1. Low emittance experience at Diamond R. Bartolini Diamond Light Source Ltd John Adams Institute, University of Oxford XI SuperB Workshop Frascati, 2 nd December 2009

2. Outline Diamond and low emittance light sources Linear optics Coupling and small V emittance LOCO closest tune approach and turn-by-turn coupling analysis low emittance measurements issues Nonlinear optics, beam stability, collective effects Conclusion XI SuperB Workshop Frascati, 2 nd December 2009

3. Diamond aerial view Diamond is a third generation light source open for users since January 2007 100 MeV LINAC;3 GeV Booster; 3 GeV storage ring 2.7 nm emittance – 300 mA – 14 beamlines in operation (10 in-vacuum small gap IDs) Oxford 15 miles

4. Diamond beamlines

5. The brilliance of the photon beam is determined (mostly) by the electron beam emittance that defines the source size and divergence Brilliance and low emittance

6. DBA used at: ESRF, ELETTRA, APS, SPring8, Bessy-II, Diamond, SOLEIL, SPEAR3... TBA used at ALS, SLS, PLS, TLS … Low emittance lattices for synchrotron light sources APS ALS Low emittance and adequate space in straight sections to accommodate long Insertion Devices are obtained in Double Bend Achromat (DBA) Triple Bend Achromat (TBA)

7. The original achromat design can be broken, leaking dispersion in the straight section ESRF 7 nm  3.8 nm APS7.5 nm  2.5 nm SPring84.8 nm  3.0 nm SPEAR318.0 nm  9.8 nm ALS (SB)10.5 nm  6.7 nm New designs envisaged to achieve sub-nm emittance involve MBA MAX-IV (7-BA): <1 nm Damping Wigglers NSLS-II: <1 nm Petra-III: 1 nm Low emittance lattices APS MAX-IV

8. Diamond storage ring main parameters non-zero dispersion lattice Energy3 GeV Circumference561.6 m No. cells24 Symmetry6 Straight sections6 x 8m, 18 x 5m Insertion devices4 x 8m, 18 x 5m Beam current300 mA (500 mA) Emittance (h, v)2.7, 0.03 nm rad Lifetime> 10 h Min. ID gap7 mm (5 mm) Beam size (h, v)123, 6.4  m Beam divergence (h, v)24, 4.2  rad (at centre of 5 m ID) Beam size (h, v)178, 12.6  m Beam divergence (h, v)16, 2.2  rad (at centre of 8 m ID) 48 Dipoles; 240 Quadrupoles; 168 Sextupoles (+ H and V orbit correctors + 96 Skew Quadrupoles) 3 SC RF cavities; 168 BPMs Quads + Sexts have independent power supplies

9. Implementation of low emittance optics Accelerator Model Linear Optics Closed Orbit Response Matrix (LOCO) Nonlinear Optics Detuning with amplitude (and momentum) Apertures and Lifetime Frequency Map Analysis Resonance driving terms Accelerator

10. Commissioning of small emittance optics (I) Linear optics studies are based on the analysis of the closed orbit response matrix (LOCO-like approach) The Response Matrix R can be inverted Using the Singular Value Decomposition (SVD) to correct the closed orbit distortion The orbit response matrix R is the change in the orbit at the BPMs as a function of changes in the steering magnets strength H V V H XI SuperB Workshop Frascati, 2 nd December 2009

11. Commissioning of small emittance optics (II) The response matrix R is defined by the linear lattice of the machine, (dipoles and quadrupoles), therefore it can be used to calibrate the linear optics of the machine The quadrupole gradients are used in a least square fit to minimize the distance  2

12. Linear optics modelling with LOCO Linear Optics from Closed Orbit response matrix – J. Safranek et al. Modified version of LOCO with constraints on gradient variations (see ICFA Newsl, Dec’07)  - beating reduced to 0.4% rms Quadrupole variation reduced to 2% Results compatible with mag. meas. and calibrations Hor.  - beating Ver.  - beating LOCO allowed remarkable progress with the correct implementation of the linear optics Quadrupole gradient variation

