Space charge effects in rings (not only ) at FAIR

Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 1

Space charge effects in rings (not only) at FAIR

Contents

o Space charge effects at FAIR

o Space charge: Protons vs. Heavy-Ions

o Simulation codes for space charge effects used at GSI

o Beam diagnostics: How accurate (and fast) can we measure space charge ?

o Conclusions

Oliver Boine-Frankenheim

Beam physics department, GSI, Darmstadt and Computational electromagnetics laboratory, TU Darmstadt


The FAIR accelerator facility

100 m

UNILACSIS-18

SIS-100/300

HESR

SuperFRS

NESR

CR

RESR

FLAIR

Radioactive Ion Production Target

Anti-Proton Production Target

Existing facility UNILAC/SIS-18 GSI facility: provides ion-beam source and injector for FAIR

p-linac L=216 m

L=1080 m

2

For Uranium beams:50 kW beam power50 kJ total energy

SIS-18 SIS-100

Reference primary ion U28+ U28+

Reference energy 200 MeV/u 1.5 GeV/u

Ions per cycle 1.5E11 4E11

cycle rate (Hz) 2.7 0.5

Protons from SIS-100: 29 GeV, 4x1013, 1 bunch, 0.2 Hz

Talk by Peter Spilleron Tuesday


4x1011 U28+

SIS 18

SIS 100 cycle

(1 s accumulation time)

Space charge @ FAIR

UNILACSIS-18

SIS-100

HESR

NESR

CR

RESR

p-linac

General: Intense heavy ions at low-medium energies.Injectors: - low energy transport- UNILAC/p-linac

Injection:

Extraction (short bunch):

SIS-18 multi-turn injection:- Final momentum spread determined by space charge- Injection efficiency vs. tune -> talk by S. Appel

SIS-100 accumulation + acceleration:- ‘space charge limit’, beam lossmodification of coherent instability thresholds-> talks by G. Franchetti, V. Kornilov

SIS-100 bunch compression:emittance growth + beam lossmodification of the dispersion-> talk by S. Aumon

Interplay of space charge with resonances, impedances, cooling, IBS, ….


Measured momentum spread of the coasting beam

Initial longitudinal beam quality in SIS-18 Debunching of UNILAC micro-bunches with space charge

SIS-18

≈ 20 turn injection36 MHz

no rf: debunching

b/a=2zm/a=5

Micro-bunch in longitudinal phase space

Longitudinal space charge field:

Momentum spread after debunching (dc beam):

Minimum momentum spread of the coasting beam:

S. Appel, O. Boine-Frankenheim, Phys. Rev. ST-AB (2012)


Space charge: Protons vs. Heavy Ions

Lifetime of intermediate charge state heavy-ions in rings- Large cross sections for electron stripping/capture - (stable) residual gas pressure of the order of 10-12 mbar required for sufficient lifetime- Beam loss causes dynamic pressure instabilities. -> at present beam intensities are limited by lifetime and not by space charge.

Production of intermediate charge state ions - Performance of ion sources compared to proton sources. - Stripping efficiency of heavy-ions at low energies.- Conventionally ‘Liouvillian’ multi-turn injection into rings.

Beam diagnostics in rings:- Profile measurements: Wire scanners vs. residual gas monitors (RGMs). -> for energetic heavy-ion beams RGMs have to be used (more complex).

Other intensity effects in rings:- Intra-beam scattering induced diffusion:

FAIR: Operation with intermediate charge state ions (e.g. U28+) to reduce space charge effects


Simulation codes (not only) for space charge effects used at GSI

MICROMAP (G. Franchetti): o 3D particle tracking with error multipoles, 2D self-consistent, 3D adaptable space charge.

G. Franchetti et al., Experiment on space charge driven nonlinear resonance crossing in an ion synchrotron, PRST-AB 2010

PATRIC (O. Boine-F., S. Appel, V. Kornilov, et al.): o 3D particle tracking with self-consistent 2.5D

space charge solver and wake fieldso MADX maps, arbitrary rf bucket forms o Implemented for multi-core CPUs using MPI.

