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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 11
Manipulation of transverse beamManipulation of transverse beamdistribution in circular accelerators:distribution in circular accelerators:beam splitting by particlesbeam splitting by particles’’ trappingtrapping
into resonance islandsinto resonance islands
M. GiovannozziM. Giovannozzi
Summary:Summary:
IntroductionIntroduction
Present multiPresent multi--turn extractionturn extraction
New multiNew multi--turn extraction (MTE)turn extraction (MTE)
Other applicationsOther applications
Measurement resultsMeasurement results
ConclusionsConclusions
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 22
IntroductionIntroduction -- II
Three approaches are normally used to extract beamThree approaches are normally used to extract beamfrom a circular machine:from a circular machine:
Fast Extraction (one turn)Fast Extraction (one turn)
A kickerA kicker (fast dipole)(fast dipole)displacesdisplaces the beam fromthe beam fromnominal closed orbit.nominal closed orbit.
A septum magnetA septum magnet deflectsdeflectsdisplaced beam towardsdisplaced beam towardstransfer line.transfer line.
This extraction can be usedThis extraction can be usedboth toboth to transfertransfer beambeamtowards atowards a ringring or anor anexperimental areaexperimental area..
Slow Extraction (millionsSlow Extraction (millionsturns)turns)
TheThe separatix of the thirdseparatix of the third--order resonanceorder resonance increasesincreasesparticlesparticles’’ amplitude until theyamplitude until theyjump beyond the septum.jump beyond the septum.
TheThe tune is changedtune is changed to shrinkto shrinkthe stable region, thus pushingthe stable region, thus pushingthe particles towards largerthe particles towards largeramplitudes.amplitudes.
This extraction is used toThis extraction is used totransfer beam towards antransfer beam towards anexperimental areaexperimental area..What is in between?What is in between?
Multi
Multi --tu
rn!
turn
!
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 33
IntroductionIntroduction -- IIII
MultiMulti--turn extractionturn extraction
The beam has to beThe beam has to be ““manipulatedmanipulated”” to increase theto increase theeffective length beyond the machine circumference.effective length beyond the machine circumference.
This extraction mode is used toThis extraction mode is used to transfer beam betweentransfer beam betweencircular machinescircular machines..
AT CERN this mode is used toAT CERN this mode is used to transfertransfer the proton beamthe proton beambetweenbetween PSPS andand SPSSPS. In the SPS the beam is used for. In the SPS the beam is used for
Fixed TargetFixed Target physics (broad sense)physics (broad sense)
Neutrino experimentsNeutrino experiments (until 1998)(until 1998)
CERN Neutrino to Gran SassoCERN Neutrino to Gran Sasso (CNGS) (from 2006)(CNGS) (from 2006)
These beams areThese beams are highhigh--intensityintensity (about(about 33××10101313 pp in thein thePS).PS).
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 44
Present multiPresent multi--turn extractionturn extraction –– II
First PS batchFirst PS batch Second PS batchSecond PS batch Gap for kickerGap for kicker
CCSPSSPS = 11 C= 11 CPSPS
PSPSPSPS
SPS circumferenceSPS circumference
Beam currentBeam currenttransformer in thetransformer in thePS/SPS transfer linePS/SPS transfer line
1 2 3 4 5 (total spill duration 0.010 ms)1 2 3 4 5 (total spill duration 0.010 ms)
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 55
Electrostatic septumElectrostatic septumbladeblade
Present multiPresent multi--turn extractionturn extraction –– IIII
LengthLength
Kicker
stre
ngth
Kicker
stre
ngth
Four turnsFour turns
Fifth turnFifth turn
XX
XX’’
1133 55
22
44
Slow bumpSlow bump
Slow bumpSlow bump
ElectrostaticElectrostaticseptumseptum(beam shaving)(beam shaving)
Extraction septumExtraction septum
Kicker magnetsKicker magnetsused to generateused to generatea closed orbita closed orbitbump aroundbump aroundelectrostaticelectrostaticseptumseptum
ExtractionExtractionlineline
EEfieldfield=0=0
EEfieldfield≠≠00
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 66
Present multiPresent multi--turn extractionturn extraction ––IIIIII
The main drawbacks of the present scheme are:The main drawbacks of the present scheme are:Losses (aboutLosses (about 15%15% of total intensity) are unavoidableof total intensity) are unavoidabledue to the presence of thedue to the presence of the electrostaticelectrostatic septum usedseptum usedto slice the beam.to slice the beam.
