Status of EuCARD WP11.2.2LHC Crab Waist

Frank Zimmermann

Input to EuCARD2011 Meeting, CNRS, Paris, 13 May 2011

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

crab waist for the LHC weak-strong beam-beam studies by Shatilov & Zobovusing 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 x/y≥ 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 w>1: For w=2: 10% gain from the flatter beam profile. For w=5: 25% gain. For w>>1 asymptotic gain of 41%.

assumed “LHC” parameters:x,y =0.5 nm , E = 7 TeVx = 30 cm, y = 7.5 cm, x/y=2,z = 11.8 cm, c= 315 rad ( =1.5), Nb = 4.0x1011,Qs =0.002, Qx,y ~ -0.0065,single IP

frequency-map analysis of Lifetrac simulation

M. Zobov, D. Shatilov, et al, PRST-AB 14, 014001 (2011)

collisions withcrossing angle

crab crossing

resonances

resonancefree!

crab waist

resonances

crab waist for the LHC

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 |====================================================================

1 IP

2 IPsx/ycrossing

LHC CW: longitudinal profile for w>1

trapezium shape of weak bunch

D.Shatilov, M. Zobov

1.29 instead of 1.41 due to trapezium shape

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

K. Ohmi

K. Ohmi

K. Ohmi

K. Ohmi

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

crab waist for the LHC

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

x 10-3

0

0.5

1

1.5

2

2.5

dp

beta

* (u

m)

bandwidth

momentum bandwidth without & with sextupoles

optics with location of 4 sextupoles

x (w/o sext)

x (w sext)y (w/o sext)

y (w sext)

order 1 2 3 4 5

x [m] (=0) 9.2 28.3 175.0 179.5 181.4

y [m] (=0) 4.6 8.5 85.4 87.5 88.2

x [m] (=3x10-4) 11.1 28.9 175.1 179.5 181.5

y [m] (=3x10-4) 4.6 8.5 85.4 87.5 88.2

effect of higher-order aberrations with MAPCLASS – further optimization needed

crab waist for LHC: L-R LHeC e- beam final-focus modelJ. Abelleira, R. Tomas, E. Marin