Slater[] Collin[] [3] [4] AR 508.6MHz λ =58.9cm 4 9.7m APSAlternating Periodic Structure 50kW.M/m 3M cm 7.5 WR500 f c TE 0 f c = 393MHz 9 90k 0
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1 OHO π APS A 40 L C R L C R Appendix
2 Slater[] Collin[] [3] [4] AR 508.6MHz λ =58.9cm 4 9.7m APSAlternating Periodic Structure 50kW.M/m 3M cm 7.5 WR500 f c TE 0 f c = 393MHz 9 90k 0A.MW 65% W m 3
3 : AR. APS k..... Q 3
4 . r=b arbitrary scale Hq Ez E z d H q c 0 r/b b : b d TM 00 E z H θ z 0 J 0χ 0r/b J χ 0r/b z χ 0 = z r θ b d E z Transverse Magnetic Mode TM E H z Transverse Electric Mode TE H TM 00 E z H θ z TM 00 E z θ E z r 3 E z z Êz Ĥθ 0 0 r =0 0 J 0 J E z = Êz cos 00 t H θ = Ĥθ sin 00 t + π E r = E θ = H z = H r =0 Ê z = E 0 J 0 χ 0 r/b Ĥ θ = E 0 ζ 0 J χ 0 r/b 00 = χ 0c b d χ 0 = ζ 0 = Ω J 0 3 4
5 c = m/s r =0 r/b = MHz π b.95cm Q Q W P Q = W 4 P P wall Q Q 0 W = µ 0 Ĥ dv = ɛ 0 P wall P wall = ζ m S Ê dv 5 Ĥ ds 6 ζ m σ µ ζ m = µ σ 7 σ = m Ω µ = µ 0 = H/m 500MHz ζ m = Ω δ δ = σζ m 8 TM 00 Q Q 0 = ζ 0 ζ m χ0d d + b 9 9 d Q d Q r.m.s. TM 00 3 L C R Q 0 00 = LC 0 Q 0 = R 00 L L C R E 0 z r =0 t =E 0 d cos 00 t 0 cos 00 t z = d/s z = d/s z t 0 z = vt t 0 5
6 L C R = R a / L = R 00 Q 0 C = Q 0 R : a t =E 0 d/ d/ = 0 T cos 00 t 0 00 z cos + 00 t 0 v a cos 00 t 0 3 T = sin 00d v 4 00d v a 0 T T 0 R a = 0 T = E 0 Td R = a P 5 P 6 R = ζ 0 d ζ m πj χ 0 bb + d T 6 R L C 3 9 rms 5 R a =R 8 5 I 0 R a I 0 d 5 6 d =0.44λ d Q T R a 4 500MHz r a r a = Ra d = E 0T P wall /d d/λ =0.9 /3 3/π [5][6] 6
7 0.8 T R/Rmax Q/Q max πd/λ 4: : f 00 = 00/π = 500MHz σ = m Ω c E 0 /m E 0 b 0.95 m d m U E 0 J 3 P wall E 0 W 3/ Q Q / R a Ω /.. δ n n W n δ n n = δw n W n 9 [7] n δw n F n F n = µ Ĥn 0 ɛ0 Ên n F n n 4 0 n δw n 7
8 δw n = F n dv δ δ δ n n = 4 δ µ Ĥn 0 ɛ0 Ên dv ɛ 0 Ên dv W n,e W n,h δ n δw n,e δw n,h 3. δ n % 56% d 0.6b C C / C δw E T 5 nose cone H q E z Pill-box Cavity Cavity with Noze Cones 5: :.3 5 8
9 500MHz PF cm cm 8cm 4cm 0cm 3cm 500MHz SU- PERFISH R a =9.9MΩ Q 0 44, 000 [8] R a T a r a r = a z E z z r a TM 0 TM 0 e jt z β g exp jβ g tilde à β g β g Ẽ z r, z = à β g π J 0 β β g r e jβgz dβ g 4 Ẽ r r, z = à β g π jβ g β βg J β β g r e jβgz dβ g 5 H θ r, z = à β g π jɛ 0 β βg J β β g r e jβgz dβ g Ẽ θ = H z = H r =0 6 β c 7 r z r = a E z z d/ { 0 z d/ E z =0 z >d/ 8 z d/ E z d 9
