Update on SuperKEKB Design Y. Ohnishi June/14/2006 3rd SuperB workshop at SLAC 1
Machine parameters and luminosity estimation Recent status of crab cavity since 2 nd SuperB WS (I reported at Frascati). 2
Luminosity formula Particle density Luminosity (Estimation of geometrical luminosity) L = f col dxdydz 1 dz 2 dsρ 1 ( x,y,z 1 ;s) ρ 2 ( x, y,z 2 ; s)δ s z 1 z 2 2 = f col dxdydz 1 dsρ 1 ( x,y,z 1 ;s) ρ 2 ( x, y,z 1 2s; s) s = z 1 z 2 2 z 1 = - ~ + z 2 = - ~ + N ρ( x, y,z;s)= 2πσ x s ()σ y () s exp x 2 2σ 2 x () s y 2 2σ 2 y () s 1 exp z2 2πσ z 2σ z 2 Beam size σ x,y s * ()= ε x,y β x,y 1+ s2 *2 β x,y Traveling focus z-dependent waist σ x,y * ( z;s)= ε x,y β x,y 1+ s az *2 β x,y ( ) 2 emittance β-function Waist locates the most density position. a = 1 2 for z = z 1, a = 1 2 for z = z 2 3
Traveling Focus The particles of the head and tail of a bunch are focused in different places, so that the focus point is running from the head to the tail. β-function (beam envelope) waist waist fixed waist Particle density s (mm) 4
Traveling Focus fixed waist s (mm) Different particles have different waist. 5 Particle density β-function (beam envelope)
SuperKEKB (geometrical) I + = 10 A / I - = 4.4 A (N b = 5000) N+= 1.26x10 11 / N-= 5.5x10 10 per bunch ε x = 18 nm ε y = 0.18 nm β x = 20 cm β y = 3 mm At s=0, beam-beam is relaxed for TF. σ z =3 mm L /Δs(cm -3 s -1 ) σ z =6 mm s (cm) Head-on: 5.33x10 35 (ξ y =0.25) Traveling focus: 5.61x10 35 Hourglass effect Head-on: 4.37x10 35 Traveling focus: 4.70x10 35 gain~ 5.3% gain~ 7.5% s (cm) 6
Beam-beam tune shift ξ x,y = β x,y 4π k x,y Beam-beam tune shift Δx'= k x x Δy'= k y y Δx'= N +r e γ Δy'= N +r e Beam-beam tune shift with beam distribution ξ x = ξ y = r e 4πγ r e 4πγ Bassetti-Erskine formula (Coulomb force) F = F y + if x dzρ + z dzρ + z ()β x ()β y () s F x δ s z x x= zθ,y= 0 2 () s F y δ s z y x= zθ,y= 0 2 = 2 π Σ w x + iy exp x 2 2 Σ 2σ y 2 x /κ + iκy 2 x 2σ w y Σ γ F x F y k=1/f, f is focal length. ( () σ 2 y () s ) ()/σ s x () s { ( )} Σ= 2 σ x 2 s x = zθ κ = σ y w(z) = exp( z 2 )1 erf iz F x = 4 1 κ exp x 2 x y= 0 Σ 2 2 2σ x 4 π x Im w x Σ 3 + 2 π x 2 exp x 2 2 Σ Σ σ x 2σ x Im w κ Σ x F y = 4 1 1 y y= 0 Σ 2 κ exp x 2 2 2σ x 4 π x Re iw x Σ 3 + 2 π 2x exp x 2 Σ Σ Σ 2 2 2σ x Re iw κ Σ x BB kick = Deflection by Coulomb force e- e + N + Crossing angle: 2θ Δx' e- 7
SuperKEKB Crab crossing Finite crossing E (LER/HER) 3.5 / 8.0 GeV I (LER/HER) 10 / 4.4 A N (LER/HER) 1.26x10 11 / 5.5x10 10 n b 5000 ε x 18 9.0 6.0 6.0 nm ε y 0.18 0.045 0.06 0.06 nm β x * 20 20 10 5 cm β y * 3 3 1 0.5 mm σ x * 60 42 25 17 μm σ y * 0.73 0.37 0.25 0.17 μm σ z 3 3 6 6 mm θ x 0 (30) 0 (30) 30 30 mrad ξ x0 *1 0.196 0.395 0.042 0.022 ξ y0 *1 0.267 (0.241 *2 ) 0.758 0.197 0.169 L geometrical 5.3(5.6 *2 ) 15 9.1 12 x10 35 cm -2 s -1 *1 nominal tune shift *2 travel focus 8
In the real machine, Finite crossing scheme degrades luminosity due to nonlinear terms. To alleviate this, we introduce crab crossing or crab waist. See ohmi-san 's talk(beam-beam simulations) 9
SuperKEKB Crab crossing Crab waist E (LER/HER) 3.5 / 8.0 GeV I (LER/HER) 10 / 4.4 A N (LER/HER) 1.26x10 11 / 5.5x10 10 n b 5000 ε x 18 9.0 6.0 6.0 nm ε y 0.18 0.045 0.06 0.06 nm β x * 20 20 10 5 cm β y * 3 3 1 0.5 mm σ z 3 3 6 6 mm θ x 0 (30) 0 (30) 30 30 mrad ν s 0.025 0.025 0.01 0.01 ξ *1 x0 0.196 0.395 0.042 0.022 ξ *1 y0 0.267 0.758 0.197 0.169 L (W.S *2 ) 6.1 8.0 6.7 10 x10 35 cm -2 s -1 L (S.S *3 ) 6.0 8.3 4.8 9.0 x10 35 cm -2 s -1 *1 nominal tune shift *2 Weak-Strong simulation *3 Strong-Strong simulation 10
