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2 I II HFSS CST STUDIO SUITE GdfidL
![[1] 2 1 d2 x = kx 1 dt2 1 x](/docs-images/87/96642148/images/3-2.jpg "k dx/dt α ω d2 x dt 2 = kx")
3 I a 1 3 MH 1 3 GH 1 3 MH 1 3 GH 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
4 = 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 A = k ω2 + iωα k ω ω 2 α 2 F t t = F k ω 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 ω 2 α [ 2 ] k ω 2 cos ωt + ωα sin ωt 1 *1 8 yt yt = I{t} 11 F = k ω ω 2 α [ 2 {ωα cos ωt k ω 2 sin ωt }] x ϕ ϕ x = Ae i k x ωt 13 ω 13 k x ωt = const *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
5 ω k ω = ω k k k 1 ω k ω k + ω k k k 16 k= k k = k + k 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 v g 18 v g = ω k k ω k / k v p v p v g k 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 = F/ 25 µ = H/ 26 D x, t = ϵ E x, t 27 B x, t = µ H x, t 28 3
6 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 = F 33 = F 2 F 34 3 k H E E H k ϵ µ E x, t 2 t = 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 A E k = 38 E A E k H 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.](/docs-images/87/96642148/images/7-0.jpg "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.")
7 µσ ϵµ E x, t t 2 t = = 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 Skin Depth [µ] E x t E e µσω Frequency [GH] δ skin = 2 µσω /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
8 ϵ r µ r 1 1 ϵ r µ r 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 = D x, ω = ϵω E x, ω 7 B x, ω = µω H x, ω 71 E HD B E x, ω iωµω H x, ω = 72 H x, ω + iωϵω E x, ω = kω 2 E x, ω = 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 x E x, ω = E x x, ω,, kω2 E x x, ω = 79 ω E x x, ωe iωt e ikω ωt 8 = e i{kω} ωt I{kω} 81 6
9 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 c = c ϵ r ω 2 cos δ ϵ ω 1 + cos δ ϵ ω 88 ϵ r TEM Transverse ElectroMagnetic ode TEM ω = t + 89 =,, 9 E = E t + E 91 E =,, E 92 H = H t + H 93 H =,, H
10 電場 磁場 7 WX77D 5 MH TEM xx E x, ω = H x, ω = 99 θ rr 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
11 H t H θ 1 r 18 H r = E r ω 2 + E c r = H θ ω 2 + H θ = 111 c 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 E = t = r = a 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 r = r H θ I = 2πr H θ 117 = 2πa ϵ µ E e iω c t Z = 1 µ b ln 2π ϵ a 119 b/a WX77D a = 16.7 b = 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
![[ [ 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](/docs-images/87/96642148/images/12-0.jpg "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")
12 [ [ ω 2 t + γ 2 + c ω 2 t + γ 2 + c 2 ] 2 ] E t = 123 H t = 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 TMTransverse Magnetic H = E = 9 x, y, a, b TETransverse Electric E = H / n = n < 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
13 π 2 nπ 2 2 ω γ = a b c γ ω c = π 2 n ϵ µ a b 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 = 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 ω2 c ω 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 v g = dω dk = dk dω ωc 2 = c ω < c 157 TE 1 1 *4 11
14 a 電場 xx b 磁場 oo c 表面電流 1 W-15 5 MH TE 1 a b c c = 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 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 c = c af 11 f c 12
15 λ c v g f c = c 2a 169 λ c = 2a 17 a θ = 1c TE 1 12 TE 2 W-15 a = f c TE 1 = c MH 2a 171 f c TE 2 = c MH a MH W-15 TE 1 TE 2 a MH 11.4 GH F TM H = E = [ 2 r r r r 2 θ 2 ] 2 ω +γ 2 + E t = 173 c E t r = = 174 E t = rθθ rθθ 1 r [r 2 2 r 2 + r r }] 2 ω +r {γ r c Θθ = 176 Θθ θ2 r θ r, θ C r C θ [r r r 2 + r r }] 2 ω +r {γ r = C r 177 c 1 2 Θθ θ 2 Θθ = C θ 178 C r + C θ = e i C θ θ e i C θ θ Θθ + 2π = Θθ C θ = 2 Θπ/2 Θθ = cos θ [r 2 2 r 2 + r r } ] 2 ω +r {γ r = 181 c r J r = J αr ω α 2 = γ c 13
