resonant multi-turn extraction: principle and experiments · massimo giovannozzi ral - july 5th...

Massimo Giovannozzi RAL - July 5th 2013 1

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

into resonance islands

M. Giovannozzi

Summary:

Introduction

Present multi-turn extraction

New multi-turn extraction (MTE)

Other applications

Measurement results

Conclusions


Introduction - I

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

Fast Extraction (one turn)

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

A septum magnet deflects displaced beam towards transfer line.

This extraction can be used both to transfer beam towards a ring or an experimental area.

Slow Extraction (millions turns)

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

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

This extraction is used to transfer beam towards an experimental area. What is in between?

Multi-tu

rn!


Introduction - II

Multi-turn extraction

The beam has to be “manipulated” to increase the effective length beyond the machine circumference.

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

AT CERN this mode is used to transfer the proton beam between PS and SPS. In the SPS the beam is used for

Fixed Target physics (broad sense)

Neutrino experiments (until 1998)

CERN Neutrino to Gran Sasso (CNGS) (from 2006)

These beams are high-intensity (about 3×1013 p in the PS).


Present multi-turn extraction – I

First PS batch Second PS batch Gap for kicker

CSPS = 11 CPS

PS PS

SPS circumference

Beam current transformer in the PS/SPS transfer line

1 2 3 4 5 (total spill duration 0.010 ms)


Electrostatic septum blade

Present multi-turn extraction – II

Length

Kicker

stre

ngth

Four turns

Fifth turn

X

X’

1 3 5

2

4 Slow bump

Slow bump

Electrostatic septum (beam shaving)

Extraction septum

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

Extraction line

Efield=0

Efield≠0


Present multi-turn extraction –III

The main drawbacks of the present scheme are: Losses (about 15% of total intensity) are unavoidable due to the presence of the electrostatic septum used to slice the beam.

The electrostatic septum is irradiated. This poses problems for hands-on maintenance.

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

The slices have different emittances and optical parameters.


Novel multi-turn extraction – I

The main ingredients of the novel extraction:

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

Nonlinear magnetic elements (sextupoles ad octupoles) to create stable islands. Slow (adiabatic) tune-variation to cross an appropriate resonance.

This approach has the following beneficial effects: Losses are reduced (virtually to zero). The phase space matching is improved with respect to the present situation. The beamlets have the same emittance and optical parameters.


Model used in numerical simulations

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

Vertical motion neglected.

Normalised (adimensional co-ordinates).

3

2

2

2

3 x

K

K

2 3

1

ˆ ˆ

ˆ ˆ ˆ ˆ' 'n n

X X

X X X X

R

Quadrupoles Sextupole Octupole

The linear tune is time-dependent


Novel multi-turn extraction – II

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

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

Left: initial phase space topology. No islands.


Novel multi-turn extraction - III

Tune variation

Phase space portrait

Simulation parameters:

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


Novel multi-turn extraction – IV

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

About 6 cm in physical space

Slow (few thousand turns) bump first (closed distortion of the periodic orbit)

Fast (less than one turn) bump afterwards (closed distortion of periodic orbit)

Bfield ≠ 0 Bfield = 0 At the septum location

Massimo Giovannozzi Oxford - July 4th 2013 12

Novel multi-turn extraction - V

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

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


Novel multi-turn extraction with other resonances - I

Tune variation



Hénon-like map with sextupole and octupole

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


Novel multi-turn extraction with other resonances - II

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

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


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

Possible applications: Four-turn extraction.

Deplete the core region to

achieve a better intensity

sharing.

Novel multi-turn extraction: 4th order unstable resonance - new application!

Master thesis Diego Quatraro Master thesis Diego Quatraro


Novel multi-turn injection: new application!


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

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

Tune variation


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


Novel multi-turn injection: new application!

Possible applications: transverse shaping of beam distribution.

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

“Standard” hollow beam distribution

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

The capture process - I

Quantitative analysis needed: To control sharing between core and beamlets.

To control the emittance sharing.