10 r R0mm R34.69mm Ez r=0 R50mm R9.375mm z 0mm R30mm 300mm 6: PF 500MHz E z = { E 0 = 0 /d z d/ =0 z >d/ 9 à β g à β g = 0 β g d sinβ g d/ 30 J 0 β βg a r = const. v z =0 φ z exp j v + φ 3 6 z z φ Ṽ φ = à β g π J 0 β βg a e j[/v βg+φ] dβ g dz = à /v J 0 β /v a e jφ = à /v I 0 v/c r e jφ 3 v I 0 x =J 0 jx acc ] acc =Re [Ṽ φ sin d v = 0 d v I 0 v I 0 v v/c r cos φ v/c a a cos φ 33 φ =0 0
11 a v = c a = 0 sin βd/ βd/ 34 T r 3 v = c r [9] β g β g = ±jγ n n =,, J 0 n χ 0n β =π/λ Γ n χ 0n /a β 36 z < d/ z > d/ z d/ sin β g d/ expjβ g d/ exp jβ g d/ E z r, z = E 0 + J 0βr J 0 βa χ 0n cosh Γ n z e Γnd/ Γ na n= J χ 0n r/a J χ 0n 37 I =πah θ a, d/ = E 0 d C C = I j C = C 0 f d a,βa 40 C 0 a d C 0 = ɛ 0 πa d 4 f C 0 fx, y = e x χ 0n y n= χ 0n y = J y yj 0 y n= e x χ 0n y χ 0n y fd/a, βa d/a = βa 7: fd/a, βa 3
12 coupler φ 0bi-periodic structure 3. 8 z φ 0 φ π π φ = π π 8: =0 = π TM C C R π π φ =0 π 0 φ =0 E H cell - cell - cell - cell mode p - mode 9: 0 π π
13 i L L C' C C i 0: C C 43 C L π 0 > π 0 ĩ ĩ jl + jc jl + jc ĩ + jc ĩ ĩ =0 ĩ + jc ĩ ĩ =0 44 ĩ = ĩ 0 0 ĩ = ĩ π π 0 ĩ = ĩ = LC 0 45 E =0 H =0 47 E =0 H = π 9 e h π ĩ = ĩ = 0 + C C π 0 + C C > < π e = 0 c h h = 0 c e e dv = h dv = 49 cell cell e =0 h =0 50 e h 3
14 e = 0 c h h = 0 c e e dv = h dv = 5 cell cell e =0 h =0 5 0 π = S A B B A dv B A A B nds 53 A e B e 9 n S S e e n = [ π c 0 ] v 0π = 0 e h nds c c iris 55 iris v 0π v 0π c e e dv 56 0 cell 55 TM k c e h nds 57 0 iris 55 [ π ] = k 58 v π 0 v 0π e e v 0π TM 00 k a λ 9 z z =0 z ± E z ±e 0 E r 0 z = aξη r = a + ξ +η 59 Φ= a π e 0 ξ tan ξ + 60 [0] e r e r iris = Φ r = z=0 r π a r e 0 6 h e 4
15 z e z e 0 49 h θ h θ iris = 0r c e k = 4 3 a3 e 0 63 b d 49 χ0 r e z = e 0 J 0 64 b k = e 0 = dj χ 0 4a 3 a3 3πb dj χ.57 0 b d k a % 3. 0?? C C n ĩ n jl + ĩ n + ĩ n ĩ n+ ĩ n jc jc =0 67 φ ĩ n+ = ĩ n e jφ 68 = 0 [ + k cos φ] / [ 0 + k ] cos φ 69 0 LC, k C C 70 φ π dispersion curve k pass band ± φ i = i 0 e jf L i 0 e jf i 0 i 0 e jf i 0 e jf C' L L L L C' C' C' C C C C C n = 0 : ñ ĩ n = Ã+e jn φ + à e jn φ 7 ĩ n = A + cos t + n φ + ψ + + A cos t n φ + ψ 7 A ± 0 ψ ± + 5
16 jl + r + ĩ n jc π + ĩ n ĩ n+ ĩ n jc = π φ 0 φ π φ r L r L : C' C' n φ =0 φ = π φ Ã+ Ã 0 d λ g β g λ g π = πd β g φ 73 C C C 3: Q exp t/q Q 3 r 9 R v p v p = ± β g = ± d φ 74 Q = L r = Cr Q = R = RC 77 L 0, 0 ± φ, v p /d 3 r r L jl jl + r 68 ĩ n+ = ĩ n e jφ α 78 α 76 α φ 75 6