Homework What is crab crossing and Recent status of the crab cavity 11
KEKB Crab Crossing The crab crossing scheme allows a large crossing angle collision without introducing any synchrotron-betatron coupling resonances. 1, 2) RF Deflector ( Crab Cavity ) 1) R.B.Palmer, SLAC-PUB-4707,1988 2) K.Oide and K.Yokoya, SLAC-PUB-4832,1989 We don't install these two cavities. HER Electrons LER Positrons 1.44 MV Head-on Collision Crossing Angle (11 x 2 m rad.) 1.41 MV 1.41 MV non-crab crossing 1.44 MV Required kick 1.44 MV 12
We use TM110 to make horizontal kick. 13
Crab crossing with a crab cavity x-position at IP induced by kick with a crab cavity: x * = β * crab xβ x cos πν x ψ * crab x ψ x 2sinπν x ( ) Θ crab x = β x 2 Dipole kick changes equilibrium position. (If ν x =integer, orbit diverges.) x Betatron oscillation: Kick angle due to crab cavity Θ x crab Crab cavity d 2 x ds 2 + kx = f external If f external is independent on x, x=x 0 +x COD. s * β x crab Θ x crab, if dx*/dz=tan(θ x /2) Crossing angle: θ x β x crab Ψ x crab x IP β x * Ψ x * Δψ x =ψ x * ψ x crab = π 2 + nπ Betatron phase advance Closed orbit distortion(cod) Bunch is crabbing in the whole ring. 14
Crab crossing with a crab cavity Transverse kick of crab cavity: dp x dt = ecb z = ct ( ) Θ crab x = p x E = ev sin 2πf rf zc E f rf : rf frequency Half crossing angle is: x Crab cavity Θ x crab p z ~E p x z tan θ x 2 = dx* dz = β * crab xβ x 2 = 2πf rf ev β * crab x β x 2c( E/e) dθ x crab dz z= 0 x IP θ x /2 Δz Δx* z Deflecting voltage of the crab cavity: V = ( ) 2c E/e 2πf rf β x* β tanθ x crab x 2 15
Requirement for the crab cavity at KEKB KEKB LER HER E 3.5 8 GeV f rf 509 MHz θ x 22 mrad β x * 0.59 0.56 m β crab x 45 250 m V 1.4 1.4 MV We have achieved 1.4 MV at horizontal test on June/8/2006. 16
Superconducting crab cavity for KEKB Crab cavity is the RF deflector which makes a time-dependent transverse kick(tm110) to tilt the beam. 2cE Input coupler V = 2πf rf β x* β tanθ x crab x 2 ΔΨ crab IP x = π (one cavity) 2 + nπ Jacket-type He vessel K. Hosoyama et al. Tuning rod Crab cavity cell Notch filter Coaxial coupler(nb) (to extract TM010,TE111,... from the cavity) Stub support Beam RF absorber 17
Results of Q-value at the vertical test for the crab cavities 21 MV/m = 1.4 MV(kick voltage) Peak electric field LER cavity has achieved the best performance for the peak electric field. HER cavity is worse performance than that of LER, however it satisfies the requirement. 18
Recent Status of Crab Cavity in KEKB Mt. Tsukuba HER Crab cavity Hosoyama-san Oide-san Akai-san 19
Assembly of the first crab cavity. Coaxial beam pipe assembly Installation of coaxial beam pipe Installation was very difficult! Coaxial beam pipe side Cavity side 20
Assembly of HER crab cavity has been done on April 21! The cavity was moved for the horizontal test. Hosoyama-san Experimental site 21
Installation of the crab cavity in the test stand Connection of the transfer line of helium Iron shield for radiation 22
Horizontal test of HER crab cavity Input coupler conditioning under cavity detuned preliminary 1.4MV We finally achieved operation level (1.4MV) on June/8 by C.W.!!! cavity quenched! 23
