1. Interpretation of beam signals for high intensities
Contents
The FAIR synchrotrons: SIS-18 and SIS-100
Transverse space charge and image current effects
Information from (transverse) beam signals at low intensity
Observations in SIS-18 at high intensities
Interpretation in terms of head-tail bunch oscillations.
Conclusions

2. The FAIR synchrotrons: SIS-18 and SIS-100
Reference primary ion
U28+ / U73+
U28+ / U92+
Reference energy
0.2 / 1 GeV/u
1.5 / 10 GeV/u
Ions per cycle
1.5E11 / 2E10
4E11 / 1E10
cycle rate (Hz)
2.7
0.5 / 0.1
FAIR parameter booklet, April 2007, (Ed.) O. Boine-F., P. Spiller, M. Steck
+ corrections for start version
SIS-18
SIS-100/300
p-linac
UNILAC
SFRS
HESR
SIS-18
SIS-100
accumulation
(ca. 1 s)
pre- and final
compression (ca. 100 ms)
200
CR/RESR
NESR

3. Simplified particle dynamics in a circular accelerator
longitudinal motion:
synchrotron oscillations
with
revolution frequency and period: s
SIS-18 synchrotron at GSI x
Qj : betatron tune
(number of transverse
oscillations per turn)
transverse motion:
focusing magnets (yellow), bending (red)
Ideal particle:
Machine parameters:
ξ : chromaticity
η : frequency slip factor
Non-ideal particles (relative deviations):
L=2πR=216 m
Main components:
-dipole (bending) magnets
-quadrupole (focusing) magnets
-rf cavities

4. Transverse space charge force betatron tune shift
beam pipe
(constant charge density !) Er
From
Gauss’s law: r Er
a: beam radius
beam
(velocity v0)
From
Ampere’s law: Bθ
Defocusing Lorentz force an a particle inside the beam:
Shift of the betatron tune:
SIS-18:
SIS-100:

5. Image current effects coherent tune shift
The beam pipe in the SIS-18 magnets
d=0.3 mm, stainless steel
-> U. Niedermayer
beam with a horizontal offset y
conducting beam pipe
Image charge/current b x
Image fields at the center of the beam:
Force on the beam center:
Coherent shift of the tune:
In SIS-18:

6. Measurements of machine/beam parameter -> beam control and feedback
Time resolved (< ms) measurements of:
Tune, tune shifts (incoherent and coherent) -> dynamic tune control, feedback
Chromaticity -> dynamic chromaticity control
Revolution frequency -> set the rf frequency
Current -> bunch profiles, beam loss
Momentum spread -> control of longitudinal beam loss
Beam width -> Emittance growth
Transverse beam offsets -> feedback systems (damping of coherent oscillations)

7. Transverse single particle ‘offset’ signal
Betatron oscillation:
Dipole moment:
ΔPU a -a
time PU
Frequency domain:
(n-Q)f nf (n+Q)f0
Looking at positive
frequencies only: f
(betatron sidebands)
(n-Q)f0+Qsf0
(synchrotron
satellites )

8. Transverse beam signals (low intensity)
Transverse Schottky band at
Difference signal : beam ‘offset’ fluctuations Δx
coasting
beam
spectrum
analyzer
Uin
bunch
Pick-up
CERN/SPS measurement (Linnecar, PAC 1981)
Synchrotron satellites (synchrotron tune Qs):
Frequency range: ≈ 1 kHz MHz
Bunch or dc beam
Tune spread in a rf bucket (bunch half-length ϕm):

9. Transverse Schottky spectrum with space charge SIS-18 experiments with coasting beams
Fit to a measured, modified Schottky band:
Measured transverse Schottky band for different
numbers of ions in the ring N.
Beam parameter: Ar18+, 11.4 MeV/u, f0=215 kHz
Result of the fit:
The space charge tune shift ΔQsc and the
space charge parameter Usc can be obtained
from the measured Schottky spectrum
using a fit to the the analytic expression S(f).
O. Boine-Frankenheim, V. Kornilov, S. Paret, Phys. Rev. ST-AB (2008)
S. Paret, V. Kornilov, O. Boine-F., T. Weiland, Phys. Rev. ST-AB (2010)

