Amplitude Detuning from Corrector Misalignments in the LHC and - PowerPoint PPT Presentation

Amplitude Detuning from Corrector Misalignments in the LHC and HL-LHC (Part II) Joschua Dilly O MC 30.10.2019 Nonlinear-Corrector Misalignments 1

Setup General Results Results split by IP Main Steps of Simulation O MC 30.10.2019 Nonlinear-Corrector Misalignments 2

Setup O MC 30.10.2019 Nonlinear-Corrector Misalignments 3

Simulation Setup • Setup LHC/HL-LHC Sequence • Add Sextupole, Octupole, Decapole and Dodecapole errors from 60 WISE to IP and close-to-IP MQ and MB • Calculate triplet corrections for the MCX • 50 uniformly distributed misalignments ∈ [ − 1 mm , 1 mm] per seed ⇒ Check Amplitude Detuning O MC 30.10.2019 Nonlinear-Corrector Misalignments 4

Simulation Setup • Setup LHC/HL-LHC Sequence • Add Sextupole, Octupole, Decapole and Dodecapole errors from 60 WISE to IP and close-to-IP MQ and MB • Calculate triplet corrections for the MCX • 50 uniformly distributed misalignments ∈ [ − 1 mm , 1 mm] per seed ⇒ Check Amplitude Detuning O MC 30.10.2019 Nonlinear-Corrector Misalignments 4

Simulation Setup • Setup LHC/HL-LHC Sequence • Add Sextupole, Octupole, Decapole and Dodecapole errors from 60 WISE to IP and close-to-IP MQ and MB • Calculate triplet corrections for the MCX • 50 uniformly distributed misalignments ∈ [ − 1 mm , 1 mm] per seed ⇒ Check Amplitude Detuning O MC 30.10.2019 Nonlinear-Corrector Misalignments 4

Simulation Setup • Setup LHC/HL-LHC Sequence • Add Sextupole, Octupole, Decapole and Dodecapole errors from 60 WISE to IP and close-to-IP MQ and MB • Calculate triplet corrections for the MCX • 50 uniformly distributed misalignments ∈ [ − 1 mm , 1 mm] per seed ⇒ Check Amplitude Detuning O MC 30.10.2019 Nonlinear-Corrector Misalignments 4

Simulation Setup • Setup LHC/HL-LHC Sequence • Add Sextupole, Octupole, Decapole and Dodecapole errors from 60 WISE to IP and close-to-IP MQ and MB • Calculate triplet corrections for the MCX • 50 uniformly distributed misalignments ∈ [ − 1 mm , 1 mm] per seed ⇒ Check Amplitude Detuning O MC 30.10.2019 Nonlinear-Corrector Misalignments 4

Calculation Feeddown: K K 5 = dx · K 5 (1) 4 K K 5 S = − dy · K 5 S (2) 4 = 1 dx 2 − dy 2 � K K 6 � · K 6 (3) 4 2 K K 6 S = − dx · dy · K 6 S (4) 4 Detuning: ∂ Q x = K 4 32 π β 2 (5) x ∂ 2 J x ∂ Q x = − K 4 (6) 16 π β x β y ∂ 2 J y ∂ Q y = K 4 32 π β 2 (7) y ∂ 2 J y O MC 30.10.2019 Nonlinear-Corrector Misalignments 5

Simulation Setup LHC HL-LHC β ∗ [m] 0.30 0.20 Energy [TeV] 6.5 7.0 Orbit Flat Q x , Q y 0.31, 0.32 O MC 30.10.2019 Nonlinear-Corrector Misalignments 6

Mistakes in the old Simulation Setup • Difference to aligned case was not calculated • MC*X F (IP1 and IP5) were not misaligned in HLLHC O MC 30.10.2019 Nonlinear-Corrector Misalignments 7