Adiabatic theory is the key concept: Probability trapping is proportional to the speed of variation of the island’s surface.

It is possible to account for the loss of adiabaticity close to the separatrix.

2D case seems under control.

The 4D case requires the usual conditions: weak coupling between the two degrees of freedom

no low order resonances in the vertical plane



The capture process - II Initial gaussian distribution Initial gaussian distribution Particles in island 2 Particles in island 2 Particles in island 4 Particles in island 4

Particles in island 6 Particles in island 6 Particles in island 8 Particles in island 8 Particles in beam core Particles in beam core

The capture process - III

Under these conditions: Scaling law for the size of the adiabatic region is well-reproduced.

Trapping probability is well-described.


Hénon-like model Hénon-like model

Size of non-adiabatic region Size of non-adiabatic region

Pendulum-like model Pendulum-like model


Analytical computation of island’s parameters

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

2 0,32 u

Distance of fixed points from origin of phase space

2

0,3

2

4 u

Distance between separatices

Normalised phase space

2

0,3

2

16 u

Island’s surface

2

sec 2 0,34 u

Distance from resonance

Secondary frequency


Experimental results

The pencil beam is kicked into the islands producing a strong coherent signal (filamentation is suppressed). Initial wiggles represent beam oscillations around the islands’ 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

on

dary

fre

qu

ency

Measurement results

Numerical simulations

Fit Pesato

Linear (Numericalsimulations)

Measured detuning inside an island compared to numerical simulations.

Measured detuning inside an island compared to numerical simulations.


Data analysis and beam parameters

The wire scanner is the key instrument for these studies.

Raw data are stored for off-line analysis.

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

Beam parameters

Intensity *H(s)/*V(s)

Low-intensity pencil beam

5×1011 2.3/ 1.3

Low-intensity large H emittance

5×1011 6.2/ 1.6

High intensity beam 6×1012 9.4/ 6.4


TimeQ

h

t

Qh=6.25

Profile measurements

180 ms Reversibility

Before

After Fast crossing: t 5 ms.

Trapped particles

Trapped particles

Slow crossing: t 90 ms.

Before

After

Large Gaussian tails

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


Influence of octupole strength Octupole action

Island size.

Detuning with amplitude.

Problems with the fit


Operational implementation - I

Sextupoles and octupoles are used to

Generate stable islands

Control size/position of islands

Control linear chromaticity

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

yxy

yxx

JhJhQ

JhJhQ

2,01,1

1,10,2

h2,0 -> detuning with amplitude (H-plane) -> x2 K3

h1,1 -> non-linear coupling -> xy K3

h0,2 -> detuning with amplitude (V-plane) -> y2 K3


Operational implementation - 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

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 s

Extraction: 0.835 s

Transverse dynamics - III


Phase space at 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

ord

er

chro

mat

icit

y,

de

tun

ing,

no

n-l

ine

ar c

ou

plin

g

Frac

tio

nal

tun

e an

d c

hro

mat

icit

y

Cycle time (s)

Qx Qx'/Qx

Qx'' h2,0

h1,1

Transverse dynamics - IV


To achieve good sharing of beam intensity between islands and core various parameters optimised (h1,1 is rather crucial).

12.0

12.5

13.0

13.5

14.0

14.5

15.0

15.5

16.0

16.5

17.0

0 100 200 300 400 500 600

Fra

cti

on

of

tra

pp

ed

pa

rti

cle

[%

]

Octupole current [A]

h11=0

h11=100

h11=200

h11=300

h11=500

Last bit achieved by exciting the beam using the transverse damper.

