-Beating, dispersion and coupling correction in the LHC R. Toms, R. - - PowerPoint PPT Presentation

• Beating, dispersion and coupling correction in

the LHC

• R. Tomás, R. Calaga,
• O. Bruning, S. Fartoukh, M. Giovannozzi,
• Y. Papaphilippou & F. Zimmermann

LHCCWG-14

• ✁
• f June, 2006

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.1/25

Magnetic measurements and allocation

• Realistic assessment of the beta-beating correction

needs of realistic b2 errors in the machine

• Magnetic measurements available in official

databases

• Information on both magnetic measurements plus

slot allocation (MEB activity) are required

• A code was developed in AT/MAS-MA by P. Hagen,

J.-P. Koutchouk & E. Todesco. This code deals with all type of magnetic errors (multipoles)

• Output: MAD-X file with magnetic errors. In case a

magnet is already assigned to a certain slot its magnetic errors are assigned to this slot. Otherwise, errors are drawn from measured distributions.

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.2/25

• beating observable
• The measurement of
• functions needs good

BPM calibration or good knowledge of focusing properties Not suitable for commissioning

• Phase advance between nearby BPMs is a robust
• bservable independent of BPM calibration,
• ffset and tilt and focusing errors, thus

phase-beating:

• ✆

is measured with standard FFT or SVD techniques of kicked data

• Synergy with J. Wenninger’s LOCO?

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.3/25

• beating Vs
• beating

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 21/2∆ φpeak [rad] ∆ β/βpeak horziontal vertical 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 21/2∆ φrms [rad] ∆ β/βrms horziontal vertical

Precise relation between

• ✆

and

• ✆

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.4/25

Dispersion observable

• Dispersion is normally measured using radial

steering and BPM readings.

• Best BPM calibration error:

4% (LHC-BPM-ES-0004)

• BPM resolution (pilot bunch): 200
• m
• Specification on Dispersion [Rep. 501]:

• In [EPAC 02, F. Zimmermann et al.] the pilot bunch

BPM resolution was not enough to measure dispersion in the range

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.5/25

• beating & dispersion correction
• We compute the non-square matrix R from ideal

MADX model as

• ✠
• ✠

• ✂

are all quad circuits in MADX (210 per ring).

• we invert R using the SVD so the correction is
• ✂

• ✠

• ✠

are weights used to choose beta-beating or dispersion correction.

• However correction is not guaranteed
• Simulations are needed to prove correction and to

assess performance.

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.6/25

Simulation ingredients I

• All

errors from measurements:

5 10 15 20 25

• 40
• 20

20 40 60 80 Counts b2 [units] MQM MQY MQX MQT

• ✁

example not really Gaussian not centered

• Extra Gaussian noise of 5 units added to quad
• ✁
• rms misalignments of chromaticity sextupoles,

mm

• rms misalignments of MCS,

mm

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.7/25

Simulation ingredients II

• Gaussian noise,

, added to the MADX phase to account for error measurements.

depends on BPM noise (

• ✟

• m), decoherence time

(N=400 turns) and kick amplitude (a=4 mm).

• From tracking simulations the error on the phase:

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Frequency [normalized] Horizontal (∆φmodel-∆φmeas)rms [deg] RMS: X RMS: Y Peak: X Peak: Y

To be on the pessimistic side we take

.

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.8/25

• beating correction (
• ✁

)

0.1 0.2 0.3 0.4 0.5 0.6 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 ∆ β/βy,peak ∆ β/βx,peak β-beat correction, LHC injection Uncorrected Corrected

• beating correction works!

Best peak corrections in the 5% level

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.9/25

What happens to dispersion? (

• ✁

)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 ∆Dx,peak [m] ∆Dx,rms [m] Dispersion-beating before and after correction Uncorrected Corrected

Dispersion remains unchanged (better than not con- sidering dispersion at all)

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.10/25

Not considering dispersion (old

table)

0.2 0.4 0.6 0.8 1 1.2 1.4 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ∆Dx,peak [m] ∆Dx,rms [m] Dispersion-beating before and after correction Uncorrected Corrected

Dispersion gets spoiled

• beating correction must consider dispersion

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.11/25

Comparing dispersion to specs. (

• ✁

)

1 1.5 2 2.5 3 3.5 4 4.5 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 (∆Dx/β1/2

x )peak [10-2m1/2]

(∆Dx/β1/2

x )rms [10-2m1/2]

Dispersion-beating before and after correction rms spec. 3 rms spec. Uncorrected Corrected

Peak specification is met for most of the seeds but not the case for the rms specification.