17 φ =0 φ = π α Cr k sin φ = kq sin φ 79 α 69 φ =0 φ d Ẽ x, y, z + d =e φ Ẽ x, y, z H x, y, z + d =e φ H x, y, z 8 [] φ 0 φ Cr φ = π α ln/k 80 r L π φ α lnπ φ 8 4 α k = 0.0 Q = 000 π R. M. Bevensee[][] TM 00 5 z = nd n z = nd ncell n 0 φ =0 φ = π 0 - mode φ = φ /rad n = 0.04 z / φ /rad 0.98 z = : Q = 000 k =0.0 α 0.0 φ 0.99π φ 0 =/ LC π - mode φ = π n = 0 z = 0 z 5: 0 π φ 0 Ẽ, H 7
18 0 Ẽ, H E, H 53 A e B E 0 55 { [ ] φ } = 0 [ c 0 A φ + right iris left iris A φ cell0 ] E h nds 83 E edv E e e e 0 E A e A = cell0 E e dv 85 A A E cell0, rightiris = A e cell0, rightiris + A e jφ e cell, leftiris = A e jφ e cell0, rightiris 86 E cell0, leftiris = A e cell0, leftiris + A ejφ e cell, rightiris = A e jφ e cell0, leftiris 87 e n { [ ] φ } 0 A c cos φ A 0 right iris e h nds = A k cos φ 88 A A /A π π 8
19 Floquet z d nπ jβg+ Ẽ z x, y, z = Ẽ n,z e d z n= = e jβgz n= nπ j Ẽ n,z e d z 89 e jβgz d β g z z z 0 π a = a φ a 6 v p v p = a φ a d 90 v b 6 φ a π 7 π φ a π mπ m m = d TW in +z direction TW in -z direction v phase = /β g = v beam φ = β g /d -π -π -φ a 0 φ a π π φ a -π π-φ a π+φ a 6: +z z φ a v phase = v beam -π 0 π π 3π 7: φ a π φ = β g /d π φ =0 0 π 8 PEP PETRA 9
20 3.4 N N 8 0 Rees[3] i L C' i L i 3 C' L i N L i N i N L L C' C' + k ĩ k 0 ĩ = ĩ + k 0ĩ k 0 ĩ k 0 ĩ3 = ĩ. + k 0ĩN k 0 ĩn k 0 ĩn = ĩ N + k ĩn k 0 ĩn = ĩ N 93 π ĩ = ĩ = ĩ 3 = = N ĩ N C C C C C C 8: N 0 =+k 95 π π L C C π 0 =+k 96 N 0 LC, k C C 9 L C L C, k C C 9 L L C C k k k Hĩ = π ĩ 97 H = k k k k k k k k k k k k k k k k 98 0
21 ĩ = ĩ ĩ ĩ 3.. ĩ N ĩ N ĩ N 99 n n / π n nπ = k cos π N k cos nπ N n =,,...,N 00 ĩn = {ĩ n,m } m =,,...,N ĩ n = mode number m = m = m = 3 m = [ ] m nπ ĩ n,m = + δ nn N sin 0 N δ nn n = N π N = π N =5 9 0 k 0.05 m / π m : N=5 k =0.05 m = 5 amplitude cell number n 0: k + jc r ĩ k 0 ĩ = ĩ + k + jcr 0ĩ k 0 ĩ k 0 ĩ3 = ĩ. +k+jcr 0ĩN k 0 ĩn k 0 ĩn = ĩ N + k + jc r ĩn k 0 ĩn = ĩ N 0 r H
22 L r L r L i i i 3 C' C' C C C : r 8 H + H ĩ = π ĩ 03 H 77 j Q j 0 Q j 0 0 Q H j Q 0 0 j Q 0 j Q 04 H = ĩt n H ĩn 05 ĩn = N m n π ĩ t m H ĩn m π n π ĩm 06 t n n n + j 07 π π Q H p δ 0 08 H p j Q j Q + δ π ĩ N 06 n = N Ṽejt H + H ĩ 0 ĩ = π jcṽ r C' L e jt C C C cell number: n n n + r : Q π = π m = C' L
23 jcṽ Ĩ 0 E N N Ĩ H + H E ĩ = 0. 0 ĩ = N a n ĩ n 3 0 a n a N = j Q N Ĩ Q sin a n = j jq n nπ N N n N 4 n n π 5 π Q N a N π N π a N 5 π m = N ĩ ĩ N 0 4 Ĩ ĩ Ĩ [ ] j Q sin N π N + N Q N ĩ Ñ I j Q N N + sin [ N N π N Q N ] 6 Q 000 ĩ N /ĩ ] arg [ N ĩ N /ĩ 3 4 N N N kπ N 7 N π i end cell / i first cell : Q N π Q = 000 k = APS φ a = π N 3