TheThe electrostaticelectrostatic septum isseptum is irradiatedirradiated. This poses. This posesproblems forproblems for handshands--on maintenanceon maintenance..
The phase space matching is not optimal (the variousThe phase space matching is not optimal (the variousslices haveslices have ““fancy shapesfancy shapes””), thus inducing betatronic), thus inducing betatronicmismatch in the receiving machine, i.e.mismatch in the receiving machine, i.e. emittanceemittanceblowblow--upup..
The slices have different emittances and opticalThe slices have different emittances and opticalparameters.parameters.
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 77
Novel multiNovel multi--turn extractionturn extraction –– II
The main ingredients of the novel extraction:The main ingredients of the novel extraction:
The beam splitting is not performed using a mechanicalThe beam splitting is not performed using a mechanicaldevice, thus avoiding losses. Indeed, the beam isdevice, thus avoiding losses. Indeed, the beam isseparated in the transverse phase space usingseparated in the transverse phase space using
Nonlinear magnetic elementsNonlinear magnetic elements (sextupoles ad octupoles) to(sextupoles ad octupoles) tocreatecreate stable islandsstable islands..
Slow (Slow (adiabaticadiabatic) tune) tune--variation to cross an appropriatevariation to cross an appropriateresonance.resonance.
This approach has the following beneficial effects:This approach has the following beneficial effects:
Losses are reducedLosses are reduced (virtually to zero).(virtually to zero).
TheThe phase space matching is improvedphase space matching is improved with respect to thewith respect to thepresent situation.present situation.
The beamlets have theThe beamlets have the same emittancesame emittance andand opticalopticalparametersparameters..
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 88
Model used in numerical simulationsModel used in numerical simulations
Standard approach: nonlinear elementsStandard approach: nonlinear elementsrepresented as a single kick at the samerepresented as a single kick at the samelocation in the ring (location in the ring (HHéénonnon--like polynomiallike polynomialmapsmaps).).
Vertical motion neglected.Vertical motion neglected.
Normalised (adimensional coNormalised (adimensional co--ordinates).ordinates).
2 3
1
ˆ ˆ
ˆ ˆ ˆ ˆ' 'n n
X X
X X X X
R 322
2
3 x
K
K
QuadrupolesQuadrupoles SextupoleSextupole OctupoleOctupole
The linear tune isThe linear tune istimetime--dependentdependent
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 99
Novel multiNovel multi--turn extractionturn extraction –– IIII
Right: intermediateRight: intermediatephase space topology.phase space topology.Islands are createdIslands are creatednear the centre.near the centre.
Bottom: final phaseBottom: final phasespace topology.space topology.Islands are separatedIslands are separatedto allow extraction.to allow extraction.
Left: initial phaseLeft: initial phasespace topology. Nospace topology. Noislands.islands.
