I

217 8

I 1 1 1 2 1 3 2 4 3 4.1.......... 3 4.2.......... 4 4.3... 5 11 27 11.1............ 27 11.2......... 28 11.3............ 28 12 28 12.1.......... 29 12.2........... 29 12.3.......... 3 13 31 14 31 5 7 5.1................. 7 5.2................. 9 6 16 6.1............... 16 6.2........... 18 6.3................ 22 6.4........ 24 II 25 7 25 8 25 8.1............... 25 8.2............... 25 8.3............... 25 8.4............... 25 9 26 9.1............... 26 9.2................ 26 9.3............ 26 1 26 1.1 HFSS.................. 26 1.2 CST STUDIO SUITE.......... 27 1.3 GdfidL................. 27

I a 1 3 MH 1 3 GH 1 3 MH 1 3 GH 1 1.1 1 59 MH 2 GH i F t b 1 1 a SuperKEKB 59 MH b SLAC 2 GH [1] 2 1 d2 x = kx 1 dt2 1 x k dx/dt α ω d2 x dt 2 = kx αdx dt + F cos ωt 2 2 ωt ωt + π/2 9 F sinωt 1 y d2 y dt 2 = ky αdy dt F sin ωt 3 1

= x + iy d2 dt 2 = k αd dt + F e iωt 4 i 4 e iθ = cos θ + i sin θ 5 t = Ae iωt 6 A 4 6 4 A = k ω2 + iωα k ω 2 2 + ω 2 α 2 F 7 7 6 t t = F k ω 2 2 + ω 2 α 2 [ k ω 2 cos ωt + ωα sin ωt + i { ωα cos ωt k ω 2 sin ωt }] 8 8 xt= {t} 9 F = k ω 2 2 + ω 2 α [ 2 ] k ω 2 cos ωt + ωα sin ωt 1 *1 8 yt yt = I{t} 11 F = k ω 2 2 + ω 2 α [ 2 {ωα cos ωt k ω 2 sin ωt }] 12 1 9 3 x ϕ ϕ x = Ae i k x ωt 13 ω 13 k x ωt = const. 14 3 13 *2 ω/ k k k 2π k 3 F x = d 3 k F k e i k x 15 F x : 15 k = k k ω ω k ω k *1 *2 2

ω k ω = ω k k k 1 ω k ω k + ω k k k 16 k= k k = k + k 17 1.75.5.25 -.25 -.5 -.75 k e iω kt 15 F x = e i k x ω k t k d 3 k F k e i k x ω k k t k= k 18 k k 18 18 2 v g 18 v g = ω k k 19 18 ω k / k v p v p v g k 16 4-1.5 1 1.5 2 2.5 3 3.5 2 4.1 E x, t + B x, t = t 2 H x, t D x, t = t 21 D x, t = 22 B x, t = 23 E H D B = x, y, 24 ϵ = 8.85418782 1 12 F/ 25 µ = 1.256637 1 6 H/ 26 D x, t = ϵ E x, t 27 B x, t = µ H x, t 28 3

2 23 E H E x, H x, t + µ t = t 29 H x, E x, t ϵ t = t 3 E x, t = 31 H x, t = 32 29 3 F 33 = F 2 F 34 3 k H E E H k 31 32 2 2 ϵ µ E x, t 2 t = 35 2 2 ϵ µ H x, t 2 t = 36 c = 1/ ϵ µ c 299,792,458 /s 13 ϵ ϵ µ µ ϵ µ 4.2 σ E x, t = A E k, ωe i k x ωt 37 J = σ E 41 37 31 A E k = 38 E A E k H 37 29 H x, t = A H k, ωe i k x ωt 39 H H k E 4 3 k c = 1/ ϵ µ J *3 D/ t E x, t + µ H x, t = 42 t H x, t ϵ E x, t σe x, t t = 43 E x, t = 44 H x, t = 45 ϵ µ 42 *3 4

