Beam-beam studies for the High- Luminosity and High-Energy LHC, plus related issues for KEKB

Transcription

1 Beam-beam studies for the High- Luminosity and High-Energy LHC, plus related issues for KEKB K. Ohmi (KEK) 24 August 21 CERN Accelerator Physics Forum Thanks to F. Zimmermann, R. Tomas, R. Calaga, O. Dominguez, O. Bruening and members of ABP group

2 Updated parameter list for LHC energy upgrade at 33 TeV centre- of- mass energy HE-LHC E=16.5TeV Radiation damping time is 1h in the transverse. nominal LHC LHC energy upgrade beam energy [TeV] dipole field [T] dipole coil aperture [mm] 56 4 beam half aperture [cm] 2.2 (x), 1.8 (y) 1.3 #bunches bunch population [1 11 ] initial transverse normalized emittance [ m] , 1.84 initial longitudinal emittance [evs] number of IPs contributing to tune shift 3 2 initial total beam- beam tune shift.1.1 (x & y) maximum total beam- beam tune shift.1.1 RF voltage [MV] rms bunch length [cm] rms momentum spread [1-4 ] IP beta function [m].55 1 (x),.43 (y) initial rms IP spot size [ m] (x), 6.3 (y) full crossing angle [ rad] 285 (9.5 x,y ) 175 (12 x ) Piwinski angle geometric luminosity loss from crossing stored beam energy [MJ] SR power per ring [kw] dipole SR heat load dw/ds [W/m/aperture] energy loss per turn [kev] critical photon energy longitudinal SR emittance damping time [h] horizontal SR emittance damping time [h] initial longitudinal IBS emittance rise time [h] initial horizontal IBS emittance rise time [h] 8 8 initial vertical IBS emittance rise time [h] ( =.2) ~4 ~4 note: IBS rise times > SR damping times events per crossing initial luminosity [1 34 cm - 2 s - 1 ] peak luminosity [1 34 cm - 2 s - 1 ] beam lifetime [h] integrated luminosity over 1 h [fb - 1 ].3.5 Octavio Dominguez, Frank Zimmermann, 24 June 21

3 Random Excitation Synchrotron radiation was a dominant excitation source in traditional electron rings. Intra-beam scattering is dominant in recent electron storage rings especially for the vertical emittance. It is also dominant in ion beam with a high Atomic number (RHIC). Radiation excitation is weaker than that of intra beam in proton beam of HE-LHC. The excitation of the intra-beam scattering depend on the beam emittance.

4 Beam size evolution with radiation damping and IBS O. Dominguez and F. Zimmermann εz keep or not. Consider p beam life or not courtesy of O. Dominguez

5 Control transverse excitation Emittance is controllable by applying external fluctuation (kicker). courtesy of O. Dominguez

6 Beam-beam simulation for HE-LHC Strong-strong simulation with a code BBSS. Single IP. The excitation rate are not put properly perhaps. I will calculate with more possibility in the future. Anyway the damping times must be faster in the present simulation to have results. Which is important excitation rate or ratio of excitation and damping? Outlook of the simulation result Dipole oscillation arises at very high beam-beam parameter >.1. Small dipole oscillation arises around ξ~.3 for excitation ON, but disappear. IBS limits the beam-beam parameter, maybe geometrically.

7 Assume 2 times faster damping time L/bunch (1 32 cm -1 s -1 ) L L L 2 times bigger excitation x1 4 turn x,y (µm) x1 4 turn Dipole oscillation limit the luminosity. The beam-beam parameter is very high ξ>.1. The dipole oscillation was seen at ξ>.5 in a flat beam such as lepton colliders for σz<<βy. y 1 y 2 x y y y,s y (µm)

8 L/bunch (1 32 cm -1 s -1 ) L/bunch (1 32 cm -1 s -1 ) Excitation ON/OFF No big difference L L L x1 4 turn y L 1 L y 2 L x y y No excitation x1 4 turn 16.2 y y Excitation x.14 y 1.12 y x,y (µm) x,y (µm) x1 4 turn x1 4 turn y,s y (µm) y, y (µm)

