Development of a New RF Accelerating Cavity
Loaded with Magnetic Alloy Cores
Cooled by a Chemically Inert Liquid for
Stabilizing and Enhancing the Performance of
J-PARC Ring Accelerator

Yuichi Morita
Department of Physics, Graduate School of Science
The University of Tokyo

Abstract
J-PARC (Japan Proton Accelerator Research Complex) is a proton accelerator constructed in Tokai-mura, Ibaraki, Japan. J-PARC was designed to produce the world’s
most intensive proton beam and provide it to advanced research facilities for the wide
range of field. T2K (from Tokai to Kamioka) is one of the most important experiment.
It is a long baseline neutrino experiment. It requires 5 × 1021 POT in approximately
5 years which corresponds to 0.75[MW]. To produce proton beam of this intensity, therepetition rate of the accelerator is planed to be increased. This method requires theaccelerating gradient to be enhanced, so that the accelerating cavity will be put in thehard environment to accelerate a large beam current in a long term. A powerful and stable accelerating cavity is indispensable. The presently installed cavities are loaded withcores made of ”FINEMET”. FINEMET is a magnetic alloy which is produced by Hitachi
Metals, Ltd.. A stable operation of the presently installed cavities in Rapid-Cycling Synchrotron (RCS) has not established yet, because they have a problem that the FINEMET
cores are damaged while the cavities are in operation. We are developing a new accelerating cavity which can realize the stable and powerful operation. We simulated the thermal
stress in the core, and performed a test of compressing samples of the core. The cause of
the damage was identified as a buckling which was caused by the thermal stress in thecore. We showed the core without impregnation is favorable to prevent the buckling. The
development of the new cavity is based on these results. The cores for the new cavity
have unique structures. They are not impregnated and each core is radially separated
into three. Fluorinert is used as the coolant. Fluorinert is a chemically inert liquid, sothat it is suited for cooling FINEMET cores which is subject to corrosion. Fluorinert
flows in the flow channel which is formed on the surfaces of the radially separated cores.
The flow channel makes Fluorinert turbulent, so that a high cooling eﬃciency is realized.
We designed RF structure of the cavity and the flow channel with FEM (Finite Element
Method) simulators. We assembled a prototype of the new cavity, and prepared the test
facility. This is the first case to use three dimensional FEM simulators for developinga cavity loaded with magnetic alloy cores. We measured the resonance frequency, theshunt impedance and the Q factor of the prototype cavity and verified they satisfied therequirements of RCS. The temperature on the surface of the small core was measured withthe thermo paint. The value was consistent to that was obtained from the simulation.
The eﬀective heat transfer coeﬃcient was obtained by measuring the time constant of thetemperature decrement of Fluorinert, and the value was consistent to that was obtained
from the simulation in 20% . The heat transfer coeﬃcient on the surface of the small core
was obtained with the simulation. The value is consistent to that was calculated with theempirical equation. The value surpassed that of presently installed cavity over 60[L/min].
We supplied the power to the prototype cavity up to 10[kW], and it worked stably. Thisis the first development of the cavity loaded with magnetic alloy cores, which is able tobe operated stably with the large input power of 10[kW] per core. Adopting this newcavity is the most realistic way to stabilize and enhance the performance of the J-PARC
ring accelerators.

Contents
1 Introduction
1.1 Physics goals and requirements to the accelerator system . . . . . . . . . .
1.2 Research background arises from the aspect of the accelerating cavity . . .
1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2
2
2
5

2 Accelerator complex at J-PARC
2.1 Ion source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Linac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 RCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 RF system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Accelerating cavity . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 FINEMET cores . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Power loss in the core and Cooling of the heat load . . . . . . . . .
2.3.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 MR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6
7
9
15
17
17
17
18
19
19

3 Numerical analysis and Experiment to identify the cause of the bucklingon RCS cores24
3.1 Background of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Calculation for power loss per core . . . . . . . . . . . . . . . . . . . . . . 25
3.3 Calculation for Thermal Stress . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 Structure of presently installed RCS cavity . . . . . . . . . . . . . . 29
3.3.2 A measurement for a thermal conductivity of FINEMET core . . . 30
3.3.3 Calculation for thermal stress with micro model . . . . . . . . . . . 32
3.4 Compression test for the core . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 Development of a new RF accelerating cavity loaded with FINEMET
cores cooled by Fluorinert
48
4.1 Selection of coolant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Overview of the accelerating cavity for RCS . . . . . . . . . . . . . . . . . 49
4.3 FINEMET core module . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Fluorinert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 Swelling test for G-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.6 Erosion test of the core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.7 RF designing for the new cavity . . . . . . . . . . . . . . . . . . . . . . . . 58

CONTENTS

ii

4.7.1
4.7.2

61

4.8

4.9

Simulations for electromagnetic fields . . . . . . . . . . . . . . . . .
Thermo-fluid simulation, and design for the flow channel with a half
sized flow channel . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assembly of the prototype cavity . . . . . . . . . . . . . . . . . . . . . . .
4.8.1 Assembly of the core module . . . . . . . . . . . . . . . . . . . . . .
4.8.2 Assembly of the prototype cavity . . . . . . . . . . . . . . . . . . .
RF test facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9.1 RF source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9.2 Cooling system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9.3 Matching box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9.4 Interlock system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65
70
70
72
72
72
73
74
76

5 RF test
5.1 Test stand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Measurement of temperature rise of Fluorinert . . . . . . . . . . . . . . . .
5.3 Measurement of the shunt impedance . . . . . . . . . . . . . . . . . . . . .
5.4 Q factor of the prototype cavity . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Cooling eﬃciency of the prototype cavity . . . . . . . . . . . . . . . . . . .
5.5.1 Measurement of temperatures on the surfaces of the cores with athermo paint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Evaluation of a heat transfer coeﬃcient on the surface of the core .

77
77
78
79
80
80

6 Summary of performance of the prototype cavity and Discussion

86

7 Conclusions

90

A Simplification of the core model against electromagnetic fields

94

B Transformation between LR series and parallel circuits

96

C Measurement of a specific heat of a FINEMET core at KEK

98

80
83

D Calculations of heat transfer coeﬃcients100
D.1 Laminar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
D.2 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
E Calculations for shunt impedances of a presently installed RCS core anda new configuration core103
F A characteristic of µ0 Q[72]106

G Selection of µs and µp for simulations of electromagnetic fields[73]109

H A relation between a heat transfer coeﬃcient and a time constant110

CONTENTS

I

1

Physics
111
I.1 T2K experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
I.1.1 Accurate measurement of νµ disappearance parameter . . . . . . . . 112
I.1.2 Discovery of νµ → νe . . . . . . . . . . . . . . . . . . . . . . . . . . 113
I.2 Search for µ− − e− conversion . . . . . . . . . . . . . . . . . . . . . . . . . 115

J An RF accelerating cavity loaded with magnetic cores for a proton andion synchrotron
118
J.1 A cavity loaded with ferrite cores . . . . . . . . . . . . . . . . . . . . . . . 118
J.1.1 Ferrites for accelerating cavites . . . . . . . . . . . . . . . . . . . . 119
J.1.2 Classification of cavities loaded with ferrite cores . . . . . . . . . . 119
J.1.3 Coaxial type cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
J.1.4 Drift tube type cavity . . . . . . . . . . . . . . . . . . . . . . . . . 126
J.2 A cavity loaded with magnetic alloy cores . . . . . . . . . . . . . . . . . . 127
J.2.1 An RF cavity in National Institute of Radiological Science . . . . . 127
J.2.2 An RF cavity in Heidelberg Ion Beam Therapy . . . . . . . . . . . 129

Chapter 1
Introduction
When a proton collides to a target, a variety of secondary particles such as kaon, pion,
neutron, antiproton are produced. Secondary particles are useful for material and life
sciences, and the characteristics of themselves are also investigated. To activate advanced
researches using secondary particles, the world’s most intensive proton beam accelerator
facility was built at Tokai-mura, Ibaraki, Japan. The accelerator named J-PARC (Japan
Proton Accelerator Research Complex) was built as a joint project between KEK and
JAEA. Many kinds of research field, such as, nuclear and particle physics, materials
science, life science are carried out there.

1.1

Physics goals and requirements to the accelerator
systemOn behalf of the experiments, T2K (from Tokai to Kamioka) is introduced in this section.
T2K is a long baseline neutrino oscillation experiment. νµ which is generated at J-PARC
flies to the detector (Kamiokande) in Kamioka, Gifu. The main goal of T2K is thediscovery of νµ → νe oscillation. This oscillation is the unique mode which has notdiscovered yet, and is expected to show the notice for CP violation measurements which
will be performed in the future. The relation between integrated beam power and sin2 2θ13
is shown in Figure 1.1. νµ → νe oscillation is expected to be discovered when sin2 2θ13
is larger than 0.018[1]. This condition corresponds to over 3750[kW×107 s]. It takes five
years to reach this value if the beam power is 0.75[MW] and the accelerator is operated
for 107 seconds per year. Therefore, the enhancement of beam is crucial.

1.2

Research background arises from the aspect of
the accelerating cavity

J-PARC accelerator has been designed to provide the world’s most intensive proton beam.
Main components are listed below.
◦ Ion source1.2 Research background arises from the aspect of the accelerating cavity

3

Figure 1.1: The relation between integrated beam power and sin2 2θ13 [1]◦ Linac◦ RCS (Rapid-Cycling Synchrotron)◦ MR (Main Ring)
The ion source produces negative hydrogens. The linac is a linear accelerator which
accelerates negative hydrogen beam up to 181 MeV. RCS is a ring accelerator which
accelerates a proton beam up to 3 GeV. MR is a ring accelerator which accelerates the
proton beam up to 30 GeV. A bird’s view of the J-PARC accelerator is shown in Figure
1.2.
The two rings are constructed for the experiments which needs a few GeV range beamand those needs a few tens GeV range beam. The total length of Linac is approximately
330 m, the circumference of RCS and MR are approximately 350 m, 1.6 km respectively.
The accelerator is at 15 m underground.
J-PARC is able to produce better results than other accelerator facilities, becauseof its unprecedented intensity of proton beam. The high beam energy and the large
beam current provide high production eﬃciency of secondary particles. Research projects
require that J-PARC accelerator supplies beam of kW order in both regions of GeV energy
and a tens of GeV energy. The synchrotrons of J-PARC is consisted with two rings.
We developed a new type of an accelerating cavity for RCS. The development of thiscavity is introduced in this thesis. The background of the development is shown below.
◦ Accelerating cavities which are installed in both synchrotrons are loaded with FINEMET
cores. As mentioned in the latter section, FINEMET is a metallic alloy whose satu-

1.2 Research background arises from the aspect of the accelerating cavity

4

Nuclear and Particle Physics Facility( Hadron Hall )Materials and Life Science Experimental Facility
Pulsed nuetron source, Muon source

Transmutation Experimental Facility
Second Stage

Neutrino Experimental Facility
To Super Kamiokande

Linac
330 m

3 GeV Synchrotron
Circumference 350 m
25 Hz, 1 MW

30 GeV Synchrotron
Circumference 1,600 m
0.75 MWFigure 1.2: A bird’s view of the J-PARC accelerator[2]ration magnetic-flux-density and Curie temperature are enough high, and this characteristic supports the high accelerating gradient with a high input power. However,presently installed RCS accelerating cavities have not been operated stably, becauseof the decrements of their impedances caused by damages on the cores.
◦ FINEMET is a Fe-based material, so that it is subject to corrosion. They are water
proofed to avoid touching water which is used as the coolant. However, the corrosion
is still concerned for long term operation. This concern is common in both RCS
and MR.
For the first issue, we simulated the thermal stress in the RCS core and compressed
samples of the core. Comparing the results of the simulation and the compression test,
we identified the damage as a buckling caused by the thermal stress in the core. Details
are shown in the next chapter.
For the second issue, Fluorinert is selected as a coolant for the new cavity. Fluorinert
is a liquid which is chemically inert, so that no corrosion is expected.
We developed a prototype cavity. The core for this cavity is not impregnated withepoxy resin to avoid the buckling, and is radially separated into three. These treatments
help the core not to be damaged by the thermal stress. Fluorinert flows in the flow channel
which is formed on the surface of the core, and is expected to be turbulent. Details are
given in Chapter 4.

1.3 Outline of the thesis

1.3

5Outline of the thesis

In chapter 2, details of the J-PARC accelerators are introduced. In chapter 3, the study
for identifying the cause of the buckling on the cores is shown. Chapter 4 describes thedevelopment of the new RF accelerating cavity loaded with FINEMET cores cooled by
Fluorinert. The results of the RF test of the prototype cavity are shown in Chapter 5.
Chapter 6 is the summary of performance of the prototype cavity and shows Discussion.
Finally, the thesis is concluded in Chapter 7.

Chapter 2
Accelerator complex at J-PARC
This chapter introduces the accelerators in J-PARC. The layout of the accelerator complex
is shown in Figure 2.1. It is consisted with three accelerators.
◦ 181 MeV Linac◦ 3 GeV Rapid-Cycling Synchrotron (RCS)◦ 30 GeV synchrotron (MR)

Figure 2.1: Layout of the accelerator complex[2]2.1 Ion source

2.1

7

Ion source

Particles generated at the ion source at J-PARC are negative hydrogens (H− ). They
travel in Linac, then two electrons are stripped at the injection to RCS and become
proton beams. The use of negative hydrogens stands on following reasons.
The harmonic number of RCS is two, which means two bunches are accelerated at
the same time. We should compose two bunches in RCS by superposing intermediatebunches which are injected from Linac to RCS one after another. The schematic view of
the injection is shown in Figure 2.2.
Electromagnets bend the orbits of intermediate bunches at the injection, and theinjected bunches and circulating bunches are superposed. If the injected bunch is anegative hydrogen, bending directions of an injected bunch and a circulating bunch areopposite and the beams can be superposed as shown in left-hand-side of Figure 2.2. If
the injected bunch is a proton, the bending direction of the injected bunch is same asthat of the circulating bunch and they cannot be superposed as shown in right-hand-sideof Figure 2.2[13].

Figure 2.2: (left) Negative hydrogens are injected. Magnets SB1 and SB2 bends theinjecting and circulating beams to opposite directions, so that they are able to be superposed. (right) Protons are injected. The injecting and circulating beams are not able tobe superposed.
The structure and parameters of the ion source are shown in Figure 2.3 and Table 2.1
respectively. The structure inside plasma chamber is the cylinder whose inside diameteris 100 mm and inside length is 130 mm. A filament made of LaB6 is installed at the centerof the top flange, which generates a source plasma with arc discharges[14]. Equations ofgeneration and extinction reactions of hydrogens are shown below.
Generation: there are two steps for reactions. ν, ν 0 are excited states of molecules[15].
H2 (ν) + e(high velocity) → H2 (ν 0 ) + e(ν < ν 0 )
H2 (ν 0 ) + e(low velocity) → H − + H 0

(2.1)
(2.2)

2.1 Ion source

8

Extinction: there are three reactions.
e + H− → e + H0 + e
H+ + H− → H0 + H0
H 0 + H − → e + 2H 0 or H2

(2.3)
(2.4)
(2.5)

As shown in Figure 2.4, the extinction reaction is active in higher electron temperature.
To suppress the extinction reaction, magnetic field of permanent magnet is applied.
The field prevents high temperature electrons from entering the down stream of the plasma
generation room (close to the beam extraction system). It is called a ”magnetic filter”.
The beam extraction system is composed with plasma electrodes (PE), extraction electrode (EXE), and ground electrodes (GE). Voltages of about 10 kV and 40 kV are applied
between PE and EXE (extraction voltage), EXE and GE (accelerating voltage), respectively. Therefore, the extracted negative ion beam has 50 keV[14].

Figure 2.3: A schematic view of the ion source[14]2.2 Linac

9

Table 2.1: Parameters of the ion source[14]Parameter
Value
Beam Energy
50 keV
Beam Current∼ 32 mA
Beam Pulse Length / Repetition
100µs / ≤25 Hz
Arc Pulse Length / Repetition Rate 350µs / 25 Hz
Filament Voltage / Current
10.2 V / 120 A
Arc Voltage / Current
146 V / 326 A
Arc Power
48 kW
H2 gas flow rate
17.9 SCCM*SCCM, Standard Cubic Centimeters per Minute

Figure 2.4: Reaction rates of extinction reactions against an electron temperature[15]

2.2

Linac

Linac which is at the first acceleration region is composed with four accelerating partto follow the gradual increase of the velocity of the proton beam. An overall view ofLinac is shown in Figure 2.5. RFQ (Radio-Frequency Quadrupole linac), DTL (Drift
Tube Linac), SDTL (Separate-type Drift Tube Linac), ACS (Annular Coupled Structure
Linac) are installed in the order of beam’s passage. The present output energy of the2.2 Linac

10linac is 181 MeV, which is planed to be upgraded to 400 MeV.

