Status of EuCARD WP11.2.2 LHC Crab Waist

1. Status of EuCARD WP11.2.2LHC Crab Waist Frank Zimmermann Input to EuCARD2011 Meeting, CNRS, Paris, 13 May 2011

2. crab waist for the LHC • initial delay due to difficulty / impossibility of recruiting a fellow at CERN • two mitigations: • contributions by external experts • Dmitry Shatilov (BINP) visiting Mikhail Zobov at INFN-LNF twice , in fall 2010 and winter 2011 • Kazuhito Ohmi (KEK) visiting Frank Zimmermann at CERN twice, in summer 2010 and winter 2011 • recruitment of doctoral student instead of fellow • Jose Abelleira started at CERN in November 2010

3. crab waist for the LHC • weak-strong beam-beam studies by Shatilov & Zobov • using Lifetrac code (Shatilov, Part.Accel.52:65-93,1996) • crab-waist (CW) application to “quasi-round” beams: • in terms of luminosity lifetime, resonance suppression and halo control, CW for HL-LHC efficient only when operating with rather flat beams of sx/sy≥ 10 [PRST-AB 14, 014001 (2011)] • luminosity gain from a longitudinally uniform or “trapezium” (as compared to Gaussian) profile for equal bunch charge and beam-beam tune shift, in the regime fw>1: For fw=2: 10% gain from the flatter beam profile. For fw=5: 25% gain. For fw>>1 asymptotic gain of 41%.

4. crab waist for the LHC M. Zobov, D. Shatilov, et al, PRST-AB 14, 014001 (2011) collisions with crossing angle resonances frequency-map analysis of Lifetrac simulation crab waist assumed “LHC” parameters: ex,y =0.5 nm , E = 7 TeV bx = 30 cm, by = 7.5 cm, sx/sy=2, sz = 11.8 cm, qc= 315 mrad (f =1.5), Nb = 4.0x1011, Qs=0.002, DQx,y ~ -0.0065, single IP resonances crab crossing resonance free!