9 Dipole oscillation π mode frequency seems to shift. y (/Symbol mm) beam 1 beam x1 4 turn y (/Symbol mm) beam 1 beam x1 4 turn

10 2 times faster damping 2 times bigger excitation Excitation ON/OFF No remarkable difference y (µm) y 1 y y =3 µm at t=2x x1 4 turn y,s y (µm) L/bunch (1 32 cm -1 s -1 ) yy y x1 4 turn y,s y (µm)

11 Tentative result for HE-LHC Coherent instability arises at ξ~.15. IBS equilibrium emittance is ~1/1 of ε. Incoherent growth time is 1 day for ξ=.3 as shown later. The beam-beam effect is weak for an ideal case treated here. Luminosity is determined by IBS equilibrium emittance geometrically, if ξ<.3. I would like to a systematic study for diffusion rate and damping rate in the beam-beam environment.

12 x-y coupling at IP x-y coupling affects the beam-beam performance essentially in KEKB. It is effect of beam-beam dynamics, but not that of geometric. Parametrization of x-y coupling x x y y = RB X X Y Y R = r r 4 r 2 r r 3 r 1 r 1 r 2 r r 3 r 4 r B = βx α x / β x 1/ β x βy α y / β y 1/ β y

13 Measurement of IP coupling at KEKB Use the Octopos monitor both side of IP..55m.75m Reconstruct 4 dimensional phase space p y x p x.5 1 R s parameters correspond to the normal vector in x-px-y (r1,r2) and x-px-py (r3,r4) phase space.

14 Correlation matrix xx xx xy xy xx x x x y x y xy x y yy yy xy x y yy y y = RB X 2 X 2 Bt R t Excite only X mode Correlation matrix for the measured phase space variables give Twiss parameters including R s. Chromatic coupling at IP was measured and corrected by skew sextupole magnets. Luminosity increased in KEKB.

15 Simulations of x-y coupling effects in beam-beam interaction Day by day tuning in KEKB is spent for the 2.5e+34 2e+34 coupling scan. chromatic coupling scan L (cm -2 s -1 ) 1.5e+34 1e+34 5e R2 (m) Coupling scan in the operation

16 x-y coupling in HE-LHC How x-y coupling affects LHC performance? Model with 2 time faster damping. Outlook of the results The answer was very weak. The reason may be in the round beam.

17 x-y coupling at IP y No remarkable effect for x-y coupling R= R1=.1 R1= x1 4 turn y R= R2=.1 R2= x1 4 turn y R= R3=.1 R3= x1 4 turn y R= R4=.1 R4= x1 4 turn

18 x (µm) R= R4=.1 R4=.5 Dipole oscillation x1 4 turn Similar behavior in all R s. Horizontal coherent motion is seen for coupled cases. y (µm) R= R4=.1 R4= x1 4 turn

19 HL-LHC Studies in 28, luminosity by simulation Nominal 1x1 34 cm -2 s -1 Crab cavity(cc) 1.15x1 34 cm -2 s -1 UT β=.5m Np=1.7x1 11, θ=315 μrad, L=2.8x1 34 cm -2 s -1, 2.5x1 34 cm -2 s -1 (cc) ES cc 1.2x1 35 cm -2 s -1 LPA1.58x1 35 cm -2 s -1 LPA2.71x1 35 cm -2 s -1

20 Beam-beam limit in the nominal LHC simulations ξ~.3 L/L L/L =.15 mrad =. mrad L/L =.15 mrad = mard Np=2.3x111 Np=4.6x turn (x1 6 ) turn (x1 ξ=.4 ) Np=1.15x1 =.15 mrad = mrad Np=3.9x turn (x1 6 ) L/L L/L =.15 mrad = mrad Np=9.6x111 =.15 mrad = mrad turn (x1 6 ) turn (x1 6 ) EPAC8

21 Crab cavity noise in LHC Collision offset fluctuates turn by turn. Emittance growth. 1e-6 (b) 1e-7 cor =1 / 1e-8 1e-9 cor =1 PAC 7 1e x/ Tolerance is Δx/σx=.1% for turn by turn noise.

