1.

HOM

HOM

HOM

2.

2.1.

1989 KEK L-bandPillbox

HFSS[7]

190mm 7.5mmPillbox

5mm

S-band Pillbox

SLAC Stanford X-band Pillbox

L-band

KEK

2.2.

LS C X

Pillbox Fig.1UHF

Fig.2

KEKB 509MHz 1.2MW

Fig. 1 : Pillbox

Fig. 2 : 508.6MHz

1 6

1 VSWR

~1.1

2

3

1

1 10 nm

TiN coating TiN

TiN

TiN(O)

[8][9]

500MHz

[9]

500MHz

[10]

4

T

d

RectangularWaveguide

Ceramic disk

l2 l1

CircularWaveguide

l l

Coaxial Line

Ceramic disk

Pillbox

Mo-Mn

900 1000 [11]

17 10-6 K-1 7.7 10-6 K-1

0 50 mMo

5.0 10-6 K-1

C 4~5 10-6 K-1

[12][13]

Mo

[14] 5

UHF CW

Mo Mo

1mm

0.3MPa

KEKB

ARES 500kW20kW

MopH

[15] pH8

Mo

[16][17]

Mo

99 Mo-Mn

loss tangent : ~10-5

6

9~10

[18]

Pillbox

TM010-like

3.

3.1.

Maxwell

TEM

V I

Pillbox

TE10

TE11

[19]

TE TM

Fig.3

Fig.4

R[Ω/m]

L[H/m] G[S/m]

C[F/m]

Fig. 3 :

Fig. 4 :

Fig.4 Kirchhoff

(3-1)

(3-2)

(3-1) (3-2)

telegrapher’s equations

, (3-3)

V I z

(3-3) (3-1) (3-2)

(3-4)

(3-5)

i

v+ v

i+ iR z

i+ i

v

L z

G z C z

zz

i

~ ZlVg

Zg i

v

z

(3-4) (3-5) V I V I(3-6) (3-7)

(3-6)

(3-7)

(3-8)

(3-6) (3-7) V I

(3-9)

(3-10)

V1 V2 I1 I2

propagation constante- z +z

e+ z -z(3-4) (3-9)

(3-11)

(3-11)

(3-9) (3-10) (3-11) +z -z

Z0

(3-12)

(3-13)

(3-10) (3-14)

(3-14)

(3-3) (3-9) v(z,t) (3-15)

(3-15)

1 2 (3-9) V1 V2

(3-15) 1 2

+z -z 1

(3-16)

(3-17)

vp

(3-18)

(3-17) λλg

(3-15) 1 e- z

+z

2 e+ z -z

attenuation constant

R=G=0(3-8)

(3-19)

(3-20)

(3-21)

=0= j (3-12)

(3-22)

(3-22)

V I(3-9) (3-14) (3-19) (3-22)

3 23 324

(3-23)

(3-24)

λ vp (3-25) (3-26)

(3-25)

(3-26)

3.2.

Fig. 5 Z0

l Zl

Z0 Zg Vg

Zg = Z0

z = 0 V0

I0 (3-23) (3-24) z 0

(3-27)

(3-28)

z=l Vl Il

(3-29)

(3-30)

(3-31)

(3-32)

(3-27)~(3-32) V1 V2 V0 I0 Vl

Il 6 V1

V2 (3-33) (3-34)

(3-33)

(3-34)

(3-23) (3-24)z V

I

(3-35)

(3-36)

(3-35) 1 2

(Vg/2)e-jβl (z = l)

Zl

(3-37)

e-jβ(l-z) (z = l) z = zΓl

z = lZl = Z0 Γl = 0

Fig. 5 :

3.3.

zz

standing wave

(3-23) (3-38)

~ Z0 ZlVg

Zg I0 Il

V0 Vl

z = 0 z = l

l

(3-38)

V2 = |V2|ejφ’ (3-38) 3 1 +z

2V2

*e-jβz V2e+jβz z

(3.39)

Γ z

(3-38) 1 (3-39)

(3-40)

(3-41)

voltage standing wave ratio : VSWR (3-41) (3-42)

(3-42)

3.4.

z

(3-35) (3-36) (3-37) Fig.5Zin(z)

(3-43)

Γl (3-37) (z = l)Γ(z) (3-35)

2 1

(3-44)

(3-37) (3-43)

(3-45)

z

(3-45)Zl Z0 l-z

Zin(z)

(3-46)

(3-47)

(3-44)

(3-48)

zl-z Γ

|Γl |l-z λg/2 360

(Fig. 6)