43 44 2 2 µσ ϵµ E x, t t 2 t = 46 47 1 = 4 x E x t = E e ik ωt 48 k 46 4 k 2 = ϵµω 2 + iµσω 49 σ/ϵω 1 µσω k ±1 + i 2 48 5 Skin Depth [µ] 4 3.5 3 2.5 2 1.5 1 E x t E e µσω 2 51.5 1 1 1 2 Frequency [GH] δ skin = 2 µσω 52 5 1/e.37 δ skin Skin depth 5 σ = 4.3 ϵ r ω = ϵ rω + iϵ r ω 53 µ r ω = µ rω + iµ r ω 54 ϵω = ϵ ϵ r ω 55 µω = µ µ r ω 56 5

ϵ r µ r 1 1 ϵ r µ r 27 28 27 28 E x, t + B x, t = t 57 H x, t D x, t = t 58 D x, t = 59 E x, t = D x, t = H x, t = B x, t = B x, t = 6 dω E x, ω e iωt 61 dω D x, ω e iωt 62 dω H x, ω e iωt 63 dω B x, ω e iωt 64 E x, ω iω B x, ω = 65 H x, ω + iω D x, ω = 66 D x, ω = 67 B x, ω = 68 e iωt F = 69 67 68 65 66 67 68 55 56 D x, ω = ϵω E x, ω 7 B x, ω = µω H x, ω 71 E HD B 7 71 65 66 E x, ω iωµω H x, ω = 72 H x, ω + iωϵω E x, ω = 73 72 73 2 + kω 2 E x, ω = 74 2 + kω 2 H x, ω = 75 k kω = ±ω ϵωµω 76 = ± ω c ϵr ωµ r ω 77 = ± ω c ϵ r µ r ϵ r µ r + iϵ rµ r + ϵ r µ r 78 74 75 74 75 x E x, ω = E x x, ω,, 74 2 2 + kω2 E x x, ω = 79 ω E x x, ωe iωt e ikω ωt 8 = e i{kω} ωt I{kω} 81 6

76 I{k} > e I{kω} I 1/I{k} 1/e.37 c ω c = 82 {kω} c = ϵr 83 ωµ r ω ε r 6 δ ε ε r ε r ϵ r δ ϵ µ r = 1 µ r = ϵ r > 1 ϵ r > kω = ω ϵ c r ω + iϵ r ω 84 = ω ϵ δϵω rω c cos δ ϵ ω ei 2 85 δ ϵ [, π/2 6 tan δ ϵ = ϵ r ϵ r 86 δ ϵ = δ ϵ δ ϵ 1 I{kω} = λ 2π 2 cos δ ϵ ω ϵ rω 1 cos δ ϵ ω 87 λ = 2πc /ω 82 85 c = c ϵ r ω 2 cos δ ϵ ω 1 + cos δ ϵ ω 88 ϵ r 5 5.1 7 TEM Transverse ElectroMagnetic ode TEM ω = t + 89 =,, 9 E = E t + E 91 E =,, E 92 H = H t + H 93 H =,, H 94 72 73 7

電場 磁場 7 WX77D 5 MH TEM xx E x, ω = H x, ω = 99 θ rr 95 98 t E t x, ω = 1 E t x, ω iωµ Ht x, ω = 11 t H t x, ω = 12 H t x, ω + iωϵ Et x, ω = 13 yy 1 12 E t 8 r, θ, H t 8 r, θ, t E t x, ω iωµ H x, ω = 95 t E x, ω + E t x, ω iωµ Ht x, ω = 96 t H t x, ω + iωϵ E x, ω = 97 t H x, ω + H t x, ω +iωϵ Et x, ω = 98 E t = E r + E θ 14 H t = H r + H θ 15 E t E θ = 16 E r 1 r 17 8

H t H θ 1 r 18 H r = 19 11 13 14 19 2 2 E r ω 2 + E c r = 11 2 2 H θ ω 2 + H θ = 111 c 11 111 e i ω c e i ω c e iωt TEM e i ω c TEM E r r,, t = ae 1 H θ r,, t = a r eiω c t ϵ µ E 1 r eiω c t 112 113 E = t = r = a 11 13 Z Z = V I 114 V I a b V E r V = b a dre r 115 = ae e iω c t ln b a 116 112 r = r H θ I = 2πr H θ 117 = 2πa ϵ µ E e iω c t 118 116 118 Z = 1 µ b ln 2π ϵ a 119 b/a WX77D a = 16.7 b = 38.5 119 25 26 Z 5 Ω 12 5 Ω 75 Ω 5 Ω 75 Ω TEM 5.2 e γ E x, ω = E t x, y, ωe γ 121 H x, ω = H t x, y, ωe γ 122 γ 121 122 74 75 9

