Minutes October 16th, 2009
Present: Fritz Caspers, Elias Métral, Nicolas Mounet, Giovanni Rumolo, Benoît Salvant, Bruno Spataro, Carlo Zannini, Bruno Zotter.
Agenda
- Carlo Zannini et Benoît Salvant
"Update on the impedance of the SPS kickers" (slides, minutes)
Minutes
Presentation by Carlo and Benoît:
Summary:
Dipolar and quadrupolar impedances of a SPS kicker were obtained from Tsutsui's theory and Benoît's improvement of this theory (to get the quadrupolar term). Clearly no simple form factor can be identified between the cylindrical structure (Zotter-Métral formalism) and the kicker model. Indeed, the Yokoya form factors are valid in the ultrarelativistic case and for metals under the approximation of a skin depth much smaller than the material thickness (classic thick wall regime). Tsutsui's theory gives also different results as Burov-Lebedev formula (more general form factor than Yokoya) applied to ferrite. From Tsutsui's theory it is seen that the form factors seem to tend toward ±p2/24 at high frequency. Also, theory for different type of ferrites don't give very different results except at high frequency (above 1GHz).
Very good agreement is obtained between Tsutsui's theory and simulations by Carlo in horizontal. In vertical there is a divergence between theory and simulation at high frequency, both for driving (=dipolar) and detuning (=quadrupolar) terms, but in an opposite way which compensate each other: the sum driving+detuning (for y1=y2, case of a displaced wire or beam) is in very good agreement with theory.
Another result is the comparison between theoretical (Tsutsui) wake function (response of a delta function, which is needed by Headtail) and simulated wake potential (response of a bunch distribution, which is what is given by CST Particle Studio): both are quite different for a simulated bunch of 10 cm but very similar for a simulated bunch of 2 cm, which makes possible to use directly the output of Particle Studio as input of Headtail (without having to perform Benoît's FFT-deconvolution technique).
When summing all the kickers, a positive tune shift is obtained, as in the SPS measurements, and some damping at intermediate beam intensities. The instability threshold in vertical is still much too high compared to reality. The kickers seem to account for 45% of the vertical effective impedance measured in SPS, and when adding the BPMs and the beam pipe about 60% of the effective impedance is obtained. In horizontal the effective impedance is much closer to the measured one.
Finally Carlo did some bench measurements on a PS kicker, displacing a wire in x and y and making a fit of the quadratic longitudinal impedance to get the transverse one. For the real part of the impedance Tsutsui's theory is in good agreement with measurements up to 0.5 GHz, then there is a kind of frequency "shift".
Discussion:
- Fritz insisted on the fact that ferrite is lossy at high frequencies (above 500 MHz), which means that the theoretical model considered by H. Tsutsui with decomposition in orthogonal modes should not be applicable at higher frequencies. Benoît mentions that this should be a problem only for the eigenmodes analysis in frequency domain, not in the time domain simulations. Also Fritz wondered about the impact of hysteresis. Nicolas said that our theories and models do not account for non linear effects.
- The same comment applies to the model chosen for the ferrite in simulations. Since the ferrite is black in optical frequencies, it should be lossy in the hundreds of THz range. What about the tens of GHz range? We need permittivity and permeability measurements to get a more accurate model.
- After the meeting Fritz provided a number of references (Krupka paper on material measurement technique, additional 4A4 data provided by Ferroxcube, data sheet for 8C11, article in which dielectric losses are considerably different from what one would expect in the simple approach, article in which the dielectric losses of ferrites in the microwave range are not at all small).
- Elias recalled that Laslett already predicted the form factors at DC. A zoom at low frequencies performed after the meeting is shown here. The convergence of the form factors is not clear, and should be studied in more detail. The difference with the Laslett coefficients could be explained by the presence of the two metallic plates.
- Elias recalled that these studies on the quadrupolar contribution were initiated by the single wire measurements on the PS kickers. In this talk, Elias had mentioned that the quadrupolar contribution of the kickers should be studied as it can be responsible for the positive tune shift with intensity in the horizontal plane, and could also affect the tune shift in the vertical plane.
- Nicolas noticed that the formulae used by Burov and Lebedev to obtain their frequency dependent form factors seemed to be in CGS units, and he wondered whether this was taken into account. After the meeting, Carlo and Benoit checked that it had been taken into account for the permeability, but not the conductivity. Carlo reproduced the plots to check that they are not affected over 1 MHz, since the conductivity impact on kappa is divided by the frequency and compared to 1.
- Fritz wondered where the energy "lost" due to the decoherence of the oscillations goes. No non linearity is taken into account, so that damping of coherent oscillations can only occur through incoherent tune spread created by the quadrupolar impedance. The total energy should therefore be conserved over the simulation time. Bruno Z. said the energy could also go in another plane. After the meeting, Benoît checked that the presence of a quadrupolar impedance in simulations leads to emittance growth when the beam is kicked (see here).
- Elias and Fritz mentioned that a next step is to simulate the displaced wire method. Benoît mentioned that we should keep in mind that ferrite is not easy to handle in microwave studio, from the experience of our colleagues from TU Darmstadt. Carlo said that maybe the time domain solver could work better than the frequency domain solver.
- Fritz said that wire measurements are long and difficult to perform and that he needs "victims".
- Bruno S. mentioned that he had seen some non linear effects in the coupling impedance (dependency in the beam offset) that should be checked in simulation and measurements.
- Nicolas briefly explained what he is trying to do to compute some generalized form factors for infinite parallel plates made of any linear material. Fritz said that he does not believe an analytical formula could exist for any lossy material, in which Nicolas agreed since he found some coefficients that are integrals that cannot be computed analytically. Fritz also mentioned an article by Sommerfeld in the 20s where the same kind of analysis is performed.
- After the meeting, Elias suggested that the next step should be to compare the new theory and the simulations with the 2-wire measurement (so dipolar impedance only) made by Fritz on a SPS MKE kicker. Those measurements were already compared to Zotter-Métral formalism in https://care-hhh.web.cern.ch/care-hhh/BEAM07/Proceedings/Proceedings/Session 3++/S43-Métral-letter.pdf, figure 7. Elias also mentioned that scanning the chromaticity in Tsutsui's model when looking at the decoherence effect and emittance growth (as Benoît did here) would be very interesting: it is known that without impedance a zero chromaticity gives no decoherence, but when impedance is also considered, is the decoherence still at a minimum at zero chromaticity, or at another value ?
AOB
- Fritz said that the collaboration with Germany for material characterization is not going to happen now.
- Fritz mentioned that the heat load in the SPS kickers is going to be checked in week 45 with strong LHC beam (25 ns, 50 ns and 75 ns).
- Christine Vollinger from the RF group also needs to perform permeability measurements on ferrite (this time magnetized and in a different frequency range).
Authors: Nicolas Mounet and Benoît Salvant CERN
BE/ABP-LIS