16 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
17 a 同じ PHS b 13 a UHF 59 MH W b X 11.4 GH W a b PHS xx θ 14 rr yy r, θ, J n j n n α α = j n 183 γ 2 = jn 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 H t = 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 cos θ 193 r J jn r sin θ 194 cos θ 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 TM
18 a 電場 b 磁場 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 θ E E r 9 r θ 15 TM 1 * d = = d *5 Dielectric-loaded accelerating strcutre [2] 16
19 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 = A + A = = E r = E θ = + TM 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 + = 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 k r J jn r sin θe ik iωt 214 r cos θe ik iωt 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 = ω np 227 = d d A + = A = 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 =
20 + 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 *6 TM TM 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 H = 246 ω = c j E H θ 2 θ E H θ *6 TM TE 18 r = 9 d *7 SuperKEKB F 59MH = c Q Quality factor Q Q Q Q UP wall *8 Q = ω U 248 P wall Q Q Q 19 = c d = 26. c Q TM 1 TM F 2 21 F F *7 TM 1 d *8 18
21 電場 : 磁場 : 17 19
22 Q Q Arbitrary Scale E Hθ j 1 r/ 18 TM 1 E H θ θ j Q P wall P ext 2 U du dt = P wall + P ext 249 Q Q ext Q ext = ω U P ext du 1 dt = ωu Q Q ext = ω Q L U 252 Q L Q Q 1 = 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 MH F 59 MH TM 1 Q β 1.3 Filling tie T f 2π µs 261 2
23 Q /1 Q / Copper Pillbox with = 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, Copper Pillbox with = 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, ,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, c 26. c Q IACS1% Ω µ = µ = H/ 21
24 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 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 ω 2Q L + ω ω 2 Eω ω 2Q L + ω ω 2 23 ω 23 Γ = ω Q L 267 Q L = d < + e> c ω 22
25 = = 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 e iω c Ẽ E t = t = ϕ = W V c ϕ = Ẽ r, Ẽ r, = dk Ẽ r, ke ik 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 t k 2 + ω2 c 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 =
26 r V c r = V c 282 d II 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 σ µ P wall = 1 2 ωµ ds H σ 2σ sh = 2 ωµ 2σ = 2 ωµ = 4π dr rj 1 J 2 d de iω c 2 ds { c ϵ J j1 r} c2 sin 2 ω ω 2 2c d + c ds ϵ J j1 1 r σ 1 8 sin 2 ω ωµ ω 2 ϵ 2 2c d j1 r πdJ1 j 1 2 J = 1 J x = J 1 x 289 ω 2c d = π/2 d TM 1 d = c π ω d d 4 *9 TM Q sh Q Q sh = V c 2 Q ωu d Ẽ,, e iω c 2 = ωϵ 2 29 dv Ẽ x, y, 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
27 sh Q sh Q 1 2 Ω 291 sh Q sh Q II 7 I 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
28 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 = kω 2 H x, ω = Q I 266 t = t = t = t = t = t ax f f 1 t ax 298 Q = 3 β = 1 Q Q L = Q /2 = Γ 2 kh t ax 1/2 kh 5 N N Q * HFSS HFSS [5] FEM *1 Slater [4] V 26
![1.2 CST STUDIO SUITE CST STUDIO SUITE [6] FIT Suite 1.](/docs-images/87/96642148/images/29-0.jpg "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.")
29 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] CST STUDIO SUITE 26 CST STUDIO SUITE Modeling 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
![[9] History List](/docs-images/87/96642148/images/30-4.jpg "28 11.")
