towards the description of long term self consistent effects in … · 2006. 11. 3. · sis100 has...

10/2/06 ICAP 2006 G. Franchetti 1

Towards the Description of Long Term Self Consistent Effects in Space

Charge Induced Resonance Trapping

G. Franchetti, GSIICAP 2006, Chamonix


Overview

High intensity challenges

Impact on computer simulations

Trapping of particle inducedby space charge

Status of the art of long term simulation


Computing & Modeling

PhysicalProblem

Modeling of ComplexSystems (analytic, numeric)

Results(observables)

Experiment

Prediction

TheoristTheoristPathPath

Unde

rsta

nding


High Intensity beams are needed in future research

JPARC SNS (J. Holmes)

∆Q ~ 0.17-0.28

Storage for 25000 turns ofBunches with tuneshift Design intensity 1.4 x 1014 protons

Stored for 1000 turns

CERN: LHC beam in PS

9.2 1012 ppp @ 26 GeV/c(01/09/04)

00.5

11.5

2

2.53

3.54

205 705 1205 1705 2205

TIME IN THE CYCLE [ms]

LOSS

ES IN

THE

PS

[% o

f the

inj.

beam

]

0

5

10

15

20

25

30

Kin

etic

ene

rgy

[GeV

]

Courtesy E. MetralHHH CERN-GSI workshop

Space charge effect not neglectable


The next generation of computational challenges at FAIR

New: Cooled pbar Beams (15 GeV)Intense Cooled Radioactive BeamsParallel Operation

Primary Beam Intensity x 100-1000Secondary Beam Intensity x 10 000

Heavy Ion Beam Energy x 30


SIS100 critial scenario

Beam Life Time

Required Intensity in SIS18 Booster (after acceleration)

1.5 x 1011 U28+ -ions /cycle

Required Intensity in SIS100

6 x 1011 U28+ -ions /cycle

Low charge states beams providehigher intensities but have shorterlife time

Beam Life Time

1 secondStorage ofThe first bunch


Requirements on Beam loss

6 1011/s 1.0 GeV/u U28+: 23 kW1 W/m tolerable beam loss

SIS 100/300 average (peak) power:

~5 % acceptable loss


The SIS100 challengesStorage time 5 x 105 turnsIntensity 1.5 x 1011/ions U+28

Space charge tuneshift ∆Q ~ 0.2SIS100 has SC dipoles --> Nonlinearities

Beam loss predictionLocalization of beam lossEmittance increase prediction

Lattice design:Collimation system

Magnet quality:Nonlinear field control

Resonance compensation system

Coherent instability threshold with space charge in theFAIR rings. Talk on Wed. by O. Boine-Frankenheim


The physics problem

Periodic crossingOf a resonance

x

Bare tune

Resonance

z


Periodic crossingOf a resonance

x

Bare tune

Resonance

Trapping into Resonances

z


Computing challenges

Grid resolution of the beam: +/- 10 grid points

Typical beam pipe/beam size ratio = 6

Transversally 125 x 125 grid points Longitudinally keep the same 125 grid points

Statistical fluctuation of 1% -> 104 particle/grid cell

PIC parameters

N = 100 x 106

particles

Integration steps/turn: 20 x Qx = 20 x 18 = 360

Tracking a bunch for 5 x 10Tracking a bunch for 5 x 1055 turns means:turns means:

Compute the space charge of 100 x 10Compute the space charge of 100 x 1066 particlesparticlesfor 200 x 10for 200 x 1066 integration stepsintegration steps


The long term effect of PIC noise

J. J. Struckmeier Struckmeier Phys. Rev. E 54, 830Phys. Rev. E 54, 830−−837837


Modeling: Example with SIS18

AG lattice modeledIn smooth approximation

Uniform focusing transport channel


Beam distribution

xWeakSpace charge

StrongSpace charge

z

Matched with a 3D uniform focusing system


Modeling of space charge and lattice nonlinearities

LatticeNonlinearities(in 2D)

Analytic space charge modeling

* Round beam* Frozen distribution

LocalLongitudinal density


Single particle equation of motion

Symplectic trackingLatticeNonlinear kickSpace charge kicks


Example for SIS18Correlation instantaneousisland position versus longitudinal position

Phase space plot of the frozen system at z = 0

R = 34.4 mQx0 ~ 4.3Qy0 = 3.2σx/y = 1 cm∆Qx = 0.1K2 = 0.05 m-2

Space charge frozen

Qx0

Qy0

3 Q

x=

13

The outer position of the island is reached at z = 0 and it depends on Qx - Qx, res. Here Qx = 4.35


Island Crossing

A particle with maximum amplitude of x = 1.5 σx willsee the island crossing its orbit at z = 1.6 - 1.7 σz

The larger the particle maximum amplitude, the smaller the longitudinal position where the island crosses the particle’s orbit


Trapping

15000 turns for 1 oscillation

x = 1.5 σx, x’ = y = y’ = 0z = 3 σz, z’ = 0Qx = 4.35

Example of full trappingIn 1 synchrotron oscillation


Halo formation

x=1.5σ x’=y=y’=z’=0 z = 3σQx = 4.35

Halo

Mechanicallimitation


Consequences on the evolution of the bunched beam

Emittance growth Halo densityHalo Size

How to simulate such a complex dynamics ?