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1010
Novel multiNovel multi--turn extractionturn extraction -- IIIIII
Tune variationTune variation
Phase spacePhase spaceportraitportrait
SimulationSimulationparameters:parameters:
HHéénonnon--likelikemap (i.e. 2Dmap (i.e. 2Dpolynomialpolynomial ––degree 3degree 3 --mapping)mapping)representingrepresentinga FODO cella FODO cellwithwithsextupole andsextupole andoctupoleoctupole
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1111
Novel multiNovel multi--turn extractionturn extraction –– IVIV
Final stage after 20000 turns (about 42 ms for CERN PS)Final stage after 20000 turns (about 42 ms for CERN PS)
About 6 cm in physical spaceAbout 6 cm in physical space
Slow (Slow (few thousandfew thousandturnsturns) bump first) bump first(closed distortion of(closed distortion ofthe periodic orbit)the periodic orbit)
Fast (Fast (less than oneless than oneturnturn) bump afterwards) bump afterwards(closed distortion of(closed distortion ofperiodic orbit)periodic orbit)
BBfieldfield ≠≠ 00BBfieldfield == 00
At the septum locationAt the septum location
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1212
Novel multiNovel multi--turn extractionturn extraction -- VV
The original goal of this study was to find aThe original goal of this study was to find areplacement to the present Continuous Transferreplacement to the present Continuous Transferused at CERN for the highused at CERN for the high--intensity proton beams.intensity proton beams.However the novel technique proved to be usefulHowever the novel technique proved to be usefulalso in different context, e.g.also in different context, e.g.
The same approach can be applied forThe same approach can be applied for multimulti--turnturninjectioninjection (time(time--reversal property of the physicsreversal property of the physicsinvolved).involved).
multimulti--turn extractionturn extraction over aover a different numberdifferent number ofofturns can be designed, provided the appropriateturns can be designed, provided the appropriateresonance is used.resonance is used.
Multiple multiMultiple multi--turnturn extractions could be considered,extractions could be considered,e.g. to extract the beam remaining in the centrale.g. to extract the beam remaining in the centralpart of phase space.part of phase space.
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1313
Novel multiNovel multi--turn extraction withturn extraction withother resonancesother resonances -- II
Tune variationTune variation
Phase spacePhase spaceportraitportrait
SimulationSimulationparameters:parameters:
HHéénonnon--likelikemap withmap withsextupolesextupoleand octupoleand octupole
The thirdThe third--orderorderresonance isresonance isused, thusused, thusgiving agiving athreethree--turnturnextractionextraction
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1414
Novel multiNovel multi--turn extraction withturn extraction withother resonancesother resonances -- IIII
The fifthThe fifth--order resonance isorder resonance isused, thus giving a sixused, thus giving a six--turnturnextractionextraction
The secondThe second--order resonance isorder resonance isused, thus giving a twoused, thus giving a two--turnturnextractionextraction
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1515
NonNon--linear elements can be used to make thelinear elements can be used to make thefourthfourth--order resonance unstable by cancelingorder resonance unstable by cancelingthe amplitude detuning.the amplitude detuning.
Possible applications:Possible applications:FourFour--turn extraction.turn extraction.
Deplete the core region toDeplete the core region to
achieve a better intensityachieve a better intensity
sharing.sharing.
Novel multiNovel multi--turn extraction:turn extraction: 44thth orderorderunstable resonanceunstable resonance -- new application!new application!
Master thesis Diego QuatraroMaster thesis Diego QuatraroMaster thesis Diego Quatraro
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1616
Novel multiNovel multi--turnturn injectioninjection: new: newapplication!application!
Simulation parameters:Simulation parameters:
ThirdThird--order polynomialorder polynomialmap representing amap representing aFODO cell withFODO cell withsextupole and octupolesextupole and octupole
The fourthThe fourth--orderorderresonance is used forresonance is used fora foura four--turn injectionturn injection
Tune variationTune variation
Phase spacePhase spaceportraitportrait
Efficient method togenerate hollow beams!
Efficient method toEfficient method togenerate hollow beams!generate hollow beams!
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1717
Novel multiNovel multi--turnturn injectioninjection: new: newapplication!application!
Possible applications: transverse shaping of beamPossible applications: transverse shaping of beamdistribution.distribution.
Observation: the proposed method seems to beObservation: the proposed method seems to bemore efficient in generating smaller emittancemore efficient in generating smaller emittancebeams than standard multibeams than standard multi--turn injection!turn injection!
