Manipulation of transverse beam Manipulation of transverse beam - - PowerPoint PPT Presentation

Massimo Giovannozzi Massimo Giovannozzi Oxford Oxford -

• July 4th 2013

July 4th 2013 1 1

Manipulation of transverse beam Manipulation of transverse beam distribution in circular accelerators: distribution in circular accelerators: beam splitting by particles beam splitting by particles’ ’ trapping trapping into resonance islands into resonance islands

• M. Giovannozzi
• M. Giovannozzi

Summary: Summary:

  Introduction

Introduction

  Present multi

Present multi-

• turn extraction

turn extraction

  New multi

New multi-

• turn extraction (MTE)

turn extraction (MTE)

  Other applications

Other applications

  Measurement results

Measurement results

  Conclusions

Conclusions

Massimo Giovannozzi Massimo Giovannozzi Oxford Oxford -

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Introduction Introduction -

• I

I

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

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

A kicker A kicker (fast dipole) (fast dipole) displaces displaces the beam from the beam from nominal closed orbit. nominal closed orbit. A septum magnet A septum magnet deflects deflects displaced beam towards displaced beam towards transfer line. transfer line. This extraction can be used This extraction can be used both to both to transfer transfer beam beam towards a towards a ring ring

• r

an

• r

an experimental area experimental area. .

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

The The separatix

• f the third

separatix

• f the third-
• rder

resonance

• rder

resonance increases increases particles particles’ ’ amplitude until they amplitude until they jump beyond the septum. jump beyond the septum. The The tune is changed tune is changed to shrink to shrink the stable region, thus pushing the stable region, thus pushing the particles towards larger the particles towards larger amplitudes. amplitudes. This extraction is used to This extraction is used to transfer beam towards an transfer beam towards an experimental area experimental area. .

What is in between? What is in between?

Multi Multi-

• turn!

turn!

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Introduction Introduction -

• II

II

Multi Multi-

• turn extraction

turn extraction

The beam has to be The beam has to be “ “manipulated manipulated” ” to increase the to increase the effective length beyond the machine circumference. effective length beyond the machine circumference. This extraction mode is used to This extraction mode is used to transfer beam between transfer beam between circular machines circular machines. . AT CERN this mode is used to AT CERN this mode is used to transfer transfer the proton beam the proton beam between between PS PS and and SPS

• SPS. In the SPS the beam is used for

. In the SPS the beam is used for

Fixed Target Fixed Target physics (broad sense) physics (broad sense) Neutrino experiments Neutrino experiments (until 1998) (until 1998) CERN Neutrino to Gran Sasso CERN Neutrino to Gran Sasso (CNGS) (from 2006) (CNGS) (from 2006)

These beams are These beams are high high-

• intensity

intensity (about (about 3 3× ×10 1013

13 p

p in the in the PS). PS).

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Present multi Present multi-

• turn extraction

turn extraction – – I I

First PS batch First PS batch Second PS batch Second PS batch Gap for kicker Gap for kicker C CSPS

SPS = 11 C

= 11 CPS

PS

PS PS PS PS SPS circumference SPS circumference Beam current Beam current transformer in the transformer in the PS/SPS transfer line PS/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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Electrostatic septum Electrostatic septum blade blade

Present multi Present multi-

• turn extraction

turn extraction – – II II

Length Length Kicker strength Kicker strength Four turns Four turns Fifth turn Fifth turn X X X X’ ’

1 1 3 3 5 5 2 2 4 4 Slow bump Slow bump Slow bump Slow bump Electrostatic Electrostatic septum septum (beam shaving) (beam shaving) Extraction septum Extraction septum Kicker magnets Kicker magnets used to generate used to generate a closed orbit a closed orbit bump around bump around electrostatic electrostatic septum septum Extraction Extraction line line

E Efield

field=0

=0 E Efield

field≠

≠0

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Present multi Present multi-

• turn extraction

turn extraction – –III III

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

Losses (about Losses (about 15% 15% of total intensity) are unavoidable

• f total intensity) are unavoidable

due to the presence of the due to the presence of the electrostatic electrostatic septum used septum used to slice the beam. to slice the beam. The The electrostatic electrostatic septum is septum is irradiated

• irradiated. This poses

. This poses problems for problems for hands hands-

• on maintenance
• n maintenance.

