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Upgrade plan of KEKB

Upgrade plan of KEKB. from 2012 to 20XX Y. Ohnishi / KEK 2008 January 24-26 Atami, Izu, Japan. What is luminosity ?. Luminosity is defined by: N is a number of events should be observed. We want to increase N to decrease a statistical error.

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Upgrade plan of KEKB

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  1. Upgrade plan of KEKB from 2012 to 20XX Y. Ohnishi / KEK 2008 January 24-26 Atami, Izu, Japan

  2. What is luminosity ? • Luminosity is defined by: • N is a number of events should be observed. • We want to increase N to decrease a statistical error. • s is a cross section of an interesting physics process. • We can do nothing. s is a constant. • T is a duration of an experiment. • Compare with our lifetime. Is T~10 years reasonable ? • What we can do is to increase a luminosity.

  3. What is luminosity ? (cont'd) • Luminosity is defined by: • N+(N-) is a number of particles per bunch for positron (electron). • sx*(sy*) is a beam size in the horizontal(vertical) plane. • Usually, flat-beam, sy*<<sx* • f is a collision frequency of positron and electron bunch. • f = nb/T0, nb is a number of bunches, T0 is a revolution time. • RL is a luminosity reduction. • geometrical loss due to a crossing angle and an hour-glass effect

  4. focusing defocusing IP beam envelope sy > sy* s sy* bunch length Reductions to luminosity • Crossing angle • Hour-glass effect overlap region y Beam

  5. Money ? • Reduction from the geometrical loss ? • Bunch length, sz < by*, where sy* = (eyby*)1/2. • Larger impedance in a ring makes bunch length longer. • Head-on collision is preferable. What limit the luminosity ? ☞ This might be true ! • Nonlinear effects limit the luminosity. • Beam-beam force is a nonlinear force. • Most elements in an accelerator are nonlinear transformations. • Machine errorswith beam-beam effects decrease luminosity significantly.

  6. Beam-beam force Er Bj v • The electric and magnetic field can be written by: • Lorentz force can be expressed by: • Beam-beam force is proportional to the electric field and an attracting force. z e+ v e- e- a cylindrical beam r Fr l l is a longitudinal line charge density.

  7. kick angle pr q p Beam-beam force (cont'd) • If the positron beam is a Gaussian distribution, a momentum deviation of the electrons is: • Horizontal and vertical deflection angle can be expressed by: where re: classical electron radius w(z): complex error function

  8. Beam-beam force (cont'd) Horizontal Vertical Analytic formula sy*=3 mm charge density 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.

  9. Luminosity • Luminosity can be expressed by the formula: • However, we do not use above formula for the machine design. Instead an alternative formula is used. • This describes L in terms of the lattice parameter by*, beam-beam parameter xy, eliminating the explicit dependence on beam size. * means value at IP (flat-beam case)

  10. Improvement of luminosity at KEKB upgrade • If small by* while keeping by*/ey constant, larger L can be realized. • However, by* > sz to suppress the hour-glass effect. • Crab-crossing andnx→0.5 to mitigate nonlinear effects makes larger xy,max with increasing I. High current scheme

  11. KEKB(crab) mitigate nonlinear effects Beam-beam limit ? How large can we achieve beam-beam parameter ? • Luminosity is proportional to a beam-beam parameter.

  12. Input Coupler Liq. Helium Vessel SUS Support Pipe Stub Support Notch Filter KEKB (exp. with crab) Coaxial Coupler RF Absorber (mA) 80 K Liq. Nitrogen Shield Copper Bellows Aluminum End Plate Aluminum End Plate Crab crossing Crab crossing will increase the beam-beam parameter by a factor of 2. K. Ohmi, et al. Head-on(crab) KEKB (Strong-strong simulation) Crossing angle 22 mrad Vertical beam-beam (at the optimum tune) Superconducting crab cavities have been produced, and under beam test at KEKB. K. Hosoyama, et al.

  13. Beam-beam effect and “Chaos” 2-dimensional 1-dimensional *near-integrable surface x0 = 5% xsx x0 = 0 py py xy=0.02 y y Particles are confined in KAM*. "chaos" Large beam-beam parameter py py xy=0.053 y y KAM is destroyed. Beam size growth py py xy=0.10 y y

  14. 3N 2N+N y x N+N+N 2N+N High beam-beam parameter • Total degree of freedom is 3N, where N is #particles. • Crab cavity resolves x-z coupling. • Betatron tune close to half integer(nx→0.5) resolves x-y coupling(y is symmetric for x or -x). • System becomes one dimensional and avoids bad resonances, the beam-beam parameter can be increased. 3N (x-y-z) x (x-y+z) z (x+y+z)

