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Optimisation de l’Optique de l’Anneau de Stockage pour la Source SOLEIL

Optimisation de l’Optique de l’Anneau de Stockage pour la Source SOLEIL. Amor NADJI, Synchrotron SOLEIL. Design Criteria for SOLEIL. High Brilliance and Coherenc e. Large beam lifetime and injection rate ( Top-Up ).

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Optimisation de l’Optique de l’Anneau de Stockage pour la Source SOLEIL

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  1. Optimisation de l’Optique de l’Anneau de Stockage pour la Source SOLEIL Amor NADJI, Synchrotron SOLEIL Rencontres LAL / SOLEIL ( 17 Avril 2008)

  2. Design Criteria for SOLEIL • High Brilliance and Coherence • Large beam lifetime and injection rate (Top-Up) • Extensive use of Insertion Devices such as Undulatorsand Wigglers (highest ratio of available straight sections to the circumference ). Variable Polarisation. • Long straight sections • Tunability: the right photon energy for the experiment • Stability: intensity (Beam Lifetime), position, size and energy • Compactness (Budget) • Upgrade potential Rencontres LAL / SOLEIL ( 17 Avril 2008)

  3. High Brilliance • A parameter of prime importance in experiments with synchrotron radiation sources is the spectral brilliance (brightness) defined as : • Apart from diffraction effects, we have : HIGH PHOTON BEAM BRILLIANCE  LOW ELECTRON BEAM EMITTANCE Rencontres LAL / SOLEIL ( 17 Avril 2008)

  4. h(s) and h’(s) are respectively the dispersion function and its derivative

  5. Equilibrium Beam Emittance • The natural horizontal emittance for an isomagnetic ring, i.e. all bending magnets having same bending radius is : Jx is the horizontal damping partition number. Jx ~1 (zero field gradient in bending magnet) Jx < 2 (vertical focusing in bending magnet) : (potentially) emittance reduction of a factor two Cq = 3.83 x 10-13 m and g is the Lorentz factor. r is the bending radius. His the so called lattice invariant or dispersion’s emittanceor H-function an average taken only in the part of the circumference where photons are emitted, that is in the bending magnets (and Insertion Devices). • In practical units, ex is given by : exis completely determined by the energy, bending field and lattice functions.

  6. H-function in a Bending Magnet b, h betatron function b(s) (b0, a0) dispersion function h(s) s q =s/r (h0=h’0=0) Bending Magnet • b0, a0, g0, h0, h’0, are the values of the lattice functions at the beginning of the BM • We assume a lattice where h0=h’0 =0 (achromatic condition). • We get after integration over one BM: For small bending angles: (sufficiently accurate for most storage rings design application) the length of the BM the full BM deflexion angle Rencontres LAL / SOLEIL ( 17 Avril 2008)

  7. We get for the natural horizontal e- beam emittance : • There isclearlya cubicdependence of the beamemittance on the deflexion angle It is a general lattice property, there is no assumption on the lattice type. Should use many short BMsto get low emittance. If the ring consists of N identical BMs : Need for a magnet focusing (quadrupoles) providing small waist for the optical functions

  8. Minimum Emittance (with Achromatic Arc Condition) The minimum possible emittance is determined only by the BM length, • In order to get the minimum possible emittance we have to vary the initial conditions b0 and a0 until the minimum is found. and • We can calculate the unknown initial conditionsb0 and a0 : • The minimum equilibrium beam emittance in an isomagnetic ring with an Achromatic Arc Condition, h0=h’0 =0, at the entrance of the BM is:

  9. Minimum Emittance (without Achromatic Condition) • By breaking the achromatic condition (non-zero dispersion in straight sections) we can obtain the configuration in which the emittance becomes the smallest. • It is smaller by a factor 3 than in the achromatic arc configuration. • The optimum values of betatron functions at the entrance of the BM are: • It is interesting to note that in this case, the dispersion and the betatron function are parabola with the symmetry axis at the middle of the bending magnet : Minimum at center of the BM.

