Recent MIA Results

Yiton T. Yan

Stanford Linear Accelerator Center

Acknowledgement: Y. Cai, F-J. Decker, S. Ecklund, J. Irwin, J. Seeman, M. Sullivan, J. Turner, U. Wienands, etc.

PEP-II MAC meeting April 16, 2004

Outline

Part I. MIA review• Buffer data acquisition• Four independent orbits• phases, beta functions, Greens Functions, Eigen ellipses• Enhanced SVD-enhanced fitting – fast fitting process• Typical MIA results (plots) - some shows current LER optics

• Virtual and wanted accelerators – MIA flow chart

Part II. Recent Application to PEP-II • HER Beta Beat studies• Dynamic Beta from Beam-Beam effect• Optics study on LER steering machine

• Summary

Buffer data acquisition

• Resonance excitation to offset radiation damping by a shaker at the horizontal betatron (eigen) tune and then at the vertical tune, each for about 1000 turns to get a complete set of data.

• Buffer data are stored in two sets of matrices, each set has two matrices, one for the x data and the other for y data.

4 independent orbits determines the linear optics.

Phase Advances

This is before MIA fitting

yx

Preliminary beta function survey

The linear Greens functions

They, along with the phase advances are used for SVD-enhanced fitting to obtain a virtual accelerator

MIA does not trust the BPM accuracy – MIA figures out BPM gain and cross coupling errors.

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 can figure out BPM errors(recall Steve Smith’s morning talk

Summary of the measurable quantities (derivable from the 4 orbits)

• The phase advances among BPMs.• Green’s functions R12, R34, R32, R14 among BPMs. Use

of 6, …, 18, 30 greens; • Eigen Ellipses’ parameters for all double-view BPMs: tilt

angles and axis ratios.

• Form these measurable quantities into a sequence (a single vector) for easier Least-squares fitting.

• Linear coupling are completed treated without any discount.

• Eigen ellipses’ parameters may not be used in fitting but be reserved for checking fitting accuracy.

Summary of variables

• All quad families normal components.• All skew (global and local) quad’s skew components.• All sextupole feed-downs’ normal and skew components.• All BPM gains and cross couplings.

• Additionally, all quad skew components and all skew quad normal components.

• Also form all these variables into a sequence (a single vector with data-structure pointers).

Enhanced SVD-enhanced Least Square fitting

Need about two iterations of enhanced SVD-enhanced fittings.

Typical MIA results (plots)

In the next pages we show the following plots

• Phase advance comparison plots• Beta function plots• Linear coupling plots at IP• eigen ellipse tilt angles and axis ratios plots for fitting

accuracy checking• Linear coupling appraisal plots

This is a complete set of linear optics (10 degrees of freedom) parameters. You can NOT get any more than this.

A typical -function plots from MIA close to the current PEP-II LER

A typical linear coupling plots near IP current PEP-II LER

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

matched?

Yan/mia/ler/2004/OCT28/1

A complete appraisal of the LER linear coupling

LER/2004/OCt28/1

MIA flow chart

10 - 15 minutes: collecting MIA data,

3 minutes: Phase advances and Beta function, dispersion measured and bad BPMs identified

6 minutes: MIA fitted with 6 greens for more accurate beta functions

20 minutes: virtual accelerator obtained with 18 greens

MIA came to work at the right time when SLAC PEP-II B-factory desperately needed advanced optics improvement in order to meet the promised performance progress.

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).

Indeed LER became way too strong for the HER. Nonetheless, consequently, PEP-II achieved its record peak luminosity at 6.5 X 10^33 /cm*2/s in June 2003. It is still a single-bunch luminosity record.

MIA was applied to improve PEP-II

HER optics after adjusting to match the very strong LER

One can see a strong X beat that is over 100% with a small X

* at about 27 cm.

The X beat can be fixed by tune trombone + global skews with MIA, but the X

* will be restored to 50 cm.

We want the X* be small

while the large beta beat be fixed.

Part II: Recent application to PEP II

• A knob for adjusting HER beta beat while changing IP beta.

• Tried to fix the HER beta beat with beta bumps.

• Optics study on LER steering machine

HER virtual machine before dialing in MIA knob of only the trombones and the global skews on Nov. 4

Beta beat has increased by additional 100%

Dialing the MIA knob into the virtual machine showed that the HER could be brought back to low beta beat but restored to near the original design X* value of 50 cm.

HER virtual machine after dial-in of the MIA beta beat knob.