[ [ ω 2 t + γ 2 + c ω 2 t + γ 2 + c 2 ] 2 ] E t = 123 H t = 124 121 122 72 73 xx aa yy bb iωϵ E t x iωϵ E t y iωµ H t x iωµ H t y = Ht y = γh t x = Et y = γe t x γh t y 125 Ht x 126 γe t y 127 Et x 128 [ ω 2 ϵ µ + γ 2] E t x [ ω 2 ϵ µ + γ 2] E t y H t = iωµ y +γ Et x H t = iωµ x +γ Et y [ ω 2 ϵ µ + γ 2] H t x = iωϵ E t y [ ω 2 ϵ µ + γ 2] H t y +γ Ht x E t = iωϵ x +γ Ht y 129 13 131 132 123 124 129 132 TMTransverse Magnetic H = E = 9 x, y, a, b TETransverse Electric E = H / n = n 5.2.1 9 < x < a < y < b TE E = TE 124 [ ] 2 ω 2 t + γ 2 + H t = 133 c H t H t H t x H t y πx x, y = Ht cos a = 134 x=,a = 135 y=,b cos nπy b 136 H t x = y = n n 1

136 133 π 2 nπ 2 2 ω γ = + 137 a b c γ ω c = π 2 n 2 + 138 ϵ µ a b 136 129 132 TE, n H t E t x E t y E t = iω nπ Ht ωc 2 ϵ b πx cos sin a = H t iω π ωc 2 ϵ a sin πx a cos nπy b nπy b 139 14 = 141 H t x = ik π Ht ωc 2 ϵ µ a πx nπy sin cos 142 a b H t y = H t ik nπ ωc 2 ϵ µ b πx nπy cos sin 143 a b πx nπy x, y = Ht cos cos 144 a b k = γ i 2 ω = = ω c c π 2 nπ a b 145 2 146 1 ω2 c ω 2 147 147 e γ iωt = e ik ω k t 148 k = γ/i v p v p = ω k c 149 = 15 1 ω2 c ω 2 > c o 151 λ wg λ wg = 2π/k v p λ wg v p v e U e P { } P =,, U e v e 152 *4 U e P ωc 2 v e = c 1 ω 153 < c 154 v g 147 19 v g = dω dk = 1 155 dk dω ωc 2 = c 1 156 ω < c 157 TE 1 1 *4 11

a 電場 xx b 磁場 oo c 表面電流 1 W-15 5 MH TE 1 a b c c 139 148 = 1 n = TE 1 E x = 158 E y = H t i ωaµ πx sin e ik iωt 159 π a E = 16 H x = H t i ka πx π sin e ik iωt 161 a H y = 162 H = H t πx cos e ik iωt 163 a x- H x H 9 1b y x = a/2 1a E y x-y E y x = x = a 11 x θ 159 11 λ 2 = a sin θ 164 v p = c / cos θ > c 165 v g = c cos θ < c 166 = c 1 sin 2 θ 167 2 c = c 1 168 2af 11 f c 12

λ c v g f c = c 2a 169 λ c = 2a 17 a θ = 1c TE 1 12 TE 2 W-15 a = 381. 138 f c TE 1 = c 393.4 MH 2a 171 f c TE 2 = c 786.9 MH a 172 786.9 MH W-15 TE 1 TE 2 a 13 59 MH 11.4 GH F 5.2.2 TM H = E = 14 123 [ 2 r 2 + 1 r r + 1 2 r 2 θ 2 ] 2 ω +γ 2 + E t = 173 c E t r = = 174 E t = rθθ 175 173 rθθ 1 r [r 2 2 r 2 + r r }] 2 ω +r {γ 2 2 + r c + 1 2 Θθ = 176 Θθ θ2 r θ r, θ C r C θ [r 2 2 1 r r 2 + r r }] 2 ω +r {γ 2 2 + r = C r 177 c 1 2 Θθ θ 2 Θθ = C θ 178 C r + C θ = 179 178 e i C θ θ e i C θ θ Θθ + 2π = Θθ C θ = 2 Θπ/2 Θθ = cos θ 18 177 [r 2 2 r 2 + r r } ] 2 ω +r {γ 2 2 + 2 r = 181 c r J r = J αr 182 2 ω α 2 = γ 2 + 183 c 13