M. Giovannozzi, J. Morel, PRST-AB, 10, 034001 (2007)M. Giovannozzi, J. Morel, PRSTM. Giovannozzi, J. Morel, PRST--AB, 10, 034001 (2007)AB, 10, 034001 (2007)
““StandardStandard”” hollowhollowbeam distributionbeam distribution
““FlatFlat”” beam distribution obtained by injecting a fifth turnbeam distribution obtained by injecting a fifth turnin the centre.in the centre.
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The capture processThe capture process -- II
Quantitative analysis needed:Quantitative analysis needed:To control sharing between core and beamlets.To control sharing between core and beamlets.
To control the emittance sharing.To control the emittance sharing.
Adiabatic theory is the key concept:Adiabatic theory is the key concept:Probability trapping is proportional to the speed of variationProbability trapping is proportional to the speed of variationof the islandof the island’’s surface.s surface.
It is possible to account for the loss of adiabaticity close toIt is possible to account for the loss of adiabaticity close tothe separatrix.the separatrix.
2D case seems under control.2D case seems under control.
The 4D case requires the usual conditions:The 4D case requires the usual conditions:weak coupling between the two degrees of freedomweak coupling between the two degrees of freedom
no low order resonances in the vertical planeno low order resonances in the vertical plane
Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1818
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 1919
The capture processThe capture process -- IIII
Initial gaussian distributionInitial gaussian distributionInitial gaussian distribution Particles in island 2Particles in island 2Particles in island 2 Particles in island 4Particles in island 4Particles in island 4
Particles in island 6Particles in island 6Particles in island 6 Particles in island 8Particles in island 8Particles in island 8 Particles in beam coreParticles in beam coreParticles in beam core
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The capture processThe capture process -- IIIIII
Under these conditions:Under these conditions:
Scaling law for the size ofScaling law for the size ofthe adiabatic region is wellthe adiabatic region is well--reproduced.reproduced.
Trapping probability is wellTrapping probability is well--described.described.
Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 2020
Hénon-like modelHHéénonnon--like modellike model
Size of non-adiabaticregion
Size of nonSize of non--adiabaticadiabaticregionregion
Pendulum-like modelPendulumPendulum--like modellike model
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 2121
Analytical computation of islandAnalytical computation of island’’ssparametersparameters
Using perturbative theory (Using perturbative theory (normal formsnormal forms) it is) it ispossible to derive analytical estimate of islandpossible to derive analytical estimate of island’’ssparameters.parameters.
2 0,32 u
Distance of fixed pointsDistance of fixed pointsfrom origin of phase spacefrom origin of phase space
20,3
2
4 u
Distance between separaticesDistance between separatices
Normalised phase spaceNormalised phase space
20,3
2
16 u
IslandIsland’’s surfaces surface
2sec 2 0,34 u
Distance from resonanceDistance from resonance
Secondary frequencySecondary frequency
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 2222
Operational implementationOperational implementation -- II
Sextupoles and octupoles are used toSextupoles and octupoles are used to
Generate stable islandsGenerate stable islands
Control size/position of islandsControl size/position of islands
Control linear chromaticityControl linear chromaticity
Control nonControl non--linear coupling (linear coupling (using an additional set ofusing an additional set ofoctupoles, normally used to combat instabilitiesoctupoles, normally used to combat instabilities))
yxy
yxx
JhJhQ
JhJhQ
2,01,1
1,10,2