It shows very much the same as predicted by dialing the knob into the MIA virtual machine

Proving MIA is a very accurate optics measurement tool.

HER Beta Beat fixes based on virtual HER of 3 Feb. 2004

Beta Beats on 4 of the 6 arcs are completely fixed while the remaining 2 arcs adjacent to IP are set up with beta bumps to offset the extra chromaticity generated by the large doublet betas. Sextupole strengths may need to be adjusted slightly to optimize the chromaticity.

But we need to understand why the beam life time is not good.

We have Much improved HER BPMs

Excellent MIA data for excellent measurement and reliable MIA virtual machine

Beta Y function directly measured by MIA without fitting, showing that PEP-II HER BPMs have been much improved.

It takes a couple of minutes to get this plot after MIA data taken.

Beta X function directly measured by MIA without fitting can immediately show the quality of beta beating. This plots can be obtained within a couple of minutes once MIA data are obtained.

Virtual HER obtained from 3 Feb, 2004 MIA data

MIA fitting is very good and HER linear coupling is very good.

QDS0XSR1 -2.1010QFS1SR01 5.5864 QDS1SR01 -0.1576 QFS2SR01 -3.3181QDS2SR01 1.0638QFS3SR01 0.1786QF5L -0.0991QF5R -0.1454QFS3SR03 1.3990QDS2SR03 -0.1545QFS2SR03 -1.3835 QDS1SR03 -1.3727QFS1SR03 6.7953QDS0XSR4 -3.2147

QFP9R04 1.7714QDP8R04 -1.0815QFP7R04 1.1231QDP6R04 -0.9091QFPL -0.4119QDPR 1.2902QFP9R06 -3.0042QDP8R06 -0.1718QFP7R06 -1.3743QDP6R06 0.2992SQG2 -0.5097SQG1 0.8352SQG4 0.1265SQG3 -0.0556

MIA knob for fixing HER beta beat while keeping IR region the same (low Beta X) and chromaticity Ok with beta bumps.

Trombone

Wanted HER approachable from the Real HER with a MIA konb

MIA knob generated wanted HER keeps linear coupling the same if not better.

Comparing the IP Betas

Bottom plots: after dialing in the knob.

Top plots: the virtual HER on 3 Feb. 2004

Top plots: the virtual HER on 3 Feb. 2004.

Bottom plots: after dialing in the knob

Comparing IP region

Bottom plots: after dialing in the knob

Top plots: the virtual HER on 3 Feb. 2004

Comparing Beta functions

Virtual HER after 75% dialed-in of the knob

Beta beats in 4 arcs are almost fixed while beta bump is kept

Linear coupling is improved

Unfortunately, there is no 100% dial-in MIA data.

Martin Donald got his data for 100% dial-in that show very much as expected results as predicted by the virtual dial-in.

Summary for MIA HER beta bump knob

• This knob seems to go in the right direction. Do not give it up easily.

• Indeed, this is the kind of solution we have been looking for: (a) keeps the same small Beta X at IP; (b) beta beat fixes; (c) Chromaticity is all right.

• Need to understand why beam life time is not good.

Dynamic Beta from Beam-Beam effect

John Seeman suggests putting a lens at IP to represent beam-beam effect in MIA virtual HER. Here are the results.

Beta beats ----Adding beam-beam effect lens on Virtual HER of 3FEB2004

NoBeambeam

FullBeambeam

2/7Beambeam

Nobeambeam

Fullbeambeam

Dynamics Beta ----- Adding beam-beam effect lens on the Virtual HER of 3FEB2004

2/7beam beam

Optics study for the LER Steering, MD data on 2-11-2004

Virtual machine of the steering LER, MD on 2-12-2004

>200% beta beat

Bad Coupling shown on the right

Large IP waist shift

Work in progress for LER steering machine optics improvement

Knob involves trombone quads, global skews, and 4 pairs of local skews (SK2,3,4,5 [R,L])

Beta beat much improved

IP waist shift left alone tentatively

Coupling improved. Need further improvement

Summary

• MIA has been used in weekly basis for studying the PEP-II accelerators optics – IP betas, linear couplings, beta functions (beta beats) etc.

• MIA has helped PEP-II improve the machines’ optics, bringing LER working tune to near half integer while fixing its beta beat and reducing its coupling, to reach a record single peak luminosity.

• MIA has been tested very positively for HER. Hopefully soon or later HER super large beta beat will be fixed. However, PEP-II is fine with this high beta beat in HER – not in a hurry.