xx aa aa θ xx aa 電場 TE 1 モード y oo θ θ vv gg vv pp λ wg = λ / cosθ 11 TE 1 v p v g 電場 磁場 12 W-15 5 MH TE 2 14

a 同じ PHS b 13 a UHF 59 MH W- 15 381. 19.5 b X 11.4 GH W-9 22.86 1.1 a b PHS xx θ 14 rr yy r, θ, J n j n n 1 174 α α = j n 183 γ 2 = jn 184 2 2 ω 185 c γ ω > j n c 186 TM f c = c j n 2π 187 E t = E t J jn r cos θ 188 129 132 H t = 129 132 E t r = γ E t α 2 r E t θ = γ α 2 1 r E t θ H t r = iωϵ 1 α 2 r H t θ = iωϵ α 2 E t r E t θ TM E t r E t θ E t H t r H t θ = E t i kj jn j n r 2 k = E t i j n = E t J jn r = E t iωϵ = E t iωϵ j n j n 189 19 191 192 cos θ 193 r J jn r sin θ 194 cos θ 195 2 r J J jn jn r r sin θ 196 cos θ 197 H t = 198 e ik iωt k = γ i 2 ω = c jn 199 2 2 TM 1 193 15

a 電場 b 磁場 15 15 5 MH TM 1 a b 198 = n = 1 E r = E t i kj j1 j 1 r e ik iωt 21 E θ = 22 E = E t J j1 r e ik iωt 23 H r = 24 H θ = E t iωϵ J j1 r e ik iωt 25 j 1 H = 26 1 j 1 2.448 θ E E r 9 r θ 15 TM 1 *5 6 6.1 16 d = = d *5 Dielectric-loaded accelerating strcutre [2] 16

xx θ rr 16 dd yy f A + E + r = + A E r = = 219 A + E + r = d + A E r = d = 22 A + E + θ = + A E θ = = 221 A + E + θ = d + A E q = d = 222 219 221 A + A = 223 + 18 = 22 222 E r = E θ = + TM + 193 198 E + r E + θ E + H + r H + θ = E t i kj jn j n 2 k = E t i j n = E t J jn = E t iωϵ = E t iωϵ r cos θe ik iωt 27 jn r sin θe ik iωt 28 r J r cos θe ik iωt 29 2 j n r J J j n jn jn r sin θe ik iωt 21 r cos θe ik iωt 211 H + = 212 + k k E r E θ E H r H θ = E t i = E t i = E t J = E t iωϵ = E t iωϵ j n j n jn kj jn r cos θe ik iωt 213 2 k r J jn r sin θe ik iωt 214 r cos θe ik iωt 215 2 j n r J jn r sin θe ik iωt 216 J jn r cos θe ik iωt 217 j n H = 218 e ikd e ikd = 2i sin kd = 224 p k = pπ d 225 2, n, p ω = c jn 2 pπ + d 2 226 = ω np 227 = d d A + = A = 1 2 228 TM E r = E t kj jn j n r cos θ sin nπ d e iωt 229 E θ = E t 2 k j n r J jn r sin θ sin nπ d e iωt 23 E = E t J jn r cos θ cos nπ d e iωt 231 H r = E t 2 iωϵ j n r J jn r sin θ cos nπ d e iωt 232 H θ = E t iωϵ J jn j n r cos θ cos nπ d e iωt 233 H = 234 17

