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  1. Study of Long-Range Collisions and Wire-Compensation for the Tevatron Frank Zimmermann February 21 – March 8 Thanks to: Bela Erdelyi, Paul Lebrun, Tanaji Sen, Vladimir Shiltsev, XiaoLong Zhang

  2. motivation wire compensation is under study for the LHC with 3 prototype wire-devices in the SPS is there a potential for wire-based compensation of long-range collisions at the Tevatron? situation is more difficult: helix (both transverse dimensions), many betatron phases, differences between bunches and between injection & collision, dispersion, coupling, etc. is it helpful to compensation a few “most harmful” long-range collisions? can I confirm the efficiency of wire correctors found at injection? which parameter can guide the compensation?

  3. I looked at • bunch A1 at injection “cog0” (A1 stays longest in the • machine and was studied by B. Erdelyi and T. Sen) • bunches A6, A1 and A12 in collision injection parameters collision parameters

  4. Phase-Space Positions of the Long-Range Collisions

  5. x-px y-py injection, A1 Image of all LRBB collisions mapped into normalized phase space. x-px y-py collision, A6

  6. Ax Ay injection, A1 Normalized distance versus index of LR collision. Ay Ax collision, A6

  7. Ay Atot injection, A1 Ax Distance Ay vs Ax (left) and total distance Atot(right) vs. index of LR collision. Ay Atot Ax collision, A6

  8. LR encounters below 7s for bunch A1 at injection: 6 LR encounters below 7s for bunch A6 in collision: 3

  9. Tracking is performed using an extended version of WSDIFF described at LHC99.

  10. phase space x-px y-py injection, A1 15 trajectories with random start amplitudes between 0 and 10s over 500 turns. y x coordinates vs time

  11. Tune Footprints

  12. all LR encounters without the 6 closest tune footprint for start amplitudes up to 6s in each plane injection, A1 not much difference…

  13. comparison of footprints from WSDIFF with BBSIM injection, A1

  14. all LR encounters without the 3 closest tune footprint for start amplitudes up to 6s in each plane collision, A6, w/o head-on a large difference!

  15. w/o head-on collision,A6,A12, A1

  16. Bela’s solution for wire compensation at injection (4 wires, which optimized dynamic aperture and/or minimized norm of the nonlinear map)

  17. LR encounters only with 4 wires tune footprint for start amplitudes up to 6s in each plane injection, A1 footprint ‘rotates’, but keeps similar extent

  18. Diffusion launch group of particles at the same amplitude with a random phase and compute increase of the average action variance per turn (scheme of John Irwin for the SSC)

  19. X Y all LR encounters injection, A1 dynamic aperture ~6s dynamic aperture ~5s X Y without the 6 closest

  20. injection, A1 with 4 wires dynamic aperture ~5.6s dynamic aperture ~5.6s ~0.5s improvement in Y (note different horizontal scale on this plot)

  21. X Y all LR encounters dynamic aperture ~8s collision, A6 dynamic aperture ~8s ~8.5s ~8.5s X Y without the 3 closest

  22. X Y all LR encounters dynamic aperture ~8s dynamic aperture ~8s collision, A6 X Y with only the 3 closest! dynamic aperture ~9.0s dynamic aperture ~9.5s

  23. X Y all LR encounters, A1 dynamic aperture ~6s dynamic aperture ~6s collision X Y all LR encounters, A12 dynamic aperture ~5s dynamic aperture ~5s

  24. Analytical estimates tune shift, chromaticity, coupling, chromatic coupling, diffusion

  25. tune shift & coupling

  26. collision A12 A6 build up over all LR encounters collision horizontal & vertical tune shift collision injection A1 A1

  27. A6 A12 build up over all LR encounters collision collision real & imaginary coupling A1 A1 collision injection

  28. chromaticity & chromatic coupling

  29. A6 build up over all LR encounters collision collision A12 horizontal & vertical chromaticity A1 collision injection A1

  30. A12 build up over all LR encounters A6 collision collision real & imaginary chromatic coupling injection A1 A1 collision

  31. Total tune shifts, chromaticities, coupling driving terms, and chromatic couplings induced by long-range collisions for various pbar bunches in collision: and for A1 at injection:

  32. diffusion coefficient in 4D no analytical solution yet for this double integral…

  33. Future Plans • extend simulations to 6D and • compute diffusion at 1sd • (chromaticity & chromatic coupling most likely important) • continue analytical calculations • study effect of unequal beta on • compensation • other suggestions welcome!