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

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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