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. 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.

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

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

What limit the luminosity ? Money ? ☞ This might be true ! 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. 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.

Beam-beam force v z e+ e- v e- cylindrical beam r Fr l Er v Bj z e+ e- v a e- cylindrical beam r Fr l 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. l is a longitudinal line charge density.

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 p pr kick angle q re: classical electron radius w(z): complex error function

Beam-beam force (cont'd) Horizontal Vertical Analytic formula charge density 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.

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)

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 and nx→0.5 to mitigate nonlinear effects makes larger xy,max with increasing I. High current scheme

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

Crab crossing Head-on(crab) Crossing angle 22 mrad KEKB Crab crossing will increase the beam-beam parameter by a factor of 2. K. Ohmi, et al. Head-on(crab) (mA) KEKB (exp. with 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. Input Coupler Liq. Helium Vessel Stub Support Coaxial Coupler Copper Bellows 80 K Liq. Nitrogen Shield Notch Filter RF Absorber Aluminum End Plate SUS Support Pipe K. Hosoyama, et al.

Beam-beam effect and “Chaos” 1-dimensional 2-dimensional *near-integrable surface x0 = 0 x0 = 5% x sx 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

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 3N 2N+N (x-y+z) z y x N+N+N 2N+N (x+y+z)

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

Experiences at KEKB ex=24 nm 1.7x1035 9.4/4.1 A nb=5018 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 ? ex=24 nm 1.7x1035 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

Luminosity upgrade Assumptions: Specific luminosity/#bunches > 22x1030 cm-2s-1mA-2 with crab cavities(factor of 2 at least) achieved at KEKB High specific luminosity at 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

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

Luminosity upgrade (cont'd) Luminosity gain and upgrade items (preliminary) Item Gain Purpose beam pipe x 1.5 high current, short bunch, electron cloud IR(b*x/y=20cm/3 mm) 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 RF/infrastructure x 3 high current DR/e+ source low b* injection, improve e+ injection charge switch x ? electron cloud, lower e+ current 3 years shutdown

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

Machine parameters (preliminary) LoI (updated) Upgrade (LER/HER) Emittance ex 24 12/13 nm ey 0.18 0.060/0.066 Beta at IP bx* 200 mm by* 3 Beam size at IP*1 sx* 50.0 37.5/39.8 sy* 1.0 2.11/2.28 Bunch length sz Transverse damping time tx 47 84/47 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 E+/E- 3.5/8.0 Beam current I+/I- 9.4/4.1 A #bunches Nb 5018 Crossing angle 2fx 30 → 0 (crab crossing) mrad Beam-beam*2 xx 0.135 0.153 xy 0.215 0.296 Beam-beam reduction*3 Rxx 0.99 Rxy 1.11 Luminosity reduction*3 RL 0.86 Luminosity L 4.0x1035 5.5x1035 cm-2s-1 *1 include beam-beam effects *2 calculated from luminosity *3 nominal values

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 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(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)

Backup slides

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

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

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

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)

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. x y n: turn number (integer) 3 DOF 2+1 DOF 1+1+1 DOF Crab-crossing (resolve xz coupling) nx=0.5 (resolve xy coupling)

Beam-beam simulation ~10% 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