  10. Emittance Achieved Ideal values (without achromatic condition): Design values : • The ideal value causes the betatron function to reach a sharp minimum inside the BM and then to increase from there on to large values in the quadrupoles, leading to extremely high chromaticity (the quadrupoles do not provide the same focussing strength for particle with energy deviation). x,z = dx,z(d pp) x,z : betatron tunes Rencontres LAL / SOLEIL ( 17 Avril 2008)

  11. This must not be tolerated for two reasons : Momentum acceptance : some variation of energy deviation has to be accepted by the storage ring for reasons of beam lifetime. Head tail instability: collective oscillation of electrons in head and tail of the bunch leading to very fast beam loss. • We must operate with zero or positive chromaticity Chromaticity :   ( - KQ + ms) ds  0 quadrupole strength (introduce negative ) Strong chromaticity correction sextupoles reduce the dynamic aperture and this negatively impacts on the beam lifetime. sextupole strength (correct the )

  12. Beam Lifetime • 2 main limitations :  Touschek Effect: scattering within the bunch High density-Touschek scattering of particles - large longitudinal transfers of energy - loss unless large acceptance : RF acceptance, physical aperture, dynamic aperture for large E deviations (SOLEIL) Dynamic Aperture (SOLEIL: eacc = 4 to 6%)  Elastic Scattering : scattering with residual gaz of pression p Transverse deflexion and subsequent lossin regions of low aperture, which are usually the narrow vertical gaps in undulators (g).

  13. Lattice Design Interface • Magnet Design: technological limits, coil space, multipolar errors • Vacuum: impedance, pressure, physical apertures, space • Radiofrequency: Energy acceptance, bunch length, space • Diagnostics: Beam Position Monitors,…, space • Alignment: Orbit distortions and correction • Mechanical Engineering: Girders, vibrations • Design Engineering: Assembling and feasibility Space requirements: Magnet, Vacuum, RF, Diagnostics and Engineering Rencontres LAL / SOLEIL ( 17 Avril 2008)

  14. Linear Optimisation • Reasonable maximum for andbz < 30m (sensitivity) • Reasonable beta split at the centre of the achromat • Natural chromaticities :xx< -100 and xz< -50 • Dispersion (hx) at the centre of the achromat > 0.25m • Lowbz (~1m) in the centre of undulator straight sections high brilliance and accomodation of low gap IDs • Minimum Beam Stay Clear for efficient injection  minimum ratio of (bx)max/(bx)inj (bxinj > 10m) Rencontres LAL / SOLEIL ( 17 Avril 2008)

  15. Sextupoles Positions • 2 purposes : - correction of both chromaticitiesxx , xz - on momentum and off momentum dynamic aperture optimisation • Phase optimisation to minimise nonlinear effects • Large number of sextupole families • LOW sextupoles strengths • Positions wherebx <<bzthen bx>>bz At least 2 such positions where thehx is large Rencontres LAL / SOLEIL ( 17 Avril 2008)

  16. Optical functions for the APD lattice One Superperiod nx= 18.28 nz= 8.38 ex= 3nm.rad at 2.5 GeV Rencontres LAL / SOLEIL ( 17 Avril 2008)

  17. Optical functions for the present lattice One Superperiod nx= 18.20 nz= 10.30 ex= 3.73nm.rad at 2.75 GeV Rencontres LAL / SOLEIL ( 17 Avril 2008)

  18. Example of Factor of Merit Rencontres LAL / SOLEIL ( 17 Avril 2008)

  19. Working point : Tune Diagram nz Systematic Resonances 2nd order 3rd order 4th order 5th order m nx+n nz =p Larger dynamic aperture Higher emittance nx Smaller dynamic aperture Lowest emittance Good Compromise between dynamic aperture and emittance Rencontres LAL / SOLEIL ( 17 Avril 2008)