22 Crab cavity noise studies in KEKB R. Tomas et al.

23 Measurement and simulation for the crab phase noise Measurement Simulation The details were given by R. Tomas.

24 Feed back noise studies L (cm -2 s -1 ) We doubted that a fast noise degrade KEKB performance. Vertical beam size is small so that vertical noise is sensitive for the luminosity degradation. Sinusoidal noise is considered first. 3e e+34 2e e+34 1e+34.1 y.2 y.5 5e+33 y.1 y.2 y Freq y(e + )/ y, y.2 y.5 y.1 y.2 y Freq

25 Luminosity degradation in measurements and simulation Relative degradation agrees by Tobiyama and Ohmi in 24 June 21 The final week of the operation. L (cm -2 s -1 ) 2.8e e e e+34 2e e e e e+34 1e+34.1 y.2 y.5 y.1 y.2 y Δy/σy Machine condition was not the best. Lower current due to electricity limit. y(e + )/ y

26 Measurement White noise.3 Δy/σy Simulation

27 What degrade the luminosity in KEKB KEKB achieved the luminosity 2.1x1 34 cm -2 s -1, twice of the design. The crab cavity contributes the luminosity. The luminosity did not increase >3 x1 34 cm -2 s -1 as is expected. Tobiyama s comment. At least the feedback system does not give such strong noise into the beam. Other sources? Coupling is still unclear, but is studied much.

28 Crab waist Condition: Large Piwinski angle, low beta smaller than the bunch length. Beam particles collide with the center of the other beam at their waist position. High beam-beam performance is expected, if bunch population is enough high. Satisfying the conditions is possible?

29 Luminosity with crab waist and/or crab cavity 1, Aug 21, K. Ohmi Np=4x1 11, βx=.3m, βy=.75m, εn=3.75μm, θ=315μm, σz=11.8cm, θσz/2σx=1.5, Nb=144 Parameters by M. Zobov Geometrical Luminosity for crab waist strength Geometrical luminosity and beam-beam parameter for crab cavity scheme with detuning βy L (cm -2 s -1 ) 1.64e e e e e+35 Δν: tune shift /IP nominal CW=2857 =-.64, CW L (cm -2 s -1 ) 2e e e e e+35 L x y y (m) Which challenge, low β or high beam-beam parameter? -

30 Dynamic aperture issue for crab waist scheme in SuperKEKB IR nonlinearity, kinematic term and Quadrupole fringe, was dominant for the dynamic aperture in SuperB factories, because of the extremely small β function, βy=2μm x y 3 25 x y 2 2 (m -1 ) s(m) s(m)

31 Kinematic nonlinearity Drift space at the interaction region (IR). Hamiltonian contain nonlinear term for px, py, δ. H =(1+δ) (1 + δ) 2 p 2 x p 2 y This nonlinearity is not negligible for very low beta IR. Chromaticity and its higher order Octupole and higher order nonlinearity

32 Chromaticity and nonlinearity H n = (1 + δ) = (p2 x + p 2 y)δ 2(1 + δ) (1 + δ) 2 p 2 x p 2 y p2 x + p 2 y (p 2 x + p 2 y) 2 (1 + δ) (p 2 x + p 2 y) 4 (1 + δ) Subtract linear (drift) motion First term gives chromaticity Second and later give octupole and higher nonlinearity 1 x =1 x 2 x2 8 x3 16 5x4 128

33 p 2 ~γj γ = 1+α2 β These nonlinearities are strong at high γ region near IP. We consider L area and QF1-QF1 area in this presentation. It means that the effects are underestimated, especially for horizontal x y 3 25 x y 2 2 (m -1 ) s(m) s(m) L=1.4m SuperKEKB-HER C=316.2m

