M. Giovannozzi

Massimo GiovannozziMassimo Giovannozzi Oxford - July 4th 2013Oxford - July 4th 2013 11

Manipulation of transverse beam Manipulation of transverse beam distribution in circular distribution in circular

accelerators: beam splitting by accelerators: beam splitting by particles’ trapping into particles’ trapping into

resonance islandsresonance islandsM. GiovannozziM. Giovannozzi

Summary:Summary:

Introduction Introduction

Present multi-turn Present multi-turn extractionextraction

New multi-turn extraction New multi-turn extraction (MTE)(MTE)

Other applicationsOther applications

Measurement resultsMeasurement results

Conclusions Conclusions


Introduction - IIntroduction - I

Three approaches are normally used to extract Three approaches are normally used to extract beam from a circular machine: beam from a circular machine:

Fast Extraction (one Fast Extraction (one turn)turn)

A kickerA kicker (fast dipole) (fast dipole) displacesdisplaces the beam from the beam from nominal closed orbit.nominal closed orbit.

A septum magnetA septum magnet deflectsdeflects displaced beam displaced beam towards transfer line.towards transfer line.

This extraction can be This extraction can be used both to used both to transfertransfer beam towards a beam towards a ringring or or an an experimental areaexperimental area..

Slow Extraction (millions Slow Extraction (millions turns)turns)

The The separatix of the separatix of the third-order resonance third-order resonance increases particles’ increases particles’ amplitude until they jump amplitude until they jump beyond the septum.beyond the septum.

The The tune is changed tune is changed to to shrink the stable region, shrink the stable region, thus pushing the particles thus pushing the particles towards larger amplitudes. towards larger amplitudes.

This extraction is used to This extraction is used to transfer beam towards an transfer beam towards an experimental areaexperimental area..

What is in What is in between?between?

Mu

lti-

turn

!M

ult

i-tu

rn!


Introduction - IIIntroduction - II

Multi-turn extractionMulti-turn extractionThe beam has to be “The beam has to be “manipulatedmanipulated” to increase ” to increase the effective length beyond the machine the effective length beyond the machine circumference.circumference.

This extraction mode is used to This extraction mode is used to transfer beam transfer beam between circular machinesbetween circular machines..

AT CERN this mode is used to AT CERN this mode is used to transfertransfer the proton the proton beam beam betweenbetween PSPS and and SPSSPS. In the SPS the beam . In the SPS the beam is used for 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 are These beams are high-intensityhigh-intensity (about (about 33××10101313 p p in the PS). in the PS).


Present multi-turn extractionPresent multi-turn extraction – – II

First PS First PS batchbatch

Second PS Second PS batchbatch

Gap for Gap for kickerkicker

CCSPSSPS = 11 C = 11 CPSPS

PSPSPSPS

SPS SPS circumferencecircumference

Beam current Beam current transformer in the transformer in the PS/SPS transfer PS/SPS transfer lineline 1 2 3 4 5 (total spill duration 0.010 1 2 3 4 5 (total spill duration 0.010

ms)ms)


Electrostatic septum Electrostatic septum bladeblade

Present multi-turn extractionPresent multi-turn extraction – – IIII

Length Length

Kic

ker

Kic

ker

str

en

gth

str

en

gth Four Four

turnsturns

Fifth Fifth turnturn

XX

X’X’

1133 55

22

44

Slow Slow bumpbump

Slow Slow bumpbump

Electrostatic Electrostatic septum septum (beam shaving)(beam shaving)

Extraction Extraction septumseptum

Kicker magnets Kicker magnets used to used to generate a generate a closed orbit closed orbit bump around bump around electrostatic electrostatic septumseptum

Extraction Extraction lineline

EEfieldfield=0=0

EEfieldfield≠0≠0


Present multi-turn extractionPresent multi-turn extraction – –IIIIII

The main drawbacks of the present The main drawbacks of the present scheme are:scheme are:

Losses (about Losses (about 15%15% of total intensity) are of total intensity) are unavoidable due to the presence of the unavoidable due to the presence of the electrostaticelectrostatic septum used to slice the beam. septum used to slice the beam.

The The electrostaticelectrostatic septum is septum is irradiatedirradiated. This . This poses problems for poses problems for hands-on maintenancehands-on maintenance..

