Elias Metral, ABP Forum, 26/02/2003 1 STABILITY OF THE LONGITUDINAL BUNCHED-BEAM COHERENT MODES E. Metral E. Metral (CERN/AB-ABP- (CERN/AB-ABP- HEI) HEI) Introduction Dispersion relation Stability diagrams Parabolic distribution Gaussian distribution Distribution used by Sacherer for his stability criterion Analytical computations for an elliptical spectrum Application to the LHC at top energy
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STABILITY OF THE LONGITUDINAL BUNCHED-BEAM COHERENT MODES
STABILITY OF THE LONGITUDINAL BUNCHED-BEAM COHERENT MODES. E . Metral (CERN/AB-ABP-HEI). Introduction Dispersion relation Stability diagrams Parabolic distribution Gaussian distribution Distribution used by Sacherer for his stability criterion - PowerPoint PPT Presentation
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Elias Metral, ABP Forum, 26/02/2003
1
STABILITY OF THE LONGITUDINAL
BUNCHED-BEAM COHERENT MODES
E. Metral E. Metral (CERN/AB-ABP-HEI)(CERN/AB-ABP-HEI)
APPLICATION TO THE LHC AT TOP ENERGY (1/2)APPLICATION TO THE LHC AT TOP ENERGY (1/2)
The most critical case is the dipole mode m = 1
F
p
pZ
BVhI eff
l
RFb
11
50
32 ˆ
32
3
32
9 20
2Bha
with
42
1 2 aaF
Elias Metral, ABP Forum, 26/02/2003
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The previous stability criterion is the same as the one used by Boussard-Brandt-Vos in the paper “Is a longitudinal feedback system required for LHC?” (1999), with
Numerical application with the same parameters as the ones used
in the above paper
1F
28.0
1100
eff
l
eff
l
p
pZ
p
pZ
35640hMV16ˆ RFV
cm5.7b 500 101.1 bfB
2105.4 a
01.1F
p/b104.2 11thbN Same value as
the one found by BBV
APPLICATION TO THE LHC AT TOP ENERGY (2/2)APPLICATION TO THE LHC AT TOP ENERGY (2/2)
TeV7E
Elias Metral, ABP Forum, 26/02/2003
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ACKNOWLEDGEMENTACKNOWLEDGEMENTSS
F. Zimmermann, who proposed to look in detail at this mechanism
J. Gareyte, F. Ruggiero, and F. Zimmermann for fruitful discussions