal coaxial line and the upper end of the vertical one are electrically shorted toform a stub-supported crossing structure. The horizontal coaxial line is equipped witha disk-type alumina RF window as shown by a green disk in Fig. 6.5. The extracted
RF power is dissipated as heat in a water-cooled dummy load attached to the lower
end of the vertical coaxial line. As shown in Fig. 6.6, the loaded Q values of the 0 andπ modes can be reduced to around 100, while the π/2 mode is not affected.
158

Figure 6.4: Top, front and side views of the ARES cavity.
The RF design parameters for the ARES cavity are listed in Table 6.2. By adjusting the height of the rectangular aperture between the storage and coupling cavities
with respect to that between the accelerating and coupling cavities, that is, 180 mm
vs. 160 mm as described above, the stored energy ratio Us /Ua was set at 9. Therefore, the detuning for the π/2 mode can be reduced by one order of magnitude as∆fπ/2 = ∆fa /(1 + Us /Ua ). The design cavity voltage of 0.5 MV is generated witha wall loss of 150 kW in total: 60 kW and 90 kW for the accelerating and storage
cavities, respectively.
In KEKB, 20 ARES cavities had been successfully operated to store positron beams
of up to 2.0 A in the LER, while 12 ARES cavities in combination with 8 super
conducting cavities had been used to store electron beams of up to 1.4 A in the HER.
Fig. 6.1 (top) shows the whole RF system of the KEKB collider, together with RFrelated machine parameters (as of Nov. 15, 2006) for physics run. Many problems
had been overcome one-by-one [7]. Roughly, the problems can be divided into two
categories: infancy problems, especially with accessory devices being used in long-term
operation, and cavity problems attributed to quality control issues, usually associatedwith the stringent cost goals in the production phase.
Judging from the operational performance of the ARES cavity system demonstrated
159

Figure 6.5: Transparent view of the ARES cavity.

160

Figure 6.6: Accelerating mode (the π/2 mode) and the damped parasitic 0 and π
modes. The vertical axis shows the transmitted power amplitude |S21 | from port #1
at one endplate of the accelerating cavity to port #2 at the other endplate, measured
with a network analyzer.
through the KEKB’s exploration, together with promising results from high power
experiments on the existing HOM loads, we have concluded that the ARES cavity
system for KEKB can be reused [8] in the SuperKEKB collider. That is because thenano-beam scheme keeps the design beam currents in both rings within approximately
double those achieved in KEKB. It is the input coupler that needs to be upgraded inaccordance with the increase in beam loading per ARES cavity.

6.2.4

Fundamental Mode Issues

Figure 6.1 (bottom) shows the whole RF system required for the SuperKEKB collider
to achieve the design luminosity of 8×1035 cm−2 s−1 at its ultimate stage, together with
RF-related machine parameters listed as an example. In accordance with the increaseof beam power, the number of RF stations each configured as one klystron driving one
ARES cavity will be increased up to 14 in the LER and up to 8 in the HER.
Figure 6.7 shows the coupling impedances (real part) of the π/2 mode per ARES
cavity, calculated for two cases. One is for the KEKB LER where a beam current of
1.8 A being accelerated with 20 ARES cavities (Vc = 0.4 MV per cavity with the input
coupling factor β = 3). The other is for the SuperKEKB LER where the design currentof 3.6 A being accelerated with 22 ARES cavities. For simplicity, it was assumed thatevery ARES cavity, with the same input coupling factor β = 5, is to be detuned by the161

Figure 6.7: Coupling impedance of the π/2 mode calculated for the SuperKEKB LER
where the design beam current of 3.6 A being accelerated with 22 ARES cavities,
compared with that for the KEKB LER.
same amount of frequency, independently of whether the RF station is configured as
one ARES cavity per klystron or two ARES cavities per klystron. The black dashedand red solid curves correspond to the KEKB and the SuperKEKB cases, respectively.
The amount of frequency detuning |∆fπ/2 | = |∆fa |/(1 + Us /Ua ) for the π/2 modeincreases from 17 kHz to 28 kHz, however, still being kept below one third of the beam
revolution frequency of 99.4 kHz. In addition, the impedance spectrum becomes broad
since the coupling factor being increased from 3 to 5. Figure 6.8 shows the growth rates
calculated for the -1, -2, and -3 modes of the longitudinal CBI in the SuperKEKB LER
due to detuning of the π/2 mode. Here normal operation condition, where all cavities
are powered with no parked cavities out of operation, is assumed. In this case, thegrowth rates of modes except for the -1 mode are lower than the radiation damping
rate. Section 6.4 describes more detail including the cases of other operation conditions
and measures.
Another issue concerns longitudinal CBIs arising from the impedance imbalance
between the parasitic 0 and π modes. The 0 and π modes are located nearly mirrorsymmetrically with respect to the π/2 mode to be tuned into the vicinity of the RF
frequency. Therefore, the impedance contributions from the damped 0- and π-mode
resonances to CBI can be counterbalanced between excitation and damping. However,detuning of the accelerating cavity by ∆fa affects the field distributions of the 0 andπ modes in the first order. Figure 6.9 shows the coupling impedance (real part) of
the damped 0 and π modes calculated for the same cases as above. The impedance
162

Figure 6.8: Growth time constants of the CBI modes of µ= -1, -2, and -3 due to theπ/2 mode, plotted as a function of the beam current in the SuperKEKB LER.

Figure 6.9: Coupling impedance (top) of the 0 and π modes, and the imbalance (bottom) with respect to the RF frequency.

163

imbalance (the difference between the original waveform and its mirror image obtainedby horizontal reverse with respect to the RF frequency) is also shown, where excitationis positive and damping is negative, and the fastest growth time is indicated for eachcase. This calculation was carried out as follows. The perturbation due to ∆fa wastaken into account up to the first order. The external Q value of the coupling cavity
to the antenna coupler (C-damper) was assumed to be 50 (the same as for KEKB),
which gives QL = 100 for the unperturbed 0 and π modes with Ua = Uc . As theaccelerating cavity is detuned downward, the field distribution changes as Ua > Uc for
the 0 mode, on the other hand, Ua < Uc for the π mode, where the energy imbalanceis proportional to ∆fa /(fπ − f0 ). As for the KEKB LER, the fastest growth time isestimated 70 ms at a beam current of 1.8 A, much slower than the radiation damping
time of 21 ms. It is consistent with the fact that any CBI due to the 0 and π modes
had not been observed in KEKB. As for the SuperKEKB LER with the design beam
current of 3.6 A, the fastest growth time is estimated 21 ms for a CBI mode number
around -40, that is about -4 MHz apart from the RF frequency. It is slightly fasterthan the radiation damping time of 22 ms, however, slow enough for a longitudinalbunch-by-bunch feedback system to cure. It should be noted that the CBI modes
arising from the impedance imbalance between the 0 and π modes are usually locatedout of the frequency band for an RF feedback system to act on the beam through the
klystron.

