Massimo GiovannozziCOULOMB'05 - 12-16 September 20051 Resonant multi-turn extraction: principle and experiments M. Giovannozzi and S. Gilardoni, M. Martini,

Massimo GiovanMassimo Giovannozzinozzi

COULOMB'05 - 12-16 SeptCOULOMB'05 - 12-16 September 2005 ember 2005

11

Resonant multi-turn Resonant multi-turn extraction: principle and extraction: principle and

experimentsexperimentsM. GiovannozziM. Giovannozzi

andand

S. Gilardoni, M. Martini, E. Métral, P. S. Gilardoni, M. Martini, E. Métral, P. Scaramuzzi, R. Steerenberg, Scaramuzzi, R. Steerenberg, CERNCERN

A.-S. Müller, A.-S. Müller, ISSISS, , Forschungszentrum KarlsruheForschungszentrum Karlsruhe

Summary:Summary:

Introduction Introduction

Present multi-turn Present multi-turn extractionextraction

New multi-turn extractionNew multi-turn extraction

Measurement resultsMeasurement results

Conclusions Conclusions



22

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!



33

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). CNGS would appreciate having even in the PS). CNGS would appreciate having even more (about more (about 4.84.8××10101313 p p in the PS). in the PS).



44

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)



55

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



66

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.



77

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..



88

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



99

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.



1010

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



1111

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



1212

The capture process - IThe capture process - I

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



1313

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Sigma

Nu

mb

er o

f p

arti

cles

(N

/N0)

Isl #2 Isl #4 Isl #6Isl #8 Isl #5

The capture process - IIThe capture process - II

Numerical Numerical simulationssimulations


Relative number of Relative number of particles in beamlets particles in beamlets vs. sigma of initial vs. sigma of initial gaussian distributiongaussian distribution

Relative number of Relative number of particles in beamlets particles in beamlets vs. sigma of initial vs. sigma of initial gaussian distributiongaussian distribution



1414

The capture process - IIIThe capture process - III

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Sigma

Rel

ativ

e em

itta

nce

(e /e 0)

Isl #2 Isl #4 Isl #6 Isl #8 Isl #5



Relative emittance Relative emittance of beamlets vs. of beamlets vs. sigma of initial sigma of initial Gaussian Gaussian distributiondistribution

Relative emittance Relative emittance of beamlets vs. of beamlets vs. sigma of initial sigma of initial Gaussian Gaussian distributiondistribution



1515

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

ee

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

20,3

2

4 ue

Distance between Distance between separaticesseparatices

Normalised phase Normalised phase

spacespace

20,3

2

16 ue

Island’s surfaceIsland’s surface

2sec 2 0,34 u e

Distance from resonanceDistance from resonance

Secondary frequencySecondary frequency



1616

Example: how to keep Example: how to keep island’s surface constantisland’s surface constant

To be tested with numerical simulations…To be tested with numerical simulations…

XX

X’X’ 1X’X’

XX

2

XX’’

XX

3

2

1

3



1717

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.



1818

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



1919

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



2020

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!

Study in progress with Study in progress with the contribution by J. the contribution by J. Morel.Morel.

Study in progress with Study in progress with the contribution by J. the contribution by J. Morel.Morel.



2121

Experimental results - IExperimental results - I

Experimental tests were undertaken since Experimental tests were undertaken since 20022002..

2002 run2002 run: proof-of-principle of the capture : proof-of-principle of the capture process using a low intensity beam.process using a low intensity beam.2003 run2003 run: detailed study of capture process : detailed study of capture process with low-intensity beam and first tests with with low-intensity beam and first tests with high-intensity proton beam.high-intensity proton beam.2004 run2004 run: main focus on high-intensity : main focus on high-intensity beam to solve problems observed in beam to solve problems observed in 20032003..

Overall strategy:Overall strategy:Phase spacePhase space reconstruction using low- reconstruction using low-intensity, pencil beam.intensity, pencil beam.CaptureCapture with with low-intensitylow-intensity, large horizontal , large horizontal emittance beam.emittance beam.CaptureCapture with with high-intensityhigh-intensity beam. beam.



2222

Extraction line

Slow bump

Sextupole magnets

Extraction septum

Octupole magnets

Flying wires

Kicker magnet

Section 71

Section 64

Section 55

Section 16

Section 21

Section 20

Section 54

Extraction line

Slow bump

Sextupole magnets

Extraction septum

Octupole magnets

Flying wires

Kicker magnet

Section 71

Section 64

Section 55

Section 16

Section 21

Section 20

Section 54Experimental results - IIExperimental results - II

Key elements for Key elements for experimental experimental tests.tests.

Phase space Phase space reconstruction is reconstruction is based on fast based on fast digitiser applied digitiser applied to closed orbit to closed orbit pick-ups.pick-ups.