Zl = Z0 (3-37)

(3-44) Γl = 0 Γ(z) = 0

z 0 z(3-43)

(3-45) Zin(z) = Z0

Fig. 7 : 2

Z0

Z0

0

Z Zg Z = Zg

*

8.5

(3-45)

Fig.7(a) Zl

Z1 Z2

l1 l2

l1

(3-45) Z0 Z1 l-z l1

= Zin1 Fig.7(b)

Zin1 l2

(3-45) Z0 Z2

l-z l2 Zin2

cascade

(3-45)

(3-49)

(3-49)

Fig.7 (3-49) Zl / Z1 Z1/ Z2 Zin2 /Z2

TE TM

Z1 Z2

Z1Zl

Z2

Zin1Zin2

l 1l 2

Z2

Zin2

l 2

Zin1

Fig. 6 : z

-1

o

1

j

-j

l

( l -

z )

(3-37) (3-43) (3-45) (3-49)

(3-50) (3-51) (3-52) (3-53)

(3-50)

(3-51)

(3-52)

(3-53)

3.5. 4

Fig.8 l F

Fig. 8 : 4 F

(3-23) (3-24)

(3-54)

(3-55)

(3-56)

(3-57)

(3-56) (3-57) V1 V2

(3-58)

(3-59)

(3-54) (3-55)

(3-60)

(3-61)

(3-62)

4 F

Fig.8 ZlF

(3-63)

(3-64)

(3-65)

(3-66)

Fig.5 (3-45)

z=0(3-66) (3-45)

cascade

F

F

TE TM

(3-66)

Z0

IS IR

VS VR

l

z = 0 z = l

F

FF F

8.4

3.6.

3.4 z

Zin(z)/Z0 Γ(z) (3-43)

360 1 1

Fig. 9 :

Γ= |Γ|ejθ

Fig.9Fig.10(a) (b)

r xΓ

Γ

Fig. 10 : (a)

r (b) x

Γ(3-67)

(3-43) (3-68)

(3-67)

(3-68)

(3−68

u

jv

jv

u-1 +1

x =

(b)

x = 0

x = 1/3

x = 1

x =

3

x = -1/3

x = -1

x =

-3

r = 0

jv

u

r = 1

/3

r = 1

r = 3

-1 +1

r =

(a)

, (3-69)

(3-70)

(3-71)

(3-70) rr/(r+1) , 0

1/(r+1) Fig.10(a)r 1

r r(1,0) (3-71)

x1, 1/x 1/| x |

1|Γ| = 1

Fig.10(b)

Fig. 11 :

Fig.9 Fig.10(a) (b) 1Fig.11

Fig.9

Fig.12

Fig. 12 :

(3-67) (3-69)

(3-72)

(3-73)

, (3-74)

(3-75)

(3-76)

(3-75) g-g/(g+1) , 0

1/(g+1) (3-76) b-1, -1/b

1/| b |

x = 0

x = 1/3

x = 1

x = 3

x = -1/3

x = -1

x = -3

r =

0

r =

1/3

r =

1

r =

3

(3-75) (3-76) gb

Fig.13

Fig. 13 :

Fig.14

Fig. 14 :

3.7.

3

1

Fig. 15 : 1 Y1

Fig. 16 : 1

1 Y1 l1Y1 (Fig.15)

Yin/Y1 Y1/Y1=1

(3-50)Γl = 0

b = 0

b = -1/3

b = -1

b = -3

b = 1/3

b = 1

b = 3

g =

0

g =

1/3

g =

1

g =

3

-1 +1u

jv

Y1

Yin

l 1

Y1

(1)(2)

o {1}

{2}

b = -1

b = -1/2

b = 1/2

b = 0

b = 1

g =

1/2

g =

2

g =

0

g = 1

(Fig.15) (1) (2)Y1

(3-48)Fig.16

{1} {2}|Γl |= 0

1+0j

Fig. 17 : 2 Y1 Y2

Fig. 18: 2

2 Fig.17 1Y2 l2

Yin/Y2 l2

Y1/Y2 = 2 1 Y1

1+0j Y2

Y1(1+0j) Y2

Y1(1+0j)/Y2 Y1/Y2 = 2 Y2 (3)