Figure 2.5: An overall view of Linac[16]RFQ (Radio-Frequency Quadrupole linac)[19]
DTL is often used to accelerate low energy beams, however it is diﬃcult to install itjust behind of the ion source. The energy of a beam extracted from the ion source is
50 keV. It corresponds to β = 0.01. Typical frequency of Alvarez type DTL is 200 Hz.
It is equivalent to λ = 150 cm. As mentioned at the following paragraph for DTL,
quadrupole magnets are installed between drift tubes in DTL in order to focus beams.
Each length of quadrupole magnet must be less than βλ = 1.5 cm. Fabricating such short
Q-magnets is impossible. Some solutions are considerable, for example, to enhance theaccelerating voltage of the ion source or to lengthen DTL. The most realistic solution is tointroduce RFQ. Structures of RFQ are shown in Figure 2.6 and Figure 2.7. Parametersof RFQ are shown in Table 2.2. Four electrodes surrounds a beam. They are two positiveelectrodes and two negative electrodes which are positioned as alternately. AC electricfield of quadruple type appears among electrodes. It focuses beams in the similar mannerof Q-magnet. Each electrodes wave along beam axis in the cycle of βλ/2. This waving
structure accelerates beams along the beam direction. The length of a cell (βλ/2) ispossible to be a few mm, and the installation just behind of the ion source becomesfeasible. Another characteristic of RFQ is bunching. DC beam is allowed to be used as
an injection beam, because RFQ is able to accelerate and focus a beam over bunching.
The output energy of RFQ is 3 MeV.

2.2 Linac

11

Figure 2.6: A structure of RFQ[18]Figure 2.7: A schematic view of the electrodes of RFQ

RF chopper[20]
To decrease the beam loss at the injection, the beam is chopped in the same cycle ofthe injection to RCS. Three RF choppers are installed at MEBT (Medium Energy BeamTransport) which is between RFQ and DTL. 46% of micro bunches are removed by the
RF choppers. Then, an intermediate bunch structure of 500 µs is produced. As shownin Figure 2.8, this intermediate bunch structure is suitable for forming two bunches at
the injection of RCS. The length of MEBT should be short in order to prevent increment2.2 Linac

12

Table 2.2: Parameters of RFQ[19]Parameter
LengthInput Energy
Output Energy
Peak Input Beam Current
Peak Output Beam Current
Transmission
Operation Frequency

Value
3.944 m0.05 MeV
3 MeV
53 mA
50 mA
94 %
324 MHzof beam emittance which is caused by the space-charge-eﬀect when the beam energy islow. Therefore, the RF choppers should be not only compact but also have high bending
electric field. This requirement is satisfied by utilizing RF cavity which has low loaded
Q. 324-MHz RF deflector (RFD) is adopted as the chopper. The configuration of RFD isshown in Figure 2.9. TE11 -like mode is excited in RFD by two electrodes. Electric fieldoscillating 324 MHz is generated. Beams are kicked to a beam dump at down stream.

Figure 2.8: A scheme for forming bunches[16]DTL (Drift Tube Linac)[17]
The function of DTL is to accelerate beams from 3 MeV to 50 MeV after RFQ. Alvalez
type DTL used in J-PARC has a structure shown in Figure 2.10. The configuration ofelectromagnetic field on resonance is shown in Figure 2.10. Accelerating electric field isseen between tubes. The resonance frequency is 324 MHz. The length of tubes are shortat upstream and long at downstream because the velocity of beam gradually increases in
DTL. Electromagnets are installed at spaces between the tubes and focus the beam. The
installation of these electromagnets are favorable for accelerating low β beam because low
β beam has strong space charge eﬀect and is easy to expand.

2.2 Linac

13

Figure 2.9: A cross-section of RFD[20]Figure 2.10: A cross-section of DTL[17]Table 2.3: Parameters of DTL[17]Parameter
LengthStructure length
Input energy
Output energy
Operation frequency
Number of DTL tanks
Number of cellsValue
27.12 [m]26.68 [m]3 [MeV]
50 [MeV]324 [MHz]3146

2.2 Linac

14

SDTL (Separate-type Drift Tube Linac)[17]
SDTL is used to accelerate beams from 50 MeV to 181 MeV in the first stage and to 191
MeV in the second stage. Its structure is shown in Figure 2.11. It is similar to the structure of DTL. The resonance frequency is 324 MHz. Diﬀerences are that electromagnets
are outside of cavity and the length of every tube is same. It is not necessary to installelectromagnets in short intervals because the space charge eﬀect is weak in this energy
range. If we take spaces to install magnets, acceleration in a high frequency becomesdiﬃcult, instead. Parameters of SDTL are shown in Table 2.4.

Figure 2.11: A cross-section of SDTL[17]ACS (Annular Coupled Structure Linac)[17]
ACS accelerates proton beams from 191 MeV to 400 MeV after SDTL. The structure of
ACS is shown in Figure 2.12. It is not utilized in the first stage, but in the second stage.
The structure is complicated at a glance. The principle of the acceleration is based ona multi-cell cavity. The eigenvalues of electromagnetic field in a multi-cell cavity are 0
mode, π/2 mode, π mode, ... in acending order. If a perturbation is applied on the cavity,
i.e. the flatness of the cavity is bad, the lowest mode whose detune from the resonancefrequency is the least is π/2 mode. That means π/2 mode is the most suitable for the
stable operation. However, as shown in Figure 2.13, cells without electric fields appear
every other cell in π/2 mode. To remove these cells and improve accelerating eﬃciency,
ACS shown in Figure 2.14 was developed. The cells without electric fields are excluded2.3 RCS

15

Table 2.4: Parameters of SDTL[17]Parameter
LengthStructure length
Input energy
Output energy
Operation frequency
Number of DTL modules
Number of quadrupoles

Value
91.2 [m]65.69 [m]50.1 [MeV]
first stage: 181 [MeV]
second stage: 190.8 [MeV]
324 [MHz]
16
62

to the sides and every accelerating cavities is next to each other. Parameters of ACS are
shown in Table 2.5.

Figure 2.12: A cross-section of ACS[17]

2.3

RCS

The ring accelerator which is down stream of the linac is RCS (Rapid-cycling Synchrotron). The circumference is approximately 350 m. It has three linear sections. Eachlinear section is specific for acceleration, injection, and extraction, respectively. Mainparameters of RCS are shown in Table 2.7. The purpose of RCS is to generate secondary
particles which have energies of a few GeV. RCS accelerates proton beams from 181 MeV(in the first stage) to 3 GeV and provides them to Materials and Life Science Experimental Facility (MLF). The design goal of the beam power is 1 MW. RCS also has a function
to provide beam to MR.

2.3 RCS

16

Figure 2.13: A π/2 mode of a multi-cell cavity[17]Figure 2.14: A schematic view of ACS[17]In the first stage, proton beams from SDTL, which have intermediate-bunch-structureof 1 MHz, are injected to RCS. The beams circulate at 0.5 MHz in RCS which corresponds to the injection energy of 181 MeV. This frequency is equal to half of the injection
frequency of the intermediate-bunch-structure. Odd bunches and even bunches in theintermediate-bunch-structure form one bunch in RCS, respectively. The harmonic number of RCS is two. As shown in Figure 2.8, odd bunches enter in one bucket, even bunches
enter in another bucket. These two bunches formed in RCS are accelerated to 3 GeV in
20 ms, and extracted to MR or MLF before next beams are injected from SDTL. The
repetition rate of this process is 25 Hz. Two bunches formed in the process are called one
cycle. Four cycles are extracted from RCS to MR, then 87 cycles are extracted to MLF.
In this 87 cycle extraction, beam acceleration and extraction are completed in MR, andnext four cycles are extracted to MR again. This process is repeated.

2.3 RCS

17

Table 2.5: Parameters of ACS[17]Parameter
LengthInput energy
Output energy
Operation frequency
Number of ACS modules
Number of quadrupoles

2.3.1

Value
108.3 [m]190.8 [MeV]
400 [MeV]
972 [MHz]
23
90

RF system

The RF system in RCS is mainly consisted with following components[68].
◦ RF power amplifier◦ Anode power supply◦ Accelerating cavity
Each RF power amplifier drives one accelerating cavity. The three gaps of each cavity
are connected in parallel and directly driven by the amplifier. The output stage of theamplifier consists of two tetrodes operated in push-pull. One dc-power supply is employed
for the two tetrodes. The detail of the accelerating cavity is given in the next subsection.

2.3.2

Accelerating cavity

Eleven accelerating cavities are installed in RCS. The cross-section of the RCS accelerating
cavity is shown in Figure 2.16. The cavity is λ/4-wave coaxial and is corresponds to typeB which is shown in Appendix J. One cavity is consists with three accelerating cells.
Each cell has one accelerating gap and two tanks are installed on both sides of eachaccelerating gap. Three magnetic alloy cores are installed in each tanks. Namely, sixcores are installed in one accelerating cell. The Q value of the RCS cavity is ∼2. No
automatic tuning system for the resonance frequency is necessary on the RF system. The
cavity is suited for the operation with the second harmonics, because the low Q allows
the second harmonics to exist. The range of the operating frequency is from 1.23[MHz]to 1.67[MHz]. The accelerating gradient per gap is 15[kV].

2.3.3

FINEMET cores

Amorphous
Most of materials such as metals, oxides, compounds are formed by crystals because
atoms are aligned in order. However, there is another type of material which has random2.3 RCS

18alignment of atoms. The material is called amorphous. Because of the randomness,
we can regard amorphous as an isotropic material in macroscopic view. It does nothave magnetic crystalline anisotropy, and no grain boundary which prevents domain wallfrom moving exists, so that amorphous possesses excellent properties as a soft magnetic
material[26]. By making it as a ribbon, eddy current is reduced and is durable in RF
field. An amorphous core of accelerating cavity in the synchrotron of National Institute ofRadiological Science (NIRS), which is introduced in Appendix J, is fabricated by winding
an amorphous ribbon of 1.5 µm thick applied with a silica insulation layer of 1.5 µm thickon one surface. A filling ratio of the core is approximately 75% .
FINEMETA magnetic material called FINEMET was developed by Hitachi Metals, Ltd.. This isa magnetic alloy which has a high permeability, saturation magnetic-flux-density, andCurie temperature. These properties is suited for the RF cavity of the proton and ion
synchrotrons. Typical properties of conventional ferrite and FINEMET (FT-3M) are
shown in Table 2.6.
In the production process of FINEMET, an amorphous ribbon which has 18 µm thickness and 35 mm width is painted with the silica on one surface. The amorphous consistsof Fe, Si, B and small amounts of Cu and Nb. The ribbon is wound into a toroidal core.
Then, it is annealed in a nitrogen atmosphere to increase magnetic properties by making
crystals small in order of 10 nm. The amorphous core becomes to have an excellent magnetic properties and is called FINEMET core[69]. The magnetic alloy cores assembled in
the RCS cavity are the FINEMET cores. The figure of the FINEMET core for RCS isshown in Figure 2.15.
Table 2.6: Properties of FINEMET[69]Relative permeability (1MHz)
Saturation magnetic-flux-density [T]Curie temperature [◦ C]
Thermal conductivity [W/m/K]

2.3.4

FINEMET (FT-3M)
2400
1.2
570
7.1

Ni-Zn ferrite
500
0.4
200
6

Power loss in the core and Cooling of the heat load

Most input powers to the cavities are dissipated in the cores. Water cooling is adopted tocool the heat load. Laminar water flows on the surfaces of the cores. The heat transfer
coeﬃcients from the surface of the core to laminar water is calculated as 500[W/m2 /K].
The calculation is shown in Appendix D.
The power loss in operation was evaluated by measuring the rise of water temperature.
It was approximately 6 kW per core.

2.4 MR19

mass: 120kg/core

φ370
φ850

width 35

Figure 2.15: The figure of the FINEMET core for RCS[2]2.3.5

Problems

The heat on the core causes a buckling and decrease the impedance of the core. Water has
a good cooling eﬃciency, however, the magnetic alloy cores are corroded by water. The
surface of the cores are coated not to touch with water. This coating strongly interrupts
the heat radiation, which raises fatal bucklings. To stabilize and enhance the performanceof RCS by solving the buckling problem, it is necessary to develop a new cavity which isable to release the thermal stress in the cores. The purpose of this paper is introducing
the development. Details of the cavity is described in the next chapter.

2.4

MR

MR (Main Ring) is located after RCS. MR has three linear sections. Its purpose is toprovide secondary particles whose energies are a few tens GeV. Each linear section has afunction of injection, acceleration, and extraction, respectively. The main parameters of
MR are shown in Table 2.8. MR accelerates proton beams from 3 GeV to 30 GeV. The
accelerated beams are used at the neutrino beam line and Hadron hall. The aiming beam
power is 0.75 MW.
Four cycles consisted of eight bunches injected from RCS to MR. One bucket is empty
because the harmonic number of MR is nine. This vacant bucket provides a time for the
standing of a kicker for ”fast extraction”.
There are two beam lines for extractions in MR. One leads to Hadron Hall, the otherleads to Neutrino experimental facility. Each method for extraction is called ”slow extraction” and ”fast extraction”, respectively.
In the slow extraction scheme, the proton beam accelerated up to 30 GeV is attracted

2.4 MR

20

Table 2.7: Parameters of RCS[2]Parameter

Value
348.333 [m]55.44 [m]0.181/0.4 [GeV]
3.0 [GeV]
8.3×1013

Circumference
Average radiusInjection energy
Extraction energy
Particle per pulse
Revolution period
at Injection
at Extraction
Repetition rate
Ramping pattern
Injection
Acceleration
Decreasing Field
Average current
Circulating current
at Injection
at Extraction

1.629 [µs]1.196 [µs]25 [Hz]Sinusoid∼500 [µs]20 [ms]20 [ms]333 [µA]
8.2 [A]
11.1 [A]to the electro-static septum (ESS) by bump magnets as shown in Figure 2.17. Thenthe beam size of horizontal direction is enlarged by means of the resonance of betatronoscillation at a resonance sextupole magnet. A thin septum electrodes are installed insideof the ring. When the beam scratches the septum electrodes, a part of the beam is
scraped. The scraped part is kicked toward the inside of the ring by the electric field. As
the scraped beam oscillates by betatron oscillation, it will close in on the original orbit.
Then it will cross the original orbit and flies toward outside of the ring. The septum is ata point where the oscillation is maximum (the phase of betatron oscillation is 270◦ at the
point). The septum lead the beams to a beam line connected to Hadron hall. ThoughHadron hall is outside of the ring, the beam is kicked toward inside of the ring in orderto take enough distance between ESS and the septum. This process is repeated and thebeam is gradually scraped. Duration time for the slow extraction is approximately 0.7
sec[22].
The fast extraction is the method that circulating eight bunches which have been accelerated up to 30 GeV are extracted by one kick. They are extracted to the neutrino beamline which is located inside of MR. Duration time for the fast extraction is approximately
5 µs[23].
The cross-section of the accelerating cavity for MR is shown in Figure 2.18. The
structure is similar with that of RCS. The cavity is λ/4-wave coaxial and is corresponds
to type B which is shown in Appendix J. One cavity is consists with three accelerating2.4 MR

21

Figure 2.16: A cross-section of the accelerating cavity in RCS. The blue area represents
the FINEMET cores.
cells. Each cell has one accelerating gap and two tanks are installed on both sides ofeach accelerating gap. Three magnetic alloy cores are installed in each tanks. Namely,
six cores are installed in one accelerating cell. The diﬀerence is that MR cavity is loadedwith cut cores while RCS cavity is loaded with non cut cores. Q value of the MR cavity
is tuned to ∼25 by adjusting the cut width. Six accelerating cavities are installed in MR.

2.4 MR

22

Figure 2.17: A scheme of the slow extraction[22]Table 2.8: Parameters of MR[2]Parameter

Value
1567.5 [m]249.475 [m]
3 [GeV]
30 [GeV]
3.3×1014

Circumference
Average radiusInjection energy
Extraction energy
Particle per pulse
Revolution period
at Injection
at Extraction
Repetition rate
Ramping pattern
Injection
Acceleration
Parabola
LinearParabola
Cycles for each repetition
Bunches per cycle

5.384 [µs]5.230 [µs]0.3 [Hz]
Parabola+Linear+Parabola
0.17 [s]1.96 [s]0.13 [s]1.7 [s]0.13 [s]422.4 MR

23

Figure 2.18: A cross-section of the MR cavity. The blue area represents the FINEMET
cores.

Chapter 3
Numerical analysis and Experimentto identify the cause of the bucklingon RCS cores
The cores in the presently installed cavity were damaged when the cavity was in operation.
This chapter reports the study about the cause of the damage.

3.1

Background of the study

RCS is a synchrotron to accelerate proton beams from 181 MeV to 3 GeV and extract
them. The accelerating cavity of RCS has a characteristic that it is loaded with FINEMET
cores. A cavity loaded with ferrite cores is conventional for a proton and ion acceleration.
FINEMET enabled twice higher accelerating gradient than ferrite. Sizes of cores in apresently installed RCS accelerating cavity are shown in Table 3.1.
In November 2008, RCS was operated with 11 cavities. In January 2009, a shunt
impedance of cavity No. 7 suddenly decreased[55]. After inspecting inside of the cavity,
damages on two cores in tank 4 were found out of 18 cores in it. Especially, one core isbuckled and elevated at the inner diameter, so that layers of FINEMET at the point arebroken. The buckling is the cause of the decrease of the shunt impedance. After that,similar damages appeared many times. As of Mar 11th, 2010, 25 cores out of 90 cores
installed in cavity No. 3, 4, 5, 6, 7 has been damaged. Two of them showed the decreaseof their shunt impedances. An operation time when the decrease of impedance appears
is approximately 1,000 hrs.
A photograph of buckling is shown in Figure 3.1. The elevation of approximately 1
cm is seen at the inner diameter of the core. Furthermore, FINEMET is rusted by watercoming through the damaged area.
We need investigate the cause of the buckling in order to design a new cavity because
the new cavity will be loaded with FINEMET cores, too. We suspected the cause of thebuckling was thermal stress caused by a heat in the cores. Simulations for investigating
the buckling problem were performed by means of ANSYS. ANSYS is an engineering
simulation software. The calculation of power loss per core is shown in section 3.2, results

3.2 Calculation for power loss per core25of the simulation for the thermal stress were shown in section 3.3, and results of thecompression test were shown in section 3.4.
Table 3.1: Sizes of presently installed RCS cores

RCS corethickness [mm]35

inner diameter [mm]371 (with a collar)

outer diameter [mm]850

Figure 3.1: A picture of a buckled core (left). A closeup of the buckled area.