5. LHC CW: longitudinal profile for fw>1 Table "flat / Gauss" profiles, geometrical factors. Slashes in the table separate "flat / trapezium“ profiles of the strong bunch; the weak bunch is trapezium in all cases. Angles are measured in units of 3.48E-4 rad (nominal value). ==================================================================== Angle | ksi_x | ksi_y | Lumi | Lumi/ksi_y | -------|---------------|---------------|-------------|-------------| 0 | 0.997 / 0.997 | 0.997 / 0.997 | 1.01 / 1.01 | 1.01 / 1.01 | 1 | 1.184 / 1.153 | 1.070 / 1.059 | 1.13 / 1.12 | 1.06 / 1.06 | 2 | 1.077 / 1.077 | 1.101 / 1.086 | 1.21 / 1.19 | 1.10 / 1.10 | 3 | 0.905 / 0.936 | 1.087 / 1.076 | 1.25 / 1.22 | 1.15 / 1.13 | 4 | 0.821 / 0.854 | 1.068 / 1.063 | 1.26 / 1.23 | 1.18 / 1.16 | 5 | 0.775 / 0.807 | 1.059 / 1.052 | 1.27 / 1.24 | 1.20 / 1.18 | 6 | 0.748 / 0.777 | 1.050 / 1.045 | 1.28 / 1.24 | 1.22 / 1.19 | 7 | 0.726 / 0.756 | 1.043 / 1.039 | 1.28 / 1.25 | 1.23 / 1.20 | 8 | 0.714 / 0.743 | 1.038 / 1.034 | 1.29 / 1.25 | 1.24 / 1.21 | 9 | 0.704 / 0.731 | 1.034 / 1.030 | 1.29 / 1.25 | 1.25 / 1.21 | 10 | 0.696 / 0.725 | 1.030 / 1.027 | 1.29 / 1.25 | 1.25 / 1.22 | 15 | 0.674 / 0.695 | 1.020 / 1.017 | 1.29 / 1.25 | 1.26 / 1.23 | 20 | 0.667 / 0.685 | 1.014 / 1.012 | 1.29 / 1.25 | 1.27 / 1.24 | 25 | 0.657 / 0.686 | 1.011 / 1.009 | 1.29 / 1.25 | 1.28 / 1.24 | 30 | 0.640 / 0.680 | 1.009 / 1.008 | 1.29 / 1.25 | 1.28 / 1.24 | ==================================================================== 0 | 0.996 / 0.997 | 0.998 / 0.998 | 1.01 / 1.01 | 1.01 / 1.01 | 1 | 1.115 / 1.096 | 1.121 / 1.101 | 1.13 / 1.12 | 1.01 / 1.02 | 2 | 1.093 / 1.082 | 1.095 / 1.084 | 1.21 / 1.19 | 1.10 / 1.10 | 3 | 1.046 / 1.044 | 1.045 / 1.043 | 1.25 / 1.22 | 1.19 / 1.17 | 4 | 1.025 / 1.025 | 1.024 / 1.023 | 1.26 / 1.23 | 1.23 / 1.20 | 5 | 1.015 / 1.015 | 1.014 / 1.014 | 1.27 / 1.24 | 1.25 / 1.22 | 10 | 1.002 / 1.002 | 1.002 / 1.001 | 1.29 / 1.25 | 1.29 / 1.25 | 15 | 1.000 / 0.999 | 0.999 / 0.999 | 1.29 / 1.25 | 1.29 / 1.25 | 20 | 0.999 / 0.998 | 0.999 / 0.998 | 1.29 / 1.25 | 1.29 / 1.25 | 25 | 0.998 / 0.998 | 0.998 / 0.998 | 1.29 / 1.25 | 1.29 / 1.25 | 30 | 0.998 / 0.998 | 0.998 / 0.998 | 1.29 / 1.25 | 1.29 / 1.25 | ==================================================================== D.Shatilov, M. Zobov 1 IP trapezium shape of weak bunch 2 IPs x/y crossing 1.29 instead of 1.41 due to trapezium shape

6. crab waist for the LHC • beam-beam & optics studies by K. Ohmi • using BBSS code • strong-strong beam-beam simulations: • - “various collision schemes (CC, CW) for HL- LHC have feasibility from the view of beam-beam; a beam-beam parameter ξ=0.03/IP is challengeable” • effect of kinematic term, quadrupole fringe fields, • and nonlinear multipole errors on LHC dynamic aperture with crab waist: • LHC crab waist scheme requires local chromaticity correction and local nonlinearity corrections • effects of kinematic term & quadrupole fringe are weak

7. K. Ohmi

8. K. Ohmi

9. K. Ohmi

10. K. Ohmi

11. crab waist for the LHC • WP11 doctoral student Jose Abelleira (EPFL Lausanne) • - started at CERN on 1 November 2010. • thesis topic: study of a high-luminosity LHC upgrade based on large Piwinski angle, flat beams, and crab waists • achievements: • getting familiar with accelerator physics and with design concepts of final-focusing systems (LHC, LC, muon collider) • learning some important tools : MAD-X, PTC and MAPCLASS. • JUAS in January 2011 • practicing with local chromatic correction of LHeC L-R e- final focus: momentum bandwidth without and with chromatic correction, and higher-order optimization of the sextupole positions and strengths with PTC and MAPCLASS • plan: • apply similar design concept to the much more complicated LHC high-luminosity upgrade, especially, as a next step, organize its chromaticity correction in view of a possible LHC crab waist scheme

12. crab waist for LHC: L-R LHeC e- beam final-focus model J. Abelleira, R. Tomas, E. Marin optics with location of 4 sextupoles b momentum bandwidth without & with sextupoles bx (w/o sext) bx (w sext) by (w/o sext) by (w sext) effect of higher-order aberrations with MAPCLASS – further optimization needed