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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<<c( m ) f T f = 1 T = eb (4) 2πm 1 ( ) PET(positron emission tomography) 10 20 MeV 1: 1.2 2 Injector (linac) RF cavity Extraction Bending magnet Injection 2: t p(t) r 0 (2) B B = p(t) er 0 (5) (4) f rf f rf = eb(t) 2πm(t)

= f 0 pc (pc) 2 +(m 0 c 2 ) 2 (6) f 0 = c/2πr 0 200 MeV 300 400 MeV 1.3 ( ) ( ) ( ) (liner accelerator) ( 3 ) () ( ) ( ) (radio frequency quadruple linac: RFQ) ( 3 ) 3: ( ) ( ) X RFQ

2 Maxwell [2, 3] 2.1 Maxwell 4 5: (rot) E rote [4] (rot) l S 4: ( ) ( ) ( ) E dl = μ H nds (7) t ( l S (rot) l S 1 ( 5 ) 1 rot E = E rot (7) rot E nds = μ H t nds rote = μ H t (8) ( ) H (8) E 6 6: ( )/ɛ 0 (div) S V ( 7 )

1 μ 0 rot B ds = j nds 1 μ 0 rot B ds = j (10) 8 ( 9 ) 7: (div) E dive E nds = 1 ɛ 0 ρdv div E = ρ (9) ɛ 0 ( 8 ) 9: div i = ρ t (11) div E = ρ ɛ 0 8: ( ) 1 B dl = j nds μ 0 5 l S rot 1 B dl = j nds μ 0 div i = t ɛ 0div E = ɛ 0 div E t E i = ɛ 0 t (12) ( E ) i ɛ 0 t (10) (10) 1 E rot B ds = j + ɛ 0 μ 0 t (13) ( )j E (13) B

2.2 10: B (14) (15) 11 12 E B TEM (transverse electric and magnetic wave) ( 10 ) div B =0 rote = B t (14) 1 E rotb = j + ɛ 0 μ 0 t (15) dive = ρ ɛ 0 (16) divb = 0 (17) 11: 1 B E [4] (14) (15) (16) (17) 12: 2 E B ɛ 0 μ 0 c = 1/ ɛ 0 μ 0 S = E H E V/m H A/m S W/m 2

13 ( 11 12) ( ) TE TM (z ) ( ) TE11 z TM01 (TM01)

(a) Plain wave (c) Rectangular (b) Coaxial TE01 (Transverse electric wave) TM11 (Transverse magnetic wave) (d) Circular cylindrical TM01 13: E B S (a) (E ) (b) (TEM ) (c) E =0 (TE ) TM ( TE ) (d) TM11 TM01 ( : (a) TE01 TM11, TM01 )

3 14 2 z R sh (Ω) R sh P = V 2 /R ( 2 2 ) E 0 = V/ (V/m) (18) Z sh = R sh / Z sh = V 2 P = E2 0 P/ (19) 14: E B e ( ) Z sh (Ω/m) 14 B P wall V P wall P (= P wall ) V R sh R sh = V 2 (18) P (V) (W) ω b E 0 b E 0 i b (20) P/ i R P/ i 2 R (21) R ρ(ω m) δ = 2ρ ωμ (22) 2 Maxwell ( ) [5] [6] ( μ ) R = ρ 2πbδ (23)

b ω (b ω 1 ) (19) (22) Z sh ω (24) φ =0 P wall (stored energy) U ω Q 0 = ωu P wall (25) Q P wall Q Q 0 Q 0 P wall ( 3 ) Q 0 (18) (25) P R sh Q 0 = V 2 ωu (26) (R/Q) 15 15: E z t ( ) φ =0 ( ) φ s cos φ s ( ) 16 p E z 3 δ [ (22) ] ( ) T = /2 /2 E z(z)cos(ωz/v)dz /2 /2 E z(z)dz (27)

V eff φ s ( 15 ) V eff = E 0 Tcos φ s (30) 16: T p E z T (27) E z E 0 = /2 /2 E z (z)dz/ (28) E 0 p E 0 T (19) E 0 E 0 T Z eff = Z sh T 2 = E2 0 T 2 P/ (29) p

4 4.1 13 17 v p 17 v p = c/ cos θ c ( ) v g c z v g = c cos θ 18: λ 0 λ g cos θ = λ 0 λ g (31) λ 0 θ ( 19) λ c λ c /2 20 λ g λ c 17: v p v g c v p >c v p v g λ g λ 0 λ c 17 18 tan θ = λ g λ c (32) (32) (31) tan θ = sin θ cos θ = λ g λ c sin θ λ g λ 0 = λ g λ c sin θ = λ 0 λ c (33) (31) (33) sin 2 θ +cos 2 θ =1 θ ( λ 0 λ c ) 2 +( λ 0 λ g ) 2 = 1

20: λ c λ g 1 λ 2 g 1 λ 2 = 1 0 λ 2 c (34) 1 λ g 1 λ 0 4 ( 21) 19: λ 0 z θ λ c a a = λ c /2 21: λ 0 λ g () 1 λ 2 c + 1 λ 2 = 1 g λ 2 0 1 λ 2 c 17 v p = c/ cos θ 4 k =2π/λ g ω =2πc/λ 0 21

(31) v p = c λ g λ 0 v p = c 1 λ 0 / 1 λ g (35) 21 v p ( c ) 17 v p = c cos θ (31) v g = c λ 0 λ g (36) (34) 1 λ g 21 2 1 λ g 2( 1 λ 0 )( 1 λ 0 ) = 0 ( 1 λ 0 ) = λ 0 λ g (37) v p 22: ( ) 4.2 v p c ( λ g λ 0 ) (disk-loaded structure) ( 22) 3 ω ω 23 λ 0 λ g () 5 5 [5] [6] Stopband Passband 23: λ 0 λ g () (passband) (stopband) z 1/3 [6, p. 17]