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

• up

up. . The slices have different emittances and

• ptical

The slices have different emittances and

• ptical

parameters. parameters.

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Novel multi Novel multi-

• turn extraction

turn extraction – – I I

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

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

Nonlinear magnetic elements Nonlinear magnetic elements (sextupoles ad octupoles) to (sextupoles ad octupoles) to create create stable islands stable islands. . Slow ( Slow (adiabatic adiabatic) tune ) tune-

• variation to cross an appropriate

variation to cross an appropriate resonance. resonance.

This approach has the following beneficial effects: This approach has the following beneficial effects:

Losses are reduced Losses are reduced (virtually to zero). (virtually to zero). The The phase space matching is improved phase space matching is improved with respect to the with respect to the present situation. present situation. The beamlets have the The beamlets have the same emittance same emittance and and

• ptical
• ptical

parameters parameters. .

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Model used in numerical simulations Model used in numerical simulations

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 (H Hé énon non-

• like

polynomial like polynomial maps maps). ). Vertical motion neglected. Vertical motion neglected. Normalised (adimensional co Normalised (adimensional co-

• ordinates).
• rdinates).

 

2 3 1

ˆ ˆ ˆ ˆ ˆ ˆ ' '

n n

X X X X X X  



                   R

3 2 2

2 3

x

K K   

Quadrupoles Quadrupoles Sextupole Sextupole Octupole Octupole The linear tune is The linear tune is time time-

• dependent

dependent

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Novel multi Novel multi-

• turn extraction

turn extraction – – II II

Right: intermediate Right: intermediate phase space topology. phase space topology. Islands are created Islands are created near the centre. near the centre. Bottom: final phase Bottom: final phase space topology. space topology. Islands are separated Islands are separated to allow extraction. to allow extraction. Left: initial phase Left: initial phase space topology. No space topology. No islands. islands.

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Novel multi Novel multi-

• turn extraction

turn extraction -

• III

III

Tune variation Tune variation Phase space Phase space portrait portrait

Simulation Simulation parameters: parameters: H Hé énon non-

• like

like map (i.e. 2D map (i.e. 2D polynomial polynomial – – degree 3 degree 3

• mapping)

mapping) representing representing a FODO cell a FODO cell with with sextupole and sextupole and

• ctupole
• ctupole

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Novel multi Novel multi-

• turn extraction

turn extraction – – IV IV

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 space About 6 cm in physical space Slow ( Slow (few thousand few thousand turns turns) bump first ) bump first (closed distortion

• f

(closed distortion

• f

the periodic orbit) the periodic orbit) Fast ( Fast (less than

• ne

less than

• ne

turn turn) bump afterwards ) bump afterwards (closed distortion

• f

(closed distortion

• f

periodic orbit) periodic orbit)

B Bfield

field ≠

≠ 0 B Bfield

field =

= 0 At the septum location At the septum location

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Novel multi Novel multi-

• turn extraction

turn extraction -

• V

V

The

• riginal

goal

• f

this study was to find a The

• riginal

goal

• f

this study was to find a replacement to the present Continuous Transfer replacement to the present Continuous Transfer used at CERN for the high used at CERN for the high-

• intensity proton beams.

intensity proton beams. However the novel technique proved to be useful However the novel technique proved to be useful also in different context, e.g. also in different context, e.g.

The same approach can be applied for The same approach can be applied for multi multi-

• turn

turn injection injection (time (time-

• reversal

property

• f

the physics reversal property

• f

the physics involved). involved). multi multi-

• turn extraction

turn extraction

• ver a
• ver a

different number different number

• f
• f

turns can be designed, provided the appropriate turns can be designed, provided the appropriate resonance is used. resonance is used. Multiple multi Multiple multi-

• turn

turn extractions could be considered, extractions could be considered, e.g. to extract the beam remaining in the central e.g. to extract the beam remaining in the central part of phase space. part of phase space.