hh2,02,0 --> detuning with amplitude (H> detuning with amplitude (H--plane)plane) -->> xx22 KK33
hh1,11,1 --> non> non--linear couplinglinear coupling -->> xxyy KK33hh0,20,2 --> detuning with amplitude (V> detuning with amplitude (V--plane)plane) -->> yy
22 KK33
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 2323
Operational implementationOperational implementation -- IIII
-600
-400
-200
0
200
400
600
0.00.10.20.30.40.50.60.70.80.91.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Cu
rren
ts(A
)
B-f
ield
(T)
Cycle time (s)
B-field Sextupole 39Sextupole 55 Octupole 39Octupole 55 Octupoles
-600
-400
-200
0
200
400
600
0.00.10.20.30.40.50.60.70.80.91.0
0.72 0.74 0.76 0.78 0.80 0.82
Cu
rren
ts(A
)
B-f
ield
(T)
Cycle time (s)
B-field Sextupole 39Sextupole 55 Octupole 39Octupole 55 Octupoles
Injection: 0.170 sInjection: 0.170 s
Extraction: 0.835 sExtraction: 0.835 s
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Transverse dynamicsTransverse dynamics -- IIIIII
Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 2424
Phase space at septumPhase space at septum
-3000
-2000
-1000
0
1000
2000
3000
0.00
0.05
0.10
0.15
0.20
0.25
0.72 0.74 0.76 0.78 0.80 0.82
Seco
nd
ord
erch
rom
ati
city
,d
etu
nin
g,n
on
-lin
ear
cou
pli
ng
Frac
tio
nal
tun
ea
nd
chro
mat
icit
y
Cycle time (s)
Qx Qx'/Qx
Qx'' h2,0
h1,1
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 2525
Evolution of beam distributionEvolution of beam distribution
Horizontal beam profiles inHorizontal beam profiles in section 54section 54 have been takenhave been takenduring the capture process (total intensityduring the capture process (total intensity ~~2.12.1××10101313).).
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Trapping performanceTrapping performance
2626OxfordOxford -- July 4th 2013July 4th 2013Massimo GiovannozziMassimo Giovannozzi
0 50 100 150 200 250 300
37 nsbin
02.0x1010
6.0x1010
1.0x1011
1.4x1011
Inte
nsity
0 50 100 150 200 250 300
37 nsbin
02.0x1010
6.0x1010
1.0x1011
1.4x1011
Inte
nsity
12 14 16 18 20
200
400
600
800
1000
Trapping (%)
Fre
qu
en
cy
5000 10000 15000 20000 25000
Time elapsed from May 1st 15:00 (s)
12
14
16
18
20
Tra
pp
ing
(%)
20% trapping20% trapping 18% trapping18% trapping
5 PS turns5 PS turns
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Extraction efficiencyExtraction efficiency
2727OxfordOxford -- July 4th 2013July 4th 2013Massimo GiovannozziMassimo Giovannozzi
Regular fluctuations inRegular fluctuations inthe extraction efficiencythe extraction efficiencyare also observed andare also observed andseem well correlated toseem well correlated tospill fluctuations.spill fluctuations.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0
100
200
300
400
500
600
700
90.
0
90.
6
91.
2
91.
8
92.
4
93.
0
93.
6
94.
2
94.
8
95.
4
96.
0
96.
6
97.
2
97.
8
98.
4
99.
0
99.
6
100
.2
100
.8
Fre
qu
ency
Extraction efficiency (%)
Frequency Cumulative %
90
91
92
93
94
95
96
97
98
99
100
14:24 15:36 16:48 18:00 19:12 20:24 21:36 22:48
Extr
act
ion
effi
cie
ncy
(%)
Time on May 1st
Distribution of extractionDistribution of extractionefficiency is peaked atefficiency is peaked atabout 98%about 98% (NB: the beam is(NB: the beam isdebunched at extraction!debunched at extraction!Unavoidable beam losses areUnavoidable beam losses areestimated at about 1estimated at about 1--2%)2%)
CT extractionCT extractionefficiency isefficiency isabout 93%about 93%
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CT vs. MTE: extraction lossesCT vs. MTE: extraction losses
For the same extracted intensity, the CT features more losses,For the same extracted intensity, the CT features more losses,about the double, compared to MTE.about the double, compared to MTE.The CT losses are spread around the ring whereas for MTE theThe CT losses are spread around the ring whereas for MTE thelosses are more concentrated on the extraction septum as anticiplosses are more concentrated on the extraction septum as anticipatedatedin the MTE Design Report.in the MTE Design Report.