The phase space matching is not optimal (the The phase space matching is not optimal (the various slices have “various slices have “fancy shapesfancy shapes”), thus ”), thus inducing betatronic mismatch in the receiving inducing betatronic mismatch in the receiving machine, i.e. machine, i.e. emittanceemittance blow-upblow-up..

The slices have different emittances and The slices have different emittances and optical parameters.optical parameters.


Novel multi-turn extractionNovel multi-turn extraction – – II

The main ingredients of the novel extraction:The main ingredients of the novel extraction:

The beam splitting is not performed using a The beam splitting is not performed using a mechanical device, thus avoiding losses. Indeed, the mechanical device, thus avoiding losses. Indeed, the beam is separated in the transverse phase space beam is separated in the transverse phase space using using

Nonlinear magnetic elementsNonlinear magnetic elements (sextupoles ad (sextupoles ad octupoles) to create octupoles) to create stable islandsstable islands..Slow (Slow (adiabaticadiabatic) tune-variation to cross an ) tune-variation to cross an appropriate resonance.appropriate 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).The The phase space matching is improvedphase space matching is improved with respect with respect to the present situation.to the present situation.The beamlets have the The beamlets have the same emittancesame emittance and and optical optical parametersparameters..


Model used in numerical Model used in numerical simulationssimulations

Standard approach: nonlinear elements Standard approach: nonlinear elements represented as a single kick at the same represented as a single kick at the same location in the ring (location in the ring (Hénon-like Hénon-like polynomial mapspolynomial maps).).

Vertical motion neglected.Vertical motion neglected.

Normalised (adimensional co-ordinates).Normalised (adimensional co-ordinates).

2 3

1

ˆ ˆ

ˆ ˆ ˆ ˆ' 'n n

X X

X X X X

R

QuadrupolQuadrupoleses

SextupoleSextupole OctupoleOctupole

The linear tune The linear tune is time-is time-dependentdependent


Novel multi-turn extractionNovel multi-turn extraction – – IIII

Right: Right: intermediate intermediate phase space phase space topology. Islands topology. Islands are created near are created near the centre.the centre.

Bottom: final Bottom: final phase space phase space topology. Islands topology. Islands are separated to are separated to allow extraction.allow extraction.

Left: initial phase Left: initial phase space topology. space topology. No islands.No islands.


Novel multi-turn extraction - Novel multi-turn extraction - III III

Tune Tune variationvariation

Phase Phase space space portraitportrait

Simulation Simulation parametersparameters::

Hénon-like Hénon-like map (i.e. map (i.e. 2D 2D polynomial polynomial – – degree 3degree 3 - - mapping) mapping) representinrepresenting a FODO g a FODO cell with cell with sextupole sextupole and and octupoleoctupole


Novel multi-turn extractionNovel multi-turn extraction – IV – IV

Final stage after 20000 turns (about 42 ms for CERN Final stage after 20000 turns (about 42 ms for CERN PS)PS)

About 6 cm in physical About 6 cm in physical spacespace

Slow (Slow (few thousand few thousand turnsturns) bump first ) bump first (closed distortion (closed distortion of the periodic of the periodic orbit)orbit)Fast (Fast (less than one less than one turnturn) bump ) bump afterwards (closed afterwards (closed distortion of distortion of periodic orbit)periodic orbit)

BBfieldfield ≠ 0≠ 0BBfieldfield = = 0 0At the septum locationAt the septum location


Novel multi-turn extraction - Novel multi-turn extraction - VV

The original goal of this study was to find a The original goal of this study was to find a replacement to the present Continuous replacement to the present Continuous Transfer used at CERN for the high-intensity Transfer used at CERN for the high-intensity proton beams. However the novel technique proton beams. However the novel technique proved to be useful also in different context, proved to be useful also in different context, e.g.e.g.

The same approach can be applied for The same approach can be applied for multi-multi-turnturn injectioninjection (time-reversal property of the (time-reversal property of the physics involved).physics involved).multi-turn extractionmulti-turn extraction over a over a different numberdifferent number of turns can be designed, provided the of turns can be designed, provided the appropriate resonance is used.appropriate resonance is used.Multiple multi-turnMultiple multi-turn extractions could be extractions could be considered, e.g. to extract the beam considered, e.g. to extract the beam remaining in the central part of phase space.remaining in the central part of phase space.


