Minutes July 10th, 2009
Present: Rama Calaga (BNL, Upton, NY, USA), Vladimir Kornilov (GSI Darmstadt, Germany), Elias Métral, Nicolas Mounet, Diego Quatraro, Federico Roncarolo, Giovanni Rumolo, Benoît Salvant, Bruno Spataro (INFN Frascati, Italy), Carlo Zannini.
Agenda
- Vladimir Kornilov
"SIMULATIONS OF HEAD-TAIL DYNAMICS IN BUNCHES WITH SPACE CHARGE USING HEADTAIL AND PATRIC CODES" (slides, minutes)
- Benoît Salvant
"Lessons from Darmstadt" (slides, minutes)
- Nicolas Mounet
- "Fourier Transforms of Wall impedance" (slides, minutes)
- "Electromagnetic fields" (slides, minutes)
Minutes
Presentation by Vladimir:
- Vladimir showed an agreement between theory, PATRIC and HEADTAIL for a gaussian bunch with chromaticity but with neither space charge nor impedance. Besides one kick per turn is enough to represent the bunch motion in this case.
- However differences appear between HEADTAIL and PATRIC when space charge is included. The general behaviour is similar, and the specifics are very sensitive to initial conditions: numerical issues may cause these differences. He then uses the theory for airbag (square-well potential) bunches for which an analytical solution exists. Good agreement between HEADTAIL and PATRIC and theory for the mode spectra (however, one kick per turn in HEADTAIL is not enough, as Diego and Giovanni also concluded). Simulations with space charge (HEADTAIL for a gaussian bunch) and theory (airbag) agree rather well, despite the difference in longitudinal bunch profile.
- Including the wake field (no space charge), Vladimir compared PATRIC simulations (airbag) with theory (airbag). The synchrotron sidebands are observed at low current, but they disappear at higher current. The real and imaginary mode spectra agree reasonably well with theory (theory does not include mode coupling, explaining the slight difference in mode shifting difference at higher current).
- Including both space charge and wake field, the +1, 0 and -1 simulated mode shifting agree well with theory (again for airbag).
- Issue of the HEADTAIL wake field module and the phase. Vladimir showed a problem with the current module for coasting beam. Applying the phase that seems to solve the problem for coasting beam does not work for bunched beams. Vladimir and Giovanni (supported by Diego and others in the audience) disagree on the need to apply an additional phase advance to the module.
- Vladimir wondered if measurements with octupole in the PS could be possible to check predictions for SIS 100 coasting beam. Elias mentioned he had already done such studies in 2000 (see pdf), which could be readily used by Vladimir.
Presentation by Benoît:
- Some comments and remarks following Benoît's trip at TU Darmstadt in the end of June. I did not talk with CST people there, so I did not get a cause for the factor 4 issue between CST 2009 and 2010 "indirect testbeams" wakefield solver issue.
- New simulations of the BPMs with CST 2010 performed at CST. The wake of the BPM was underestimated but its effect on the single bunch wake is small compared to the kickers. Rama wondered about the important effect on the long range wake compared to the relatively small effect on the short range wake. The HEADTAIL simulated instability threshold using the BPVs and BPHs wake is between 2e12 and 3e12 p/b.
- First CST simulations of the HEADTAIL monitor and Directional Coupler were presented, showing the expected signals at the ports when beam passes by. An increased ripple is seen following the bunch when a transition is put before the bunch. However, more checks have to be performed to track numerical errors.
- Bruno mentioned that the ECHO code (I. Zagorodnov) could be useful to simulate short bunches (few mm).
- Rama asked why taking the value at one mesh cell from the beam center was so important, since the aperture is much bigger. Benoît answered that it was needed to stay in the linear domain (at 10% of the aperture it is already in the nonlinear domain).
- Bruno said that before verifying the impact of the mesh, we should first check if the behaviour is correct when scanning the beam position with respect to the ferrite (it should decrease the broad band impedance).
- Striplines: Bruno said it was surprising that Benoît did not find the trapped mode when looking at the striplines. Rama said we might want to add some extra beam pipe at the ends, instead of the direct open boundaries, but Benoît said it's not easy because we would then need a lot of meshes.
