LHC optics measurement, modeling, and correction with MIA

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LHC optics measurement, modeling, and correction
with MIA

• Yiton T. Yan
• SLAC

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What is MIA?

• We have a series of MATLAB programs called MIA
  that has been proven robust for PEP-II optics
  correction.
• MIA, through a model-independent analysis (MIA)
  of turn-by-turn BPM orbit data and an auto
  SVD-enhanced fitting process, brings the real
  hardware storage ring to a computer -- the
  virtual machine that matches the real machine in
  optics.
• MIA goes on figuring out an approachable better
  virtual machine (lower beta beat, lower coupling,
  lower dispersion beat, etc) for the real machine
  to listen to and follow.
• MIA has helped PEP-II overcome many optics
  improvement milestones and has had major
  contributions for PEP-II luminosity enhancement.
• For example, If there were no MIA, we could be
  wondering if we had been able to bring the
  Low-Energy Ring (LER) to operate at half integer,
  which helped nearly double PEP-II luminosity
  subsequently.

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Outline

• Review MIA
• contributions to PEP-II improvement.
• Propose MIA for LHC optics commissioning, and
  possible easier implementation of future
  upgrading.

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PEP-II MIA Buffer data acquisition

• Resonance excitation at the horizontal, vertical
  betatron (eigen) tune and then at the synchrotron
  tune, each for about 1000 turns.
• LHC needs driven oscillation and more turns.

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Validation of MIA data symplecticity and noise
check

• Check BPM data symplecticity without the need to
  know the BPM aberrations a strong criterion.
• Check BPM data correlation (SVD) to rank the BPM
  noise level a weak criterion.
• So we have good bases for selecting reliable BPM
  data. Through years, we have helped PEP-II
  correct and improve BPM performance.

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Four independent linear orbits, dispersions, and
phase advances

• Obtaining three pairs of conjugate (sine- and
  cosine-like) orbits from zooming FFT (focused
  individual component analysis).
• Phase advances can then be calculated by talking
  ratio of the conjugate orbits.
• Betatron motion amplitude and dispersive motion
  amplitude can be calculated,
• Note that If there is no focused excitation,
  such as pulse-by-pulse jittered Linac BPM orbit
  data, then one uses principal component analysis
  instead of individual component analysis.

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The linear Greens functions
Where, in the measurement frame, R is a function
of BPM gain and BPM cross-plane coupling.
Q12 and Q34 are the two invariants representing
the excitation strength..
MIA does not trust the BPM accuracy MIA figures
out BPM gain and cross coupling errors.
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Semi-Infinite Greens functions for enough
constraints that add on accuracy and fitting
convergence
b
a
b
Redondancy?
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The Coupling Ellipses
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Check MIA fitting accuracyAre eigen ellipse
tilt angles and axis ratios automatically matched?
Yan/mia/ler/2004/OCT28/1
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Auto SVD-enhanced Least-Square fitting for Green
functions and phases

• Variables normal quad family strengths,
  individual skew quad strengths, normal and skew
  strengths for sextupole feed-downs, BPM linear
  gains and linear cross couplings and one
  invariant.
• Response quantities Greens functions and phase
  advances, dispersion coupling ellipses, etc.
  among BPMs.
• Unlimited Greens functions
• self-consistent phase advances
• Auto optimal selection of SVD modes.
• Unstable modes are automatically avoided to
  guarantee convergence.

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Virtual machine

• Once we are satisfied with the fitting accuracy,
  we call the updated lattice model the virtual
  machine (Virtual LER, Virtual HER).

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Optics correction with wanted model

• we can select a limited number of key magnets for
  fitting the virtual machine toward a wanted
  model. We then generate a knob for dialing into
  the machine. The cold machine responded to our
  expectation very well.