Crab cavity cool-down toward 4K The cavity was cooled down very slowly. The resonant frequency was lowered by about 300kHz than the operation frequency(508.8mhz). Now we are investigating the reason. 1 week preliminary 2K/hour preliminary Due to the adjustment of the helium flow The loaded Q value measured by network analyzer was 1.6x10 5. It was consistent with the estimation (2x10 5 ) by HFSS. In high power test, the loaded Q value was 1.7x10 5. 24
What needs to be fixed Discrepancy between resonant frequency and operation frequency is about 300kHz. Range of tuner position is smaller than that of expected. Tuner feedback stability 25
Near future plan Tuner reforming Cavity pre-tuning HPR for the cavity Re-assembly of the HER crab cavity Assembly of the LER crab cavity Two crab cavities will be ready for the installation to the tunnel in the end of this year(hopefully). Please wait... 26
Optics for crab cavity We have already used crab optics for luminosity run. Crab cavity will be installed here! Large horizontal beta region 27
Summary Machine parameters are reconsidered. Both of crab crossing and crab waist are hopeful to achieve higher luminosity.( BB simulation) Extremely small beta has to be achieved for the crab waist. Traveling focus provides luminosity gain about 5-7%. In case of crab crossing, better betatron tune is 0.503/.55, however it might be prevented by physical aperture around IR due to dynamic effects.( IR issues) Other things such as electron cloud, CSR, etc. should be also solved at SuperKEKB. Crab cavity is assembled successfully and have been operated at the horizontal test. Required deflecting voltage of 1.4 MV has been achieved. 28
Major achievements expected at SuperKEKB M. Hazumi Case Case 1: 2: 1: 2: All New All New Consistent Physics with with Extended Kobayashi-Maskawa Flavor Flavor Structure Theory Search for New CP-Violating Phase in b s with 1 degree precision Discovery of of Lepton Flavor Violation in inτ μγ μγdecays # # CKM Angle Measurements with 1 degree precision Discovery of B Kνν Discovery of T Violation in B Λpπ Vub with 5% Precision Discovery of B Dτν Discovery of B μν Discovery of of New New Right-Handed Current in in b s s Transitions # # Discovery of New Subatmic Particles Discovery sin of of 2 θnew W with CP O(10 CPViolation -4 ) precision in inb 0 0 φk φk 0 0 Decays # # L peak =8x10 35 L ave =4x10 35 200 days/year Observations with Υ(5S), Υ(3S) etc. Discovery with sigfinicance > 5σ # SUSY GUT with gluino mass = 600GeV, tanβ = 30 Discovery of CP Violation in Charged B Decays Discovery of Direct CP Violation in B 0 Kπ Decays (2005) Discovery of CP Violation in Neutral B Meson System (2001) 29
Backup slides 30
Projection of integrated luminosity and expected discoveries at SuperKEKB 50 50 ab ab 1 1 Discoveries of B Κνν We are here. We are here. L=4x10 35 15 15 ab ab 1 1 Discovery of new CP violation in B 0 φks 1 ab 1 Discoveries of 1 ab 1 B 0 Dτν, τν 31
Discoveries at SuperKEKB and required integrated luminosities (discovery = significance > 5σ) Item Integrated luminosity (ab 1 ) New physics B τν 0.5 charged Higgs B Dτν New CP violation in B 0 η Ks New CP violation in B 0 φks B μν B Kνν 1* 10** 15** 30*** 50* charged Higgs SUSY breaking, extra dimension, GUT, baryogenesis/leptogenesis SUSY breaking, extra dimension, GUT, baryogenesis/leptogenesis SUSY MFV EW baryogenesis, dark matter, SUSY * From SuperKEKB. Estimations will be updated in Autumn 2006. ** Assuming WA values as of August 2005. *** Guestimation assuming Br=4x10-7, full rec. eff. = 0.1%, and no background. Need simulation studies. 32