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Novel multi Novel multi-

• turn extraction with

turn extraction with

• ther resonances
• ther resonances -
• I

I

Tune variation Tune variation Phase space Phase space portrait portrait

Simulation Simulation parameters: parameters: H Hé énon non-

• like

like map with map with sextupole sextupole and octupole and octupole The third The third-

• rder
• rder

resonance is resonance is used, thus used, thus giving a giving a three three-

• turn

turn extraction extraction

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Novel multi Novel multi-

• turn extraction with

turn extraction with

• ther resonances
• ther resonances -
• II

II

The fifth The fifth-

• order

resonance is

• rder

resonance is used, thus giving a six used, thus giving a six-

• turn

turn extraction extraction The second The second-

• order resonance is
• rder resonance is

used, thus giving a two used, thus giving a two-

• turn

turn extraction extraction

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Non Non-

• linear elements can be used to make the

linear elements can be used to make the fourth fourth-

• order resonance unstable by canceling
• rder resonance unstable by canceling

the amplitude detuning. the amplitude detuning. Possible applications: Possible applications:

Four Four-

• turn extraction.

turn extraction. Deplete the core region to Deplete the core region to achieve a better intensity achieve a better intensity sharing. sharing.

Novel multi Novel multi-

• turn extraction:

turn extraction: 4 4th

th order

• rder

unstable resonance unstable resonance -

• new application!

new application!

Master thesis Diego Quatraro Master thesis Diego Quatraro Master thesis Diego Quatraro

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Novel multi Novel multi-

• turn

turn injection injection: new : new application! application!

Simulation parameters: Simulation parameters: Third Third-

• order polynomial
• rder polynomial

map representing a map representing a FODO cell with FODO cell with sextupole and octupole sextupole and octupole The fourth The fourth-

• order
• rder

resonance is used for resonance is used for a four a four-

• turn injection

turn injection Tune variation Tune variation Phase space Phase space portrait portrait

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

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Novel multi Novel multi-

• turn

turn injection injection: new : new application! application!

Possible applications: transverse shaping of beam Possible applications: transverse shaping of beam distribution. 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 beams than standard multi-

• turn injection!

turn injection!

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

AB, 10, 034001 (2007) “ “Standard Standard” ” hollow hollow beam distribution beam distribution “ “Flat Flat” ” beam distribution obtained by injecting a fifth turn beam distribution obtained by injecting a fifth turn in the centre. in the centre.

The capture process The capture process -

• I

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 variation Probability trapping is proportional to the speed of variation

• f the island
• f the island’

’s surface. s surface. It is possible to account for the loss of adiabaticity close to It is possible to account for the loss of adiabaticity close to the 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 freedom weak coupling between the two degrees of freedom no low order resonances in the vertical plane no low order resonances in the vertical plane

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Massimo Giovannozzi Massimo Giovannozzi Oxford Oxford -

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The capture process The capture process -

• II

II

Initial gaussian distribution Initial gaussian distribution Initial gaussian distribution Particles in island 2 Particles in island 2 Particles in island 2 Particles in island 4 Particles in island 4 Particles in island 4 Particles in island 6 Particles in island 6 Particles in island 6 Particles in island 8 Particles in island 8 Particles in island 8 Particles in beam core Particles in beam core Particles in beam core

The capture process The capture process -

• III

III

Under these conditions: Under these conditions:

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

• reproduced.

reproduced. Trapping probability is well Trapping probability is well-

• described.

described.

Massimo Giovannozzi Massimo Giovannozzi Oxford Oxford -

• July 4th 2013

July 4th 2013 20 20 Hénon-like model H Hé énon non-

• like model

like model Size of non-adiabatic region Size of non Size of non-

• adiabatic

adiabatic region region Pendulum-like model Pendulum Pendulum-

• like model

like model

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

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

2 0,3

2 u   

     Distance

• f

fixed points Distance

• f

fixed points from origin of phase space from origin of phase space

2 0,3 2

4 u      

Distance between separatices Distance between separatices

Normalised phase space Normalised phase space

2 0,3 2

16 u  



 

Island Island’ ’s surface s surface

2 sec 2 0,3

4 u      

Distance from resonance Distance from resonance Secondary frequency Secondary frequency

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Operational implementation Operational implementation -

• I

I

Sextupoles and octupoles are used to Sextupoles and octupoles are used to Generate stable islands Generate stable islands Control size/position of islands Control size/position of islands Control linear chromaticity Control linear chromaticity Control non Control non-

