AHIPA, Oct.19-21, 2009, FNAL FFAG for High Intensity Proton Accelerator Yoshiharu Mori Kyoto University, Research Reactor Institute (KURRI)
AHIPA, Oct.19-21, 2009, FNAL Contents Introduction Features Transeverse focusing Zero chromaticity (scaling: fixed tunes) ”zero chromaticity” Non-zero chromaticity(non-scaling: variable tunes) ”fast resonance crossing” History of development Acceleration(RF) cf. induction: inefficinet Variable frequency Constant frequency Advancement of FFAG Proton driver Summary: beam power efficiency
AHIPA, Oct.19-21, 2009, FNAL FFAG: Fixed Field Alternating Gradien t Static magnetic field It is like cyclotron, but not much orbit excursion Fast acceleration Fixed magnetic field allows the beam acceleration only by RF pattern. No needs of synchronization between RF and magnets. Large repetition rate High intensity with large repetition rate and modest number of particles in the ring Space charge and collective effects are below threshold. 6D-Strong focusing (AG focusing, phase focusing) It is like synchrotron. Large acceptance with small gap magnet Various longitudinal RF gymnastics become possible. Bunching, Stacking, Coalescing, etc.
AHIPA, Oct.19-21, 2009, FNAL Type of FFAG optics Zero chromaticity Fixed betatron tunes Fields are non-linear. Free from betatron resonance crossing Non-zero chromaticity Varied betatron tunes Linear optics Fast resonance crossing
AHIPA, Oct.19-21, 2009, FNAL Zero chromaticity FFAG Betatron eqs. in cylindrical coordinate d θ 2 + r 2 d 2 x ( ) x = 0 ρ 2 1 − K ρ 2 K = − 1 ∂ B d θ 2 + r 2 d 2 z ( ) z = 0 ρ 2 K ρ 2 B ρ ∂ r Zero chromacitiy: Constant betatron tunes Sufficient condition --> Scaling d r 2 ρ 2 ( ) k r = 0 r ∝ ρ ( ) B z = B 0 f θ dp → r ∂ B z r ( ) = k d K ρ 2 0 B ∂ x = 0 z = 0 dp Note: Above is not necessary & sufficient condition!
AHIPA, Oct.19-21, 2009, FNAL Magnetic field of scaling FFAG Momentum compaction: 1/k+1
AHIPA, Oct.19-21, 2009, FNAL Scaling FFAG lattice Scaling type of FFAG Original idea ---> Ohkawa (1953) “Zero chromaticity” radial sector betatron eq. x + g x x = 0 ; g x = K 2 negative bend 2 (1 " n ) ! ! K 0 FODO(DFDO) z + g z z = 0 ; g z = K 2 2 n ! ! K 0 field index geometrical # n $ ' K # & ) = 0 = 0 # p * = const . # p K 0 % ( * = const . orbit similarity no p-dependence spiral sector n 0 $ ' r F * " + ln r $ ' edge focus ( ) = B i i & ) B r , * % ( r % r ( FFDO i AG focusing
AHIPA, Oct.19-21, 2009, FNAL Dynamic Aperture of Scaling FFAG 6th 5th 4th 3rd Quite large! cf. A>10,000mm.mrad for phase advance of ~90degree/cell Momentum Comapction: no higher orders 1 α = : momentum compaction factor -------- momentum acceptance : large k +1 -------- kinematic effects : small enough
AHIPA, Oct.19-21, 2009, FNAL Non-zero chromaticity FFAG non-scaling Fields are linear: B,Q fields. α ≅ C 1 ξ 2 , ξ = Δ p momentum compaction: small enough ~parabolic p Tunes are varied: Fast resonance crossing tune variation P momentum compaction transverse offset for all momentum
AHIPA, Oct.19-21, 2009, FNAL FFAG Accelerators :history Ohkawa (1953), Kerst & Symon, Kolomenski MURA project e-model, induction acceleration ~’60s No proton FFAG for 50years! Proton FFAG (POP:World first p-FFAG, Mori et al.,2000) Complicated field configuration : 3D design MA(Magnetic Alloy) RF cavity : Variable Frequency & High Gradient. 150MeV p-FFAG (Mori et al.,2004) PRISM FFAG(Kuno et al.,2008,Osaka) p-FFAG for ADSR study, ERIT neutron source (KURRI,2008) EMMA(e-FFAG for nuFact:World first non-scaling FFAG, England,under development)
AHIPA, Oct.19-21, 2009, FNAL MURA FFAG (‘60) Electron Model Radial & Spiral Induction & RF (const. f) No proton acceleration
AHIPA, Oct.19-21, 2009, FNAL History of FFAG Proton Accelerator 1953: Basic concept by Ohkawa Proton FFAG accelerator was not successful until recent → difficulty in fabricating RF cavity with variable frequency & high gradient field 1998 ： Development of RF cavity using Magnetic Alloy Grant-in-Aid for Scientific Res. by MEXT ： Y. Mori, KEK Proof-of-Principle (PoP)-Proton FFAG Accel. 2000 ： Demonstration of Proton FFAG Accelerator -POP FFAG- 150MeV multipurpose proton FFAG Grant-in-Aid for Scientific Res. by MEXT: Y. Mori, KEK WORLD ʼ s FIRST PROTON FFAG! 2004 ： Development of 150MeV multipurpose FFAG accelerator 100Hz Operation! Grant-in-Aid for Creative Basic Res.:Y.Mori