V. Kornilov, O. Boine-F., Head-tail instability and Landau damping in bunches with space charge, PRST-AB 2010

pyorbit (A. Shishlo, S. Cousineau, J. Holmes, et al.) o https://code.google.com/p/py-orbit/o Teapot trackingo 2D/3D space chargeo MPI

LOBO (O. Boine-F.): o Longitudinal dynamics with space charge,

impedances, cooling, IBS, internal targets o direct Vlasov-Fokker-Planck solver or PIC

O. Boine-F., rf barrier compression with space charge, PRST-AB 2010Al-khateeb et al, Longitudinal collective echoes in coasting particle beams, PRST-AB 2003

VORPAL (Tech-X) 3D EM PIC O. Boine-F., E. Gjonaj, F. Petrov, F. Yaman, T. Weiland, G. Rumolo, Energy loss and longitudinal wakefield of short proton bunches in electron clouds, PRST-AB 2012

S. Appel, this workshop

Used also for studies of laser ion acceleration at GSI

https://code.google.com/p/py-orbit/

https://code.google.com/p/py-orbit/

Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013

PArticle TRackIng Code: PATRIC

∆sm << betatron wave length

The transfer maps M are

‘sector maps’ taken from MADX.

x

z

y

s

M(sm|sm+1)

Sliced bunch

sm: position in the lattice z: longitudinal position in the bunch

slice-length: ∆z≠∆s (N macro-slices for MPI parallelization)

2D space charge field for each slice:

(3D interpolation)

(fast 2.5D Poisson solver)

3D Grid-> Particle / Particle->Grid interpolation

GPU implementation: -> talk by Jutta Fitzek

macro-slice

ghost layers

2D grids

MPI send/receive to neighbor slices

Space charge and PIC: Birdsall, Langdon (2005),…….


PATRIC: Matched 3D bunch distribution (in a dual rf bucket)

A. Luccio, N. D’Imperio, Eigenvalues of the one-turn matrix, BNL (2003)

Tune footprint with space charge (SIS18)

- The bunch distribution can be matched to arbitrary rf bucket forms (Hofmann-Pedersen 1979) - Transverse matching with space charge (Venturini, Reiser, PRL 1998)

Bunch distribution (longitudinal-horizontal)

Current profile

Local dipole (offset) moment (‘noise’)

-> FFT-> tune spectra


Measurement of transverse space charge in rings

Why: - to characterize the beam and understand the (space charge) intensity limit- set machine parameters (feed-forward) according to the space charge tune shift.

How: Beam profiles for heavy-ions from RGM

P. Forck et al.

A. Parfenova (2010)

(rms beam radius)

(rms emittance)Integration time - presently: msecs- future: μsecError bar ?


Transverse beam offset signals

Schottky signals: Using a pick-up + spectrum analyzer (SA)

BTFs: Using exciter/pick-up + network analyzer (NA)


Transverse offset oscillations of coasting beams

Oscillation of a beam inside a pipe.

Er

Bθ

Space charge field

Ex

bx

ax

ba

Ex

Space charge force cancels:The transverse space charge force doesnot act on the beam center(in contrast to image forces):

(Transverse equation of motion)

(beam center equation of motion)

-> Measurement of the beam offset fluctuations.

-> This does not hold for head-tail modes in bunches !

(beam center)


Fit to a measured, modified Schottky band:

Transverse Schottky spectrum with space charge SIS-18 experiments with coasting beams

Beam parameter: Ar18+, 11.4 MeV/u f0=215 kHz

S. Paret, O.Boine-Frankenheim, V.Kornilov, T Weiland, Phys. Rev. ST-AB (2010)

Space charge parameter:

from RGM profiles

Measurement time: ≈ 100 msecs

Space charge tune shift from Schottky/BTF is systematically (factor 2) larger than the one from RGM profiles.


Tune spectra for bunched beams (Head-tail modes)

Blaskiewicz, Phys. Rev. ST Accel. Beams (1998)Boine-F., Kornilov, Phys. Rev. ST Accel. Beams (2009), Burov (2009), Balbekov (2009)

space charge parameter:

SIS-18/100: qsc=10-20CERN PSB/PS: qsc ≥100

positive k

negative k

strongly damped

Strong space charge

positive k:

negative k:

or

Shift of synchrotron satellites (synchrotron tune Qs):

Weak space charge: or


Transverse tune spectra measured in the SIS18

Intensity

R.Singh, O. Boine-F., O.Chorniy, P. Forck, P. Kowina, et al., Phys. Rev. ST-AB (2013)

Integration time: ≈ 100 msecs

Head-tail tune shifts

Tune spectra

Weak space charge: Width of lines caused by nonlinear synchrotron motion.Moderate space charge:Width of the lines caused by nonlinear space charge

TOPAS: Tune, Orbit, Position, Measurement System (Forck, Singh, et al. )


Space tune shifts: RGM vs. tune spectraR.Singh, O. Boine-F., O.Chorniy, P. Forck, P. Kowina, et al., Phys. Rev. ST-AB (2013)

from RGM profiles

from

tune

spe

ctra

Space charge tune shiftfrom tune spectra is lower(factor 1.5) than the one from RGM profiles.