• linear coupling (

linear coupling (using an additional set of using an additional set of

• ctupoles, normally used to combat instabilities
• ctupoles, normally used to combat instabilities)

)

y x y y x x

J h J h Q J h J h Q

2 , 1 , 1 1 , 1 , 2

     

h h2,0

2,0 -

• > detuning with amplitude (H

> detuning with amplitude (H-

• plane)

plane) -

• >

>    x

x 2 2 K

K3

3

h h1,1

1,1 -

• > non

> non-

• linear coupling

linear coupling -

• >

>    x

x

y

y K

K3

3

h h0,2

0,2 -

• > detuning with amplitude (V

> detuning with amplitude (V-

• plane)

plane) -

• >

>    y

y 2 2 K

K3

3

Massimo Giovannozzi Massimo Giovannozzi Oxford Oxford -

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Operational implementation Operational implementation -

• II

II

• 600
• 400
• 200

200 400 600 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Currents(A) B-field (T) Cycle time (s) B-field Sextupole39 Sextupole55 Octupole39 Octupole55 Octupoles

• 600
• 400
• 200

200 400 600 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.72 0.74 0.76 0.78 0.80 0.82 Currents(A) B-field (T) Cycle time (s) B-field Sextupole39 Sextupole55 Octupole39 Octupole55 Octupoles

Injection: 0.170 s Injection: 0.170 s Extraction: 0.835 s Extraction: 0.835 s

Transverse dynamics Transverse dynamics -

• III

III

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Phase space at septum Phase space at septum

• 3000
• 2000
• 1000

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 Second order chromaticity, detuning, non-linear coupling Fractional tune and chromaticity Cycle time (s) Qx Qx'/Qx Qx'' h2,0 h1,1

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Evolution of beam distribution Evolution of beam distribution

Horizontal beam profiles in Horizontal beam profiles in section 54 section 54 have been taken have been taken during the capture process (total intensity during the capture process (total intensity ~ ~2.1 2.1× ×10 1013

13).

).

Trapping performance Trapping performance

26 26 Oxford Oxford -

• July 4th 2013

July 4th 2013 Massimo Giovannozzi Massimo Giovannozzi

50 100 150 200 250 300 37nsbin 2.0x1010 6.0x1010 1.0x1011 1.4x1011 Intensity 50 100 150 200 250 300 37nsbin 2.0x1010 6.0x1010 1.0x1011 1.4x1011 Intensity

12 14 16 18 20 200 400 600 800 1000 Trapping (%) Frequency

5000 10000 15000 20000 25000 Time elapsed from May 1st 15:00 (s) 12 14 16 18 20 Trapping (%)

20% trapping 20% trapping 18% trapping 18% trapping 5 PS turns 5 PS turns

Extraction efficiency Extraction efficiency

27 27 Oxford Oxford -

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July 4th 2013 Massimo Giovannozzi Massimo Giovannozzi

Regular fluctuations in Regular fluctuations in the extraction efficiency the extraction efficiency are also

• bserved

and are also

• bserved

and seem well correlated to seem well correlated to spill fluctuations. spill fluctuations.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 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 Frequency 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 Extraction efficiency (%) Time on May 1st

Distribution

• f

extraction Distribution

• f

extraction efficiency is peaked at efficiency is peaked at about 98% about 98% (NB: the beam is (NB: the beam is debunched at extraction! debunched at extraction! Unavoidable beam losses are Unavoidable 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 losses CT 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 the The CT losses are spread around the ring whereas for MTE the losses are more concentrated on the extraction septum as anticip losses are more concentrated on the extraction septum as anticipated ated in the MTE Design Report. in the MTE Design Report.

CT CT MTE MTE

28 28 Oxford Oxford -

• July 4th 2013

July 4th 2013 Massimo Giovannozzi Massimo Giovannozzi

First observations of intensity First observations of intensity-

• dependent effects

dependent effects -

• I

I

Usual process for trapping the beam into Usual process for trapping the beam into stable islands. stable islands. Varying parameter: total beam intensity. Varying parameter: total beam intensity.