CTCT MTEMTE
2828OxfordOxford -- July 4th 2013July 4th 2013Massimo GiovannozziMassimo Giovannozzi
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First observations of intensityFirst observations of intensity--dependent effectsdependent effects -- II
Usual process for trapping the beam intoUsual process for trapping the beam intostable islands.stable islands.
Varying parameter: total beam intensity.Varying parameter: total beam intensity.
Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 2929
Beamlets are moving with intensity!Beamlets are moving with intensity!
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First observations of intensityFirst observations of intensity--dependent effectsdependent effects -- IIII
The observedThe observedeffect can beeffect can beexplained with anexplained with anintensityintensity--dependent shiftdependent shiftof the singleof the singleparticle tune.particle tune.
Possible sources:Possible sources:Image currents.Image currents.
Direct effectsDirect effects(interaction between(interaction betweenbeamlets).beamlets).
Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 3030
Consider projection effectConsider projection effect
No change in beamlets sizeNo change in beamlets size
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 3131
Summary and OutlookSummary and Outlook -- II
A novel multiA novel multi--turn extraction is studied since a few years:turn extraction is studied since a few years: ititallows manipulating transverse emittances in a synchrotron!allows manipulating transverse emittances in a synchrotron!
First MTE beam delivered to the SPS by midFirst MTE beam delivered to the SPS by mid--SeptemberSeptember2009 (about 1.52009 (about 1.5××10101313 p/extraction).p/extraction).
Equal sharing for islands/core achieved by the end of 2009.Equal sharing for islands/core achieved by the end of 2009.
In February 2010 the commissioning was resumed.In February 2010 the commissioning was resumed.
High intensity beam was extracted (about 2.1High intensity beam was extracted (about 2.1××10101313
p/extraction) with record intensity 2.6p/extraction) with record intensity 2.6××10101313 p/extraction.p/extraction.
2010 physics run at SPS was started using MTE beam.2010 physics run at SPS was started using MTE beam.
Open issues:Open issues:
Variation of the fraction of particles trapped in islands.Variation of the fraction of particles trapped in islands.
Activation of extraction septum due to the longitudinalActivation of extraction septum due to the longitudinalstructure of the beam (destructure of the beam (de--bunched as needed by the SPS).bunched as needed by the SPS).
New optimised extraction scheme to avoid losses onNew optimised extraction scheme to avoid losses onextraction septumextraction septum --> beam commissioning in 2014.> beam commissioning in 2014.
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 3232
Summary and OutlookSummary and Outlook -- IIII
The same principle can be used for injectionThe same principle can be used for injection..
Transverse shaping is possible, i.e. generationTransverse shaping is possible, i.e. generationofof hollow buncheshollow bunches..
Lines of research:Lines of research:Complete study of splitting process in 2D and extendComplete study of splitting process in 2D and extendto 4D.to 4D.
Study trapping in 4D, i.e., manipulations in xStudy trapping in 4D, i.e., manipulations in x--yyplane.plane.
Study intensityStudy intensity--dependent effects.dependent effects.
And many more!And many more!
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Massimo GiovannozziMassimo Giovannozzi OxfordOxford -- July 4th 2013July 4th 2013 3333
Selected referencesSelected references
S. Gilardoni, M. Giovannozzi, C. Hernalsteens (2013).S. Gilardoni, M. Giovannozzi, C. Hernalsteens (2013). ““First observations ofFirst observations ofintensityintensity--dependent effects for transversely split beams during multiturndependent effects for transversely split beams during multiturnextraction studies at the CERN Proton Synchrotronextraction studies at the CERN Proton Synchrotron””, Phys. Rev. ST Accel. Beams ., Phys. Rev. ST Accel. Beams .