30 27 CST STUDIO SUITE 2 出力したいステップを選択 29 CST STUDIO SUITE CST STUDIO SUITE History List CST STUDIO SUITE VBA CST STUDIO SUITE GdfidL [9] History List CST STUDIO SUITE 29 3 CST STUDIO SUITE 11.3 Q CST STUDIO SUITE 3 12 CST STUDIO SUITE 28
31 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 Frequency Doain Solver TE 1 I 1 TM 1 I 15 3 F 11.4 GH GH π π GH 31 π Q 9 Q π I Γ = ω 299 Q L 2π GH MH t ax MH 6.3 µs 33 ns a GH 31 CST STUDIO SUITE Tie Doain Solver Excitation Signals New Excitation Signal Signal Type User defined Edit VBA 31 29
32 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 GH a a 33b π Filling tie Filing tie Q GH r=7 r= =-1 = = Q L = 9/2 = 45 I T f = 34 2π GH 125 ns 35 ns Eigenode Solver 5 MH 35 TM 1 36 TM 11 3
33 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 = 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 [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. TUPEA [3] E. L. Ginton: Microwave Measureents, Ann Arbor, Michigan [4] J. C. Slater: Microwave Electronics, D. Van Nostrand 195. [5] [6] Overview.php. 31
34 モード MH モード MH モード MH モード MH 35 32
![空洞領域 r=7 r= ζ []](/docs-images/87/96642148/images/35-0.jpg "36 255 39 5 空洞領域")
![[7] http://www.](/docs-images/87/96642148/images/35-1.jpg "gdfidl.de/. [8] K.")
![[9]](/docs-images/87/96642148/images/35-8.jpg "http://research.")
35 空洞領域 r=7 r= ζ [] 空洞領域 [7] [8] K. L. Bane and T. Weiland: Wake Force Coputation in the Tie Doain for Long Structures, Conf. Proc., C83811, pp [9] Manual.pdf. ζ [] r= r=7 r=7 r=
II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R
![II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R](/thumbs/95/125540821.jpg "II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R")
II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =
x A Aω ẋ ẋ 2 + ω 2 x 2 = ω 2 A 2. (ẋ, ωx) ζ ẋ + iωx ζ ζ dζ = ẍ + iωẋ = ẍ + iω(ζ iωx) dt dζ dt iωζ = ẍ + ω2 x (2.1) ζ ζ = Aωe iωt = Aω cos ωt + iaω sin
2 2.1 F (t) 2.1.1 mẍ + kx = F (t). m ẍ + ω 2 x = F (t)/m ω = k/m. 1 : (ẋ, x) x = A sin ωt, ẋ = Aω cos ωt 1 2-1 x A Aω ẋ ẋ 2 + ω 2 x 2 = ω 2 A 2. (ẋ, ωx) ζ ẋ + iωx ζ ζ dζ = ẍ + iωẋ = ẍ + iω(ζ iωx) dt dζ
1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B
9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
W u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2)
3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)
QMII_10.dvi
65 1 1.1 1.1.1 1.1 H H () = E (), (1.1) H ν () = E ν () ν (). (1.) () () = δ, (1.3) μ () ν () = δ(μ ν). (1.4) E E ν () E () H 1.1: H α(t) = c (t) () + dνc ν (t) ν (), (1.5) H () () + dν ν () ν () = 1 (1.6)
No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2
No.2 1 2 2 δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i δx j (5) δs 2 = δx i δx i + 2 u i δx i δx j = δs 2 + 2s ij δx i δx j
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OHO.dvi
1 Coil D-shaped electrodes ( [1] ) Vacuum chamber Ion source Oscillator 1.1 m e v B F = evb (1) r m v2 = evb r v = erb (2) m r T = 2πr v = 2πm (3) eb v
1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0
1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0 0 < t < τ I II 0 No.2 2 C x y x y > 0 x 0 x > b a dx
