Prof. V. Vaccaro seminar: minutes

May 19^th & 20^th, 2009

Invited talk given by Prof. Vaccaro, from Università degli Studi di Napoli “Federico II” and INFN Sezione di Napoli

• Slides (ppt)
   
• Summary of discussions:
   
  • About measuring the coupling impedance with a wire: Prof. Vaccaro says that one must be very careful because the wire in the axis of the structure changes fundamentally the e.m. boundary conditions of the problem, and turns a typical wave guide problem into a coaxial cable-type problem. The most elementary perturbation introduced by the wire is for example that, while in the structure without the wire frequencies below the cut off frequency of the beam pipe cannot propagate out of the structure, when we insert a wire all frequencies will be able to propagate because a coaxial cable allows the propagation of the TEM mode, which has 0 cut-off frequency. Also the longitudinal electric field on axis, which defines the longitudinal impedance, is the most perturbed quantity when a wire is put in the structure, since it is forced to be 0 (ideally, for perfectly conducting wire) by the presence of the wire.
    Also, Prof. Vaccaro showed very nice agreement between measured scattering parameters (e.g. S21) and what was calculated analytically with the matching technique. Despite the wire perturbation and the fact that the TEM mode propagates also below cutoff, the agreement with theory is excellent. The mode matching technique is independent of the wire.
    Then, to infer the longitudinal impedance one needs to pass through approximations that Prof. Vaccaro does not really trust (such as, according to Federico Roncarolo, the 'log formula' - not discussed in the seminar) which may introduce discrepancies between this method (in the frequency domain) and other methods (such as fft of wake fields calculated in the time domain).
     
  • About the definition of impedance: Elias Métral points out that there exist several definitions of impedances, and asks Pr. Vaccaro a general definition for it. Prof. Vaccaro answers that impedance is not really an abstract concept that can be defined once for all, but rather something that evolves depending and what we want to use it for.
     
  • About the mode matching technique: Nicolas Mounet asks what was meant by "solving numerically the infinite set of equations in a clever way" (when matching the modes). Prof. Vaccaro answers that across a boundary between two cavities of different lengths, one needs to compute only modes that are commensurate to one another: in one cavity one needs to consider only modes that have harmonics related to the other cavity harmonics (the relation being the ratio of the two lengths).
     
  • About the cutoff frequency: Elias mentions that the lowest cut-off frequency (for the wave propagation) should be given by the beam pipe with the largest aperture (i.e. the cavity with the radius b2) and not by the (small) radius b1 of the beam pipe. Prof. Vaccaro and Giovanni Rumolo disagree, saying this is the opposite because there is no energy loss related to modes trapped in a cavity. Elias pointed out he made some simulations last year related to that (pdf). In these the real part of the longitudinal impedance is 0 below the 1st cut-off frequency (as expected by Prof. Vaccaro) but it seems that the lowest cut-off frequency is given by b2 (as Elias would have expected). Elias thinks this could be quite interesting to make some simulations.
    Prof. Vaccaro showed several results from impedances calculated with the wave or mode matching techniques, in which the spectra for PEC structures always show a zero real part of the longitudinal impedance below the cut-off frequency of the beam pipe attached to the simulated structure. He claims that this is not surprising, because energy can only be lost because of propagation through the beam pipe (which can only happen above the pipe cut-off frequency) in absence of other loss mechanisms inside the structure. He says that below the cut-off frequency of the beam pipe there can be only reactive impedance, which represents the energy that remains stored in the cavity and will keep being exchanged with the beam. E. Métral says that he would only expect the real part of the impedance to be zero below the lowest resonant frequency of the structure, which is usually lower than the pipe cut-off frequency because it has a larger size. In fact, he believes that also the energy in the resonating field is lost - as seen by the beam.
    According toe G. Rumolo, what point of view is correct probably depends on the definition of coupling impedance and whether the periodicity of the passages of the beam in the structure are considered or not. One question is: do we consider a delta-like excitation of the structure or a periodic one (continuous, in the limit) ?
     
  • Prof. Vaccaro tends not to believe the results of electromagnetic codes when they solve Maxwell's equations with open boundaries. That's why he proposes to use them only to calculate the modes of closed structures and then apply the mode/wave matching technique at the borders of the structure with an attached beam pipe (his last slide).
     

AOB:

• The organization of a workshop devoted to impedances and wake fields was discussed (it was already evoked at the GSI workshop). Elias would prefer that CERN organizes it as a lot of work was done there in the last few years (and will continue to be done). The organization of this workshop will be discussed during the next impedance meeting (planned in 2 weeks). Prof. Vaccaro said he would gladly accept to be part of the organization if we decided to have the workshop hosted by a different site than CERN (somewhere close to Naples, for instance).
   
• Prof. Vaccaro also said he would like to open a formal collaboration with CERN on impedance related issues.

Follow-up:

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