Current in octupoles 39/55 (A)

30 RAL - July 5th 2013 Massimo Giovannozzi

y = -0.0185x + 0.896R² = 0.0026

y = -0.1852x + 4.3783R² = 0.2631

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

12 14 16 18 20

Rat

io o

f co

re e

mit

tan

ce (

afte

r an

d b

efo

re s

plit

tin

g)

Fraction of particles trapped in islands (%)

Improving capture: beam excitation

Effect of transverse excitation

revprev TtNtfAtx 25.016sin'

Noise component


Evolution of beam distribution

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

Trapping performance


0 50 100 150 200 250 300

37 nsbin

0

2.0x1010

6.0x1010

1.0x1011

1.4x1011

Inte

nsity

0 50 100 150 200 250 300

37 nsbin

0

2.0x1010

6.0x1010

1.0x1011

1.4x1011

Inte

nsity

12 14 16 18 20

200

400

600

800

1000

Trapping (%)

Fre

quency

5000 10000 15000 20000 25000

Time elapsed from May 1st 15:00 (s)�

12

14

16

18

20

Tra

ppin

g (

%)

20% trapping 18% trapping

5 PS turns

Extraction efficiency


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

en

cy

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

Ext

ract

ion

eff

icie

ncy

(%

)

Time on May 1st

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

CT extraction efficiency is about 93%

CT vs. MTE: extraction losses

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

CT MTE


First observations of intensity-dependent effects - I

Usual process for trapping the beam into stable islands.

Varying parameter: total beam intensity.


Beamlets are moving with intensity!

First observations of intensity-dependent effects - II

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

Ntotal is expressed in units of 1010 p.

Possible sources: Image effects.

Direct effects (interaction between beamlets).


Consider projection effect

No change in beamlets size


Summary and Outlook - I

A novel multi-turn extraction is studied since a few years: it allows manipulating transverse emittances in a synchrotron! First MTE beam delivered to the SPS by mid-September 2009 (about 1.5×1013 p/extraction). Equal sharing for islands/core achieved by the end of 2009. In February 2010 the commissioning was resumed. High intensity beam was extracted (about 2.1×1013 p/extraction) with record intensity 2.6×1013 p/extraction. 2010 physics run at SPS was started using MTE beam. Open issues:

Variation of the fraction of particles trapped in islands. Activation of extraction septum due to the longitudinal structure of the beam (de-bunched as needed by the SPS).

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


Summary and Outlook - II

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

Complete study of splitting process in 2D and extend to 4D. Study trapping in 4D, i.e., manipulations in x-y plane. Study intensity-dependent effects. Study coupling with longitudinal dynamics (strong non-linear elements generate non-linear terms in the momentum compaction)

And many more!


Selected references

S. Gilardoni, M. Giovannozzi, C. Hernalsteens (2013). “First observations of intensity-dependent effects for transversely split beams during multiturn extraction studies at the CERN Proton Synchrotron”, Phys. Rev. ST Accel. Beams . M. Giovannozzi, D. Quatraro, G. Turchetti, (2009). “Generating unstable resonances for extraction schemes based on transverse splitting”, Phys. Rev. ST Accel. Beams 12 024003. A. Franchi, S. Gilardoni, M. Giovannozzi, (2009). “Progresses in the studies of adiabatic splitting of charged particle beams by crossing nonlinear resonances”, Phys. Rev. ST Accel. Beams 12 014001. M. Giovannozzi and J. Morel, (2007). “Principle and analysis of multiturn injection using stable islands of transverse phase space”, Phys. Rev. ST Accel. Beams 10 034001. S. Gilardoni, M. Giovannozzi, M. Martini, E. Métral, P. Scaramuzzi, R. Steerenberg, A.-S. Müller, (2006). “Experimental evidence of adiabatic splitting of charged particle beams using stable islands of transverse phase space”, Phys. Rev. ST Accel. Beams 9 104001. R. Cappi, M. Giovannozzi, (2003). “Multi-turn Extraction and Injection by Means of Adiabatic Capture in Stable Islands of Phase Space”, Phys. Rev. ST Accel. Beams 7 024001. R. Cappi, M. Giovannozzi, (2002). “Novel Method for Multi-Turn Extraction: Trapping Charged Particles in Islands of Phase Space”, Phys. Rev. Lett. 88 104801. The same principle can be used for injection.

resonant multi-turn extraction: principle and experiments · massimo giovannozzi ral - july 5th...

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