AHIPA, Oct.19-21, 2009, FNAL FFAG complex for ADSR study at KURRI
FFAG-ADSR project at KURRI
First experimental data prompt neutrons delayed neutrons k eff C.H.Pyeon et al., Journ. of Jap.Atom.Ene.Soc. FFAG-KUCA for ADSR study
KUCA reactor core At various positions in the reactor Neutron time sturucture 600 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 f f f f い #1 ろ f f f f #2 BF は f f f UIC#6 #3 f fs fs fs f に #4 b bs bs bs b ほ b bs bs bs b へ 400 s s s と counts s s s ち s' り UIC#5 C3 F ' SV F ' S5 ぬ He F F SV F F N る S4 C1 F F SV F F を F F F F F わ C2 F F F F F S6 200 か FC#3 FC#1 He よ た れ そ つ FC#2 UIC#4 ね な 0 0 500 1000 ら む time ( μ sec)
AHIPA, Oct.19-21, 2009, FNAL Non-zero chromatic FFAG EMMA the World's First Non-Scaling FFAG Accelerator Susan Smith STFC Daresbury Laboratory
AHIPA, Oct.19-21, 2009, FNAL Acceleration(RF) Beam acceleration in FFAG: various and flexible Momentum compaction can be tuned along orbit swing. Keeping phase stability like synchrotron Realizing isochronism like cyclotron Variable frequency RF Broad-band RF cavity : Scaling & Non-scaling MA(magnetic alloy) cavity Q~1 Fixed frequency RF Stationary RF bucket acceleration : Scaling constant momentum compaction(MC) Gutter RF acceleration : Non-scaling relativisitc beam & small MC(parabolic) :semi-isochronous Harmonic number jump acceleration : Scaling (non-scaling) non-zero slippage factor
AHIPA, Oct.19-21, 2009, FNAL Variable RF frequency Broad-band RF cavity : MA(magnetic alloy) cavity Fast acceleration requires fast frequency(phase) change. Low Q (Q~1) is essentianl ! Adequate both for scaling and non-scaling FFAGs.
AHIPA, Oct.19-21, 2009, FNAL Fixed RF frequency(1) Stationary bucket acceleration Constant & small enough phase slip --- Large energy gain relativistic beam η = 1 1 2 − α ≅ − α = − constant Momentum Compaction 18MHz, k + 1 γ Adequate for scaling FFAG 1MV/m RF cavity slow & constant
AHIPA, Oct.19-21, 2009, FNAL Fixed frequency (2) Stationary bucket acceleration Non-relativistic to relativistic Longitudinal Hamiltonian in scaling FFAG 2 − 1 γ 2 − 1 − λ + 1 λ ( ) ( ) γ s + eV rf H = 2 π m 0 c 2 f 0 cos φ + γ ( ) 2 γ s 1 − λ h k λ = ( ) 2 k + 1 dp = 0 : p = γ 1 and γ 2 dT
cf. S.Machida AHIPA, Oct.19-21, 2009, FNAL Fixed RF frequency(3) Gutter RF acceleration Parabolic & small enough phase slip relativistic beam small parabolic Momentum Compaction Adequate for non-scaling FFAG slow & parabolic
cf. A.Ruggiero(BNL) AHIPA, Oct.19-21, 2009, FNAL Fixed RF frequency(4) Harmonic number jump acceleration m:integer, m<0: before transition, m>0: after transition Energy gain/turn can be automatically tuned if the RF voltage is high enough. ---> Phase stability Time slip/turn: m x Trf T i + 1 − T i = m f RF
AHIPA, Oct.19-21, 2009, FNAL Advancement of FFAG Zero chromaticity (scaling) FFAGs Pro/ Fixed field & Strong focusing Zero chromaticity constant betatron tunes → no-resonance crossing Large acceptance (longitudinal & transverse) Con/ Relative large dispersion:Orbit excursion is large. Large horizontal aperture magnet Large horizontal aperture rf cavity → Low frequency Short straight section Injection/Extraction difficulties → Kicker/Septum needs large apertures. Available space for rf cavity is limited. Need long straight section with small dispersion keeping “Zero Chromaticity”.
AHIPA, Oct.19-21, 2009, FNAL Scaling FFAG linear line Is it possible to make a linear FFAG straight line? keeping a scaling law: zero chromaticity reducing dispersion: dispersion suppressor making a good match with ring: insertion Magnetic field configuration for FFAG linear line? × Obviously not: k r ( ) B = B 0 f θ r 0
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