MG - ABP PTC review 1
Multi-Turn Extraction studies
and PTC M. Giovannozzi
PS and its model
MTE principle
Trapping simulations and PTC
Computing higher order fixed points
Outlook
Acknowledgements: A. Franchi, S. Gilardoni, C. Hernalsteens,
R. de Maria, F. Schmidt
09/11/2011
09/11/2011 MG - ABP PTC review 2
PS and its model - I
The PS in a nutshell:
Hundred main magnets
Combined function magnets (dipole and quadrupole fields)
Each main magnet is made of two half-unit (focusing and defocusing).
Each half unit is made of five blocks.
The main magnet is bent.
Additional coils are used to control the working point (tunes and chromaticity – see next slide).
The circumference is 200 p m.
The lattice features ten super periods.
Ideal application for PTC!
09/11/2011 MG - ABP PTC review 3
PS and its model - II
Courtesy S. Gilardoni
09/11/2011 MG - ABP PTC review 4
PS and its model - III
The PS model:
Thin multipoles are used to reproduce non-linear chromaticity measurements.
Quadrupolar, sextupolar, octupolar multipoles are enough to reproduce experimental observations.
Six three parameters (F/D half-units three multipoles each).
09/11/2011 MG - ABP PTC review 5
Multi-Turn Extraction (MTE)
The main ingredients of multi-turn extraction:
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. No mechanical device to slice the beam is used).
The phase space matching is improved with respect to the present situation.
The beamlets have the same emittance and optical parameters.
09/11/2011 MG - ABP PTC review 6
Transverse dynamics - I
-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
rre
nts
(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
rre
nts
(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 - II
09/11/2011 MG - ABP PTC review 7
•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
ma
tici
ty,
de
tun
ing,
no
n-l
ine
ar c
ou
plin
g
Frac
tio
nal
tu
ne
an
d c
hro
mat
icit
y
Cycle time (s)
Qx Qx'/Qx
Qx'' h2,0
h1,1
09/11/2011 MG - ABP PTC review 8
Evolution of beam distribution
Horizontal beam profiles in section 54 have been taken
during the capture process (total intensity ~2.1×1013).
Script code developed by A. Franchi.
PTC is used for the tracking.
Initial conditions are divided into
various sets for different batch jobs.
5D script code (no synchrotron
motion included) with transverse
and momentum distributions
included.
Possibility to specify the time-
dependence of magnets’ strength.
Post processing included: islands
recognition, dispersion computation
for islands (implemented according
to definition).
CAPTURE_PTC - I
9 MG - ABP PTC review 09/11/2011
Key weak point: impossible to change dynamically strength
inside PTC.
Particles’ coordinates are written out after one turn.
The parameters are changed (horizontal tune, strength of sextupoles and
octupoles).
Final coordinates are used as initial coordinates for a new turn.
Overall, the CPU-time is NOT used very effectively!
Limitations on number of turns/initial conditions
PTC/ORBIT will allow to overcome this issue and
CAPTURE_PTC will be re-written in PTC/ORBIT.
The way the non-linearities of the PS main magnet are
modelled should be changed (from thin multipoles to
distributed errors).
CAPTURE_PTC - II
10 MG - ABP PTC review 09/11/2011
Capabilities of
TRACKING_PTC
Plain tracking
Aperture model
CAPTURE_PTC - III
11 MG - ABP PTC review 09/11/2011
Example of simulation of the splitting process. Distributions at
the location of the magnetic septum.
CAPTURE_PTC - III
12 MG - ABP PTC review 09/11/2011
Other PTC-based tools - I
Transverse phase space portrait (trivial)…another script
code developed around PTC_TRACK (A. Franchi).
13 MG - ABP PTC review 09/11/2011
SS01, qx=0.261, qy=0.30
SS01, qx=0.261, qy=0.30
nl coupling corrected
yxy
yxx
JhJhQ
JhJhQ
2,01,1
1,10,2
The h2,0, h1,1, h0,2 can
be computed easily
with PTC_NORMAL
Other PTC-based tools - II
Recently the possibility of working around a fixed point
different than the origin was introduced (R. de Maria)!
The fixed point at the centre of each stable island is a
closed orbit.