34 Quadrupole edge nonlinearity Quadrupole nonlinearity at its face of IR E. Forest H E = k 1+δ yp y (3x 2 + y 2 ) xp x (3y 2 + x 2 ) 12 k = eb p B k~6m -2

35 Simple IR model (like beam-beam simulation) QF1-QF1 area M IR = e H QF e H L1 e H QD e H L e H L e H QD e H L1 e H QF M rev = M IR M arc Arc is assumed to be linear. M arc = M arc = M 1 IR M MIR is linear part of IR transfer matrix M,i=xyz = cos µi + α i sin µ i γ i sin µ i β i sin µ i cos µ i α i sin µ i M IR = M IR M 1 IR M rev = M IRM M IR contains only nonlinear terms.

36 Crab waist e :H K:L e :xp2 y :/θ M e :xp2 y :/θ e :H K:L M e :xp2 y :/θ e :H K:L e :H K:L e :xp2 y :/θ If IR nonlinearity HK is negligible, crab waist nonlinearity is cancelled outside of IR. IR nonlinearity breaks to cancel between the crab waist sextupoles. x 3 terms of the sextupole may affect something but are neglected now. The fact that the kinematic nonlinearity affect the aperture for crab waist scheme has been investigated by H. Koiso using SAD since several years ago.

37 On momentum aperture QF1-QF1 area KEKB (model) βx=.6m βy=6mm L=1.3m,LQD=2.3m KQD=-.69m -1, L1=2.57m, LQF=2.7m, KQF=.24m NoCW CW νx=.53, νy=.58 y/ y 1 5 KEKB x,y =(2,.2) nm Agree with SAD result by H. Koiso x/ x

38 On momentum aperture SuperKEKB, L =.73m,LQD=.39m KQD=-1.7m -1, L1=.69m, LQF=.35m, KQF=.83m -1, βx=2cm βy=.2mm SuperB, L =.4m,LQD=.45m KQD=-2.7m -1, L1=.4m, LQF=.2m, KQF=1.2m -1, βx=2cm βy=.2mm y/ y NoCW,Qfr CW, Qfr NoCW,NoQfr CW,NoQfr SuperKEKB x,y =(2,.5) nm y/ y NoCW,Qfr CW, Qfr NoCW,NoQfr CW,NoQfr SuperB x,y =(2,.5) nm x/ x νx=.53, νy=.58 x/ x

39 M IR = Chromaticity correction e H 2,i e H ξ,i e H K,i IR e H i i = e H 2,i e H ξ,i e H K,i e H 2,i i : Linear transformation IP to i-th element : Chromatic terms, Quadratic term times a function of δ : Higher order kinematic terms 1. Remove chromatic term element by element M IR = i Aperture is independent of δ. This fact may be trivial. e H 2,i e H K,i e H 2,i

40 More realistic chromaticity correction Chromaticity correction outside of IR using Hc, quadratic term of x,px,y,py times f(δ). Choice of Hc e H c,in(out) = e H c,out M IRe H c,in up(down)stream i e H 2,i e H ξ,i e H 2,i Chromaticity is corrected IP and outside of IR, but chromatic aberrations in IR section are remained. Possible perfect chromaticity correction

41 Off momentum aperture Synchrotron oscillation. Δp/p x-y oscillation, y/σy=2x/σx. νx=.53, νy=.58 x/ x KEKB x,y =(2,.2) nm y/ y =2 x/ x NoCW,Qfr CW, Qfr p/p x/ x SuperKEKB x,y =(2,.5) nm y/ y =2 x/ x NoCW,Qfr CW, Qfr p/p x/ x NoCW,Qfr CW, Qfr SuperB x,y =(2,.5) nm y/ y =2 x/ x p/p CW=1(nominal 1/.8=12.5) CW=12.5(nominal 1/.5=2)

42 xy (m) Dynamic aperture in Crab waist scheme in LHC γ is lower than that of Super B factories k is also weaker. k=.1m -2 (~6m -2 for Super KEKB) IP s (m) x y xy (m -1 ) IP s (m) Effect of Kinematic term and Quadrupole fringe is weak. x y

43 Quadrupole nonlinearity in LHC Triplet of IP1, MQXA.1R(L)1, MQXB.A2R(L)1, MQXB.B2R(L)1, MQXA.3R(L)1 Multipole components of these magnets are dominant for the limit of the dynamic aperture. Kinematic term and fringe field was negligible in LHC. Study with a model containing the 8 IR magnets. IR triplet Multipole table of Quadrupole is given by T. Rogelio.