6.2.5

HOM loads

Figure 6.10 shows the HOM-damped accelerating cavity part and close-up views of thetwo types of HOM loads. Four rectangular HOM waveguides (WGs) are directly brazed
to the upper and lower sides of the accelerating cavity in order to damp the monopole
HOMs and the vertically polarized dipole HOMs. The extracted HOM power is guided
through each waveguide and finally dissipated in two bullet-shaped SiC ceramic absorbers inserted at the WG end (see WG HOM load in Fig. 6.10). The bullet-shaped
absorber (55 mm in diameter and 400 mm in length including the tapered head) is
directly water-cooled. In order to damp the dipole HOMs deflecting the beam in thehorizontal direction, two grooved beam pipes (GBPs) [9, 10] is attached to both endplates of the accelerating cavity. The GBP, with an inside diameter of 150 mm for its
circular pipe, has two grooves (dimensions: 30 mm in width and 85 mm in depth) on
the upper and lower sides. Inside each groove, there are eight SiC tiles (dimensions: 48
mm × 48 mm × 10 or 20 mm) arranged in a line and brazed to a water-cooled copper
plate (see GBP HOM load in Fig. 6.10). The details of the HOM loads for the ARES164

Figure 6.10: Front and side views of the HOM-damped accelerating cavity, and close-up
views of the waveguide (WG) and GBP HOM loads.
165

KEKB LER
Sep. 21, 2004
Beam current [A]
1.6
Number of bunches
1293
Bunch length [mm]7Loss factor [V/pC]
0.40 (0.39† )P HOM /ARES [kW]5.4†
P HOM /WG [kW]1.05†
P HOM /Groove [kW]0.3††
Based on calorimetric measurement.
††

SuperKEKB
LER
3.6
2503
6
0.44
17
3.3
0.93

Rating††Achieved†††

5.0
1.2

20
1.5

Continuous power handling rating.

†††

Maximum power handling capability achieved in experiment.
Table 6.3: HOM power estimates for SuperKEKB LER.

cavity were reported in Ref. [11].
Table 6.3 summarizes the HOM power estimates for the ARES cavity operated
in the SuperKEKB LER and the results of measurements in the KEKB LER as areference. The power handling ratings determined from a set of high power experiments
are also listed, together with the records achieved therein. First of all, the total HOM
power per cavity is estimated to be 17 kW for the SuperKEKB LER with the design
beam current of 3.6 A consisting of 2503 bunches with a bunch length of 6 mm. Thisvalue is about three times higher than the reference value of 5.4 kW for the KEKBLER.
The WG load is expected to show excellent power handling capability since thebullet-shaped SiC absorbers with a relatively high thermal conductivity of 125 Wm−1 K−1(at room temperature) are directly water-cooled. Before this SuperKEKB project was
launched, a WG load detached from a spare ARES cavity had been tested up to 20
kW (10 kW per absorber) [12, 13]. As part of R&D efforts [14, 15] for the former
project aimed at the luminosity enhancement based on ‘high-current’ scheme, a seriesof high-power experiments on the WG load had been carried out from 2006 through2009 at a test stand equipped with an L-band klystron capable of delivering RF powerof up to several tens of kilowatts. Figure 6.11 shows the setup of an experiment formeasuring the surface temperature distribution along the SiC absorber in situ withuse of an infrared thermometer. Conductive heat transfer inside the SiC absorber isdominant over others from its surface to the surroundings by radiation or convection.
Therefore, the experiment was carried out in the atmosphere so as to allow us to elim166

Figure 6.11: Setup for in situ measurement of the surface temperatures (at the points
A through E) along each of the bullet-shaped SiC absorbers in a HOM waveguide.

Figure 6.12: Surface temperature rises along a type-96 bullet-shaped SiC absorber for
KEKB are plotted as a function of the absorbed power per HOM waveguide, together
with the reflection coefficient from the load.
167

inate systematic errors in temperature measurement. Figure 6.12 is a graph showing
the temperature rises at five points along the surface of the absorber (as indicated byletters “A” through “E” in Fig. 6.11), plotted as a function of the absorbed power,
together with the reflection coefficient for the WG load. When the absorbed power
exceeds 5 kW, the surface temperature around the tip of the nosecone, for which cooling efficiency is not good compared with the rest part, shows a rapid increase, whichis accompanied with a small step-like change in the reflection coefficient. Probably, a
positive feedback loop can explain this phenomenon: increased temperature around thetip of the nosecone leads to increased dielectric constant there which leads to locallyincreased RF power absorption therein [12]. The small step-like change in the reflection
coefficient might be explained in the following way: excessive temperature rise at the
tip of the nosecone leads to non-uniformity in dielectric constant along the nosecone
section, which resulted in increased RF shockwave arising from there. In order to suppress the excessive temperature rise at the tip, a new bullet-shaped SiC absorber (type06 in Fig 6.13) with improved cooling efficiency especially for the nosecone section wasdeveloped and successfully tested up to 20 kW [12] as shown in Fig 6.14. However,according to Table 6.2, the power handling capability of the existing absorber (type
96 in Fig. 6.13) is enough for use in the SuperKEKB collider based on the nano-beamscheme. Conservatively, the continuous power handling rating for the WG load should
be set at 5 kW (2.5 kW per absorber). This rating still leaves a margin of 50% withrespect to the HOM power estimate of 3.3 kW (Table 6.2).
Since the SiC tiles for the GBP load are indirectly cooled (Fig. 6.10), we should pay
more attention to the effect of the absorber temperature on the reflection coefficientand the vacuum pressure. Therefore, we carried out a series of experiments with two
different setups. Figure 6.15 shows the setup of our first experiment using a standard
rectangular waveguide (WR650). As shown in Fig 6.16, a GBP load unit was fit intoa rectangular opening at the top wall of the waveguide chamber and fixed thereto andhermetically sealed by TIG welding. Figure 6.17 shows the setup for our second experiment, which was devised to reproduce the actual electromagnetic boundary conditions
as faithfully as possible. A GBP was detached from a spare cavity by cutting, and afitting flange was attached to the machined end face by TIG welding. The GBP chamber thus prepared was connected to a rectangular waveguide port via a custom-madewaveguide transformer (Fig. 6.18). Every flange-to-flange joint was made vacuum-tightwith use of a metal gasket. Figure 6.19 shows a graph summarizing the results of thetwo experiments, where the vacuum pressure and the VSWR are plotted as a functionof the absorbed power normalized per groove (or per GBP load unit). In the firstexperiment, the vacuum pressure rapidly increased when the absorbed power exceeded
168

Figure 6.13: Newly developed type-06 bullet-shaped SiC absorber (bottom), comparedwith type-96 (top) for KEKB.

Figure 6.14: Surface temperature rises along a newly developed type-06 bullet-shaped
SiC absorber are plotted as a function of the the absorbed power per HOM waveguide,
together with the reflection coefficient from the load.

169

Figure 6.15: Setup for high-power testing of a GBP load unit, placed inside a standard
rectangular waveguide at L band.
1.2 kW, but no electric discharge inside the waveguide chamber was seen through aviewing port. What was worse, RF conditioning over a long time proved ineffective
for mitigating this phenomenon. On the other hand, in the second experiment, theresponse of the vacuum pressure was smooth up to 1.5 kW per groove. So far, we haveno clear evidence to answer what brought this distinct difference in vacuum pressure
response. It might be due to accidental sample-to-sample variation in performance,or due to the systematic difference in electromagnetic boundary conditions. Probably,
the latter case gives a higher limit than the former. Although further investigation
with more samples is needed, for the time being we should adopt a limit of 1.2 kW
per groove as the power handling capability for the GBP load. This limit still leaves a
margin of 29% since the estimated HOM power is 0.93 kW per groove.

6.2.6

Input Coupler

The ARES cavity is fed with RF power through one input coupler attached to a drive
port of the storage cavity (Fig. 6.5). The power handling capability of the input coupler
170

Figure 6.16: Inside of the rectangular waveguide (Fig. 6.15) with a GBP HOM load
unit (Fig. 6.10) attached on the ceiling.

Figure 6.17: Setup for high-power testing of a GBP unit, detached from a spare cavity
and modified to flange-mount type.

171

Figure 6.18: Waveguide transformer from a standard rectangular waveguide to a GBP
unit with 8 SiC tiles per groove.