Novel multi-turn extraction Novel multi-turn extraction with other resonanceswith other resonances - I - I



Simulation Simulation parameterparameters:s:

Hénon-like Hénon-like map with map with sextupole sextupole and and octupoleoctupole

The third-The third-order order resonance resonance is used, is used, thus thus giving a giving a three-turn three-turn extractionextraction


Novel multi-turn extraction Novel multi-turn extraction with other resonanceswith other resonances - II - II

The fifth-order resonance is The fifth-order resonance is used, thus giving a six-turn used, thus giving a six-turn extractionextraction

The second-order The second-order resonance is used, thus resonance is used, thus giving a two-turn giving a two-turn extractionextraction


Non-linear elements can be used to make Non-linear elements can be used to make the fourth-order resonance unstable by the fourth-order resonance unstable by canceling the amplitude detuning.canceling the amplitude detuning.

Possible applications:Possible applications:Four-turn extraction.Four-turn extraction.

Deplete the core region toDeplete the core region to

achieve a better intensity achieve a better intensity

sharing.sharing.

Novel multi-turn extraction: Novel multi-turn extraction: 44thth order unstable resonanceorder unstable resonance - new - new application!application!

Master thesis Diego Master thesis Diego QuatraroQuatraro

Master thesis Diego Master thesis Diego QuatraroQuatraro


Novel multi-turn Novel multi-turn injectioninjection: : new application!new application!

Simulation Simulation parameters:parameters:

Third-order Third-order polynomial map polynomial map representing a representing a FODO cell with FODO cell with sextupole and sextupole and octupoleoctupole

The fourth-order The fourth-order resonance is used resonance is used for a four-turn for a four-turn injectioninjection



Efficient method to Efficient method to generate hollow generate hollow beams!beams!

Efficient method to Efficient method to generate hollow generate hollow beams!beams!


Novel multi-turn Novel multi-turn injectioninjection: : new application!new application!

Possible applications: transverse shaping of Possible applications: transverse shaping of beam distribution. beam distribution.

Observation: the proposed method seems to be Observation: the proposed method seems to be more efficient in generating smaller emittance more efficient in generating smaller emittance beams than standard multi-turn injection!beams than standard multi-turn injection!

M. Giovannozzi, J. Morel, PRST-AB, 10, 034001 M. Giovannozzi, J. Morel, PRST-AB, 10, 034001 (2007)(2007)

M. Giovannozzi, J. Morel, PRST-AB, 10, 034001 M. Giovannozzi, J. Morel, PRST-AB, 10, 034001 (2007)(2007)

““Standard” Standard” hollow beam hollow beam distributiondistribution

““Flat” beam distribution obtained by injecting a Flat” beam distribution obtained by injecting a fifth turn in the centre.fifth turn in the centre.

The capture process - IThe capture process - I

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 Probability trapping is proportional to the speed of variation of the island’s surface.variation of the island’s surface.

It is possible to account for the loss of adiabaticity close It is possible to account for the loss of adiabaticity close to the separatrix.to 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 process - IIThe capture process - II

Initial gaussian Initial gaussian distributiondistribution

Initial gaussian Initial gaussian distributiondistribution

Particles in island 2Particles in island 2Particles in island 2Particles in island 2 Particles in island 4Particles in island 4Particles in island 4Particles in island 4

Particles in island 6Particles in island 6Particles in island 6Particles in island 6 Particles in island 8Particles in island 8Particles in island 8Particles in island 8 Particles in beam Particles in beam corecore

Particles in beam Particles in beam corecore

The capture process - IIIThe capture process - IIIUnder these conditions:Under these conditions:

Scaling law for the size of Scaling law for the size of the adiabatic region is the adiabatic region is well-reproduced.well-reproduced.

Trapping probability is Trapping probability is well-described.well-described.


Hénon-like modelHénon-like modelHénon-like modelHénon-like model

Size of non-adiabatic Size of non-adiabatic regionregion

Size of non-adiabatic Size of non-adiabatic regionregion

Pendulum-like Pendulum-like modelmodel

Pendulum-like Pendulum-like modelmodel


Analytical computation of Analytical computation of island’s parametersisland’s parameters

Using perturbative theory (Using perturbative theory (normal formsnormal forms) ) it is possible to derive analytical estimate it is possible to derive analytical estimate of island’s parameters. of island’s parameters.

