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Minutes of the ABP-RLC section meeting of 28.01.05
present: EB, AG, WH, EM, TP, FR, EV, FZ
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(1) Revised impedance estimates for LHC vacuum flanges (FZ)
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Karl Bane kindly computed the longitudinal wake for a single LHC flange with a 7.5 cm rms bunch length by TBCI.
His result shows a purely inductive wake with an impedance of 0.21 nH, which is to be compared with 0.20 nH predicted by Bill Ng's formula. The agreement is very good. Using then Bill's formula and assuming 2000 flanges in LHC, the total broadband impedance from the flanges is Z/n~29 mOhm. This is significant for a total impedance estimate of Z/n~70-76 mOhm, which did not include any contribution from flanges.
FZ sent the following questions to Miguel Jimenez on 14.01.05:
- what is the total number of flanges (2000?)
- are these flanges only in the long straight sections or also in the arcs?
- is there a beam screen at the location of some or most of these flanges?
- are the chambers mostly elliptical or mostly circular?
(and what are the most common dimensions of adjacent beam pipes?)
- what is the material of the flanges?
what is the dark box inside the flange in your drawing (copper?)
There was no answer so far and Miguel has not been reachable by phone.
ACTION => contact Pierre Strubin (FZ)
(2) New results on LHC collimator impedance
- numerical calculations of trapped modes etc. (AG)
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AG presented new results on the impedance of the collimator prototype in the SPS. He compared HFSS simulations of longitudinal mode frequencies and impedances vs. gap size with the measurements by F. Caspers and T. Kroyer. There are two dominant modes as discussed in the previous meeting. The measurements and simulations are in good agreement and exhibit the same dependence on the gap size. The measurement shows an additional bunch-harmonics structure due to weak coupling.
Updated values for the head loads are 6 W (instead of 10 W) for the 1st mode and 32 W (instead of 280 W) for the 2nd mode, for an rms bunch length of 80 mm. For the old numbers an incorrect form factor had been used.
ACTION => inform collimation team of revised heat load (FR)
Next, AG presented calculations for the transverse modes. There are two modes at the same frequencies as the two strong longitudinal modes, but in addition many additional ones. The transverse modes can ge grouped into tank modes, transition modes, and gap modes. Only the last two types of modes are a potential danger to the beam, while the tank modes have a high Q values, but very low impedances. Electrical field patterns were shown for a gap of 5 mm. There are families of gap modes, which differ by the number of nodes along the length of the jaw. AG also showed a summary table of transverse-mode parameters. HFSS results were confirmed by GdfidL time-domain calculations.
The expected single-bunch tune shift is 1.2e-6 for the SPS collimator, which is small both compared with the expected effect of resistive wall and with the measured tune change of order 1e-4.
AG also commented on the definition of impedance. It is calculated in two different ways: (1) from the transverse derivative of the longitudinal field, and (2) from the sum of electric and magnetic field on axis at the location of the test charge.
(3) Minutes from previous meetings and pending actions
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ACTION => WH will provide Yannis Papaphilippou with a first test file.
PENDING.
ACTION => compare the size of the longitudinal geometric wake with RW longitudinal wake from A. Koschik (FR)
PENDING.
OLD ACTION: compute the transverse modes (AG)
DONE. See above.
ACTION => perform numerical simulations of flange to determine broadband impedance and trapped modes (AG)
Flange BB impedance was confirmed by Bill Ng and Karl Bane (see above)
OLD ACTION: obtain more information on the flanges from M. Jimenez, e.g. exact total number, material, chamber dimensions, details of the drawing, location of flanges and possible presence of a beam screen (FZ)
Waiting for Response.
(4) Analytic estimates of collimator RW impedance (EM)
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EM recalled that Lebedev/Burov, Vos, and Tsutsui all agree on res.-wall impedance. The only exception appeared to be Bruno Zotter, whose formula had been said to predict a 100 times higher impedance at low frequencies.
EM received a draft of BZ's paper and re-derived the equations. He found some additional terms (inconsequential for the actual numerical result). The final result is indistinguishable from those of the other three. In particular, there is no factor 100,unless an error was made in the re-derivation. This is good news for the LHC collimator impedance.
Bruno Zotter will give a talk on 11th of February.