2+0jΓl2 (3-50) Γl2 = -1/3l2

Γ2 (3-48) |Γ2 | =|Γl2 | = 1/3 – 2 l2(2π/λg2) radian

2 l2(2π/λg2) radian l2 =λg2/8

π/2 radian Fig.18 {4}Fig.18

l2

Fig.18 {4} Yin/Y2 = 0.8-0.6j l2

Γ2 Fig.18 C1

l2

C1

Fig. 19 : 3 Y1 Y2 Y3

3 Fig.19 2 l2 =λg2/8 Y3 l3

Y1

Y1

Y2

Yin

l 1l 2

(1)(2)(3)(4)

o

C1

l2

{1},{2}{3}

{4}

Y1

Y1

Y2

Yin

l1l 2

(1)(2)(3)(4)

Y3

l 3

(5)(6)

l3 =λg3/16

Y1/Y2 = 2 Y2/Y3 = 1/3

2 Y2

Fig.19 40.8-0.6j

Y3 Fig.19 (5)Y2(0.8+0.6j)

Y3

(5)Y2(0.8+0.6j)/Y3 Y2/Y3 = 1/3 0.8/3+0.6/3j Γl3 (3-50)

Γl3 = 0.5405+0.2432j = |0.5927|arg(0.4228 radian) l3

Γ3 (3-48)|Γ3 | = |Γl3 | = 0.5927

-2l3(2π/λg3) radian Fig.20{5} 2l3(2π/λg3) radian

l3 =λg3/16/4

Fig.20 {6} {6}Yin/Y3 =0.2637+0.1709j

4 Fig.21 3l2 Y3

Y1/Y2 = 2 Y2/Y3 = 1/3

2 l2Y2

Fig.18

Fig.22 C1

Y3

l2 C1

1 Y2/Y3

l2 Y3

C1

Y2/Y3

Fig. 20 : 3

Fig. 22 : 4

Fig. 21 : 4 Y1 Y2 Y3

o

C1C2

l2

l3

{1},

{2}

{3}

{4}{5}

{6}

o

C1

l2

l3

{3}

{4}{5}

{6}

{1},

{2}

Y1

Y1

Y2

Yin

l1l 2

(1)(2)(3)(4)

Y3

l 3

(5)(6)

C2

o8.1

Fig.23 C1 18C2 C2

C2

Y3 l3 Y3

l2 Y2/Y3

C2 o2l3(2π/λg3) radian

Y3

l2 C2

oFig.22 {4} {5}

{6} 3

5 Fig.24 1jB

Y2 l2Y1 jB

Yin1 Y2

Yin2 l2Y2

Yin

jB/Y1 = 0.2j Y1/Y2 = 2

Y1

jB1+0j jB

(2)Yin1/Y1 = 1+jB/Y1 1+0.2j

Fig.25 {2} Y2

Y2

(1+ jB/Y1)Y1

(1+ jB/Y1)Y1/Y2

(1+0.2j)×2 Fig.25 {3}Y2 l2

o2l2(2π/λg2) radian

Fig.25 C1’ l2

Fig. 23 : 4 C1 C2

Fig. 24 : 5 Y1 Y2

jB

Fig. 25 : 5

o

C1'

{2}

{3}

{1}

Y1

Y1

Y2

Yin

l 1l 2

(1)(2)(3)(4)

jB

Yin1Yin2

Yin

4.

4.1.

Fig.26

εr 9 10

1/3 4.1.2.

4.1.1.

T

Fig.26

jB1

8.2

(4-1)

Y1 λ0

jB1

jB1

Fig.27

500MHz

500MHz CW

[20][9]

Fig. 26 :

T

Fig. 27 :

4.1.2. λg(ceramics)/2

Pillbox

Pillbox

Fig.26 T

=λg(ceramics)/2

TEM

T Ceramic disk

Y1 Y1

jB1

Ceramic disk

Choke

9Y1

Y2 = 3Y1 Y1/Y2 = 1/3Fig.28

Y1

Fig. 28 : T=λg(ceramics)/2

1 (3-52) Y1 (5)

(4-2)

Y1 2 Fig.28 Y1

Y1 (2)1+0j Y2

(3)(1+0j)(Y1/Y2) = 1/3+0j Y2

λg(ceramics)/2Y2

Fig.29 360Fig.28 (2) (3) (4)

Fig.29 {2} {3} {4} Y1

(5)(4) Y1

(Y2/Y1=3 )1+0j

Fig 29 : T=λg(ceramics)/2

λg(ceramics)/2

Pillbox

λg(ceramics)/2Pillbox

4.1.3.