Figure 6.19: Vacuum pressure (red) is plotted as a function of the absorbed power per
groove (or per absorber unit of 8 SiC tiles): open rectangles for an absorber unit placed
inside a standard rectangular waveguide and closed circles for a GBP unit detachedfrom a spare cavity, together with the VSWR response (blue) for each case.
172

Figure 6.20: Input Coupler for the ARES cavity.
needs to be upgraded in accordance with the increase of RF input power (including awall power of 150 kW for generating a cavity voltage of 0.5 MV) from 400 kW (KEKB
design) to 750 kW for RF stations each configured as one klystron driving one ARES
cavity. The good news to our upgrade considerations was that some input couplers for
KEKB had been tested up to 950 kW [5] in 1997, surpassing the above design value.
Figure 6.20 shows a schematic drawing of the input coupler [5] for the ARES cavity.
The RF power is transmitted from the rectangular waveguide input, via a doorknob
transition with a capacitive iris, to the coaxial line with a disk-type alumina window.
The coaxial line is tapered down and ends with a magnetic coupling loop. The input
coupling factor to the cavity can be adjusted by rotating the loop angle with respect tothe direction of the magnetic field, and becomes maximum when the magnetic field isperpendicular to the loop. However, the maximum input coupling factor attained with
the KEKB-type coupler was limited below 3.2, while an input coupling factor over 6
is required for the SuperKEKB. Then, we decided simply to extend the coupling loop
into the cavity. Figure 6.21 shows the results from measurements using a cold model(Fig. 6.22) of input coupler attached to a spare ARES cavity. The input coupling
factor is plotted as a function of the loop height, easily changed for the cold model by
replacing copper spacers. The response of the unloaded Q value of the π/2 accelerating
mode is also shown. Accordingly, the loop height was extended from 17 mm (KEKB)
to 60 mm, which gives an input coupling factor over 6 with enough margin while being
accompanied with a decrease around 3% in the unloaded Q value. In addition, some173

Figure 6.21: Input coupling factor, measured using a cold model, is plotted as a functionof the loop height, together with the unloaded Q value of the π/2 mode.
improvements have been applied to the input coupler for more stable operation. Fine
grooving inside the outer conductor (Fig. 6.23) of the coaxial line (WX77D) proved
quite effective in suppressing the multipactoring discharge occurring there [16].
In June 2010, a prototype input coupler for SuperKEKB, with the input coupling
factor set at 6.4 (cold), was tested at the RF station D5-C (see Fig. 6.1: top), in which
one klystron drove one ARES for the KEKB HER. Figure 6.24 shows the forward andreflected RF power (red and green, respectively) together with the vacuum pressure(black) in the cavity, plotted as a function of the HER beam current. About 750 kW of
RF power was successfully fed through a single coupler, 130 kW for generating a cavity
voltage of 0.47 MV and 610 kW delivered to the beam. Thus, the performance of the
prototype input coupler was successfully demonstrated under the practical operating
conditions probably expected to be similar to those in SuperKEKB.
Following three input couplers fabricated as the pre-production model in JFY 2010
and 2011, the production of input couplers was started and is underway: 6, 10 and 4
input couplers in JFY 2012, 2013 and 2014, respectively. From the prototype to the
production model via the pre-production, some minor changes were made in stepwise
to the metal fittings brazed to the alumina disk in order to improve the fabrication
yield of the RF windows [17]. So far, 13 input couplers have been processed up to174

Figure 6.22: Cold model of input coupler.

Figure 6.23: Fine grooving inside the outer conductor of the coaxial line WX77D(Fig. 6.17) to suppress multipactoring discharge.
175

Figure 6.24: Forward and reflected RF power and vacuum pressure for the ARES cavity
at the RF station D5-C, equipped with a first prototype input coupler for SuperKEKB.
750-800 kW in a high-power test stand (Fig. 6.25). This test stand was constructedusing a spare storage cavity in order to reproduce the operating conditions expected inSuperKEKB as faithfully as possible [18]. Since April 2013 when a dedicated ozonizedwater generator became available, ozonized water rinsing of the RF window, followedby vacuum baking, has been our standard pretreatment before high power testing. This
pretreatment, which had been applied to some KEKB input couplers for elimination ofmultipactoring discharge at the RF window [19], has proved effective also in suppressing
vacuum pressure spikes during RF conditioning as shown in Fig. 6.26, and consequently
shortened the net total time of high-power testing for one input coupler from 100 hours
to 70 hours.
KEKB-type input couplers are to be replaced with upgraded ones for 14 RF stations each configured as one klystron driving one ARES cavity for the initial stage ofSuperKEKB. Before the phase 1 beam commissioning of the rings, 10 input couplers
in the OHO section are to be replaced: 6 and 4 in sections D5 and D4, respectively. In
the summer shutdown right after the phase 1 commissioning, 4 input couplers in the
FUJI section are going to be replaced.

176

Figure 6.25: Setup using a storage cavity for high-power testing of the input coupler,where another coupler is attached and the extracted RF power is dissipated in a dummy
load.

Figure 6.26: RF processing history for an input coupler pretreated with ozonized water
rinsing followed by baking (right) is compared with that for another input coupler
without pretreatment (left).
177

Figure 6.27: Schematic diagram of the superconducting cavity.

6.3

Superconducting Cavity

6.3.1

Superconducting Cavities

Superconducting accelerating cavities have been developed for the KEK B-factory(KEKB) to accelerate the electron beams in the high energy ring (HER) [20]. The
cavity has a 509 MHz single cell to provide the accelerating voltage of 1.5 MV at 4.4K.
A schematic diagram of the cavity is shown in Fig. 6.27. The first four cavity cryomodules were installed in December 1998 and commissioned. The other four were installedin the summer of 2000 [21]. Figure 6.28 shows the cryomodule installed in the KEKB
tunnel. Those eight cavities were operated until the machine shutdown (June 2010).
Those superconducting cavities will be re-used at SuperKEKB. The design parameters,
achieved values at KEKB and required values at SuperKEKB are listed in Table 6.4.
In order to accelerate the beam current of 2.6 A, measures for beam instabilities
are important. The large stored energy of the cavity, which is 7.6J at the voltage of 1.5
MV, suppresses the frequency detuning for the optimum tuning well below the beam
revolution frequency. The large stored energy also contributes to suppress the phaseoscillation due to a long bunch train gap. The higher order mode-induced coupled
bunch instabilities also should be avoided. Large beam pipes and two ferrite HOM
dampers are applied to the SCC [22]. One of the HOM dampers is attached on a small

178

Figure 6.28: Cryomodule installed in the KEKB tunnel.

Parameter
Beam energy (GeV)
Beam current (A)Bunch charge (nC)
Bunch length (mm)RF voltage (MV)Beam power (kW/cavity)
HOM power (kW/cavity)

KEKB (design)
8.0
1.1
2
4
1.5
250
5

KEKB (achieved)
8.0
1.4
10
6
1.2-2
400
16

SuperKEKB
7.0
2.6
10
5
1.5
400
37

Table 6.4: Design parameters, achieved values at KEKB, and required values at SuperKEKB.