  20. Tune vs Emittance Resonances Error sensitivity vs Low emittance (resistive wall) Beta functions Emittance, Brilliance, Injection, Error sensitivity, Chromaticity, Symmetry OPTIMISATION STRATEGY Sextupoles positions x  z Large x Chromaticity correction and Dynamic Aperture Optimisation Resonances Momentum Acceptance Rencontres LAL / SOLEIL ( 17 Avril 2008)

  21. Optimization Strategy Knobs : quadrupoles sextupoles • Tune shift w/ amplitude • Tune shift w/ energy • Robustness to errors multipoles couplingIDs Lattice design Fine tuning Tracking NAFF • 4D tracking • 6D tracking NAFF suggestions • (x-z) fmap  injection eff. • (x-d) fmap  Lifetime • Touschek computation • Resonance identification Dynamics analysis Improvement Needed Yes No Good Working Point (NAFF: J. Laskar)

  22. Minimizing the Strengths of Sextupolar Resonances Rencontres LAL / SOLEIL ( 17 Avril 2008)

  23. Adjusting the Linear Terms of Tune Shift with Amplitude Rencontres LAL / SOLEIL ( 17 Avril 2008)

  24. Simultaneous Minimization Rencontres LAL / SOLEIL ( 17 Avril 2008)

  25. Nonlinear Optimisation • THE QUALITY FACTORS : • Tune shift with amplitude • Phase space plots • Tune shift with energy • Dynamic aperture (on and off momentum) • Maximum sextupole strengths • Frequency Map Analysis • TOOLS : • BETA-SOLEIL code • TRACYII code • NAFF Rencontres LAL / SOLEIL ( 17 Avril 2008)

  26. Horizontal tune shift with amplitude nx 5nx= 92 (z=0.) RESONANCES 3nx= 55 4nx= 73 X(m) Rencontres LAL / SOLEIL ( 17 Avril 2008)

  27. On-Momentum dynamic aperture Z(m) 500 turns X(m) Rencontres LAL / SOLEIL ( 17 Avril 2008)

  28. Phase Space diagram Rencontres LAL / SOLEIL ( 17 Avril 2008)

  29. Frequency Map Analysis (NAFF) Launched particles over a fine X-Z grid plotting Numerical tunes Highlighting, nonlinearity (diffusion rate) Without IDs, Physical aperture included and 1% coupling Working point1 Working point 2 Rencontres LAL / SOLEIL ( 17 Avril 2008)

  30. Frequency Map Analysis Off-momentum Without IDs, Physical aperture included and 1% coupling Working point1 Working point 2 Rencontres LAL / SOLEIL ( 17 Avril 2008)

  31. Frequency Map Analysis With 3 x U20 (full gap=5mm) and 1% coupling Working point 2 Working point1 Rencontres LAL / SOLEIL ( 17 Avril 2008)

  32. Frequency Map Analysis Off-momentum With 3 x U20 (full gap=5mm) and 1% coupling Rencontres LAL / SOLEIL ( 17 Avril 2008)

  33. USERS High Brilliance B  I  x z Constant Intensity Impedance Heat load, vacuum… Low Emittance  Long beam lifetime High current I Bend angle     3 Touschek- scattering dominates Ring size Budget Small ,  in dipole centres Max Max Magnet gaps Large Energy Acceptance Short cell length Strong focusing Rencontres LAL / SOLEIL ( 17 Avril 2008)

  34. Strong focusing Large Quadrupole Strength KQ Chromaticity  = d(d pp)   ( - KQ  + ms  ) ds  0 Chaos BZ x2 – z2 BX x z Large Sextupole Strength ms Dynamic Aperture (Acceptance)  Physical Aperture Lattice Energy Acceptance  RF Energy Acceptance Closed Orbit Distorsion from Magnet displacements AC & DC Steerers Magnet groups on girders Bump Injection RF Beam Lifetime Rencontres LAL / SOLEIL ( 17 Avril 2008)

  35. SOLEIL Machine Physics group • P. Brunelle • Loulergue • A. Nadji • L. Nadolski • M. A. Tordeux Rencontres LAL / SOLEIL ( 17 Avril 2008)

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