Y Ohnishi KEK Upgrade plan of KEKB from
Y. Ohnishi / KEK Upgrade plan of KEKB from 2012 to 20 XX Y. Ohnishi / KEK 2008 January 24 -26 Atami, Izu, Japan
Y. Ohnishi / KEK What is luminosity ? l Luminosity is defined by: l N is a number of events should be observed. l l s is a cross section of an interesting physics process. l l We can do nothing. s is a constant. T is a duration of an experiment. l l We want to increase N to decrease a statistical error. Compare with our lifetime. Is T~10 years reasonable ? What we can do is to increase a luminosity. 2
Y. Ohnishi / KEK What is luminosity ? (cont'd) l Luminosity is defined by: l N+(N-) is a number of particles per bunch for positron (electron). l sx*(sy*) is a beam size in the horizontal(vertical) plane. l l f is a collision frequency of positron and electron bunch. l l Usually, flat-beam, sy* << sx* f = nb/T 0, nb is a number of bunches, T 0 is a revolution time. RL is a luminosity reduction. l geometrical loss due to a crossing angle and an hour-glass effect 3
Y. Ohnishi / KEK Reductions to luminosity l Crossing angle overlap region l Hour-glass effect y focusing IP beam envelope sy > sy * bunch length defocusing s Beam 4
Y. Ohnishi / KEK What limit the luminosity ? l Money ? l Reduction from the geometrical loss ? l ☞ This might be true ! Bunch length, sz < by*, where sy* = (eyby*)1/2. l Larger impedance in a ring makes bunch length longer. l l Head-on collision is preferable. Nonlinear effects limit the luminosity. Beam-beam force is a nonlinear force. ◆ Most elements in an accelerator are nonlinear transformations. ◆ Machine errors with beam-beam effects decrease luminosity significantly. ◆ 5
Y. Ohnishi / KEK Beam-beam force Bj v er l v a Er z e+ ecylindrical beam Fr l The electric and magnetic field can be written by: l is a longitudinal line charge density. l Lorentz force can be expressed by: l Beam-beam force is proportional to the electric field an attracting force. 6
Y. Ohnishi / KEK Beam-beam force (cont'd) l If the positron beam is a Gaussian distribution, a momentum deviation of the electrons is: pr l Horizontal and vertical deflection angle can be expressed by: kick angle q p re: classical electron radius where w(z): complex error function 7
Y. Ohnishi / KEK Beam-beam force (cont'd) charge density Horizontal Vertical sy*=3 mm sx*=200 mm Beam-beam force is nonlinear. This region is almost linear. Dpx/p Dpy/p We call this slope(xx, y) a beam-beam parameter. 8
Y. Ohnishi / KEK Luminosity l Luminosity can be expressed by the formula: * means value at IP l However, we do not use above formula for the machine design. Instead an alternative formula is used. (flat-beam case) l This describes L in terms of the lattice parameter by*, beam parameter y, eliminating the explicit dependence on beam size. 9
Y. Ohnishi / KEK Improvement of luminosity at KEKB upgrade If small by* while keeping by*/ey constant, larger L can be realized. l However, by* > sz to suppress the hour-glass effect. l Crab-crossing and nx→ 0. 5 to mitigate nonlinear effects makes larger y, max with increasing I. l 10
Y. Ohnishi / KEK How large can we achieve beam-beam parameter ? KEKB(crab) mitigate nonlinear effects Beam-beam limit ? l Luminosity is proportional to a beam-beam parameter. 11