1 1/3 c λ g λ 0 1 d d = λ 0 /3 v p = c ( ) 24 2π/3 1/4 z (19) Z sh = E2 0 dp/dz (38) P z (dp/dz < 0) Q (25) Q 0 = ωu P wall U P ( ) (stored energy) w Q 0 = ωw dp/dz (39) Z sh (38) (39) Z sh /Q 0 Z sh Q 0 = E2 0 ωw (40) R/Q [ (26) ] 24: z 2π/3 1/4 ( [7, p. 7] ) α de dz = αe (41) P E 2 dp dz dp dz = 2αP (42) Z sh

(42) α z P P = P 0 exp ( z ) 2 α(z)dz 0 (43) P 0 z 0 α(z)dz τ τ = 0 α(z)dz (44) (z = ) P τ P = P 0 e 2α = P 0 e 2τ (45) P P 0 P /P 0 = e 2τ [ (t f )] 25 ) Vector network analyzer (41) (42) E(z) = E 0 e αz = E 0 e τ z (47) P (z) = P 0 e 2αz = P 0 e 2 τ z (48) z (=) [ (42)] ( ) (z = ) P z P P (z) = P 0 (P 0 P )z/ (49) (45) P τ P = P 0 e 2τ (49) 25: [8] α z τ = α (46) P (z) = P 0 (P 0 P 0 e 2τ )z ( = P 0 1 1 ) e 2τ z (50) dp dz = P 0 1 e 2τ (51) v g

26 P v g (stored energy)w P = w v g (52) (52) 26: P v g w ( ) P P = w v g Q 0 (39) v g ωp v g = Q 0 (dp/dz) (53) (42) (46) τ dp dz dp dz = 2τP v g ωp v g = Q 0 (2τP/) = ω 2Q 0 τ (54) v g z (t f ) v g t f = v g = 2Q 0τ ω (55) t f t f P dp dz (50) (51) ( P = P 0 1 1 ) e 2τ z dp dz = P 0 1 e 2τ (53) ωp v g = Q 0 (dp/dz) ) v g = ωp 0 (1 1 e 2τ z 1 e Q 0 ( P 2τ 0 ) = ω 1 1 e 2τ z Q 0 1 e 2τ (56) v g z (t f ) dz v g (z) z 0 t f = = Q 0 ω = Q 0 ω dz 0 v g 0 [ = 2Q 0τ ω 1 e 2τ 1 1 e 2τ z ( ln 1 1 )] e 2τ z 0 (57) t f

5 1.3 RFQ RFQ J-PARC 324 MHz DT 6 5.1 (Alvarez) Drift tube linac (DT) ( ) 27 TM01 z ( ) 28: J-PARC DT ( 324 MHz) ( 5.2 ) Drift tube 29 z 1/4 v 1 T = vt = βλ (58) 27: 28 6 DT (KEK-PS DT 200 MHz ( ) [9] )

β = v/c ( ) [10] D d g g = βλ 0 0 μ 0βλ 2π ln D (59) d ( μ 0 ) d C 0 C 0 πd2 g (60) ( ɛ 0 ) 0,C 0 ω 0 c = 1/ ɛ 0 μ 0 ω 0 = 1 0 C 0 2gc2 βλd 2 ln D d (61) β βλ g/βλ 29: z 1/4 β = v/c 1 βλ ω g d C 0 g 30 [ (29) ]

Effective shunt impedance [MΩ/m] 40 30 20 10 Alvarez (DT) linac Coupled cavity linac (CC) 0 40 80 120 160 Proton energy [MeV] ( ) 31 0 mode π/2 mode 30: ( [11] ) π mode 5.2 4 v = c ( ) v c (v <<c) ( ) [ β(= v/c) > 0.4 ] ( ) 3 ( ) ( 23 ) 31: ( ) 0,π/2,π λ g 31 0,π/2,π 32 ( 23) 31 0 λ g = ( )

Disk loaded structure max. π/2 π (mode) (π/2 mode) 0 Passband Alternating periodic structure (APS) 32: λ g 0,π/2,π v g 0,π 0 π/2 Side coupled structure (SCS) π/2 1 23 v g ( ) π 23 v g =0 ( 5 ) π/2 33 APS π/2 () APS 33: π/2 ( ) π/2 ( ) APS π/2 ( ) π/2 ( 34 ) Disk-and-washer (DAW) Annular-ring coupled structure (ACS) ( 34 ) Disk-and-washer (DAW) Annular-ring coupled structure (ACS) ( 35) π/2 31 33 π/2 π/2

Coupling cell Accelerating mode (E) M E M E M E M (E) Accelerating cell Coupling mode M E M E M E M E M 34: Accelerating cell Coupling cell 36: E () M ( ) ( ) 35: Annular-ring coupled structure (ACS) 36 ( 31 33 ) ( 36) π/2

(confluence) π/2 v g 0 7 ( 37) TM010 (Accelerating mode) E E E E E E Confluence 0 π/2 π (mode) Passband Post 0 mode (Coupling mode) M M M M M M 37: (confluence) 38 π/2 5.1 = βλ Post coupler 38: ( )[9] ( ) ( π/2 S 7 [5] [6]

6 OHO [10]. (II). OHO 01, 2001. [11],.., 1993. [1].. 2004. [2].., 1965. [3],,. III., 1969. [4].., 1987. [5].. OHO 97, 1997. [6].. KEK Report 2003-11, 2004. [7].. OHO 02, 2002. [8],,. KEKB. KEK Report 98-12, 1999. [9].. OHO 84, 1984.

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