Manipulation of transverse beam
distribution in circular accelerators:
beam splitting by particles’ trapping
into resonance islands
M. Giovannozzi
Summary:

Introduction

Other applications

Present multi-turn extraction

Measurement results

New multi-turn extraction (MTE)  Conclusions
Massimo Giovannozzi
Oxford - July 4th 2013
1
Introduction - I
Three approaches are normally used to extract beam
from a circular machine:
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.
What is in between?
Massimo Giovannozzi
Slow
turns)
Multi-turn!
Fast Extraction (one turn)
Extraction
(millions
The separatix of the thirdorder
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.
Oxford - July 4th 2013
2
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).
Massimo Giovannozzi
Oxford - July 4th 2013
3
Present multi-turn extraction – I
CSPS = 11 CPS
PS
PS
SPS circumference
First PS batch Second PS batch Gap for kicker
Beam current
transformer in the
PS/SPS transfer line
1 2 3 4 5 (total spill duration 0.010 ms)
Massimo Giovannozzi
Oxford - July 4th 2013
4
Slow bump
Electrostatic
septum
(beam shaving)
Kicker magnets
used to generate
a closed orbit
bump around
electrostatic
septum
Slow bump
Extraction
line
Massimo Giovannozzi
Extraction septum
Oxford - July 4th 2013
Kicker strength
Present multi-turn extraction – II
Fifth turn
Four turns
Efield=0
X’
E
field≠0
2
3
5
4
Length
1
X
Electrostatic septum
blade
5
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.
Massimo Giovannozzi
Oxford - July 4th 2013
6
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.
Massimo Giovannozzi
Oxford - July 4th 2013
7
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).
The linear tune is
time-dependent
 Xˆ 


Xˆ

   R   

2
3
ˆ
ˆ
ˆ
ˆ
X
'
X
'

X


X
 n 1

n
Quadrupoles Sextupole
Massimo Giovannozzi
Oxford - July 4th 2013
2 K3

2
3 K2  x
Octupole
8
Novel multi-turn extraction – II
Left: initial phase
space topology. No
islands.
Right: intermediate
phase space topology.
Islands are created
near the centre.
Bottom: final phase
space topology.
Islands are separated
to allow extraction.
Massimo Giovannozzi
Oxford - July 4th 2013
9
Novel multi-turn extraction - III
Simulation
parameters:
Hénon-like
map (i.e. 2D
polynomial –
degree 3 mapping)
representing
a FODO cell
with
sextupole and
octupole
Tune variation
Phase space
portrait
Massimo Giovannozzi
Oxford - July 4th 2013
10
Novel multi-turn extraction – IV
Final stage after 20000 turns (about 42 ms for CERN PS)
At the septum location
Bfield = 0
Bfield ≠ 0
Slow (few thousand
turns)
bump
first
(closed distortion of
the periodic orbit)
Fast (less than one
turn) bump afterwards
(closed distortion of
periodic orbit)
About 6 cm in physical space
Massimo Giovannozzi
Oxford - July 4th 2013
11
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.
Massimo Giovannozzi
Oxford - July 4th 2013
12
Novel multi-turn extraction with
other resonances - I
Simulation
parameters:
Hénon-like
map
with
sextupole
and octupole
Tune variation
The thirdorder
resonance is
used,
thus
giving
a
three-turn
extraction
Phase space
portrait
Massimo Giovannozzi
Oxford - July 4th 2013
13
Novel multi-turn extraction with
other resonances - II
The second-order resonance is
used, thus giving a two-turn
extraction
The fifth-order resonance is
used, thus giving a six-turn
extraction
Massimo Giovannozzi
Oxford - July 4th 2013
14
Novel multi-turn extraction: 4th
order unstable resonance - new
application!
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.
Massimo Giovannozzi
Master
Oxford - July 4th
2013
thesis Diego Quatraro
15
Novel multi-turn injection: new
application!
Simulation parameters:
Third-order polynomial
map representing a
FODO
cell
with
sextupole and octupole
Tune variation
The
fourth-order
resonance is used for
a four-turn injection
Phase space
portrait
Efficient method to
generate hollow beams!
Massimo Giovannozzi
Oxford - July 4th 2013
16
Novel multi-turn injection: new
application!
Possible applications: transverse shaping of beam
“Flat” beam distribution obtained by injecting a fifth turn
distribution.
in the centre.
“Standard” hollow
beam distribution
Observation: the proposed method seems to be
more efficient in generating smaller emittance
beams than standard multi-turn injection!
M. Giovannozzi, J. Morel, PRST-AB, 10, 034001 (2007)
Massimo Giovannozzi
Oxford - July 4th 2013
17
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
Massimo Giovannozzi
Oxford - July 4th 2013
18
The capture process - II
Initial gaussian distribution
Particles in island 2
Particles in island 4
Particles in island 6
Particles in island 8
Particles in beam core
Oxford - July 4th 2013
19
Massimo Giovannozzi
The capture process - III
Size of non-adiabatic region
Under these conditions:
Scaling law for the size of
the adiabatic region is wellreproduced.
Trapping probability is welldescribed.
Pendulum-like model
Massimo Giovannozzi
Hénon-like model
Oxford - July 4th 2013
20
Analytical computation of island’s
parameters
Using perturbative theory (normal forms) it is
possible to derive analytical estimate of island’s
parameters.
Normalised phase space