Luminosity Luminosity formula (well-known) Number of particles/bunch (e+) Number of particles/bunch (e-) Collision frequency L = N e +N e f 4πσ x* σ y * R L Luminosity reduction due to geometrical effect Horizontal beam size at IP Vertical beam size at IP 33
Luminosity Luminosity formula for machine design Beam current 1.8/1.35 A (KEKB) 9.4/4.1 A (SuperKEKB) Beam-beam parameter (Strength of interaction between colliding beams) 0.055 (KEKB) 0.19 (SuperKEKB) It correlates with many things. Lorentz factor L = γ e ± 2er e 1+ σ * y * I e ±ξ ye ± σ * x β R L y R ξ y Limited by beam-beam effect Geometrical factor due to hour-glass effect and crossing angle 0.8 ~ 1 (short bunch) Classical electron radius Luminosity 1.63x10 34 cm -2 s -1 (KEKB) 4.0x10 35 cm -2 s -1 (SuperKEKB) Beam size ratio 1 ~ 2 % (flat beam) Vertical beta function at IP (Focal depth) 6.5 mm/6.2 mm (KEKB) 3 mm/3 mm(superkekb) Limited by bunch length Bunch length (σ z < β y *) ~7 mm (KEKB) 3 mm (SuperKEKB) Luminosity is proportional to beam currents, beam-beam parameter, and inverse of vertical beta function at IP. Limited by HOM, CSR 34
Lattice parameters w/o and w/ beam-beam effect SuperKEKB bare lattice with beam-beam unit Beam current (LER/HER) I 9.4/4.1 9.4/4.1 A Beam energy (LER/HER) E 3.5/8.0 3.5/8.0 GeV Emittance ε x 24 130 Dynamic nm Horizontal beta at IP β x * 20 1.9 effect cm Vertical beta at IP β y * 3 2.4 mm Horizontal beam size σ x * 69 50 mm Vertical beam size σ y * 0.73 1.0 mm Bunch length σ z 3 3 mm Crossing angle (30 mrad crab crossing) Horizontal beam-beam (estimated with S-S simulation) Vertical beam-beam (estimated with S-S simulation) θ x 0 0 mrad Luminosity reduction R L 0.86 0.82 ξ x reduction R ξx 0.99 0.98 ξ y reduction R ξy 1.11 1.16 Reduction ratio R L /R ξy 0.78 0.70 ξ x 0.152 0.030 ξ y 0.215 0.187 Luminosity L 4.0 x 10 35 cm -2 s -1 35
Head-on and finite-crossing collision Vertical beam-beam parameter (ξ y ) Strong-strong simulations Head-on (crab-crossing) L=4x10 35 cm -2 s -1 ν x /ν y =.503/.550 Crossing angle: 30 mrad Number of particles/bunch (HER) x10 10 Head-on collision will boost the beam-beam parameter up to 0.19. Crab cavity is one of the most important components, because it can realize head-on collision. 36
Head-on collision with crab cavity Finite-crossing collision without crab cavity e+ e- x θ x =30 mrad Crab cavity tilts the beam to make head-on collision. s IP Development of crab cavity applicable for high beam current(~10 A) New crab cavity for SuperKEKB This is different from the cavity will be installed at KEKB. 37
Cold test of porototype crab cavity Time variation of the cavity and cryostat vacuum The temperature dependence of the frequency The cold test was done! The prototype in the pit 38
Traveling focus (in longitudinal direction) Traveling focus Crab waist (Traveling focus in transverse plane) H ± = a 2 zp 2 y H ± = a 2 xp 2 y Swap z and x in the left y = y + H ± p y = y + azp y y = y + H ± p y = y + axp y y = 1 az y p y 0 1 p y Transformation of Twiss parameters: y = 1 ax y p y 0 1 p y Transformation of Twiss parameters: β α α = 1 az β 0 1 az γ 0 1 0 1/β 0 1 T = β + az2 /β az /β az /β 1/β β α α = 1 ax β 0 1 ax γ 0 1 0 1/β 0 1 T = β + ax 2 /β ax /β ax /β 1/β Waist point moves along z position. β()= z β + az2 β Waist point moves along x position. β()= x β + ax 2 β 39