The Universe of CodesF. Zimmermann et al. EPAC2006 http://oraweb.cern.ch:9000/pls/hhh/code_website.startup

Optics

BETALieMathMADXSADSixTrack�

Electron Cloud

Build-Up SimulationsCSECECLOUDFaktor2POSINST

IncoherentHEADTAILMICROMAP

Multi-Bunch InstabilitySimulationsPEI-M

MultipactingESA ESTEC

Self-Consistent SimulationsFaktor2ORBITQUICKPICWARP

Single-Bunch Instability SimulationsHEADTAIL

Synchrotron RadiationPHOTON��

Intrabeam Scattering

MADXMOCAC�

ConventionalInstabilitiesHEADTAILMOSESORBITTRISIMWARP� ��

VacuumVAKDYNCollimation

SixTrack VAKLOOPImpedancesVAKTRAKABCILAWALLAWATPATRICREWALL

NonlinearDynamics Strong-Strong

BBSSBEAMXBeamBeam3DCOMBI

Weak-StrongBBSIMBBTrackWSDIFF��

Ctrack Space Charge

IMPACTMICROMAPORBITPATRICSimpsonsWARP��

MICROMAP

��

Electron Cooling

BETACOOLMOCACVORPAL

IonsFIIATFWARP

Luminosity PerformanceNAFFEVOLNERO

PLATOSODDSUSSIXSixTrackgrr


MICROMAP Library

Arbitrary linear maptransportNonlinear

kick

2D PIC solver: Square or arbitrary boundaryNonlinear kicks: Lattice nonlinearities

Space charge


Frozen space charge modelingA. Orzekhovskaya poster

Normalizeddistribution

Ellipsoidalsimmetry

For beam of arbitrary sizes the modeling is more complex

Are computedonly once


Benchmarking / Validation

Code2(modeling)

Code1(modeling)

ExperimentalResult

PhysicalProblem

Code-code Benchmarking

Modeling-Physics Benchmarking

Brute force modeling ?Step-by-step modeling ?


Emittance evolution in a full bunch

Q s = 10-3

105 turns103 macroparticles

In SIMPSONS (S. Machida)the longitudinal dynamicsIs nonlinearIn MICROMAP (G.Franchetti)the longitudinal dynamicsIs linear

http:http://www//www--linuxlinux..gsigsi..de/~giuliano/research_activity/trapping_benchmarking/mainde/~giuliano/research_activity/trapping_benchmarking/main.html.html

Code-code benchmarking

G. Franchetti,I. Hofmann, S. Machida HB2006

Excellent Agreement !!

Qx = 4.3604

SIS18 (full AG lattice)


Simulations of the CERN-PS Experiment

16% beam loss

Including chromaticity Without chromaticity

9% beam loss

Maximum beam loss do not match measurements

Modeling-Experiment Benchmarking

G.Franchetti, I.Hofmann, M.Giovannozzi, E.Metral, M.Martini


E-cloud incoherent effectsCode-simplified-model benchmarking

Periodic crossing of resonancesand particle trapping Inducedby EC pinch

E.Benedetto, G.Franchetti, F. ZimmermannPRL, 97, 034801 (2006)


The complexity of the self-consistency

Resonance conditiondetuning

Particle amplitudegrowth

Beam sizegrowth

Particleloss

Halo particles


Including beam loss effect

CF modeling of PSIncluding chromaticity

2x106 turns

Measurementat CERN-PS

Attempt of longTerm beam lossPrediction includingSemi-self consistency4x105This prediction is not correct because

The effect of the self-consistency is very Critical on how many particles are pushedInto the resonance


Effect of beam lossParticles whichCross the resonanceAre trapped and lost

New particle arePushed into a periodicResonance crossing

The result on long term beam loss are sensitiveTo the modeling on how new particles are drawnClose the resonance.

ISSUES: better modeling and further Experiment-code Benchmarching


Benchmarking Experiments @ GSI

• 4 Measurement campaign starting from December 2006.

• 24 shifts of beam

Experiment S317

Controlled highly resolved measurement data will be available for benchmarking codes, on emittance growth and beam loss perdition

SIS18

Scheduling


Conclusion / Outlook

Understanding of the mainIngredients of the long termStorage of high intensity bunches

Developed a modeling whichGives result consistent withMeasurements

Work for including the effect of the Self consistency is in Progress

At GSI measurement for code Benchmarking will be performedAs part of an approved experiment

towards the description of long term self consistent effects in … · 2006. 11. 3. · sis100 has...

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