Amplitude Detuning from misaligned Triplets and IR multipolar Correctors Joschua Dilly Humboldt Universit¨ at zu Berlin, CERN 18.02.2020
Outline Setup • – Motivation – Misaligning Correctors – Misaligning Triplets – Simulation and Measurement details Results • – Corrector Misalignments – Triplet Misalignments – Conclusion 18.02.20 Joschua Dilly Amp.Det. from Misalignments 1
Outline Setup • – Motivation – Misaligning Correctors – Misaligning Triplets – Simulation and Measurement details Results • – Corrector Misalignments – Triplet Misalignments – Conclusion 18.02.20 Joschua Dilly Amp.Det. from Misalignments 1
Motivation With the advent of the HL-LHC, new triplets with larger aperture and new corrector packages 1 , for corrections of high-order non-linear magnetic field errors, will be installed in the low β Interaction Points (IP1 & IP5), which will require precise orbit control. The goal of this study is, to investigate the influence of the expected remaining orbit deviations 2 in the triplets and the associated non-linear corrector packages on Amplitude Detuning. A preliminary study showed large detuning, which turned out to be a bug, but triggered this more extensive study. 1O. Br¨ uning et al - LHC Report 504: Dynamic aperture studies for the LHC separation dipoles , 2004. https://cds.cern.ch/record/742967 2D. Gamba et al - IP ORBIT CORRECTION UPDATE FOR HL-LHC , IPAC, 2018. http://cds.cern.ch/record/2648556 18.02.20 Joschua Dilly Amp.Det. from Misalignments 2
Misaligning Correctors LHC HL-LHC Figure: Schematic representation of half of the IR region in the accelerator. � setup LHC/HL-LHC Sequence � 60 WISE error realizations: octupole, (skew-)decapole and (skew-)dodecapole to MQX and MBX � calculate triplet corrections for the MCX � 50 misalignment realizations for MCX , uniformly distributed ∈ [ − 1 mm , 1 mm] ⇒ check Amplitude Detuning 18.02.20 Joschua Dilly Amp.Det. from Misalignments 3
Misaligning Correctors LHC HL-LHC Figure: Schematic representation of half of the IR region in the accelerator. � setup LHC/HL-LHC Sequence � 60 WISE error realizations: octupole, (skew-)decapole and (skew-)dodecapole to MQX and MBX � calculate triplet corrections for the MCX � 50 misalignment realizations for MCX , uniformly distributed ∈ [ − 1 mm , 1 mm] ⇒ check Amplitude Detuning 18.02.20 Joschua Dilly Amp.Det. from Misalignments 3
Misaligning Triplets LHC HL-LHC Figure: Schematic representation of half of the IR region in the accelerator. � setup LHC/HL-LHC Sequence � 60 WISE error realizations: octupole, (skew-)decapole and (skew-)dodecapole MQX and MBX � calculate triplet corrections for the MCX � 50 misalignment realizations for Q1-Q3 , truncated-gaussian distributed σ = 0 . 4 mm (0 . 8 mm Q3), cut at 2.5 σ ⇒ check Amplitude Detuning 18.02.20 Joschua Dilly Amp.Det. from Misalignments 4
Misaligning Triplets LHC HL-LHC Figure: Schematic representation of half of the IR region in the accelerator. � setup LHC/HL-LHC Sequence � 60 WISE error realizations: octupole, (skew-)decapole and (skew-)dodecapole MQX and MBX � calculate triplet corrections for the MCX � 50 misalignment realizations for Q1-Q3 , truncated-gaussian distributed σ = 0 . 4 mm (0 . 8 mm Q3), cut at 2.5 σ ⇒ check Amplitude Detuning 18.02.20 Joschua Dilly Amp.Det. from Misalignments 4
Setup Measurements 1 Simulation LHC HL-LHC (v1.3) LHC Energy 6 . 5 TeV 7 . 0 TeV 6 . 5 TeV β ∗ 30 cm round optics Orbit flat orbit Q x , Q y 0.31, 0.32 MO Power off (see later) off b 4 corrected yes 1 in MD3311 http://cds.cern.ch/record/2692810 18.02.20 Joschua Dilly Amp.Det. from Misalignments 5
Calculate Detuning Detuning: Feeddown: ∂ Q x = K 4 32 π β 2 K 5 → K 4 = dx · K 5 ∂ 2 J x x K 5 S → K 4 = − dy · K 5 S ∂ Q x = − K 4 16 π β x β y K 6 → K 4 = 1 ∂ 2 J y dx 2 − dy 2 � � · K 6 2 ∂ Q y = K 4 32 π β 2 K 6 S → K 4 = − dx · dy · K 6 S ∂ 2 J y y K n ( S ): Integrated (skew) magnetic field strength, with n = 4 ⇒ octupole etc. dx , dy : Beam offset from element center J x , y : Action 18.02.20 Joschua Dilly Amp.Det. from Misalignments 6
Outline Setup • – Motivation – Misaligning Correctors – Misaligning Triplets – Simulation and Measurement details Results • – Corrector Misalignments – Triplet Misalignments – Conclusion 18.02.20 Joschua Dilly Amp.Det. from Misalignments 6
Subsection 1 Corrector Misalignments 18.02.20 Joschua Dilly Amp.Det. from Misalignments 6