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

First observations of intensity First observations of intensity-

• dependent effects

dependent effects -

• II

II

The

• bserved

The

• bserved

effect can be effect can be explained with an explained with an intensity intensity-

• dependent

shift dependent shift

• f

the single

• f

the single particle tune. particle tune. Possible sources: Possible sources:

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

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Consider projection effect Consider projection effect No change in beamlets size No change in beamlets size

Massimo Giovannozzi Massimo Giovannozzi Oxford Oxford -

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Summary and Outlook Summary and Outlook -

• I

I

A novel multi A novel multi-

• turn extraction is studied since a few years:

turn extraction is studied since a few years: it it allows manipulating transverse emittances in a synchrotron! allows manipulating transverse emittances in a synchrotron! First MTE beam delivered to the SPS by mid First MTE beam delivered to the SPS by mid-

• September

September 2009 (about 1.5 2009 (about 1.5× ×10 1013

13 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 2.1 High intensity beam was extracted (about 2.1× ×10 1013

13

p/extraction) with record intensity 2.6 p/extraction) with record intensity 2.6× ×10 1013

13 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

• f

extraction septum due to the longitudinal Activation

• f

extraction septum due to the longitudinal structure of the beam (de structure of the beam (de-

• bunched as needed by the SPS).

bunched as needed by the SPS).

New

• ptimised

extraction scheme to avoid losses

• n

New

• ptimised

extraction scheme to avoid losses

• n

extraction septum extraction septum -

• > beam commissioning in 2014.

> beam commissioning in 2014.

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Summary and Outlook Summary and Outlook -

• II

II

The same principle can be used for injection The same principle can be used for injection. . Transverse shaping is possible, i.e. generation Transverse shaping is possible, i.e. generation

• f
• f hollow bunches

hollow bunches. . Lines of research: Lines of research:

Complete study of splitting process in 2D and extend Complete study of splitting process in 2D and extend to 4D. to 4D. Study trapping in 4D, i.e., manipulations in x Study trapping in 4D, i.e., manipulations in x-

• y

y plane. plane. Study intensity Study intensity-

• dependent effects.

dependent effects.

And many more! And many more!

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Selected references Selected references

S. Gilardoni, M. Giovannozzi, C. Hernalsteens (2013). S. Gilardoni, M. Giovannozzi, C. Hernalsteens (2013). “ “First

• bservations
• f

First

• bservations
• f

intensity intensity-

• dependent

effects for transversely split beams during multiturn dependent effects for transversely split beams during multiturn extraction studies at the CERN Proton Synchrotron extraction 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 unstable Generating unstable resonances for extraction schemes based on transverse splitting resonances for extraction schemes based on transverse splitting” ”, Phys. Rev. ST , Phys. Rev. ST

• Accel. 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 of Progresses in the studies of adiabatic splitting of charged particle beams by crossing nonlin adiabatic splitting of charged particle beams by crossing nonlinear resonances ear 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 injection Principle and analysis of multiturn injection using stable islands of transverse phase space using stable islands of transverse phase space” ”, Phys. Rev. ST Accel. Beams 10 , Phys. Rev. ST Accel. Beams 10 034001. 034001. S. Gilardoni, M. Giovannozzi, M. Martini, E. M S. Gilardoni, M. Giovannozzi, M. Martini, E. Mé étral, P. Scaramuzzi, R. tral, P. Scaramuzzi, R. Steerenberg, A. Steerenberg, A.-

• S. M
• S. Mü

üller, (2006). ller, (2006). “ “Experimental evidence of adiabatic splitting Experimental evidence of adiabatic splitting

• f charged particle beams using stable islands of transverse pha
• f charged particle beams using stable islands of transverse phase space

se 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). “

“Multi Multi-

• turn Extraction and Injection by Means

turn Extraction and Injection by Means

• f Adiabatic Capture in Stable Islands of Phase Space
• f 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 Multi Novel Method for Multi-

• Turn

Extraction: Turn Extraction: Trapping Charged Particles in Islands

• f

Phase Space Trapping Charged Particles in Islands

• f

Phase Space” ”, Phys. Rev. Lett. 88 , Phys. Rev. Lett. 88

• 104801. The same principle can be used for injection
• 104801. The same principle can be used for injection.

.