Y. Ohnishi / KEK Crab crossing will increase the beam-beam parameter by a factor of 2. Vertical beam-beam K. Ohmi, et al. Head-on(crab) KEKB (Strong-strong simulation) KEKB (exp. with crab) Crossing angle 22 mrad (at the optimum tune) Superconducting crab cavities have been produced, and under beam test at KEKB. Input Coupler (m. A) Liq. Helium Vessel SUS Support Pipe Stub Support Notch Filter Coaxial Coupler RF Absorber Aluminum End Plate 80 K Liq. Nitrogen Shield Copper Bellows Aluminum End Plate K. Hosoyama, et al. 12
Y. Ohnishi / KEK Beam-beam effect and “Chaos” py y=0. 02 py y Particles are confined in KAM*. y "chaos" py y=0. 053 y py y KAM is destroyed. Beam size growth y=0. 10 y py *near-integrable surface Large beam-beam parameter 2 -dimensional x 0 = 5% x sx 1 -dimensional x 0 = 0 py y 13
Y. Ohnishi / KEK High beam-beam parameter l Total degree of freedom is 3 N, where N is #particles. 3 N l Crab cavity resolves x-z coupling. 3 N l y 2 N+N x (x-y+z) z Betatron tune close to half integer(nx→ 0. 5) resolves x-y coupling(y is symmetric for x or -x). x l (x-y-z) 2 N+N N+N+N (x+y+z) System becomes one dimensional and avoids bad resonances, the beam-beam parameter can be increased. 14
Y. Ohnishi / KEK Tune Scan with Beam-beam Simulation Crab-crossing collision Tune Survey in upgraded KEKB without parasitic collision effect. ex=24 nm case: Lpeak=4. 0 x 1035 cm-2 s-1 (L/bunch=8. 0 X 1031, Nb=5000) Head-on Betatron tunes (. 503, . 550) } Beam-beam parameter y ~0. 2 Better working point is very close to the half integer ! Simulation by K. Ohmi and M. Tawada 15
Y. Ohnishi / KEK Experiences at KEKB ex=24 nm what is a slope ? l Lower bunch current product makes luminosity twice of the crossing-angle collision. l However, slope of the specific luminosity is NOT understood well. l If the reason is an electron cloud, no problem after upgrade. l If luminosity is limited by something else, we must investigate it. 1. 7 x 1035 Crab crossing 49 sp nb=50 Crab crossing 3. 06 sp nb=1548 22 mrad crossing 3. 5 sp nb=1388 9. 4/4. 1 A nb=5018 Synchro-beta resonance ? ◆ Other nonlinear effects ? ◆ 16
Y. Ohnishi / KEK Luminosity upgrade l Assumptions: l Specific luminosity/#bunches > 22 x 1030 cm-2 s-1 m. A-2 with crab cavities(factor of 2 at least) ü achieved at KEKB l High specific luminosity at high currents(9. 4 A at LER) can be kept. l 5000 bunches can be stored. l l No electron cloud and a bunch-by-bunch feedback system works completely. Believe a beam-beam simulation 17
Y. Ohnishi / KEK ey/ex=0. 5%, sz=3 mm ex=12 nm 30% ex=24 nm L/#bunches (cm-2 s-1) Beam-beam simulation(Strong-Strong ) 16% sz=4 mm (m) sz=3 mm <y 2> L/#bunches (cm-2 s-1) tx=84/47 msec tx=84/84 msec ey/ex=0. 5%, sz=3 mm #turns ey/ex=0. 5%, ex=12 nm tx=47/47 msec HER(13 nm, 47 msec) LER(12 nm, 84 msec) ey/ex=0. 5%, sz=3 mm #turns 18
Y. Ohnishi / KEK Luminosity upgrade (cont'd) 3 years shutdown l Luminosity gain and upgrade items (preliminary) Item Gain beam pipe x 1. 5 high current, short bunch, electron cloud IR(b*x/y=20 cm/3 mm) x 1. 5 small beam size at IP low emittance(12 nm) & nx → 0. 5 x 1. 3 mitigate nonlinear effects with beam-beam crab crossing x 2 mitigate nonlinear effects with beam-beam RF/infrastructure x 3 high current DR/e+ source charge switch x 1. 5 x? Purpose low b* injection, improve e+ injection electron cloud, lower e+ current 19
Y. Ohnishi / KEK Projected luminosity (preliminary) Integrate luminosity (ab-1) operation time : 200 days/year KEK roadmap Target for roadmap Peak luminosity (cm-2 s-1) RF upgrade 3 years shutdown Damping Ring Year Target for roadmap 20
