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Measuring Beta Functions with K-Modulation Method at Individually Powered Quadrupoles

The K-Modulation method offers an innovative approach to measure beta functions at locations with individually powered quadrupoles. This method is essential for locations where the phase advance between Beam Position Monitors (BPMs) is non-optimal, such as IR4, allowing for accurate measurements crucial for emittance determination. By varying quadrupole strength and observing corresponding tune changes, this alternative method enhances measurement precision despite limitations such as tune noise and time efficiency. Future updates aim to integrate the K-Modulation tool into the LHC control system, improving online analysis capabilities.

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Measuring Beta Functions with K-Modulation Method at Individually Powered Quadrupoles

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  1. K-Modulation Plans M. Kuhn, B. Dehning, R. Garcia, V. Kain, R. Steinhagen, G. Trad

  2. Motivation Individually powered quadrupoles IP4 • Alternative method for measuring b functions at locations with individually powered quadrupoles • Essential for locations with non-optimum phase advance between BPMs for turn-by-turn phase advance measurement • e.g. b*, IR4 • Model independent • Example IR4: • Essential for absolute emittance measurement

  3. K-Modulation Method CAVEAT: NOT SUITABLE TO MEASURE BETA FUNCTIONS AROUND THE WHOLE RING - TOO TIME CONSUMING • Method: • Vary quadrupole strength • Measure consequent beam tune change D • determine b at quadrupole location • Average b function along magnet length : • From trace of transport matrix for one turn • For small tune changes far from integer and half integer tune resonances: Accurate measurement of Dand precise knowledge of D

  4. Example – 2012 Measurements (1) G. Trad • Measured b at quadrupoles in IR4 at injection, flattop and with squeezed optics • One quadrupole at a time • “manual” measurement via LSA Trim Editor • Required beam conditions: • Transverse damper off • Injection tunes (less coupling) • Only few bunches • Offline analysis, transported measured b values at quadrupole to transverse profile monitor locations

  5. Example – 2012 Measurements (2) Quadrupole strength k current I varied in steps Tune noise ~ 10-3!!! Linear fit to determine DQ ( DI ) transfer function from LSA to determine b G. Trad

  6. Example – 2012 Measurements (3) • Quadrupoleb beam instrumentation location b • Analytical method: interpolation via transfer matrices • Matching with MADX • Results: errors reduced wrt turn-by-turn phase advance measurement, but still large… G. Trad

  7. Limitations (1) Current application • LSA look-and-feel • Uses LSA trim client and transfer functions • Trim range to be entered in k (would desire tune) • No online tune plot • “Manual” trims on k – time consuming, error prone • Application was in pipeline, could not be fully debugged • Application offered only basic functionality

  8. Limitations (2) – Tune Precision require total tune change in range of 10-2 for k-modulation 30 s • Tune noise level with damper off: 10-3 require total tu change in rang of 10-2 for k-modulation • (Max. possible tune change limited by 3rdorder resonance) • Time estimate per beam mode ~ 10 min • 1 – 2 min per quadrupole • Machine set up to reduce tune noise (coupling correction, tune separations, …) most time consuming • Parasitic measurements with physics beam excluded • Unless using sacrificial 6 bunches and excitation • (K-modulation with colliding beams not possible)

  9. Limitations (3) – Knowledge of Dk Measurement of the transfer function for MQM (similar for MQY) Example: MQM.7R4.B1 23 units = 0.23 % 450 GeV 4 TeV W. Venturini Absolute error on transfer function~ 0.1 – 0.2 % Transfer function error from hysteresis~ 0.2 % or smaller Total estimated error on b~ 10 % (mainly due to tune noise)

  10. Plans for K-Modulation Tool Post LS1 • Modify and debug existing application • Add tune acquisition + filtering • Possibility to enter steps in “tune change” instead of trims on k, using LSA knowledge • Interpolation – calculate b at any point • Integrated into LHC control system (LSA, JMAD,…) • ONLINE ANALYSIS • Additional measurement mode: SINUSOIDAL EXCITATION • Smaller amplitudeand higher frequency than for step function • More quadrupoles at the same time with different frequencies • Details (QPS limits,…) to be checked

  11. K-Modulation Tool First Preview

  12. Sinusoidal K-Modulation ATS-Note-2011-043 MD Current time • Example measurements (2010): • Sinusoidal strength modulation to quadrupole directly at power converter • Power converter parameters: number of periods, amplitude, frequency • …triplet model more complicated • Fit tune response with

  13. Sinusoidal Excitation - Simulation fsampling= 1 Hz foscillation = 0.02 Hz Width ~ 23 units (very pessimistic) • Hysteresis has no measurable effect on b function determination • Noisy tune gives large b errors ~ 5 % error! with 10-3 tune noise A first look at hysteresis

  14. Conclusion • Alternative method for measuring b functions: k-modulation • For locations with individually powered quadrupoles • Was successfully used in 2011/12 • No dedicated tools operational • Results only obtainable offline • b function measurement accuracy via k-modulation in the LHC mainly limited by tune noise • Online tool for K-modulation planned for post LS1 • Will also offer sinusoidal excitation of quadrupoles • Application to be tested in the SPS in 2014

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