Second Order Dispersion Analysis Status Acknowledgements Felix Carlier

Second Order Dispersion Analysis - Status Acknowledgements Felix Carlier, Jaime Coello de Portugal, Joschua Dilly, Elena Fol, Ana Garcia-Tabares, Michael Hofer, Lukas Malina, Ewen Maclean, Tobias Persson, Rogelio Tomas, Andreas Wegscheider J ACQUELINE K EINTZEL T U V IENNA, A USTRIA CERN, G ENEVA OMC Meeting 04. April 2019

Introduction • Change in orbit due to momentum offset dp/p (δ) • Second order dispersion (SOD) term (η 1) • Quadratic fit instead of linear fit (orbit offset over momentum offset) • Leads to beam size growth as OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 2

Analytical Formula • Paper by A. Franchi et al. • Analytic Formulas for the Rapid Evaluation of the Orbit Response Matrix and Chromatic Functions from Lattice Parameters in Circular Accelerators, ar. Xiv: 1711. 06589 v 2, 2018 • Paper by J. P. Delahaye et al. • Variation of the Dispersion Function, Momentum Compaction Factor and Damping Partition Numbers with Particle Energy Deviation, Part. Accel. 18, 1985 • Approximation: Ideal Lattice, no coupling, no Xing • ηx, 2 generated by dipoles, quads and sextupoles • ηy, 2 equals zero In real lattice • Skew elements • Higher order terms (higher order RDTs) • Momentum dependence of coupling OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 3

Analysed Data • Correct crossing scheme did not always agree with OMC/OP Logbook (checked with timber and online-model) • E. g. no entry in logbook regarding Beam 2 measurements at 3 rd Nov. ’ 18 OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 4

SOD in ATS Optics • ηy, 1 corrected with orbit bumps correct for ηy, 2 too (red line) • No measurements with non-zero Xing • ηy, 2 damped without orbit bumps (blue line) • model calculations only • Independent of sextupole strengths and crossing angle • possibility to measure in Run III • Works best for 90° phase advance OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 5

Results th 10 OMC MEETING 04. APR 2019 May 2016 - protons JACQUELINE KEINTZEL SECOND ORDER DISPERISON 6

Results th 10 May 2016 - protons residual orbit? OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 7

Results th 10 May 2016 - protons Vertical dispersion up to two times larger OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 8

Results th 10 OMC MEETING 04. APR 2019 May 2016 - protons JACQUELINE KEINTZEL SECOND ORDER DISPERISON 9

Results th 10 May 2016 - protons Peaks around IR 3, IR 7, IR 4 OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 10

Results th 10 OMC MEETING 04. APR 2019 May 2016 - protons JACQUELINE KEINTZEL SECOND ORDER DISPERISON 11

Results th 10 May 2016 - protons Same qualitative behaviour for normalised dispersion OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 12

Results rd 3 OMC MEETING 04. APR 2019 Oct. 2016 - ATS JACQUELINE KEINTZEL SECOND ORDER DISPERISON 13

Results rd 3 Oct. 2016 - ATS Larger peaks at IR 1, IR 5 Bump around IR 6 OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 14

rd 3 Results Nov. 2018 - ions OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 15

rd 3 Results Nov. 2018 - ions OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 16

Conclusion • Various measurements analysed • SOD often higher than predicted in IRs • Coupling • Orbit discrepancies • … • SOD in ATS is self-damping measurement in Run III • Normalised vertical dispersion measurements in Run III • Test analytical formula on LHC, maybe extension necessary ongoing OMC MEETING 04. APR 2019 JACQUELINE KEINTZEL SECOND ORDER DISPERISON 17

Thank you! J ACQUELINE K EINTZEL T U V IENNA, A USTRIA CERN, G ENEVA Acknowledgements Felix Carlier, Jaime Coello de Portugal, Joschua Dilly, Elena Fol, Ana Garcia-Tabares, Michael Hofer, Lukas Malina, Ewen Maclean, Tobias Persson, Rogelio Tomas, Andreas Wegscheider OMC Meeting 04. April 2019