  15. Tune Scan with Beam-beam Simulation Crab-crossing collision Tune Survey in upgraded KEKB without parasitic collision effect. ex=24 nm case: Lpeak=4.0x1035 cm-2s-1 (L/bunch=8.0X1031, Nb=5000) Beam-beam parameter Head-on } y ~0.2 Betatron tunes (.503, .550) Better working point is very close to the half integer ! Simulation by K. Ohmi and M. Tawada

  16. Experiences at KEKB • Lower bunch current product makes luminosity twice of the crossing-angle collision. • However, slope of the specific luminosity is NOT understood well. • If the reason is an electron cloud, no problem after upgrade. • If luminosity is limited by something else, we must investigate it. • Synchro-beta resonance ? • Other nonlinear effects ? 1.7x1035 ex=24 nm Crab crossing 49 sp nb=50 what is a slope ? Crab crossing 3.06 sp nb=1548 22 mrad crossing 3.5 sp nb=1388 9.4/4.1 A nb=5018

  17. Luminosity upgrade • Assumptions: • Specific luminosity/#bunches > 22x1030 cm-2s-1mA-2 with crab cavities(factor of 2 at least) • achieved at KEKB • High specific luminosityat high currents(9.4 A at LER) can be kept. • 5000 bunches can be stored. • No electron cloud and a bunch-by-bunch feedback system works completely. • Believe a beam-beam simulation

  18. ey/ex=0.5%, sz=3 mm ex=12 nm tx=47/47 msec HER(13 nm, 47 msec) L/#bunches (cm-2s-1) <y2> (m) 30% L/#bunches (cm-2s-1) tx=84/47 msec LER(12 nm, 84 msec) tx=84/84 msec ex=24 nm ey/ex=0.5%, sz=3 mm #turns #turns #turns ey/ex=0.5%, ex=12 nm sz=3 mm 16% L/#bunches (cm-2s-1) sz=4 mm ey/ex=0.5%, sz=3 mm #turns Beam-beam simulation(Strong-Strong )

  19. 3 years shutdown Luminosity upgrade (cont'd) • Luminosity gain and upgrade items (preliminary)

  20. Integrate luminosity (ab-1) KEK roadmap RF upgrade Damping Ring Peak luminosity (cm-2s-1) 3 years shutdown Year Projected luminosity (preliminary) operation time : 200 days/year Target for roadmap Target for roadmap

  21. Machine parameters (preliminary) *1 include beam-beam effects *2 calculated from luminosity *3 nominal values

  22. Miscellaneous • Energy asymmetry is determined by a physics requirement. • Larger asymmetry is preferable so far. • Power consumption does not change so much, even though HER energy is decreased. Instead we will give up wigglers. • Final focus magnets and detector solenoidaffects 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(3S) and U(5S) can be available. • Extremely low energy operation is not trivial. If detector solenoid can be scaled to the energy, it is possible. • Polarization is not considered. • Very difficult so far rB=106 m (HER) >> 16 m (LER)

  23. Backup slides

  24. Sensitivity of physics Higher asymmetry can achieve higer sensitivity for the physics results. Lower aymmetry(LER E=3.8 GeV), luminosity degradation is about 10~12 % luminosity. B→J/YKs B→fKs Tajima

  25. Synchrotron Radiation Loss LER wiggler total Prad (MW) LER LER wiggler HER LER E (GeV) *E=3.8 GeV in LER is maximum to perform Y(5S) experiment.

  26. No. SCC in HER = 8 (fixed) LER+HER No. ARES cavities LER HER LER E (GeV) No. ARES cavities No wiggler in LER / #SCC is 8. #RF cavities = ~40 → constant LoI: ARES/SCC=16/12

  27. Power consumption (RF only) No wiggler in LER / #SCC = 8 in HER Total power consumption is 60~66 MW less dependent of energy asymmetry. LER+HER AC plug power (MW) [RF only] LER HER LER E (GeV)

  28. 3 DOF 2+1 DOF 1+1+1 DOF nx=0.5 (resolve xy coupling) Crab-crossing (resolve xz coupling) y x Horizontal Tune close to Half Integer nx=0.5 • In the collision of two beams, particles interact with fixed beam at either x or -x for nx=0.5. • 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. • System becomes one dimensional and avoids bad resonances, the beam-beam parameter can be increased. • This technique realizes high luminosity at KEKB/SuperKEKB. To make this possible, machine errors must be reduced significantly. n: turn number (integer)

  29. Beam-beam simulation I+/I- = 9.4/4.1 A E+/E- = 3.5/8.0 GeV Nb = 5018 ex = 12 nm ey/ex = 0.5 % nx/ny = .505/.550 LER/HER trans. damping time L(x1035)=6.6295-0.021747*t 47/47 msec 57/57 msec Luminosity (x1035 cm-2s-1) Luminosity (x1035 cm-2s-1) ~10% 57/47 msec 84/84 msec Trans. damping time (msec) Number of turns

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