2 0,32 u

Distance of fixed points Distance of fixed points from origin of phase from origin of phase spacespace

20,3

2

4 u

Distance between Distance between separaticesseparatices

Normalised phase Normalised phase

spacespace

20,3

2

16 u

Island’s surfaceIsland’s surface

2sec 2 0,34 u

Distance from resonanceDistance from resonance

Secondary frequencySecondary frequency


Operational implementation Operational implementation - I- I

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 non-linear coupling (Control non-linear coupling (using an additional set using an additional set of octupoles, normally used to combat instabilitiesof octupoles, normally used to combat instabilities))

yxy

yxx

JhJhQ

JhJhQ

2,01,1

1,10,2

hh2,02,0 -> detuning with amplitude (H-plane) -> -> detuning with amplitude (H-plane) -> xx22

KK33

hh1,11,1 -> non-linear coupling -> -> non-linear coupling -> xxy y KK33

hh0,20,2 -> detuning with amplitude (V-plane) -> -> detuning with amplitude (V-plane) -> yy22

KK33


Operational implementation Operational implementation - II- II

-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

Curr

ents

(A)

B-fi

eld

(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

Curr

ents

(A)

B-fi

eld

(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 dynamics - IIITransverse dynamics - III


Phase space at Phase space at septum septum

0.72 0.74 0.76 0.78 0.80 0.82

-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 o

rder

chr

omati

city

, de

tuni

ng, n

on-li

near

cou

plin

g

Frac

tion

al tu

ne a

nd c

hrom

atici

ty

Cycle time (s)

Qx Qx'/QxQx'' h2,0h1,1


Evolution of beam Evolution of beam distributiondistribution

Horizontal beam profiles in Horizontal beam profiles in section 54section 54 have been have been taken during the capture process (total intensity taken during the capture process (total intensity ~~2.1×102.1×101313).).

Trapping performanceTrapping performance

2626Oxford - July 4th 2013Oxford - July 4th 2013Massimo GiovannozziMassimo Giovannozzi

0 50 100 150 200 250 300

37 nsbin

02.0x1010

6.0x1010

1.0x1011

1.4x1011

Inte

nsi

ty

0 50 100 150 200 250 300

37 nsbin

02.0x1010

6.0x1010

1.0x1011

1.4x1011

Inte

nsi

ty

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% 20% trappingtrapping

18% 18% trappingtrapping

5 PS turns5 PS turns

Extraction efficiencyExtraction efficiency


Regular fluctuations in Regular fluctuations in the extraction efficiency the extraction efficiency are also observed and are also observed and seem well correlated to seem well correlated to spill 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

Freq

uenc

y

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

acti

on e

ffici

ency

(%)

Time on May 1st

Distribution of Distribution of extraction efficiency is extraction efficiency is peaked at about 98% peaked at about 98% (NB: the beam is (NB: the beam is debunched at debunched at extraction! Unavoidable extraction! Unavoidable beam losses are beam losses are estimated at about 1-estimated at about 1-2%)2%)

CT extraction CT extraction efficiency is efficiency is about 93%about 93%

CT vs. MTE: extraction CT vs. MTE: extraction losseslosses

For the same extracted intensity, the CT features more For the same extracted intensity, the CT features more losses, about the double, compared to MTE.losses, about the double, compared to MTE.The CT losses are spread around the ring whereas for MTE The CT losses are spread around the ring whereas for MTE the losses are more concentrated on the extraction septum the losses are more concentrated on the extraction septum as anticipated in the MTE Design Report.as anticipated in the MTE Design Report.

CTCT MTEMTE


First observations of First observations of intensity-dependent effects intensity-dependent effects - I- I

Usual process for trapping the beam Usual process for trapping the beam into stable islands.into stable islands.

Varying parameter: total beam Varying parameter: total beam intensity.intensity.


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

First observations of First observations of intensity-dependent effects intensity-dependent effects - II- II

The observed The observed effect can be effect can be explained with explained with an intensity-an intensity-dependent shift dependent shift of the single of the single particle tune.particle tune.

Possible Possible sources:sources:

Image currents.Image currents.

Direct effects Direct effects (interaction (interaction between beamlets).between beamlets).


