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Linear and Non-Linear Beam Dynamics in the Presence of IDs M.A. Tordeux

Linear and Non-Linear Beam Dynamics in the Presence of IDs M.A. Tordeux On behalf of the Accelerator Physics Group. Present undulator configuration. HU256 + HU60. U20. HU52. HU80 + HU44. *  x = 18 m. HU256. U20. HU256 + HU80. U20. HU640. HU80 + HU44. U20. HU52.

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Linear and Non-Linear Beam Dynamics in the Presence of IDs M.A. Tordeux

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  1. Linear and Non-Linear Beam Dynamics in the Presence of IDs M.A. Tordeux On behalf of the Accelerator Physics Group ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  2. Present undulator configuration HU256 + HU60 U20 HU52 HU80 + HU44 * x = 18 m HU256 U20 HU256 + HU80 U20 HU640 HU80 + HU44 U20 HU52 ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  3. Apple II : magnetic characterisation • Example of HU52 closed at minimum gap 15.5 mm Beam based measurement of vertical and horizontal field integrals Comparison with magnetic measurements in laboratory Field integrals have been measured on beam (using local horizontal orbit bumps) Measurements are corrected from natural focusing (field roll off incidence is calculated by RADIA code) • Magnetic measurements and beam based measurement differ by less than 0.1 G (~ magnetic measurement resolution) ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  4. Apple II : magnetic characterisation • Example of HU52 Beam based measurement of vertical and horizontal field integrals Comparison with magnetic measurements in laboratory Good agreement for all undulator phases Beam based measurement (after RADIA correction) Conclusion : confidence in magnetic measurements Magnetic measurements ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  5. U20 : magnetic characterisation Magnetic measurements : evolution from U20 SWING (June 2006) to U20 GALAXIES (July 2008) • Example of in vacuum U20 (4 presently installed out of 6) 5.5 mm minimum gap Cancellation of the skew gradient More and more experience in using the Genetic Algorithm based IDBuilder for magnetic shimming (cf O. Chubar, EPAC 08) Cancellation of the normal gradient Remaining dipolar field will be corrected on beam by feedforward process ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  6. U20 : magnetic characterisation Magnetic measurements : evolution from U20 SWING (June 2006) to U20 GALAXIES (July 2008) • Example of in vacuum U20 Undulator effect (*) On beam measurements (**) Expected from magnetic measurement ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  7. HU640 : beam based characterisation • Example of HU640 Beam based measurement of vertical and horizontal field integral Linear Vertical mode (LV) ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  8. HU640 : beam based characterisation • Example of HU640 • Pinhole camera measurement Linear Vertical mode (LV) • Bare Machine coupling is modelled thanks to crosstalk closed orbit acquisition • Then measured skew gradient from HU640 is introduced in the model • Bare Machine coupling is modelled thanks to crosstalk closed orbit acquisition • Then measured skew gradient from HU640 is introduced in the model Nominal working point x = 18.20 / z = 10.30 x = 2 / z = 2 ¾ filling pattern, Ibeam= 200 mA HU640 in the 12 m long straight section ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  9. Undulator effects on machine performances (1) Nominal working point x = 18.200 / z = 10.300 x = 2 / z = 2 • Measurement of beam lifetime ¾ filling pattern,Ibeam= 200 mA Pmean = 10-9 mbar, VRF = 2.8 MV 8 bunches,Ibeam= 60 mA Pmean = 6.4 10-10 mbar, VRF = 2.8 MV  Strong lifetime reduction is observed in presence of the 3 U20 closed at their minimum gap and the HU640 in LV mode ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  10. Undulator effects on machine performances (1) Nominal working point x = 18.200 / z = 10.300 x = 2 / z = 4 8 bunches, Ibeam= 55 mA • Measurement of beam lifetime versus RF voltage 4.2% 4.0% 3.5% 1.2% 1.7% 2.2% 2.6% 3.0% 3.4% 3.7% 4.0% 4.3% 4.5% Corresponding RF Energy Acceptance  Reduction of the energy acceptance caused by roll-off (U20) and transverse field integral variation (HU640 in LV mode) ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  11. Undulator effects on machine performances (1) • HU640 effect on ON-momentum dynamic aperture Blue circle size: lost rate Red: unstable horizontal aperture for injection : significantly reduced ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  12. Undulator effects on machine performances (2) • First optimisation of injection by moving betatron tunes New working point x = 18.202 / z = 10.317 April 2008 The most disadvantageous undulator configuration = 3 x U20 (gap 10 mm for injection) HU80 ( 0 phase, min gap 15.5 mm) HU256 HU640 intermediate Bx, LV mode Adopted until now for daily user operation ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  13. Undulator effects on machine performances (2) Nominal working point x = 18.202 / z = 10.317 x = 2 / z = 2 ¾ filling pattern,Ibeam= 200 mA Pmean = 8 10-10 mbar, VRF = 2.8 MV • Measurement of injection rate and beam lifetime Future Undulator configuration is anticipated No compensation of the focusing effect of insertion devices ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  14. Undulator effects on machine performances (3) • Second optimisation of injection by moving betatron tunes Not any more optimized November 2008 3 x U20 (gap 10 mm for injection) 2 x HU80 (+/2 phase, min gap 15.5 mm) 2 x HU52 (0 phase  gap 15.5) 2 x HU44 (+/2 phase, min gap 15.5 mm) HU60 (0 phase  gap 15.5) HU640 Bx max, LV mode Now in further evaluation Possible good working point x = 18.27 / z = 10.32 ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  15. Undulator effect on machine performances (3) Recovery of the whole Bare Machine aperture ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  16. Next steps • HU640 : Local compensation for tune shift (feedforward) • Off momentum studies (time consuming because of low speed RF tuner variation) • Magnetic shimming : Natural focusing suppression (case of the APPLE II) thanks to IDBuilder ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  17. Linear Model • Motivation in revisiting the linear model : Reminding of the first day nominal lattice tunes  A relative scaling of all quadrupole gradients of +8 10-3has been applied to recover x = 18.23 and z = 10.31 • This scaling is not comprehensible with the Quad bench quality that has been estimated: reproducibility 10-4 - precision 2 10-3 • Argument for a new model : calculation of tune shift taking into account the quadrupole fringe field (sensitive for SOLEIL lattice) • Objective : to test 2 lattices with very different optics and different tunes : • x = 18.20 / z = 10.30 (Nominal one) • x = 20.72 / z = 9.200 ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  18. Linear Model • Quadrupole calibration is Q current dependant (saturation)  taken into account • Quadrupole magnetic length is Q current dependant (length dispersion up to 6 10-3) • choice of a mean magnetic length value • LOCO code will be used to correct for Quadrupole gradient dispersion (discrepancy due to magnet construction – a few 10-3) ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  19. Non-Linear Model • First Non-linear model includes fringe field and gradient in dipole in the TRACY II Code • Introduction of thick sextupoles instead of thin lenses • Introduction of all multipolar components deduced from magnetic measurements 0 chromaticities chromaticities = 2 0 chromaticities chromaticities = 2 ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  20. Non-Linear Model • Fringe field in quadrupole Model of the kick : E. Forest, Beam dynamics, A new attitude and frame work, p: 390 0 chromaticities chromaticities = 2 It remains some disagreement between model and beam based measurements (FMA) ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

  21. Optical functions for the nominal working point lattice ESLS 16 - 27 & 28 November 2008 Linear and non-linear dynamics in the presence of IDs M.-A. Tordeux

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