SPS Impedance Meeting

Minutes August 27th, 2009

Present:  Fritz Caspers, Elias Métral, Nicolas Mounet, Giovanni Rumolo, Benoît Salvant, Carlo Zannini. 

   Agenda

-  Carlo Zannini 

        "Simulations of the SPS kickers with CST Particle Studio"  (slides, minutes)
        

-  Nicolas Mounet  

        - "Electromagnetic fields in a resistive cylindrical beam pipe"  (slides, minutes)

 

 

 

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    Minutes

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Presentation by Carlo:

- Carlo presented CST Particle Studio time domain simulation results for simple kicker structures studied by Tsutsui (wakefield solver, direct integration). A good  agreement between the simulation and Tsutsui theory (pdf and pdf) for the longitudinal impedance and transverse driving impedance was obtained. To our knowledge, no theory is available for the detuning part of the impedance. The simulated detuning impedance differs from  the current model using Yokoya/Laslett factors to relate the driving and detuning impedance in flat chambers of high conductivity. For the kicker model showed (an MKE), both the shape and the amplitude of the detuning terms can not be easily related  to the driving terms (in both horizontal and vertical planes). Elias mentioned that the imaginary detuning term of that simple model of MKE is larger than the imaginary driving term up to 400 Mhz, which could lead to a negative total imaginary impedance, and explain the positive tune shift observed in many machines.

- These simulations could then be very valuable inputs for an improved impedance model that could be imported into Headtail. As for the BPMs, Headtail requires a wake function and small bunch length have to be achieved to accurately create a wake function through dft-division by charge spectrum-dft. These DFTs back and forth strongly deter the accuracy of the obtained wake, and Giovanni wondered whether we could directly use the wake potential given by CST PS without deconvolution of the source charge. Benoît pointed out that the BPMs wake function and wake potentials looked quite different close to the source bunch and that these significant differences overlap with several slices of the bunch. After the meeting, it was mentioned that we could try to find a ratio Headtail slice dimension/CST bunch length over which we could use directly the wake potential output from Headtail.

- Fritz insisted that we should be careful not to use perturbative approach to simulate a ferrite (i.e. assuming first a metallic boundary condition and then using a perturbation scheme to enter the ferrite properties), and also that the wire measurements are not easy to perform. He also said that we should not use the classical formula of skin depth for ferrite, since the imaginary part of the permeability m is not present in the formula, and it is in the case of ferrite very significant. We should look at the characteristic length of penetration of a wave into ferrite.

- Carlo mentioned that a consequence of going to high frequencies is a decrease in accuracy of the ferrite permeability model used by CST. This should be discussed with Monika and Ulrich to see if there is a way around that issue.

- Fritz mentioned that ferrite have losses at high frequency (over a few hundreds of MHz) that are not accounted for in general. There is therefore a problem of extrapolation and the collaboration with Frankfurt in the frame of the phase II collimation could help giving more accurate ferrite models. Literature on the subject should be checked,  as the measurements of this material properties are heavy to perform. He also mentioned that the properties change a lot when the kicker is fired, but Elias said that kickers are not fired all along the cycle and this should be a small effect for instabilities.

- Carlo showed that contrary to previous simulations with good conductors, the kicker model impedance is not really linear with length. It is not a huge effect but accounts for 20 to 30% when going from 20 cm to 1 m long kickers. Fritz said that intuitively this makes sense as filling the ferrite with energy costs more in relative terms if the ferrite is short. The agreement with Tsutsui's theory is better when simulating a longer kicker, which, according to Elias, makes also sense since Tsutsui assumed an infinite length.

- Refining the structure of the kicker (cells, beam pipe, stripes...) is foreseen, and we should get together with Mike Barnes.

- The simulations with cylindrical and rectangular ferrite show that the Yokoya/Laslett factors do not hold for ferrite. Burov and Lebedev found a frequency dependence of the Yokoya/Laslett factors in one of their papers, and it would be interesting to see if such a dependence can be found in the case of ferrite.

- Carlo showed results with a small bunch length (s=1.5cm) in which divergence with Tsutsui formula is observed, and oscillations of the impedance at high frequencies. He said that the problem with shorter bunches is more a memory problem (due to the need for a finer mesh) than a computational time problem (which is still in the order of a few hours). Fritz said the oscillations could be attenuated using a smooth gating.

Fritz's sentence of the day: "Do not make the same mistakes people did 10 years ago...
                                                    ...Please make new ones...."

Presentations by Nicolas:

- Nicolas presented the general layout of his analytic calculations of the electromagnetic fields generated by a hollow ring source of arbitrary velocity in a cylindrical multilayer medium, for any azimuthal mode m, based on Bruno Zotter and Elias's formalism. He mentioned he was at this point trying to find useful approximations valid in the first and second frequency regime, to find simple formulas for the field components.

- Nicolas presented (in more details than at the last meeting) a matrix approach to solve the multilayer resistive wall impedance. Implemented in Mathematica, this approach enables to gain a lot in simplicity of the computation result in comparison with solving the whole system of equations. Using this new implementation enables to obtain the result much quicker than the previous implementation (130 times quicker actually), and Mathematica does not crash if more than 3 layers are used. This approach has been compared to existing formulas with two layers, the previous Mathematica code with three layers, and other formalisms (L. Vos and Burov Lebedev) with three layers. Burov-Lebedev exhibits a close agreement with the matrix formalism, except at high frequencies, but Fritz said that above GHz it is not use looking in the case of LHC. A computation with up to five layers was performed for a copper coated LHC graphite collimator in a stainless steel holder. Fritz mentioned that we should not always focus on copper for the coating, that are other candidates. Fritz also said that between graphite and copper coated graphite the difference is still in favour of copper coating as far as the beam stability is concerned, since most of the betatron lines are in the domain where the graphite alone has a much bigger impedance (classic thick wall regime). Elias answered that he looked at that in the past and several new results were obtained due to the new nature of the wall impedance. After the meeting it was decided that Nicolas will check these computations as it is important to understand them for his PhD thesis and for the LHC (of course!).

- Nicolas also showed an approximation for low frequency transverse impedance that leads to an interesting dependence of the real part of the impedance with f (f.log(f)) and sigma (higher sigma leads to higher impedance). This is of particular interest for LHC graphite collimators.

- Finally, Nicolas wanted to address the question of Vladimir on July 10th 2009: "Where is the limit due to causality on a wake field plot before the bunch, i.e. where is the point after which it must be zero?", and Nicolas showed a logic that would answer "nowhere". As a matter of fact, Bruno Zotter also writes in his book p. 44 :

Fritz also referred us to a representation of the EM fields created by a particle by A. Hoffman in a beam diagnostics course (Beam instrumentation / Bosser, Jacques (ed.) et al. CERN-PE-ED-001-92, 1992. - 296 p... Beware 50 MB document...).

AOB

- Elias said he will try to invite Christian Boccard to make a presentation on his recent measurements on a collimator BPM prototype. He also mentioned that Stéphane Fartoukh and Mike Barnes should be invited to our impedance meeting.

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