1. Elias Métral, APC meeting, 09/06/20051/15 E. Métral (10 min) AMPLITUDE AND POWER SPECTRA COMPARISON BETWEEN DIFFERENT TYPES OF LONGITUDINAL BUNCH PROFILES FOR THE SPS MKE KICKER HEATING u This is a follow-up of the APC presentation of Jan Uythoven on 17/09/04 (presented at RLC meeting on 01/10/04) u Theory u Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven)

2. Elias Métral, APC meeting, 09/06/20052/15 APC presentation of Jan Uythoven on 17/09/04 (1/2) Bump

3. Elias Métral, APC meeting, 09/06/20053/15 For the operational scenarios presented at APC on 03/10/03 only (afterwards real measured spectra were used) APC presentation of Jan Uythoven on 17/09/04 (2/2)

4. Elias Métral, APC meeting, 09/06/20054/15 THEORY (1/5)

5. Elias Métral, APC meeting, 09/06/20055/15 THEORY (2/5) Bumps

6. Elias Métral, APC meeting, 09/06/20056/15 THEORY (3/5) The bumps disappear in the power spectra

7. Elias Métral, APC meeting, 09/06/20057/15 Computation of the power loss in the case of a broad-band resonator impedance (fit used by Elena Shaposhnikova for the longitudinal impedance of 1 SPS MKE kicker, Chamonix XIII, p. 47) THEORY (4/5)

8. Elias Métral, APC meeting, 09/06/20058/15 THEORY (5/5) Average power deposited per unit length [W/m] from theory u Parabolic amplitude density = 893 u Parabolic line density = 677 u Gaussian amplitude density = 605 u Water-bag bunch = 530  Power (Parabolic amplitude density) = 1.48 × Power (Gaussian)  Power (Parabolic line density) = 1.12 × Power (Gaussian)  Power (Water-bag bunch) = 0.88 × Power (Gaussian) 

9. Elias Métral, APC meeting, 09/06/20059/15 Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (1/6)

10. Elias Métral, APC meeting, 09/06/200510/15 Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (2/6)

11. Elias Métral, APC meeting, 09/06/200511/15 Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (3/6) The bump is well fitted here

12. Elias Métral, APC meeting, 09/06/200512/15 Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (4/6) The bump is well fitted here

13. Elias Métral, APC meeting, 09/06/200513/15 Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (5/6) u Spectrum2003@8p4sec = 509 u Spectrum2003@16p8sec = 958 u Spectrum2004@17sec = 593 u Spectrum2004@34sec = 590 Average power deposited per unit length [W/m] from measured spectra  ~600 W/m for 2004, with more stable spectra

14. Elias Métral, APC meeting, 09/06/200514/15 Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (6/6) For 4  72 bunches, Jan finds ~600 W/m before acceleration  In good agreement with the previous estimates

15. Elias Métral, APC meeting, 09/06/200515/15 CONCLUSION u Good agreement between Jan and myself u The estimates of Jan are made using the real measured spectra (one cannot do better than that if the spectra measurement is reliable) u ~600 W/m are found for 4  72 bunches, with 1.2  10 11 p/b, using either the measured spectrum or the measured bunch length (0.7 ns rms) assuming a Gaussian distribution u No bumps appear in the amplitude spectrum for a Gaussian bunch, but these bumps are not important for the power loss as they disappear in the power spectrum!