3.2

Calculation for power loss per core

The power loss of the presently installed RCS core is approximately 6 kW per core. The
value is based on the temperature increase of cooling water. We calculated the power loss
by hand and compared with 6 kW. An accelerating pattern of RCS is shown in Figure 3.2.
Solid line is the accelerating voltage of fundamental mode, broken line is the accelerating
voltage of secondary mode, and dotted line is the frequency. Secondary mode is notconsidered in the calculation.
The number of accelerating cavities installed in RCS is eleven and one cavity has threegaps, so that the accelerating voltage per gap Vgap (t) can be written as
Vgap (t) =

V (t)
V (t)
=
,
(11cavites) × (3gaps)
33

where V(t) is a function representing the solid line in Figure 3.2.
We apply Faraday’s law to an integral pass shown in Figure 3.3.
I∫∫
∂B(r, t)Edc = −
dS
∂t
S

(3.1)

(3.2)

3.2 Calculation for power loss per core

26

Figure 3.2: A ramping pattern of RCS. The accelerating voltage in the graph is thevalue per round of RCS.[57]Left-hand-side is a line integral and right-hand-side is a surface integral.
Because a strength of magnetic field is inversely proportional to r, it can be writtenasα(t) jω(t)t
B(r, t) =
e
.
(3.3)
r
Substituting equation 3.3 to equation 3.2, the right-hand-side can be written as∫∫
100jω(t)tdS(3.4)(Right-hand-side) = − [α (t) + jα(t) (ω(t) + ω (t)t)] e
r
S
∫∫
1
0
0
jω(t)t= − [α (t) + jα(t)(ω(t) + ω (t)t)] e
dS × 6cores (3.5)
rcross-sectionof a core0= −6 × 2.864 × 10−2 × [α0 (t) + jα(t) (ω(t) + ω (t)t)] ejω(t)t .

(3.6)

Where, the first term α0 (t) in the parenthesis has an order of α(t)/(10−3 [s]) = α(t) × 103
and the second term has an order of α(t) × 106 , so that the first term is negligible.
Therefore, equation 3.6 can be written as(Right-hand-side) = 6 × 2.864 × 10−2 × α(t) (ω(t) + ω 0 (t)t) ej(ω(t)t−π/2) .

(3.7)

Hence,(Left-hand-side) = 6 × 2.864 × 10−2 × α(t) (ω(t) + ω 0 (t)t) ej(ω(t)t−π/2) ≡ Vgap (t)ej(ω(t)t−π/2) .
(3.8)

3.2 Calculation for power loss per core

27

Figure 3.3: An integration path for Faraday’s law. The accelerating voltage for one gap
is derived by a line integral of electric fields on the path. Integrals on 1 and 3 are zero
because they are perpendicular to electric fields. An integral on 2 is also zero because
no electric field exists. An integral on 4 equals the accelerating voltage for one gap.
Therefore, α of t can be expressed asα(t) =

Vgap (t).
6 × 2.864 × 10−2 × (ω(t) + ω 0 (t)t)(3.9)

Hence, a stored energy U (t) at a certain time t for one core is written as
∫

2

1
1
√ B(r, t) dV
U (t) =2µ(t)2core volume()2∫
Vgap (t)1
1
6dV= 6.75 × 10 × 0
0µs (t) ω(t) + ω (t)tr2
core volume()2
1
Vgap (t)= 1.22 × 106 × 0,µs (t) ω(t) + ω 0 (t)t(3.10)(3.11)(3.12)

where µ(t) = µ0 µ0s (t). µ0s (t) is a real part of relative permeability of the core. A loss ofthe core at a certain time t can be expressed as
(
)2
ω(t)
Vgap (t)6P = ω(t)U (t) (tanδ) (t) = 1.22 × 10 × 0(tanδ) (t)dt.
(3.13)µs (t) ω(t) + ω 0 (t)t3.2 Calculation for power loss per core

28

Considering the period of the pattern is 40 ms and the voltage is applied for 20 ms, theaverage loss P̄ can be written as
1.22 × 106
P̄ =40 × 10−3

20×10
∫ −3

0

ω(t)
µ0s (t)(Vgap (t)ω(t) + ω 0 (t)t)2(tanδ) (t)dt.

(3.14)The time dependencies of µ0s , µ00s , and tanδ are shown in Table 3.2. The time dependenciesof the frequency and Vgap in Table 3.2 are obtained from Figure 3.2.
Table 3.2: Time dependences of the properties of the presently installed cavity
time [ms]frequency [MHz]µ0s (t)µ00s (t)(tanδ)(t)Vgap (t) [V]

0
0.94
1919
3087
1.61
2.42×103

5
1.29
1510
2515
1.67
1.15×104

10
1.58
1296
2206
1.70
1.18×104

15
1.65
1254
2145
1.71
9.09×103

20
1.67
1242
2128
1.71
4.55×103

The time derivative of the frequency in Table 3.3 is derived by diﬀerentiating thefunction of the frequency in Figure 3.2.
Table 3.3: Time derivatives of the frequencies
time [ms]A time derivative of
frequency [Hz/s]

0

5

10

15

20

8.67×107

6.16×107

3.65×107

1.14×107-1.37×107

Parameters in Table 3.2 and 3.3 are assigned to the equation 3.14 and the plot of theintegrand is obtained as shown in Figure 3.4.
The integral part of P̄ is calculated by substituting the integrand which is derived
with a fitting in Figure 3.4. The integral part is written as(Integral part) = 1.88 × 10−4 .
Hence,(3.15)

1.22 × 106
× 1.88 × 10−4 = 5.73 [kW].
(3.16)
40 × 10−3This value is consistent with the value of 6 kW which is obtained from the temperaturerise of the cooling water. To calculate more accurately, it should be taken into accountthat the frequency of input power does not always stay at the resonance point of thecavity.
P̄ =3.3 Calculation for Thermal Stress29

Figure 3.4: A plot of the integrand which is in the equation 3.14

3.3

Calculation for Thermal Stress

Accelerating cavities in RCS are loaded with FINEMET cores. The cores are fabricatedby winding amorphous ribbons into a toroidal core. The ribbons are coated with silica
on one surface. The silica works as an insulator. As mentioned above, a phenomenon
that cores are buckled and its impedance decreases appears while RCS is in operation.
We suspected a cause of the buckling is the thermal stress on the cores. We performeda simulation to identify the cause by means of ANSYS. The calculation of thermal stresswith a micro model is shown in this section.

3.3.1

Structure of presently installed RCS cavity

There are three types of cores. A core model called ”Type 3” is used in the simulation.
The cross-section of Type 3 is shown in Figure 3.5. This type of core is applied with low
viscous epoxy resin impregnation and surface coating (high viscous epoxy resin + glass
cloth = 300µm). On the inner diameter of the core, a cylindrical G-10 collar whose wall
thickness is 2 mm is attached. Type 3 core is damaged with the greatest numbers among
three types. Following parameters are required to simulate the thermal stress in the core.

Figure 3.5: A schematic view of a cross-section of a core

3.3 Calculation for Thermal Stress30· Young’s ratio· Poisson’s ratio· Thermal expansion· Thermal conductivity
The Young’s ratio, Poisson’s ratio and thermal expansion of FINEMET are given
by Hitachi Metal, Ltd.. The thermal conductivity of FINEMET was measured. The
next subsection reports the measurement. The Young’s ratio, Poisson’s ratio, thermal
expansion, and thermal conductivity of epoxy resin are obtained from the reference [60].

3.3.2

A measurement for a thermal conductivity of FINEMET
core

A thermal conductivity of FINEMET is dispensable for the calculation of thermal stress.
We obtained the thermal conductivity by measuring a coeﬃcient of thermal diﬀusion of
the FINEMET core by means of the laser flash method in cooperation with National
Institute of Advanced Industrial Science and Technology (AIST). The configuration of
the laser flash method is shown in Figure 3.6. It is the method to obtain the coeﬃcientof thermal diﬀusion by measuring the increase of the temperature on the back surfaceof the sample after applying a heat flux on its forward surface with a pulsed YAG laser.
Half time method is used in the measurement. Details of half time method is shown in a

Figure 3.6: A schematic view of the laser flash method[62]following paragraph.
Initial temperature of a solid in adiabatic state, which has density D [g/cm3 ], specificheat at constant pressure C [cal/g/◦ C], thickness L [cm] is defined as T(x,0). Then, atemperature distribution at time t is written as[63]1
T (x, t) =
L

∫L
0

2∑
T (x, 0)dx +
exp
L n=1
∞

(

−n2 π 2 αt
L2

)
cos

( nπx ) ∫LL

T (x, 0) cos( nπx )
Ldx,

0

(3.17)

3.3 Calculation for Thermal Stress31

where α [cm2 /s] is a coeﬃcient of thermal diﬀusion. Assuming heat Q [cal/cm2 ] is applied
isotropically and absorbed in depth g [cm] at x = 0 and t = 0, T (x, 0) can be written as
Q(0 < x < g),DCg
T (x, 0) = 0 (g < x < L).
T (x, 0) =Therefore, equation 3.17 can be expressed as[( 2 2 )]∞
( nπx ) sin nπg∑Q−n π αtLT (x, t) =
1+2
cos
exp
.
nπg
DCL
L
L2
L
n=1

(3.18)(3.19)(3.20)The opaque has small g, so that, the sinusoidal function can be approximated as
sin

nπg
nπg
≈
.
L
L

The temperature rise on the back surface (x = L) can be written as[( 2 2 )]∞∑
Q−n π αtT (L, t) =1+2(−1)n exp
.
2
DCL
L
n=1

(3.21)(3.22)

Two nondimensional parameters are introduced.
T (L, t)
TM
2
π αt
ω≡ 2
L

V (L, t) ≡(3.23)(3.24)

Q
where TM (= DCL) is a peak temperature on the back surface. Then, a following equation
is deduced.
∞∑()
V =1+2(−1)n exp −n2 ω(3.25)
n=1

The plot of this function is shown in Figure 3.7. ω = 1.38 at V = 0.5 is obtained fromthe plot. Substituting the value into definition 3.24, α is derived asα=

1.38L2,π2t 1(3.26)

2

where t 1 is a time when the temperature of the back surface is half of its peak value
2(V = 0.5).
Hence, a thermal conductivity λ [cal/cm/◦ C] is obtained from a following equation.[64]λ = αCD(3.27)

Because the core has the structure that FINEMET ribbon is wound into a toroidal core,
the thermal conductivity must be anisotropic. As shown in Figure 3.8, measurements in3.3 Calculation for Thermal Stress32

Figure 3.7: A nondimensional plot of the temperature of the back surface
two cases were performed. One is that the laser is applied perpendicular to FINEMET
layers (radial direction), the other is that the laser is applied parallel to the layers (circumferential direction and beam direction). Two samples were prepared for each measurement. Measurements were performed twice for each samples. The results are shownin Table 3.4. The specific heat of the core at the constant pressure was measured by themeasurement service with Physical Properties Measurement System (PPMS) at Cryogenic
Research Center in the University of Tokyo.

Figure 3.8: Definitions of the directions of the laser
Obtained anisotropic-thermal-conductivity of FINEMET cores are,0.6 [W/m/K] for radial direction, and7.1 [W/m/K] for circumferential direction and beam direction.[59]3.3.3

Calculation for thermal stress with micro modelCalculations for thermal stress on the core were performed with a model which represents
the layered structure of the core (micro model). Considering the aging property of theepoxy resin, calculations in two cases were performed.
1. Percentages of Young’s ratio were changed into 100% , 10% ,and 1 % .

3.3 Calculation for Thermal Stress

33

Table 3.4: Results of the measurements for the thermal conductivity

Mass [g]Vertical [mm]Horizontal [mm]Height [mm]Volume [mm3 ]Density [g/cm3 ]Specific heat capacity [J/g/K]
Half time [s]Thermal diﬀusivity [10−7 m2 /s]
Thermal conductivity [W/m/K]

Normal to layers
Along to layers
Sample 1
Sample 2
Sample 3
Sample 4
Trial Trial Trial Trial Trial Trial Trial Trial
1
2
1
2
1
2
1
2
1.00
1.59
1.48
1.65
10.21
8.59
9.08
10.19
9.83
9.56
9.47
9.55
1.84
3.42
3.04
3.09
184.67280.85261.40300.70
5.39
5.66
5.67
5.49
0.500
2.20 2.15 6.95 7.36 0.497 0.502 0.525 0.519
2.14 1.93 2.34 2.21 25.8 25.6 25.2 25.6
0.577 0.520 0.661 0.624 7.317 7.241 6.930 7.018

2. A contact simulation for the no impregnation core was performed.
ANSYS is utilized for these calculations. All of them are two dimensional calculations.
1. Model of 20,000 layers
The structure of the core is shown in Figure 3.9. The number of the layers of FINEMET
is approximately 20,000. Sizes of each material are shown in Table 3.6. The model of
2,000 layers (thickness of FINEMET, impregnated epoxy resin, water proof coating, andG-10 collar are 180µm, 60µm, 300µm, and 2 mm, respectively) is used for the calculationof the temperature distribution. To represent a real structure that FINEMET ribbons andepoxy resins are laminated alternately, the model of 20,000 layers (FINEMET and epoxy
are approximately 10,000 layers for each) is required. However, the number of layers is
too much and impossible to model it on a computer, so that the model of 2,000 layers is
adopted for the calculation of the temperature distribution. This model corresponds tothe model that that the number of layers in Figure 3.9 is reduced to 2,000.
Heat distribution used for the calculation was derived by normalizing the distributionof squared magnetic-flux-density with the power loss per core (6kW). The magnetic-fluxdensity was derived from a simulation with HFSS. In the simulation, 30◦ C for isotropic
temperature of coolant and 500 [W/m2 /K] for isotropic heat transfer coeﬃcient on thesurfaces of the core are assumed.
As shown in Figure 3.10, adiabatic conditions are applied at inner diameter and outer
diameter of the core, and center of the core also has an adiabatic condition because of thesymmetry of the model.
The thermal conductivity of each material are shown in Table 3.5. The measured

3.3 Calculation for Thermal Stress34

thermal conductivity of circumferential and beam directions is used for simple FINEMET.
The temperature distribution obtained from the calculations is shown in Figure 3.11.

Approximately 20,000 Layres

Epoxy resin 6µm

Figure 3.9: A structure of the core

Figure 3.10: An adiabatic condition on the core for the simulation of the core temperature

Table 3.5: Thermal conductivities of materials used in the simulation
FINEMET
Epoxy resin, water proof coating[60]G-10[60]

7.1
0.2
radial: 0.4, circumference and beam direction:
0.8

Using the temperature distribution obtained above, a simulation for the thermal stressagainst various Young’s ratios of epoxy was performed. This variation represents the aged
deterioration of the epoxy resin. The model of 20,000 layers was used for the simulation.
In this case, 20,000 layers was feasible, because only the elements along the center line of
the core were used. These elements are in the area surrounded by blue lines in Figure 3.9.
As shown in Figure 3.12, displacement of upside and downside of the model are assumed

3.3 Calculation for Thermal Stress35

Figure 3.11: A temperature distribution along radial direction in the core, which is
obtained from the simulation

Figure 3.12: A condition of constraint against displacements of the elements, which isused in simulations for thermal stresses
to be constraint along the direction of center axis. Properties of each material are shownin Table 3.7. Measured values in Hitachi Metal are used for properties of FINEMET.
Figure 3.13, 3.14, and 3.15 are results of the calculations for circumferential components of thermal stress which are applied on FINEMET, epoxy resin, and G-10 collar,
respectively. The percentages of Young’s ratio of epoxy resin are changed into 100% ,10% , and 1% . Plus and minus values represent tensile and compressive stresses, respectively. The result shows the stresses drastically decrease as the Young’s ratio of the epoxy
resin decreases. A conclusion is that a methods to decrease Young’s ratio of cores, forexample, adopting no resin core, using soft resin, transform the epoxy resin into sponge,
are eﬀective. In fact, the cores without epoxy resin among presently installed RCS cores
have never experienced buckling.
2. Contact simulation
No impregnation is assumed. Only FINEMET ribbon was input for modeling and thecontact simulation was performed. The temperature distribution in Figure 3.11 was usedagain. Values in Table 3.7 are used for FINEMET properties. A result in Figure 3.16 was3.4 Compression test for the core

36

Table 3.6: Sizes of materials used in the simulations for the thermal stresses

FINEMET ribbon
Epoxy resin
Water proof coating

width [mm]3535-

thickness [µm]
18
6
300

Table 3.7: Properties of each material

FINEMET ribbon
Epoxy resin[60]G-10[60]

Young’s ratio [GPa]Poisson’s ratio

200
3.2 or 0.32 or 0.032
7.8

0.32
0.34
0.32

Coeﬃcient ofthermal expansion[10−6 /K]
10.6
60
radial: 23
circumference: 7
beam direction: 7

obtained for a circumferential component of stress. This result shows the circumferential
component of stress is less than 20 kPa. A large stress can be seen at the inner diameter.
This stress is caused that one end of the FINEMET ribbon contacts with the G-10 collar,
and is unavoidable. A part of Figure 3.16 is zoomed and shown in Figure 3.17. Periodical
spikes are seen. A reason for this phenomenon is that input values of the temperature
are only 100 points, so that temperature varies at every 24 cm. Spikes appear at the
points. If smooth distribution of the temperature is used, the stress is expected to beless than 20 kPa. Displacement of FINEMET ribbon and circumferential component ofstress at contact point are shown in Figure 3.18 and 3.19, respectively. The results ofthe simulation showed that thermal stresses drastically decrease by using the core without
epoxy resin. Therefore, cores for a new cavity are not impregnated.

