1. An ultra-low emittance lattices for Iranian Light Source Facility storage ring Esmaeil Ahmadi On behalf of beam dynamics group Iranian Light Source Facility (ILSF), Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

2. Introduction Different Approaches to Low Emittance The Nonlinear Optics Challenges in a 5BA Lattice ILSF storage ring design Nonlinear optimization results in ILSF storage ring Errors study (Closed orbit correction) Life time issues Content

3. What do synchrotron radiation users care about?  A lot of photons into a small spot  A lot of coherent photons  A lot of photons in a short pulse  A high pulse repetition rate  fast switched polarization  etc… Many parameters are captured with: average brightness Introduction (ILSF storage ring design philosophy), Reducing the electron emittance is the more effective way to increase the brightness

4. Figure of merit of the ILSF storage ring follows design trend of the modern synchrotron light sources Introduction (ILSF storage ring design philosophy)

5. Natural horizontal equilibrium emittance for a flat storage ring: Different Approaches to Low Emittance  Theoretical Minimum Emittance (TME): find optimized H to minimize emittance  Gradient bends increase Jx with vertical focusing gradient in the dipoles.  Dispersive straights, damping wigglers, longitudinal gradient bends, etc.  Multibend achromat (MBA): many weak bends

6. ILSF storage ring design 3.9 0 3.15 0 5 Bends Achromat lattice has been chosen for ILSF storage ring

7. Matching cell Unit cell Matching cellUnit cell Unit cell with Supper bend (Asymmetry) 528Circumference (m) 0.286Natural emittance (nm-rad) 20Number of symmetry 7Length of straight section (m) 44.27/12.18 Working point -110.41/-71.45Natural chromaticity 1.81×10 −4 Mom.Comp.factor 0.815e-3Energy spread 40Max.4pole.gradient (T/m) 2200Max.6pole.gradient B ″ (T/m 2 ) 0.56Dipole field (T) 1.9Super Bend field (T) ILSF storage ring design (Lattice functions and parameters) Transverse beam size Straight section σ x (μm)/σ y (μm) 72.2/3.2

8. The Nonlinear Optics Challenges in a 5BA Lattice large negative natural chromaticity ( tune spread due to momentum spread ) Strong focusing optics In general in order to study the nonlinear behavior of the lattice we resort to The Poincaré map which represented by Lie serires: : is the linear one-turn map, and the Lie generator h represents the nonlinear kicks transferred to the entrance of the lattice where J, φ are the action-angle variables and β, μ the beta functions and phase advances at the sextupoles, n. for a systematic approach, the Lie generator and the working point (M linear )have to be optimized simultaneously Large negative chromaticity must not be tolerated for two reasons:  The machine tune has to stay away from integer or half integer numbers otherwise field or gradient errors will amplify coherently and destroy the beam  Negative chromaticity excites the fundamental mode of the head tail instability, a collective oscillation of electrons in head and tail of the bunch leading to very fast beam loss. Suppression of the fundamental mode requires non negative chromaticity

9. The Nonlinear Optics Challenges in a 5BA Lattice h 11001 and h 00111 are the linear chromaticity

10. Nonlinear optimization result in ILSF storage ring  The resonance driving terms are suppressed by properly optimizing the harmonic sextupole strength and the phase advance between them.  OPA is an extremely useful tool for this work → direct interaction, weighting, display of sextupole kicks and RDTs in complex plane, RDT minimization, optimization of octupoles/decapoles (SVD), etc.  In reality, lattice performance determined by magnet errors, misalignments, ID matching, IBS, etc. → require tracking to verify → in ILSF, we are using Elegant, MADx and AT codes. The color bar shows tune diffusion. It is an indicator of chaotic behavior Frequency map analysis Resonance crossing Tune diagram Suitable position for putting chromatic sextupoles

11. Nonlinear optimization result in ILSF storage ring The tracking has been done for 3000 turns. RF is included in the tracking.

12. Nonlinear optimization result in ILSF storage ring momentum acceptance tracking: Dp/p S (m)  Half inner gap of vacuum chamber o @ the straight section g x =12 mm, Limited by inj. septum g y =3 mm, Limited by the IDs The resulting Tuscheck life time is 26 hours ( RF voltage is considerd 1.1 Mv)

13. Errors study (Closed orbit correction) ParameterUnitValue(1σ) Transverse displacement of dipoles, sextupoles and quadrupoles μm40 Roll of dipoles, quadrupoles, sextupolesμrad200 Dipoles fractional strength error (ΔB/B)-5×10 −4 Quadrupoles fractional strength error (ΔK/K)-1×10 −3 Sextupoles fractional strength error (ΔM/M)-5×10 −3 In order to correct the orbit distortion, 200 corrector magnets and 200 BPM are utilized. The correctors are placed as additional coils in the sextupoles (global orbit correction by response matrix calculation ) Challenging point for alignment people

14. Errors study (Closed orbit correction) Kicker strength (rms) Kicker strength(rms) BPM read back (rms) Kicker strength (largest) BPM read back (largest) Kicker strength (largest) BPM read back (largest)

15. Errors study (multipole errors) OrderMultipoleSystematicRandom Dipole Bn/B 1 @ 11.7 mm 24-pole0.004.00E-5 36-pole-9.00E-44.00E-5 48-pole0.004.00E-5 510-pole1.00E-44.00E-5 612-pole-8.00e-54.00E-5 714-pole6.00E-54.00E-5 816-pole0.004.00E-5 Quadrupole Bn/B 2 @11.7mm 36-pole0.004.00E-5 48-pole1.0e-54.00E-5 510-pole0.004.00E-5 612-pole-3.00E-54.00E-5 714-pole0.004.00E-5 816-pole0.004.00E-5 918-pole0.004.00E-5 Sextupole Bn/B 3 @ 11.7 mm 48-pole0.004.00E-5 510-pole0.004.00E-5 612-pole0.004.00E-5 714-pole0.004.00E-5 816-pole0.004.00E-5 918-pole-4.00E-64.00E-5 1530-pole-1.00E-74.00E-5  For random multipole, it is assumed the distribution of errors is Gaussian and cut of at 2σ.  We just consider the normal multipoles.

16. Lifetime issues For the typical vacuum pressure P=1.5 nTorr, the total life time is about 10 hours

17. Thank you very much