Post on 29-Jul-2020
Space charge effect on the second order coupled resonance
G. Franchetti, GSIS. Gilardoni, A. Huschauer, F. Schmidt, R. Wasef, CERN
HB2016 – Malmo, Sweden
3-8 / 7/ 2016 G. Franchetti 1
The quest of the incoherent effects of space charge
April 12th 2016 G. Franchetti 2
2002 2007 2012
study of the space chargeon 1D 4th order resonance
study of the space chargeon 1D 3th order resonance: proofof principle
PSSIS18
study of the space chargeon 2D 3th order resonance
PS
2015
Experimental discovery of the fixed-lines
SPS
1 week 12 days (as users) 1 week 4 days
IOTA
SIS18, SIS100
PS, SPS, ..
resonancecompensation
withspace charge
2014
SIS18
~2 days
3-8 / 7/ 2016 G. Franchetti 3
3-8 / 7/ 2016 G. Franchetti 4
AB
PS campaign: “towards the unknown”
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Beam Profiles @ (A)
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Beam Profiles @ (B)
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Code experiment benchmarking
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Distance from the resonance
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Bare optics
Bare optics + space charge of one particle at amplitudes X,Y
Resonance condition
Resonant particles
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XhYh
X / σx
Y / σy
-0.19
Comparison with simulations
Yh
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Xh
Something seems wrong !The -x- profile does not exhibit
an halo that ends at Xh
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Xh
Including the chromaticity
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Bare tunes effect of chromaticityAMPLITUDE INDEPENDENT
consider a test particle with maximum dp/p
0.037
effect of space chargeAMPLITUDE DEPENDENT
incoherent tune-shift
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Expectedhalo @ 9σ
shift
ed o
f 0.0
37
Including chromaticity
Only ~ 5.5σand not 9σ !
No halo in x, but only core growth
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Something seems very wrong!The -x- profile does not exhibita halo, and the -y- profile have a smaller halo than expected
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with chromaticity
without chromaticity
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Coupled dynamics on the resonance
fixedlines
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G. Franchetti and F. Schmidt Phys. Rev. Lett. 114, 234801 (2015).
G. Franchetti and F. Schmidt http://arxiv.org/abs/1504.04389
F. Schmidt PhD thesis, and others
SPS campaign on May 2015:”Dream of glory”
Y|åxw Ä|Çxá xå|áàY|åxw Ä|Çxá xå|áà3-8 / 7/ 2016 G. Franchetti 20
Experiment organized by F. Schmidt
Space charge induced coupled dynamics in a bunch
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z
longitudinal motion keep frozen, to make retrieve orbits
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look at the x-y projection of resonant orbits
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two larger resonant orbits: situation very different than 1D resonances. There areinfinite fixed lines !!
Transverse Space charge is weaker
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z
½ length
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two larger resonant orbits: now the amplitude of the orbits is smaller. We still have infinite fixed lines.
Periodic crossing of fixed lines induced by space charge and
synchrotron motion
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Scattering (of the invariants)
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Adiabatic limit
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Artificially very slow synchrotron motion
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Halo asymmetry explained with fixed lines
beam size
x - axes
y -
axes
Conclusion / Outlook
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• A benchmarking on the 3rd order coupled resonance is achieved for the full PS structure.
• Outstanding asymmetric halo are formed and decently well retrieved by the simulations
• Thinking in terms of resonance detuning arises paradoxes
• The “fixed-lines” are the new objects that explain the dynamics of the resonance
• “Fixed lines” are measured in the SPS
• Simulations shows that the periodic crossing of the fixed-lines causes the asymmetric halo as result of fixed lines geometry.
• Although there are infinite fixed lines, halo diffuses to “one” value adiabatic limit
• The doors are open for massive studies of all coupled resonances and space charge