Minutes of the ABP-LCE team meeting on 06.02.04
present: EB, WH, AK, JJ, EM, FR, DS, EV, FZ
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(1) Minutes & Pending Actions
-----------------------------
Following a pending action, FR informed L. Tavian
about an earlier e-cloud heat load plot by FZ and
asked for an update of the official beam screen
cooling capacity, to be included in the new LHC
design report. The reply of L. Tavian was received
only after the LCE meeting and is currently being
analysed.
The LTC e-cloud presentation by DS was shortly
discussed with FR last Monday as foreseen.
(2) Geometric Collimator Impedance (DS)
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DS presented Gdfidl calculations of the LHC
collimator impedance. The thickness of the
collimators was increased to close a gap.
There are still slits around the moving jaw.
Resistivity is not taken into account in
these simulations. So the purely geometric
impedance is computed, due to limitations
of the Gdfidl code.
DS computed all resonances at frequencies up
to 2-4 GHz. The results do not depend much on
whether or not the tank is included, or whether
the slits are closed, i.e., the tank contribution
can be neglected.
The effective impedance was first computed for
each mode individually. The resonator impedances
extend up to 35 MOhm/m. In particular there is
trapped mode between the jaws at frequency 2.25 GHz.
Making the conservative assumption that all
resonances drive the same multibunch mode,
DS estimated the total effective impedance
per collimator. It corresponds to an imaginary
tune shift of about 5e-6.
This value could then be multiplied by the
total number of collimators to get a worst-case
scenario.
FZ remarked that the trapped mode between
the jaws might affect the electron-cloud
build up.
(3) Resistive-Wall Impedance with Inductive Bypass (AK,EM)
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AK presented curves of the resistive-wall impedance
for thin and thick pipes with and without the inductive
bypass. For 'normal' parameters where the beam pipe
radius is larger than the beam-pipe wall, the thick
and thin formulae with and without bypass intersect
roughly in a single point. For the LHC collimators
the pipe (collimator) thickness is much larger than
the pipe radius (collimator gap), and the results
with and without the bypass are widely apart.
Without inductive bypass the crossing occurs around
8.8 kHz. Here the formula for the thick wall with
inductive bypass, considered for the LHC baseline, is
a factor of 2 lower than that for the thin pipe.
EM showed that using the thick pipe formula is
reasonable for our parameters.
The correct behavior at the transition point is
currently under study by AK and Bruno Zotter.
The real parts of both impedances with inductive
bypass show the correct behavior (approaching zero)
as the frequency goes to zero.
AK presented an impressive movie illustrating the
effect of a decrease in pipe radius b.
(4) Stability Diagram for a Beam with Non-Gaussian Tails (EM)
-------------------------------------------------------------
EM first commented on the minutes of the last meeting.
Not only for the higher order distribution function n=15,
but also for the standard n=2, the beam stability exceeds
that of a Gaussian for the bad sign of the octupoles.
He next studied the stability of a distribution with enhanced
tails, where 2% of the beam was described by n=16 and the remaining
98% by n=2. The distributions were chosen to correspond to
collimator jaws at 6 sigma. A factor 4 was gained in stability
for the real tune shifts, compared with the baseline.
The next step will be to use the real transverse profile,
fit it to a sum of distributions of various order, and
then obtain the stability diagram for the real beam.
(5) Follow-Up on Electron-Cloud Presentation at LTC (DS)
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DS presented the slides he had shown at the LTC.
FR mentioned that there was a concern expressed
by the management that the simulations had no
predictive power. FZ objected that the code does
have a predictive power, if the input parameters
are well defined, and that the LHC predictions
had not much changed since 2 years.
-> We should measure all parameters at the same time
as the e-cloud flux, heat-load, energy spectrum etc.
are measured,
DS illustrated the dependence of the build up time
and threshold on beam size, bunch length, delta_max,
and bunch intensity.
-> FR raised the question whether the build up time along
the batch changes during scrubbing and that we should
aim to get the pertinent information.