Key elements for Key elements for experimental experimental tests.tests.

Phase space Phase space reconstruction is reconstruction is based on fast based on fast digitiser applied digitiser applied to closed orbit to closed orbit pick-ups.pick-ups.



2323

Experimental results - IIIExperimental results - III

The pencil beam is The pencil beam is kicked intokicked into the islands producing a the islands producing a strong strong coherent signalcoherent signal (filamentation is (filamentation is suppressed).suppressed).Initial Initial wiggleswiggles represent represent beam beam oscillationsoscillations around the around the islands’ islands’ centre.centre.

Normalized Coordinates

-15 -5 5 15-15

15

X

-5

5

H Signal PU1: blue - PU2: red

50 150 250 350 450 550 650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850 1950-20-10

01020

Turn

y = -0.9211 x + 0.0398

y = -0.7566 x + 0.0408

0.020

0.025

0.030

0.035

0.040

0.045

0.000 0.002 0.004 0.006 0.008 0.010 0.012

Linear invariant

Sec

ond

ary

freq

uen

cy

Measurement results

Numerical simulations

Fit Pesato

Linear (Numericalsimulations)

Measured detuning Measured detuning inside an island inside an island compared to numerical compared to numerical simulations.simulations.

Measured detuning Measured detuning inside an island inside an island compared to numerical compared to numerical simulations.simulations.



2424

Data analysis and beam Data analysis and beam parametersparameters

The wire scanner is the key The wire scanner is the key instrument for these studies.instrument for these studies.

Raw data are stored for off-line Raw data are stored for off-line analysis.analysis.

Five Gaussians are fitted to Five Gaussians are fitted to the measured profiles to the measured profiles to estimate beam parameters of estimate beam parameters of five beamlets.five beamlets.

Beam parametersBeam parametersIntensityIntensity ee**HH(()/)/ee**VV(())

Low-intensity Low-intensity pencil beampencil beam 55××10101111 2.3/ 1.32.3/ 1.3

Low-intensity Low-intensity large H emittancelarge H emittance 55××10101111 6.2/ 1.66.2/ 1.6

High intensity High intensity beambeam 66××10101212 9.4/ 6.49.4/ 6.4



2525

TimeQ

h

t

Qh=6.25

Profile measurements

180 msReversibilitReversibilityy

BeforeBefore

AfterAfterFast crossing: Fast crossing: t 5 ms.t 5 ms.

Trapped Trapped particlesparticles

Trapped Trapped particlesparticles

Slow Slow crossing: crossing: t t 90 ms.90 ms.

BeforeBefore

AfterAfter

Large Large GaussianGaussian tailstails

No difference No difference observed if observed if t > 20-t > 20-40 ms.40 ms.

No difference No difference observed if observed if t > 20-t > 20-40 ms.40 ms.



2626

Influence of octupole Influence of octupole strengthstrength

Octupole action Octupole action

Island size.Island size.

Detuning with Detuning with amplitude.amplitude.

Problems with the Problems with the fitfit



2727

Crucial part: high-intensity Crucial part: high-intensity beam - Ibeam - I

Reduction of octupole Reduction of octupole strength to move the strength to move the beamlets outwardsbeamlets outwards

- 5.0

- 4.0

- 3.0

- 2.0

- 1.0

0.0

1.0

2.0

3.0

4.0

5.0

0 200 400 600 800 1000 1200 1400 1600Time (ms)

A.

U.

New Octupole function Standard Octupole function

Magnetic field Focusing quadrupoles

Defocusing quadrupoles

14 GeV/c flat-top14 GeV/c flat-top

1.4 GeV flat-1.4 GeV flat-bottombottom

Tune Tune sweep sweep



2828

After optimisation of After optimisation of transverse and longitudinal transverse and longitudinal parametersparameters

Capture losses are Capture losses are reduced to zero…reduced to zero…

Horizontal beam Horizontal beam profileprofile

Horizontal beam Horizontal beam profileprofile

Depleted region: Depleted region: extraction septum extraction septum blade will not blade will not intercept any intercept any particleparticle

Depleted region: Depleted region: extraction septum extraction septum blade will not blade will not intercept any intercept any particleparticle



2929

A movie to show the A movie to show the evolution of beam evolution of beam distributiondistribution

A series of A series of horizontal beam horizontal beam profiles in profiles in section section 5454 have been have been taken during the taken during the capture process.capture process.

The beam is the The beam is the high-intensity high-intensity one.one.