Y. Ohnishi / KEK Machine parameters (preliminary) Lo. I (updated) Upgrade (LER/HER) Bunch length Transverse damping time ex ey b x* b y* sx * sy * sz tx 24 0. 18 200 3 50. 0 1. 0 3 47 12/13 0. 060/0. 066 200 3 37. 5/39. 8 2. 11/2. 28 3 84/47 nm nm mm mm msec Betatron/synchrotron tune nx/ny/ns M+0. 506/N+0. 545/-0. 031*1 M+0. 505/N+0. 550/-0. 025 M, N: integer Beam Energy Beam current #bunches E+/EI+/INb 3. 5/8. 0 9. 4/4. 1 5018 A Crossing angle 2 fx 30 → 0 (crab crossing) mrad x 0. 135 0. 153 y R x 0. 215 0. 296 0. 99 R y 1. 11 Luminosity reduction*3 RL 0. 86 Luminosity L 4. 0 x 1035 5. 5 x 1035 Emittance Beta at IP Beam size at IP*1 Beam-beam*2 Beam-beam reduction*3 *1 include beam-beam effects *2 calculated from luminosity *3 nominal values cm-2 s-1 21
Y. Ohnishi / KEK Miscellaneous l Energy asymmetry is determined by a physics requirement. Larger asymmetry is preferable so far. l Power consumption does not change so much, even though HER energy is decreased. Instead we will give up wigglers. l r. B=106 m (HER) >> 16 m (LER) l l Final focus magnets and detector solenoid affects both beams of LER and HER. We can not change energy asymmetry easily because beam orbits is already optimized by the IR design lattice. Energy is not flexible in principle due to the above reason. The range between U(3 S) and U(5 S) can be available. l Extremely low energy operation is not trivial. If detector solenoid can be scaled to the energy, it is possible. l l Polarization is not considered. l Very difficult so far 22
Y. Ohnishi / KEK Backup slides
Y. Ohnishi / KEK Sensitivity of physics Higher asymmetry can achieve higer sensitivity for the physics results. Lower aymmetry(LER E=3. 8 Ge. V), luminosity degradation is about 10~12 % luminosity. B→J/YKs B→f. Ks Tajima 24
Y. Ohnishi / KEK Prad (MW) Synchrotron Radiation Loss LER wiggler total LER wiggler HER LER E (Ge. V) *E=3. 8 Ge. V in LER is maximum to perform Y(5 S) experiment. 25
Y. Ohnishi / KEK No. ARES cavities No wiggler in LER / #SCC is 8. #RF cavities = ~40 → constant Lo. I: ARES/SCC=16/12 No. ARES cavities No. SCC in HER = 8 (fixed) LER+HER LER E (Ge. V) 26
Y. Ohnishi / KEK Power consumption (RF only) AC plug power (MW) [RF only] No wiggler in LER / #SCC = 8 in HER Total power consumption is 60~66 MW less dependent of energy asymmetry. LER+HER LER E (Ge. V) 27
Y. Ohnishi / KEK Horizontal Tune close to Half Integer nx=0. 5 l In the collision of two beams, particles interact with fixed beam at either x or -x for nx=0. 5. y x n: turn number (integer) l In the case of crab crossing, the phase space structure in y-py at x is the same as that at -x because of symmetry of the fixed beam. l System becomes one dimensional and avoids bad resonances, the beam-beam parameter can be increased. 3 DOF 2+1 DOF Crab-crossing (resolve xz coupling) l 1+1+1 DOF nx=0. 5 (resolve xy coupling) This technique realizes high luminosity at KEKB/Super. KEKB. To make this possible, machine errors must be reduced significantly. 28
Y. Ohnishi / KEK LER/HER trans. damping time I+/IE+/ENb ex ey/ex nx/ny 47/47 msec 57/57 msec 57/47 msec 84/84 msec Number of turns ~10% = 9. 4/4. 1 A = 3. 5/8. 0 Ge. V = 5018 = 12 nm = 0. 5 % =. 505/. 550 Luminosity (x 1035 cm-2 s-1) Beam-beam simulation L(x 1035)=6. 6295 -0. 021747*t Trans. damping time (msec) 29
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