13. Comparison model/machine for linear optics Model emittance Measured emittance  -beating (rms) Coupling* (  y /  x ) Vertical emittance ALS 6.7 nm 0.5 %0.1%4-7 pm APS 2.5 nm 1 %0.8%20 pm CLS 18 nm17-19 nm4.2%0.2%36 pm Diamond 2.74 nm2.7-2.8 nm0.4 %0.08%2.2 pm ESRF 4 nm 1%0.25%10 pm SLS 5.6 nm5.4-7 nm4.5% H; 1.3% V0.05%2.8 pm SOLEIL 3.73 nm3.70-3.75 nm0.3 %0.1%4 pm SPEAR3 9.8 nm < 1%0.05%5 pm SPring8 3.4 nm3.2-3.6 nm1.9% H; 1.5% V0.2%6.4 pm * best achieved

14. Linear coupling numerical studies: sensitivity to machine errors Quadrupole transverse displacement0.1 mm Sextupole transverse displacement0.1 mm Dipole transverse displacement0.05 mm Dipole longitudinal displacement0.05 mm Dipole Field Errors0.1 % Quadrupole roll errors0.2 mrad Dipole roll error0.2 mrad BPM transverse displacement0.05 mm BPM reading 0.5  m Horizontal C.O. r.m.s. (m) 1.0  10 –4 Vertical C.O. r.m.s (m) 1.1  10 –4 Average Linear Coupling (%)1.5 r.m.s. Linear Coupling (%)1.0 After orbit correction – 150 seeds Coupling dominated by V misalignment of sextupoles (> 60 % of total) Average emittance ratio εy/εx along the ring Measured K = 0.9% with skew quadurpoles off XI SuperB Workshop Frascati, 2 nd December 2009

15. Numerical correction with crossed orbit response matrix 1)2) Horizontal C.O. r.m.s. (mm)0.10 Vertical C.O. r.m.s. (mm)0.11 Average Linear Coupling  (%) 0.100.03 r.m.s. Linear Coupling (%)0.110.07 r.m.s. H corrector str. (mrad)0.32 r.m.s. V corrector str. (mrad)0.27 r.m.s. Skew Quad str. (m –1 )0.02 Linear coupling can be reduced (…on the computer) to the limit set by the radiation opening angle: V emittance ~0.6 pm corresponding to K ~ 0.02% (BETA_LNS code) 1) Crossed orbit response matrix 2) Simultaneous minimisation of vertical dispersion

16. Linear coupling correction with LOCO (II) Skew quadrupoles can be simultaneously zero the off diagonal blocks of the measured response matrix and the vertical disperison

17. BPMs coupling LOCO fits also the BPM gain and coupling BPM coupling includes mechanical rotation and electronics cross talk These data are well reproducible over months XI SuperB Workshop Frascati, 2 nd December 2009

18. Measured emittances Coupling without skew quadrupoles off K = 0.9% (at the pinhole location; numerical simulation gave an average emittance coupling 1.5% ± 1.0 %) Emittance [2.78 - 2.74] (2.75) nm Energy spread [1.1e-3 - 1.0-e3] (1.0e-3) After coupling correction with LOCO (2*3 iterations) 1 st correction K = 0.15% 2 nd correction K = 0.08% V beam size at source point 6 μm Emittance coupling 0.08% → V emittance 2.2 pm Variation of less than 20% over different measurements

19. Residual vertical dispersion Without skew quadrupoles offr.m.s. Dy = 14 mm After LOCO correction r.m.s. Dy = 700 μm (2.2 mm if BPM coupling is not corrected) XI SuperB Workshop Frascati, 2 nd December 2009

20. Betatron coupling measurement: closest tune approach The linear betatron coupling ( χ ) is given by C is the minimum separation of the betatron tunes at the resonance is crossed Δ is the distance of the betatron tunes at the nominal working point betatron coupling emittance coupling before0.47 %1.3% after0.002 %0.15% After one LOCO iteration K = 0.15% and C ~ 0

21. Linear coupling correction with turn-by-turn measurements excite the beam diagonally measure tbt data at all BPMs colour plots of the FFT frequency / revolution frequency BPM number H V Q X = 0.22 H tune in H Q y = 0.36 V tune in V All the other important lines are linear combination of the tunes Q x and Q y m Q x + n Q y All BPMs have turn-by-turn capabilities XI SuperB Workshop Frascati, 2 nd December 2009

22. Emittance and coupling measurements (I) Measurements of emittance, energy spread and coupling are made with two X-rays pinhole cameras which take the synchrotron radiation from the two dipoles in cell 1 Emittance and emittance coupling are measured indirectly from measurement of beam spot at the camera point spread function of the system (→ beam size at the camera) magnification of the optics (→ beam size at the source point) electron beam optics functions at the source point (→ emittance)