+ TM TE E = H / n = E r = E t iωµ j k 2 r J E θ = E t iωµ k 2 j n J n j r sin θ sin nπ d e iωt 235 n r cos θ sin nπ d e iωt 236 E = 237 H r = E t 1 pπ j n j k 2 d J n r cos θ cos pπ d e iωt 238 H θ = E t 1 pπ j k 2 d r J n r sin θ cos pπ d e iωt 239 j H = E t J n r cos θ sin pπ d e iωt 24 TE np TM np, n, p 2 = onopole = 1 dipole n rte E θ,h r TM E θ,e,h r p 17 TM TE 229 234 235 24 *6 TM TM 1 229 234 E r = 241 E θ = 242 E = E t J j1 r e iωt 243 H r = 244 H θ = E t ωϵ J j1 j 1 r e iωt π 2 245 H = 246 ω = c j 1 247 E H θ 2 θ E H θ *6 TM TE 18 r = 9 d *7 SuperKEKB F 59MH = 22.56 c Q Quality factor Q Q Q Q UP wall *8 Q = ω U 248 P wall Q Q Q 19 = 22.56 c d = 26. c Q TM 1 TM 1 6.2 F 2 21 F F *7 TM 1 d *8 18

電場 : 磁場 : 17 19

Q Q Arbitrary Scale 1.8.6.4.2 E Hθ.5 1 1.5 2 2.5 j 1 r/ 18 TM 1 E H θ θ j 1 2.448 1 Q P wall P ext 2 U du dt = P wall + P ext 249 Q Q ext Q ext = ω U P ext 25 248 25 249 du 1 dt = ωu + 1 251 Q Q ext = ω Q L U 252 Q L Q Q 1 = 1 + 1 253 Q L Q Q ext β β = Q Q ext 254 Q = Q L 1 + β 255 β = P ext /P wall = 1 P wall = P ext β 1 β < 1 β > 1 β Q [3] 252 U U = U e ω Q L t 256 E, H e ω 2Q t L 257 = e t T f 258 T f = 2Q L ω 259 Filling Tie T f 1/e.37 22 59 MH F 59 MH TM 1 Q β 1.3 Filling tie 259 2 3 1+1.3 T f 2π 59 26 8.1 µs 261 2

Q /1 Q /1 2 18 16 14 12 1 8 6 4 2 2 18 16 14 12 1 8 6 4 2 Copper Pillbox with = 22.56 c d = 26. c = ~ 4 n = 1 ~ 5 p = ~ 6,1, 1,1,,1,1 1,1,1 2,1, TM np Modes,2,,2,1,1,2 2,1,1 3,1, 1,1,2 3,1,1 1,2,,2,2 4,1, 2,1,2 1,2,1 4,1,1.5 1 1.5 2 2.5 3 Copper Pillbox with = 22.56 c d = 26. c = ~ 4 n = 1 ~ 5 p = 1 ~ 6 1,1,1 2,1,1,1,1 3,1,1,3,,1,3 3,1,2 2,2, 1,1,3,3,1 2,2,1 1,2,2 4,1,2 1,3,1 3,1,3 1,3,,3,2 3,2,1 2,2,2,2,3 3,2, 2,1,3 esonance Frequency [GH] TE np Modes 1,1,2 4,1,1 1,2,1 2,1,2,1,2 3,1,2 2,2,1 4,1,2 1,2,2,2,1 3,1,3 1,3,1,1,3,2,2 2,1,3 2,2,2 3,2,1 1,1,3 1,2,3 4,2,1 4,1,3 3,2,2 4,2,,1,4 4,2,2,2,4 2,1,4,4,1 2,3,1,3,3 2,2,3,4, 2,3, 1,1,4 1,3,2 3,3, 1,3,3 1,2,4,4,2 2,3,2 3,2,3 3,1,4,3,3 4,3,1 2,3,3 1,4,2,2,4 2,2,4 3,3,2 4,2,3.5 1 1.5 2 2.5 3 4,1,3 4,2,1 3,2,2 1,2,3 4,2,2,2,3 2,2,3,3,1 2,3,1 1,3,2 4,1,4 3,3,1 1,4,,3,4,1,5 4,2,3 2,2,4 1,4,1 esonance Frequency [GH] 1,1,4 3,1,4 3,3,1,1,4,3,2 3,2,3 2,1,4 2,3,2 4,1,4 1,2,4 1,4,1 1,3,3 2,3,3 3,3,2 1,1,5,1,5 3,3,3 2,1,5 4,3,2 1,3,4 1,1,5 3,2,4,4,1 2,4,1 19 22.56 c 26. c Q IACS1% 1.72 1 8 Ω µ = µ = 1.25664 1 6 H/ 21