179

Frequency (MHz)508.9
R/Q (Ω/cavity)93
Gap length (m)0.243
Diameter of iris (m)0.220
Geometrical factor (Ω)
253
Field ratios*
Eacc /Vc (m−1 )4.11−1
Esp /Vc (m )7.65
Esp /Eacc
1.84
Hsp /Eacc (G/(MV/m))
40.3
Total cryomodule length (m)3.701Volume of Liq. He (L/module)
290
Static loss (W)30
HOM damper size (mm)SBP
4t × 220φ × 120
LBP
4t × 300φ × 150
Maximum HOM impedanceTM011 (kΩ)
2
TM110 (kΩ/m)37
Loss factor for σ=5 mm (V/pC) 1.37 V/pC
* Vc , Eacc , Esp and Hsp are accelerating voltage, accelerating field, surface peak electricfield and surface peak magnetic field, respectively. Eacc is defined as Eacc = Vc /L,
where L is the gap length.
Table 6.5: Geometrical parameters of the cavity module.
beam pipe (SBP damper), while the other is attached on a large beam pipe (LBP
damper). The HOM dampers heavily damp the Q factors of the HOM’s. Geometricalparameters of the cavity module [23] are listed in Table 6.5.
An antenna type coaxial input coupler is attached to deliver the beam power of
400 kW [24]. The inner conductor is made of copper and cooled with water. A
TiN-coated ceramic disk seals the vacuum and supports the inner conductor. The
optimum external Q factor (Qext ) was first set to 70000 for the designed parametersat the beginning of the KEKB operation. This value was changed to 50000 for thehigher current operations than the design beam current. We adjusted the coupling byinserting the inner conductor using a 4 mm thinner metal gasket at the inner conductor
joint. The input and reflected RF power as a function of beam current are shown in180

Figure 6.29: Input and reflected power as a function of beam current.
Without SiC
(kW)
1.3
15.7
8.6
11.7
37.4
-

Backward radiation
Forward radiation
SBL damper
LBP damper
Total
SiC damper (240mm)

With SiC
(kW)
1.4
4.0
9.5
12.8
27.7
26.1

Table 6.6: Calculated HOM power loads with and without SiC damper at the beam
current of 2.6A.
Fig. 6.29 for the cavity voltage of 1.5 MV and 1.2 MV with the Qext of 50000. The
optimum Qext for the operation at SuperKEKB is 60000, however, the present Qext
is applicable since the reflected power is less than 10 kW at the beam current of 2.6
A. Even if the lower cavity voltage operation is required (1.2 MV, for example), thepresent Qext is still acceptable. Therefore, further coupling adjustment is not needed
for SuperKEKB.
The HOM dampers attached on the beam pipes absorb the beam-induced HOM
power. The dampers successfully absorbed the HOM power up to 16 kW without any
troubles at the KEKB operation. However, the HOM power will increase to 37 kW at
the design beam current of SuperKEKB. It is rather difficult to absorb such large HOM
power in the present HOM dampers. Measures for the large HOM power absorption
have to be taken [25], as described in the next section.

181

Figure 6.30: Geometry used in the power flow calculation of the CST-PS solver.

6.3.2

Measures for Large HOM PowerThe most serious issue of the cavity operation at SuperKEKB will be the large HOM
power. The expected HOM power is 37 kW per cavity at the 2.6 A operation witha bunch charge of 10 nC. The present HOM dampers may absorb the HOM power,
however, the temperature rise of the ferrite increases the outgas rate that may trigger
the high voltage breakdown of the cavity. Reduction of HOM power loads is necessary.
Recently, a new power flow calculation of the HOM power was developed using theComputer Simulation Technology: Particle Studio (CST-PS) wake field solver. With
this method the absorbed power at each HOM damper can be calculated. The results
showed that the HOM power load on each damper is not as high as that expected
before, but a significant amount of HOM power is radiated to the downstream throughthe beam pipe. The radiated HOM power becomes a power load on the cavities inthe downstream. The calculation results also showed that an additional HOM damperon the beam pipe could absorb the radiated HOM power. Results of the damper load
calculation with and without the additional SiC damper of 240 mm in length are listed
in Table 6.6 for the beam current of 2.6 A. Figure 6.30 shows a geometry used in the
CST-PS solver. With the additional HOM damper, the present ferrite HOM dampers
can absorb HOM power without difficulties and the radiated HOM power becomes
acceptable for the cavities in the downstream. Furthermore, the additional damper
can be attached on the beam pipe outside the gate valve without vacuum breaking of
the cavity, so that we can avoid the risk of particle contamination.

182

The R&D of the additional HOM dampers is ongoing to optimize its size andsetting position. The SiC material was chosen for the additional damper because
the fabrication of this size is established for the normal conducting cavities, and its
outgas rate is low compared to the ferrite material. Prototype SiC dampers have been
fabricated for the high power testing.

6.3.3

Performance Recovery

In the long term operation at KEKB, the Q factors of several cavities significantly
degraded at 2 MV with strong field emission. The degradation was mainly caused by
the particle contamination at repairs of indium joints or gasket exchange of the input
couplers. The performance of the degraded cavities is still acceptable for SuperKEKB,
since the required operating voltage is 1.5 MV. However, further degradation may
cause serious problems in the long-term operation. Therefore, performance recovery isdesired.
The high pressure water rinsing (HPR) is an effective method to clean the particle
contamination. However, in order to apply the usual HPR, the cavity has to be disassembled from the cryomodule. Furthermore, re-assembly of the cavity after the HPRmakes another risk of leakage at the indium joints or metal gaskets. If the HPR canbe directly applied to the cavity in the cryomodule, we can save time and costs for thedisassembly, and avoid the risk of leakage at re-assembly.
Therefore, we have developed a horizontal HPR (HHPR), which can be directly
applied to the cavity in the cryomodule [26]. This method uses horizontal insertionof a high pressure water nozzle and an aspirator pump inlet through the beam pipe.
Figure 6.31 shows a schematic diagram of the HHPR. The aspirator pump is used
to evacuate the wasted water. We started R&D in 2009 using a test cavity, thenestablished this method. In 2012, the HHPR was applied to recover the performanceof a spare cavity, which was degraded at the repair of the indium joints. The HHPR
was applied to clean the cavity cell and iris for 15 minutes. The Q factors before andafter the HHPR are shown in Fig. 6.32; the Q factor was successfully recovered by the
HHPR. This cavity was installed in the HER of SuperKEKB. Following this success,the HHPR was also applied to another degraded cavity. The Q factor at 2 MV wasdrastically recovered from 2 × 108 to 1.3 × 109 .

183

Figure 6.31: Schematic diagram of the horizontal HPR system.

Figure 6.32: Q factors before the helium leakage, after the degradation and after thehorizontal HPR.

184

6.4

Low Level RF Control System

6.4.1

Preface

The existing analog-based LLRF system had been operated stably for KEKB [27].
While they can also be used for SuperKEKB, a new digital LLRF system is being
developed for higher accuracy and flexibility. In the design of the new LLRF system,compatibility between the existing and new systems was taken into consideration, sothat both systems coexist in different RF stations without problems for the beam
operation. This strategy enables us to replace the existing system with the new systemstep by step, which matches the construction plan with available budget. Furthermore,
it allows us to have timely improvements on the new system based on experiences infuture beam operation.
A prototype of the new LLRF system was fabricated, and a high power test was
performed with an ARES cavity. Good performance of the prototype one was confirmedin the test, and mass production started. Before the Phase 1 commissioning, theanalog LLRF systems of nine RF stations for the ARES in the OHO straight section
will be replaced with new digital ones. After the beam commissioning, the analog
LLRF systems of other RF stations will be replaced with new ones step by step,
according to available budget. Meanwhile, a new digital LLRF for the SCC will be
developed; basically it has the same functions as the new LLRF for the ARES has,but modifications are needed for the tuner control and interlock system for the SCC.
Details of the new digital LLRF system is described in Sec. 6.4.2.
Other improvements required for SuperKEKB LLRF system include: upgrading of
the RF reference distribution and stabilization system and upgrading of the dampers tosuppress longitudinal coupled-bunch instability (CBI) associated with the accelerating
mode of cavities. A new RF reference system is being constructed by using “Phase
Stabilized Optical Fiber” and optical transceivers. A new CBI damper has been developed to meet the requirements for higher damping rate as well as capability of curing
the µ = −2 and −3 modes in addition to the µ = −1 mode. Finally, gap transient
effects and possible mitigations were investigated with an advanced simulation tool,
which treats the transient behavior of the three-cavity system of the ARES. These
topics are described from Section 6.4.3 to Section 6.4.5.

