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POWER SPECTRA COMPARISON BETWEEN DIFFERENT TYPES OF LONGITUDINAL BUNCH PROFILES

POWER SPECTRA COMPARISON BETWEEN DIFFERENT TYPES OF LONGITUDINAL BUNCH PROFILES FOR THE LHC BUNCH AT 3.5 TEV. Elias Métral. Examples of measured bunch spectra Comparison of 4 very different longitudinal bunch profiles and corresponding power spectra

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POWER SPECTRA COMPARISON BETWEEN DIFFERENT TYPES OF LONGITUDINAL BUNCH PROFILES

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  1. POWER SPECTRA • COMPARISON BETWEEN DIFFERENT TYPES • OF LONGITUDINAL BUNCH PROFILES • FOR THE LHC BUNCH AT 3.5 TEV EliasMétral • Examples of measured bunch spectra • Comparison of 4 very different longitudinal bunch profilesand corresponding power spectra • Comparison of several longitudinal bunch profiles close to Gaussian ones (BUT with finite tails), and corresponding power spectra • What is the distribution fitting best (one) measurement? • Analysis by ThemisM from BQM data and associated spectrum • Conclusion 16

  2. EXAMPLES OF MEASURED BUNCH SPECTRA • Measurements on B1 by Themis and Philippe on fill # 2261 It was mentioned that it is in fact the power spectrum Reminder on the Average power deposited per unit length [W/m] 16

  3. 4 THEORETICAL LONGITUDINAL BUNCH PROFILES 16

  4. CORRESPONDING POWER SPECTRA (1/2) 16

  5. CORRESPONDING POWER SPECTRA (2/2) 16

  6. COMPARING LONGITUDINAL BUNCH PROFILES CLOSE TO GAUSSIAN BUT WITH FINITE TAILS (1/6) Family of distributions, depending on nand converging to a Gaussian when n goes to infinity Gaussian n= 5 n= 1

  7. COMPARING LONGITUDINAL BUNCH PROFILES CLOSE TO GAUSSIAN BUT WITH FINITE TAILS (2/6) Power spectrum Gaussian n= 5 16

  8. COMPARING LONGITUDINAL BUNCH PROFILES CLOSE TO GAUSSIAN BUT WITH FINITE TAILS (3/6) Power spectrum Gaussian n= 4 16

  9. COMPARING LONGITUDINAL BUNCH PROFILES CLOSE TO GAUSSIAN BUT WITH FINITE TAILS (4/6) Power spectrum Gaussian n= 3 16

  10. COMPARING LONGITUDINAL BUNCH PROFILES CLOSE TO GAUSSIAN BUT WITH FINITE TAILS (5/6) Power spectrum Gaussian n= 2 16

  11. COMPARING LONGITUDINAL BUNCH PROFILES CLOSE TO GAUSSIAN BUT WITH FINITE TAILS (6/6) Power spectrum Gaussian n= 1 16

  12. WHAT IS THE DISTRIBUTION FITTING BEST (ONE) MEASUREMENT? Theoretical power spectrum for the Water-bag bunch with Measurements on B1 by Themis and Philippe on fill # 2261

  13. ANALYSIS BY THEMIS FROM BQM DATA • The BQM reports the full-width at half maximum (FWHM) scaled by sqrt(2/ln(2)). The scaling is set to report a 4-sigma width assuming a Gaussian bunch • If we assume a Water-bag bunch distribution, the FWHM equals tau*sqrt(3)/2, where tau is the full width of the Water-bag model. As such, for a Water-bag bunch, the BQM will report tau*sqrt(3/2/ln(2)) • Therefore, a reported value of 1.1 ns (from the BQM) corresponds to a width of just 0.75 ns for the Water-bag model • The BQM reported bunch lengths at the end of the ramp for fill 2261 of 1.2 and 1.15 ns for B1, B2 respectively. These values correspond to a bunch width of 0.81 and 0.78 ns respectively for a Water-bag bunch • =>Seems that the bunch spectra together with the BQM data are consistent with a bunch distribution close to a Water-bag with ~ 0.75 – 0.8 ns (full bunch length at the base)

  14. WHAT IS THE PREDICTED POWER SPECTRUM FOR THE VALUE DEDUCED BY THEMIS FROM BQM => ~ 0.8 ns? Theoretical power spectrum for the Water-bag bunch with Measurements on B1 by Themis and Philippe on fill # 2261 Theoretical power spectrum for the Water-bag bunch with

  15. CONCLUSION • The best fit of (one of) the measured power spectra in stable beams (of the previous slide) is obtained for a Water-bag bunch with a total bunch length (at the base) of 0.75 ns • This distribution is very different from Gaussian-types with finite tails • According to the analysis done by ThemisM from BQM data, it seems that the bunch spectra together with the BQM data are consistent with a bunch distribution close to a Water-bag with a full bunch length at the base close to 0.75 ns (a reported value of 1.1 ns from the BQM corresponds to a width of just 0.75 ns for the Water-bag model) • Comment from AlexeyB: Theoretically, the distribution after the emittance blow-up must be water-bag if the width of the excitation line is much smaller than its detuning from 2*(maximal synchrotron frequency) => To be followed-up (and discussed also with J. Tuckmantel et at.)

  16. ACKNOWLEDGEMENTS • Many thanks to AlexejGrudiev, AlexeyBurov, Benoit Salvant, Carlo Zannini, Elena Shaposhnikova, HannesBartosik, Hugo Alistair Day, NicoloBiancacci‎, Olav EjnerBerrig, Philippe Baudrenghien, ThemistoklisMastoridis, etc. for very interesting discussions => To be followed up

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