Pillbox

1/3

Fig.30[21]

Fig.31

Y1

Y1

Y2

Yin

T

(1)(2)(3)(4)

Y1

(5)(6)

Ceramics

T= g(ceramics)/2

o{4}

{3}

{5}

{1},

{2}

{6}

Fig. 30 : 508.6MHz

Fig. 31 : Fig.30

508.6MHz

Fig.30

Fig.32

l l = 19.5mm l = 87.8mm HFSS

l

Fig. 32 : VSWR508.6MHz l = 19.5mm l = 87.8mm

4.2. Pillbox

Fig.33 Pillbox

Fig.34 [22]

TE10

TE11 jB

Y1 Y2 Y3

Y1/Y2 Y2/Y3

Y1/Y2 jB/Y1

HFSS

8.3 Y2/Y3

l l

Coaxial Line

Ceramic disk

T

l' l'

Coaxial Line

Ceramic disk

Fig. 33 : Pillbox

Fig. 34 : Pillbox

4.3.

Fig.35

Fig.34 Pillbox

[23]

Fig. 35 :

TEM

jB

Y1 Y2 Y3

TEM

Y1 Y2 Y3

TEM

jB HFSS

4.4.

4.2 4.3 Fig.33 Fig.35

Fig.34

Pillbox

Table 1 L-band Pillbox

Y1/Y2 jB/Y1HFSS Y2/Y3

Table 1 : L-band Pillbox

1296MHz

WR650 165.1 82.55mm

TE10

λg =0.324 m

190mm

l1 l2 TE11

λg =0.330 m

190mm

T

εr=9.9

TE11

λg ceramics =0.075 m

B/Y1=0.3221

Y1/Y2=1.921

Y2/Y3=0.2286

T

d

RectangularWaveguide

Ceramic disk

l2 l1

CircularWaveguide

Y1 Y2 Y3 Y2 Y1

jBjB

T l1l2

T

d

Coaxial Line

Ceramic disk

l2 l1

5.

5.1.

3

ΓYin

(5-1)

(5-2)

Y0

Fig.36

Yin/Y0=g+jb

Fig. 36 :

5.2.

Fig.34

Fig.36 Fig.34 Table

1

=

jB/Y1 Y1/Y2 Y2/Y3 Table 1

Fig.37

1) Y1 jB/Y1

2)

Y2/Y3

3)