-> The decay time of the cloud is sensitive to our
model of elastic reflection, and measurements
should be conducted for various batch spacings.
FR stressed that untrapped coasting beam could
influence the results, and that the intensity
calibration might have a large error.
FZ pointed out that the different detectors
may be at locations with different delta_max.
-> Changes in e-cloud signals with bunch length
could be a valuable calibration and benchmarking
tool.
In the new LHC design report the bunch length at
injection was erroneously listed as 17.5 cm. The
electron cloud simulations will need to be
repeated for the correct length.
FR deplored that after 7 years of study there is
no analytical formula for the dependence of the
heat load on the bunch length.
The general conclusions of the LHC simulations
are that with 25 ns spacing the luminosity is
limited to 1/4 of the design. With 75 ns spacing
there is no electron cloud heat-load problem expected
and the luminosity would be at least 1/3.
(6) BPM Impedance with and w/o Copper Coating (FZ)
--------------------------------------------------
Following a request by Gerhard Schneider,
FZ tried to answer the question whether the warm
BPMs in LHC should be coated with a 100-micron
copper layer.
He noted that various formulae for the resistive
wall impedance make widely differing predictions,
and the formulae with inductive bypass typically
predict 10 times less impedance than formulae
based on a solution of Maxwell-s equation in 2D,
such as the derivation by Burov and Lebedev at EPAC02.
Nevertheless, even in the most pessimistic
case the uncoated BPMs do not contribute to more
than 1% of the total impedance. Using the Burov/
Lebedev expression for a coated chamber, the
impedance actually increased slightly at low
frequencies, reversing its sign. There is a
concern that neither of these formulae may be
applicable (private communication by F. Caspers).
However, they should represent the worst case.
In view of these results, the answer is that
coating the warm BPMs in LHC is not strictly
necessary
=>ACTION: FZ will inform Gerhard Schneider.
-> FR and EM underlined that L. Vos' formula for
the resistive wall impedance with inductive by-pass
applied to a collimator is in excellent agreement
with HFSS results obtained by H. Tsutsui, based
on a numeric solution of Maxwell's equations in 3D.
According to EM and FR, this was already discussed
at the LCE meeting of 1st August 2003.
(7) Touschek in MAD-X (FZ)
--------------------------
With Catia Milardi, visiting from INFN Frascati,
and FS, a Touschek module was developed for MAD-X.
It is based on the general theory of Piwinski
and computes the rate all around the machine.
Momentum spread, bunch length, and rf acceptance
are presently considered as constant (as it is
for the IBS calculations). This is not correct
for the planned upgrade DAFNE-2 operating with
strong rf focusing. An extension to this
general case is intended in the near future.
(8) E-cloud Simulations at Injection and Top
Energy in LHC and E-Cloud in DAFNE (FZ)
---------------------------------------------
The LHC results were already shown by Daniel.
For 75 ns spacing the heat load will be ok up to
nominal intensity. With 25 ns spacing, delta_max
values of 1.1 are required to operate at nominal
intensity.
M. Zobov informed FZ that DAFNE is now observing
a horizontal electron-cloud instability in the
positron ring. The instability growth time increases
along a bunch train, and an additional positive tune
shift is observed in both planes. The threshold
increases by a factor of two, when the rf frequency
is changed bu 10 kHz. The reason is unknown.
The instability is suppressed in collision by the
beam-beam interaction.
(9) Suppression of E-Cloud Instability by Chromaticity (EM)
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Parametrizing the e-cloud wake by a broadband resonator
and appropriately scaling with bunch length and beam size,
EM computed the instabiltiy thresholds in SPS and
LHC as a function of chromaticity and bunch length.
For the SPS a large chromaticity xi close to 1 is required
to suppress the instability, consistent with observations.
For the LHC at injection, a similar chromaticity of 0.8-1
is needed for 0.7 eVs longitudinal emittance and a
somewhat lower chromaticity of 0.5 for 1 eVs.
A shorter bunch length for the same emittance
also acts stabilizing.
At top energy, the LHC beam is always stable.
Enclosed: Slides by AK, FZ.