M. Giovannozzi, D. Quatraro, G. Turchetti, (2009).M. Giovannozzi, D. Quatraro, G. Turchetti, (2009). ““Generating unstableGenerating unstableresonances for extraction schemes based on transverse splittingresonances for extraction schemes based on transverse splitting””, Phys. Rev. ST, Phys. Rev. STAccel. Beams 12 024003.Accel. Beams 12 024003.
A. Franchi, S. Gilardoni, M. Giovannozzi, (2009).A. Franchi, S. Gilardoni, M. Giovannozzi, (2009). ““Progresses in the studies ofProgresses in the studies ofadiabatic splitting of charged particle beams by crossing nonlinadiabatic splitting of charged particle beams by crossing nonlinear resonancesear resonances””,,Phys. Rev. ST Accel. Beams 12 014001.Phys. Rev. ST Accel. Beams 12 014001.
M. Giovannozzi and J. Morel, (2007).M. Giovannozzi and J. Morel, (2007). ““Principle and analysis of multiturn injectionPrinciple and analysis of multiturn injectionusing stable islands of transverse phase spaceusing stable islands of transverse phase space””, Phys. Rev. ST Accel. Beams 10, Phys. Rev. ST Accel. Beams 10034001.034001.
S. Gilardoni, M. Giovannozzi, M. Martini, E. MS. Gilardoni, M. Giovannozzi, M. Martini, E. Méétral, P. Scaramuzzi, R.tral, P. Scaramuzzi, R.Steerenberg, A.Steerenberg, A.--S. MS. Müüller, (2006).ller, (2006). ““Experimental evidence of adiabatic splittingExperimental evidence of adiabatic splittingof charged particle beams using stable islands of transverse phaof charged particle beams using stable islands of transverse phase spacese space””, Phys., Phys.Rev. ST Accel. Beams 9 104001.Rev. ST Accel. Beams 9 104001.
R. Cappi, M. Giovannozzi, (2003).R. Cappi, M. Giovannozzi, (2003). ““MultiMulti--turn Extraction and Injection by Meansturn Extraction and Injection by Meansof Adiabatic Capture in Stable Islands of Phase Spaceof Adiabatic Capture in Stable Islands of Phase Space””, Phys. Rev. ST Accel., Phys. Rev. ST Accel.Beams 7 024001.Beams 7 024001.
R. Cappi, M. Giovannozzi, (2002).R. Cappi, M. Giovannozzi, (2002). ““Novel Method for MultiNovel Method for Multi--Turn Extraction:Turn Extraction:Trapping Charged Particles in Islands of Phase SpaceTrapping Charged Particles in Islands of Phase Space””, Phys. Rev. Lett. 88, Phys. Rev. Lett. 88104801. The same principle can be used for injection104801. The same principle can be used for injection..
Manipulation of transverse beam distribution in circular accelerators: beam splitting by particles’ trapping into resonance islandsIntroduction - IIntroduction - IIPresent multi-turn extraction – IPresent multi-turn extraction – IIPresent multi-turn extraction –IIINovel multi-turn extraction – IModel used in numerical simulationsNovel multi-turn extraction – IINovel multi-turn extraction - IIINovel multi-turn extraction – IVNovel multi-turn extraction - VNovel multi-turn extraction with other resonances - INovel multi-turn extraction with other resonances - IINovel multi-turn extraction: 4th order unstable resonance - new application!Novel multi-turn injection: new application!Novel multi-turn injection: new application!The capture process - IThe capture process - IIThe capture process - IIIAnalytical computation of island’s parametersOperational implementation - IOperational implementation - IITransverse dynamics - IIIEvolution of beam distributionTrapping performanceExtraction efficiencyCT vs. MTE: extraction lossesFirst observations of intensity-dependent effects - IFirst observations of intensity-dependent effects - IISummary and Outlook - ISummary and Outlook - IISelected references