http://www.ns.kogakuin.ac.jp/~ft13389/lecture/physics1a2b/ pdf I 1 1 1.1 ( ) 1. 30 m µm 2. 20 cm km 3. 10 m 2 cm 2 4. 5 cm 3 km 3 5. 1 6. 1 7. 1 1.2 ( ) 1. 1 m + 10 cm 2. 1 hr + 6400 sec 3. 3.0 10 5 kg
振動と波動
Report JS0.5 J Simplicity February 4, 2012 1 J Simplicity HOME http://www.jsimplicity.com/ Preface 2 Report 2 Contents I 5 1 6 1.1..................................... 6 1.2 1 1:................ 7 1.3
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20 21 2 8 1 2 2 3 21 3 22 3 23 4 24 5 25 5 26 6 27 8 28 ( ) 9 3 10 31 10 32 ( ) 12 4 13 41 0 13 42 14 43 0 15 44 17 5 18 6 18 1 1 2 2 1 2 1 0 2 0 3 0 4 0 2 2 21 t (x(t) y(t)) 2 x(t) y(t) γ(t) (x(t) y(t))
1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1
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1 I 1.1 ± e = = - =1.602 10 19 C C MKA [m], [Kg] [s] [A] 1C 1A 1 MKA 1C 1C +q q +q q 1 1.1 r 1,2 q 1, q 2 r 12 2 q 1, q 2 2 F 12 = k q 1q 2 r 12 2 (1.1) k 2 k 2 ( r 1 r 2 ) ( r 2 r 1 ) q 1 q 2 (q 1 q 2
n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)
D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y
ma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d
A 2. x F (t) =f sin ωt x(0) = ẋ(0) = 0 ω θ sin θ θ 3! θ3 v = f mω cos ωt x = f mω (t sin ωt) ω t 0 = f ( cos ωt) mω x ma2-2 t ω x f (t mω ω (ωt ) 6 (ωt)3 = f 6m ωt3 2.2 u ( v w) = v ( w u) = w ( u v) ma22-9
meiji_resume_1.PDF
β β β (q 1,q,..., q n ; p 1, p,..., p n ) H(q 1,q,..., q n ; p 1, p,..., p n ) Hψ = εψ ε k = k +1/ ε k = k(k 1) (x, y, z; p x, p y, p z ) (r; p r ), (θ; p θ ), (ϕ; p ϕ ) ε k = 1/ k p i dq i E total = E
ii p ϕ x, t = C ϕ xe i ħ E t +C ϕ xe i ħ E t ψ x,t ψ x,t p79 やは時間変化しないことに注意 振動 粒子はだいたい このあたりにいる 粒子はだいたい このあたりにいる p35 D.3 Aψ Cϕdx = aψ ψ C Aϕ dx
i B5 7.8. p89 4. ψ x, tψx, t = ψ R x, t iψ I x, t ψ R x, t + iψ I x, t = ψ R x, t + ψ I x, t p 5.8 π π π F e ix + F e ix + F 3 e 3ix F e ix + F e ix + F 3 e 3ix dx πψ x πψx p39 7. AX = X A [ a b c d x
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構造と連続体の力学基礎
II 37 Wabash Avenue Bridge, Illinois 州 Winnipeg にある歩道橋 Esplanade Riel 橋6 6 斜張橋である必要は多分無いと思われる すぐ横に道路用桁橋有り しかも塔基部のレストランは 8 年には営業していなかった 9 9. 9.. () 97 [3] [5] k 9. m w(t) f (t) = f (t) + mg k w(t) Newton
9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L) du (L) = f (9.3) dx (9.) P
9 (Finite Element Method; FEM) 9. 9. P(0) P(x) u(x) (a) P(L) f P(0) P(x) (b) 9. P(L) 9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L)
08-Note2-web
r(t) t r(t) O v(t) = dr(t) dt a(t) = dv(t) dt = d2 r(t) dt 2 r(t), v(t), a(t) t dr(t) dt r(t) =(x(t),y(t),z(t)) = d 2 r(t) dt 2 = ( dx(t) dt ( d 2 x(t) dt 2, dy(t), dz(t) dt dt ), d2 y(t) dt 2, d2 z(t)
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I 1 1 1.1 1. 3 m = 3 1 7 µm. cm = 1 4 km 3. 1 m = 1 1 5 cm 4. 5 cm 3 = 5 1 15 km 3 5. 1 = 36 6. 1 = 8.64 1 4 7. 1 = 3.15 1 7 1 =3 1 7 1 3 π 1. 1. 1 m + 1 cm = 1.1 m. 1 hr + 64 sec = 1 4 sec 3. 3. 1 5 kg
ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +
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128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds
127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds
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199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)
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Gmech08.dvi
