Solenoid modeling
The meeting focused on "Solenoid modeling" with four presentations each with slides and extended discussions
Solenoids using slicing with standard MAD-X elements, Helmut Burkhardt
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Helmut starts by numerically solving the equations of motion to obtain particle trajectories in magnetic fields.
He observes excellent agreement between GEANT4 and his dedicated "FieldStep" which converges quickly for small lattice sections, typically +/- 6 m around IPs. He illustrates this for the idealized FCC-ee interaction region based on four each 1m long 2T solenoid and anti-solenoid magnets. He calculates the field harmonics in the local system around the design passage, and studies their effects and how to model them using MAD-X elements. The dominant effect is a vertical kick produced by the local field in the horizontal plane. Just using zero order multipole or orbit corrector (HKICK, VKICK) slices, he can reproduce the positions, directions and dispersion observed in "field stepping" with MAD-X.
As a test he also uses the higher order harmonics as multipole strength and finds that he can get coupling in agreement with tracking in one plane, and opposite sign in the other plane, as can be expected for a solenoid that focuses in both planes in contrast to multipoles. He also tried to match the observations with MAD-X using standard solenoid slices. He shows that the higher field harmonics peak at magnet boundaries and are small in the center of the magnets and says that matching this would require new or extended solenoid slice elements. Another alternative could be using the MAD-X matrix element with suitable parameters.
Rogelio encourages further studies based on solenoid slices as this would already contain impact on beta-functions and coupling. Laurent proposes the use of more general multipole elements that include ks components (currently not yet available in MAD-X).
Generalized multipoles for solenoid modeling, Barbara Dalena
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Barbara Dalena described fringe field studies, performed with Thomas Pugnat (PhD) and others, published in https://doi.org/10.1016/j.nima.2020.164350, of the HL-LHC final focus quadrupoles. The methods were used to study detuning and effects on the HL-LHC dynamic aperture, and also compared with tracking through the CLIC interaction region with a detector solenoid. The modeling uses a computation of generalized gradients from magnetic field harmonics, it can be extended to the Detector Solenoid fringe fields provided the overlap with the final focus quadrupoles and the coordinate transformations to the local solenoid reference system and back to the beam reference system is added.
Rogelio commented that these studies and the implementation in SixTrack are very useful, but also required a substantial amount of work and time (about 4 years) and that a similar effort might be needed here.
Katsunobu commented on differences between the CLIC and FCC-ee interaction region. FCC-ee is designed with shielded solenoids, anti-solenoids and small overlap with quadrupole fields, and lower beam energies.
Katsunobu also clarified that SAD contains these generalized multipoles, but in a simplified form without the radial dependency of Bz as this is considered negligible. Frank suggests to use this code as reference with the caveat that variables used in SAD and MAD are different.
MADX - PTC comparison, Tobias Persson
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Tobias compares MADX and PTC for a single tilted (dtheta=0.015) solenoid with a normalized strength of ks=0.013 as relevant for FCC-ee Z.
The study is done for what we now refer to as "block solenoid". Slicing is used to obtain approximately smooth curves and reproduces exactly the single block twiss. He finds excellent agreement in orbits and twiss parameters from MADX and PTC.
The PTC results are practically identical to MADX when the PTC option exact is set to false. For the tilted solenoid, a very small difference is observed for PTC with exact = true, which according to Tobias is related to the use of an exact drift element going beyond what is implemented in MADX. The impact of radiation has not yet been compared between the two codes.
MAD and SAD solenoids, Leon Van Riesen-Haupt
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Leon compares the twiss parameters obtained from MADX and SAD for the FCC-ee ZZ V213 sequence.
Without solenoid, both programs agree very well in their predictions of twiss parameters, detuning and emittances.
Implementing the tilted (block) solenoid in this lattice has been non-trivial. It is now done on the MADX side using
a tilt DTHETA equal to the half crossing angle. On the SAD side, the solenoid is defined by turning on the fields between markers defining the start and end of the solenoid. In SAD, this slightly increases the sequence length (L sol divided by cos of the half crossing angle). MADX and SAD still agree very well using a solenoid without tilt. The agreement with a tilted solenoid is not so good.
Leon also had a first look at emittances, using an energy of 1 GeV to minimize complications from sawtooth/tapering.
It seems MADX emittances remain unchanged by the tilted solenoid,while in SAD a small change in vertical emittance is seen (one would expect a larger change).
With tracking, he finds agreement in emittances from both codes for untilted solenoid.
Rogelio suggests to check and compare orbits in MADX and SAD. The tilted solenoid will slightly change trajectories, to be taken into account, but not to be considered as error.
Tobias and Laurent expect that EMIT should be able to take the solenoid tilt into account and agree this should be checked.
Frank Zimmermann asks if the opening angle of the synchrotron radiation is taken into account.
Katsunobu expects that the effect would still be small for FCC-ee. Currently this is not taken into account in the codes.
Frank recommends to read https://accelconf.web.cern.ch/ipac2018/papers/thpak068.pdf by Gorlov / Oak Ridge
Laurent points us to the paper by Gorlov https://journals.aps.org/prab/abstract/10.1103/PhysRevAccelBeams.23.034001
and says, the code implementing Eq. 28 and 29 of the paper is there as
https://github.com/MethodicalAcceleratorDesign/MAD/blob/e875a8f10c7685b4344a99e4787408068376fce3/src/madl_dynmap.mad#L1899
and proposes this for benchmarking with the FCC-ee solenoid.
Actions in the short term:
-Explore combinations of thin solenoids and other elements
-Tilted solenoid, check orbit and adapt MAD input (user level) to follow same conventions as SAD. Check vertical emittances from 'emit' calculations in both codes. Is MAD taking into account the tilt? Is calculation of SAD correct? Check with tracking too.
-Check impact of non-linear fringe field in SAD. If important a comparison to MAD-NG could be done to see if Gorlov's approximation matches SAD. If so eventually implement in MAD.
Actions in the mid term:
-Investigate / explore implementation of generalized multipoles in MAD-X for the solenoid, possibly inspired by SAD. This is mostly in view to insert multipoles from magnetic models or measurements into the lattice. In the current design phase this not yet needed.