3.4

Compression test for the core

We suspect the cause of the buckling is thermal stress on the core, however, there is noexperiment which measures the required stress for the buckling. Therefore, we measured
the buckling stress in cooperation with NIMS. In this section, results of the compression
test for the core which was performed at NIMS in November 2009 are shown.

3.4 Compression test for the core37

Figure 3.13: Thermal stresses on the FINEMET. Three calculations were performed.
The Young’s ratio of the epoxy resin (E) is varied in the three cases.
Fatigue Testing System
A fatigue-testing-system INSTRON 8802 shown in Figure 3.20 was used for the compression test. TCLP-50KNB of Tokyo Sokki Kenkyujo Co., Ltd. was used for a load cell. 50
kN is possible for the maximum-compression-force. A jig for the compression is shown in
Figure 3.21.
High resolution camera
A transform of the sample by the compression was measured with a high resolution camera
shown in Figure 3.22. The camera monitors the positions of two markers shown in Figure
3.21. The amount of the deformation of the sample is measured by the camera.
Samples used in this test are not RCS core’s but MR core’s. They were cut out
from quoter sized MR core (product number: KE081-8) and 1/8 sized MR core (productnumber: unknown) with a diamond cut machine of Ryowa Inc. which was at the machine
shop bldg. in KEK. The coating had been damaged at some areas on the surface of thequoter sized core. We cut out samples from non damaged areas. Compression direction
is defined as shown in Figure 3.23.
The direction of the beam axis is selected as the compression direction. Circumferential
direction is the best direction because the thermal stress on this direction is the strongest.
However, beam direction and circumferential direction are consistent in the meaning of thedirection along layers, so that the beam direction was selected. Circumferential direction
is not suited for compression because FINEMET layers have a curvature in this direction.
The sample is shown in Figure 3.24. Original positions of samples and their Young’s
ratios and buckling stresses are shown in Figure 3.25. Buckled and sheared samples
are shown in Figure 3.26 and 3.27, respectively. Filling ratios of samples, which arecalculated from their volumes and masses, are also shown in Figure 3.25.

3.4 Compression test for the core38

Figure 3.14: Thermal stresses on the epoxy resin
As the result above, Figure 3.28, 3.29, 3.30, and 3.31 are obtained. A plot showing
a buckling stress of 129.6 MPa (sample 13) is not a buckling but a shear failure.
As shown in Figure 3.28 and 3.29, filling ratios and buckling stress are not dependent
on positions where samples were cut. Figure 3.30 shows buckling stresses are not dependent on filling ratios. Figure 3.31 shows buckling stresses of samples are proportional toYoung’s ratios.
All samples except sample 13 are buckled under 70 MPa. The simulation for thethermal stress in previous section shows the maximum thermal stress in the RCS core
is over 70 MPa. The result of this simulation backs the expectation that the cause ofbuckling is the thermal stress.

3.4 Compression test for the core

Figure 3.15: Thermal stresses on the G-10

Figure 3.16: A result of the contact simulation

39

3.4 Compression test for the core

Figure 3.17: A closeup of Figure 3.16

Figure 3.18: Displacement of the elements40

3.4 Compression test for the core

Figure 3.19: A stress emerging at a contact point41

3.4 Compression test for the core

Figure 3.20: A fatigue-testing-system ”INSTRON 8802” at NIMS

42

3.4 Compression test for the core

Figure 3.21: A jig for the compression test

Figure 3.22: A high resolution camera

433.4 Compression test for the core

Figure 3.23: A definition of the compressing direction

Figure 3.24: A sample for the compression test

44

3.4 Compression test for the core45

Figure 3.25: Original positions of samples and results of the compression test

Figure 3.26: A buckled sample

Figure 3.27: A sheared sample

3.4 Compression test for the core

Figure 3.28: A position dependency of a filling ratio

Figure 3.29: A position dependency of a buckling stress46

3.4 Compression test for the core

Figure 3.30: A filling ratio dependency of a buckling stress

Figure 3.31: A Young’s ratio dependency of a buckling stress47

Chapter 4
Development of a new RF
accelerating cavity loaded withFINEMET cores cooled by
Fluorinert
Development of a new cavity is introduced in this chapter. We adopted the cores without
impregnation in order to avoid the buckling. Fluorinert is selected as a coolant. First ofall, we propose essential parameters for developing an accelerating cavity.
◦

Resonance frequency◦

Shunt impedance◦

Q factor

These parameters have to have suﬃcient values in order to carry out successful development. In addition to these parameters, two more parameters which are specific for ourcavity have to be examined.
◦

Cooling eﬃciency for the core◦

Breakdown voltage on the surface of the core

We will check them in chapter 7.

4.1

Selection of coolant

The coolant is required not to oxidize the cores. We had three candidates. They are
Fluorinert, Normal paraﬃn, and Novec. Properties of them are shown in Table 4.1.

4.2 Overview of the accelerating cavity for RCS

49

Table 4.1: Properties of the candidates for the coolant[58]FC-3283

Chemical formula
Boiling point [◦ C]
Flash point [◦ C]
Density [kg/m3 ]Dynamic viscosity [m2 /s]Specific heat [J/kg/K]
Thermal conductivity [W/m/K]
Breakdown voltage [kV/2.54 mm gap]
Relative permittivity (1 kHz)Electric loss tangent (1 kHz)

(Sumitomo 3M
FC-3283)(C3 F7 )N3
128
1780
0.59×10−61076
0.062443
1.91<4×10−4

Normalparaﬃn(ENEOS
Glade L)C11 H24 , C12 H26
190∼21071751
1.36×10−6
2180
0.126
30
2.0
∼1×10−4

Novec(Sumitomo 3M
HFE-7300)
C6 F13 OCH3
98
1660
0.7×10−6
1137
0.062
27
6.14
0.016

Normal paraﬃn is aﬀordable and has a high breakdown voltage which is favorable
as the coolant. But Normal paraﬃn is not adopted because it is flammable. Novec is
not accepted because it has a large permittivity and tanδ, and it has an oxygen in thechemical formula. We concluded the FINEMET cores without impregnation cooled by
Fluorinert is the best choice.

4.2

Overview of the accelerating cavity for RCS

The beam energy at injection and extraction of RCS are 181 MeV and 3 GeV, respectively.
The circumference of RCS is 348.333 m, so that the frequency for a beam to circulate
RCS is 0.47 MHz for 181 MeV, 0.84 MHz for 3 GeV. Because the harmonic number istwo, the resonance frequency of RCS cavity should be 0.938 MHz for 181 MeV and 1.67
MHz for 3 GeV. This is twice of an RCS revolving frequency. The accelerating voltage
per turn of the ring is proportional to the product of the average radius of the ringand maximum-time-derivative of magnetic-flux-density. The voltage is obtained from thefollowing equation.
d(Bρ)
(4.1)
V0 sin(ωt) = 2πR
dt
Where, V0 is the peak voltage, R is the average radius of the ring, ρ is the radius of curvature at a bending magnet. In the case of RCS, R=55.44 m, ρ=12.578 m, sin(ωt)=sin(28.09[deg])=0.4709 at maximum voltage (at a point of 6 ms in 20 ms cycle) which corresponds
to accelerating phase φs =28.09 deg. Magnetic flux densities around this time are 0.394 [T]and 0.443 [T] at 5 ms, 7 ms, respectively. The time derivative of magnetic-flux-density
is calculated as (0.443-0.394)/1×10−3 =0.490 [T/s]. Therefore, V0 ∼450 [kV][65]. Ten

4.2 Overview of the accelerating cavity for RCS

50

cavities and one spare cavity are able to be installed in a space of linear section in RCS.
One cavity is approximately 2 m long. In the case of ten cavities installation, an accelerating voltage per cavity is 450 [kV] / 10 [cavities] = 45 [kV]. One cavity has 3 gaps, sothat an accelerating voltage per gap is 45 [kV] / 3 [gaps] = 15 [kV]. Therefore, a cavity
should have a resonance frequency of 0.938-1.67 [MHz] and an accelerating voltage of 15[kV] per gap. A geometry of a cell is a structure of λ/4-wave coaxial resonance cavity
as shown in Figure 4.1. It is the structure that 3 cores are installed in each side of theaccelerating gap. In this paper, fabrication of a prototype cavity which is loaded with acore module and results of performance test for the cavity are shown. The cross-sectionof the prototype cavity is shown in Figure 4.2. A variable vacuum capacitor is attachedinstead of an accelerating gap. The resonance frequency is tuned to 1.7 MHz by adjusting
the capacitor, which is the maximum frequency of the cavity operated in RCS.

4.2 Overview of the accelerating cavity for RCS

Figure 4.1: A cross-section of the new accelerating cavity

51

4.3 FINEMET core module

52

Figure 4.2: A cross-section of the prototype cavity

4.3

FINEMET core module

Presently installed RCS cores are impregnated with epoxy resin and the structure is solid.
However, cores which we use are not impregnated because a maximum temperature forthe cores is limited by a glass-transmission-temperature of epoxy resin. Furthermore,considering the results in previous section, even a resin which is endurable against heat4.3 FINEMET core module53

is available, it should not be used to prevent the buckling. A geometry of the core is a
structure that it is radially divided into three. They are called small core, middle core,and large core. Te winding thickness of each core becomes thin, which means the control
of wounding stress becomes easy, and the magnetic properties are possible to increase.
The thin winding thickness makes it easy to deal with no impregnation core, what we calla ”raw core”. A structure which is fabricated by binding raw cores with two G-10 plates iscalled a ”core module”. The structure is shown in Figure 4.3. Only collars are structural
material and no stress is applied on FINEMET cores (functional material). The aperturesurrounded by the G-10 plates and the surfaces of the cores is the flow channel.

Figure 4.3: A cross-section of a core module
Raw cores have following advantages. 1. Release of thermal stress
The raw core is not impregnated and soft. It is able to release the thermal stress andprevent the buckling. 2. Self cleaning
As the surface of the raw core contacts with the coolant directly, self cleaning that
seeds of spark are removed by the coolant which flows fast is expected. The coolant enter
between FINEMET layers. Seeds move to the surface by diﬀusion and are removed by
the flowing coolant.

4.3 FINEMET core module

54

Figure 4.4: A schematic view of the new cores

Table 4.2: Sizes of the new cores

Small core
Middle core
Large core

Inner diameter [mm]
396
592
788

Outer diameter [mm]
558
754
950

Sizes of small, middle, large cores are decided to make their total cross sections sameas that of an RCS core. Their configuration and sizes are shown in Figure 4.4 and Table
4.2, respectively. Values of relative permeability, shunt impedance, and µp Qf are shownin Table 4.3 and 4.4, respectively.

4.4 Fluorinert

55

Table 4.3: Permeabilities of the new coresµ0s
Small core
Middle core
Large core
Averageµ00s
Small core
Middle core
Large core
Average

0.5 MHz
4100
4300
4100
4200
0.5 MHz
4400
5000
4300
4600

1 MHz
2400
2600
2700
2600
1 MHz
3200
3400
3000
3200

5 MHz
760
1000
1200
980
5 MHz
1200
1200
1200
1200

10 MHz
480
730
860
690
10 MHz
780
820
810
800

Table 4.4: Shunt impedances and µp Qf of the new cores
Small core

0.5[MHz]1[MHz]
5[MHz]
10[MHz]4.4

Rp [Ω]
46.9
56.9
95.1
121.3

µp Qf
3.14
3.81
6.37
8.12

Middle coreRp [Ω]
34.6
42.7
83.2
117.8

µp Qf
3.27
4.04
7.87
11.14

Large coreRp [Ω]
25.0
32.4
70.5
104.5

µp Qf
3.08
3.99
8.69
12.89

Sum ofthreecores
Rp [Ω]
106.5
132
248.8
343.6

Core
moduleRp [Ω]
103.7
127
222.3
287.9

Fluorinert

FINEMET which is an Fe-based magnetic alloy can be oxidized. A coolant for cores must
not contain oxygen. Fluorinert (FC-3283, Sumitomo 3M, Inc.) which is a perfluorinatedinert liquid is used. Properties of Fluorinert and water are shown in Table 4.5.

4.4 Fluorinert

56

Table 4.5: A comparison of properties of Fluorinert and water

Chemical formula
Boiling point [◦ C]
Density [kg/m3 ]Dynamic viscosity [m2 /s]Specific heat [J/kg/K]
Thermal conductivity [W/m/K]
Break down voltage [kV/2.54 mm gap]
Relative permittivity (1 kHz)Electric loss tangent (1 kHz)Heat transfer coeﬃcient [W/m2 /K]
Price [thousands yen/L]

FC-3283(C3 F7 )N3
128
1780
0.59×10−61076
0.062443
1.91<4×10−4
530 (turbulence)∼19

Water[70]H2 O
100992.2150.6580× 10−6
4192
0.628
81
0.16
500 (laminar)-

By using FC-3283 on the condition of turbulence, the cooling eﬃciency is comparablewith presently installed cavities. Reasons of selecting FC-3283 are listed below.
◦ The breakdown voltage is high.
◦ The relative permittivity is low.
◦ The kinetic viscosity is low.
◦ The boiling point is high.
An ion decomposition rate of FT-3283 is shown in Figure 4.5. Though the boilingpoint is high, its ion decomposition rate begins increasing around 120◦ C, so that thetemperature of Fluorinert in operation must be lower than 120◦ C.

4.5 Swelling test for G-10

57

Figure 4.5: A temperature dependency of the ion decomposition rate of FT-3283[66]4.5

Swelling test for G-10

G-10 is a material used for fabricating a flow channel. We put three small plates of G-10
into Fluorinert, and observed them for 5 months. Their appearances and textures did notchange. As shown in Table 4.6, no significant increment of masses were seen.
Table 4.6: A result of the swelling test

G-10 sample No. 1
G-10 sample No. 2
G-10 sample No. 3

4.6

Before test
(18/12/2009)
41.98
43.31
43.27

After test
(27/5/2010)
41.98
43.32
43.28

Diﬀerence of mass [g]
0.00
0.01
0.01

Erosion test of the core

To examine appearance of erosion on the surfaces of the core, which is expected in a
flowing fluid, the surfaces of the core whose outer diameter was 200 mm were exposed
to flowing Fluorinert. The velocity of the flow was over 0.7 m/s (∼4 m/s at an inlet).
A strainer was checked 14 days after from the start of the operation. Some small piecesof FINEMET were seen, which were considered to have initially existed on the surface

4.7 RF designing for the new cavity

58

or between FINEMET layers. One small piece was seen 33 days after. Its diameter
was 0.2∼0.3 mm. Operation was continued, however, no piece was observed. The total
operation time was two months. The surface of the core was observed by bare eyes andmicroscope (magnification: 25-175). No defect was seen.

Figure 4.6: An experimental apparatus for the erosion test

4.7

RF designing for the new cavity

The new cavity was designed and its resonance frequency is determined to be ω0 . ω0
is determined by the inductance L and capacitance C of the prototype cavity. C (thecapacitance of the accelerating gap) was determined in the designing, because L was fixedby the sizes of cores. HFSS (High-Frequency Structure Simulator) which is a product of
ANSYS, Inc. was used for the RF designing. Three issues were simulated.
◦ The value of the gap capacitance which is obtained by tuning the resonance frequency to 1.7 MHz◦ The heat distribution in the cores◦ The voltage on the core surfaces
Properties of the core such as relative permittivity or permeability are not isotropic because of the layered structure of the core. To introduce them to the simulation with
HFSS, we assumed as following. According to Appendix A, a capacitive transmission ofa signal is dominant over 76 kHz. That means the core is possible to be expressed as a
combination of a lot of cylinders whose diameters are diﬀerent each other. A schematic
view is shown in Figure 4.7. The operational frequency of the test cavity is 1.7 MHz
which is enough larger than 76 kHz. Then, in more macroscopic view, it is able to be
expressed as a bulk which has anisotropic permittivity and permeability in cylindrical4.7 RF designing for the new cavity

59

coordinate system. However, HFSS does not have a function to represent anisotropy incylindrical coordinate system. We adopted a method which is introduced below.
Each core are circumferentially separated 60 parts. Their angles are equally 6◦ . HFSS
is able to define local coordinate systems. As shown in Figure 4.8, local coordinate systems
drawn in red are defined at each separated part. Relative permittivity and permeability
which are orthogonally anisotropic are defined in them. This procedure has a same eﬀect
as defining anisotropy in cylindrical coordinate system. The anisotropy becomes moreaccurate in a finer separation, however, circumferential separation of 60 was selected toreduce a time for calculating. Properties of orthogonal anisotropy which are defined in
the local coordinate systems are shown in Table 4.7. A method to obtain these values
are introduced in following subsections.

