Loading in 2 Seconds...
Loading in 2 Seconds...
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
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
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?
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
Phase-Space Positions of the Long-Range Collisions
x-px y-py injection, A1 Image of all LRBB collisions mapped into normalized phase space. x-px y-py collision, A6
Ax Ay injection, A1 Normalized distance versus index of LR collision. Ay Ax collision, A6
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
LR encounters below 7s for bunch A1 at injection: 6 LR encounters below 7s for bunch A6 in collision: 3
Tracking is performed using an extended version of WSDIFF described at LHC99.
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
all LR encounters without the 6 closest tune footprint for start amplitudes up to 6s in each plane injection, A1 not much difference…
comparison of footprints from WSDIFF with BBSIM injection, A1
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!
w/o head-on collision,A6,A12, A1
Bela’s solution for wire compensation at injection (4 wires, which optimized dynamic aperture and/or minimized norm of the nonlinear map)
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
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)
X Y all LR encounters injection, A1 dynamic aperture ~6s dynamic aperture ~5s X Y without the 6 closest
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)
X Y all LR encounters dynamic aperture ~8s collision, A6 dynamic aperture ~8s ~8.5s ~8.5s X Y without the 3 closest
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
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
Analytical estimates tune shift, chromaticity, coupling, chromatic coupling, diffusion
collision A12 A6 build up over all LR encounters collision horizontal & vertical tune shift collision injection A1 A1
A6 A12 build up over all LR encounters collision collision real & imaginary coupling A1 A1 collision injection
chromaticity & chromatic coupling
A6 build up over all LR encounters collision collision A12 horizontal & vertical chromaticity A1 collision injection A1
A12 build up over all LR encounters A6 collision collision real & imaginary chromatic coupling injection A1 A1 collision
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:
diffusion coefficient in 4D no analytical solution yet for this double integral…
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!