![05 5: 500 MHz APS 0 0 π/ 6 SCS side coupled structure [6] ACS](/docs-images/91/105189250/images/24-1.jpg "annular coupled structure [7] DAW diskand-washer [8] 5 APS")
![alternating peiodic structure[4][5] π 0 π 0 φ = π 0 π 0](/docs-images/91/105189250/images/24-2.jpg "biperiodic structure π/ 6: APS SCS side coupled structure ACS")
24 Arg{- N- i end cell / i first cell} rad N : Q N π Q = 000 k =0.05 5: 500 MHz APS 0 0 π/ 6 SCS side coupled structure [6] ACS annular coupled structure [7] DAW diskand-washer [8] 5 APS alternating peiodic structure[4][5] π 0 π 0 φ = π 0 π 0 biperiodic structure π/ 6: APS SCS side coupled structure ACS annular coupled structure DAW disk-and-washer coupling cell APS 6 4
25 l s φ 0 Ω l Ω φ s = K cos i = i exp-j l -jf i s exp-j -jf/ L l C' L s Ll L s L l C' i i expjf/ i expjf l s C' C' l 4 φ =0 φ = π =Ω, Ω φ =0 C l C s C l Cs C l 7: jl l + jc l ĩ l jc jl s + = jc s jc = φ φ ej j + e jc ĩ l ĩ s φ φ ej j + e jc ĩ l 8 φ/ z k l C l C k s C s C 9 8 ĩ k l l l cos φ = ĩ s + k l l = + k s s + k s s 0 Ω l l +kl Ω s l +ks K l s kl k s = Ω =Ω l, Ω s φ = π 3 Ω l +Ω s Ω ± K + l Ω s 4 φ = π v g d φ d K sin φ v g = 4 Ω l Ω s d 5 Ω l Ω s φ = π v g =0 Ω l =Ω s Ω confl 6 π d = ± K 7 4Ω confl Ω l =Ω s confluence 9 C l C s 5 TM 00 APS k s k l k l =0.03 k s =0.09 Ω l /Ω s
26 8 l s = Ω l Ω s φ = π 0 = Ω l = Ω s /Ω l Ω s /.0 Ω l /Ω s = φ 9: φ = π APS = Ω > Ω 8: TM 00 APS φ = π 9 φ =0 30 =Ω =Ω 0 π Ω Ω s < Ω l l s = Ω 30: φ =0 APS Ω Ω l =Ω s Ω Ω = K l Ω s Ω l Ω s 8 Ω Ω l Ω s Ω kl k s 9 Ω l Ω s k s,k l k Ω Ω /Ω l k 6
27 k s k l 6 l s = +k s +k l > 30 φ = ĩs ĩ l = +k s +k l > 3 k s k l C s C l 3 ĩ s C s ĩ l C l 33 4 aperture loop matched coupling undercoupling overcoupling well-padded 3 S a S a S S a 3 S m S a S m S a S m S z 7
28 k k S a n k Sa n = k 導波管 z 方向 k = n Sm on S a 実際の結合穴 空洞 3: S a e n, h n 34 e n, h n e jt e n, h n + n e nr c =0 h n r n =,, 3, n S e n r =0 h n r =0 37 n e n r =0 n h n r =0 38 δ nn e n e n dv = δ nn h n h n dv = δ nn 39 e n r e n r m 3/ e n r = c h n r n h n r = c e n r n 40 Ẽ H Ẽ + jµ 0 H =0 H jɛ 0 Ẽ =0 Ẽ H Ẽ H n A B =A B n 4 A B dv = A Bdv + S [A B] n ds 4 8
29 n Ẽ e n dv + n c n Ẽ h n ds S m = n c n j µ 0 S m = j µ 0 S a H h n dv n Ẽ h n ds n Ẽ h n ds S a n Ẽ h n ds 43 Ẽ Ẽ H δ = µ 0 σ n Ẽ = +j µ 0δ H 44 Q n Q n 45 δ n S m h nds δ n = n Q n n Q Q n 43 /Q n H h n dv j S a n Ẽ µ 0 j n Q n n n h n ds 46 n 47 Q n Q n 46 n e n, h n 0 rotational irrotational [9] H g m g m g m r =0 + m c g m r =0 48 S g m n =0 49 Ẽ n Ẽ g mds 50 S a m H n + m h n j S a n Ẽ h n ds µ 0 j n Q n n [ j ] g m n µ 0 Ẽ g m ds S a 5 n =0 9