185

6.4.2

New Digital LLRF System

Design concept
The new LLRF control system for SuperKEKB consists of µTCA-standard platformed
FPGA boards and Programmable Logic Controller (PLC) [28]. They have PowerPC
CPU’s running on Linux-OS and an EPICS-IOC is embedded in each of them [29],which can be operated remotely via EPICS-Channel Access. The FPGA’s perform RF
signal control such as feedback (FB) control and cavity tuning like hardware modules,
while the parameters for the RF control are provided from EPICS records. The PLC,
for which the Yokogawa FA-M3 series is adopted, has two CPU modules: one is a normal logic controller and the other is a linux-OS CPU (F3RP61); the former behaves
as a monitoring recorder and slow-interlock system for cooling water flow, temperature, vacuum and so on, while the latter performs as an EPICS-IOC. The operation
sequences such as cavity-start up and auto-conditioning are run by EPICS-sequencers
embedded in the PLC. For new graphical user interface, the CSS-BOY [30] is adopted
as development and runtime environment.
A block diagram of the new digital LLRF control system for an RF station for the
ARES cavity in the SuperKEKB main ring (MR) is shown in Fig. 6.33. It includes
digital feedback loops for the cavity field and tuner control. Figure 6.34 shows a picture of the new LLRF system for one RF station, housed in three 19"-racks. The main
components for the RF signals are installed in the left-side rack, whereas the middle
and the right racks accommodate the PLC unit, GUI, arc sensors, vacuum control, etc.
Figure 6.35 shows a picture of the µTCA digital control unit. It has five FPGA boards:
Digital FB Controller (DFBCNT), Tuner Controller (TNRCNT), Interlock Controller(INTLCNT), RF-Detector Monitor (RFDETMON) and Arc-discharge Monitor (ARCMON). Figure 6.36 shows monitored RF signals and connections between the FPGA
boards.

System components and control mechanics for LLRF control
Figure 6.37 shows a block diagram of the FPGA implemented in the DFBCNT board.
In this system, in-phase and quadrature (I/Q) components of RF signal are handled
for vector control, instead of the amplitude and phase. Therefore, the driving RF iscontrolled by using an I/Q modulator as shown in Fig. 6.33. The I/Q handling method
is one of the most standard techniques for digital RF control in recent days. Required
stability and regulation accuracy in the accelerating field is typically ±1% in amplitude186

Figure 6.33: Block diagram of the new digital LLRF including the ARES cavity FB
control and tuning control. Instead of the amplitude and phase control, the I/Q components of the RF signals are digitally handled by FPGA’s.

187

Figure 6.34: Photo of LLRF System for the SuperKEKB for one klystron.

188

Figure 6.35: Digital LLRF Unit which consists of five FPGA boards based on µTCAstandard platform.
and ±1 degree in phase. But target values for the new LLRF control system are set±0.3% and ±0.3 degrees (both are peak-to-peak values) in the amplitude and phase,respectively, including long term stability such as thermal stability. Then the required
resolutions of the amplitude and phase control are less than 0.1% and 0.1 degrees,
respectively.
The RF monitor signals (508.9 MHz) are down-converted into 10.6 MHz IF signals with a LO signal (519.5 MHz). The IF signals are sampled by 16-bit ADC’s on
the FPGA board at quadruple frequency of the IF, so that the I/Q components are
directory obtained (see Fig. 6.37). In this sampling method called the I/Q-sampling,
the DC component and the second harmonic can be cancelled [31], and both of theorthogonal components of the vectors are almost ideally separated with each other for
high-purity wave signal. Consequently, they can be more accurately measured for any
vector (any phase) within the dynamic range of the ADC compared with the amplitude
and phase detection method. In addition, the phase calibration is simplified by calculating the vector rotation. The LO and clock signals for these boards are generated in
the Distribution Unit (in the left rack in Fig. 6.34) from the reference RF signal.
In the DFBCBT board, proportional-integral (PI) FB control is digitally applied
to both of the sampled I/Q components in parallel, and the control signals are output
from the 16-bit DAC’s to the I/Q modulator, as shown in Fig. 6.37. A selector chooses
one of the klystron output and cavity pickup signal to perform the FB control loop.
The parameters for the IIR digital filters implemented in the loop are also switchedby the selector accordingly, to the values optimized to each loop. The DFBCNT also
189

Figure 6.36: Monitored RF signals and connections between the FPGA’s.

190

detects the klystron output power for the interlock. In addition, a klystron phase lockfunction is implemented in the FPGA, as described later.
Furthermore, the DFBCNT is equipped with measures to cure possible issues related
to the high stored beam current. One is that the I/Q offsets or feed-forward (FF)parameters can be flexibly controlled for beam loading compensation according to thebeam current measured by a DCCT. Another is related to suppression of the CBIassociated with the accelerating mode. As shown in Fig. 6.33, the mode FB signal
coming from a mode damper is combined with the FB control signal. The µ = −1
mode damper used in KEKB is reported in Ref. [1]. A new damper for SuperKEKB,
which treats not only the µ = −1 mode, but also the µ = −2 and −3 modes, will be
described in detail in Sec. 6.4.4. On the other hand, the direct FB control loop usedin the analogue LLRF system is not adopted in the new digital LLRF system, because
the new system is expected to have sufficiently wide band and precision in the feedback
control.
The TNRCNT board controls two tuners of the ARES, one is for the storage (S-)
cavity and the other is for the accelerating (A-) cavity. It monitors the cavity input
signal and three pickup signals of the S-, C-, and A- cavities of the ARES, and calculates
the tuning phases of the S- and A- cavities from these signals. Then it generates
pulse trains to drive the tuner motors according to the tuning phases, as shown in
Fig. 6.36. Theoretical approach for the tuning control of ARES cavity has been studied
in Ref. [32]. The FPGA in the TNRCNT board also has a function to control a piezo
tuner of the SCC, for future use of the new digital LLRF to replace the existing analog
LLRF system for the SCC.
The INTLCNT board switches RF power off when any abnormal operation sign isdetected. It monitors the IF signals with the I/Q-sampling of the input and reflect
RF power and calculates the VSWR. The interlock request signal also comes from theother four boards to the INTLCNT board, as shown in Fig. 6.36. Each of three FPGA
boards, DFBCNT, TNRCNT and INTLCNT, has 16-bit 4-channel ADC’s and 16-bit
2-channel DAC’s. The RFDETMON and ARCMON have eight 14-bit ADC’s each, andacquire waveforms of RF log detectors and photo-detectors, respectively, at 42.4 MS/s
like an oscilloscope. An arc-sensor unit has photo-detectors made of photo-multipliertubes. Large-core optical fibers of 600 µm diameter are used to transfer discharging
flash from the cavity to the arc-sensors.

191

Figure 6.37: Block diagram of FB control and klystron phase lock loop in the DFBCNT.
RF monitor signals are down-converted into IF signals and sampled by ADC’s at 4-timefrequency of the IF (I/Q-sampling). PI-FB control is applied to the I/Q components
separately for vector control.