Distance from resonance
  


2

u
2
0,3
2
 sec  4  2  u 0,3 
Distance of fixed points
from origin of phase space
Secondary frequency

  16
u 0,3  2
2
4
Island’s surface
Massimo Giovannozzi
Oxford - July 4th 2013

2
u 0,3  2
Distance between separatices
21
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)
 Qx  h2,0 J x  h1,1 J y
 Qy  h1,1 J x  h0, 2 J y
h2,0 -> detuning with amplitude (H-plane) ->  x2 K3
h1,1 -> non-linear coupling ->  xy K3
h0,2 -> detuning with amplitude (V-plane) ->  y2 K3
Massimo Giovannozzi
Oxford - July 4th 2013
22
B-field
Sextupole 55
Octupole 55
B-field (T)
400
0
-200
-400
-600
B-field
Sextupole 55
Octupole 55
0.74
Sextupole 39
Octupole 39
Octupoles
0.76
0.78
Cycle time (s)
0.80
0.82
600
400
Extraction: 0.835 s
200
0
-200
Injection: 0.170 s
0.0 Giovannozzi
0.2
Massimo
600
200
0.72
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Sextupole 39
Octupole 39
Octupoles
-400
-600
0.4
0.6 - July 0.8
Oxford
4th 2013
Cycle time (s)
1.0
1.2
23
Currents (A)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Currents (A)
B-field (T)
Operational implementation - II
Transverse dynamics - III
Phase space at septum
0.74
0.76
0.78
0.80
0.82
3000
0.25
Qx
Qx''
h1,1
0.20
Qx'/Qx
h2,0
2000
1000
0.15
0
0.10
-1000
0.05
-2000
0.00
-3000
0.72
Massimo Giovannozzi
0.74
0.76
0.78
0.80
Oxford - July 4th 2013
Cycle time (s)
0.82
Second order chromaticity,
detuning, non-linear coupling
Fractional tune and chromaticity
0.72
24
Evolution of beam distribution
Horizontal beam profiles in section 54 have been taken
during the capture process (total intensity ~2.1×1013).
Massimo Giovannozzi
Oxford - July 4th 2013
25
20% trapping
5 PS turns
1.0x 1011
Intensity
1.4x 1011
18% trapping
1.4x 1011
1.0x 1011
6.0x 1010
6.0x 1010
2.0x 1010
0
0
2.0x 1010
0
0
50
100 150 200 250 300
37 nsbin
50
100 150 200 250 300
37 nsbin
1000
20
Frequency
Trapping (%)
Intensity
Trapping performance
18
800
16
600
14
400
12
200
5000
10000
15000
20000
25000
Time elapsed from May 1st 15:00 (s)
Massimo Giovannozzi
Oxford - July 4th 2013
12
14
16
18
20
Trapping (%)
26
Extraction efficiency
700
400
80%
70%
60%
50%
300
40%
30%
200
20%
100.8
100.2
99.6
99.0
98.4
97.8
97.2
96.6
96.0
95.4
94.8
94.2
93.6
93.0
92.4
91.8
0%
91.2
0
90.6
99
10%
90.0
100
100
98
Extraction efficiency (%)
90%
Cumulative %
CT
extraction
efficiency
is
about 93%
500
Frequency
Regular fluctuations in
the extraction efficiency
are also observed and
seem well correlated to
spill fluctuations.
Frequency
600
100%
Extraction efficiency (%)
97
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%)
96
95
94
93
92
91
90
14:24 15:36
16:48 18:00
Massimo
Giovannozzi
19:12
Time on May 1st
20:24 Oxford
21:36 22:48
July
4th 2013
27
CT vs. MTE: extraction losses
CT
MTE
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.
Massimo Giovannozzi
Oxford - July 4th 2013
28
First observations of intensitydependent effects - I
Usual process for trapping the beam into
stable islands.
Varying parameter: total beam intensity.
Beamlets are moving with intensity!
Massimo Giovannozzi
Oxford - July 4th 2013
29
First observations of intensitydependent effects
- IIin beamlets size
No change
The
observed
effect can be
explained with an
intensitydependent shift
of
the
single
particle tune.
Possible sources:
Consider projection effect
Image currents.
Direct
effects
(interaction
between
beamlets).
Massimo Giovannozzi
Oxford - July 4th 2013
30
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
extraction septum -> beam commissioning in 2014.
Massimo Giovannozzi
Oxford - July 4th 2013
on
31
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.
And many more!
Massimo Giovannozzi
Oxford - July 4th 2013
32
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.
Massimo Giovannozzi
Oxford - July 4th 2013
33