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IBS in MAD-X

IBS in MAD-X. Frank Zimmermann. Thanks to J. Jowett, M. Korostelev, M. Martini, F. Schmidt. Motivations (1) CERN experiments at low or moderate energy are said to disagree with MAD predictions (J.-Y. Hemery); Michel Martini recommended the

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IBS in MAD-X

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  1. IBS in MAD-X Frank Zimmermann Thanks to J. Jowett, M. Korostelev, M. Martini, F. Schmidt Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  2. Motivations (1) CERN experiments at low or moderate energy are said to disagree with MAD predictions (J.-Y. Hemery); Michel Martini recommended the implementation of the Conte-Martini formulae, which are a non-ultrarelativistic generalization based on Bjorken-Mtingwa (2) check of algorithm implemented in MAD (3) extend formalism to include vertical dispersion which is important for damping rings and for the LHC (neglecting vertical dispersion often gives shrinkage of ey) Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  3. References: J.D. Bjorken, S.K. Mtingwa, “Intrabeam Scattering,” Part. Acc. Vol. 13, pp. 115-143 (1983) general theory and ultrarelativistic limit M. Conte, M. Martini, “Intrabeam Scattering in the CERN Antiproton Accumulator,” Part. Acc. Vol. 17, p.1-10 (1985). non-ultrarelativistic formulae M. Zisman, S. Chattopadhyay, J. Bisognano, “ZAP User’s Manual,” LBL-21270, ESG-15 (1986). possible origin of MAD-8 IBS formulae? K. Kubo, K. Oide, “Intrabeam Scattering in Electron Storage Rings,” PRST-AB 4, 124401 (2001) factor 2 correction for bunched beam There is an alternative earlier theory by Piwinski as well as a “modified Piwinski” algorithm by Bane – however we stayed with the BM approach, since it was already implemented in MAD-8 and should give the same answer Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  4. Outline • re-derive general formulae including • vertical dispersion • in the limit of zero vertical dispersion • compare with Conte-Martini expressions; • find a slightly different result in x • example 1: LHC • example 2: LHC upgrade • example 3: CLIC Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  5. IBS growth rates in general Bjorken-Mtingwa theory where a=x,l, or y, r0the classical particle radius, m theparticle mass, N bunch population, log=ln(rmax/rmin) --- with rmax the smaller ofsxand Debye length, and rminthe larger of classical closest approach and quantum diffraction limit from nuclear radius, typicallylog~15-20 ---, g Lorentz factor, G=(2p)3 (bg)3 m3exeysdszthe 6-D invariant volume vertical dispersion enters here note: above formulae refer to bunched beams Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  6. Bjorken-Mtingwa gave solution for zero vertical dispersion in ultrarelativistic limit, neglecting bx/ex and by/ey relative to (gDx)2/(exbx), (bx/ex)g2fx2 and g2/sd2 Conte-Martini kept the terms neglected by B-M, which are important for g<10 Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  7. big surprise! contrary to the prevailing belief in the AB/ABP group, it was found that MAD8 & the previous MAD-X version had already implemented the Conte-Martini fomulae and not the original ultra-relativistic ones from Bjorken-Mtingwa Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  8. The general form of all solutions is with 9 coefficients in the integral to be determined Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  9. denominator coefficients (from determinant) for x, z, s in the limit of zero vertical dispersion new coefficients reduce to CM ones Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  10. numerator coefficients for x in the limit of zero vertical dispersion, CM does not agree with our derivation, namely the two red terms are absent on the right for the example applications, which follow, the contribution from these two terms turns out to be negligible Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  11. numerator coefficients for l numerator coefficients for z in the limit of zero vertical dispersion new coefficients reduce to CM ones Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  12. 1st example: LHC - dispersion vertical dispersion is generated by the crossing angles at IP1 and 2, as well as by the detector fields at ALICE and LHC-B; the peak vertical dispersion is close to 0.2 m x & y dispersion Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  13. 1st example: LHC – dispersion cont’d Dy [m] Dx [m] y dispersion x dispersion s [m] s [m] Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  14. 1st example: LHC – IBS growth rates Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  15. 1st example: LHC – local y IBS growth rate local vertical IBS growth rate around the LHC with nominal crossing angles at all 4 IPs, zero separation, and ALICE & LHC-B detector fields on, as computed by the new MAD-X version; the highest growth rates are found in the IRs 1 and 5 1/ty [1/s] s [m] Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  16. 2nd example: LHC upgrade higher bunch charge, possibly larger transverse emittance, possibly smaller longitudinal emittance, higher harmonic rf, larger crossing angles, etc. IBS tends to get worse Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  17. 3rd example: CLIC damping ring - dispersion IBS is dominant effect determining equilibrium emittance; field errors creating vertical dispersion have a profound effect on the vertical IBS growth rate and, thereby, on the emittance example: CLIC-DR dispersion functions obtained with random quadrupole tilt angles of 200 mrad, cut off at 3 s wiggler arc Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  18. 3rd example: CLIC DR – IBS growth rates → in tuning studies for CLIC DR, dependence of IBS y growth rate on residual vertical dispersion must be taken into account in new MAD-X, y growth time decreases by factor 6 when errors are included Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  19. 3rd example: CLIC-DR – local IBS growth rates 1/tl [1/s] with quadrupole random tilt angles, computed by new MAD-X longitudinal arc wiggler s [m] 1/tx [1/s] 1/ty [1/s] horizontal vertical s [m] s [m] Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

  20. conclusions: • applying B-M recipe, generalized expressions for the three IBS growth rates were derived • the new formulae are valid also if the beam energy is non-ultrarelativistic, or if vertical dispersion is present either by design or due to errors • in the limit of zero vertical dispersion, we recover the Conte-Martini result, except for a small difference in the horizontal growth rate • 3 examples illustrate that the effect of vertical dispersionis significant • the new formulae have been committed to MAD-X Frank Zimmermann, IBS in MAD-X, MAD-X Day, 23.09.2005

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