Γo

λg/2 360

Fig. 37 : Pillbox

Y1

Γ 0

Fig.37

Fig.38 {1} {10}

o

b = -1

b = -1/2

b = 1/2

b = 0

b = 1

g =

1/2

g =

2

g =

0

g =

1

Y1 Y2 Y3 Y2 Y1

jBjB

l2

Y1

l1T

Fig.38 Fig.37

Y1/Y1=1 o

1+jB/Y1=1+0.3221j {2}

(1+0.3221j)Y1/Y2=1.921+0.6188j{3}

o

C1 {4}

l1C1

Fig. 38 : 1 10

{1} {10}

C1

{4} Y2/Y3C1

Y2/Y3 C2

o

8.1 {5} l1

C2

1

Y2/Y3 1

C1 C2 C2 C1

C1 C2 Table 1 jB/Y1 Y1/Y2Y2/Y3

=

C1 C2

C1 C2

C1 C2

6

o

T

{6} C2

T

{7}

C1 {7} {6}

Y3/Y2 Fig.38

{5} {6}

{8} l2C1

Fig.38 l2 {8}

b=0 Γ {3}

{9} {10}

1.921-0.6188j(1.921-0.6188j)Y2/Y1=1-0.3221j1-0.3221j+0.3221j=1

Fig.37

1 1

Fig.38

{9} {8}

{7} {6} C1 C2

o

C2

C1

T

l1

l2

{5} {6} o

{5} {6} C2

Fig. 39 : {5} {6}

C2

Fig. 40 : {5} {6}

C2

1) =

C1 C2

{1} {2} {3}

{8} {9} {10}

2) l1 C1 {4} C2 {5}

l1

3) {5} {6} {6}

C2 T

l2{6} C2

{5} {6}

Fig.39 Fig.41 3

Fig.41 {5} {6} l1{5} C2

Fig. 41 : {5} {6}

360 T=λg(ceramics)/2

l1 l2 T

360

λg /2 λg /2 λg(ceramics)/2

360

C2

C1

o T=T1

o

C1

C2

T=T2

o

C2C1

T

5.3. {5} {6} C2

Fig.39 {5} {6}

C2 {5} C2

{4}

C1

l1= l2

Fig. 42 : {5} {6} C2

T1=3.0 mm l1 =l2 = 58.4 mm

Fig. 43 : {5} {6} C2

T1=3.0 mm l1 =l2 = 16.4 mm

Fig.42 {5}

o {5}

C2

Fig.42 T1

Fig.43

Fig.30 Fig.32 l

Fig. 44 : T1max

T1 = T1max = 3.0 mm l1 =l2 = 30.0 mm

Fig. 45 : T1max Fig.30

10 14.7mm

508.6MHz VSWR

Fig.42 Fig.43

{5} {6}

o Fig.43

C1

o

C2

T1

= 3

.0 m

ml1

= 5

8.4

mm

l2 = 58.4

mm

o

C2

C1

T1

= 3

.0 m

m

l2 =

16

.4 m

m

l1 =

16

.4 m

m

C1

C2

o

T1

= 5

.16

mm

l1 =

30

.0 m

m

l2

= 30.0

mm

Fig.44 {5} oC2 Fig.42 Fig.43

l1 (=l2) T1

=T1max

(T1max) (T1max)

l1 (=l2)

l1 (=l2)Pillbox

(T1max)

HFSS

Fig.45 508.6MHz(T1max)

Fig.30 10mm14.7mmT1max=14.737mm Fig.32

l

Fig. 46 : {5} {6} C2

T2=34.74 mm l1 =l2 = 126.8 mm

{5} {6}C2

T1 0<T1≤T1max

{5} {6}

5.4. {5} {6} C2

Fig.40 {5} {6}

C2 {5} C2

{4} C1

l1 =l2 T2

Fig.46 Fig.47 l12

Fig. 47 : {5} {6} C2

T2=34.74 mm l1 =l2 = 3.7 mm

Fig.48 {5} oC2 l1 2

T2 =T2min

(T2min)

T1max+T2min=λg(ceramics)/2 (T2min) (T1max)

l1 (=l2)(T2min)

C1

C2

o

T2 = 34.74 mm

l2 = 126.8

mm

l1 = 1

26.8

mm

C1

C2

o

T2 =

34.7

4 m

m

l2 =

3.7

mm

l1 =

3.7

mm

HFSS {5} {6}

C2 T2

T2min≤T2≤λg(ceramics)/2

{5} {6} Γ

Fig. 48 : T2min

T2 = T2min = 32.59 mm l1 =l2 = 155.2 mm

5.5. {5} {6} 360

Fig.41 {5} {6}

360 {5} C2

{5}Γ C2 l1

=l2 l1 ≠ l2T T=λg(ceramics)/2

Fig.49

Fig. 49 : {5} {6} 360

T=λg(ceramics)/2 l1 = 58.4mm l2 = 126.8 mm

5.6.

L Pillbox

1 =

C1 C2

{5}{6} {5} {6} C2

2 {5} {6} 35 3

3 {5} {6} C2

1 0<T1<T1max T1

l1 (= l2) l1 =

l2 2 (T1max) T1=T1max

l1 (= l2)l1

C1

C2

o

T2

= 3

2.5

9 m

m

l2 =

155.2

mm

l1 = 155.2

mm

C1

C2

o

T = 37.74 mm

l1 =

58.4

mm

l2 =

126.8 m

m

(= l2)

3 {5} {6} Γ

4 T1 l1 (= l2)

{5} {6}

4 {5} {6} C2

1 T2min<T2≤λg(ceramics)/2 T2

l1 (= l2)

l1 = l2

2 (T2min) T2=T2min

l1 (= l2)

l1 (= l2)

3 {5} {6} Γ

5 {5} {6} 360 1 T=λg(ceramics)/2 2 {5} Γ

l1 ≠ l2 6 T1max<T<T2min T

7 T=T0 l1 = l10 l2 = l20

T=T0+n1λg(ceramics)/2 l1 = l10+n2λg /2 l2 = l20 + n3λg

/2 n1 n2 n3

1

8 T l1 l2

9

6.

6.1.

5 L Pillbox

=

C1 C2

Fig.37

l1

oC1

C1 o

{1}{10} {5} C1

Y2/Y3 C2

1 Y2/Y3<1

C2 C1

C2

C1

Fig. 50 : C2 o

Fig. 51 : C2

o

C1 C2

3

1) C2 oFig.50

2) C2

o Fig.51

3) C2

oFig.52

l1 {5} {6}C2 l2

T {5} {6}

Fig. 52 : C2

o

Fig.53 C1 18C2 C2

C2

6.2. C2 o

C2 oFig.50 5

5.6C1 C2

T 0<T1<λg(ceramics)/4 λg(ceramics)/4<

T2≤λg(ceramics)/2 T1max<T<T2min

Pillbox

Fig.42 Fig.44

C1

C2

o

C1

C2

o

C1

C2

o

{5} {6} C2

Fig.46 Fig.48 {5} {6}

C2

(T2min) 5

Fig. 53 : C1 C2 Table 1

C1 18

6.3. C2

o

5 PillboxB/Y1

C1

Y1/Y2

C1

Fig.51C1 C2

C2

o Fig.51

oC2

o 5.3 5.4(T1max) (T2min)