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MIA constraints and weights for wanted machine
an example
Initial constraint
weight snap-shot special Residuals
start end start end residuals
quantities 0.00041393 1 Tunex
1 1 1000 5000 0.0019588
38.5064 0.000169228 2 Tuney
2 2 1000 5000 0.00485956
36.581 0.000245875 3 nux
3 28 100 100 0.000305344
0.499811 0.00375321 4 nuy
29 54 100 100 0.00387669
0.496279 26.9007 5 Betax
55 425 0.5 1 10.7411
37.0005 4.88197 6 Betay
426 796 0.3 1 4.55298
24.0697 2.06367 7 axay
797 1538 0.3 1 0.836578
5.15022 0.306315 8 tiltxy
1539 2280 10 25 0.329449
0.330447 0.116435 9 axisRatio
2281 3022 10 25 0.151386
0.169479 0.0872007 10 sinPsxt
3023 3393 10 25 0.0806435
0.110078 0.0550547 11 bxIP
3394 3394 1000 1000 0.00382164
0.306178 0.0016697 12 byIP
3395 3395 5000 200 0.0021166
0.0096224 0.604155 13 axIP
3396 3396 300 2000 0.02563
0.0256379 0.00224 14 ayIP
3397 3397 300 10000 0.000989
0.000989447 0.0468993 15 TiltxIP
3398 3398 100 5000 0.002646
0.00264634 1.52045 16 TiltyIP
3399 3399 100 1000 0.00710
0.00710003 0.06326 17 baxIP
3400 3400 100 1000 0.0133853
0.0133853 0.564624 18 bayIP
3401 3401 100 200 0.425895
0.425895 0.17073 19 sinP0IP
3402 3402 100 100 0.0533182
0.0533182 0.192546 20 eta13SF
3403 3506 20 30 0.163688
0.425425 0.165198 21 eta13SD
3507 4144 20 30 0.146349
0.381311 0.0716958 22 eta1234IP 4145
4148 100 30 0.0571557 0.0571557
0.0675275 23 eta1234SKEW 4149 4212 20
500 0.0667764 0.282782 0.0636338 24
eta1234INJ 4213 4220 20 2000
0.032879 0.43337
Tune
- I
Beta Beat
coupling
Beta
IP waist
IP coupling
dispersion
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We summarize MIA with the flow chart
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• some examples of MIA for PEP-II optics
  improvement

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Example Brought PEP-II LER to half integer
working tune

• MIA successfully brought LER to a half integer
  working tune and improve LER beta beats and
  linear coupling. Instantly, LER beam became the
  stronger one of the two (LER and HER beams).
  Without MIA, this was almost impossible because
  of strong LER coupling.
• Indeed LER became way too strong for the HER.
  Nonetheless, consequently, PEP-II luminosity
  increased about 40 .

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Example fixed beta beat Virtual HER Feb 1,
2006comparing beta function bewteen the machine
and the ideal latticea dramatic example for beta
beat fix
mac2006
we had a very strong HER X beta beat during the
beginning period of 2006 run.
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Virtual HER after one-shot MIA correction Feb
16, 2006

• Beta beating fixing mainly from QF5 (we use only
  the left one).

mac2006
We have an updated ideal lattice at BetaX 33 cm.

• We had also added trombones, local and global
  skews to simultaneously improve couplings,
  dispersion, and IP optics.

• We had a max-out of SQ3L that caused an
  imperfection of the offline solution.

• Since then we had enjoyed an HER record-low
  residual from the ideal lattice till we ramped
  the currents at later stage of the run.

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Example Successful LER major orbit steering
mac2006

• Another key improvement for PEP-II optics in 2006
  is the successful LER major orbit steering.
• It is usually difficult to correct the optics
  after a major steering for the coupled LER.
• We relyed on MIA modeling after the steering to
  generate wanted approachable optics model and
  dial in the solution for restoring the linear
  optics.