30 4. z k S a S a 5 h n S a Ẽ k +z t z x, y z A x, y, z e jt =[A t x, y+a z x, y] e jt βgz 5 β g z TM transverse magnetic z TE transverse electric Z g H t,g x, y =±k E t,g x, y 53 [0] + e jβgz +z e jβgz z Z g wave impedance ζ 0 = Ω β β g TM Z g = = β g Y g β TE 54 Z g = Y g = β β g 55 Y g e g x, y h g x, y Ẽ g,t x, y, z =Ṽ ze g x, y H g,t x, y, z =Ĩzh g x, y 56 e g x, y h g x, y S g e g e g dxdy = h g h g dxdy = 57 S g S g eg x, y = hg x, y z + z Ṽ + z =Z g Ĩ + z =Ĩ+z/Y g e jβgz Ṽ z = Z g Ĩ z = Ĩ z/y g e +jβgz 59 z =0 Z L z 0 Ṽ z =Ṽ+z+Ṽ z Ĩz =Ĩ+z+Ĩ z 60 30
31 z =0 Ṽ 0 = Z L Ĩ Ṽ 0 Ṽ + 0 = Z L Z g Z L + Z g R 6 R z Z in = Z g +Re jβgz Re jβgz = Z g Z L jz g tan β g z Z g jz L tan β g z 63 S a Ẽ t aperture =Ṽge gt H t aperture =Ĩgh gt 64 z Ṽg Ĩg 64 5 Ĩ g h gt n + m h n jṽg S a n e gt h n ds µ 0 j n Q n n [ ] jṽg g m n e gt g m ds µ 0 S a 65 e gt n A B = n A B e gt h gt kds S a = e gt h gt nds S a = 66 S a Ĩ g jṽg n jṽg m [ Sa n e gt h n ds] µ 0 j n Q n [ µ 0 n S a n e gt g m ds ] 67 [ ] 67 n n 67 Ṽ g Ĩ g µ 0 n Q n [ S a n e gt h n ds ] r n 68 r n r n C n n r nq n 69 L n r nq n n 70 3
32 L 0 µ 0 [ ] 7 n S n e a gt g m ds r C L Ω Farad Henry S a Ỹ in =/ Z in Ỹ in = Ĩg Ṽ g = jl 0 + n 7 jc n + r n + jl n 3 L 0 L L r r C C 3: 0 7 n Ỹ Ỹ in 0 jl 0 + Ỹ 73 Q 0 n Ỹ n Ỹ in n + jc n + r n + jl Ỹ n n 74 3 Y g /Z g 45 Q Q n Q Q ext, n Ln Q ext, n Y g = r n Y g Q n 75 C n 74 Ỹ in n j n Q ext, n Y g + Ỹ n 76 n + Q n 4 S a /4 z = ± π β g Ỹ in / Z in S a Ỹ in / Z in Ỹ in = Z in = Y g = Z in Ỹ in Z Z in = n jl + jc n + n R n C 0 L 0 Y 0 C n L n Y 0 L n C nz 0 + jc 0 78 R n r n Z
33 33 L' L' C' 0 C' C' R' R' k = M m 0 F ideal = 83 0 m 35 Z Z Z /m 33: 3 3 λ g/ [ ] 34 F F = L M jm L L m : I = F I jl L M M L M I M I L M L M 34: M 80 8 L L M m = sqrtl /L k = M/ L L 8 m : Z = I = m I = Z m 84 Z m Z 35: 68 7 [ ] e gt h n g n e gt h n g n S a h n g n e gt c n m n = S a e gt h n nds c 0 m 0 = [ ] m S e a gt h n nds 85 c 0 c n 33
34 C n = C n /m n L n = m nl n r n = m n r n L 0 = m n L 0 86 m n m m n Q ext, n n Q n Q ext, n 3 : m 0 : m : m L'' 0 r'' L'' r'' L'' C'' C'' : 3 k 34