T1max = T2min =λg(ceramics)/4

l1 (= l2)

Fig. 54 :

{5} {6}T

1+0j

S.Yu.Kazakov

[24]

T=(2n-1)λg(ceramics)/4 n

C1

o

C2

l 2

l1

Fig.54

Table 1

165.1mm 41.275mm WR650 1/2

195.42mm

l1 = l2 =165.537mm

1 HFSS

6.4. C2

o

C1

Fig.52 C1

C2

C2

o

Fig.52 5

5.2

1) {5} {6} C2

2) {5} {6} C2

3) {5} {6} 360

3

C1

7.

7.1.

Fig.34

Pillbox

TE10

TE11

TE11

TEM

TEM

Pillbox l1 l2TM11

[25]

TM11

l1 l2TM11

jB

5 L

l1 l2

TM11

l1 l2HFSS

TEM

Fig.32 l =10mm

HFSS l

7.2.

Pillbox

1)

2) l

3)

4)

T2min

5)

1939 Phillip H.

Smith [26]

[27]

8.

8.1. C1 C2

|Γ1| = constant C1

aC1

Y1 Y1 aY1 (=Y2)

(8-1)

(8-2)

Y2

Γ2

(8-3)

(8-3) (8 1)

(8-4)

(8-4) Γ1

Γ2 a=1 Γ2=Γ1 |Γ1| =

constant C1 C1 a≠1 (8-4)

(8-4)(8-5)

(8-5)

a a≠1 (8-5) |(1+a)/(1-a)| > 1

{Γ1+(1+a)/(1-a)}

(8 5)C1 C2

8.2.

Fig. 26T λg(ceramics)

(8-6)

(8-6)

Fig.26Y1

Fig.55 Y2

(4)

Yin2/Y2 (3-53)

(8-7)

εr

(8-8)

(8-9)

jβ1 jβ2 Y1 Y2

λ0 Y1 TEM

Fig. 55 :

Y1 (5)

Yin β2T

(8-10)

(8-10) Fig.56

(8-11)

Pillbox

T λg(ceramics)

(8-12)

(8-12)

c λ0 λg1

Pillbox λg( )

Fig. 56 :

T λg(ceramics)

T λg(ceramics)

Pillbox

Fig.34 Y3

jB1

5.3 {5} {6} C2

T Tmax 0<T<Tmax

T l1 (= l2)l1 = l2

T=Tmax

5.4 {5} {6}

C2

T λg(ceramics)

Y1

Y1

Y2

Yin

T

(1)(2)(3)(4)

Y1

(5)(6)

Ceramics

Yin2

Y1

Y1Yin

Y1

jB1

8.3. Fig.34 Y1/Y2 jB/Y1

Table 1 HFSS

Fig.57

Fig.58

TE10 4 port1

TE11 1 port2

port1 S11

port2 TE11

(2) (3) port

λg

Fig. 57 : Y1/Y2 jB/Y1

HFSS

S11

Fig.58 4 Γ(4)

Γ(4) (3-48) (3)

Γ(3) Γ(3)

(5-1)

Yin/Y1 (8-13)

(8-13)

Fig.58 (3)

(8-14)

(8-14)

(8-13) (8-14) Y1/Y2 jB/Y1

Fig. 58 : Y1/Y2 jB/Y1

HFSS

8.4. Fig.37 F

Pillbox Fig.59 Fig.37

Fig. 59 : Pillbox

Y1

Fig.59

F (8-15)

(8-15)

(8-16)

Z1=1/Y1 Z2=1/Y2 Z3=1/Y3

VS/IS

VS/IS= Z1

Y2

Y2Yin

Y1

jB

(1)(2)(3)(4)

d

Rectangular

Waveguide

CircularWaveguide

(1)(2)(3)

(4)

Port 1

Port 2

TE10 mode

TE11 mode

Y1 Y2 Y3 Y2 Y1

jBjB

l2

Y1

l1T

Pillbox

TE TM

Z2 Z3

(8-15)

F

F

Z0

F

F

(8-17) Z0

F Fn (8-18)

(8-17)

(8-18)

Fig.59

(2)~(3) (4)~(5) (6)~(7)

(8)~(9) Fig.59 Pillbox

F (8-19)

(8-19)

(8-20)

VS/IS

VS/IS= 1

2.1 1988

SLAC X-band Pillbox

[22]

8.5.

