multi-turn extraction studies and ptc · 2018. 11. 14. · ptc/orbit will allow to overcome this...

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!


PS and its model - II

Courtesy S. Gilardoni


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).


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.


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


•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


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


Capabilities of

TRACKING_PTC

Plain tracking

Aperture model

CAPTURE_PTC - III


Example of simulation of the splitting process. Distributions at

the location of the magnetic septum.

CAPTURE_PTC - III


Other PTC-based tools - I

Transverse phase space portrait (trivial)…another script

code developed around PTC_TRACK (A. Franchi).


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


-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


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


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

multi-turn extraction studies and ptc · 2018. 11. 14. · ptc/orbit will allow to overcome this...

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