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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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 2
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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 3
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 loss- modification 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, ….
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 4
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)
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 5
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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 6
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
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),…….
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 8
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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 9
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 ?
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 10
Transverse beam offset signals
Schottky signals: Using a pick-up + spectrum analyzer (SA)
BTFs: Using exciter/pick-up + network analyzer (NA)
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 11
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)
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013
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.
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 13
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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 14
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. )
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 15
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.
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 16
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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 17
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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 18
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.
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 19
Additional material (not part of the presentation)
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 20
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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 21
Tune spectra: Effect of image currents
Image impedance
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 22
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
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 23
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)
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013 24
‘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:
Oliver Boine-Frankenheim, ICFA mini-workshop, CERN, April 2013
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)