MEW Thursday Meeting
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1 MEW Thursday Meeting H. Day, F. Caspers, A. Grudiev, E. Metral, B. Salvant, T. Mastoridis, P. Baudrenghien November 22, 2011
2 Goal: Estimate the beam induced heating on the collimator, particularly with respect to the heating of the ferrites used to damp cavity modes Use both analytical (gaussian) bunch spectra and those measured using the RF system in the LHC Also useful to recombine the impedances from the eigenmode simulations to obtain the broadband impedance for comparison to time domain simulations to ensure we aren t missing any important modes R s Z(f ) = (1) 1 + jq (f /f res f res /f ) where Z is the longitudinal impedance, R s the shunt impedance, Q the quality factor and f res the frequency of the cavity mode
3 TCTP Eigenmode Results f (MHz) Q R/Q long R s (Ω)
4 TCTP Eigenmode Results f (MHz) Q R/Q long R s (Ω)
5 TCTP Eigenmode Results f (MHz) Q R/Q long R s (Ω)
6 TCTP Eigenmode Results f (MHz) Q R/Q long R s (Ω)
7 TCTP Broadband Impedance Real Impedance Imaginary Impedance Impedance (Ω) Frequency (Hz) 1e9 Figure 1: Longitudinal impedance of the TCTP Collimator from summing cavity modes
8 Heating Estimates We have two ways of estimating heating We can assume a gaussiaan bunch distribution and assume that each cavity mode falls exactly on a bunch harmonic ( q P loss = t b ) 2 R sexp ( ( ωσz ) ) 2 c where q = 18.4nC is the bunch charge, t b = 50ns is the bunch spacing, R s is the shunt impedance, ω the mode frequency, σ z = 7.5cm the RMS bunch length, c the speed of light (2)
9 We can calculate the broadband impedance from all resonances and convolve with a calculated/measured bunch sprectrum and sum across a given frequency range [ ] P loss = I 2 R = 2n bunch (N b ef 0 ) 2 Z (kω s ) P (kω s ) (3) where P loss is the total power lost, n bunch the number of bunches, N b the bunch population, e the electron charge, f 0 the bunch repetition frequency, Z the real longitudinal impedance and P the power spectrum. We can also take measured multibunch spectra and simply convolute the spectrum with the impedance (Thanks to Themis and Phillipe for the spectral measurements) k=1
10 Heating Estimates Spectrum Total Power Loss (W) Gaussian 0.92 Meas (R. Steinhagen - Single bunch spectra) 9.45 Meas (Before Ramp - Multibunch spectra) 61 Meas (Ramp - Multibunch spectra) 57 Meas (Flat Top - Multibunch spectra) 58 Meas (Squeeze - Multibunch spectra) 56 Meas (Adjust - Multibunch spectra) 56 Meas (Stable Beams - Multibunch spectra) 56
11 0 20 Real Impedance Imaginary Impedance S(f) (db) Ramp P loss = W Impedance (Ω) Cumulative Power Loss (W) Frequency (Hz) 1e9 (a) Frequency (Hz) 1e9 (b) Power Loss (W) Frequency (Hz) 1e9 (c) Figure 2: 2(a) Power Spectra overlaid with impedance, 2(b) cumulative power loss and 2(c) frequency dependent power loss of spectra during ramp
12 Comparison of single bunch and multibunch spectra Figure 3: Comparison of single bunch and multibunch spectra
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