Elias Métral, APC meeting, 09/06/2005

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E. Métral (10 min)E. Métral (10 min)

AMPLITUDE AND POWER SPECTRA

COMPARISON BETWEEN DIFFERENT TYPES

OF LONGITUDINAL BUNCH PROFILES

FOR THE SPS MKE KICKER HEATING

This is a follow-up of the APC presentation of Jan Uythoven on 17/09/04 (presented at RLC meeting on 01/10/04)

Theory Comparison with measured spectra in 2003 and 2004 (given

by Jan Uythoven)

Elias Métral, APC meeting, 09/06/2005

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APC presentation of Jan Uythoven on 17/09/04 (1/2)APC presentation of Jan Uythoven on 17/09/04 (1/2)

Bump

Elias Métral, APC meeting, 09/06/2005

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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)APC presentation of Jan Uythoven on 17/09/04 (2/2)

Elias Métral, APC meeting, 09/06/2005

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THEORY (1/5)THEORY (1/5)

1.5 1 0.5 0.5 1 1.5

0.5

1

1.5

2

2/b

4bb density Line

density amplitude Parabolic

density line Parabolicdensity amplitudeGaussian

bunch bag-Water

Elias Métral, APC meeting, 09/06/2005

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200 400 600 800

0.2

0.4

0.6

0.8

1

MHzf

spectrumAmplitude

ns7.0

4bdensity amplitude Parabolic

density line Parabolic

density amplitudeGaussian

bunch bag-Water

THEORY (2/5)THEORY (2/5)

Bumps

Elias Métral, APC meeting, 09/06/2005

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200 400 600 800

0.2

0.4

0.6

0.8

1

MHzf

spectrumPowerTHEORY (3/5)THEORY (3/5)

The bumps disappear in the power spectra

Elias Métral, APC meeting, 09/06/2005

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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)

200 400 600 800

1000

2000

3000

4000

5000

6000

kΩ6sR

0.95QMHz600rf

MHzf

lZRe

THEORY (4/5)THEORY (4/5)

Elias Métral, APC meeting, 09/06/2005

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THEORY (5/5)THEORY (5/5)

Average power deposited per unit length [W/m] from theory

Parabolic amplitude density = 893 Parabolic line density = 677 Gaussian amplitude density = 605 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)

ns7.04 b

p/b102.1 11bN

bunches724 M

m 1.66 length Kicker L

LZIMP SBlossbloss /2

1

00 rumPowerSpectRe2p

lSBloss fpfpZZ

0feNI bb

Elias Métral, APC meeting, 09/06/2005

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Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (1/6)

200 400 600 800

0.2

0.4

0.6

0.8

103@8p4secSpectrum20

MHzf

spectrumAmplitude

ns9.0

density amplitude Parabolic

Elias Métral, APC meeting, 09/06/2005

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Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (2/6)

200 400 600 800

0.2

0.4

0.6

0.8

103@16p8secSpectrum20

MHzf

spectrumAmplitude

?ns85.0

Elias Métral, APC meeting, 09/06/2005

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Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (3/6)

200 400 600 800

0.2

0.4

0.6

0.8

104@17secSpectrum20

MHzf

spectrumAmplitude

ns7.0

The bump is well fitted here

Elias Métral, APC meeting, 09/06/2005

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Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (4/6)

200 400 600 800

0.2

0.4

0.6

0.8

104@34secSpectrum20

MHzf

spectrumAmplitude

ns7.0

The bump is well fitted here

Elias Métral, APC meeting, 09/06/2005

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Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (5/6)

Spectrum2003@8p4sec = 509 Spectrum2003@16p8sec = 958 Spectrum2004@17sec = 593 Spectrum2004@34sec = 590

Average power deposited per unit length [W/m] from measured spectra

~600 W/m for 2004, with more stable spectra

Elias Métral, APC meeting, 09/06/2005

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Comparison with measured spectra in 2003 and 2004 (given by Jan Uythoven) (6/6)

For 472 bunches, Jan finds ~600 W/m before acceleration In good agreement with the previous estimates

Elias Métral, APC meeting, 09/06/2005

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CONCLUSIONCONCLUSION

Good agreement between Jan and myself

The estimates of Jan are made using the real measured spectra (one cannot do better than that if the spectra measurement is reliable)

~600 W/m are found for 472 bunches, with 1.21011 p/b, using either the measured spectrum or the measured bunch length (0.7 ns rms) assuming a Gaussian distribution

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!