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Strategies for setting the LHC corrector circuits in simulations

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### Strategies for setting the LHC corrector circuits in simulations

M. Giovannozzi

Acknowledgements: all those working on this topic since many years…

M. Giovannozzi - FiDeL Meeting

Families of linear corrector circuits

- Closed orbit correctors: in each SSS and standalone quadrupole (also warm). Used also to generate the crossing scheme. Not covered in this presentation.
- Normal tuning quadrupoles: in the SSS (between Q14-21 L/R) for tune control.
- Skew quadrupoles: in the SSS for linear coupling compensation. Four correctors/arc (Q23/27 L/R) powered:
- Series (L/R): sectors 1-2, 3-4, 5-6, 7-8 (Ring 1)
- Independent (L/R): sectors 2-3, 4-5, 6-7, 8-1 (Ring 1)

M. Giovannozzi – Extended LTC

Families of non-linear corrector circuits

- Spool pieces: at dipole ends for b3, b4 and b5; powered differently per arc and per beam; total number of circuits 48
- Lattice correctors: in the SSS for a3, b3, and b4; total number of circuits 112
- Correction coils for triplet field errors: a3, b3, a4, b4, and b6; total number 40

In total, 200 independent correction circuits.

M. Giovannozzi – Extended LTC

Circuits composition

M. Giovannozzi – Extended LTC

Target and tolerances for observables

These tolerances are reported in LHCPR 501 (by S. Fartoukh and O. Brüning).

In numerical simulations the magnetic error distributions are known (either from statistical distributions or from the measured values – WISE) and are used to set the correctors prior to the actual simulations.

M. Giovannozzi – Extended LTC

Coupling correction

- Sources of coupling
- a2 in dipoles
- Roll angle in quadrupoles
- Feed down effects:
- From b3 due to vertical closed orbit/misalignment
- From a3 due to horizontal closed orbit/misalignment
- Correction strategy:
- Use the single MQS circuit in sectors 1-2, 3-4, 5-6, 7-8 (Ring 1) to correct the systematic a2.
- Use the two MQS circuits in sectors 2-3, 4-5, 6-7, 8-1 (Ring 1) to correct the random part.

M. Giovannozzi - FiDeL Meeting

Lattice sextupoles

- All but four/sector SSS are equipped with chromaticity sextupoles (SF1/2, SD1/2 families):
- Natural chromaticity is Q’x=-93, Q’y=-87
- Correction of natural chromaticity is essential for tune measurement (decoherence) and to avoid instabilities.
- Only two families (SF1=SF2, SD1=SD2) are needed to correct H/V chromaticity
- The use of the four families of sextupoles is imposed whenever Q’’ is to be corrected.
- In first approximation (e.g., neglecting feed down effects) these corrections depend on the machine optics, only!

M. Giovannozzi - FiDeL Meeting

Lattice skew sextupoles

- In each sector 2 SF1 and 2 SF2 normal sextupoles are rolled to convert them into skew sextupoles.
- MSS are located at:
- Q29L/33L/33R/29R in sectors 1-2, 3-4, 5-6, 7-8 (Ring 1)
- Q30L/34L/32R/28R in sectors 2-3, 4-5, 6-7, 8-1 (Ring 1)
- The knowledge of the magnetic error distribution (a3) allows computing the required strength of MSS (see also LHC PR 278).
- Remark: the contribution of the a3 of the dipoles is such that MSS where not considered fundamental for the initial commissioning.

M. Giovannozzi - FiDeL Meeting

Spool pieces: b3, b4, b5

- All MBs are equipped with sextupolar correctors (MCS), while only half of them are equipped with octupolar and decapolar correctors (MCDO).
- Strategy for setting them:
- Compensate the integrated field error in the MBs. They introduce a local compensation of the errors.
- Remark: The MCO can correct only up to 0.11 units of b4 at 7 TeV (nominal current is 100 A). At few TeV they run out of strength and the b4 in the dipoles is left uncompensated (but it has a small impact on dynamic aperture).

Remark: The b2 component in the dipoles has not global effect (change of sign between the apertures). However, locally it changes the phase advance along the arc...

M. Giovannozzi - FiDeL Meeting

Landau octupoles

- Lattice octupoles: all SSS not equipped with MQT or MQS are equipped with a Landau octupole (MO). This gives 168 elements/ring
- Not used at injection (they should be set to zero field). This requires a special de-Gaussing cycle.
- Used to stabilise the beams at top energy (before putting beam in collision). They should be set at maximum strength at top energy.
- NB: Under the beam conditions of the initial commissioning they should not be used. However, the beam brightness is the relevant parameter (e.g. TOTEM, see E. Métral and A. Vérdier LHC PN 345).

M. Giovannozzi - FiDeL Meeting

Corrector packages in the triplets - I

- Dipoles: used to separate the beams and correct the closed orbit.
- MQSX: used to compensate the a2 and roll angle of the triplets.

M. Giovannozzi - FiDeL Meeting

Corrector packages in the triplets - II

- Nonlinear corrector package in the triplet quadrupoles:
- Correctors not needed if beta* > 1 m (based on dynamic aperture studies).
- MCSX in IP2 might be useful in any case:
- Vertical crossing angle in IP2
- Change of polarity in spectrometer will change a2 generated from feed-down of b3.
- a2 correction with MQSX not possible for both beams and with MQS not effective
- MCSX could be used to correct the b3

M. Giovannozzi - FiDeL Meeting

Corrector packages in the triplets - III

- Correction strategy:
- Compute resonance driving terms across the insertion. This includes contributions from the cold D1s (IR2/8) and D2.
- Use the correctors to minimise some of the terms, e.g. (see LHC PR Note 349),
- MQSX -> correct coupling resonance Qx+Qy
- MCSX -> correct the resonance Qx+2Qy (nearest to LHC working point)
- MCSOX (a3) -> correct the resonance 3Qy (nearest to the LHC working point)
- ...

M. Giovannozzi - FiDeL Meeting

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