192

Klystron phase lock loop
The klystron anode voltage is controlled depending on the driving RF power to reduce
collector loss for high efficiency [33]. In a high power test, a phase shift of 80 degreesof the klystron output was observed due to the anode voltage change. Such a large
phase shift will invalidate the I/Q based FB control; according to our calculation andsimulation, an acceptable phase shift for the I/Q based FB control is approximately
within ±50 degrees in our operation condition, which was consistent with the highpower test result.
In order to solve the problem, a klystron phase lock loop (KLY-PLL) is implemented
in the DFBCNT, as shown in Fig. 6.37. For the KLY-PLL, an additional phase-rotation
function is inserted before the DAC outputs to the I/Q modulator. The klystron phaseis detected and compared with the FB-output phase as the reference. The total phaseshift of the klystron, “θ” in the figure, is accumulated by an increment constant tocancel the phase shift, and then the phase rotation parameters (cos θ and sin θ) are
given dynamically by a preset table in 2-degree steps with linear interpolation. The
required loop band is less than 1 kHz, because the response of the anode voltage control
is only about 1 Hz.

LLRF performance evaluation
The FB control stability was evaluated by an “out-of-loop” measurement in the highpower operation. The results for short term stability and regulation resolution is shownin Fig. 6.38. This figure shows the amplitude and phase of the cavity-pickup signal
under FB-control measured by using an RF detector and a mixer, respectively, which
are acquired in a oscilloscope for 4 ms time duration. Some small beat is seen in thephase, though it is negligibly small for our specification. In the whole, sufficiently goodstability was obtained: the regulation resolution in r.m.s is 0.02% in amplitude and0.02 degree in phase.
Figure 6.39 shows phase noise spectrum of the ARES cavity pickup signal under
FB control in the frequency range from 10 Hz to 10 MHz. The signal source used forthis measurement was Agilent E8663D-UNY. The noise is reduced above 10 kHz due
to the frequency property of the ARES cavity which has a high-Q value. Sufficiently
low noise characteristic was achieved: the time jitter obtained from integral of thisspectrum is 71 fs (rms), while the source signal has a 60 fs (rms) time jitter in thesame integral region.

193

Figure 6.38: Short-term amplitude and phase stability under the FB control evaluatedby an out-of-loop measurement. Obtained regulation resolution (r.m.s) is 0.02% inamplitude and 0.02 degree in phase.

Figure 6.39: Phase noise spectrum of the ARES cavity pickup signal under the FB
control (10 Hz ∼ 10 MHz). The time jitter obtained by integral of this spectrum is
71 fs (rms), while the source signal has a 60 fs (rms) time jitter in the same integral
region.

194

Disturbance rejection characteristics inside the closed loop is shown in Fig. 6.40.
The disturbance such as klystron noise or fluctuation is assumed in this evaluation.
Modulation magnitude and phase response at base band are plotted for various FBgains (P: proportional gain, I: integral gain). The values of P and I in the figure arejust setting values in this specific digital system. The real FB gains for continuous
system (P 0 , I 0 ) have following relations: P 0 = P /8 and I0 = I × 2−15 × CLK, where
CLK is 85 MHz.
The solid lines indicate calculated transfer functions for the tuned cavity, and thecircle marks are measured data in a high power test including the klystron property.
A good agreement is seen between the calculation and measurement. The disturbancenoise reduction around 10∼30 kHz is approximately −10 dB: this frequency range isabout the same as the bandwidth of the ARES. The response characteristics for beamloading are almost similar with the data shown in Fig. 6.40. The effect of synchrotron
oscillation (∼2 kHz) is reduced to approximately −20 dB by the FB control. On theother hand, the effects of revolution (∼100 kHz) such as the bunch gap transient simply
conform to the cavity response. The amplitude and phase modulation due to the bunch
gap transient can be effectively eliminated by neither the FB nor FF control of LLRF,
because the bandwidth of klystrons is about 100 kHz and the bandwidth of the loop
is less than 100 kHz corresponding to the group delay of longer than 1 µs, which aremuch lower than 1 MHz needed for the compensation.
Temperature characteristics for long-term stability is also important. Our target
values for the stability are less than ±0.3% in amplitude and ±0.3 degrees in phase,respectively. Since temperature change during operation with air conditioning is typically ±2 deg. C, the acceptable temperature coefficient is about 0.1%/deg. C in amplitude and 0.1 deg. /deg. C in phase, respectively. From measurements of temperature
characteristics of components in the LLRF, it was found that band pass filters (BPF)
implemented in the down-converter units are the most dominant for thermal stability.
However, the BPF is indispensable for the LO generation and pick-up RF monitoringin our system. In order to improve the thermal stability, cavity type BPFs were chosen
instead of lumped-constant circuit type ones, because the cavity type one has smaller
scattering in characteristics for different manufacture lots. Furthermore, fine tuning
was applied to every BPF; an example of the results is shown in Fig. 6.41. After thefine tuning, the phase property was significantly improved. Although the amplitude
property was slightly degraded in this specific case shown in Fig. 6.41, it is sufficiently
small both before and after the tuning. Since the amplitude and phase properties
are not independent, an iteration work of the adjustment is needed to optimize both

195

Figure 6.40: Disturbance rejection characteristics inside the closed loop (e.g. driver
amplifier noise) for various FB-gains (P: proportional gain, I: integral gain). The solidline indicates the calculation for the tuned cavity, and the circle marks are measured
results in a high power test. Response to beam loading has similar property with thisplot.
characteristics.
Figure 6.42 shows measured thermal stability of the overall LLRF system before
and after the improvement of the BPFs. In the figure, trend histories of monitored
amplitude and phase are plotted for two days. The green line indicates the room
temperature. The red and blue lines correspond to the cavity-pickup channel (ch 4)
and the reference channel (ch 1), respectively. Before the improvement, the stability
did not satisfy the requirements. After the improvement, the temperature coefficient of
0.06%/deg. C in amplitude and 0.09 deg. /deg. C in phase was obtained, which satisfy
the requirements. Further improvement was also added in the system: by taking
the relative phase between the cavity pickup and the reference, that is, the difference
between Ch4 and Ch1, then 0.02 deg. /deg. C of phase stability is expected, as shownin the lower right of Fig. 6.42. This can be justified by that both BPFs for ch 4 and ch 1
are housed in a common module case and thus they are affected by similar temperaturechange.

196

Figure 6.41: Fine-tuning of BPF temperature characteristics was applied for improvement of thermal stability.

Figure 6.42: Measured thermal stability of the overall LLRF system before and after
the BPF-improvement. Trend histories of monitored amplitude and phase are shown.

197

Figure 6.43: Transmission paths of the optical cables installed in the accelerator tunnel
for the new RF reference system.