The possibility of computing it and to use it as a
reference orbit opens up many possibilities:
Computation of optical parameters of islands (PTC_TWISS
around the fixed point)
Computation of normal forms around the fixed point.
All this is available with madx_dev.
The current implementation imposes to build a lattice
that is N times the original machine, where N is the
order of the resonance. 14 MG - ABP PTC review 09/11/2011
Applications - I
15 MG - ABP PTC review 09/11/2011
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0 400 800 1200 1600 2000 2400
Fixe
d p
oin
t p
osi
tio
n (
m)
S (m)
Fixed point trajectory: h1,1 ≠ 0
Four times PS circumference
Applications - II
16 MG - ABP PTC review 09/11/2011
0
10
20
30
40
50
60
70
0 400 800 1200 1600 2000 2400
Ho
rizo
nta
l bfu
nct
ion
(m
)
S (m)
Beta H - island
Beta H - core
b-functions: h1,1 ≠ 0
Optics perturbation
for the islands:
island-dependent
Applications - III
17 MG - ABP PTC review 09/11/2011
0
5
10
15
20
25
30
0 400 800 1200 1600 2000 2400
Ve
rtic
al b
fun
ctio
n (
m)
S (m)
Beta V - island
Beta V - core
b-functions : h1,1 ≠ 0
Optics perturbation
for the islands:
island-dependent
MG - ABP PTC review
-5
-4
-3
-2
-1
0
1
2
3
4
5
-0.010 -0.005 0.000 0.005 0.010
DD
Dp/p
Delta D H - island
Delta D V - island
Delta D H - core
Delta D V - core
Applications - IV
18 09/11/2011
Dispersion : h1,1 ≠ 0
Optics perturbation for the islands:
island-dependent
-1
0
1
2
3
4
5
6
0 400 800 1200 1600 2000 2400
Dis
pe
rsio
n fu
nct
ion
(m
)
S (m)
Disp H - islandDisp V - islandDisp H - coreDisp V - core
MG - ABP PTC review
Applications - V
19 09/11/2011
Chromaticities and momentum compaction for
the islands: island-independent (h1,1 ≠ 0).
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
-0.010 -0.005 0.000 0.005 0.010
DQ
Dp/p
Delta Q H - islandDelta Q V - islandDelta Q H - coreDelta Q V - core
-0.0020
-0.0015
-0.0010
-0.0005
0.0000
0.0005
0.0010
-0.010 -0.005 0.000 0.005 0.010
Da
c
Dp/p
Alpha_c - island
Alpha_c - core
Total momentum
spread about ±10-3.
MG - ABP PTC review
Applications - VI
20 09/11/2011 -2
-1
0
1
2
3
4
5
6
7
0 400 800 1200 1600 2000 2400
Dis
pe
rsio
n fu
nct
ion
(m
)
S (m)
Disp H - island Disp V - island
Disp H - core Disp V - core
-5
-4
-3
-2
-1
0
1
2
3
4
5
-0.010 -0.005 0.000 0.005 0.010
DD
Dp/p
Delta D H - island
Delta D V - island
Delta D H - core
Delta D V - core
Optics perturbation for the islands:
island-dependent Dispersion : h1,1 = 0
MG - ABP PTC review
Applications - VII
21 09/11/2011
Chromaticities and momentum compaction for
the islands: island-independent (h1,1 = 0).
-0.0020
-0.0015
-0.0010
-0.0005
0.0000
0.0005
0.0010
-0.010 -0.005 0.000 0.005 0.010
Da
c
Dp/p
Alpha_c - island
Alpha_c - core
Total momentum
spread about ±10-3.
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
-0.010 -0.005 0.000 0.005 0.010
DQ
Dp/p
Delta Q H - island
Delta Q V - island
Delta Q H - core
Delta Q V - core
MG - ABP PTC review 22
Outlook
PTC proved to be very useful for MTE!
Latest simple developments opened up new possibilities.
PTC/ORBIT is the tool for tracking (even without space charge) thanks to time-dependence of magnet’s strength.
Documentation not always easy to understand:
trial and error approach
oral transmission from colleagues
proved to be very effective in building experience...
09/11/2011