Optics modeling and correction Yiton T. Yan Stanford 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.

___________________________ PEP-II MAC2007 Y. Yan 2 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

___________________________ PEP-II MAC2007 Y. Yan 3 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.

___________________________ PEP-II MAC2007 Y. Yan 4 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

___________________________ PEP-II MAC2007 Y. Yan 5 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.

___________________________ PEP-II MAC2007 Y. Yan 6 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.

___________________________ PEP-II MAC2007 Y. Yan 7 The Coupling Ellipses

___________________________ PEP-II MAC2007 Y. Yan 8 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

___________________________ PEP-II MAC2007 Y. Yan 9 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.

___________________________ PEP-II MAC2007 Y. Yan 10 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.

___________________________ PEP-II MAC2007 Y. Yan 11 HER emittance on July 18 (red), 2007

___________________________ PEP-II MAC2007 Y. Yan 12 LER emittance in July, 2007

___________________________ PEP-II MAC2007 Y. Yan 13 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.

___________________________ PEP-II MAC2007 Y. Yan 14 Optics corrections We wish to achieve 2e34 cm -2 s -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 cm -2 s -1 during 2006 P5 meeting. We did not break this record during But we indeed have a breaking specific luminosity at high current.

___________________________ PEP-II MAC2007 Y. Yan 15 Selected examples of optics corrections in 2007

___________________________ PEP-II MAC2007 Y. Yan 16 HER emittance improvement Virtual HER06FEB07 Virtual HER08FEB07 MIA solution from Virtual HER06FEB07 Ideal HER lattice

___________________________ PEP-II MAC2007 Y. Yan 17 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.

___________________________ PEP-II MAC2007 Y. Yan 18 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).

___________________________ PEP-II MAC2007 Y. Yan 19 Dialing PSK knob in MIA: emittance Y is indeed reduced significant for ideal lattice

___________________________ PEP-II MAC2007 Y. Yan 20 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 1 st 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 So we were “very hopeful” to use trombone only to get stable machine after coming out from tunnel with PSK installed.

___________________________ PEP-II MAC2007 Y. Yan 21 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.

___________________________ PEP-II MAC2007 Y. Yan 22 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

___________________________ PEP-II MAC2007 Y. Yan 23 Reducing LER coupling – C12 : Decker, Yocky, et. al. managed dialing in 50% of the solution during collision. Regional BPM problem caused inaccuracy.

___________________________ PEP-II MAC2007 Y. Yan 24 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

___________________________ PEP-II MAC2007 Y. Yan 25 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!