LHC optical model and necessary corrections (aperture model, tune, β -beat, coupling, chromaticity...) M. Aiba, C. Alabau, R. Calaga, J. Cardona, O. Dominguez, M. Giovannozzi, S. Fartoukh, V. Kain, M. Lamont, E. Mcintosh, R. Miyamoto, G. Mueller, S. Redaelli, F. Schmidt, R. Tomás, G. Vanbavinckhove, J. Wenninger, S. White and F. Zimmermann LHC beam commissioning workshop - 2010 Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.1/31
Contents • Effect of precycling (prehistory) • LHC status (optics and aperture) • Optics error sources at injection: • Errors in IR3 and IR7 (warm) • Triplet errors in IR2 and IR8 • Dipole b 2 correction • IR5 squeeze • Software needs • Commissioning needs Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.2/31
The effect of precycling - Beam 2 0.4 0.2 ∆β/β x 0 -0.2 -0.4 IR8 IR1 IR2 IR3 IR4 IR5 IR6 IR7 0.6 precycling not precycling 0.4 0.2 ∆β/β y 0 -0.2 -0.4 0 5000 10000 15000 20000 25000 Longitudinal location [m] Large differences! → Must precycle Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.3/31
Beam 2, 2008-2009 Simulations, observations and tolerances 1 LHCB2 2008 Measured b2+5units 450GeV 0.8 Sext. misalignments 2mm ∆ β/β y,peak 0.6 LHCB2 2009 0.4 LHCB2 2009 450GeV 1.18TeV 0.2 Tolerances Measured b1 and b2 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 ∆ β/β x,peak Injection optics still far from tolerances Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.4/31
Beam 2, 2008-2009 Simulations, observations and tolerances 1 LHCB2 2008 Measured b2+5units 450GeV 0.8 Sext. misalignments 2mm ∆ β/β y,peak 0.6 ? LHCB2 2009 0.4 LHCB2 2009 450GeV 1.18TeV 0.2 Tolerances Measured b1 and b2 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 ∆ β/β x,peak Why the large difference between 450GeV and 1.18TeV? Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.5/31
LHC optics status summary Beam 1 Beam 2 Tol. E [TeV] 0.45 1.18 0.45 1.18 ∆ β x /β x [%] 35 20 40 15 14 ∆ β y /β y [%] 50 16 55 20 16 ∆ D q f x /D q f [%] 19 11 16 ? 30 x y /D q f ∆ D q d [%] 8 12 11 ? 28 x Dispersion is within tolerances even at injection! Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.6/31
Aperture measurements (IR6 example) +8 σ -7 σ Measured closed orbit + 3 σ envelope using measured optics and ǫ x,n = 3 . 5 µ m. 5R6 losses expected, 11R6 losses to be understood. Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.7/31
Summary of aperture measurements Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.8/31
☎ ✑ ✕ ✒ ✜ ☎ ✒ ☛ ✟ ☞ ✞ ✒ ✓ ✓✔ ✕ ☎ ✟ ☞ ☛ ✕ ✒ ✜ ☎ ✄ ☛✏ ☛ ✒ ✓ ✕ ✒ ✜ ☎ ✒ ☛ ✟ ☎ ☞ ✑ ✛ ✒ ✓✔ ✕ � ✟ ☞ ✑ ✕ ✒ ✖ ✒ ✟ ☎ ✒ ☛ ✑ ✒ ✓✔ ✕ ☎ ✟ ☞ ✟ ✕ ✜ ✟ ☎ ✒ ☛ ✟ ☞ ☛ ✕ ✘ ✑ ✓✢ ☞ ☎ ☞ ☛ ☛ ✖ ✑ ✒ ✓ ✔ ✕ ☎ ✟ ☞ ✕ ✕ ✒ ✜ ☎ ✒ ☛ ✟ ☞ ✓ ✑✒ ✓✔ ☞ ✍ ✗ ☛ ☛ ☎ ✞ ✄✞ ✠ ✡ ✄ ✟ ✄ ☎ ✎ ✂ ☞ ✌ ✁ ✍ ☎ ✎ ✎✏ ✄ ✑✒ ✓✔ ☛ ✁ ☎ ✞ ✁ ✂ ✄ ☛ ✝✞ ✟ ✠ ✡ ✞ ☞ ✟ � ☛ ☞ ✌ ✁ ✍ ☎ ✎ ✎ ✎ ✎ ✕ ✟ ✄ ☎ ✒ ✗✘ ✕ ☎ ✙ ☞ ✟ ✘ ✄ ✍ ☞ ✟ ✕ ✕ ✒ ✔ ✛ ☛ ✏ ✓ ✄ ✘ ✑ ☞ ☞ ✓ ✟ ✑✒ ✗✘ ✕ ☎ ✙ ☞ ✟ ✑ ✒ ✔ ✙ ✕ ☎ ✟ ☞ ☎ ✑ ✒ ✗✘ ✕ ☎ ☎ p.9/31 Aperture tolerance with measured β -beat – � Traditional values ǫ n = 3 . 75 µ m, and CO budget =4mm. measured CO and corrections lower ǫ n help necessary ☛✆✖ ☛✆✖ ✚✆☎ ✚✆☎ � Beam 1 lines at N 1 =7 σ ☛✆✖ and Aperture is out of budget due to β -beating ☛✆✖ model ☛✆✖ optical LHC • Measured ☛✆✖ ☛✆✖ ☛✆✖ ☛✆✖ ☛✆☎ ✄✆☎ ıa Garc´ as Tom´ Rogelio
LHC aperture status • Beam clearance seems to be OK, above or equal to 7 σ . • Some measured bottlenecks agree with model predictions using measured β functions. • Aperture is out of budget due to the large β -beating, N 1 < 7 σ even reducing the CO budget to the measured ≈ 3.2mm peak CO. • Correcting β -beating is mandatory. Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.10/31