44 On momentum aperture Degradation is seen for CW=3, 3μrad crossing. Ay (x ) NoCW CW=1 CW=2 CW=3 x 3 term of CW is not considered now. 4 2 dp/p= Ax (x )

45 Chromaticity correction, local or global In super B factories, local chromaticity correction is adopted, because IR chromaticity is extremely large, and large beta function at IR is helpful for the chromaticity correction. e H c,out M IRe H c,in local or global e :xp2 y :/θ e H c,out M IRe H c,in e :xp2 y :/θ e H c,out e :xp2 y :/θ M IRe :xp2 y :/θ e H c,in Chromaticity correction of Hc is done inside or outside of the crab waist.

46 Off-momentum aperture dp/p=5x1-4 where σdp/p=1x1-4 local global NoCW CW=1 CW=2 CW= NoCW CW=1 CW=2 CW=3 Ay (x ) 8 6 Ay (x ) dp/p=5x1-4 4 dp/p=5x1-4 2 Local Chrom. correction 2 Non Local Chrom. correction Ax (x ) Ax (x ) Local chromaticity correction is better.

47 Summary Some simulations were carried out for HE-LHC. Beam-beam effect for ideal (HE-)LHC machine is weak. Effect of x-y coupling is weak in (HE-)LHC. Various collision scheme for HL-LHC have feasibility from the view of the beam-beam. Beambeam parameter ξ=.3/ip is challengeable. Crab cavity studies are on-going favorably. In the crab waist scheme, local chromaticity and local nonlinearity corrections are required.

48 Summary II (the future) The strong-strong code is based on single IP collision. The weak-strong (BBWS) is extended two IP. The strong-strong code will be extended multi IP and including IR nonlinearity.

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50 Oide-Kubo method in SAD Calculate p i p j under sychrotron radiation P i P j in the beam frame. P i P j = L 3 p i p j L 3 L 3 = Diagonalizing P i P j, eigenvalues are obtained as. RP i P j R t = u 1,u 2,u 3 u 1 u 2 u /γ

51 w1 2 t w2 2 t w3 2 t Calculate diffusion rate of the where eigen-momentum = c I [(g 2 g 1 )+(g 3 g 1 )] = c I [(g 1 g 2 )+(g 3 g 2 )] = c I [(g 1 g 3 )+(g 2 g 3 )] g 1 = g 2 = g 3 = π/2 π/2 π/2 (sin 2 q + u 1 2u 1 sin 2 q cos qdq c I = r2 en(log) 4πγ 3 ε 1 ε 2 ε 3 u 2 cos 2 q)(sin 2 q + u 1 u 3 cos 2 q) 2u 2 sin 2 q cos qdq (sin 2 q + u 2 u 1 cos 2 q)(sin 2 q + u 2 u 3 cos 2 q) 2u 3 sin 2 q cos qdq (sin 2 q + u 3 u 1 cos 2 q)(sin 2 q + u 3 u 2 cos 2 q)

52 Return to the physical coordinate in the lab frame. p i p j = L 1 3 R w 2 1 w 2 2 w 2 3 R t L 1 3

53 Solve beam envelope equation Not used. It is enough to get the diffusion x i x j = M(s)x i x j M t (s)+ rate for single path issues s+c s M(s + C, s 1 ) x i x j M(s + C, s 1 )ds 1 x i =[x, p x /p,y,p y /p,z,(p z p )/p ] M: transfer matrix containing the radiation damping The IBS diffusion term p i p j is incorporated in x i x j together with the radiation excitation. p i p j is a function of x i x j or p i p j, these processes are iterated.