HiLumi LHC FP7 High Luminosity Large Hadron Collider Design Study - PDF document

CERN-ACC-SLIDES-2014-0075 HiLumi LHC FP7 High Luminosity Large Hadron Collider Design Study Presentation Field quality requirements from dynamic aperture: including matching section Nosochkov, Y (CERN) 12 November 2013 The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement 284404. This work is part of HiLumi LHC Work Package 2: Accelerator Physics & Performance . The electronic version of this HiLumi LHC Publication is available via the HiLumi LHC web site <http://hilumilhc.web.cern.ch> or on the CERN Document Server at the following URL: <http://cds.cern.ch/search?p=CERN-ACC-SLIDES-2014-0075> CERN-ACC-SLIDES-2014-0075

Field Quality Requirements for Separation Dipoles and Matching Quadrupoles at Collision Energy Based on Dynamic Aperture Yuri Nosochkov (SLAC) Y. Cai, M.-H. Wang (SLAC) S. Fartoukh, M. Giovannozzi, R. de Maria, E. McIntosh (CERN) 3 rd Joint HiLumi LHC — LARP Meeting 11 — 15 November 2013, Daresbury, UK The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement 284404. Work supported by the US LHC Accelerator Research Program (LARP) through US Department of Energy contracts DE-AC02-07CH11359, DE-AC02-98CH10886, DE-AC02-05CH11231, and DE- AC02-76SF00515.

Introduction • New large aperture magnets are planned for the HL-LHC lattice: superconducting 150 mm D1 and 105 mm D2 separation dipoles, 90 mm Q4 and 70 mm Q5 matching quadrupoles near IP1 and IP5. • High beta functions in these magnets enhance sensitivity to their field errors causing reduction of dynamic aperture (DA). • Field quality in these magnets needs to be evaluated and optimized to satisfy two conflicting requirements: the field errors must be small enough to provide a sufficient DA (~10 s ), but large enough to be realistically achievable. • Estimates of field quality obtained from measured data and magnetic field calculations are used as a starting point for evaluation and optimization. • Impact of the field errors on DA is determined in tracking simulations using SixTrack. • Lattice: SLHCV3.1b with b *=15/15 cm at IP1 and IP5, SC IT quadrupoles with 150 mm coil diameter and 150 T/m gradient, 7 TeV beam energy.

Beta functions High b -functions in the D1, D2, Q4, Q5 enhance beam sensitivity to their field errors. Field correctors for the IT also compensate the low order D1 field errors (n=3-6) since the two beams share the D1 aperture. 2-in-1 D2 and Q4, Q5 magnets do not have local correctors. ≈180 ° Q5 Q4 D2 D1 D2 Q4 Q5 D1

IT field quality specifications at r 0 = 50 mm (“IT_errortable_v66”) These IT specifications is the result of previous optimization studies. In this study, the IT specification errors are always included. skew mean uncertainty random normal mean uncertainty random a3 0 0.800 0.800 b3 0 0.820 0.820 a4 0 0.650 0.650 b4 0 0.570 0.570 a5 0 0.430 0.430 b5 0 0.420 0.420 a6 0 0.310 0.310 b6 0.800 0.550 0.550 a7 0 0.152 0.095 b7 0 0.095 0.095 a8 0 0.088 0.055 b8 0 0.065 0.065 a9 0 0.064 0.040 b9 0 0.035 0.035 a10 0 0.040 0.032 b10 0.075 0.100 0.100 a11 0 0.026 0.0208 b11 0 0.0208 0.0208 a12 0 0.014 0.014 b12 0 0.0144 0.0144 a13 0 0.010 0.010 b13 0 0.0072 0.0072 a14 0 0.005 0.005 b14 -0.020 0.0115 0.0115     x iy        4 n 1 B iB 10 B b ia ( ) y x ref n n r  n 1 0

Q4 field errors at r 0 = 30 mm (“Q4_errortable_v1”) Estimate is based on scaling from the measured field of existing MQY quadrupole with 70 mm aperture and applied to 90 mm Q4. This estimate is expected to be updated. skew mean uncertainty random normal mean uncertainty random a3 0 0.682 1.227 b3 0 1.282 1.500 a4 0 0.428 0.893 b4 0 0.483 0.465 a5 0 0.177 0.406 b5 0 0.203 0.431 a6 0 0.484 0.277 b6 0 5.187 1.487 a7 0 0.094 0.189 b7 0 0.094 0.189 a8 0 0.193 0.257 b8 0 0.193 0.257 a9 0 0.088 0.088 b9 0 0.088 0.088 a10 0 0.120 0.120 b10 0 3.587 0.956 a11 0 0.326 0.489 b11 0 0.326 0.489 a12 0 0.445 0.222 b12 0 0.445 0.222 a13 0 0.606 0.303 b13 0 0.606 0.303 a14 0 0.827 0.413 b14 0 2.067 0.413 a15 0 1.127 0.564 b15 0 1.127 0.564

Q5 expected field quality at r 0 = 17 mm (“Q5_errortable_v0”) Estimate is based on the measured field of existing MQY quadrupole with 70 mm aperture which is of the same type as Q5. skew mean uncertainty random normal mean uncertainty random a3 0 0.500 0.900 b3 0 0.940 1.100 a4 0 0.230 0.480 b4 0 0.260 0.250 a5 0 0.070 0.160 b5 0 0.080 0.170 a6 0 0.140 0.080 b6 0 1.500 0.430 a7 0 0.020 0.040 b7 0 0.020 0.040 a8 0 0.030 0.040 b8 0 0.030 0.040 a9 0 0.010 0.010 b9 0 0.010 0.010 a10 0 0.010 0.010 b10 0 0.300 0.080 a11 0 0.020 0.030 b11 0 0.020 0.030 a12 0 0.020 0.010 b12 0 0.020 0.010 a13 0 0.020 0.010 b13 0 0.020 0.010 a14 0 0.020 0.010 b14 0 0.050 0.010 a15 0 0.020 0.010 b15 0 0.020 0.010

