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12th FCC-ee Optics Design meeting
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Europe/Zurich
6/R-012 - conference room (CERN)
Participants: Andreas Doblhammer, Bastian Haerer, Mike Koratzinos, Katsunobu Oide, Sandra Aumon
Status chromaticity correction in the arcs by Bastian Haerer
Bastian summarized the work he has performed about his chromaticity correction scheme in the arcs. He begins with the preliminary results of the dynamical aperture simulations performed by Luis Medina in August. 12 fold lattices with 2 and 4 IPs were studied for 1 mm beta_y* and the first version of the baseline layout (Racetrack, 2 IPs). Concerning the baseline, the DA results show that the DA in the vertical plane for the 12 fold lattice with 4IPs is basically very low, almost zero. Reducing the number of IPs from 4 to 2 does not increase the momentum acceptance, but the DA increases for small deltaps about several sigmas. With a slight detuning of the phase advance per cell from 0.250/0.167 to 0.249/0.166 the momentum acceptance could be increased by 83 %. In general, the DA is very low for any lattice at 1mm beta_y*, except for 2IPs. Katsunobu asked whether the lattice fits the hadron layout. Bastian said yes, it does. Mike Koratzinos asked why the DA curves are not symmetric, Bastian replied that this comes from different chromaticities for positive and negative energy deviation.
Bastian continued with the results of the chromaticity correction of the Racetrack layout lattice using the Montague formalism and matching the W function from an IP to another. Although matched in Arc 2 and Arc 3 the Wx still has a relatively high value between 10 and 15 and Katsunobu asked why it cannot be better corrected. He suggested to increase the number of sextupole families. Bastian showed the plotted momentum acceptance calculated by MADX, which reaches from -0.24% to 0.07%. Since the vertical tune crosses the half integer resonance at -0.15% the actual momentum acceptance is in fact smaller the the one calculated by MADX. By adding an artificial linear chromaticity of Q’y=15, the momentum acceptance is improved by 27%. Bastian studied as well the 2mm beta_y*, in which the higher chromaticity terms are significantly lower (-88% for the fourth order). After matching the W functions the third order chromaticity is less than a third compared to the 1 mm beta_y* case. The main difference is the second order, which is in the same order of magnitude than before but positive now. This increases the momentum acceptance from -0.21%/+0.07% to -0.29%/+0.11%. Contrary to the results of the DA studies slightly modifying the phase advance of the FODO cells does not increase the momentum acceptance in this case.
In order to understand above mentioned behavior and to use an analytical approach to decrease second and third order chromaticity components, Bastian started to analyze the chromatic derivatives of the beta function. Katsunobu strongly suggested to add the local chromaticity correction scheme.
Bastian will also set up a lattice with individually powered interleaved sextuple pairs. Katsunobu pointed out, for canceling geometric aberrations between every sextuple pair a -I (or-I/I) transformation has to be obtained in both planes.
Status coupling correction and tolerance study for FCC-ee by Sandra Aumon
Sandra presented the tolerance study for the 12 fold layout with 2 IPs and 2mm betay*. For 120GeV, the targeted vertical emittance is reached for 0.040mm quadrupole misalignments, with a beta beating of about 15-20% after orbit and chromaticity correction. A preliminary method was used to correct the coupling and the vertical dispersion, by decreasing the Re13 component of the transfert matrix. 3990 skews were installed into the lattice. Katsunobu objected that the number of skews is too high and should be of the order of the betatron tune (500). A response matrix was built and since the computation was very long (3990 madx runs), it has been parallelized. Katsunobu said that it is possible to obtain the variation of the Re13 analytically. After coupling correction, the tolerance increases to 0.060mm in misalignments. Above this limit , the correction is counter-productive due to the beta-beating. The horizontal emittance is well corrected (0.47nm @ 0.150mm). Sandra pointed out that not only the number of skew is high but also the number of eigen values should be optimized. An alternative method would be the RDT method used in ESRF. Sandra started to work on the racetrack lattice from Katsunobu at 120GeV and 175GeV. The sawtooth effect is about 1mm for max 60% of beta beat, therefore 120GeV needs tapering.
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