145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2
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Z: Q: R: C: sin 6 5 ζ a, b
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II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )
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量子力学 問題
3 : 203 : 0. H = 0 0 2 6 0 () = 6, 2 = 2, 3 = 3 3 H 6 2 3 ϵ,2,3 (2) ψ = (, 2, 3 ) ψ Hψ H (3) P i = i i P P 2 = P 2 P 3 = P 3 P = O, P 2 i = P i (4) P + P 2 + P 3 = E 3 (5) i ϵ ip i H 0 0 (6) R = 0 0 [H,
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18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb
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r 1 r 2 r 1 r 2 2 Coulomb Gauss Coulomb 2.1 Coulomb 1 2 r 1 r 2 1 2 F 12 2 1 F 21 F 12 = F 21 = 1 4πε 0 1 2 r 1 r 2 2 r 1 r 2 r 1 r 2 (2.1) Coulomb ε 0 = 107 4πc 2 =8.854 187 817 10 12 C 2 N 1 m 2 (2.2)
I ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT
I (008 4 0 de Broglie (de Broglie p λ k h Planck ( 6.63 0 34 Js p = h λ = k ( h π : Dirac k B Boltzmann (.38 0 3 J/K T U = 3 k BT ( = λ m k B T h m = 0.067m 0 m 0 = 9. 0 3 kg GaAs( a T = 300 K 3 fg 07345
H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [
![H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [](/thumbs/99/141438442.jpg "H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [")
3 3. 3.. H H = H + V (t), V (t) = gµ B α B e e iωt i t Ψ(t) = [H + V (t)]ψ(t) Φ(t) Ψ(t) = e iht Φ(t) H e iht Φ(t) + ie iht t Φ(t) = [H + V (t)]e iht Φ(t) Φ(t) i t Φ(t) = V H(t)Φ(t), V H (t) = e iht V (t)e
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Gmech08.dvi
51 5 5.1 5.1.1 P r P z θ P P P z e r e, z ) r, θ, ) 5.1 z r e θ,, z r, θ, = r sin θ cos = r sin θ sin 5.1) e θ e z = r cos θ r, θ, 5.1: 0 r
( ; ) C. H. Scholz, The Mechanics of Earthquakes and Faulting : - ( ) σ = σ t sin 2π(r a) λ dσ d(r a) =
1 9 8 1 1 1 ; 1 11 16 C. H. Scholz, The Mechanics of Earthquakes and Faulting 1. 1.1 1.1.1 : - σ = σ t sin πr a λ dσ dr a = E a = π λ σ πr a t cos λ 1 r a/λ 1 cos 1 E: σ t = Eλ πa a λ E/π γ : λ/ 3 γ =
1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2
1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2
1. z dr er r sinθ dϕ eϕ r dθ eθ dr θ dr dθ r x 0 ϕ r sinθ dϕ r sinθ dϕ y dr dr er r dθ eθ r sinθ dϕ eϕ 2. (r, θ, φ) 2 dr 1 h r dr 1 e r h θ dθ 1 e θ h
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I-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co
16 I ( ) (1) I-1 I-2 I-3 (2) I-1 ( ) (100 ) 2l x x = 0 y t y(x, t) y(±l, t) = 0 m T g y(x, t) l y(x, t) c = 2 y(x, t) c 2 2 y(x, t) = g (A) t 2 x 2 T/m (1) y 0 (x) y 0 (x) = g c 2 (l2 x 2 ) (B) (2) (1)
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1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f =
1 8, : 8.1 1, z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = a ii x i + i
chap03.dvi
99 3 (Coriolis) cm m (free surface wave) 3.1 Φ 2.5 (2.25) Φ 100 3 r =(x, y, z) x y z F (x, y, z, t) =0 ( DF ) Dt = t + Φ F =0 onf =0. (3.1) n = F/ F (3.1) F n Φ = Φ n = 1 F F t Vn on F = 0 (3.2) Φ (3.1)
() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)
4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7
IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................