D1 expected field quality at r 0 = 50 mm (“D1_errortable_v1”) Estimate is based on magnetic field calculations for 160 mm aperture D1 magnet (T. Nakamoto, E. Todesco, CERN-ACC-2013-002). skew mean uncertainty random normal mean uncertainty random a2 0 0.679 0.679 b2 0 0.200 0.200 a3 0 0.282 0.282 b3 -0.9 0.727 0.727 a4 0 0.444 0.444 b4 0 0.126 0.126 a5 0 0.152 0.152 b5 0 0.365 0.365 a6 0 0.176 0.176 b6 0 0.060 0.060 a7 0 0.057 0.057 b7 0.4 0.165 0.165 a8 0 0.061 0.061 b8 0 0.027 0.027 a9 0 0.020 0.020 b9 -0.59 0.065 0.065 a10 0 0.025 0.025 b10 0 0.008 0.008 a11 0 0.007 0.007 b11 0.47 0.019 0.019 a12 0 0.008 0.008 b12 0 0.003 0.003 a13 0 0.002 0.002 b13 0 0.006 0.006 a14 0 0.003 0.003 b14 0 0.001 0.001 a15 0 0.001 0.001 b15 -0.04 0.002 0.002

D2 field errors at r 0 = 35 mm (“D2_errortable_v3”) Estimate is based on magnetic field calculations for 2-in-1 D2 dipole (E. Todesco 01-Jan-2013). These values were obtained for a shorter magnet, therefore they may be potentially reduced for the longer D2. The large values of b2, b3, b4, b5 terms are due to field saturation. skew mean uncertainty random normal mean uncertainty random a2 0 0.679 0.6790 b2 ±65 3.0 3.0 a3 0 0.282 0.2820 b3 -30 5.0 5.0 a4 0 0.444 0.4440 b4 ±25 1.0 1.0 a5 0 0.152 0.152 b5 -4.0 1.0 1.0 a6 0 0.176 0.176 b6 0 0.060 0.060 a7 0 0.057 0.057 b7 -0.2 0.165 0.165 a8 0 0.061 0.061 b8 0 0.027 0.027 a9 0 0.020 0.020 b9 0.09 0.065 0.065 a10 0 0.025 0.025 b10 0 0.008 0.008 a11 0 0.007 0.007 b11 0.03 0.019 0.019 a12 0 0.008 0.008 b12 0 0.003 0.003 a13 0 0.002 0.002 b13 0 0.006 0.006 a14 0 0.003 0.003 b14 0 0.001 0.001 a15 0 0.001 0.001 b15 0 0.002 0.002

Latest D2 field estimate at r 0 = 35 mm (“D2_errortable_v4”) The recent optimization of iron geometry and coil in D2 (E. Todesco) resulted in significant reduction of b2, b3, b4, b5 terms at collision energy (D2_errortable_v4). It also significantly reduced the mean values of b3 (95.8→3.8) and b5 (15→3.0) at injection energy. However, for most of this study, the D2_errortable_v3 was used as a reference table. skew mean uncertainty random normal mean uncertainty random a2 0 0.679 0.6790 b2 ±65 → ±25 3.0 → 2.5 3.0 → 2.5 a3 0 0.282 0.2820 b3 -30 → 3.0 5.0 → 1.5 5.0 → 1.5 a4 0 0.444 0.4440 b4 ±25 → ±2.0 1.0 → 0.2 1.0 → 0.2 a5 0 0.152 0.152 b5 -4.0 → -1.0 1.0 → 0.5 1.0 → 0.5 a6 0 0.176 0.176 b6 0 0.060 0.060 a7 0 0.057 0.057 b7 -0.2 0.165 0.165 a8 0 0.061 0.061 b8 0 0.027 0.027 a9 0 0.020 0.020 b9 0.09 0.065 0.065 a10 0 0.025 0.025 b10 0 0.008 0.008 a11 0 0.007 0.007 b11 0.03 0.019 0.019 a12 0 0.008 0.008 b12 0 0.003 0.003 a13 0 0.002 0.002 b13 0 0.006 0.006 a14 0 0.003 0.003 b14 0 0.001 0.001 a15 0 0.001 0.001 b15 0 0.002 0.002

Typical set-up for SixTrack tracking • 100,000 turns • 60 random error seeds • 30 particle pairs per amplitude step (2 s  • 11 angles • 7 TeV beam energy • Initial D p/p = 2.7e-4 • Tune = 62.31, 60.32 • Normalized emittance = 3.75 m m-rad • Arc errors and correction are included • IT local correctors to compensate an, bn errors of order n=3-6 in IT quads and D1 dipoles are included

DA without D1, D2, Q4, Q5 errors This is our starting DA with only IT and arc errors included. The goal is to optimize D1, D2, Q4, Q5 errors in order to keep minimum DA near 10 s .

Kicks due to an, bn terms in D1, D2 at x=10 s x  s x 10       b 4 n 1 x ( ) (and similar for y’ from a n ) 10 b / / n x  b r / 0 x Largest kicks are produced by b2m, b3m, b4m in D2_v3 table. They are further amplified by ≈180 ° phase between left and right side D2 magnets around IP, and by the fact that mean bn terms of even order are of opposite sign in the left and right D2. These kicks are substantially reduced in the D2_v4 error table.