Misalign LHC Correctors Simulation Fit Gauss before misalignments measured Meas.: (0.8 ± 0.5) · 10 3 m − 1 Sim.: (6.9 ± 0.5) · 10 3 m − 1 100 Samples 50 − σ + σ 0 0 2 4 6 8 � 10 3 m − 1 � ∂Q x /∂ 2 J x 3 1 � Shown: result for Beam 1 direct horizontal term � Simulation ”offset” from zero due to amplitude detuning from arc-sextupoles � Gaussian detuning distribution (from uniform misalignments) ⇒ compare for both beams and all detuning components 18.02.20 Joschua Dilly Amp.Det. from Misalignments 7
Misalign LHC Correctors B1 before misalignment B2 before misalignment B1 misaligned B2 misaligned B1 measured B2 measured 10 5 1 ] Detuning [10 3 m 0 5 10 15 Q x / (2 J x ) Q y / (2 J y ) Q x / (2 J y ) � amplitude detuning spread from misalignments is small compared to expected detuning without misaligments � also smaller or of similar order as measured amplitude detuning � contribution only from feeddown from b 6 as, this is the only corrector 18.02.20 Joschua Dilly Amp.Det. from Misalignments 8
Misalign HL-LHC Correctors B1 before misalignment B2 before misalignment B1 misaligned B2 misaligned B1 measured B2 measured 10 5 Detuning [10 3 m − 1 ] 0 − 5 − 10 − 15 ∂ Q x /∂ (2 J x ) ∂ Q y /∂ (2 J y ) ∂ Q x /∂ (2 J y ) � amplitude detuning spread from misalignments is small compared to expected detuning without misalignments � also smaller or of similar order as measured amplitude detuning � contribution from feeddown from b 5 , a 5 , b 6 , and a 6 (see appendix) 18.02.20 Joschua Dilly Amp.Det. from Misalignments 9
Subsection 2 Triplet Misalignments 18.02.20 Joschua Dilly Amp.Det. from Misalignments 9
Misalign LHC Triplets B1 before misalignment B2 before misalignment B1 misaligned B2 misaligned B1 measured B2 measured 10 5 1 ] Detuning [10 3 m 0 5 10 15 Q x / (2 J x ) Q y / (2 J y ) Q x / (2 J y ) � amplitude detuning spread from misalignments is of equal order compared to expected detuning without misalignments, but not problematic � large spread compared to HL-LHC; reasons under investigation (possibly: cancellation due to shorter magnets / independent misalignments, differences in error-tables) 18.02.20 Joschua Dilly Amp.Det. from Misalignments 10
Misalign HL-LHC Triplets B1 before misalignment B2 before misalignment B1 misaligned B2 misaligned B1 measured B2 measured 10 5 1 ] Detuning [10 3 m 0 5 10 15 Q x / (2 J x ) Q y / (2 J y ) Q x / (2 J y ) � amplitude detuning spread from misalignments is small compared to expected detuning without misalignments � also spread smaller or of similar order as measured amplitude detuning 18.02.20 Joschua Dilly Amp.Det. from Misalignments 11
Misalign Triplets ... and compare to powered MO’s B1 before misalignment B2 before misalignment B1 misaligned B2 misaligned B1 Sim. w/ MO 300 A B2 Sim. w/ MO 300 A 100 � MO powering of 1 ] LHC 50 Detuning [10 3 m 300 A causes amplitude 0 detuning to 50 increase from Q x / (2 J x ) Q y / (2 J y ) Q x / (2 J y ) ∼ 5 · 10 3 m − 1 up to B1 before misalignment B2 before misalignment B1 misaligned B2 misaligned ∼ 100 · 10 3 m − 1 B1 Sim. w/ MO 300 A B2 Sim. w/ MO 300 A 100 in the direct HL-LHC 1 ] terms. 50 Detuning [10 3 m 0 50 Q x / (2 J x ) Q y / (2 J y ) Q x / (2 J y ) 18.02.20 Joschua Dilly Amp.Det. from Misalignments 12
Conclusion � Expected amplitude detuning spread is larger from investigated triplet misalignment than from corrector misalignments in the LHC . � Expected amplitude detuning spread is marginally larger from investigated corrector misalignments than from triplet misalignments in the HL-LHC . � The investigated misalignments, with spreads of ± 1 mm in the MCX and ± 0 . 4 mm(0 . 8 mm) in the MQX do not cause problematic amplitude detuning in either machine. � Amplitude detuning is negligible when comparing to expected detuning from MO powering. � Expected detuning from triplet-misalignments is smaller for HL-LHC than for LHC for the same β ∗ = 30 cm. 18.02.20 Joschua Dilly Amp.Det. from Misalignments 13
Thank you for your attention! 18.02.20 Joschua Dilly Amp.Det. from Misalignments 14
Outline Setup • – Motivation – Misaligning Correctors – Misaligning Triplets – Simulation and Measurement details Results • – Corrector Misalignments – Triplet Misalignments – Conclusion 18.02.20 Joschua Dilly Amp.Det. from Misalignments 14
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