MKI transverse impedance measurements Vlachodimitropoulos Vasilis Acknowledgements Mike

MKI transverse impedance measurements Vlachodimitropoulos Vasilis Acknowledgements: Mike Barnes, Yves Sillanoli

Outline ØCST simulations Ø 2 -wire method ØDisplaced wire method 11/02/2019 Impedance Meeting 2

MKI transverse impedance simulations Ø A few modes up to 50 MHz Ø Above 50 MHz their amplitude is significantly lower Ø Wakelength used: 750 m -> longer wakelengths for better frequency resolution may be needed 11/02/2019 Impedance Meeting 3

2 -wire method 11/02/2019 Impedance Meeting 4

The 2 -wire method Ø Wires were displaced horizontally/vertically to estimate horizontal/vertical dipolar impedance Ø 180 -hybrid to create the phase difference – fourth port matched to 50Ω Ø Information only about dipolar impedance Ø For further info on the method see [1] Matching resistors 180°-hybrid 11/02/2019 DUT Matching resistors VNA Impedance Meeting 180°-hybrid 5

Physical Realization (for vertically displaced wires)Thanks to BE-RF-BR Hybrid Connections 180° output Matching Resistors for the hybrids! 0° output Matched Output VNA output 11/02/2019 Impedance Meeting 6

Signal post-processing Ø Along most of its length, the MKI beam screen is symmetric under 90° rotation – asymmetry only at one end (capacitively couple – beam input) due to their arrangement (staggered upper half and taped lower half) Ø Therefore, the mismatch of the set-up and the corresponding “noise” in the two set-ups will be the very similar (left figure) Ø By subtracting the two signals the noise is removed and only the real signal remains (to a good approximation!) Ø If SD = SX – SY -> negative peaks: horizontal impedance modes, positive peaks: vertical impedance modes 11/02/2019 Impedance Meeting 7

Comparison to simulations ØUse standard conversion formulas from [1] – in the present work the log formula was used ØUse Panofsky-Wenzel theorem to convert to transverse impedance ØVery good agreement between measurements and simulations both in resonant frequencies and in amplitudes 11/02/2019 Impedance Meeting 8

Displaced wire method 11/02/2019 Impedance Meeting 9

The displaced wire method Ø Measure longitudinal impedance in a symmetric structure as a function of the displacement of the wire (x, y) from the center of the structure Ø Displace wire in single plane -> perform quadratic fit to determine the quadratic coefficient Ø Estimate generalized impedances from measured data Schematic of measurement set-up 11/02/2019 Matching resistors DUT Matching resistors VNA Impedance Meeting 10

Displaced wire method - Results ØMeasure s 21 parameter – data were corrected by their maximum value to account for additional losses (e. g. in the matching resistors) ØConvert to longitudinal impedance using one of the standard formulas (see ref [1]) ØIn this work the log formula was used Vertically displaced wire 11/02/2019 Horizontally displaced wire Impedance Meeting 11

Displaced wire method – Results (continued) ØFor a single frequency perform a quadratic fit to estimated impedance ØRepeat for all frequencies to estimate the generalized impedance Vertically displaced wire Horizontally displaced wire f = 45 MHz 11/02/2019 f = 9. 8 MHz Impedance Meeting 12

Comparison to simulations ØCompare the generalized impedances as estimated from displaced wire method and simulations ØPartial agreement between measurements and simulations ØDisagreement is noticed in the quadrupolar modes of the MKI 11/02/2019 Impedance Meeting 13

Comparison to simulations and 2 -wire method ØCompare the sum of generalized impedances as estimated from the two measurement methods and the simulations 11/02/2019 Impedance Meeting 14

Remarks on displaced wire method ØTime constraints and workload in the workshop didn’t allow for an optimal measurement set-up -> wire displacement was performed and verified manually -> Qualitatively good results but accuracy may improve with a better set-up ØGood agreement with simulations and 2 -wire method for the dipolar transverse impedance ØQuadrupolar impedance that was predicted from simulations was not measured -> Something wrong with simulations or set-up? To be further understood! ØEven after calibration the VNA used for measurements had a S 21 signal for disconnected cables of ~-90/-80 d. B for frequencies below ~8 MHz, compared to ~-120/-100 d. B for higher frequencies 11/02/2019 Impedance Meeting 15

Conclusion ØTwo standard methods were used to measure the MKI’s transverse impedance: 2 -wire and displaced wire method ØGood agreement was found between measurement and simulations for the dipolar transverse impedance in both planes – discrepancies in quadrupolar impedance still to be understood ØResults give confidence in the simulation model ØExperience gained can be used in measuring future MKI designs such as the MKI-Cool! 11/02/2019 Impedance Meeting 16

Thank you for your attention!

References • T. Kroyer, F. Caspers, E. Gaxiola, “Longitudinal and Transverse Wire Measurements for the Evaluation of Impedance Reduction Measures on the MKE extraction kicker”, AB-Note-2007 -028 12/09/2021 24 th IWG meeting 18