Figure 4.7: A macroscopic treatment for the core model4.7 RF designing for the new cavity

60

Figure 4.8: Definitions of local coordinate systems[67]Table 4.7: Anisotropic properties defined at each local coordinate system

X direction
Y direction
Z direction

Relative permittivity
15
1
1

Relative permeability
4
3500
3500

Relative permittivity in radial direction
As shown in Figure 3.9, the core has a structure that FINEMET ribbon and silica arelaminated alternately. Microscopically, the layered structure is a capacitor whose distanceof two electrodes is h [m] and the area of the electrode is S [m2 ]. The capacitance of thecapacitor, C [F], can be written as
S(a + b),(4.2)
bhwhere a=18[µm] and b=2[µm]. They are thicknesses of a FINEMET ribbon and silica,
respectively. =2 is a relative permittivity of silica. We treated this layered structure
in macroscopic way. We assumed the structure has a eﬀective relative premittivity ef f .
Then, a capacitance Cef f can be expressed asS(4.3)
Cef f = ef f 0 .
h
C = 04.7 RF designing for the new cavity

61

Assuming these two capacitance are consistent, ef f ∼ 20 is derived. Considering thefilling ratio of the FINEMET core is 75 % , ef f ∼ 15.
Relative permittivity in circumferential and beam directions
Relative permittivities in these directions are considered to be infinite, because these
directions are along conductive FINEMET layers. Results of the calculation with relative permittivities of 9999 in these directions showed that higher order modes appeared,
which should not appear in reality. 9999 is the maximum value which is able to be input
into HFSS. This is because a wavelength in the cores was shorten by the large relative
permittivity. In a real condition, layered FINEMET ribbons are expected to force thedirection of an electric field to be along a radial direction. To represent this condition,some layers of perfect-electric-conductor are concentrically assembled in the core model.
Electric fields only exist along a radial direction, so that the relative permittivities in circumferential and beam directions are arbitrary. ”1” was used as the relative permittivity
in these directions.
In the case of the new cavity, radial thickness of the core is thin, so that the directionsof electric fields are along radial direction naturally. Hence, no perfect electric conductive
layer is assembled and the relative permittivity is ”1”.
Relative permeability in a radial direction
The relative permeability of simple FINEMET and the insulating layer (the impregnatedepoxy resin) are 1900 and 1, respectively at 1.7 MHz. Treating the layered structure
macroscopically, an eﬀective relative permeability can be written as
75 + 25
75
25
=
+ .
µef f
1900
1

(4.4)

Hence, a following result is deduced.
µef f =

(75 + 25) · 1900
=475 · 1 + 25 · 1900

(4.5)

Where, 75 and 25 represent filling ratios of FINEMET and the insulating layer, respectively.
Relative permeability in circumferential and beam directions
These directions are along FINEMET layers. Therefore, relative permeabilities of 1400
are derived by multiplying a filling ratio of 75% to the relative permeability of simple
FINEMET. According to Appendix G, µ0p must be used in no loss calculation, and is
calculated as 3500 in the present case.

4.7.1

Simulations for electromagnetic fields

Using relative permittivity and permeability derived above, we performed calculations forthe eigen mode with HFSS. A resonance frequency of the prototype cavity was tuned to4.7 RF designing for the new cavity

62

1.7 MHz by adjusting a permittivity of the accelerating gap. The result showed optimum
capacitance of the gap was 660 pF. The accelerating gap of the actual cavity will be madeof alumina, however, variable capacitor is connected for the prototype cavity instead of
the alumina gap. Distributions of the electric field along the beam axis and magneticflux-density in the core, which are normalized with the power loss of a presently installed
RCS core (6 kW), are shown in Figure 4.9 and 4.10, respectively. A distribution of theheat in the core is proportional to the squared distribution of magnetic-flux-density inthe core, and is shown in Figure 4.11. A distribution of electric fields on lines which are
shown in Figure 4.12 are shown in Figure 4.13. Properties of each material used in thissimulation are shown in Table 4.8. All of them are lower than the breakdown voltage ofFluorinert ∼40 [kV] per 2.54 [mm], so that no breakdown is expected.

Figure 4.9: A distribution of an electric field along the beam axis, which was derived
from the simulation

4.7 RF designing for the new cavity

63

Figure 4.10: A distribution of magnetic fields in the cores, which were derived from thesimulation. A blue circle, red rectangular, and green triangle represent the magnetic-fluxdensities in the gap side core, center core, and short plate side core, respectively.

Figure 4.11: A distribution of a calorific value in the cores, which is proportional to thesquared distribution of magnetic-flux-density in Figure 4.10

4.7 RF designing for the new cavity

Figure 4.12: Lines where electric fields on the core surfaces are calculated[58]Figure 4.13: Electric fields on the lines which are shown in Figure 4.12

64

4.7 RF designing for the new cavity

65

Table 4.8: Electromagnetic properties of materials used in the simulation

FINEMET core

Fluorinert
G-10
Alumina

4.7.2

Relative permittivity
radial: 15
circumferential: 1
beam direction: 1
1.91
4.5
38

Relative permeability
radial: 4
circumferential: 3500
beam direction: 3500
1
1
1

Thermo-fluid simulation, and design for the flow channel
with a half sized flow channel

A flow channel is formed on the surface of the cores to make the flow turbulent by
increasing the velocity of Fluorinert, and enhance the cooling eﬃciency. The apertures
surrounded by the surfaces of the cores and G-10 plates in Figure 4.3 form flow channels(3mm hight × 81 mm width). A geometry of the flow channel is shown in Figure 4.14.
Fluorinert enters inner diameter and exits outer diameter. Reynolds number of over 2320
is necessary to make the flow turbulent. It corresponds to a velocity of over 0.33 m/s. In
the flow channel, the flow rate of Fluorinert is set to approximately 45 L/min to gain avelocity of 0.7 m/s which is enough to realize the turbulence.

4.7 RF designing for the new cavity

66

Figure 4.14: A schematic view of a flow channel
A distribution of the velocity calculated with ANSYS CFX is shown in the left-handside of Figure 4.15. A velocity which is needed for a turbulence is seen in almost whole
region of the flow channel. In the left-hand-side of Figure 4.16, the upper limit of thecontour is set to 0.4 m/s in order to help us to identify the area of turbulence. The red
area represents turbulence.
Some stagnations are seen at connections between the flow channels with the diﬀerent
diameters. To evaluate the adequacy of the simulation, a half sized flow channel (1.5mm height × 38 mm width) was fabricated and a visualization test for the flow was
performed. The flow channel is shown in Figure 4.18. Both sides of the container are
made of a transparent acrylic-acid-resin to observe the flow. Dummy cores are made ofaluminum and painted white to help the visualization. The fluid is water. Black ink ismixed into the fluid and the flow is visualized. Stagnations are seen at the same regions
as the simulation. This result shows the simulation is reliable. At the beginning of thetest, bubbles were trapped in the flow channel. They disappeared in an hour. The resultsof the test are shown in Table 4.9.
Rudders made of G-10 are mounted and spout holes are fabricated to solve stagnations.
These ideas are based on the design of an airplane. The rudders also have a function tokeep the shape of the soft cores. Positions and geometries of the rudders are optimized
with ANSYS CFX. An optimum geometry of the rudder and positions of them are shownin Figure 4.19 and 4.20, respectively. Geometries and positions of the spout holes are4.7 RF designing for the new cavity

67

also shown in Figure 4.20.
The result of the simulation for the velocity of the Fluorinert after the optimizationis shown in the right-hand-side of Figure 4.15. The upper limit of the contour is set to
0.4 m/s in the right-hand-side of Figure 4.16. The stagnations disappeared.

Inlet
1.5[m/s]

Inlet
1.5[m/s]OutletOutletFigure 4.15: Distributions of Fluorinert velocity calculated by means of ANSYS CFX.
Left-hand-side is the calculation before the optimization of the flow channel. Right-handside is after optimization.[58]4.7 RF designing for the new cavity

68

Inlet
1.5[m/s]

Inlet
1.5[m/s]OutletOutletFigure 4.16: The upper limit of the contour in Figure 4.15 is changed to 0.4[m/s].
Fluorinert is turbulent over 0.33[m/s], so that red area represents turbulent flow.[58]Figure 4.17: The distribution of the temperature at the center of the core. Left-hand-side
is before the optimization of the flow channel. Right-hand-side is after optimization.[58]4.7 RF designing for the new cavity

69

Figure 4.18: A half sized flow channel

Table 4.9: A result of the visualization test
Velocity [m/s]
0.73
1.0
1.4
1.8
2.2
2.6
2.9
3.3

Pressure [kgf/cm2 ]
0.2
0.3
0.5
0.9
1.4
1.8
2.6
3.2

Laminar or Turbulence
Turbulence
Turbulence
Turbulence
Turbulence
Turbulence
Turbulence
Turbulence
Turbulence

Figure 4.19: A schematic view of a rudder

4.8 Assembly of the prototype cavity

70

Figure 4.20: Positions of rudders and spout holes

4.8

Assembly of the prototype cavity

In this thesis, we introduce the development of the prototype cavity for the new cavity,
which is loaded with one core module. The process of the assembly of the prototype
cavity is given in this section.

4.8.1

Assembly of the core module

The core module was assembled by binding small, middle, large cores with two G-10
plates at a factory of Hitachi Metal, Inc. in Tottori. A picture of the assembly is shownin Figure 4.21.
Results of the measurements for the shunt impedances of small, middle, large cores,
and a core module are shown in Figure 4.22 and Table 4.10. The shunt impedance of thecore module is less than the sum of 3 diﬀerent diameter cores by approximately 6% . We
guess this is the systematic error which comes from the diﬀerence of the circumstances.
Screws are made of G-10. EPDM rubber is selected as a sealant. EPDM rubber issuited to Fluorinert and it has an excellent durability against radioactivity[61]. EPDM
rubbers are attached on the surface of the rudders not to damage the cores by the directcontacts between the rudders and the cores. Because of this attachment, we modified theheight of the flow channel from 3 [mm] to 5 [mm].

4.8 Assembly of the prototype cavity

Figure 4.21: A core module under fabrication

Figure 4.22: Shunt impedances of the three cores and the core module714.9 RF test facility

72

Table 4.10: Shunt impedances of the three cores and the core module at 1.7 MHz
Large core

Middle core

Small core

41Ω

52Ω

67Ω

4.8.2

Sum of threevalues160Ω

Core module
151Ω

Assembly of the prototype cavity

The prototype cavity was assembled in July, 2010. As shown in Figure 4.23, the coremodule was assembled into a container made of stainless, then, we stood it up. Initially,
we examine the airtightness of the container with nitrogen gas of 2 [atm], then, poured
Fluorinert. This is because pouring expensive Fluorinert without an advance examination
is risky. We selected a brass as the material for plugs and connectors. Use of a material
which is diﬀerent from container prevents plugs and connectors from being locked after
assembly. Brass plugs and connectors are not corroded in Fluorinert and they are easily
available.

Figure 4.23: An assembly of the prototype cavity

4.9

RF test facility

4.9.1

RF source

A semiconductor RF source shown in Figure 4.24 is used. Output power (continuouswave): 0-10 kW, output frequency: 800 kHz-3 MHz, output impedance: 50Ω (LC connector).

4.9 RF test facility

73

Figure 4.24: A semiconductor RF source

4.9.2

Cooling system

A schematic view of a cooling system is shown in Figure 4.25. The magnetic pump isused. The pump often slipped in the early operation, because the density of Fluorinert isapproximately twice as large as that of water, and the pump was designed for water. We
solved this problem by attaching a weight on the shaft of the motor in order to performa dynamic matching. The heat exchanger has the ability to cool 100 kW. Pure water ofapproximately 30◦ C flows in the secondary cooling system. The independent circulatory
system is connected to the cooling system, which has filters for water, organic substances,
and acid generated by radiations on Fluorinert.

4.9 RF test facility

74

Figure 4.25: A conceptual diagram of the cooling system[67]4.9.3

Matching box

On resonance, the impedance of the prototype cavity seen from the RF source is a pureresistance. The value was directly measured as 146 Ω. As shown in Figure 4.26, the pureresistance of 146 Ω is on the horizontal axis of the immittance chart, so that two ways areavailable to match with the output impedance of the RF source (50 Ω). They are paths
passing upper region and downer region on the immittance chart. Diagrams of them areshown in Figure 4.27 and 4.28. The capacitor is connected in series in Figure 4.27. The
inductor is connected in series in Figure 4.28. The connection in Figure 4.28 is accepted,
because a large current of 20 A flows in the series wire and an inductor is stronger against
a current than a capacitor. The capacitor has 890 pF and the inductor has 6.6 µH in
Figure 4.28. The circuit is shown in Figure 4.29. After assembling the matching box,
VSWR was improved from 2.7 to 1.1.

4.9 RF test facility

Figure 4.26: Impedance matching with the immittance chart

Figure 4.27: A circuit schematic of the matching box with the series capacitance

Figure 4.28: A circuit schematic of the matching box with the series inductance75

4.9 RF test facility

76

Figure 4.29: A circuit schematic of the matching box used in the RF test

4.9.4

Interlock system

We set up an interlock system for the test facility. We connected two outputs of DC
currents on the control panel of the cooling system and the paperless-pen-recorder. Eachoutput is for monitoring the flow rate and the Fluorinert temperature at the inlet. External relays of the paperless-pen-recorder is adjusted to be open under 34[L/min] for theflow rate or over 70[◦ C] for the inlet temperature. These relays are connected to the RF
source. Therefore, the RF source is turned oﬀ on the condition of these states.

Chapter 5
RF testThis chapter reports the results of RF test. The temperature rise of Fluorinert, theresonance frequency, the shunt impedance, and Q value were measured. The coolingeﬃciency was evaluated.

5.1

Test standRF test was performed at D7 RF experimental hall in KEK. The completed prototype
cavity with the matching box is shown in left of Figure 5.1. We adjusted the capacitanceof the variable capacitor over checking the impedance of the cavity with the LCR meter,
and tuned the resonance frequency to 1.7 MHz. The capacitance was fixed as 406 pF.
While the RF source is on, the prototype cavity and the matching box were covered withan aluminum shelter shown in right of Figure 5.1 to confine an electromagnetic wave.

Figure 5.1: (Left) The completed prototype cavity with the matching box. (Right) The
aluminum shelter to confine the electromagnetic wave

5.2 Measurement of temperature rise of Fluorinert

5.2

78

Measurement of temperature rise of Fluorinert

A temperature rise of Fluorinert (a flow rate: 80[L/min]) was measured on the condition
that RF power of 0-10 kW (1.7 MHz) were provided to the prototype cavity. P , L, ρ,and C are defined as a dissipated power in the cores, a flow rate, a density of Fluorinert,
and a specific heat of Fluorinert, respectively. Then, the temperature rise of Fluorinert
can be written as
P [W]
.
(5.1)
∆T [K] =3
L[m /s] × ρ[kg/m3 ] × C[J/kg/K]
The comparison between the measurement and the calculation of the temperature riseis shown in Figure 5.2. Red and blue circles represent the measurement and the calculation, respectively. The density of 1792[kg/m3 ] and the specific heat of 1068[J/kg/K]
which correspond to the values at 35◦ C were used for the calculation. They reflect thetemperature of Fluorinert at inlet of 34◦ C. P includes the correction of the cable loss.
The loss is 0.0054[dB/m]. The length of the cable is 7[m]. Hence, The loss for one way isderived as
0.0054[dB/m] × 7[m] = 0.038[dB].
(5.2)
Namely, the loss for one way is 0.88% . The plot shows the measurement and the calculation have a good agreement, so that we are able to conclude the powers are suppliedcorrectly.

Figure 5.2: A relation between the temperature rise of Fluorinert and the dissipatedpower in the cavity. Red and blue circles represent the measurement and the calculation,
respectively.

5.3 Measurement of the shunt impedance

5.3

79

Measurement of the shunt impedanceUsing values of voltages on the accelerating gap (the variable capacitor) and dissipatedpowers in the cores, shunt impedances were calculated and are shown in Figure 5.3. The
definition of the shunt impedance shown below was used.
Rp ≡

V2
2P

(5.3)

Where, Rp is a shunt impedance, V is an accelerating voltage, and P is a dissipated powerin the cores. The shunt impedances in Figure 5.3 are steady at any dissipated powers, sothat we are able to conclude no unusual heating and no discharge appear.

