Transcript Session 6: COLLECTIVE INSTABILITIES Convener: V.G.Vaccaro

Session 6: COLLECTIVE INSTABILITIES
Convener: V.G.Vaccaro, Secretary: G. Rumolo
• Overview of collective instabilities
by Elias Métral (CERN)
• Intensity limitations by combined and/or unconventional
impedances
by Giovanni Rumolo (GSI)
• Panel discussion: A. Adelmann, E. Métral, L. Palumbo, M.
Zobov
Overview of collective instabilities
by Elias Métral (CERN)
Low intensity
Example: Measurement at the CERN-PS in 1999
Without linear coupling
At low intensity the different modes of oscillation (head-tail for the transverse
plane and longitudinal) are standing-wave patterns, which can be treated
independently.
+ simulation with MOSES (Chin) and HEADTAIL (Rumolo),
including different ingredients, presented at the ICFA-HB2004
 Chromaticity stabilizes !!!
First observation of high intensity Transverse Mode Coupling
Instability for protons.
The stabilizing methods to cure the low-intensity instabilities have
been discussed:
- Landau damping (for the transverse plane) =>
- From octupoles only (work by S. Berg and F. Ruggiero).
- From both octupoles and space-charge nonlinearities: the result
of Mohl-Schonauer in the presence of space-charge only is
recoverd => no Landau damping.
- Next work: include the longitudinal motion.
- Feedbacks.
- Linear coupling between the transverse planes (with and without
external, i.e. from octupoles, nonlinearities). In particular this method
is used in the CERN PS machine to stabilize the beam for LHC
Example of stabilization by linear coupling
Intensity limitations by combined
and/or unconventional impedances
by Giovanni Rumolo (GSI)
Unconventional impedance:
electron cloud wake field
• The dipole wake field of an electron cloud
depends on the transverse coordinates (x,y)
• Differently located displacements along a bunch
create differently shaped wake fields
• The wake field depends:
– Strongly:
• On the initial electron distribution
• On the bunch particle transverse distribution
– Weakly:
• On the boundary conditions for a wide pipe
• On the electron space charge for low degrees of neutralization
Dependence on the electron distribution
Distributions with vertical stripes (one or two) can exist in dipoles.
Different initial distributions lead to different resulting wake fields.
1. The frequency content in the wake decreases as the
separation between the two stripes increases.
2. The vertical wake is weakened by the two stripes.
3. The horizontal wake, which is anyway much weaker due
to the dipole field, is not much affected.
Features (continues) and possible
future work
• A description in terms of double frequency
impedance Z(w,w‘) is necessary for a correct TMC
analysis (E. Perevedentsev, ECLOUD02)
• Numerical tool to handle the calculation of
Z(w,w‘) has been developed.
• To be yet investigated:
– Dependence of the wake on the longitudinal shape of
the bunch
– The electron cloud wake field for long bunches might
strongly depend on the trailing edge electron production
and multiplication
Tune line shifts in a barrier bucket
with a Broad-Band impedance
• The coherent tune shift DQ of a bunch in a barrier bucket as a function
of the bunch current depends on
– Shunt impedance (proportional)
– Bunch length (inversely proportional)
• The DQ follows that of a usual bunch in a sinusoidal bucket and low
current with the same longitudinal emittance
• Coherent envelope modes depend on the chamber shape:
– Round chamber has two modes both in x and y, one current
dependent and one current independent.
– Flat chamber has one mode in x with a positive shift with
increasing current, and two modes in y, both with a negative shift
with current.
Instabilities of barrier buckets with a
Broad-Band impedance
• The threshold for strong head-tail instability is not found for bunches
in a barrier bucket, but there is rather a regime of slow growth at high
currents.
• Regular head-tail instability driven by negative Q‘ (above transition)
exhibits similar features as for bunches in sinusoidal buckets.
– Growth rates are proportional to the shunt impedance
– The quickest instability occurs when wx=wr
– In a flat chamber growth times in the x direction are about double
of the growth times in the y direction
• Longer bunches slow down the instability (because of the decay of the
wake along the bunch or because of the lower synchrotron frequencies
?)
• Analytical model (maybe few particles model or kinetic model based
on Vlasov equation) needed.
Threshold for strong head-tail
instability
Gaussian bunch in a
sinusoidal bucket
Rectangular bunch in a
barrier bucket
Bunches with the same longitudinal emittance (0.8 eVs):
o A regular Gaussian bunch in a sinusoidal bucket has a clear threshold above which
TMC occurs
o A bunch in a barrier bucket exhibits a slow growth (threshold ?), but no violent
instability sets in
Coherent tune shift as a function of
the bunch current (II)
We look at the tune shift through Fourier analysis of the transverse motion
of a (transversely) kicked bunch.
.... and the spectrum of envelope oscillation
Horizontal modes
Vertical modes
Proton number is scanned from 0.1 to 2 x 1011, chamber is round
Panel discussion: A. Adelmann, E.
Métral, L. Palumbo, M. Zobov
Some statements have been
agreed upon
• It was pointed out that in numerical calculation
of the wake fields, Gaussian bunches are used as
pseudo-point source. This could be a source of
error, mainly in the resolution of the high
frequencies (L. Palumbo)
• More computing power and advanced algorithms
are required to solve extensive and large scale
3D problems (A. Adelmann)
How accurate ?
Impedance frequency spectrum
response to point charge excitation
Pseudo-Green function
gaussian bunches << bunch-length
Pipe cut-off
For LHC s = 7 cm
Pseudo-Green function with
s = few mm ?
Micro-density modulation?
Coasting beam? Landau ….
How reliable are the tools ?
• Haissinskii equation OK
• Mode-coupling theory for the threshold OK, .. not for the lengthening regime
• Missing an analytical theory above threshold….
• Tracking codes seem to be OK (CERN, SLAC, LNF…) however there is no
comparison among different codes in particular for:
- modeling and use of the pseudo-green function
- results for different benchmark cases
Similar arguments apply to the transverse case…..
Finally, new dynamics of interest?
Longitudinal instabilities of the square shaped beam…. Saw tooth instab.
• E. Métral pointed out that a benchmark
between analytical formulae, MOSES and
HEADTAIL has been carried out to study
the TMCI in the SPS.
• Very good agreement between the
predictions of HEADTAIL and MOSES.
• Analytical investigations are very useful to predict
thresholds and initial growth rates, but up to now
they do not describe the phenomena above
thresholds (M. Zobov)
• Concerns for LHC:
– Longitudinal impedance of collimators (Zobov)
– Space charge even at top energy for a very long storage
time (Adelmann)
• Is it possible to simulate resistive wall + electron
cloud to explain DAFNE‘s observations ?
• Maybe long range wake fields from e-cloud can
explain DAFNE‘s observations (Ohmi)