Manipulation of transverse beam distribution in circular ...jaiweb/slides/2013_Giovannozzi.pdf ·...

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


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

!


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).


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)


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


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.


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..


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


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.


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


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


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.


Novel multiNovel multi--turn extraction withturn extraction withother resonancesother resonances -- II



SimulationSimulationparameters:parameters:

HHéénonnon--likelikemap withmap withsextupolesextupoleand octupoleand octupole

The thirdThe third--orderorderresonance isresonance isused, thusused, thusgiving agiving athreethree--turnturnextractionextraction


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


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


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



Efficient method togenerate hollow beams!

Efficient method toEfficient method togenerate hollow beams!generate hollow beams!


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.

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



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

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.


Hénon-like modelHHéénonnon--like modellike model

Size of non-adiabaticregion

Size of nonSize of non--adiabaticadiabaticregionregion

Pendulum-like modelPendulumPendulum--like modellike model


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


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


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

Transverse dynamicsTransverse dynamics -- IIIIII


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


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).).

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

Extraction efficiencyExtraction efficiency


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%

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


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.


Beamlets are moving with intensity!Beamlets are moving with intensity!

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).


Consider projection effectConsider projection effect

No change in beamlets sizeNo change in beamlets size


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.


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!


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

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