23. The point spread function (PSF) Σ 0 is the spot size measured at the camera for a zero emittance electron beam. Emittance and coupling measurements (II) The computation of the beam size at the camera S is made with a deconvolution of the PSF Σ 0 assuming Gaussian distributions The beam size at the source σ is computed from the beam size at the camera S and the magnification m of the X-ray pinhole camera The computation of the PSF Σ 0 requires the computation of the diffraction contributions from the square aperture of the pinhole (Fresnel diffraction + spectrum dependence) ~ 15 μm for pinhole 1 and 2 (CdWO 4 ) if S = 0 → Σ = Σ 0 m = 2.4 for pinhole 1; m = 2.7 for pinhole 2 XI SuperB Workshop Frascati, 2 nd December 2009

24. Blue is pinhole 1 Red is pinhole 2 Σ/m (μm) Emittance and coupling measurements (III) Data with the deconvolution (open diamonds) provide the expected linear relation Experimental confirmation of the contribution of the PSF Σ 0 to the beam size were based on the simultaneous measurements of the beam lifetime (Touschek dominated) – proxy for σ y and measured vertical beam size at the source without/with the deconvolution of the PSF Σ 0 Σ = 20.9 um Σ 0 = 15.3 um m = 2.4 σ = 5.9 um The vertical beam size is varied scanning the skew quads taking care that the momentum aperture is unchanged Pinh 1

25. The optics functions at the source point can be either inferred from LOCO or measured directly measure dispersion at the pinhole added pinhole as a BPM in the LOCO procedure to make sure the optics function at the source point (inside the bending magnet) are correct. Difference is not significant (good linear model) The resolution of our system is about 3 μ m which is adequate to measure a 6 μ m V beam size. (C. Thomas et al. submitted to PRSTAB – DLS internal note TDI-DIA-OPT-0002) Emittance and coupling measurements (III) XI SuperB Workshop Frascati, 2 nd December 2009

26. SLS experience with low V emittance SLS has reported a vertical emittance of 2.8 pm (±0.4 pm) The coupling correction procedure is similar to the one used at Diamond. But less skew quadrupoles and separated dispersion free regions High precision emittance measurement with the “emittance monitor” Resolution of 1 um Courtesy SLS

27. Nonlinear dynamics comparison machine to model (I) ModelMeasured Detuning with momentum: operation at positive chromaticity (2/2) Calibration tables for sextupole families were off by few % The most complete description of the nonlinear model is mandatory ! Fringe fields in dipoles (2 nd order –symplectic integration) and in quadrupoles Higher order multipoles in dipoles and quadrupoles (from measurements)

28. Nonlinear dynamics comparison machine to model (II) DA measured FM measured FM model DA model

29. Significant reduction of the rms beam motion up to 100 Hz; Higher frequencies performance limited mainly by the correctors power supply bandwidth Global fast orbit feedback: Diamond 1-100 Hz Standard Straight H Standard Straight V Position (μm) Target12.30.64 No FOFB2.53 (2.1%)0.37 (5.8%) FOFB On0.86 (0.7%)0.15 (2.3%) Angle (μrad) Target2.420.42 No FOFB0.53 (2.2%)0.26 (6.2%) FOFB On0.16 (0.7%)0.09 (2.1%)

30. Collective effects XI SuperB Workshop Frascati, 2 nd December 2009 Single bunch instabilities microwave instability 1.2 mA (mainly due to large tapers). head-tail 0.6 mA at (0,0) chromaticity can be easily damped with higher chromaticity. We normally operate at (2,2). Multi-bunch instabilities SC RF reduced HOM some evidence fast-ion instability now reduced with better vacuum RW manageable (even with 5 mm gap IDs). Can operate at 300 mA with (2,2) chromaticity in 900/936 fill. With 100/936 fill the threshold is 50 mA. TMBF in place allows the operation at 300 mA at (0,0) chromaticity Heating effect in BPM blocks were reduced with additional air cooling

31. Conclusions Diamond is a state-of-the-art third generation light source Careful alignment and independent power supplies in all quadrupoles have allowed a very good control of the linear optics Sufficient provision for independently powered skew quads have allows good coupling correction With LOCO a V emittance of 2.2 pm has been achieved An intense campaign of Accelerator Physics studies is ongoing to better understand and improve the machine performance Future work on coupling: Can we correct the linear coupling better than LOCO? Is sextupole BBA and realignment necessary to achieve lower V emittance? (…zero push from users... but damping rings and B-factories are interested)