6.4.3

RF Reference Distribution System

For the RF reference of the LLRF control, the required phase stability during beam
operation is 0.1 degrees (pk-pk). The RF reference signal of 508.9 MHz is optically
distributed from the central control room (CCR) to each RF section, the damping ring,and the Belle-II detector by using “Phase Stabilized Optical Fiber (PSOF)” cables.
The PSOF cable has very small temperature coefficient of less than 1 ppm/deg. C(5 ps/km/deg. C). Figure 6.43 shows transmission paths of the optical cables installedin the accelerator tunnel between the stations. They are distributed from the CCR bymeans of “Star” topology links.
To satisfy the required phase stability, a phase feedback control (or phase lock loop)
is needed to compensate for thermal drift of each optical transfer line, even using the
PSOF cables. For this we have developed an optical transmitter and receiver system forthe thermal drift compensation. A block diagram of this system is shown in Fig. 6.44.
The transmitter system is located at the CCR and the receiver systems are locatedat each control room of the RF section. In the transmitter system, the reference
signal of wavelength λ1 is optically amplified and divided into eight transfer lines.
The transferred signal received at each RF section is, after converted to a different

198

Figure 6.44: Functional block diagram of the RF reference distribution system.
wavelength λ2 for isolation, returned back passing through the same fiber cable to the
CCR by means of Wavelength Division Multiplex (WDM) method. The phase of the
return signal is digitally measured by a µTCA-platformed FPGA with direct-sampling
method [34] without down-conversion, and then a variable optical delay line (VODL)
is controlled to cancel the phase change. Every transfer line has a VODL inserted
after the optical divider, and each of them is controlled by the corresponding FPGA
individually, as shown in Fig. 6.44. The VODL is a reflection-type optical delay line
like a trombone, and it is equipped with a pulse-driven motor, as shown in Fig. 6.45.
The FPGA outputs pulse trains to control the VODL to compensate for the phasedrift, so that the phases of all RF section are directory locked with a master oscillator
at the CCR.
The performance of the phase drift compensation system was evaluated with ameasurement setup shown in Fig. 6.46. Phase stability of the transferred signal wasmeasured by using a vector volts meter (VVM) as temperature of the optical cable
was changed. A normal optical fiber of the length of 100 m, which has a large thermal
coefficient (1.7 deg. /deg. C for 100 m), was used in the transmission. The result isshown in Fig. 6.47: the red line indicates the phase of the transferred signal measured
by the VVM, and the dashed blue line is the pulse counts sent to the VODL from the199

Figure 6.45: Photo of variable optical delay line (Santec Corp., ODL-340), which isadditionally equipped with pulse-motor driving mechanism and limit switches.
FPGA. The pulse counts correspond to the phase change of 17 degrees, which is thesame value to compensate for the phase change of the cable due to the temperaturechange. The required phase stability of ±0.1 degrees was obtained with this driftcompensation control system.
The optical transmitter and receiver (E/O and O/E) are the same as those developed for the J-PARC Linac [35], and they have shown long-term reliability during
ten-years J-PARC operation. Each of them is equipped with a Pertier device fortemperature stabilization. Figure 6.48 shows the phase noise of the optically transmitted signal via the E/O and O/E including an optical amplifier. Sufficiently small
phase noise of less than −100 dBc/Hz above 10 Hz was achieved. The noise floor at−140 dBc/Hz due to the E/O and O/E conversion is observed above 10 kHz. This is
not a problem, because the frequency range above 10 kHz is out of the bandwidth of
the accelerating cavity. The time jitter obtained from the integral of the spectrum from
1 Hz to 10 MHz is 160 fs (rms), which corresponds to the RF phase of 0.03 degrees at
509 MHz. This value includes the time jitter of 80 fs (rms) in the same integral region
due to the signal source, Agilent E8663D-UNY, used in this measurement.

6.4.4

CBI Damper

Excitation of longitudinal coupled bunch instabilities (CBI) due to the accelerating
mode of RF cavities is a serious concern for a large circumference ring with a highcurrent stored beam. The growth rate of the CBI due to RF cavities can be estimated200Figure 6.46: Evaluation setup of the VODL control for the temperature drift compensation.

Figure 6.47: Transferred signal phase measured by a vector volt meter (red solid line),
and the pulse counts to control the VODL (blue dashed line) in the temperature driftcompensation system. Temperature at the cables was changed from 30 to 20 deg. C.

201

Figure 6.48: Sideband phase noise spectrum of optically-transferred signal (output of
the receiver system) in the reference distribution system including a optical amplifier.
Noise floor at −140 dB comes from the optical transceiver (E/O and O/E). The time
jitter obtained from the integral of the spectrum from 1 Hz to 10 MHz is 160 fs (rms),
including the time jitter of 80 fs (rms) due to the signal source.
from the cavity impedance Zc asτµ−1 = AIb∞X{ωp(µ+) ReZc (ωp(µ+) ) − ωp(µ−) ReZc (ωp(µ−) )},p=0

ωp(µ+)= (ph + µ)ω0 + ωs ,(6.1)

ωp(µ−) = {(p + 1)h − µ}ω0 − ωs ,where A is a coefficient which depends on the accelerator operation parameters, Ib isthe beam current, ω0 is the revolution angular frequency, ωs is the angular frequencyof the synchrotron oscillation, h is the harmonic number, and µ is the mode number of
the CBI. In usual operation with the optimum tuning of the cavities to minimize theinput power, the cavities are detuned to the lower side of the RF frequency, ωrf = hω0 ,to compensate for the reactive component of beam loading. Then the excitation of theµ = h − 1 mode (called the µ = −1 mode), µ = h − 2 mode (µ = −2 mode), and soon, will be a concern. In the KEKB operation, even with the ARES and SCC cavities,
the µ = −1 mode was excited at the beam current of about 1 A. In order to suppress
the CBI, a feedback system, so called the µ = −1 damper, was implemented [1, 36].
Fig. 6.49 shows a block diagram of the µ = −1 damping system used in KEKB. It
consists of a single sideband pass filter (SSBF) and a digital narrow bandpass filter(DBPF).
202

Figure 6.49: Block diagram of the µ = −1 mode damper system used in KEKB
operation.

Figure 6.50: Illustration of filtering property of the SSBF (left) and the DBPF (right).

203

Figure 6.50 illustrates filtering functions of the SSBF (left) and the DBPF (right).
The SSBF transmits only the lower sideband of hω0 (= ωrf ) and rejects the higher(µ+)
sideband: the frequencies contributing to the excitation of CBI, ωp
in Eq. 6.1, arelocated in the lower side of ωrf for the modes µ = −1, −2, −3, and so on. The DBPF
transmits only the offset-frequency (baseband) of −µω0 − ωs (µ = −1 for the case of
KEKB), which corresponds to the exciting oscillation frequency in the single sideband.
The growth rate of CBI in SuperKEKB is evaluated by Eq. 6.1; the result is shownin Fig. 6.51 for the LER (upper plot) and HER (lower plot) as a function of stored
beam current. The solid lines indicate the growth rates in normal operation condition,
where all cavities are operated. The growth rate of the µ = −1 mode at the design
beam current is much higher than that in KEKB. The dashed lines indicate the growth
rates for the case where one cavity is parked at −150 kHz away from the RF frequency
due to some trouble in the RF system. In this case, the µ = −2 mode needs to be cured
in addition to the µ = −1 mode. Furthermore, in cases when the parked cavity needs
to be located at an other frequency, for example at −250 kHz, or when more cavities
need to be parked, the µ = −3 mode may also need to be cured. Consequently, a
new advanced damper system has been developed for SuperKEKB, which has a higher
damping rate as well as capable of curing not only the µ = −1 mode but µ = −2 and−3 modes [37].
A block diagram of the new CBI damper is shown in Fig. 6.52. The DBPF of the
new CBI damper is composed of three independent circuits in parallel connection, eachadjusted to one of the µ = −1, −2 and −3 modes. The functional block diagram of eachcircuit of DBPF, implemented in a FPGA, is shown in Fig. 6.53. It has two first-order
IIR low-pass filters to make the passband narrower. The center frequency (−µω0 −ωs ), the bandwidth, the gain and output phase of the passband can be controlled
independently for each mode. The SSBF of the new CBI damper utilizes the I/Q
modulator and demodulator of recent commercial products. Measured characteristicsof the new SSBF is shown in Fig. 6.54, together with that of KEKB for comparison.
The rejection property for the higher frequency side is significantly improved for the
new damper by 40 dB, compared to that used in KEKB. The feedback performance ofthe new CBI damper system was evaluated in a test bench by using a simulant cavity.
As shown in Fig. 6.55, the impedance is successfully suppressed at the frequencies
corresponding to the excitation of the µ = −1, −2 and −3 modes.