EM made no assumptions, and can even obtain a formula which is valid in the non-relativistic case. FR and FZ were surprised by the simplicity of the result. FZ mentioned his paper with Oide, where the formulae looked more complex and the expressions had to be expanded. FR recalled a paper by Cappetta, Petracca et al., which also contained much lengthier terms. The reference is:
S. Petracca, L. Cappetta, T. Demma, and U. Sannio, 'Electromagnetic Fields of an Off-axis Bunch in a Circular Pipe with Finite Conductivity and Thickness', Proc. EPAC'04.
ACTION => FR will contact Stefania Petracca to see whether their theory can be applied to LHC collimator
(5) Instability growth rates after first CNGS extraction kick (EV)
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EV compared simulations and measurements of resistive-wall growth rates including the non-flatness of the kicker pulse. The kicker pulse was measured directly by Enrique Gaxiola, and it was also deduced from the bunch-to-bunch positions after 1 turn measured by Wolfgang Hofle and E. The latter shape was used as the starting condition for the simulation. The shape of the instability was reproduced in detail. There are 5 regions with large growth rates along the CNGS batch, both in simulations and in the measurement. The high-growth regions correspond to places following groups of bunches with large injection errors. The measured growth rates at the tail of the batch are slightly larger than the simulated ones, which could be attributed to additional wake fields.
(6) Summary of the "PS&SPS days" (EM)
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The SP&SPS days were modelled after the Chamonix workshop, with provocative talk titles, addressing the burning problems
of the PS/SPS complex, but without formal proceedings and without official summary. Among the outstanding and challenging
problems figure the PS internal beam dump, and the reliability of the PSB sieve operation, needed to produce pilot bunches for LHC. Another issue is to improve efficiency by a faster switch between supercycles and by reducing the booster cycle time from 1.2 s to 900 ms.
Remark: After the minutes were sent, Karlheinz Schindl added the following information in the sieve. This is a carbon sieve located between Linac2 and the PSB. It features small holes covering about 1/5 of its surface, thus reducing the Linac2 proton beam intensity and density by a factor of ~5 at 50 MeV, indispensable for producing the LHC pilot beam. This device can be inserted from pulse to pulse. While for many years the sieve was in use for MD's only, it has now become a device to be used in LHC operation. The expert has left CERN without appropriate documentation and nobody prepared to take over.
(7) Follow-up from "Chamonix"- ecloud impedance and electron pinch tune spread (FZ)
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FR noted that quoting only a broadband impedance value for the e-cloud effect ignores additional damping from the electron-induced tune spread. E. Perevedentsev did not include the full effect, but only the change of average tune along the bunch. However, the larger tune spread also increases along the bunch. In addition, FR pointed out that the resonator frequency and the wake should also change with z position. An even larger complication may be that the interaction force (and hence the wake) between electrons and the beam is nonlinear. FR recommended a concerted action to determine the stabilization
from these additional unconventional Landau damping phenomena.
Also, many instability simulations were done for field-free regions (an exception are recent LHC simulations presented at HHH-2004). A dipole field could further weaken the electron wake field.
FR stressed that RLC team should make a better communication effort to the outside.
(8) Possible implementation of a wavelet-based Poisson solver (EB)
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EB presented details of a novel scheme which use wavelets to solve the Poisson equation in PIC codes, in order to speed up the simulation and to suppress the PIC noise. She is in contact with the proponents of this idea, and we may receive a wavelet-based Poisson solver by this summer.
FR warned of possible pitfalls of such an approach.
(9) AOB
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FZ presented a slide prepared for Steve Myers, where he addressed the question of He leaks - their effect and how to detect them - that came up during the Chamonix workshop. He declared that the energy losses are likely localized near the location of a helium leak and not spread over the machine, a view supported by B. Jeanneret and S. Gilardoni. He mentioned RA's viewpoint that if the magnets quench prior to any effect on the beam there would be no problem and the leak easily identified. FR remarked that in a situation with many leaks it would be difficult to draw conclusions, and one would only detect one leak at a time.
A possible scheme to identify a region with a He leak had been proposed by A. Poncet in 1995. It consists in debunching a test proton beam and measuring the electrons from ionization with clearing electrodes. The BPMs could temporarily be biased for this purpose.
After the meeting it was remarked by B. Jeanneret that the BLM specification includes a 'BLM snake' with BLMs spaced at 2 m, which could be deployed to find and localize beam losses due to a He leak.
Attached: Slides by AG, EM, EV, FZ