Computer tune spectraPATRIC simulations with self-consistent space charge

o Good agreement with measurements (Positions and widths !)o Self-consistent space charge model is required ! o Image charges can suppress the head-tail modes (k≥0)! -> see talk by V.Kornilov -> tune spectra: not very useful for space charge measurement


Quadrupolar tune spectra

M. Chanel, Proc. EPAC 1996R. Bär, I. Hofmann, NIMA 1998

Quadrupolar Pickup (QPU)

PATRIC simulation: Damping of an initial transverse mismatch oscillation in a bunchwith a transverse KV distribution.

Problem: Strong damping of the quadrupolar mode for transverse Gaussian distributions.

Shift of the quadrupole mode:

Measurement time: < msec


Conclusions

o The FAIR design intensities for protons and heavy ions are determined by the ‘space charge limit’. - For (intermediate charge state) heavy ions there at present other intensity limitations (lifetime).

o For heavy ions the default measurement of space charge tune shift relies on RGM profiles. - Issues: Error bars. Integration time.

o Schottky and tune spectra provide an independent alternative for dc and bunched beams. - Long integration times needed. Does not work for strong space charge. - In the SIS18: discrepancies with RGM measurement (not understood so far). o Transverse quadrupolar lines provide a direct link to the incoherent space charge tune shift. - Successful measurements in dc beams at CERN and GSI. - Simulations indicate well pronounced quadrupolar tune lines also in intense bunches. - Dedicated quadrupolar pickup (and exciter) needed !

o For the optimization of the GSI and FAIR rings, including the important interplay of incoherent and coherent collective effects, different simulations codes are employed, in combination with dedicated beam physics experiments in the GSI SIS-18 and in the CERN PSB/PS.


Additional material (not part of the presentation)


Octupoles as a cure for transverse coherent instabilities in SIS-100coasting beams at SIS-100 injection

Ion Energy N

U28+ 200 MeV/u 4E11 4E-4 -0.1

V. Kornilov et al., PRST-AB (2007)

Octupoles in combination with space charge can be used for the stabilization of dc and head-tail instabilities in SIS-100.

For K3=50: DA lower by 20 %

stability boundary with octupoles

nonlinear space charge

octupoles chromaticity

Incoherent tune:

Resistive wall instability:

stability boundary with no octupoles

nonlinear space charge

SIS-100 injection -> unstable


Tune spectra: Effect of image currents

Image impedance


Measured SIS-18 tune spectra (noise excitation)

R. Singh, P.Forck, P. Kowina, O. Boine-F., et al., Interpretation of tune spectra for high intensity, to be published-> see presentation by Oleksandr Chorniy

11.4 MeV/u (injection energy)0.1-1.0 x 109 U73+

Bunching factor: 0.35

: from beam profile measurement (IPM)

: from longitudinal Schottky signal

noise excited tune spectrum


Intrinsic Landau damping of head tail modes

Damping rate of head-tail modes from PATRIC

Landau damping of head-tail modes for:and

with

-space charge can suppress head tail instabilities!- image currents/charges increase the damping rate.-damping depends crucially on bunch tails.

A. Burov, Phys. Rev ST-AB (2009)V. Kornilov, O. Boine-F., Phys. Rev. ST-AB (2010)V. Balbekov, Phys. Rev. ST-AB (2009)


‘Space charge limit’ in SIS-18 (and SIS-100)

We presently assume that the maximum beam intensities in SIS-18 and SIS-100are ‘space charge limited’.

2

2 30 0

4 1

1scy

f y y x

q NQ

m B

Space charge tune spread:

: bunching factor

εx,y: transverse emittancesN: number of particles in the ring

‘Space charge limit’:

‘Cures’: flattened bunch profiles + resonance compensation

1

0

pf

IB

I

A. Parfenova, G. Franchetti, GSI (2011)

( , ) (4.17,3.29)x yQ Q High current working point:


Multi-stream instability during debunching

25

Length

Δp/p

LengthΔp

/p

Time

Length

Δp/p

I. Hofmann, Part. Accel. (1990)

Longitudinal space charge impedance:

Normalized space charge impedance:

Critical number of streams/filaments: Time needed to form M filaments:

S. Appel, O. Boine-Frankenheim, Phys. Rev. ST-AB (2012)

Space charge effects in rings (not only ) at FAIR

Documents

space charge limit

aumoninterplay of space

fairspace charge

space charge4 sis

ionbeam source

debunching dc beam

beam loss modification

present beam intensities