10. Head-tail modes with space charge
Unstable head-tail oscillations in the CERN PS
positive k
negative k
Bunch profile:
Head-tail offset:
Chromatic phase:
head-tail tune shifts:
Head-tail intensity
parameter:
M. Blaskiewicz, Phys. Rev ST-AB (1998)
O. Boine-Frankenheim, V. Kornilov, Phys. Rev. ST-AB (2009)

11. Head tail modes with space charge and image currents

12. Intrinsic Landau damping of head tail modes
Incoherent band:
Head-tail modes for small qsc:
Landau damping of head-tail modes for:
and
with
A. Burov, Phys. Rev ST-AB (2009)
V. Kornilov, O. Boine-Frankenheim, Phys. Rev. ST-AB (2010)
V. Balbekov, Phys. Rev. ST-AB (2009, 2011, 2012)

13. Transverse tune spectra from PATRIC simulation
qsc=0
PATRIC: 3D PArticle TRackIng Code with space
charge and impedances.
qsc=1
Head tail modes (no image currents):
Landau damping:
qsc=10

14. Measurements of the tune spectrum in SIS-18
Tune, Orbit and Position
Measurement System (TOPOS)
~0.02
~0.01
Set fractional horizontal tune = 0.29
~0.003
Ar18+
11.4 MeV/u
Rahul Singh, Peter Forck, et al. (2012)

15. Interpretation of the tune spectrum in SIS-18
measurement time: 600 ms
is used as a fitting parameter !
qs≈0.6
qs≈1.4
R. Singh, P. Forck, O. Boine-F., et al.,

16. Transverse decoherence of kicked bunches
Beam pipe
A. W. Chao, et al, SSC 1987
Initial offset
Offset:
bunch
Offset:
-> For low intensity: Measurement of the tune, chromaticity, …..

17. Transverse decoherence of kicked bunches
Measurement in the SIS-18 with Ar18+ (100 MeV/u)
Initial rigid bunch offset:
For finite chromaticity the rigid offset is not a pure k=0 mode:
V. Kornilov, O. Boine-Frankenheim,
Transverse decoherence and coherent spectra in long bunches with space charge
submitted to Phys. Rev. ST-AB

18. Tune spectrum and BTF in RHIC Collaboration with BNL
Similar set-up !
Profit from BNL experience !
Space charge + beam-beam +…
PhD thesis Paul Görgen
Co-supervisor: Wolfram Fischer
-> obtain tune spread
(Landau damping) from BTF

19. Conclusions
In the SIS-18 and SIS-100 space charge and image currents will be very important
(especially a lower energies).
The interpretation of transverse beam signals in the presence of space charge
and image current effects can be rather complex.
Head-tail oscillations play a key role in the analysis of tune spectra for high intensities !
From the transverse tune spectra we can obtain:
betatron tune (sometimes very difficult !)
synchrotron tune
chromaticity (with high accuracy)
incoherent space charge tune shift
coherent tune shifts
Landau damping rates !
Outlook: Head-tail oscillations in dual rf buckets (future standard operation in SIS-18/100)

20. Space charge limit in a ‘real’ synchrotron
Bf =0.33
ΔQx ≈ -0.1
ΔQy ≈ -0.2
Qx = 4.17, Qy = 3.24
G. Franchetti, O. Chorniy, et al, Phys. Rev. ST-AB 2010
Beam loss for high beam intensities
Resonance scan (low intensity beam )in the SIS-18.
A. Parfenova, G. Franchetti, GSI (2011)
Measures (there is no cure !):
- Resonance compensation
- Flattened bunches (dual harmonic rf)