Error sources @ injection Estimated impact of sources ordered by size: Beam 1 Beam 2 ∆ β x /β x ∆ β y /β y ∆ β x /β x ∆ β y /β y IR3 15 10 15 10 IR7 15 6 12 8 IR2 6 9 6 10 IR8 8 8 8 8 dip. b 2 6 7 5 9 Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.11/31
IR7 local error @ 450GeV & 1.18 TeV LHCB1 IP7 K 1 L 0.04 1.18 TeV 0.03 450 GeV 0.02 ∆φ x [2 π ] 0.01 0 -0.01 -0.02 16400 16600 16800 17000 17200 17400 0.04 0.03 0.02 ∆φ y [2 π ] 0.01 0 -0.01 -0.02 16400 16600 16800 17000 17200 17400 s [m] IR3 and IR7 errors disappear at 1.18 TeV, why? Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.12/31
Suspects of IR7 and IR3 errors MQW, courtesy of P. Hagen • Q6 in IR7 and IR3 are also suspects since they were not precycled Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.13/31
IR7 proposed local correction - Beam 1 LHCB1 IP7 K 1 L 0.05 Measurement 0.04 Q6L-1%, MQWA+3% 0.03 ∆φ x [2 π ] 0.02 0.01 0 -0.01 -0.02 16400 16600 16800 17000 17200 17400 0.05 0.04 0.03 ∆φ y [2 π ] 0.02 0.01 0 -0.01 -0.02 16400 16600 16800 17000 17200 17400 s [m] Q6 and MQWA seem to correct IR7 beam 1 Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.14/31
Same IR7 corr for Beam 2 LHCB2 IP7 K 1 L 0.08 0.07 Measurement Q6L-1%, MQWA+3% 0.06 0.05 ∆φ x [2 π ] 0.04 0.03 0.02 0.01 0 -0.01 22700 22800 22900 23000 23100 23200 23300 23400 23500 23600 0.06 0.05 0.04 0.03 ∆φ y [2 π ] 0.02 0.01 0 -0.01 -0.02 22700 22800 22900 23000 23100 23200 23300 23400 23500 23600 s [m] Same correction is not fully satisfactory for beam 2 Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.15/31
What about IR3? LHCB1 IP3 K 1 L 0.06 0.05 Measurement MQWA+3% 0.04 0.03 ∆φ x [2 π ] 0.02 0.01 0 -0.01 -0.02 3000 3200 3400 3600 3800 4000 0.06 0.05 0.04 0.03 ∆φ y [2 π ] 0.02 0.01 0 -0.01 -0.02 3000 3200 3400 3600 3800 4000 s [m] Similar correction in IR3 ( MQWA+3% ) rather effective Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.16/31
IR3 and IR7 local error summary • MQWA (main quads) seem to be effective for a good fraction of the correction • Q6 also effective to a lesser extent • The precycling of Q6 should be attempted in 2010 (even if in MD mode) • The residual errors should be corrected iteratively with MQWB (the IR3/7 trims) Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.17/31
Dipole b 2 correction - Beam 1 0.2 0.1 ∆φ x [2 π ] 0 -0.1 IR2 IR3 IR4 IR5 IR6 IR7 IR8 IR1 0.1 0 ∆φ y [2 π ] -0.1 Before b2 correction After b2 correction -0.2 0 5000 10000 15000 20000 25000 s[m] The magnetic dipole b 2 is used to compute the required correction with KQT → Excellent agreement! Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.18/31
Also from injection tests - Beam 2 arcs8-6 KCS.A67.B2 6 Exp. 4 No b 2 , b 3 2 Dipole b 2 , b 3 x [mm] 0 -2 -4 -6 6000 7000 8000 9000 10000 11000 12000 6 4 2 y [mm] 0 -2 -4 -6 6000 7000 8000 9000 10000 11000 12000 Longitudinal location [m] The magnetic dipole b 2 and b 3 were also confirmed during sector tests. Congratulations to magnet experts and MAD modelers! Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.19/31
Predicted IP2 local correction - Beam2 LHCB2 IP2 K 1 L 400 Measurement 350 Design with initial cond 300 ktqx2.l2=-5e-5;ktqx2.r2=7e-5 250 β x [m] 200 150 100 50 0 6000 6200 6400 6600 6800 7000 350 300 250 200 β y [m] 150 100 50 0 6000 6200 6400 6600 6800 7000 s [m] 50/70 units in QX2R/L seemed to correct IR2 Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.20/31
Measured IP2 local correction - Beam2 LHCB2 IP2 K 1 L 0.02 0.01 0 ∆φ x [2 π ] -0.01 -0.02 -0.03 -0.04 6100 6200 6300 6400 6500 6600 6700 6800 6900 7000 0.02 0.01 0 ∆φ y [2 π ] -0.01 -0.02 Before IR2 corr. -0.03 After IR2 corr. -0.04 6100 6200 6300 6400 6500 6600 6700 6800 6900 7000 s [m] The measurement confirmed a good correction Rogelio Tom´ as Garc´ ıa LHC optical model and necessary corrections – p.21/31
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