# Presentation: 177379

##  LHC optics measurement, modeling, and correction with MIA 

- Yiton T. Yan
- SLAC

## 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.

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Outline

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

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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.

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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.

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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.}

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Slide 7

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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.**

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Semi-Infinite Greens’ functions for enough constraints that add on accuracy and fitting convergence

- a

- b

- b

**Redondancy?**

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## The Coupling Ellipses

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Check MIA fitting accuracy:Are eigen ellipse tilt angles and axis ratios automatically matched?

- Yan/mia/ler/2004/OCT28/1

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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:  Green’s functions and phase advances, dispersion  [coupling ellipses, etc.] among BPMs.
- Unlimited Green’s functions
- self-consistent phase advances
- Auto optimal selection of SVD modes.
-     Unstable modes are automatically avoided to guarantee convergence.

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Virtual machine

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

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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.

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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  bx**IP                 3394  3394  1000   1000   0.00382164     0.306178
-  0.0016697   12  by*IP                  3395  3395  5000    200    0.0021166     0.0096224
-    0.604155   13  ax*IP                  3396  3396   300   2000    0.02563         0.0256379
-     0.00224    14  ay*IP                  3397  3397   300  10000   0.000989       0.000989447
-   0.0468993  15  Tiltx*IP               3398  3398   100   5000    0.002646        0.00264634
-     1.52045    16  Tilty*IP               3399  3399   100   1000    0.00710         0.00710003
-     0.06326    17  bax*IP                3400  3400   100   1000    0.0133853     0.0133853
-    0.564624   18  bay*IP                3401  3401   100    200     0.425895       0.425895
-     0.17073    19  sinP0*IP             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

**- I**

**Beta***

**IP coupling**

**dispersion**

**Beta Beat**

**Tune**

**coupling**

**IP waist**

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## We summarize MIA with the flow chart

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

-  some examples of MIA for PEP-II optics improvement

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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% .*

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Example: fixed beta beat Virtual HER – Feb 1, 2006comparing beta function bewteen the machine and the ideal latticea dramatic example for beta beat fix

**we had a very strong HER X beta beat during the beginning period of 2006 run. **

- mac2006

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Virtual HER after one-shot MIA correction– Feb 16, 2006

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

- 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.

**We have an updated ideal lattice at BetaX* =33 cm.**

- mac2006

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Example: Successful LER major orbit steering 

- 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.

- mac2006

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## Example: MIA for HER emittance improvement in 2007

**Virtual HER06FEB07**

**Virtual HER08FEB07**

**MIA solution from Virtual HER06FEB07**

**Ideal HER lattice**

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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)

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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.

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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)

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## 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.

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007

## FTE, Time Frame and Milestones

- I would propose myself at 1⁄2  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!

- ___________________________LARP Colaboration meeting 9                                                    Y. Yan

- 10-18-2007