35 beam loading J t, x, y, z H E + µ 0 t =0 E H ɛ 0 t = J 87 Ẽ H S a 0 40 E H h n J dv 88 h n =0 h n J dv = J h n dv = n J e n dv 89 c h n J dv J h n dv = J hn dv = J hn n =0 S t + n Ẽ e n dv + n c n Ẽ h n ds S = J e n dv 90 ɛ 0 t t + n H h n dv + n µ 0 t Ẽ h n ds S =+ n c J e n dv j Ẽ e n dv = J e n dv 9 ɛ 0 n j Q n n n 35
36 Ẽ x, y, z = e n x, y, z Ẽ e n dv n = n j e n x, y, z J e n dv ɛ 0 n n 93 j Q n n = q z x = y =0 c +z T =π/ J t, x, y, z [ = ki 0 δxδy + p= cos p t z c ] 94 k +z p δx δy x y I 0 I 0 = q T 95 p = n = J t, x, y, z ki 0 δxδycos t z c z qz =q 0 δz J x, y, z =ki 0 δxδye jz/c n = Ẽ x, y, z e n x, y, z j k e 0, 0,z e jz/c dz I 0 ɛ 0 j Q = e n x, y, z j e z z e jz/c dz I 0 98 ɛ 0 j Q e z e z z n = = Ẽ x, y, z = e x, y, z Q I 0 ɛ 0 e z z e jz/c dz e jz/c E t, x, y, z =Re [Ẽ ] x, y, z e jt e n x, y, z Q I 0 ɛ 0 e z zcos t z dz c 99 z z E t, z qz = q 0 e z σz πσz σ z r.m.s. q 0 I 0 e σ z c I 0 36
37 e z z z E t, z = e z zcost Q I 0 ɛ 0 e z zcos z c dz 00 z = ct br br = = Q I 0 ɛ 0 E z/c,z dz [ e z zcos z ] c dz 0 = 0 e e dv = [ e z zcos z ] c dz [ ] E z zcos z c dz = E 0 E dv 4 Q Q = ɛ 0 E E dv 03 P wall 0 br = br 04 I 0 P wall R a br = I 0 R a =I 0 R Ṽ b = I 0 jc + jl + R a 06 C = Q R a L = R a Q I 0 e jt L C R = R a / 37: I 0 e jt L C R = R a / L C R = R a / 38:
38 39 R = R a / jb = j Q R Y 0 = /Z 0 ±z ṽ g± Ĩg Y 0 n I g e jt v g+ v g Y 0 /R jb I 0 e jt クライストロン導波管加速空洞ビーム Y 0 = /Z 0 : n 39: /n n Z 0 /n I g e jt v g+ v g β/r /R jb I 0 e jt クライストロン導波管加速空洞ビーム β/r 40: 39 β Ṽ g+ = R β Ĩg Ṽ g = R β Ĩg 0 5 Ṽ g+ + Ṽg Ĩ g + Ĩg 40 I 0 =0 Ṽg I g =0 Ṽb Ṽg 0 40 Ṽ g = Ṽg+ + Ṽg = R β Ĩg Ĩg β R Z 0 /n 09 = Ĩg + Ĩg + jb R Ṽg± = ṽ g± /n / Ĩg R /β Ĩg Ṽ g = R +β + jbr Ĩ g
39 tuning angle ψ Im < ' = ' g > ' gr ξ ψ tan ξ 4 0 ψ θ Re ξ BR +β = Q +β 5 Ṽ g = gr cos ψe jψ+jθ 6 gr = gr R Ĩ g +β 7 θ 6 R gr P g = R Ĩg β 8 gr = β R P g = β Ra P g 9 +β +β 4 gr Ĩg =0 Ṽb Ṽ b = R I 0 +β cos ψejψ = br cos ψe jψ 0 6 π 4: Ṽg ψ θ br R I 0 +β = R a I 0 +β 7 Ṽc Ṽ c = Ṽg + Ṽb c e jφ c φ [] Perry Wilson 4 [] Ṽc a a = c cos φ 3 P b = I 0 a β β 39
40 ψ br b br Im 0 c ψ a θ g ψ gr gr e jθ Re 4: P. B. Wilson c a λ/4 /S µq 0 S µ Q 0 Q P b c β β =+ [][3] P b P wall 5 P wall = c 6 R A OHO96 λ/4 λ/4 S µq 0 S µq 0 µ µ Q 0 S µq 0 [] SLATER, J.C.:Microwave Electronics D. an Nostrand Co., Inc., 950. [] COLLIN, R. E.: Foundations for Microwave Engineering, nd Ed. MacGrawhill, 99. [3] MONTGOMERY, C. G., DICKE, R. H. and PURCELL, E.M.:Priciples of Microwave Circuits, M. I. T. RadiationLaboratory Series ol. 8 MacGrawhill, 948. [4] STRATTON, J. A.: Electromagnetic Theory MacGrawhill, 94. [5] GINZTON, E. L.: An Electron Linear Accelerator, Rev. Sci. Instr., [6] CHODOROW, M., et al.: Stanford High-Energy Linear Electron Accelerator Mark III, Rev. Sci. Instr., [7] LANDAU, L. D. andlifshitz, E. M.: Mechanics, 3rd Ed. [8] YAMAZAKI, Y., et al.: KEK Report, KEK