204

Figure 6.51: Estimated growth rate of CBIs due to the acceleration mode as a functionof stored beam current in SuperKEKB. The upper and lower plots are for the LER and
HER, respectively. Solid lines indicate the cases for normal operation when all cavities
are powered. Dashed lines indicate the cases when one cavity is parked at −150 kHz
away from the RF frequency due to some trouble in the RF system.

205

Figure 6.52: Configuration of the new CBI damper for SuperKEKB. The DBPF is
composed of three independent circuits in parallel connection, each of which is adjusted
to one mode.

Figure 6.53: The functional block diagram of DBPF, which is implemented in FPGA.

Figure 6.54: Measured characteristics of the new SSBF. The rejection property for thehigher frequency side band is significantly improved compared to the damper used in
KEKB.
206

Figure 6.55: Feedback performance of the new CBI damper system evaluated with asimulant cavity. The impedance is successfully suppressed at the frequencies corresponding to the excitation of the µ = −1, −2 and −3 modes.

6.4.5

Bunch Gap Transient

Transient effect caused by an abort gap inserted in a bunch train is a concern for acollider with multi-bunch high current beams. The train gap modulates the amplitude
and phase of the accelerating field in the cavities, then the synchronous position changes
from bunch to bunch along the train. Relative position shift between the colliding
bunches makes a longitudinal displacement of the collision point from bunch to bunch.
In the KEKB operation, the phase shift along the bunch train was observed. The
measured phase shift along the bunch train agreed well with a simple simulation result
for the bunches in most parts of the train. However, a rapid phase change of a few
degrees was found at the leading part of the train, which was suspected to be attributed
to the excitation of parasitic 0 and π modes of the ARES cavity [38]. No degradation
was observed of the luminosity due to the bunch gap transient in the KEKB operation.
However, in the SuperKEKB operation, the beam phase difference due to the gap
transient will be much larger than that of KEKB due to higher beam currents, eventhe gap length will be reduced from 5% of the ring in KEKB to 2% in SuperKEKB by
improving the rise time of the abort kicker. Furthermore, for the nanobeam collision
scheme, where bunches collide at a large crossing angle with a very small βy∗ , this effectmay cause some unknown crucial issues to the colliding beams: not only luminosity
degradation but even some unknown serious degradation of the beam performance may
occur in the worst case.
207

Figure 6.56: Time-domain simulation results of amplitude and phase modulation
caused by 2%-bunch gap in LER-ARES cavity. This simulation is including threecavity structure of ARES.
To evaluate the bunch-gap transient effect for SuperKEKB, we developed a new
simulation method [39], which takes into account the parasitic 0 and π modes by treating the three-cavity system of the ARES, instead of an equivalent single cell used in
the previous simulation [27]. The gap transient behavior was evaluated using the new
simulation with typical operation parameters with the design beam currents of SuperKEKB. Figure 6.56 shows modulation in time-domain of the amplitude and phaseof an ARES cavity field in the LER. In the figure, a periodic interval of 10 µs corresponds to the revolution frequency of 100 kHz and the length of the abort gap is 2%of the circumference, ie. ∆tg = 200 ns. The modulation of the amplitude and phase in
the main part of the train except for the leading bunches is approximately 0.8% and 2
degrees, which agrees well with an analytical calculation given by [40]
 
 
∆Vc
ωrf R
ωrf R
=
Ib ∆tg · tan φacc , ∆φ =Ib ∆tg ,
(6.2)
Vc
2Vc Q
2Vc Q
respectively. In the gap region and at the leading bunches, however, a large phasechange of 7 degrees (pk-pk) is seen, as shown in Fig. 6.57, which is a zoomed viewof Fig. 6.56 around the gap region. It was confirmed that the large phase change isattributed to the excitation of the parasitic 0 and π modes of an ARES cavity.
Figure 6.58 shows simulation results for the case of the HER, which has two typesof cavities: the ARES and SCC. The rapid phase change is also observed for the ARESin the HER, similar as the ARES in the LER. On the other hand, the SCC has no208

Figure 6.57: Zoomed plot of the phase change shown in Fig. 6.56 at the leading bunches
after the bunch gap. The phase of the leading bunches of the train changes approximately 6.5 degrees, which is attributed to the excitation of parasitic 0 and π modes of
the ARES cavity.
rapid phase change at the leading bunches, because the SCC’s are single-cell cavities.
The phase modulation in the most part of the train except for the leading bunches islarger for the SCC compared to the ARES. The vector sum of the field of all SCC and
ARES cavities in the HER, which is the field that the HER beam feels in one turn, isshown in Fig. 6.59.
Figure 6.60 (left) shows the phase difference between the LER and HER (∆φHER −∆φLER ), obtained from Fig. 6.56 and 6.59. The red solid line indicates the phasedifference between the LER and HER. The phase difference in the most part of the
train except for the leading bunches is well less than ± 1 degree. The relative phaseshift at the interaction point (IP) between both beams for these bunches is ±(∆φHER −∆φLER )/4 = ±(2.5 − 2.0)/4 = ±0.125 degrees, which corresponds to a longitudinal
displacement of only 0.04 σz for the bunch length σz of 5 mm. The right side ofFig. 6.60 shows a zoomed plot around the gap region of the left side of Fig. 6.60. As
seen in the figure, at the leading bunches, the phase difference amounts to 5.5 degrees,
which may cause some harmful effects for SuperKEKB. As described in Sec. 6.4.2, thegap transient effect can be effectively eliminated neither by the FB nor FF control.
In order to avoid possible harmful effects to the colliding beams, mitigation mea209

Figure 6.58: Time-domain simulation of phase modulation due to the gap transient for
the HER, which has two kinds of cavities: the ARES and SCC.

Figure 6.59: Phase modulation of the vector sum of ARES and SCC voltage simulatedfor HER.

210

Figure 6.60: Phase difference between the LER and HER; the red solid line indicates∆φHER − ∆φLER . A zoomed plot around the gap region is shown in the right side.

Figure 6.61: An example of the mitigation to avoid possible harmful effects to thecolliding bunches due to the gap transient: the gap delay for the HER and filling
pattern change for the LER.

211

Methodno cureHER gap delay
HER gap delay
LER 2 steps +HER gap delay

Bunch
gap

HER
delay
[ns]

2%
2%
3%
2%

0
200
300
160

Phase difference|∆φHER − ∆φLER |[deg.]
leading
rest
5.5
0.9
2.4
0.9
<0.2
1.6
0.4
0.5

Longitudinal
displacement@IP

Num. ofcollidingbunches0.44 σz0.19 σz0.13 σz0.07 σz

−2.0%
−4.0%
−1.6%

Table 6.7: Results of the proposed mitigation measures to reduce the phase difference
between the colliding beams.
sures were also investigated. Two mitigation methods were proposed, as shown in
Figure 6.61. One method is simply making a delay of the HER gap timing with respect to the LER gap at the cost of a reduced number of colliding bunches. Then thecollision is avoided for the leading part of the LER train that has the large rapid phasechange. Another method is changing the bunch fill pattern: for example, the LER
bunch train is filled up in two steps. Then the phase shift at the leading bunches of the
LER is significantly reduced by cancellation of the two step responses of the opposite
RF phase. The results with these measures are summarized in Table 6.7. The relative
phase difference at the leading part of the colliding bunches is effectively reduced toless than 1 degree. It should be noted that the optimization of the parameters for the
mitigation strongly depends on beam operation conditions, which will be investigatedduring beam operation. For more details of the new simulation and the mitigation
results, refer to Ref. [39].

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