導波管 空洞 Ch.1: eflected Wave fro the Cavity Ch.3: Control Voltage Modulator Ch.2: Input Wave to the Cavity Ch.4: Pickup Wave fro the Cavity 2 µs PP ext UU PP wall 2 22 59 MH F Ch. 4 Eω 21 Q ΓΓ = ωω QQ LL 22 Ch. 4 8 µs 261 Filling tie ω 257 Et = E e ω 2Q L t e iω t Eω = 1 2π = E 2π = E 2π 262 dt Et e iωt 263 dt e ω 2Q +iω ω t L ω 2Q L iω ω 264 2 265 ω 2Q L + ω ω 2 Eω 1 2 266 ω 2Q L + ω ω 2 23 ω 23 Γ = ω Q L 267 Q L 6.3 24 = d < + e> c ω 22

= = dd I V c f dd 24 φ = { V } V c c cosφ W 25 d W = d e {E,,, t + /c } 268 { } d = e d Ẽ,, e iωt +/c 269 = e {V c } 27 = e V c cos ϕ 271 V c = e iωt d d Ẽ,, e iω c 272 25 e iω c Ẽ E t = t = ϕ = W V c ϕ = Ẽ r, Ẽ r, = dk Ẽ r, ke ik 273 272 V c r = e iωt d dk k Ẽ r, k e i c ω 274 δ V c r = e iωt 2π dk Ẽ r, k δ k ωc 275 E r,, t = Ẽ r, e iωt 276 = dk Ẽ r, ke ik ωt 277 35 2t k 2 + ω2 c 2 275 278 2 t V cr = e iωt 2π = e iωt 2π dk Ẽ r, k = 278 dk 2 t Ẽ r, k δ k ω c 279 k 2 ω2 c 2 Ẽ r, k δ k ωc 28 = 281 23

r V c r = V c 282 d II 6.4 2 sh sh = V c 2 P wall 283 Q TM sh = V c 2 /2/P wall 283 β 1 P inp V c = sh P wall 284 sh P inp 285 TM 1 243 272 σ µ P wall = 1 2 ωµ ds H 2 286 2σ 2σ sh = 2 ωµ 2σ = 2 ωµ = 4π dr rj 1 J 2 d de iω c 2 ds { c ϵ J j1 r} 2 287 4 c2 sin 2 ω ω 2 2c d + c ds ϵ J j1 1 r 2288 2σ 1 8 sin 2 ω ωµ ω 2 ϵ 2 2c d j1 r 2 289 + 2πdJ1 j 1 2 J = 1 J x = J 1 x 289 ω 2c d = π/2 d TM 1 d = c π ω 289 2 d d 4 *9 TM Q sh Q Q 248 272 sh = V c 2 Q ωu d Ẽ,, e iω c 2 = ωϵ 2 29 dv Ẽ x, y, 2 291 P wall sh Q L Ẽ 2 Ẽ L 3/2 ω L 1 dv L 3 d L 291 L L sh Q sh Q *9 24

sh Q sh Q 1 2 Ω 291 sh Q sh Q II 7 I 8 8.1 Finite Eleent Method 8.2 Boundary Eleent Method 8.3 Finite Difference Method 7 16 Finite-Difference Tie-Doain ethod: FDTD 8.4 Finite Integration Technique: FIT FIT FDTD FIT 25

9 E x, t + B x, t = t 292 H x, t D x, t = t 293 D x, t = 294 B x, t = 295 I 2 + kω 2 E x, ω = 296 2 + kω 2 H x, ω = 297 9.1 Q I 266 t = t = + 9.2 t = t = t = t ax f f 1 t ax 298 Q = 3 β = 1 Q Q L = Q /2 = 15 267 Γ 2 kh t ax 1/2 kh 5 N N 9.3 74 75 Q * 1 1 1.1 HFSS HFSS [5] FEM *1 Slater [4] V 26