41 980. [9], [0] WENDT, G.: Handbuch der Physik, Band 6, p.40 Springer, 958. [] BEENSEE,R. M.: Electromagnetic Slow Wave Systems John Wiley & Sons, 964. [] BEENSEE, R. M.: Periodic Electromagnetic and Quantum Systems, Annals of Physics, 96. [3] REES, J. R.: A Perturbation Approach to Calculating the Behavior of Multi-cell Radiofrequency Accelerating Structures, PEP Notes, PEP , SLAC. [4] NISHIKAWA, T., et al.: Rev. Sci. Instr., [5] AKAI, K., et al.: Proc. of 3th Int. Conf. High Energy Accelerators, [6] KNAPP, E. A., et al.: Rev. Sci. Instr., [7] KAGEYAMA, T., et al.: Particle Accelerators, [8] ANDREE,. G.: Soviet Physics - Technical Physics, [9] BORGNIS, F. E. and PAPAS, C. H.: Handbuch der Physik, Band 6, p. 44 Springer, 958. [0] JACKSON, J. D.: Classical Electrodynamics, nd edition John Wiley & Sons, 975. [] NISHIKAWA, T.: Proc. of st Particle Accelerator Conference, IEEE NS [] WILSON, P. B.: Beam Loading in High-energy Storage Rings, Proc. 9th Int. Conf. High Energy Accelerators [3] WILSON, P. B.: KEK Lecture Notes on Beam Loading and Impedance Problems in e+e- Storage Rings, KEK-Accelerator
2 [1] KEK Report L C R L C R [2] 2
![2 [1] KEK Report L C R L C R [2] 2](/thumbs/91/105189328.jpg "2 [1] KEK Report L C R L C R [2] 2")
Fundamentals of RF Acceleration Revised Edition Koji TAKATA 2 [1] KEK Report L C R L C R [2] 2 3 Slater [3] Collin [4] [5] [6] [7] MIT Radiation Laboratory Series 8 Principles of Microwave Circuits [8]
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液晶の物理１：連続体理論（弾性，粘性）
The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers
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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
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2003/12/04 TASK PAF A. Fukuyama et al., Comp. Phys. Rep. 4(1986) 137 A. Fukuyama et al., Nucl. Fusion 26(1986) 151 TASK/WM MHD ψ θ ϕ ψ θ e 1 = ψ, e 2 = θ, e 3 = ϕ ϕ E = E 1 e 1 + E 2 e 2 + E 3 e 3 J :
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第3章
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