Presentations by Nicolas:
1) Fourier Transforms
To accurately compute the wakes, impedances have to be Fourier transformed over very large frequency intervals, meaning huge number of data points to store and handle (more than 1 billion). Nicolas introduced a Fourier Transform method that can be used with unevenly sampled set of points meaning the possibility to reduce greatly the number of points to handle for a smooth function. This method has been benchmarked with classical DFT. Giovanni wondered what is different between this method and the one published in Numerical Recipes (NR). Nicolas answered that the method in NR is not really the same. After the meeting Giovanni and Nicolas looked at the method in NR, called the Lomb normalized periodiagram, and agreed it was indeed not applicable: this method does not compute a Fourier transform but another kind of power spectrum, which anyway gives only the modulus and no information on the phase.
Nicolas introduced some results on the wake function before the bunch, showing we can with this method obtain more accurate results than with classic DFT (in particular it seems to go to zero in a . Vladimir asked where should be the limit due to causality in front the bunch, i.e. from which distance in from the bunch there should not be any wake because the speed of light is finite. Nicolas said he doesn't know, but that is was a point to investigate (follow-up in the 4th impedance meeting minutes).
2) Electromagnetic Fields
Nicolas presented quickly a first result of a matrix approach to solve the multilayer resistive wall impedance (also used - in a different formalism - by others: Ivanyan et al and Hahn in particular). 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, and Mathematica does not crash if more than 3 layers are used.
Nicolas also initiated a discussion on the permittivity definition problem he encountered, for a linear conductive material. He mentioned there was an issue with radial electric boundary conditions in Bruno Zotter's formalism if we don't write the permittivity of a medium as the full complex permittivity, including both dielectric constant and conductivity (which is usually not done in many textbooks). He argued that in a medium Maxwell's equation comes from the vacuum Maxwell's equation, taking into account all sources of charge and current densities present in the material, and that there was some charge density associated with Ohm's law current density (j=sigma E) that needs to be taken into account in Gauss's law (div D=rho). Giovanni disagrees, saying that such a charge density should be macroscopically zero everywhere. After the meeting discussions went on between Giovanni, Nicolas, Elias and Benoît, the conclusion being that there are two way to see things, formally leading to the same results:
- either one uses in the electric displacement D the full complex permittivity, as Nicolas said, and consider there is no surface charge density at the boundary,
- either one uses the usual electric displacement with only the dielectric constant part, but then there must be a time varying surface charge density at the boundaries (even with a resistive material, i.e. not perfectly conducting).
AOB
- Discussions with Bruno S., Rama, Federico, Giovanni, Benoît, Carlo and Prof. Vacaro (over the phone) took place in the afternoon to understand the results obtained by Carlo with CST Particle and Microwave studio for the impedance of a perfect conducting (PEC) pillbox cavity attached to a beam pipe. CST Particle Studio finds the cavity resonance peak with a significant real part below the cutoff of the pipe attached to the cavity. Since no energy should be lost as the pipe is PEC and we are below the cutoff, Prof Vacaro claims that these kinds of simulations are not correct. Carlo showed that the cavity mode below cutoff is trapped, and the wake is oscillating without decay. Since the integration has to window the wake at some point, this operation transforms the dirac delta into a sinc function, leading the resonance peak to display an artificial width. However, it is interesting to note that the integration of a dirac delta yields anyway a non zero value, yielding a non zero real effective impedance. This non zero impedance is due to the fact that the observed system is the bunch that passes the cavity once and is bound to lose energy. This energy is however stored, and when another bunch passes by the cavity, this energy can be reused by this other bunch. After a certain number of passes (how many???? this should depend on many beam and machine parameters!) this initial transient regime is followed by a permanent regime where a passing bunch leaves as many energy as it gains. As a consequence, for a circular accelerator with many bunches and slowly decaying wakes, it can be more relevant to assess the wake reached in the permanent regime than the wake left by the first bunch. Which definition of impedance should we then use?
- Elias mentioned that a new PhD student from GSI might come at CERN and work with Mike Barnes on kickers and collimators impedance.
Author: Benoît Salvant CERN
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