General Results O MC 30.10.2019 Nonlinear-Corrector Misalignments 8

Table: LHC simulation summary [10 3 m − 1 ] SODT DT SO S O SODT w/ CC ∂ Q x / ∂ 2J x PTC -0.02 ± 2.72 0.00 ± 0.53 -0.03 ± 2.68 -0.04 ± 0.05 0.08 ± 0.81 0.08 ± 0.99 FD 0.00 ± 0.53 0.00 ± 0.53 – – – 0.00 ± 0.53 Beam 1 ∂ Q y / ∂ 2J y PTC -0.02 ± 5.62 0.00 ± 0.52 -0.02 ± 5.60 -0.02 ± 0.05 0.15 ± 0.81 0.14 ± 1.01 FD 0.00 ± 0.52 0.00 ± 0.52 – – – 0.00 ± 0.52 ∂ Q x / ∂ 2J y PTC 0.52 ± 8.13 0.00 ± 0.68 0.56 ± 8.10 0.06 ± 0.07 0.27 ± 1.16 0.29 ± 1.46 FD 0.00 ± 0.68 0.00 ± 0.68 – – – 0.00 ± 0.68 ∂ Q x / ∂ 2J x PTC -0.13 ± 6.02 0.00 ± 0.52 -0.12 ± 5.99 -0.05 ± 0.06 0.09 ± 0.50 0.08 ± 0.63 FD 0.00 ± 0.52 0.00 ± 0.52 – – – 0.00 ± 0.52 Beam 2 ∂ Q y / ∂ 2J y PTC -0.02 ± 5.62 0.00 ± 0.53 0.02 ± 2.86 -0.06 ± 0.06 0.16 ± 0.30 0.14 ± 0.57 FD 0.00 ± 0.53 0.00 ± 0.53 – – – 0.00 ± 0.53 ∂ Q x / ∂ 2J y PTC 0.62 ± 8.96 0.00 ± 0.68 0.62 ± 8.92 0.11 ± 0.12 0.26 ± 1.03 0.29 ± 1.07 FD 0.00 ± 0.68 0.00 ± 0.68 – – – 0.00 ± 0.68 Simulation Parameters: S = Sextupole Errors, O = Octupole Errors, D = Decapole Errors, T = Dodecapole Errors, CC = Coupling Correction Methods: PTC = From PTC simulations, FD = From Feed-Down calculations O MC 30.10.2019 Nonlinear-Corrector Misalignments 9

Table: HL-LHC simulation summary [10 3 m − 1 ] SODT DT SO S O SODT w/ CC ∂ Q x / ∂ 2J x PTC -0.03 ± 1.57 0.02 ± 1.56 -0.06 ± 0.13 -0.07 ± 0.11 0.01 ± 0.06 – FD -0.02 ± 1.57 -0.02 ± 1.56 – – – – Beam 1 ∂ Q y / ∂ 2J y PTC -0.05 ± 1.58 0.01 ± 1.58 -0.06 ± 0.12 -0.07 ± 0.11 0.01 ± 0.04 – FD -0.01 ± 1.59 -0.01 ± 1.59 – – – – ∂ Q x / ∂ 2J y PTC 0.02 ± 1.74 -0.02 ± 1.73 0.15 ± 0.26 0.13 ± 0.21 0.01 ± 0.14 – FD 0.00 ± 0.68 0.02 ± 1.74 – – – – ∂ Q x / ∂ 2J x PTC -0.07 ± 1.59 -0.01 ± 1.58 -0.07 ± 0.16 -0.07 ± 0.12 0.01 ± 0.11 – FD 0.01 ± 1.59 0.01 ± 1.59 – – – – Beam 2 ∂ Q y / ∂ 2J y PTC -0.08 ± 1.56 -0.02 ± 1.56 -0.07 ± 0.14 -0.08 ± 0.13 0.01 ± 0.04 – FD 0.02 ± 1.56 0.02 ± 1.56 – – – – ∂ Q x / ∂ 2J y PTC 0.18 ± 1.76 0.02 ± 1.73 0.17 ± 0.25 0.15 ± 0.24 0.02 ± 0.06 – FD -0.02 ± 1.73 -0.02 ± 1.74 – – – – Simulation Parameters: S = Sextupole Errors, O = Octupole Errors, D = Decapole Errors, T = Dodecapole Errors, CC = Coupling Correction Methods: PTC = From PTC simulations, FD = From Feed-Down calculations O MC 30.10.2019 Nonlinear-Corrector Misalignments 10