3.4 Z0

Z0

0

ZZg Z = Zg

*

4 6

9.

9.1.

HOM

( )

( )

loss tangent < 0.3

KEKB

SiC

HE11-like

(f )

9.2. KEKB HOM

KEKB 2A

HOM

1994 1998 KEKB

HOM

SiC

HOM

HOM

SiC

Fig.60 S-KEKB

SiC

SiC

1982 1983 KEK

S-band

KEKB

SiC

10 S-band

10. SiC

HOM

10.1.

KEKB HOM 0.8

2GHz |Γ|< 0.2

SiC 1 1.25kW

S-band

L-band

3

HFSS

SiC

TEM

Fig.61~Fig63

Fig. 61 : 15mm 20mm 25mm 400mm

HFSS 100mm

Fig.61 Fig.62

critical frequency : fc

Fig. 60 : SiC

SiC

fc

εr”=6 15 22

30

Fig.62 Fig.63

nosecone

Fig. 62 : 20mm 400mm εr

’=15 2230 εr

” = 6 HFSS100mm

Fig. 63 :

SiC

10.2. SiC

SiC

2 HFSS

Fig.64

Fig. 64 : 220mm εr

’=221/4

1.5GHz TEM

Fig.64

(a)1.5GHz (b)0.7GHz

9.44 107 m/sec 2.19

108 m/sec

Fig.64 (a) (b)

HE11

(a)1.5GHz

(b)0.7GHz

10.3.

SiC

Magnetic short Magnetic short

Magnetic short Magnetic short

Ele

ctri

c sh

ort

Ele

ctri

c sh

ort

Ele

ctri

c sh

ort

Ele

ctri

c sh

ort

(a) f = 1.5 GHz (b) f = 0.7 GHz

[28]r θ z

zaε1 ε2 z(10-1)~(10-3)

(10-1)

(10-2)

(10-3)

z(10-4)~(10-6)

(10-4)

(10-5)

(10-6)

Jn 1 Kn 2Er Eθ Hr Hθ

Ez Hz (10-4) (10-5)Kn r

r = a Ez Eθ

Hz Hθ

(10-7)

(10-7)

(10-8)

(10-9)

(10-10)

(10-11)

u w (10-12)

(10-12)

(10-7) HE11 n = 1 u w

Fig.65 (10-12) u-wωa((ε1-ε2)μ0)1/2 ≡ v

Fig.65 (10-12)HE11 (10-12)v v = 0

HE11

Fig.65 : HE11

n=0 u w 1/4(10-12)

w ( = αta) wr K1(wr/a)Fig.66 K1(x)

Fig.65 ε1/ε2

u wu (10-13) v

wv vt

v vt

v vt

v = vt

(10-12) v ω a ε1

Fig. 66 : y = K1(x) x

Fig. 67 : w/a ( = αt) 3

Fig.67 w/a ( = αt)

3

Fig.68

3

Fig.67 Fig.68 w/a

v = vt

SiC

Fig.61 Fig.62

fc

Fig. 68 : w/a ( = αt) 3

10.4.

TEM TE10

HE11 HE11

0Hz

SiC

20@1GHz

HE11

fc

f fc

f fc

loss tangent<0.3

fc

f<fc

f>fc

SiC

SiC HFSS

KEKB

SiC 55mm

SiC

KEKB HOM

HOM

TE10 SiC 2

1 4

HOM [29]

KEKB SiC

HOM

HOM

[30]

fc

11.

11.1. SiC

11.1.1. SiC

9 10 HOM

SiC

SiC

εr

= ε’r – jε”r

SiC

HOM

SiC

1982

NGK M.Watanabe KEK

[31] 1983 8

KEK S

[32] 1990

KEK 500MHz

HOM

SiC [33]

Fig. 69 : SiCSiC-A SiC-B

Fig. 70 : SiCSiC-A SiC-B

1993 KEKB

ARES HOM

KEK SiC

SiC

2 SiC

ARES HOM

SiC

SiC-A ARES

SiCSiC-B SiC

Fig.69 Fig.70 ARES 2

SiC SiC

1985SiC BeO

SiC-BAl

S-KEKBHOM

SiC

11.1.2. 2

SiC 3eV

6 10SiC

SiC-A SiC-B Fig.69 Fig.70

SiC-B

SiC

SiC 1980

BeOSiC

1 SiC

10-1Ωm

2Fig.71

3

SiC

[34][35][36]