Figure 5.3: A relation between shunt impedances of the cavity and dissipated powers in
the cores5.4 Q factor of the prototype cavity

5.4

80

Q factor of the prototype cavity

Figure 5.4: A shunt impedance of the prototype cavity which has a resonance at 1.7[MHz]A result of measurement for the shunt impedance of the cavity around its resonance pointis shown in Figure 5.4. The Q factor of the cavity can be derived with the definition.
Q≡

f0
∆f

(5.4)

Where, f0 is the frequency at the point where the shunt impedance is on the peak, and∆f√is the band width between two points where the values of the shunt impedances are
1/ 2 of the peak. Hence, the Q factor is derived asQ=

1.96 × 106= 0.8.
2.47 × 106(5.5)

The Q factor of the presently installed cavity is ∼2. This value is realized by connecting
a parallel inductor to the cavity. The original Q of the presently installed cavity is 0.6.
The Q of the prototype cavity is consistent to that of the presently installed cavity within
25% , and can be tuned to ∼2 by the same scheme.

5.5

Cooling eﬃciency of the prototype cavity

5.5.1

Measurement of temperatures on the surfaces of the coreswith a thermo paintWe measured temperatures on the surfaces of the cores with a thermo paint. It is a
product of Nichiyu Giken Kogyo Co., Ltd.. The product number is No.5. The range of5.5 Cooling eﬃciency of the prototype cavity

81

the temperature where the color of the thermo paint changes was measured on a hotplate.
The initial color of light pink began to change to blue at 47◦ C. Then, it gradually turned
deeper blue as the temperature rises. The end of the change was at 55◦ C. We painted iton the surfaces of small, middle, and large cores. Positions where we painted are shown in
Figure 5.5. At these positions, sapphire view ports are assembled to observe the colors.
The view ports are shown in Figure 5.6.
We supplied powers to the cavity up to 8[kW] by 1[kW] step. In the equilibrium
condition at each step, we turned oﬀ the RF source and removed the panel of the shelter,
then, checked the colors by the bare eyes. The color was only changed on the small core.
No change was observed on the middle and large cores. A result for the small core is shownin Figure 5.7. The green area is the region where the color is supposed to vary. The color
began to change in the observation at 4[kW], and ended at 7[kW]. These values are shownwith red lines. The blue line represents the temperature of the surface of the small core,
which were obtained from the simulation. The blue line is expected to diagonally crosstwo vertexes of the rectangular consisted with the green area and the two red lines, whenthe measurement and the simulation are consistent. The thermo paint have the error of
approximately ±10◦ C, so that we are able to conclude they have a good agreement.

Figure 5.5: Blue circles are the positions where the thermo paint is painted.

5.5 Cooling eﬃciency of the prototype cavity

82

Figure 5.6: Sapphire view ports to observe the color of the thermo paintFigure 5.7: A result of the measurement for the temperature on the surface of the smallcore5.5 Cooling eﬃciency of the prototype cavity

5.5.2

83

Evaluation of a heat transfer coeﬃcient on the surface ofthe core

A heat transfer coeﬃcient is obtained by measuring the time constant of the temperature
decrement of Fluorinert after sudden oﬀ of the RF source which is supplying a power incontinuous operation. The heat transfer coeﬃcient which is obtained with this method isexpressed as the series connection of the heat transfer in the core and that on the surfaceof the core.
1
1
1
=
+
(5.6)
hef f
hC h
Where, hC is the heat transfer coeﬃcient in the core, h is the heat transfer coeﬃcient on
the surface of the core, hef f is the eﬀective heat transfer coeﬃcient. The heat transfer
coeﬃcient obtained with the time constant is hef f . We measured time constants in various
flow rates. On the other hand, time constants in the same conditions are figured out
with simulations. Results are shown in Figure 5.8. Then, heat transfer coeﬃcients arecalculated with these time constants and plotted in Figure 5.9. The used formula isshown in Appendix H. The measurements and the simulations are consistent in 20% .

Figure 5.8: Results of the measurements for the time constants and results of the simulation

5.5 Cooling eﬃciency of the prototype cavity

84

Figure 5.9: Heat transfer coeﬃcients derived with the time constants
Above results support the reliability of the simulation. The essential heat transfer
coeﬃcient is h, because it characterizes the direct cooling eﬃciency of Fluorinert. h isdirectly obtained from the simulation. The values of h at the position of the blue circle
on the small core in Figure 5.5 is shown in Figure 5.10. h in the region over 60[L/min]surpass that of the presently installed RCS cavity (500[W/m2 /K]). Thus, we are able toconclude the prototype cavity has the enough cooling eﬃciency.

5.5 Cooling eﬃciency of the prototype cavity

Figure 5.10: Results of the simulation for heat transfer coeﬃcients85

Chapter 6
Summary of performance of the
prototype cavity and Discussion
J-PARC will produce the world’s most intensive proton beam and provide it to advanced
research facilities for variety of fields. However, a buckling problem of FINEMET cores in
RCS appeared and a stable operation has not established yet. Despite this situation, weplan to enhance the present intensity of the beam. We are developing a new accelerating
cavity which can be replaced with a presently installed RCS cavity to contribute to thestabilization and enhancement for the performance of J-PARC accelerator.
For this purpose, we carried out experiments listed below.
◦

Calculation of the calorific value of the core which is assembled in thepresently installed RCS cavity
The result was consistent to the value which was obtained from a measurement of atemperature rise of water in the presently installed RCS cavity.
◦

Measurements of a specific heat and a thermal conductivity of the core
The specific heat was 0.500[J/kg/K]. The thermal conductivities were 0.6[W/m/K] fora radial direction and 7.1[W/m/K] for circumferential and beam directions.
◦

Design for the core module
The FINEMET core is not impregnated with a epoxy resin. The core is used as afunctional material, so that no stress is applied on it in the core module.
◦

Swelling test
No swelling was observed.
◦

Erosion test
No erosion was observed.
◦

Establishment of a macro model of the core for the electromagnetic calculation
The FINEMET core was modeled as a bulk which had anisotropic relative permittivities (r =15, θ =1, Z =1) and permeabilities (µr =4, µθ =3500, µZ =3500) in a cylindricalcoordinate system.

87◦

RF designing
Distributions of the electric field along the beam axis, the magnetic field in the cores,
the electric field on the surfaces of the cores, and heat in the cores were derived.
◦

Simulations for thermal stresses and contact simulation for the core, anda compression test to verify the simulation
The results showed a raw core was favorable.
◦

Optimization of the geometry of the flow channel with a simulation anda flow visualization test with a half sized flow channel
The result of the visualization test showed a good agreement with the simulation.
Rudders and spout holes were designed and assembled in the flow channel.
◦

Interlock system
The RF source is turned oﬀ on the condition of under 34[L/min] for the flow rate orover 70[◦ C] for the inlet temperature.
◦

Fabrication of the prototype cavity◦

RF test
The resonance frequency of the prototype cavity is 1.7[MHz]. The shunt impedanceis 146[Ω]. The Q factor is 0.8. The heat transfer coeﬃcient is shown in Figure 5.10.

As mentioned at the beginning of chapter 6, the cavity have to satisfy three parameters.
Resonance frequency
We adjusted the capacitance of the variable capacitor over checking the impedance of thecavity with an LCR meter, and tuned the resonance frequency to 1.7[MHz].
Shunt impedance
A shunt impedance of the cavity was measured when we tuned the resonance frequency.
It was 146[Ω]. On the other hand, a shunt impedance was calculated in the RF test.
The shunt impedance was derived as 146[Ω] and this value was consistent to the previous
one. The value was steady at any dissipated power, so that it was concluded no unusual
heating and no discharge appeared.
Q factor
A Q factor of the cavity was obtained with a definition of the equation 5.4. The value
was 0.8. In this development, Q is not a practical value of ∼2, however, it will tuned byconnecting a parallel inductor to the cavity in the next step.

88

Therefore, we are able to conclude we have established a method for the development ofan accelerating cavity. Current statuses of other two parameters are mentioned below.
Cooling eﬃciency
A temperature on the surface of the small core was measured with a thermo paint. The
temperature was 47◦ C at a dissipated power in the cores of 4[kW], and 55◦ C at 7[kW].
These values have a good agreement with the simulation. On the one hand, time constantsof the decrements of the Fluorinert temperature were measured. They also have a good
agreement with the simulation. The heat transfer coeﬃcients which are obtained fromthis reliable simulation are shown in Figure 5.10. Values over 60[L/min] surpass that ofthe presently installed cavity.
Breakdown voltage
We fabricated an apparatus shown in Figure 6.1 for the breakdown test. The test will beheld promptly after preparing a power source and a pulse generator.
For a next stage, we will fabricate a one gap prototype cavity loaded with six coremodules and carry out a performance test. The cross-section is shown in Figure 4.1.
A set of three one gap prototype cavities consists a complete accelerating cavity. The
semiconductor RF source is not able to provide an enough power for the prototype cavity.
A tube amplifier is necessary. An RF test with a large power which is expected after the
beam enhancement will be also performed. In parallel with the development of the one
gap prototype cavity, a test for a long term operation will be also performed with theprototype cavity which is introduced in this paper. To evaluate a breakdown voltage ofthe core soaked in Fluorinert, we fabricated a container shown in Figure 6.1 and perform
a breakdown test. A small core will be put in the container and applied with pulsed
voltages in flowing Fluorinert. Then, we will observe discharges of the core.

89

Figure 6.1: An apparatus for the breakdown test
A new cavity for MR is also planed to be developed. The new cavity will be loadedwith the FINEMET cores which are radially separated into three and cooled by Fluorinert. Under the existing condition of MR, cut cores are assembled in presently installed
accelerating cavities to tune Q factor to ∼25. In the case of the new figure cores, cut isalso needed to tune Q. A diamond cutting machine at the machine shop bldg. in KEK
will be used to cut cores. The cores of new figure are ”raw core”, so that they will fallapart to pieces with direct cuts. we have to solidify a part of the core before cutting.
We are studying about the method for cutting in cooperation with institute of industrial
science at the University of Tokyo. Development except cutting will be done with a sameprocess as the new cavity for RCS.
In the future, we will develop an evaporative-cooling-system. Fluorinert suited forevaporation is supposed to be FC-72 which has a low boiling point (56◦ C). However, weshould solve following problems to develop it.
◦ A FINEMET ribbon can be damaged by a shock wave which appears when a bubble
is generated.
◦ Electric field will concentrates to a bubble remaining between FINEMET layers,
and the breakdown voltage will decrease.
◦ A mechanism to stabilize a pressure inside the cavity, which cancel the variation of
the pressure caused by an evaporation and condensation of FC-72, is necessary.

Chapter 7
Conclusions
J-PARC was designed to produce the world’s most intensive proton beam and provide
it to advanced research facilities for the wide range of field. T2K is one of the mostimportant experiment. It requires 5 × 1021 POT in approximately 5 years which corresponds to 0.75[MW]. To produce proton beam of this intensity, the enhancement of beam
is necessary.
There are three methods for the enhancement.
◦ Increasing the energy of beam
◦ Increasing the number of proton in the bunch◦ Increasing the repetition rate of the accelerator
The third method was accepted. This method requires the accelerating gradient to
be enhanced, so that the accelerating cavity will be put in the hard environment toaccelerate a large beam current in a long term. A powerful and stable accelerating cavity
is indispensable.
The presently installed cavity is loaded with cores made of FINEMET. FINEMET isa magnetic alloy which has characteristics listed below.
◦ The permeability is high.
◦ The saturation magnetic-flux-density is high.
◦ The Curie temperature is high.
These characteristics are suited for the cavity in J-PARC. The cavity is a λ/4-wave
coaxial type. It has three accelerating gaps and each gap has three FINEMET cores onboth sides. A stable operation of the presently installed cavities has not established yet,because they have a problem that the FINEMET cores are damaged while the cavities arein operation. We are developing a new accelerating cavity which can be replaced with thepresently installed RCS cavity in order to contribute the stabilization and enhancement
for the performance of J-PARC ring accelerators.

91

We simulated the stress in the core, and performed a test for compressing samplesof the core. The cause was identified as the buckling which was caused by the thermal
stress in the core. We showed the core without impregnation is favorable to prevent thebuckling. The development of the new cavity is based on these results.
The new cavity has design concepts which have never been seen before.
◦ The cores have unique structure named core module.
· Each FINEMET core is radially separated into three. This structure helps toclearly diﬀerentiate between constructional materials and functional materials.
· These cores are not impregnated. The thermal stresses in the cores are relieved
because the cores are soft.
◦ A turbulent fluid is used to cool the cores.
· Fluorinert is used as the coolant. Fluorinert is chemically inert, so that it issuited for cooling FINEMET cores which is subject to corrosion. Fluorinert
flows in the flow channel which is formed on the surfaces of the radially separated cores. The flow channel makes Fluorinert turbulent, so that a highcooling eﬃciency is realized.
The development of the new cavity has significances below.
◦ It has a high degree of potential for solving the diﬃculty of the stabilization andthe enhancement.
◦ It can be a prototype of next-generation cavities.
We designed RF structure of the cavity with HFSS and designed the flow channel with
ANSYS CFX. We assembled a prototype of the new cavity, and prepared the test facility.
This is the first case to use three dimensional FEM (Finite Element Method) simulatorsfor developing a cavity loaded with magnetic alloy cores. The process of this development
is scientifically meaningful. We carried out the performance test of the prototype cavity
and measured several properties which are essential for an accelerating cavity.
◦ The resonance frequency is 1.7[MHz].
◦ The shunt impedance is 146[Ω].
◦ The Q factor is 0.8.
Results of the measurement for the cooling eﬃciency are shown below.
◦ The temperature on the surface of the small core was measured with the thermo
paint. The value was consistent with that was obtained from the simulation.
◦ The eﬀective heat transfer coeﬃcient was obtained by measuring the time constantof the temperature decrement of Fluorinert, and the value was consistent with thatwas obtained from the simulation in 20% .

92◦ The heat transfer coeﬃcient on the surface of the small core was obtained withthe simulation. The value is consistent with that was calculated with the empiricalequation. The value surpassed that of presently installed cavity over 60[L/min].
We supplied the power to the prototype cavity up to 10[kW], and it worked stably.
We accomplished following significant researches.
◦ We revealed the cause of the buckling of the cores was the thermal stress in the
cores. We showed the cores without impregnation is eﬀective to avoid the buckling.
◦ We assembled the prototype cavity and carried out the performance test. The
results of the test satisfy the requirements of RCS so far.
The results of the researches support the feasibility of developing the new cavity. Thisis the first development of the cavity loaded with magnetic alloy cores, which is able tobe operated stably with the large input power of 10[kW] per core. Adopting this newcavity is the most realistic way to stabilize and enhance the performance of the J-PARC
ring accelerators.

Acknowledgements
In the first place, the author would like to express the sincere appreciation and gratitude
to the supervisor, Prof. Satoru Yamashita, for his help and encouragement throughout
six years. The author is thankful to Prof. Tatsuya Kageyama for many discussions andsuggestions for the whole work.
Toru Suehiro and Takeshi Takahashi, who were master students in Yamashita laboratory, worked with the author. The author appreciates them for the discussions and thecooperations.
The author are thankful to Prof. Nobuhiro Yoshikawa at Institute of Industrial Science, the University of Tokyo for his help and expertise with the simulation for the thermal
stress and the knowledge of the material science.
The author appreciates Dr. Jun Kameda and Dr. Katsushi Hasegawa for the discussions and the instructions of the simulation soft wares.
The author would like to thank Dr. Shiro Torizuka, Dr. Masatoshi Tsukamoto and
Dr. Etsuko Tsuchiya at National Institute for Materials Science (NIMS). They strongly
assisted the test for compressing the samples of the core.
The author would like to thank Dr. Megumi Akoshima at Advanced Industrial Scienceand Technology (AIST) for the help to measure the thermal conductivity of FINEMET.
Prof. Hiroo Yoshida at Kanagawa Institute of Technology and Dr. Takehiko Segawa,Dr. Norihiko Iki at AIST gave the suggestions about the development of the flow channel.
The author would like to express sincere appreciation to them.
The author appreciates Mr. Yoshisato Funahashi at the machine shop building in
KEK for cutting samples of the core.
The author appreciates Dr. Mitsuhiro Yoshida for the advices about the high voltage
pulse generator.
The author would like to thank Mr. Katsuhiro Ogura at Hitachi Metals, Ltd. for the
informations about FINEMET cores and the production of the core module.
The author appreciates SKILLWELL CO., LTD for the support at the every scene ofthe development of the prototype cavity.
The author appreciates Taiyo valve MFG. CO., LTD for the cooling system, THAMWAY
CO., LTD for the RF source, Sumitomo 3M Limited for Fluorinert.
The author appreciates Dr. Tomohiko Tanabe for checking English of this thesis.
The author extend the appreciation to all staﬀ members of J-PARC and ICEPP for
their assistance and support.
This work was supported in part by Japan Society for the Promotion of Science (JSPS)and most part by KEK.

Appendix A
Simplification of the core model
against electromagnetic fields

Figure 1.1: An equivalent circuit for a wound structure of a FINEMET core
An equivalent circuit for a wound structure of a FINEMET core can be shown as Figure
1.1. An impedance of this circuit is written as
1
R
=
.
f
+
jωC
1
+
j
R
f

Z= 1

(A.1)

CR

1
Where, fCR = 2πCR
. fCR is a critical frequency which determine a path of a signaltransmission. A capacitive component is dominant on the condition of f > fCR , while, aresistive component is dominant on the condition of f < fCR . We define a as an averageradius of a core of 0.26[m], w as a width of a FINEMET ribbon of 0.035[m], d1 as athickness of the FINEMET ribbon of 18×10−6 [m], d2 as a thickness of an insulating layerof 2×10−6 [m], r as a relative permittivity of the insulating layer of 4, and ρ as a resistivity

95
of a FINEMET ribbon of 1.2×10−6 [Ω·m]. Then, R and C are written as2πa
2π × 0.26= 1.2 × 10−6 ×= 3.11,
wd1
0.035 × 18 × 10−6

(A.2)

0 r S
0 × 4 × 2π × 0.26 × 0.035= 6.75 × 10−7 .
=d2
3 × 10−6

(A.3)

R=ρ×
C=

Hence, the critical frequency is derived as fCR = 76[kHz]. It is concluded that capacitive component is extremely dominant at 1.7 MHz, so that we can model the core as aconcentrically stacked FINEMET cylinders.