第3章
5 5.. Maxwell Maxwell-Ampere E H D P J D roth = J+ = J+ E+ P ( ε P = σe+ εe + (5. ( NL P= ε χe+ P NL, J = σe (5. Faraday rot = µ H E (5. (5. (5. ( E ( roth rot rot = µ NL µσ E µε µ P E (5.4 = ( = grad
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211 ( 4 2 1. 3 1.1............................... 3 1.2 1- -......................... 13 1.3 2-1 -................... 19 1.4 3- -......................... 29 2. 37 2.1................................ 37
(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y
[ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)
II 1 II 2012 II Gauss-Bonnet II
II 1 II 212 II Gauss-Bonnet II 1 1 1.1......................................... 1 1.2............................................ 2 1.3.................................. 3 1.4.............................................
A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π
4 4.1 4.1.1 A = f() = f() = a f (a) = f() (a, f(a)) = f() (a, f(a)) f(a) = f 0 (a)( a) 4.1 (4, ) = f() = f () = 1 = f (4) = 1 4 4 (4, ) = 1 ( 4) 4 = 1 4 + 1 17 18 4 4.1 A (1) = 4 A( 1, 4) 1 A 4 () = tan
(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
![(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x](/thumbs/104/162595168.jpg "(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x")
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
JIS Z803: (substitution method) 3 LCR LCR GPIB
LCR NMIJ 003 Agilent 8A 500 ppm JIS Z803:000 50 (substitution method) 3 LCR LCR GPIB Taylor 5 LCR LCR meter (Agilent 8A: Basic accuracy 500 ppm) V D z o I V DUT Z 3 V 3 I A Z V = I V = 0 3 6 V, A LCR meter
p = mv p x > h/4π λ = h p m v Ψ 2 Ψ
II p = mv p x > h/4π λ = h p m v Ψ 2 Ψ Ψ Ψ 2 0 x P'(x) m d 2 x = mω 2 x = kx = F(x) dt 2 x = cos(ωt + φ) mω 2 = k ω = m k v = dx = -ωsin(ωt + φ) dt = d 2 x dt 2 0 y v θ P(x,y) θ = ωt + φ ν = ω [Hz] 2π
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) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4
![) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4](/thumbs/92/107866707.jpg ") ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4")
1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +
x E E E e i ω = t + ikx 0 k λ λ 2π k 2π/λ k ω/v v n v c/n k = nω c c ω/2π λ k 2πn/λ 2π/(λ/n) κ n n κ N n iκ k = Nω c iωt + inωx c iωt + i( n+ iκ ) ωx
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II 6 ishimori@phys.titech.ac.jp 6.. 5.4.. f Rx = f Lx = fx fx + lim = lim x x + x x f c = f x + x < c < x x x + lim x x fx fx x x = lim x x f c = f x x < c < x cosmx cosxdx = {cosm x + cosm + x} dx = [
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医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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1 1 1.1 I R 1.1.1 c : I R 2 (i) c C (ii) t I c (t) (0, 0) c (t) c(i) c c(t) 1.1.2 (1) (2) (3) (1) r > 0 c : R R 2 : t (r cos t, r sin t) (2) C f : I R c : I R 2 : t (t, f(t)) (3) y = x c : R R 2 : t (t,
Gmech08.dvi
63 6 6.1 6.1.1 v = v 0 =v 0x,v 0y, 0) t =0 x 0,y 0, 0) t x x 0 + v 0x t v x v 0x = y = y 0 + v 0y t, v = v y = v 0y 6.1) z 0 0 v z yv z zv y zv x xv z xv y yv x = 0 0 x 0 v 0y y 0 v 0x 6.) 6.) 6.1) 6.)
