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Minutes of the ABP-RLC section meeting of 18.03.05
present: EB, HB, AG, WH, EM, FR, DS, EV, FZ
web site: http://ab-abp-rlc.web.cern.ch/ab%2Dabp%2Drlc/
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(1) Minutes of last meeting and pending actions
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DS had sent a comment on the minutes, concerning ECLOUD benchmarking,
which was included in the minutes of last week's meeting.
=> ACTION => Maintaining IP knobs of W. Wittmer, check with optics team
and with W. Wittmer (WH, FZ)
STATUS: WH discussed this matter with M. Giovannozzi. WH will prepare
a working version and the LOC team will take over the maintenance
as soon as it is ready (almost done).
=> ACTION => compare the size of the longitudinal geometric wake with
RW longitudinal wake from A. Koschik (FR)
STATUS: PENDING.
=> ACTION => confirm bunch length, intensity, and collimator gaps during
tune-shift measurement (EM, FZ).
STATUS: ONGOING, EM compared collimator gaps from Stefano with
numbers of Marek and found them in close agreement; next he plans
to look at intensity and bunch length.
=> ACTION => volunteer to make an LTC presentation of the new results (FZ)
STATUS: Presentation is being scheduled by O. Bruning, probably for
next week
(2) Effect of ac conductivity on graphite collimator resistive-wall
impedance (AG)
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AG briefly reviewed the effect of ac conductivity in the resistive-wall
wake theory, as developed by Karl Bane and others. The electronic
relaxation time determines the frequency at which the effect is relevant.
In the Drude model, this can be obtained from conductivity and free
electron density. For graphite and carbon the density is 4 orders of
magnitude lower than for copper. For Cu the ac conductivity introduces
a peak in the impedance at 10 THz, for graphite and/or C-C the peak
is larger (increase by 3-4 orders above the nearby values) and at 1 THz.
The frequency is still too high to be harmful for the LHC.
AG assumed an epsilon=4 for C-C (which he estimated from the
average over different directions graphite).
FR mentioned that another effect comes into play at high
frequencies, where the displacement-current becomes important.
This is described in A. Chao's book.
(3) Tune shift from nonlinear RW collimator wake (FZ)
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Starting from the Piwinski-Bane-Irwin-Raubenheimer formula for the
nonlinear resistive-wall wake field, FZ derived formulae for the
coherent and incoherent tune shift induced by a collimator, including
the effect of the finite beam size (plus loss in intensity and change
of distribution by scraping)
Application to the parameters of the SPS LHC-collimator measurement
yields a good agreement between theory and measurement when the beam
sizes in the two planes are taken into account. Reducing the beam sizes
by a factor of 10 reduces the prediction to that for a pencil beam
(e.g., Burov-Lebedev impedance). Increasing one of the beam sizes
by a factor of 2 also changes the result drastically (hence, a similar
measurement technique could be used for monitoring beam sizes as
remarked by HB).
While the coherent tune shift steeply increases as the collimator
gap is closed, the incoherent tune spread is predicted to reach a
maximum for a half gap about equal to the rms beam size.
The predicted incoherent tune spread is quite large, of the
order of 0.002 at the maximum. This may imply that for LHC Landau
damping could be restored by the nonlinearity of the wake itself.
The Piwinski theory does not include the phenomenon of inductive
bypass.
=> ACTION => Attempt to derive a general nonlinear theory including
the inductive bypass (EM)
(4) Updated e-cloud simulations: LHC arc heat load &
modified cooling capacity (FZ)
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FZ presented updated simulations of average arc heat load,
electron density and electron flux on the wall vs. the bunch
intensity. The values shown are averages over an arc cell,
including quadrupoles and drifts. The curves were calculated
for R=0.5 (a factor 2 smaller than in previous simulations).
The latest estimate of the cooling capacity was included.
For delta_max=1.5, the intensity limit is about 1e11 protons
per bunch, and the nominal intensity can be reached for
smaller values of the emission yield. FZ also presented
the simulated heat load in the arc dipoles as a function
of bunch spacing. The results indicate that a spacing of
12.5 ns can be achieved for delta_max=1.1.
DS suggested to repeat the simulations for more than 1 bunch
train and also for R=1.0. He explained, how he had obtained
R=0.5 by fitting the SPS data, and that higher R and lower
delta_max may describe most measurements similarly well.
(5) Update on MAD-X Touschek and Dynap modules (FZ)
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FZ summarized recent modifications to the MAD-X DYNAP module.
Results for Lyapunov and smear are now printed for multiple
particles, and the calculations of tune error and Lyapunov
coefficient were both improved.
FZ also presented the new web documentation and examples
for the TOUSCHEK model. He thanked F. Schmidt and C. Milardi
for their help in the TOUSCHEK effort, and he showed suggestions
for further extensions of TOUSCHEK by C. Milardi.
(6) Transverse resistive-wall impedance for 2 layers derived from Zotter formalism (EM)
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EM numerically solved the 2-layer impedance in the Zotter theory for the
case of a Cu-coated graphite collimator in the LHC. The agreement with the
Burov-Lebedev theory is excellent. The differences are smaller than 1% both for
coated and uncoated graphite collimators. The only significant difference
between these two theories, of about 30%, was noted for the SPS MKE kickers,
and this is attributed to the effect of the complex permeability. More
precisely the 30% is the remaining difference for the amended Burov-Lebedev
theory, which takes a complex permeability into account.
FR recommended to obtain physical insight in addition to the mathematical
formula, and also to compute impedances for different values of epsilon
(in particular for epsilon=4, which appears to be the best estimate for the
collimator).
FZ remarked that the gain by the coating is significant, at high frequencies
up to a factor of 10, and that only one line of the summation should fall
into the region where the coating does not help (i.e., below 1 MHz). Even if
the total gain is only a factor of 2 it might be worth the effort, since
it would allow reaching the ultimate intensity.
FR commented that the effect of the coating may be more positive when
epsilon=4 is considered.
Posted on the web: Slides by AG, EM, FZ (3x)
Web site: http://ab-abp-rlc.web.cern.ch/ab%2Dabp%2Drlc/