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Analytic IBS Growth Times Calculation & Emittance Evolution Study

Preliminary studies on Intra-Beam Scattering (IBS) including adaptive emittance calculations, bug fixes in MAD-X module, comparisons with JSPEC, and analyses on beam intensity effects and tunes. Explore IBS calculations and measurements in detail.

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Analytic IBS Growth Times Calculation & Emittance Evolution Study

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  1. LEIRIBS studies (preliminar) Angela Saa Hernandez

  2. Layout • On IBS calculations • Analytic calculation of growth times • Adaptive emittance calculations • Bugfix in MADX IBS module • IBS calculations for a given input beam • Bunched vs. coasting beams • Implementation of intensity decay • IBS vs. beam intensity • IBS vs. tunes • IBS calculations vs. measurements • Aperture model and threshold emittances • Coasting beam • Bunched beam

  3. On IBS calculations

  4. Analytic calculation of IBS growth times Intra Beam Scattering: caused by the interaction via Coulomb scattering and momentum exchange of the charged particles within a bunch. For small scattering angles the random addition of events can lead to an emittance growth. Analytic calculations: • using the IBS module included in the MADX code [1], derived from the formalism presented by Bjorken and Mtingwa [2], including the expansion by Conte and Martini [3], generalized to the case of nonzero vertical dispersion. • assume a transverse bi-gaussian input distribution of the beam (fulfilled by the measured beam) • Lattice described element-by-element (RF cavities, all magnetic elements including quad. fringe fields) The emittance growth times are obtained as outputs [1] F. Antoniou and F. Zimmermann, Revision of Intrabeam Scattering with Non-Ultrarelativistic Corrections and Vertical Dispersion for MAD-X, CERN Note: CERN-ATS-2012-066 (2012). [2] J. D. Bjorkenand S. K. Mtingwa, Intrabeam Scattering, Technical Report FERMILAB-Pub-82/47-THY (1982). [3] M. Conte and M. Martini, Intrabeam scattering in the CERN antiproton acumulator, Particle Accelerators, Vol 17 (1985).

  5. Adaptive emittance calculations Calculate emittance evolution due to IBS along the injection plateau (1 s)  update the input parameters with a time step (dt) and recalculate the emittances as: Convergence tests:

  6. MAD-X IBS module • Works fine for bunched beams (compared to calculations from other codes –JSPEC tested- and measurements ) Comparison* MADX vs JSPEC for bunched beams *JSPEC hardcodes the value of the Coulomb logarithm =20, in MADX instead it is calculated from the input parameters. I had to hardcode it to 20 in the source code in order to do the comparison

  7. MAD-X IBS module • Works fine for bunched beams (compared to calculations from other codes –JSPEC tested- and measurements ) • Runs with no errors for coasting beams but gives extremely small ibs times (does not compare with measurements nor with analytical calculations from other codes) Comparison* MADX vs JSPEC for bunched beams *JSPEC hardcodes the value of the Coulomb logarithm =20, in MADX instead it is calculated from the input parameters. I had to hardcode it to 20 in the source code in order to do the comparison

  8. Bug fix in MADX IBS module • MAD-X transforms beam inputs npart ↔ bcurrentnot taking into account the charge of the particle! • Very wrong in the case of ions: results will depend on which input was given • Issue discussed with L. Deniau • IBS module fixed, recompiled and tested, pull request in MAD-X github approved Comparison coasting beams

  9. IBS calculationsas a function of input beam parameters

  10. Emittance growth Pb-ion beam (q = 54, A = 208) at injection plateau (Ekin= 4.2 MeV/nucleon) Input beam parameters (arbitrary though realistic for a single injection from Linac3)

  11. Intensity decay • Analytic calculations cannot provide any info on particle losses and intensity decay. However, losses are non-negligible during the injection plateau. • Intensity can also be updated in the adaptive calculations, with inputs from measurements

  12. Dependence on beam intensity • IBS effects as a function of the bunch intensity for a period of 1s • single injection from Linac3: intensity ~ 2e10 charges • Nominal operation with 7 injections: intensity ~ 10e10 charges • The ex growth up to 600% if beam kept at the injection energy during 1 s. However, in the nominal case with 7 injections the ramp-up of the dipoles occurs immediately after the rf capture.

  13. Dependence on tunes • The Bjorken-Mtingwa formalism takes into account the variation of the optics functions around the machine. • 2D tune scans of the horizontal emittance blow-up (left) and vertical emittance blow-up (right) caused by IBS during the 1 s flat bottom.

