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18th FCC-ee Optics Design meeting
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Europe/Zurich
6/R-012 - conference room (CERN)
Present: Michael Benedikt, Andreas Doblhammer, Bastian Haerer, Bernhard Holzer, Mike Koratzinos, Katsunobu Oide, Frank Zimmerman, Jorg Wenninger, Sandra Aumon
Wigglers in FCC-ee: Preliminary results, by Andreas Doblhammer
The motivation of the study is to find out whether wigglers can be use for emittance tuning in FCC-ee: can we manipulate the emittance by factor 2, as for example in LEP or PETRA3 ?
Andreas studied a LEP-like 3-pole wiggler (1 T) and he found that 200 of those would be needed to reduce the horizontal emittance by half. They would be more use as excitation wiggler to increase the emittance by a factor 2. Katsunobu asked why wigglers were installed into LEP. Frank Zimmermann replied that they were used to reduce the polarization time. LEP-like 3-pole wiggler would be used as excitation wiggler.
Andreas went then for 39-pole-wiggler on the racetrack from Bastian. By inserting these new elements in the LSS sections, Andreas had to rematch the optics due the change of dispersion in the wigglers. With this configuration, the hor. Emittance can be reduced by a factor 2, however the synchrotron radiation goes up to 14.9GeV. As excitation wiggler, this scheme can increase the emittance by a factor 2 with 6% more synchrotron radiation.
Chromatic derivatives of the beta function - first results, by Bastian Haerer
The motivation of this study is to develop an analytical approach for higher order chromaticity correction, which allows a better understanding and thus predictions of the non-linear dynamics. Bastian uses the racetrack lattice V17 with 2 sextupoles families per arc in the horizontal plane and 3 in the vertical plane, which he used to match the linear chromaticity and the W-functions in the adjacent arc to the IR. Katsunobu asked about the the asymmetry in W function (slide 6), since the lattice is symmetric. Bastian replied it can be due to a mismatch in the phase advance. Moreover the sextuple strengths are not symmetric.
Using the already corrected lattice Bastian first calculated the beta functions for a relative energy deviation of =/- 0.001. In the first straight section and the beginning of the first arc the W function is still high and the chromatic vertical beta function is highly mismatched reaching a beta beat of 500%. As the W function is iteratively corrected in the first arc the beta beat as well gets smaller, which nicely illustrates effective performance of the Montague formalism.
Then Bastian looked at the chromatic derivatives b1, b2, a1 and a2. b1 and a1, which are used to define the W functions decrease linearly as expected, again illustrating the performance of the Montague formalism. In order to understand the behaving of the second order derivatives further investigation is necessary. For example the contribution of the arc itself needs to be studied.
The chromatic derivatives of the beta functions are calculated because Anton Bogomyagkov derived analytical formulas for the first three orders of chromaticity using said derivatives. The product of the beta function with the derivatives b1 and b2 indicates places in the lattice where sextupoles can be placed modifying the second and third order chromaticity. Using free sextupole pairs at the beginning of the first arc and numerical optimization of their strengths Bastian already managed to increased the momentum acceptance. With above described pointed chromaticity correction Bastian hopes to increase the momentum acceptance even further. He did first investigations which had mainly positive results, but the additional sextupole fields induce a W-function mismatch and spoiled the optics in the res of the lattice, which also created higher order chromaticity. As next step, Bastian will apply the correction while simulataneously rematching the W functions. After optimizing the arcs he combine them with a local CCS
Bernhard asked why do we need a CCSX in Anton's lattice. Sandra replied that Anton showed this summer that taking away the CCSX decreases the momentum acceptance. However, Anton did not use an optimized sextupole scheme in the arcs.
BPM Errors for the tolerance study: first results, by Sandra Aumon
From the outcome of the review of September, it was strongly recommanded to look at the impact of BPM errors (misalignments, reading etc..) on the vertical emittance. The first results were computated on a perfectly aligned lattice (KO 175GeV racetrack, tapered), except the BPMs. The misalignments were increased step by step, and for each increment of the BPM errors, the orbit is corrected, introducing mainly vertical dispersion.
It was found that the required vertical emittance is reached for BPM errors between 1 and 2 micrometers RMS, due to the large vertical dispersion.
Katsunobu and Jorg pointed out that the problem is the orbit correction itself, and that the problem should taken the other way around: rough correction of the orbit, and concentrate on the vertical dispersion by matching or steering. Discussions were triggered by the very high vertical dispersion at 5micrometers. Sandra thinks that this is a question of bad seed, to be checked on more seed. Jorg proposed to try an orbit correction with tools they use for LHC, which might be more efficient than SVD in MADX. As a next step, Sandra will try to concentrate on vertical dispersion rather than orbit correction. Katsunobu suggested to use less BPM/correctors.
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