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Minutes of the ABP-RLC team meeting of 14.07.2006
present: RA, OB, UD, EM, TP, GR, RT, FZ
excused: WH, FR
web site: http://ab-abp-rlc.web.cern.ch/ab-abp-rlc/
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(1) Reports from meetings
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ABMB (OB): ABP LD contracts are not affected by CERN staff reduction.
(2) Scaling of Collimator Impedance with Gaps Size, Beta Function,
Chromaticity, Conductivity and Bunch Length (FZ)
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Following a request from FR, FZ computed the dependencies described in the title,
for a possible LTC presentation. FZ computed the impedance using the Burov-Lebedev theory.
He summarized the formulae used and illustrated the dependence on the multibunch mode number,
head-tail mode number, and chromaticity.
He found that the highest growth rate scales approximately inversely with the gap size,
while the maximum coherent tune shift scales as the inverse 2.7th power for C jaws and
as the inverse 2.3rd power for Cu. The maximum tune shift for Cu is almost 10 times smaller
than for C. Cu jaws would maintain a stable beam for the LHC upgrade with 2x more bunches,
half the bunch length and ultimate bunch charge. There is a rather weak dependence
on the beta function, namely DQ~1/b^0.25, i.e., a factor 10 higher beta function
yields a factor 2 reduction of the tune shift. Halving bunch length increases
DQ by ~50%. The correction from the nonlinear wake field contribution is only
a few percent for half gaps of 6 sigma or larger.
OB recommended including a curve for the injection bunch length of ~11.5 cm,
and a figure illustrating the dependence on the number of bunches.
OB and FZ suggested two possible approaches for LHC operation: (1) damp higher
order modes with chromaticity and m=0 mode with feedback, or (2) suppress
higher-order modes with Landau damping and use chromaticity to damp m=0 mode.
(3) LHC Collimator Transverse Impedance Status Report (EM)
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Following the same request by FR, EM computed the dependence of the coherent tune shift
on gap, bunch spacing, and bunch length, and he included other results which could also
be presented at the LTC. He first flashed slides from several earlier presentations,
including a presentation at the LTC from 2004, explaining the inductive-bypass
effect. He illustrated that at 8 kHz Cu collimators have a larger impedance than carbon.
He proposed that GR implements the approximate wake of AK in HEADTAIL for simulation studies.
He introduced two different definitions of critical mode, referring to the mode with the
largest total tune shift and with the largest growth rate, respectively.
For the mode with largest growth rate, EM found that the real part of the tune shift
scales as 1/b^2.5 and the imaginary part as 1/b^2. For the mode with largest tune shift,
the real part still scales as 1/b^2.5 but the imaginary part as 1/b.
The real part of the tune shift does not change with bunch spacing, but the imaginary
part scales as the inverse of the spacing. The real part of the tune shift scales
as 1/(bunch length)^(0.25) or 1/^bunch length)^(0.2), the imaginary part is constant.
RA asked how much confidence we have in the predictions, as transient effects at the
entrance and exit of the collimator and possibly surrounding conductors are not taken into
account. FC may have a different interpretation. The model of EM and FZ assumes a
steady-state situation.
FZ remarked that the SPS experiment was not sensitive to the inductive bypass effect.
EM confirmed this and explained the reasons: only the real part of the tune shift was
measured, the SPS revolution and betatron frequencies are much higher than that of the
LHC, and only a few bunches were in the machine.
After the meeting, it occurred to FZ that we could move the betatron tune closer to
the integer to enhance the sensitivity.
FZ also commented that e-cloud had been found to be by far the largest source of
impedance in the SNS, by beam-based measurements, supporting the estimates provided
for EM's 2004 LTC presentation.
RA recommended that a clear statement be made at the LTC as to which intensity can be
reached in view of the collimator impedance. In reply EM illustrated that at top energy all
modes can be stabilized with a sufficiently high chromaticity. The RLC team or the
CWG should decide which statement to be made.
OB recommended looking at the two most critical mode at top energy and at injection.
So far reported by FZ. Continuation by GR.
EM next showed the stability diagrams for LHC including the impedance of the collimators.
The unstable mode m=0 has a point outside the stability region defined by the octupole damping,
but can be made stable by using Q'>5. The stable modes corresponding to higher m
(points inside the stability region) tend to move outward when chromaticity is increased,
but with Q' of about 5 units they remain inside the stability region.
By showing the working point with and w/o taking into account the impedance of the collimators,
EM stressed out that the main limitation really comes from the contribution they give to the
total LHC impedance. OB observes that it could be difficult to have full control of chromaticity,
especially during the ramp, which might make the instability control through chromaticity hard
especially at the beginning of operation. RA says that the collimators will actually be closed
only at top energy, so what really counts is to have a good chromaticity control at top energy
and chromaticity swings during the ramp would not harm.
EM showed then the stability diagram at injection, where space charge plays a role.
Here increasing chromaticity seems not to help much, so that stable operation would better
rely on an active damping system through feedback (which in this case should be able to damp
not only the injection oscillations but also the 0 mode of the resistive wall instability).
RA asked what recommendations it is possible to give in terms of collimator design or operation
(to be presented in the collimation meeting on next Monday).
OB said that the main message from EM's presentation is that collimators certainly
significantly increase the total LHC impedance, but the instability they could potentially
drive can be controlled and actually suppressed through chromaticity setting at top energy
and with an active feedback at injection energy. EM will perform a wider scan in chromaticity
from -10 to 10 units in order to be able to give a clear recommendation with some safety margin.
Posted on the web: Slides by EM and FZ
Web site: http://ab-abp-rlc.web.cern.ch/ab-abp-rlc/