Appendix B
Transformation between LR series
and parallel circuits
A series circuit with a resistance Rs and an inductance Ls , and a parallel circuit with aresistance Rp and an inductance Lp are shown in Figure 2.1. In the case of the series
circuit, an impedance Z=Rs +jωLs is transformed as
1
1= 2 2(
ω
L
Z
s
1+
Rs

Rs2
ω 2 L2s

(

)+
jωLs

1
2
1 + ωR2 Ls 2
s

)

(B.1)

In the case of the parallel circuit, an impedance is written as
1
1
1
=
+
.
Z
Rp jωLp
Equaling them, a following equation is deduced.
()
ω 2 L2s
Rs2
Rp =1+ 2 2
Rs
ω Ls

(B.2)

(B.3)

Thus, we are able to transform a series circuit to a parallel circuit. In the case of ωLs 
Rs , the equation is approximated asRp ≈ω 2 L2s
Rs

(B.4)

97

Figure 2.1: A series circuit and a parallel circuit

Appendix C
Measurement of a specific heat of a
FINEMET core at KEK
A specific heat of the FINEMET core was measured at KEK, independently of the measurement at the Cryogenic Research Center. The sample which was heated up to 100◦with a hotplate was dipped in water, then, its specific heat was calculated with temperature variations of the water and the sample. Their temperatures were monitored withthermocouples. Cw , Mw , and ∆Tw are a specific heat, a mass, and a temperature variationof the water, respectively. Cc , Mc , and ∆Tc are a specific heat, a mass, and a temperature
variation of the sample, respectively. We assumed a calorific value which was radiated by
the sample and that was absorbed by the water are equal, namely, the radiation to theout of system was small. Then, a following equation is deduced.
Cw Mw ∆Tw = Cc Mc ∆Tc(C.1)

Hence, a specific heat of the sample is deduced as
Cc =Cw Mw ∆Tw.
Mc ∆Tc(C.2)

The measurements were performed twice.
◦ First trial
Mass of the water: 633.63[g], Mass of the sample: 372.45[g], Specific heat of the water:
4.2[J/g/K]
Table 3.1: Specific heat measurement (First trial)

temperature of water [◦ C]
temperature of sample [◦ C]

initial state

final state

18.3
108.1

24.3
24.3

diﬀerence oftemperature
6
83.8

99

Specific heat of sample: 0.511[J/kg/K]◦ Second trial
Mass of the water: 681.86[g], Mass of the sample: 372.45[g], Specific heat of the water:
4.2[J/g/K]
Table 3.2: Specific heat measurement (Second trial)

temperature of water [◦ C]
temperature of sample [◦ C]

initial state

final state

20.7
152.9

29.3
29.3

diﬀerence oftemperature
8.6
123.6

Specific heat of sample: 0.535[J/kg/K]
Averaging the results of the measurements, we derived the specific heat of the sample
of 0.523[J/kg/K]. This value was consistent with that was measured at the Cryogenic
Research Center.

Appendix D
Calculations of heat transfer
coeﬃcients
A transfered calorific value per area, which is based on a diﬀerence between a temperatureof certain substance of T [K] and that of a circumstance of T∞ [K] is represented as h(T −T∞ )[W/m2 ] using a coeﬃcient h. h[W/m2 /K] is called a heat transfer coeﬃcient. Thatis,
ρV C dT= h(T − T∞ )
(D.1)
A dt
is deduced. Where, ρ[kg/m3 ], V [m3 ], A[m2 ], and C[J/kg/K] are a density, volume, area,and specific heat of the substance. In the simulation by ANSYS CFX, a temperatureof the core is calculated with Prandtl number first, then, h is determined. In the handcalculation, h is calculated by a following procedure. The heat transfer coeﬃcient h isdetermined by introducing Nusselt number N u.
h=

λ · NuL(D.2)

Where, λ[W/m/K] is a heat transfer coeﬃcient of the fluid, and L[m] is a characteristic
linear dimension of the flow channel. Considering a rectangular flow channel with theirsides of a[m] and b[m], the L can be written as
L=4

ab
.
2(a + b)(D.3)

The equation (D.2) shows N u is needed for determining h. The procedures to obtain N u
are diﬀerent between the cases of a laminar and a turbulence.

D.1

LaminarN u of laminar is a constant which is determined by the geometry of the flow channel anda heating condition.
N u = 4.9
(D.4)

D.2 Turbulence

101

Hence, h can be written as
h=

D.2

4.9λ
.
L

(D.5)

Turbulence

Using Reynolds number Re and Prandtl number P r, N u is written as[70]N u = 0.023Re0.8 P r0.33 .

(D.6)

Reynolds number is a nondimensional parameter which is defined as
Re ≡

UL
.
ν

(D.7)

Where, U [m/s] is a mean velocity of the flow and ν[m2 /s] is a dynamic viscosity of thefluid. Prandtl number is a nondimensional parameter which is defined asνPr ≡ .
(D.8)
α
Where, α[m2 /s] is a thermal diﬀusivity of the fluid and is defined as
α≡

λ
.
ρC

(D.9)

h is derived by substituting N u of the equation D.6 to the equation D.2. Schematic viewof the presently installed core in RCS (cooled by laminar water) is shown in Figure 4.1.
A characteristic linear dimension is written as
0.2395 × 0.003
L=4= 5.926 × 10−3 [m].
(D.10)
2(0.2395 + 0.003)

Figure 4.1: RCS flow channel
A thermal conductivity of water is λ = 0.6151 [W/m/K] (30◦ C), so that, h can be
written as
4.9 × 0.6151
h== 500[W/m2 /K].
(D.11)
5.926 × 10−3
A flow channel geometry of the new cavity (cooled by turbulent Fluorinert) is shown in
Figure 4.2. Therefore, the characteristic linear dimension is written as
L=40.081 × 0.005= 9.42 × 10−3 [m]2(0.081 + 0.005)(D.12)

D.2 Turbulence102

An inlet temperature of Fluorinert was approximately 40[◦ C] in the RF test. Propertiesof Fluorinert at 40[◦ C] are shown below.
density: 1780[kg/m3 ]specific heat: 1076[J/kg/K]
thermal conductivity: 0.0624[W/m/K]
dynamic viscosity: 5.9×10−7 [m2 /s]
Hence, Re, α, P r of U =0.5[m/s] are written as
0.5 × 9.42 × 10−3
= 7.98 × 103 ,−7
5.9 × 100.0624α== 3.26 × 10−8 [m2 /s],
1780 × 1076
5.9 × 10−7
Pr == 18.1
3.26 × 10−8
Re =(D.13)(D.14)(D.15)

Therefore,
N u = 0.023 × (7.98 × 103 )0.8 × (18.1)0.33 = 79.9.
Hence,
h=0.0624 × 79.9
= 530[W/m2 /K].
9.42 × 10−3

Figure 4.2: Prototype flow channel(D.16)(D.17)

Appendix E
Calculations for shunt impedances ofa presently installed RCS core and a
new configuration core
A complex relative permeability of a FINEMET core is written asµ0 = µ0s − jµ00s .

(E.1)

Then, an impedance of a one turn coil with the FINEMET core whose circuit schematicis shown in Figure 5.1 can be written as
Z = jωµL0 = jω(µ0s − jµ00s )L0 = ωµ00s L0 + jωµ0s L0 = r + jωL.

(E.2)

Where, r and L are defined asr ≡ ωµ00s L0 ,L ≡ µ0s L0 .

(E.3)
(E.4)

L0 is an inductance of an air cored coil. An inductance per unit length is written as∫µ0 r2 1
L0u =
dr.
(E.5)
2π r1 r
Where, r1 and r2 are an inner diameter and outer diameter of the core, respectively.

104

Figure 5.1: A circuit of a one turn coil with a FINEMET core
Applying the result of Appendix B, we can write a shunt impedance R as
ω 2 L2
R=r+
.
r

(E.6)

The presently installed RCS core has an inner diameter of 187.5[mm], an outer diameterof 425[mm] and a thickness of 35[mm]. Hence,
0.425
∫

1
dr = 0.130µ0 [H/m].
r

(E.7)

L0 = 0.035 × L0u = 5.72 × 10−9 [H]

(E.8)

µ0
L0u =
2π

0.1875

Therefore,

is derived. Average relative permeabilities of the core at 1.7 MHz areµ0s = 1200,µ00s = 2100.

(E.9)(E.10)A shunt impedance of the presently installed RCS core can be written asω 2 (µ0s L0 )200= 170[Ω].
R = ωµs L0 +
ωµ00s L0

(E.11)In the case of radially separated cores, a shunt impedance R of a core module is derived
by summing shunt impedances of a small, medium, and large core.
small core: RS =71.4[Ω]medium core: RM =50.3[Ω]105

large core: RL =39.0[Ω]Hence, R is deduced as
R = RS + RM + RL = 161[Ω].

(E.12)The value is almost same as the shunt impedance of the presently installed RCS core (Thediﬀerence is 5%) .

Appendix F
A characteristic of µ0Q[72]Figure 6.1: gap core
A magnetic resistance Rm in Figure 6.1 is written as
Rm =

lg
l
+
.
µA µ0 A

(F.1)

Where, µ is a permeability of the core. Introducing an eﬀective permeability µapp , Rm
can be written asl + lgRm =.
(F.2)µapp AThe equation (F.1) and the equation (F.2) lead an following equation.
µ0
µ0 l
lg
=
+
µapp
µ l + lg l + lg

(F.3)

107
lg
Assuming l  lg , approximations of l+ll g ≈ 1, l+l≈ llg ≡ k are derived. Then, thegequation F.3 can be written as
1
1
=
+ k.
(F.4)
µe
µr
Where, µe is an eﬀective relative permeability, and µr is a relative permeability of thecore. By using a complex representation of relative permeability, which is defined asµe = µ0e − jµ00e ,µr = µ0r − jµ00r ,

(F.5)
(F.6)

1
1
=
+ k.
µ0e − jµ00eµ0r − jµ00r(F.7)

the equation F.4 can be written as

After rationalization, the equation can be expressed as
µ0e
µ00e
µ0r
µ00r
+
j
=
+
k
+
j
.
002
002
002
002
µ02
µ02
µ02
µ02
e + µee + µer + µrr + µr(F.8)

Equaling both real parts and both imaginary parts respectively, two equations are derived.
µ0e
µ0r
=
+k
002
002
µ02
µ02
e + µer + µrµ00µ00
Imaginary part: 02 e 002 = 02 r 002µe + µeµr + µr
Real part:(F.9)(F.10)We define tanδe and tanδ as below.
µ00e
µ0e
µ00
tan δ ≡ r0
µrtan δe ≡(F.11)(F.12)

Then, the equation (F.10) can be written as
µ0r
µ0e
tan
δ
=
tan δ.
e
002
002
µ02
µ02
e + µer + µr(F.13)

(
(
)
)
1
1
0
Qe +
= µr Q +Qe
Q(F.14)

Hence,µ0e

is derived with the definitions of1,
tan δe
1
Q≡
.
tan δ

Qe ≡

(F.15)(F.16)

108
In most cases, 1  Qe and 1  Q hold, so that the equation (F.14) can be written asµ0e Qe = µ0r Q.

(F.17)

After cutting a core, the relative permeability increase and Q decrease, however, theequation F.17 shows a product of them µ0r Q does not vary. Thus, this product is a very
important practice.

Appendix G
Selection of µs and µp for simulationsof electromagnetic fields[73]There are two expressions of a complex representation for a relative permeability.
µ = µ0s + jµ00s
11
1= 0 − j 00
µ
µp
µp

(G.1)
(G.2)

In the case of a coil with a core of relative permeability µ, the loss of the inductor is able
to be represented by a resistance which is connected in series in the equivalent circuit asshown in left of Figure 2.1. An impedance of the inductor is written as
Z = jωL = jωµL0 = jωL0 (µ0s − jµ00s ) = ωµ00s L0 + jωµ0s L0 ≡ Ls + jωRs .

(G.3)

Where, L0 is an inductance of an air-cored coil. On the other hand, if we assume theresistance is connected in parallel as shown in right of Figure 2.1, the impedance of theinductor is expressed as
(
)
1
1
1
1
1
1
1
1
1
=
=
− 00 =
+
≡
+
.
(G.4)
0
00
0
Z
jωµL0
jωL0 µp jµp
ωµp L0 jωµp L0
Lp jωRp
Therefore, µ0s and µ0p have to be utilized for simulations of electromagnetic fields in thecase of lossy calculation and no loss calculation, respectively.

Appendix H
A relation between a heat transfer
coeﬃcient and a time constant
The equation D.1 introduced in Appendix D is shown here, again.
ρV C dT= h(T − T0 )A dt
Assuming T = T0 at t = 0, a solution of the equation (H.1) is written as()
hA
T = T∞ − (T∞ − T0 ) exp −
t .
ρV C

(H.1)

(H.2)

Therefore, a time constant for the variation of a temperature can be expressed as
1
hA
=
.
τ
ρV C
Values of A, ρ, V , and C are known, so that h is obtained by a measurement of τ .

(H.3)

Appendix I
Physics
Many researches of wide range of fields are carried out at J-PARC. In this section, we
introduce these researches focused on elementary particle physics experiments.

I.1

T2K experiment

J-PARC neutrino oscillation experiment (T2K: from Tokai to Kamioka) is a long baseline
neutrino oscillation experiment to detect νµ neutrino beam which is emitted from theneutrino beam line in J-PARC. The detector is a Large Water Cherenkov detector called”Super Kamiokande” (SK) in Hida-shi, Gifu-ken which is 295 km away from J-PARC.
The beam line for T2K experiment is shown in Figure 9.1. It is allocated inside of 30
GeV proton synchrotron (MR). 8 bunches injected MR are accelerated up to 30 GeV,
then they are kicked by a kicker and extracted to the beam line. This process is called”Fast Extraction” comparing with the ”Slow Extraction” (the extraction to the Hadron
Experimental Hall). After being bended right angle at the arc, the proton beam is focusedby electromagnets, then collides with a target and produces pions. These pions decay while
they are traveling in a decay pipe (93 m long), then, neutrinos which are produced by
the decays of pions travel to SK. The direction of the carbon target is shifted 2.5◦ fromthe direction of SK on purpose[3]. This shift allows the neutrino beam to have a narrowenergy band. This method is called an oﬀ-axis scheme.

I.1 T2K experiment112

Figure 9.1: The beam line for T2K experiment[6]After the beam enhancement, the peak energy of neutrino beam will be Epeak = 0.7[GeV], the neutrino flux will be νµ = 19.25 × 106 /cm2 /yr on the condition that the beam
power of MR is 0.75 MW, the fiducial volume is 22.5 kton, and OA2◦ (shift the emitting
neutrino beam direction 2◦ from SK). The neutrino flux was calculated by the Monte
Carlo simulation using GEANT[7] based on Calor-Fluka model. The event rate measured
at near detector of K2K shows this Monte Carlo is correct within 20% accuracy. This flux
is 50 times larger than that of K2K experiment. The aim is 5×1021 POT in approximately
5 years operation. Main purposes of T2K are below.[3]I.1.1

Accurate measurement of νµ disappearance parameter

An accurate measurement of the oscillation parameter of νµ disappearance (sin2 2θµτ ,∆m223 ) which is established by the measurement of atmospheric neutrino at SK and K2K
experiment will be performed. A Charged Current Quasi-Elastic interaction (CC-QE
interaction) of neutrino in SK is expressed asνl + n → l + p.