Fig. 71 : BeO SiC2

KEK KEKB-ARESHOM

SiC SiC-BDebye

[37] 1B5 m p

2 SiC

BeO < B < Al [38]

BeO 10-1Ωm3

2 103 Ωm 4SiC

BeO SiC

Fig.71Maxwell-Wagner [39]

11-1 11-2

Electrode

Grains

DepletionLayers

Cg

Cd

Rg

Rd

(11-1)

(11-2)

2 103 Ωm 11-2

2 0.2GHz 0.05

11-1 11-2

11-3 Debye SiC-B

Debye

(11-3)

= RgRd(Cg+Cd)/(Rg+Rd)

Cg Rg

Cd Rd

Rg Rd

Rg<<Rd Cg<<Cd

≈ RgCd Rg Cd

Rg

εr0 εr 0

ε'r Rg<<Rd Cg<<Cd

εr0 Cd εr Cg

Fig. 72 : SiC-B Debye

Fig.72 SiC-B

(11-3) Debye fitting

Debye

2

fitting

εr0 εr τ

11.1.3.

SiC-B SiC-A

30~80 6 Fig.73

Fig.74 SiC-B

SiC-B

SiC-B

ε” fr Debye

fr=1/(2πτ)Debye

11-3 εr0 εr τ50K εr0

20% εr

1/3

Fig.75

Fig. 73 : SiC-B 27.7~79.9

Fig.71

≈RgCd εr0

Cd

Rg

Rg

SiC

6H-SiC

p B 0.3~0.723eV

Ga 0.317~0.333eV Al

0.19~0.49eV [40] kT k

T 300K

0.026eV 0.3eV

Rg

exp(- E/2kT)

exp( E/2kT) [41]

E Fig.75

fitting

E

E≈0.36eV B

Al Ga

Fig. 74 : SiC-A 27.9~81.8

SiC-A SiC-B

Fig.75

0.2 GHz ε”r 0

[42]

1985

[35] SiC

Fig. 75 : εr0 εr τ SiC-B

11.1.4.

2009 2011 S-KEKB

HOM R&D SiC-B

[43][44]

SiC-B

Al

B p

p

Al SiC-B

Al

Al

180~530wtppmFig.76 Fig.77

Al 180~530wtppm SiC-B

Fig.78 Al εr0

εr τ

Fig. 76 : AlAl 180~530 wtppm

Fig. 77 : AlAl 180~530 wtppm

AlSiC

Al650~2100wtppm

μ’r 1GHz 1[43]

Fig. 78 : Al εr0 εr τSiC-B

11.2. HOM RFRF

11.2.1. RF

9 10 SiCKEKB HOM

Fig.79

Fig. 79 : ARES HOM

240 28 mmfc 0.7GHz

WR975HOM 240 28 mm

Fig.80 1000mm

SiC ceramics

Fig.80

TRL

0.7~1.1GHz

Fig.79 HOM

S11

Fig. 80 : RF

Fig.81 : ARES HOMS11

Fig.81 S11 RF

MW STUDIO RF

HOM

SiC

1

fc 0.7GHz

2

RF

3

[45]

11.2.2. RF

KEKB ARES

HOM S-KEKB R&D

RF 2009 [45]

L 1.25GHz

20kW

SiC

Fig.82

HOM

Fig.82

20

E A~J 10 H a~j

10

7 L/min

Fig. 82 : RF

Fig.83 E SiC

2.5kW B

5~10kW A

A 20kW

320 5~10kW

10kW

A

WR975 WR975

Taper : 1000 mm Taper : 1000 mm

Reference PlaneReference Plane

I

A B C D E

a b c d e

F G H J

f g h i j

SiC SiC-A

10MHz1GHz

SiC-B1GHz

SiC-B

Fig.74

Fig. 83 : ARES HOM

RF

5~10kW

SiC

2.5kW 9 10

RFSiC

1.25GHz

12. OHO

HOM

OHO’17

3 [1]~[4]4 ~ 6 [5]

9 ~ 10[6]

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[2] 1975 .

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.

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2008 TP013.

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.

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WX-152D

,

GEMINI DESIGN REPORT (KEK Progress Report 86-4), pp. 560-576.

.

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6.3 1939

1937

.

[27] UHF

2016 TUP029.

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2012 THPS102.

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[42] SiC

2013

SAP059.

[43] SiC

2010 WEPS072.

[44] HOM SiC

2011 TUPS137.

[45] SiC

KEKB ARES HOM

2009 FPACA56.