Amplitude Detuning LHC (SODT) Beam 1 Beam 2 Sum K6L Sum K6L 200 Beam 1: (-0.02 ± 2.72) · 10 3 m − 1 Sum: (0.00 ± 0.53) · 10 3 m − 1 Sum: (0.00 ± 0.52) · 10 3 m − 1 Beam 2: (-0.13 ± 6.02) · 10 3 m − 1 K6L: (0.00 ± 0.53) · 10 3 m − 1 K6L: (0.00 ± 0.52) · 10 3 m − 1 100 100 Samples Samples Samples 100 50 50 0 0 0 − 20 − 10 0 10 20 − 2 − 1 0 1 2 − 2 − 1 0 1 2 ∆ ∂Q x /∂ 2 J x � 10 3 m − 1 � ∂Q x /∂ 2 J x � 10 3 m − 1 � ∂Q x /∂ 2 J x � 10 3 m − 1 � 200 Beam 1: (-0.02 ± 5.62) · 10 3 m − 1 Sum: (-0.00 ± 0.52) · 10 3 m − 1 Sum: (-0.00 ± 0.53) · 10 3 m − 1 Beam 2: (0.01 ± 2.92) · 10 3 m − 1 K6L: (-0.00 ± 0.52) · 10 3 m − 1 K6L: (-0.00 ± 0.53) · 10 3 m − 1 100 Samples 100 Samples Samples 100 50 50 0 0 0 − 20 − 10 0 10 20 − 2 − 1 0 1 2 − 2 − 1 0 1 2 � 10 3 m − 1 � ∆ ∂Q y /∂ 2 J y ∂Q y /∂ 2 J y � 10 3 m − 1 � ∂Q y /∂ 2 J y � 10 3 m − 1 � 200 Beam 1: (0.56 ± 8.13) · 10 3 m − 1 Sum: (-0.00 ± 0.68) · 10 3 m − 1 Sum: (0.00 ± 0.68) · 10 3 m − 1 Beam 2: (0.62 ± 8.96) · 10 3 m − 1 K6L: (-0.00 ± 0.68) · 10 3 m − 1 K6L: (0.00 ± 0.68) · 10 3 m − 1 Samples 100 100 Samples Samples 100 50 50 0 0 0 − 20 − 10 0 10 20 − 2 − 1 0 1 2 − 2 − 1 0 1 2 � 10 3 m − 1 � ∆ ∂Q x /∂ 2 J y � 10 3 m − 1 � � 10 3 m − 1 � ∂Q x /∂ 2 J y ∂Q x /∂ 2 J y Beam 1 Beam 2 PTC Feed-Down Calculations • centered around 0 m − 1 • almost centered around 0 m − 1 • only contributions from b 6 • σ up to 9 · 10 3 m − 1 • much lower σ than from PTC O MC 30.10.2019 Nonlinear-Corrector Misalignments 11

Amplitude Detuning LHC (DT) Beam 1 Beam 2 Sum K6L Sum K6L Beam 1: (0.00 ± 0.53) · 10 3 m − 1 Sum: (0.00 ± 0.53) · 10 3 m − 1 Sum: (0.00 ± 0.52) · 10 3 m − 1 Beam 2: (0.00 ± 0.52) · 10 3 m − 1 K6L: (0.00 ± 0.53) · 10 3 m − 1 K6L: (0.00 ± 0.52) · 10 3 m − 1 100 100 100 Samples Samples Samples 50 50 50 0 0 0 − 2.0 − 1.5 − 1.0 − 0.5 0.0 0.5 1.0 1.5 2.0 − 2 − 1 0 1 2 − 2 − 1 0 1 2 � 10 3 m − 1 � ∆ ∂Q x /∂ 2 J x ∂Q x /∂ 2 J x � 10 3 m − 1 � ∂Q x /∂ 2 J x � 10 3 m − 1 � Beam 1: (-0.00 ± 0.52) · 10 3 m − 1 Sum: (-0.00 ± 0.52) · 10 3 m − 1 Sum: (-0.00 ± 0.53) · 10 3 m − 1 Beam 2: (-0.00 ± 0.53) · 10 3 m − 1 100 100 K6L: (-0.00 ± 0.52) · 10 3 m − 1 100 K6L: (-0.00 ± 0.53) · 10 3 m − 1 Samples Samples Samples 50 50 50 0 0 0 − 2.0 − 1.5 − 1.0 − 0.5 0.0 0.5 1.0 1.5 2.0 − 2 − 1 0 1 2 − 2 − 1 0 1 2 � 10 3 m − 1 � ∆ ∂Q y /∂ 2 J y ∂Q y /∂ 2 J y � 10 3 m − 1 � ∂Q y /∂ 2 J y � 10 3 m − 1 � Beam 1: (-0.00 ± 0.68) · 10 3 m − 1 Sum: (-0.00 ± 0.68) · 10 3 m − 1 Sum: (0.00 ± 0.68) · 10 3 m − 1 Beam 2: (0.00 ± 0.68) · 10 3 m − 1 100 K6L: (-0.00 ± 0.68) · 10 3 m − 1 K6L: (0.00 ± 0.68) · 10 3 m − 1 Samples 100 100 Samples Samples 50 50 50 0 0 0 − 2.0 − 1.5 − 1.0 − 0.5 0.0 0.5 1.0 1.5 2.0 − 2 − 1 0 1 2 − 2 − 1 0 1 2 ∆ ∂Q x /∂ 2 J y � 10 3 m − 1 � ∂Q x /∂ 2 J y � 10 3 m − 1 � ∂Q x /∂ 2 J y � 10 3 m − 1 � Beam 1 Beam 2 PTC Feed-Down Calculations • centered around 0 m − 1 • same σ as from PTC • very similar shapes PTC ↔ FDC • σ a third of HL-LHC O MC 30.10.2019 Nonlinear-Corrector Misalignments 12