(I.1)

Where, l is lepton and l = e or µ. A neutrino energy of this interaction can be written asEν =mN El − m2l /2.
mN − El + pl cosθl(I.2)

Where, mN is the mass of neutron, ml is the mass of lepton, El is the energy of lepton, plis the momentum of lepton, θl is the scattering angle of lepton. Subtracting CC non-QE
event and neutral current (NC) event that are backgrounds from the neutrino energy
spectrum, a true neutrino energy spectrum is obtained. Numbers of each event on thecondition of OA2.5◦ , 5 × 1021 POT are shown in Table 9.1. A ratio between the spectrum
expected to be measured at SK, which is calculated by sweeping the oscillation parameteron Monte Carlo, and that is calculated in the case of no oscillation is shown in Figure
9.2. The spectrum simulation subtracted background events is used for the ratio. The

I.1 T2K experiment113

oscillation peak is seen at Eν ∼ 0.65 GeV. This results the statistical errors of sin2 2θ23
and ∆m23 are 0.009 and 5 × 10−5 eV2 respectively. 5 × 1021 POT used in the simulationis the value of 5 years operation on the condition of enhanced MR beam power of 0.75
MW (130 days per year for the operation of the accelerator is assumed). Therefore,
enhancing accelerator performance is essential to achieve target values of δ(sin2 2θ23 ) =0.01, δ(∆m223 ) = 10−4 eV2 .[3]Table 9.1: Numbers of each event on the condition of OA2.5◦ , 5×1021 POT[3]∆m223 (eV2 )No oscillation
2.0 × 10−3
2.3 × 10−3
2.7 × 10−3
3.0 × 10−3

CC-QE
3,620
933
723
681
800

CC-nonQE
1,089
607
525
446
414

NC
96
96
96
96
96

all νµ
4,805
1,636
1,344
1,223
1,310

Figure 9.2: A ratio between the spectrum expected to be measured[5]I.1.2

Discovery of νµ → νeνµ → νe oscillation will be investigated 20 times more sensitive than the present upper
limit reported by CHOOZ in 5 years operation of T2K experiment. CHOOZ is a nuclear
reactor experiment to examine the ν̄e → ν̄x (x = ν or τ ) oscillation. The aim is sin2 2θ13 ∼2sin2 2θµe > 0.006. This oscillation is the unique mode which has not discovered yet, andI.1 T2K experiment114

is expected to show the notice of CP violation measurements in the future. Hence, it is
the most important measurement of T2K. Because the momentum of protons in CC-QE
interaction is lower than the Cherenkov threshold, only an e-like ring can be seen as asignal for discovery of νe . There are three expected backgrounds.
1. the misidentification between e and µ
2. the νe contamination in νµ beam
3. the photon generation from the pion decay
For 1, the µ background will be excluded by extracting single ring e-like event in SK. For
2, it is known that the contamination is 0.2 ∼ 0.3% at peak energy of νµ spectrum which
is derived from the simulation. For 3, the cause is misidentifying the 2 photons generated
by π0 decays. These π0 are generated in the NC interaction and CC non-QE interaction.
To eliminate this background, cutting the interaction having a sharp peak which is uniqueto π0 decay is applied. Numbers of events after each separation are shown in Table 9.2.
Table 9.2: Numbers of events after each separation[9]OAB 2◦
Generated in F.V.
1R e-likee/π 0 separation
0.4GeV<Erec <1.2GeVνµ C.C.
10713.6
14.3
3.5
1.8

νµ N.C.
4080.3
247.1
23.0
9.3

Beam νe
292.1
68.4
21.9
11.1

Oscillated νe
301.6
203.7
152.2
123.2

A reconstructed neutrino energy spectrum is shown in left of Figure 9.3. Where, anoperation time of 5 years and ∆m2 = 3 × 10−3 eV2 , sin2 2θµe = 0.05 are assumed. 90%
C.L. parametrized with the operation time and 3σ restriction are derived by integrating
the number of events in the region 0.4-1.2 GeV. They are shown in right of Figure 9.3.
Therefore, sin2 2θµe = 0.003, 90% C.L. is obtained on the condition of 5 × 1021 POT after
beam enhancement. The variation of sin2 2θµe on the condition of sweeping ∆m2 is shownin Figure 9.4. Focusing on the expected region 1.6 × 10−3 eV2 < ∆m2 < 4 × 10−3 eV2 ,the statistics error is better than at least sin2 2θµe = 0.005 namely sin2 2θ13 = 0.01, 90%
C.L. . The aim is sin2 2θ13 ∼ 2sin2 2θµe > 0.008[10]. Hence, the beam enhancement isdispensable.

I.2 Search for µ− − e− conversion

115

Figure 9.3: A reconstructed neutrino energy spectrum in the left. 90% C.L. parametrizedwith the operation time and 3σ restriction are in the right. [3]Figure 9.4: The variation of sin2 2θµe on the condition of sweeping ∆m2 [3]I.2

Search for µ− − e− conversion

PRIME (PRISM Mu E conversion) is an experiment to search LFV µ− − e− conversion(µ− +Ti→ e− +Ti) in µ atom with the sensitivity of 10−18 by means of an intensive µsource called PRISM (Phase Rotated Intense Slow Muon source). PRISM aims the µI.2 Search for µ− − e− conversion

116

rate of 1011 − 1012 µ/sec on the condition of an injection rate of 1014 [protons/sec] (after
the beam enhancement). The experimental hall is in MLF (Materials and Life Science
Experimental Facility) shown in Figure 1.2. Single event sensitivity in 5 years will reachB(µ− +Ti→e− +Ti)∼ 3 × 10−18 on the condition of 3.0 × 1010 µ− /sec.
Particles which fly backward with an angle over 55◦ are reflected by a solenoidal
magnetic field at target section. As a result, approximately 80% of µ − e conversion
electrons are injected into the spectrometer at downstream. The spectrometer is shownin Figure 9.5. It has a curve and magnetic field is applied on. This configuration lets only
the particles having the momentum of 105 MeV/c pass. Other particles are excluded bya blocker installed in the spectrometer. The transmissivities through this structure are
53.0% for vertical direction and 100% for horizontal direction. If the angle of electrons
from the target is small, the radius of solenoidal orbits of the electrons become too small
to measure the momentum of them with enough accuracy. Therefore, the limitation ofsinθ > 0.33 is imposed. This limitation corresponds to pt > 86 MeV/c. The acceptancefor this limitation is 82.3% . The product of these values leads to a detector geometricalacceptance of 34.6% . Acceptances at each part are shown in Table 9.3. Assuming theanalysis eﬃciency is 80% , detection eﬃciency which is derived by multiplying all values
is 22%[11]. Then, to achieve the branching ratio of
B(µ− +Ti → e− +Ti) ∼1< 1018Nµ Ȧµ(I.3), number of µ Nµ > 1019 is needed. That means the proton beam enhancement is essential.

Figure 9.5: A schematic view of the curved solenoid spectrometer[11]I.2 Search for µ− − e− conversion

117

Table 9.3: Acceptances at each part of the curved solenoid spectrometer[11]Condition
Forward direction
Blocker cut (vertical)
Blocker cut (horizontal)sinθ >0.33

SectionTargetCurved solenoid
Curved solenoid
Detector

Fraction
79.3%
53.0%
100%
82.3%

Net acceptance
79.3%
42.0%
42.0%
34.6%

As stated above, the beam enhancement is required by each experiment.

Appendix J
An RF accelerating cavity loadedwith magnetic cores for a proton andion synchrotron
J.1

A cavity loaded with ferrite cores

Toroidal ferrite cores are widely used for RF accelerating cavities in proton and ion synchrotrons. The core has a function of increasing the inductance of the cavity. It allows
the resonance frequency of the cavity to be in the order of MHz. An accelerating cavity
loaded with FINEMET cores has almost same structure, however it does not have a feedback system for tuning its resonance frequency. Details are shown in a following section.
An accelerating gradient of the cavity is expected to be approximately twice as high asthat of the cavity loaded with ferrite cores, because FINEMET has relative magnetic permeability, saturation magnetic-flux-density and Curie temperature which are higher thanthose of ferrite. In this section, we will review cavities loaded with ferrite cores, whichhave been used for a long time and classify them based on their characteristics. A list of
proton and ion accelerating cavities loaded with ferrite cores is shown in Table 10.1.

J.1 A cavity loaded with ferrite cores

119

Table 10.1: A chronology of accelerating cavities loaded with ferrite cores
Year
1958
1959
1960[28]1967
1971[31]
1972[32]
1972[34]
1974
1976
1982
1982
1984
1987[39]
1988[41]
shelved
1990[45]
1991[47]
1993[49]
1999[50]
2006

Accelerator
SATURNEPS
AGS
U70
BOOSTER
PSB
LAMPF
PSB
PS
LEAR
IPNS
ISIS
MIMAS
CELSIUS[42]The Kaon Factory
SIS
BOOSTER
COSY
MI
SNS

Laboratory
SACLAYCERNBROOKHAVEN
IHEP
FNAL
CERN
Los Alamos
KEK
KEK
CERN
ARGONNERAL
SACLAYCELSIUSTRIUMF
GSI
BROOKHAVEN
IKP
FNAL
ORNL

Type
Coaxial B[54]Coaxial A
Coaxial A[29]
Coaxial B[30]
Drift Tube
Coaxial B[33]Coaxial D[35]Coaxial B[36]Coaxial B[37]Coaxial C
Coaxial B[38]Coaxial A
Coaxial C[40]
Coaxial C[43]
Coaxial D[44]Coaxial B*[46]Coaxial B[48]
Coaxial B[77]Drift Tube[51]Coaxial C[52]*Not push-pull arrangement

J.1.1

Ferrites for accelerating cavites

Mn-Zn type and Ni-Zn type ferrites are generally used for producing cores. Mn-Zn ferrite
has electrical resistivity from 10 to a few hundreds [Ωcm]. A few hundreds kHz is anupper limit as a low loss core because of the presence of an eddy current. The relative
magnetic permeability is a few thousand. On the other hand, the electrical resistivity of
Ni-Zn ferrite is over 105 [Ωcm]. It can be used up to a few MHz. However the limit of
the relative permeability is approximately 1000[56]. Ni-Zn ferrite is widely used for an
accelerating cavity[53].

J.1.2

Classification of cavities loaded with ferrite cores

There are two types of a accelerating cavities loaded with ferrite cores. One is a coaxial
type, the other is a drift tube type[37].

J.1 A cavity loaded with ferrite cores

J.1.3

120

Coaxial type cavity

A structure of a coaxial type cavity is the λ/4-wave coaxial resonator loaded with toroidal
ferrite cores. The cores increase the inductance of the cavity and its resonance frequency
decreases to the value which is suited to the acceleration of protons and ion beams.
This type cavity is used on the condition of the frequency from a few hundreds kHz toapproximately 10 MHz. The coaxial cavity is classified to four groups[37].
Type AA Schematic view of an ISIS cavity is shown in Figure 10.1. Black parts represent ferrite
cores. Ferrite is used as a medium in the coaxial tube. Electromagnetic field existing in
the coaxial tube can penetrates an accelerating gap made of alumina. The penetrated
field accelerates beams. The resonance frequency is tuned in order to follow the increaseof the beam velocity. A tuning method is to control the relative magnetic permeabilityof ferrite cores. The way of the control is to apply bias magnetic fields on the cores. The
resonance frequency is tuned in order to follow the increase of the beam velocity. Wiresare wound on cores, which are shown in Figure 10.1, carry DC current and induce bias
magnetic fields.

Figure 10.1: A schematic view of a type A cavity[54]J.1 A cavity loaded with ferrite cores

121

Figure 10.2: An equivalent circuit of a type A cavity[54]Type BA push-pull voltage is impressed on the accelerating gap. Wires are wound like a figureof eight which is able to cancel out induced RF voltages.

Figure 10.3: A schematic view of a type B cavity[54]J.1 A cavity loaded with ferrite cores

Figure 10.4: An equivalent circuit of a type B cavity[54]Figure 10.5: A DC circuit to apply a bias field on cores of type B cavity[54]122J.1 A cavity loaded with ferrite cores

123

Type CThis type of coaxial cavity has only one accelerating gap. Wires for inducing bias magnetic
field are connected to points where RF voltages are zero, which balances out the RF
voltage induced on the wires. And the wires are wound to have a shape of figure of eightin a same way of type B.

Figure 10.6: A schematic view of a type C cavity[54]Figure 10.7: An equivalent circuit of a type C cavity[54]Type DAs shown in Figure 10.8, a loss of ferrite (hysteresis loss) is small in a high magnetic
field. A DC magnetic field is applied on a ferrite core and Q factor of a cavity increases.
A control of a permeability of the core is shown in Figure 10.9. When a bias magnetic
field is applied parallel to an RF magnetic field, a slope of the tangent of B-H curveJ.1 A cavity loaded with ferrite cores

124

corresponds to the permeability. When the bias magnetic field is applied perpendicular
to the RF magnetic field, a slope of the straight line passing through origin and a pointon the B-H curve corresponds to the permeability. Considering to tune the permeabilityof the core, the parallel bias field is better at low magnetization, while perpendicular bias
field is better at high magnetization. Therefore, a solenoidal magnetic field is applied
perpendicular to the core in the cavity of Type D.

Figure 10.8: A hysteresis loop of a ferrite[54]J.1 A cavity loaded with ferrite cores

125

Figure 10.9: A control of a permeability of a ferrite core with a bias magnetic field. In
the case that the bias field is applied parallel to an RF field, a slope of a tangent of theB-H curve, such as A and C, corresponds to a permeability. In the case that the bias field
is applied perpendicular to the RF field, a tangent of a line which is drawn from the origin
to a point on the curve, such as B and D, corresponds to a permeability. In the region ofsmall magnetization, the parallel bias field which is able to vary the permeability strongly
is favorable. In the region of large magnetization, the perpendicular field is of advantage,
because the slope of the curve almost stays constant[78].

Figure 10.10: A schematic view of a type D cavity[54]J.1 A cavity loaded with ferrite cores

126

Figure 10.11: An equivalent circuit of a type D cavity[54]J.1.4

Drift tube type cavity

Cavities loaded with ferrite cores are mounted on a drift tube. Directions of RF voltages
in each half coaxial tube are opposite, so that RF voltages are canceled to be zero on thebias wires. Only one ferrite coaxial tube is shown in Figure 10.12, however, three tubes
are mounted in actual configuration. A length of the drift tube is long at low frequency,
so that a phase is changed while a beam is passing in the drift tube. Therefore, the usable
frequency is over a few tens MHz.

Figure 10.12: A schematic view of a drift tube[54]J.2 A cavity loaded with magnetic alloy cores

127

Figure 10.13: An equivalent circuit of a drift tube[54]J.2

A cavity loaded with magnetic alloy cores

As mentioned above, a bias magnetic field is applied on the ferrite cores in the accelerating
cavity and the resonance frequency is tuned. On the contrary, a cavity which is excitedby forced oscillation without tuning exists. Magnetic alloys are installed in this type ofcavity. The cavity loaded with magnetic alloys has a small Q-factor because of the large
loss of eddy current, so that a reflection is small even slightly oﬀ resonance. A feedback
system for bias field is not needed. Therefore, we are able to simplify the accelerating
system.

J.2.1

An RF cavity in National Institute of Radiological Science

National Institute of Radiological Science (NIRS) simplified an accelerator system andreduced costs by introducing untuned accelerating system into the synchrotron named
HIMAC. Magnetic cores which has low Q are installed in an accelerating cavity for untuned
acceleration in order to be oscillated in wide range of frequency. Adopted cores for HIMAC
are Co-based amorphous cores which have Q∼0.5. A cavity loaded with these cores areoperated between 0.4 MHz and 8 MHz. An accelerating voltage is 4 kV with an input
power of 8 kW. One cavity has two accelerating gaps and each gap has six cores. Sizesof the core and a cross-section of the cavity are shown in Table 10.2 and Figure 10.14,
respectively. Magnetic alloys are conductive, so that large heat appears. Indirect coolingwas selected to cool the heat. Cooling plates made of copper are attached on the surfacesof the cores. Current paths appear as shown in Figure 10.15 when cooling plates areattached on both surfaces. Therefore, the plates are attached on only one surface. An
epoxy resin which is mixed with alumina in order to increase the tharmal conductivity isused as an adhesive. A semiconductor amplifier is used for excitation. A transformer of
1:9 is connected between the cavity and the amplifier to match their impedance.

J.2 A cavity loaded with magnetic alloy cores

128

Table 10.2: Sizes of the Co-based amorphous core of a cavity in HIMAC[74]
Inner diameter [mm]310

Outer diameter [mm]550

Thickness [mm]30

Figure 10.14: A cross-section of the cavity in HIMAC[74]Figure 10.15: A path of an eddy current in the Co-based amorphous core. It emerges
when cooling plates made of copper are attached on both surfaces of the core.

J.2 A cavity loaded with magnetic alloy cores

J.2.2

129

An RF cavity in Heidelberg Ion Beam Therapy

A synchrotron for heavy particle radiotherapy was constructed in a hospital of Heidelberg
University. The synchrotron accelerates heavy ions, like C6+ , up to 430 MeV/u. Two
RF cavities of multi feed scheme, which is developed by Hitachi, Ltd., are installed in
the synchrotron. A schematic view of the cavity and parameters are shown in Figure
10.16, Table 10.3, respectively. Eight FINEMET cores are installed in each cavity.
One turn loops for excitation are crossed each core, and input powers are provided by asemiconductor amplifier. Matching boxes are not necessary because an impedance of thecore is designed as 50 Ω which is same as that of coaxial cable for power supply. A power
combiner of kW order is not needed to be set after the output of the amplifier because
powers are superposed in the cavity, so that we can simplify the system.

Figure 10.16: A schematic view of an RF cavity in Heidelberg Ion Beam Therapy[75]J.2 A cavity loaded with magnetic alloy cores

130

Table 10.3: Parameters of an RF cavity in Heidelberg Ion Beam Therapy[75]Frequency range
Accelerating voltage
VSWR
Sizes of the cavity
Material of core
Sizes and number of the cores

Impedance
Dissipated power
Cooling system

1-7[MHz]2.5[kVp ] for a fundamental wave with higher order modes
Over 3.3[kVp ] without higher order modes
below 2Outer diameter: 750[mm]
Inner diameter: 200[mm]
FT-3M
Outer diameter: 675[mm]Inner diameter: 300[mm]Thickness: 25[mm]8 cores100-140[Ω]/core
7.0[kW] (880[W]/core, 440[W]/ch)
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