Optics modeling and correction

Yiton T. YanStanford Linear Accelerator Center

Thanks to: Y. Cai, W. Colocho, F-J. Decker, M. Donald, Y. Nosochkov, J. Seeman, M. Sullivan, M. Wang, U. Wienands, W.

Wittmer, M. Woodley, G. Yocky, etc.

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Optics modeling and correction

Other than time consuming online tuning, the PEP-II optics correction has a large portion been centered on MIA modeling. We review activities related to MIA model.

• optics measurement

• optics Modeling

• optics correction

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Remind: What is MIA?• We have a series of MATLAB programs called MIA that has been proven robust for

PEP-II optics modeling and 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 follow.

• MIA passes the optics model to the lattice and tracking programs MAD / LEGO for optics and beam-beam studies.

• MIA passes the optics model to online.

• MIA has helped PEP-II overcome optics improvement milestones and has had major contributions in helping PEP-II luminosity enhancement.

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MIA measurement

• BPM turn-by-turn data acquisition – 3 resonance excitations.

• Validation of MIA data – strong criterion: symplecticity – weak criterion: noise check

• Four independent linear orbits and dispersion

• phases, beta functions, Greens Functions, Eigen ellipses

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A typical comparison of phase advance between model (red) and measurement (blue) for LER

Note that the phase measurement is accurate regardless of BPM gains, BPM cross couplings and linear couplings.

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The linear Greens functionsWhere, 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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The Coupling Ellipses

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

matched?

Yan/mia/ler/2004/OCT28/1

Red: Model; Blue: data; Green: IP

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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: 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.

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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).

• We can calculate the emittance

• We “may” also calculate the luminosity roughly.

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HER emittance on July 18 (red), 2007

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LER emittance in July, 2007

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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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Optics corrections

• We wish to achieve 2e34 cm-2s-1

• We have very limited resource, where should we look for this 2e34? Currents or optics?

• HER may not match LER.

• We achieved luminosity record at 1.2 X 1034 cm-2s-1 during 2006 P5 meeting. We did not break this record during 2007. But we indeed have a breaking specific luminosity at high current.

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Selected examples of optics corrections in 2007

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HER emittance improvement

Virtual HER06FEB07

Virtual HER08FEB07

MIA solution from Virtual HER06FEB07Ideal HER

lattice

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Test of HER 60 degree to HER 90 degree – see W. Wittmer’s talk

• Toward the end of 2007 run, we tried to test converting HER 60 degree lattice to HER 90 degree lattice aiming at shorter bunch length.

• We got HER MIA data. came up with MIA model and pass to MAD. M.H. Wang and W. Wittmer then test the conversion in MIA2MAD to make sure a successful dialing-in.

• HER 90 degree was successfully achieved with one-shot dialing in.

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Installation of permanent skews in LER by Franz-Josef Decker. et. al.• We knew we could improve the LER ideal lattice by

adding local skew quads in IR to reduce the coupling, thereby, reduce the vertical emittance dramatically.

• The ideal LER vertical emittance is 0.5 nm.rad while the real LER best vertical emittance from MIA measurement was 1.4 nm.rad on August 15, 2006 when we had the peak luminosity.

• But we have no $ for regular skew quads. Franz-Josef Decker came up with the idea of very cheap permanent Skews (PSK).

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Dialing PSK knob in MIA: emittance Y is indeed reduced significant for ideal lattice

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Dialing PSK knob in MIA for Virtual LER on Apr 17, 2007

On Apr. 17 we took LER MIA data in the morning, came up with MIA virtual LER, dialing the knob into MIA …and hurry up for presentation at Noon.

MIA model showed that we could fix the machine, at the 1st step, with trombone and global skews although vertical dispersion was not good yet. However it could be easily fixed with asymmetric sextupole bumps at a later time

Dialing PSK knob in MIA: emittance x

Dialing PSK knob in MIA: emittance Y

Dialing PSK knob in MIA: emittance Y

Dialing PSK knob in MIA: emittance Y

So we were “very hopeful” to use trombone only to get stable machine after coming out from tunnel with PSK installed.

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Dialing PSK knob in MIA for Virtual LER - continued

• Got MIA LER virtual machine and then dialing PSK installation to MIA virtual machine, finding a correction Knob. -- Installing PSK (permanent skew quarupole) successful. LER vertical emittance dropped from previous best 1.4 nm.rad to 0.8 nm.rad.

• We could further reduce the LER vertical emittance. But we faced a weaker HER.

• So running at Lower LER current, we managed to get record peak specific luminosity but not the luminosity in 2007.

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Reducing LER coupling – dimensionless C12 : Lacey Kitch’s summer science project

With Aug. 7 MIA LER data, Lacey was helped to get a MIA model and find a solution that reduced LER c12 with vertical symmetric sextupole bumps.

Red: virtual LER Aug07

Blue: solution

M = A C R C-1 A-1

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Reducing LER coupling – C12 :

Decker, Yocky, et. al. managed dialing in 50% of the solution during collision.

Regional BPM problem caused inaccuracy.

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Record peak specific luminosity obtained in 2007 after reducing LER coupling for lower Y emittance

Although we did not manage to get a breaking record peak luminosity in 2007, we did manage to get a peak specific luminosity (as shown on red) with a lower LER current.

28-aug 9:00am, peplog

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Summary• We are able to get accurate models for PEP-II “cold machine” with MIA.

• MIA can provide wanted model for optics correction -- beta beat correction, bringing operation to half integer, linear coupling reduction, IP optics improvement, and catastrophic converting into a new configuration.

• MIA virtual machine can be passed to lattice codes MAD and LEGO for optics and beam-beam studies.

• We have improved LER coupling so as to reduce LER vertical emittance with the insertion of PSKs. Thanks to Franz-Josef Decker.

• In 2007, We have achieved record breaking specific luminosity at high current but not the luminosity.

• We may need to work harder on HER to match LER. Need higher HER current and/or need lower HER emittance and/or need HER lower beta_Y and lower coupling at IP, and/or need reduced HER bunch length.

• We have challenges:– Warm machine vs. cold machine. – Beam-beam effect on the model.– Orthogonal and dynamical IP knob dialing technique.– And more … Thanks!