3030

Other studies with high-Other studies with high-intensity beams: how to intensity beams: how to increase the fraction of increase the fraction of trapped particlestrapped particles

The horizontal emittance delivered by the PS-The horizontal emittance delivered by the PS-Booster was increased at its maximum value.Booster was increased at its maximum value.The strength of the octupole was varied to The strength of the octupole was varied to change the island sizechange the island sizeThe strength of the sextupoles was changed The strength of the sextupoles was changed too (more difficult as this has an impact on too (more difficult as this has an impact on chromaticity).chromaticity).Summary of results (detailed data analysis is Summary of results (detailed data analysis is in progress)in progress)

The fraction of trapped particles reached about 18% The fraction of trapped particles reached about 18% ((NB: the limit set by SPS on the turn-by-turn NB: the limit set by SPS on the turn-by-turn intensity variation is 20% intensity variation is 20% ±±5% for the last beamlet5% for the last beamlet).).Some losses were observed during resonance Some losses were observed during resonance crossing (about 2-3%).crossing (about 2-3%).



3131

-450

-350

-250

-150

-50

50

150

250

150 350 550 750 950 1150

Time (ms)

Cu

rren

t (A

)

OctupoleSextupole

Experimental conditions Experimental conditions sextupoles and octupole scansextupoles and octupole scan

InjectioInjectionn

Free parameter Free parameter during octupole during octupole scanscan

Free parameter Free parameter during sextupole during sextupole scanscan

Profile Profile measurementmeasurement

Beginning of Beginning of magnetic flat-magnetic flat-toptop



3232

Best result in terms of captureBest result in terms of capture

Assuming that:Assuming that:

Beamlets are Beamlets are affected by a affected by a different solid angledifferent solid angle

Beamlets are fitted Beamlets are fitted using five gaussians. using five gaussians. Instead of imposing Instead of imposing the same integral for the same integral for the four beamlets the four beamlets (physical (physical arguments), only arguments), only three have such a three have such a constraint (solid constraint (solid angle consideration). angle consideration).

Fit constraint: Fit constraint: same integralsame integral

CaptuCapturere

18%18% three three rightmost rightmost beamletsbeamlets

16%16% single single leftmost beamletleftmost beamlet

Scintillator Scintillator is on this is on this side!side!



3333

Fast-extraction tests in TT2Fast-extraction tests in TT2

The high-intensity The high-intensity beam is fast beam is fast extracted towards extracted towards the dump D3. the dump D3.

Prior to extraction Prior to extraction beamlets are beamlets are partially merged partially merged back with central back with central core.core.

The OTR in TT2 allows visualising the The OTR in TT2 allows visualising the 2D beam distribution (pixel size is 2D beam distribution (pixel size is 225 225 m).m).

The OTR in TT2 allows visualising the The OTR in TT2 allows visualising the 2D beam distribution (pixel size is 2D beam distribution (pixel size is 225 225 m).m).

Beamlets projected onto x-Beamlets projected onto x-axisaxis

Beamlets projected onto x-Beamlets projected onto x-axisaxis



3434

Summary and Outlook - ISummary and Outlook - I

A novel multi-turn extraction is under study A novel multi-turn extraction is under study since a few yearssince a few yearsThis approach allows manipulating the This approach allows manipulating the transverse emittance in a synchrotron!transverse emittance in a synchrotron!Numerical simulations on a simple model Numerical simulations on a simple model confirmed the validity of the principle.confirmed the validity of the principle.Experimental tests showed that:Experimental tests showed that:

Capture into stable islandsCapture into stable islands: : successfully*successfully* obtained obtained with both with both low-low- and and high-intensityhigh-intensity, single-bunch beam., single-bunch beam.Beamlets separationBeamlets separation: : successfully*successfully* obtained with both obtained with both low-low- and and high-intensityhigh-intensity, single-bunch beam., single-bunch beam.multi-turn extraction propermulti-turn extraction proper: attempted. Hardware : attempted. Hardware limitations might prevent realistic tests.limitations might prevent realistic tests.Increased trapping fractionIncreased trapping fraction: latest tests showed that : latest tests showed that about 18 % can be trapped inside islands. However, about 18 % can be trapped inside islands. However, some beam losses at resonance crossing where some beam losses at resonance crossing where observed (2-3 %).observed (2-3 %).

*without measurable losses*without measurable losses



3535

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..

Next steps:Next steps:Final decision should be taken in Final decision should be taken in Fall 2005Fall 2005 about the definition of a project to implement about the definition of a project to implement the proposed multi-turn extraction.the proposed multi-turn extraction.

Critical issue is the construction of Critical issue is the construction of kickers kickers for for the novel extraction layout.the novel extraction layout.

Exact time scale has to be definedExact time scale has to be defined..

The The implementationimplementation will be will be stagedstaged (two steps) (two steps)

First stage should be operational by First stage should be operational by 20082008

Documents

Massimo GiovannozziCOULOMB'05 - 12-16 September 20051 Resonant multi-turn extraction: principle and experiments M. Giovannozzi and S. Gilardoni, M. Martini,