1.2 CST STUDIO SUITE CST STUDIO SUITE [6] FIT Suite 1.3 GdfidL GdfidLGitter drüber, fertig ist die Laube [7] FDTD GdfidL PC PC GdfidL PC GdfidL Moving Mesh [8] 1 1 11 3 CST STUDIO SUITE 26 CST STUDIO SUITE Modeling 11.1 26 2 3 26 History List CST STUDIO SUITE VBA Visual Basic for Applications 27 With Brick.eset.Nae "solid1".coponent "coponent1".material "Vacuu".Xrange "", "1".Yrange "", "1".Zrange "", "1".Create End With History List VBA VBA 27

27 CST STUDIO SUITE 2 出力したいステップを選択 29 CST STUDIO SUITE 1 3 28 CST STUDIO SUITE History List CST STUDIO SUITE VBA CST STUDIO SUITE GdfidL [9] History List 28 11.2 CST STUDIO SUITE 29 3 CST STUDIO SUITE 11.3 Q CST STUDIO SUITE 3 12 CST STUDIO SUITE 28

W-9 矩形導波管内 TE 1 モード 銅の電気伝導率を持ったソリッド 電場の強さ WC-9 円形導波管内 TM 1 モード 12.7 電場ベクトル 22.86 32 31 267 12.1 31 Frequency Doain Solver TE 1 I 1 TM 1 I 15 3 F 11.4 GH 22.86 12.7 11.424 GH π π 32 11.424 GH 31 π Q 9 Q π I Γ = ω 299 Q L 2π 11.424 GH 3 45 1.6 MH 31 298 1 t ax 32.16 MH 6.3 µs 33 ns 12.2 33a 11.424 GH 31 CST STUDIO SUITE Tie Doain Solver Excitation Signals New Excitation Signal Signal Type User defined Edit VBA 31 29

Noralied Aplitude Aplitude [a.u] Charging Step 入力波 赤色 Maintaining Step 試験空洞内に励振されるモードの振幅 紫色 Tie [ns] 反射波 緑色 a b 33 11.424 GH a 31 33 33a 33b π Filling tie Filing tie Q 9 11.424 GH 15 444 1 255 1 r=7 r= =-1 = =1255 34 Q L = 9/2 = 45 I 259 2 45 T f = 34 2π 11.424 GH 125 ns 35 ns 12.3 34 Eigenode Solver 5 MH 35 TM 1 36 TM 11 3

Q I 282 r = x 2 + y 2 36 V c r = > V c r = 7 = 1 = ζ W W ζ, r = ζ 1 d Ẽ r, e iω c 36 W 1, r = V c r W 37 ζ < 255 r = 7 r = r = r 38 5 V c r = < V c r = 7 39 r = r = 7 r = 7 r = 282 13 1. 2. 3. 4. 5. 14 OHO 17 tetsuo.abe@kek.jp [1] M. Dal Forno, et al.: rf breakdown easureents in electron bea driven 2 GH copper and copper-silver accelerating structures, Phys. ev. Accel. Beas, 19, 11, p. 11131 216. [2] C. Jing, et al.: Experient on Multipactor Suppression in Dielectric-loaded Accelerating Structures with a Solenoid Field, Proceedings, 4th International Particle Accelerator Conference IPAC 213: Shanghai, China, May 12-17, 213, p. TUPEA87 213. [3] E. L. Ginton: Microwave Measureents, Ann Arbor, Michigan 1957. [4] J. C. Slater: Microwave Electronics, D. Van Nostrand 195. [5] http://www.cybernet.co.jp/ansys/product/lineup/hfss/. [6] http://www.aetjapan.co/software/cst Overview.php. 31

モード 1 528. MH モード 2 68.8 MH モード 3 796.3 MH モード 4 82. MH 35 32

空洞領域 r=7 r= ζ [] 36 255 39 5 空洞領域 [7] http://www.gdfidl.de/. [8] K. L. Bane and T. Weiland: Wake Force Coputation in the Tie Doain for Long Structures, Conf. Proc., C83811, pp. 314 316 1983. [9] http://research.kek.jp/people/tabe/ss2gd Manual.pdf. ζ [] 37 255 r= r=7 r=7 r= 38 5 33