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Example MIA for HER emittance improvement in 2007
MIA solution from Virtual HER06FEB07
Ideal HER lattice
Virtual HER08FEB07
Virtual HER06FEB07
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Proposal

• my proposal of MIA for LHC optics
  commissioning, and easier implementation of
  future upgrading.
• (recalling that, with MIA precision modeling,
  Franz-Josef, at one-shot, install many permanent
  skew quads at LER IR. Also Walter had tested
  successfully one-shot conversion of HER 60-degree
  machine to HER 90-degree machine)

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Fruitful visit to CERN and very much encouraged
for applying MIA to LHC

• Earlier this month I had a very fruitful visit to
  CERN. I had visited Oliver Bruning, Frank
  Zimmermann, and others. Especially I had very
  pleasant meetings with Rogelio Tomas, Frank
  Schmidt Iiya Agapov, Rama Calaga, Akio Morita
  (KEK), Masamistu Aiba (KEK support), Javier
  Serrano, and M. Bai (BNL), . I visited AC dipoles
  and other facilities. I also gave a seminar on
  MIA. They had high expectation of my long-term
  visit. And actually has listed me as a
  collaborator. (shown in the presentation by S.
  Kopp for AC dipole report yesterday as I copied a
  small paragraph from a slide made by M. Bai
  below)
• Meeting Summary Rogelio
• Yiton Yan offered his collaboration in the
  implementation of the MIA analysis for the LHC,
  with the advantage of obtaining a virtual machine
  that would reprocuce the observations. A perfect
  communication between the optics measurement
  on-line application and the on-line model
  application is being established.
• Indeed, I have been very much encouraged for
  applying MIA to LHC.

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MIA for LHC optics commissioning and improvement

• Non-invasive (or tiny invasive) process rely on
  orbit fluctuations may be useful for
  identifying BPM problems.
• (unknown before a dedicated study with real
  data)
• Invasive process but no machine stopping need
  well done AC dipoles for adiabatic oscillation
  driving process to preserve emittance. Need to
  know LHC optics well beforehand(?).
• Invasive process with dedicated MD time for MIA
  data acquisition just as we have done for PEP-II.
  20 to 30 minutes needed(?) for a complete set of
  data acquisition. Beside the two AC dipoles
  (still under development at CERN) for applying
  MIA to driven oscillation, We would still wish to
  have synchrotron oscillation which Fox and
  companies had helped me done very well for
  PEP-II.
• (single bunch representing single-particle
  dynamics)

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CERN contacts

• I wish to list my general contacts Oliver
  Bruning and Frank Zimmerman at CERN.
• My close-work contacts Rogelio Tomas who is
  coordinating LHC optics correction at CERN, and
  Mei Bai for my visiting BNL.
• Online-work contact Frank Schmidt Iiya Agapov
  for those MIA generated products that are judged
  suitable for online process. Indeed, I had given
  the two 13 slides talk during my visiting CERN.
  They expressed highly interest and urged me to
  contact them as often as possible.

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FTE, Time Frame and Milestones

• I would propose myself at ½ FTE both for FY 2008
  and FY 2009.
• In 2008 before LHC has beam, preparation
  (modification) of MIA to suit for the proton
  (Heavy ion) storage rings is needed.
• RHIC at BNL is a very good candidate for testing
  updated MIA, especially they have already made an
  invitation (from M. Bai). I would expect at least
  a visit or two in and after March 2008. the
  success of applying MIA to RHIC will definitely
  make a strong case for LHC.
• I would expect that I could be at CERN at very
  beginning when LHC has beam for testing precision
  MIA measurement of the LHC optics and help
  identifying BPM problems if there is. It could be
  a long-term visit of 3 months in 2008.
• I would also expect a long-term visit to CERN (a
  total of half a year) in 2009. In collaboration
  with the CERN team as mentioned in a previous
  slide, we would expect to get LHC optics model
  and start LHC optics improvement (beta beat and
  coupling correction, etc.) with MIA.
• I would wish some time down stream, we could also
  have remote control process to LHC at SLAC for
  in-time test of MIA updated technique and certain
  minor studies of LHC optics. However, I
  understand, ultimately personal appearance at
  CERN is still needed.

Thanks!