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.12/25

Strengths of quadrupoles (

• ✁

) I

1 10 100 1000

• 20
• 15
• 10
• 5

5 10 15 20 Counts Power supply percentage deviation [%] Cumulative KQ[4-10] KQX KQF KQD KQT

Variation in the percent level with respect to nomi- nal setting at injection

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.13/25

Strengths of quadrupoles (

• ✁

) II

1 10 100 1000

• 120
• 110
• 100
• 90
• 80
• 70

Counts Strength percentage deviation with respect to collision[%] Lower limit (not for KQT) KQ[4-10] KQX KQF KQD KQT

Strengths are within good limits

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.14/25

Can we correct dispersion only? (

• ✁

)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.05 0.1 0.15 0.2 0.25 0.3 ∆Dx,peak [m] ∆Dx,rms [m] Dispersion-beating before and after correction Uncorrected Corrected

No BPM calibration error has been assumed Some seeds’ dispersion-beating not correctable! Probably due to misuse of Q[7-7], to be clarified

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.15/25

Coupling

• A robust global coupling correction is presented

at: R. Jones et al, CERN-AB-2005-083 BDI0

• Local coupling is also measurable from the

secondary spectral lines of BPM data around the ring:

• ✄

• Independent of BPM calibration errors and

succesfully used at SPS and RHIC.

• What about LHC? The BPM data comes for free

with the

• beat correction

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.16/25

Local coupling measurement simulation

Random quad tilts and rms orbit are assumed plus a large tilt error (15mrad) at

• 6km. BPM

resolution=200

• m, BPM tilts=2mrad, 400 turns.

0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 5 10 15 20 25 |f1001| Longitudinal location [km] MADX Simulation

Large tilt error identified Thanks to A. Franchi Measurable under realistic conditions

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.17/25

Local coupling correction

Using all the skew quadrupole correctors:

0.02 0.04 0.06 0.08 0.1 0.12 5 10 15 20 25 30 |f1001| Longitudinal location [km] Uncorrected Corrected

• ✁

• ✁

Satisfactory local correction Not perfect due to the particular distribution of errors/correctors. Best local correction is realignment

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.18/25

Questions

• Required facilities: BPM system in turn-by-turn

mode (good synchronization is crucial)

• How long does it take?

5 iterations are enough for

• beat correction. An

iteration consists of: Data acquisition, analysis, change quad strenghts and probably injection and chromaticity re-optimization.

• Who will do it?

Studies: I am very interested Software applications: Also interested but resources needed (LARP, KEK?) Commissioning: Again, I am very interested in taking part

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.19/25

Conclusions & outlook

• beat correction can be achieved without

spoiling dispersion-beat

• Dispersion-beat correction does not seem robust

yet

• Important coupling sources identifiable from the

same BPM data used for

• beat

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.20/25

Gaussian errors:

• beat

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 ∆ β/βy,peak ∆ β/βx,peak Gaussian errors: 30 units in indep. quads and 1.1 in dipoles Uncorrected Corrected

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.21/25

Gaussian errors: Dispersion-beat

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ∆Dx,peak [m] ∆Dx,rms [m] Gaussian errors: 30 units in indep. quads and 1.1 in dipoles Uncorrected Corrected

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.22/25

Illustration of

• beat at the BPMs

100 200 300 400 500 600 700 5 10 15 20 25 30 βy [m] Longitudinal location [km] Illustrative β-beat at BPMs Ideal With corrected errors

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.23/25

Illustration of phase-beat at the BPMs

20 40 60 80 100 120 140 5 10 15 20 25 30 ∆ φy [degrees] Longitudinal location [km] Illustrative phase-beat from consecutive BPMs Ideal With corrected errors

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.24/25

Measurement of

• 0.1

0.1 5 10 15 20 25 Re(f1001) Longitudinal location [km]

• 0.1

0.1 0.2 Im(f1001) Measured MADX

Thanks to A. Franchi

Rogelio Tom´ as Garc´ ıa

• Beating,

dispersion and coupling correction in the LHC – p.25/25