  14. IBS calculationsvsmeasurements

  15. Aperture model and threshold emittances • To calculate the threshold emittances (from which losses start): • define closed orbit  we took zero-orbit (instead could also take a measured one with injection bumps, etc) • coasting beam: Dp/p = 7e-4 • assume bi-gaussian transverse distribution  well fulfilled in LEIR • calculate beam envelope: 1s = 68%, 2s = 95%, 3s = 99.7% ions  we define threshold for 3s • find for which value of ex and ey is there a collision with a physical aperture : ex= 26e-6, ey = 6e-6 [m*rad] Identify limiting apertures in both planes Updated aperture model from D. Moreno ”LEIR aperture database” presentation at LEIR beam performance meeting, 26/06/2018

  16. Coasting Beam Nominal working point: Qx = 1.82, Qy = 2.72 Measured horizontal emittance blow-up quite well explained by IBS Measured vertical emittance blow-up much larger than the predicted by IBS

  17. Sources of vertical emittance growth Following [4], emittance growth due to IBS can have 3 sources: • Direct contribution: transverse growth from collisions, even where Dy = 0 (as two particles with y’=0 will have y’≠ 0 after colliding). Very slow growth, only dominates for ultralow emittances • Dispersion contribution: changes in p after collision, at a position where Dy ≠ 0  effective change in y respect to off-energy axis. Growth velocity ∝ to dispersion magnitude. • Coupling contribution: if there is some betatron coupling the horizontal IBS emittance growth feeds into the vertical plane K. Kubo, S. Mtwinga and A. Wolski, “Intrabeam Scattering formulas for high energy beams”, PRAB 8, 2005

  18. Vertical emittance growth from direct contribution How small should ey be to justify all measured growth from direct contribution? • Offsetting ey to overlap measurements • Input ey/4 to have similar blow-up from direct contribution • ex calculation no longer matches measurements!!! • Reasonable to have such a discrepancy from IPM measurements? • Measured ey blow-up = 40% • Calculated eyblow-up (direct contribution) = 6%

  19. Vertical emittance growth from vertical dispersion Vertical dispersion from vertical dipoles of Electron Cooler --> up to 10 mm Measurements from 2016 do not show indications of larger Dy Negligible effect in the vertical plane compared to the difference between measurements and calculations

  20. Vertical emittance growth from coupling contribution • Betatron coupling present in LEIR due to solenoid of Electron Cooler • IBS module does not include a consistent treatment of linear betatron coupling (MADX manual, p. 184) • Replace adaptive emittance calculation to couple growths with free parameter re taking values between [0, 1]

  21. Vertical emittance growth from coupling contribution • Betatron coupling present in LEIR due to solenoid of Electron Cooler • IBS module does not include a consistent treatment of linear betatron coupling (MADX manual, p. 184) • Replace adaptive emittance calculation to couple growths with free parameter re taking values between [0, 1]

  22. Vertical emittance growth from coupling contribution • Betatron coupling present in LEIR due to solenoid of Electron Cooler • IBS module does not include a consistent treatment of linear betatron coupling (MADX manual, p. 184) • Replace adaptive emittance calculation to couple growths with free parameter re taking values between [0, 1] dependence with re re = 0.85 re = 0.78 re = 0.70

  23. Bunched beam Nominal working point: Qx = 1.82, Qy = 2.72

  24. IBS calculationsvsmeasurements Dependence with intensity and with working point

  25. Emittance growth vs. vertical tune • Approx. constant intensity (variations between 1.5e10 - 2.5e10 charges • Emittance growth measurements after 480 ms • Resonance at Qy=2.66 not excited Further analysis to be done!

  26. Emittance growth vs. intensity • Nominal working point: Qx = 1.82, Qy = 2.715 • Vary intensity by mis-steering beam in • Emittance growth measurements after 480 ms Further analysis to be done!

  27. Extra slides

  28. Tune dependence: coasting beam below Qy = 2.66 We take a working point for which the space-charge contribution is negligible Qx = 1.82, Qy = 2.65 making re = 0.84

  29. Coasting beam above Qy = 2.66 We investigate a working point for which the space-charge contribution is large: Qx = 1.82, Qy = 2.69 Resonance excited by means of a pair of skew sextupoles making re = 0.6 Measured horizontal emittance blow-up quite well explained by IBS Measured vertical emittance blow-up larger than the predicted by IBS and different growing trend: starts as e –t/t but then more linear with t ???

  30. Coasting beam below Qy = 2.66 We look for a vertical working point for which the space-charge contribution is negligible:Qy = 2.65 (constant Qx=1.82) 4 injections Skew sextupoles exciting Qy=2.66 resonance Ecol off at 1316 m  500 ms evolution No RF capture Consistent with this other measurement? 1 injection Skew sextupolesoff Ecol off at 526 ms 1300 ms evolution RF capture  bunched beam

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