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6 20 ( ) sin, cos, tan sin, cos, tan, arcsin, arccos, arctan. π 2 sin π 2, 0 cos π, π 2 < tan < π 2 () ( 2 2 lim 2 ( 2 ) ) 2 = 3 sin (2) lim 5 0 = 2 2 0 0 2 2 3 3 4 5 5 2 5 6 3 5 7 4 5 8 4 9 3 4 a 3 b
1. 2 P 2 (x, y) 2 x y (0, 0) R 2 = {(x, y) x, y R} x, y R P = (x, y) O = (0, 0) OP ( ) OP x x, y y ( ) x v = y ( ) x 2 1 v = P = (x, y) y ( x y ) 2 (x
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n=1 1 n 2 = π = π f(z) f(z) 2 f(z) = u(z) + iv(z) *1 f (z) u(x, y), v(x, y) f(z) f (z) = f/ x u x = v y, u y = v x
n= n 2 = π2 6 3 2 28 + 4 + 9 + = π2 6 2 f(z) f(z) 2 f(z) = u(z) + iv(z) * f (z) u(x, y), v(x, y) f(z) f (z) = f/ x u x = v y, u y = v x f x = i f y * u, v 3 3. 3 f(t) = u(t) + v(t) [, b] f(t)dt = u(t)dt
dynamics-solution2.dvi
1 1. (1) a + b = i +3i + k () a b =5i 5j +3k (3) a b =1 (4) a b = 7i j +1k. a = 14 l =/ 14, m=1/ 14, n=3/ 14 3. 4. 5. df (t) d [a(t)e(t)] =ti +9t j +4k, = d a(t) d[a(t)e(t)] e(t)+ da(t) d f (t) =i +18tj
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chap1.dvi
1 1 007 1 e iθ = cos θ + isin θ 1) θ = π e iπ + 1 = 0 1 ) 3 11 f 0 r 1 1 ) k f k = 1 + r) k f 0 f k k = 01) f k+1 = 1 + r)f k ) f k+1 f k = rf k 3) 1 ) ) ) 1+r/)f 0 1 1 + r/) f 0 = 1 + r + r /4)f 0 1 f
sec13.dvi
13 13.1 O r F R = m d 2 r dt 2 m r m = F = m r M M d2 R dt 2 = m d 2 r dt 2 = F = F (13.1) F O L = r p = m r ṙ dl dt = m ṙ ṙ + m r r = r (m r ) = r F N. (13.2) N N = R F 13.2 O ˆn ω L O r u u = ω r 1 1:
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M3 x y f(x, y) (= x) (= y) x + y f(x, y) = x + y + *. f(x, y) π y f(x, y) x f(x + x, y) f(x, y) lim x x () f(x,y) x 3 -
M3............................................................................................ 3.3................................................... 3 6........................................... 6..........................................
c y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l
![c y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l](/thumbs/85/91372642.jpg "c y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l")
c 28. 2, y 2, θ = cos θ y = sin θ 2 3, y, 3, θ, ϕ = sin θ cos ϕ 3 y = sin θ sin ϕ 4 = cos θ 5.2 2 e, e y 2 e, e θ e = cos θ e sin θ e θ 6 e y = sin θ e + cos θ e θ 7.3 sgn sgn = = { = + > 2 < 8.4 a b 2
December 28, 2018
e-mail : kigami@i.kyoto-u.ac.jp December 28, 28 Contents 2............................. 3.2......................... 7.3..................... 9.4................ 4.5............. 2.6.... 22 2 36 2..........................
第1章 微分方程式と近似解法
April 12, 2018 1 / 52 1.1 ( ) 2 / 52 1.2 1.1 1.1: 3 / 52 1.3 Poisson Poisson Poisson 1 d {2, 3} 4 / 52 1 1.3.1 1 u,b b(t,x) u(t,x) x=0 1.1: 1 a x=l 1.1 1 (0, t T ) (0, l) 1 a b : (0, t T ) (0, l) R, u
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