Consider projection effectConsider projection effect

No change in beamlets No change in beamlets sizesize


Summary and Outlook - ISummary and Outlook - I

A novel multi-turn extraction is studied since a few A novel multi-turn extraction is studied since a few years: years: it allows manipulating transverse emittances in a it allows manipulating transverse emittances in a synchrotron!synchrotron!First MTE beam delivered to the SPS by mid-September First MTE beam delivered to the SPS by mid-September 2009 (about 1.5×102009 (about 1.5×101313 p/extraction). p/extraction).Equal sharing for islands/core achieved by the end of Equal sharing for islands/core achieved by the end of 2009.2009.In February 2010 the commissioning was resumed. In February 2010 the commissioning was resumed. High intensity beam was extracted (about 2.1×10High intensity beam was extracted (about 2.1×101313 p/extraction) with record intensity 2.6×10p/extraction) with record intensity 2.6×101313 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 longitudinal Activation of extraction septum due to the longitudinal structure of the beam (de-bunched as needed by the SPS).structure of the beam (de-bunched as needed by the SPS).

New optimised extraction scheme to avoid losses on New optimised extraction scheme to avoid losses on extraction septum -> beam commissioning in 2014.extraction septum -> beam commissioning in 2014.


Summary and Outlook - IISummary and Outlook - II

The same principle can be used for The same principle can be used for injectioninjection..Transverse shaping is possible, i.e. Transverse shaping is possible, i.e. generation of generation of hollow buncheshollow bunches..Lines of research:Lines of research:

Complete study of splitting process in 2D and Complete study of splitting process in 2D and extend to 4D.extend to 4D.Study trapping in 4D, i.e., manipulations in x-Study trapping in 4D, i.e., manipulations in x-y plane.y plane.Study intensity-dependent effects.Study intensity-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 First observations of intensity-dependent effects for transversely split beams during of intensity-dependent effects for transversely split beams during multiturn extraction studies at the CERN Proton Synchrotronmultiturn extraction studies at the CERN Proton Synchrotron”, Phys. ”, Phys. Rev. ST Accel. Beams . Rev. ST Accel. Beams . M. Giovannozzi, D. Quatraro, G. Turchetti, (2009). “M. Giovannozzi, D. Quatraro, G. Turchetti, (2009). “Generating unstable Generating unstable resonances for extraction schemes based on transverse splittingresonances for extraction schemes based on transverse splitting”, Phys. ”, Phys. Rev. ST Accel. Beams 12 024003. Rev. ST Accel. Beams 12 024003. A. Franchi, S. Gilardoni, M. Giovannozzi, (2009). “A. Franchi, S. Gilardoni, M. Giovannozzi, (2009). “Progresses in the Progresses in the studies of adiabatic splitting of charged particle beams by crossing studies of adiabatic splitting of charged particle beams by crossing nonlinear resonancesnonlinear 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 Principle and analysis of multiturn injection using stable islands of transverse phase spaceinjection using stable islands of transverse phase space”, Phys. Rev. ST ”, Phys. Rev. ST Accel. Beams 10 034001. Accel. Beams 10 034001. S. Gilardoni, M. Giovannozzi, M. Martini, E. Métral, P. Scaramuzzi, R. S. Gilardoni, M. Giovannozzi, M. Martini, E. Métral, P. Scaramuzzi, R. Steerenberg, A.-S. Müller, (2006). “Steerenberg, A.-S. Müller, (2006). “Experimental evidence of adiabatic Experimental evidence of adiabatic splitting of charged particle beams using stable islands of transverse splitting of charged particle beams using stable islands of transverse phase spacephase space”, Phys. Rev. ST Accel. Beams 9 104001. ”, Phys. Rev. ST Accel. Beams 9 104001. R. Cappi, M. Giovannozzi, (2003). “R. Cappi, M. Giovannozzi, (2003). “Multi-turn Extraction and Injection by Multi-turn Extraction and Injection by Means of Adiabatic Capture in Stable Islands of Phase SpaceMeans of Adiabatic Capture in Stable Islands of Phase Space”, Phys. ”, Phys. Rev. ST Accel. Beams 7 024001. Rev. ST Accel. Beams 7 024001. R. Cappi, M. Giovannozzi, (2002). “R. Cappi, M. Giovannozzi, (2002). “Novel Method for Multi-Turn Novel Method for Multi-Turn Extraction: Trapping Charged Particles in Islands of Phase SpaceExtraction: Trapping Charged Particles in Islands of Phase Space”, Phys. ”, Phys. Rev. Lett. 88 104801. The same principle can be used for injectionRev. Lett. 88 104801. The same principle can be used for injection..

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M. Giovannozzi

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