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Dynamic Aperture studies & BeamBeam effect simulations

Dynamic Aperture studies & BeamBeam effect simulations. Alexandr Netepenko. NFMCC Meeting January 2010. Dynamic Aperture vs Constant Momentum Deviation. DELTAP = 0.005. DELTAP = 0. DELTAP = -0.005. (Calculated using MAD-8 with lie4 method, BeamBeam included, 1024 turns).

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Dynamic Aperture studies & BeamBeam effect simulations

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  1. Dynamic Aperture studies & BeamBeam effect simulations Alexandr Netepenko NFMCC Meeting January 2010

  2. Dynamic Aperture vs Constant Momentum Deviation DELTAP = 0.005 DELTAP = 0 DELTAP = -0.005 (Calculated using MAD-8 with lie4 method, BeamBeam included, 1024 turns) A. Netepenko NFMCC Meeting

  3. Dynamic Aperture Radius vs Momentum Deviation DA diagonal, MAD-8 calculation (4D tracking) for different constant dp/p, BeamBeam included, 1024 turns MAD-X calculation 6D tracking with synchrotron oscillations, no BeamBeam, 1024 turns A. Netepenko NFMCC Meeting

  4. BeamBeam Element Simulation (Mathematica) Number of slices = 23 Thin lens model used: As far as the transfer matrix for the rest of the ring is known, we calculate new revolution matrix introducing the focusing effect of opposite beam slices for each slice at different points and find new beta-functions and tunes respectfully. A. Netepenko NFMCC Meeting

  5. Converged Iteratively Calculated new Beta-Functions First slice of the bunch (black dots) (red dots represent initial beta-function) Middle slice of the bunch (black dots) Tuneshifts for different slices of the bunch A. Netepenko NFMCC Meeting

  6. Dipole Magnet Field Imperfections Magnetic field multipole expansion: IR dipole:Rref=40mmb1=10000b3=-5.875b5=-18.320b7=-17.105b9=-4.609b11=0.390b13=0.103 Ring dipole:Rref=20mmb1=10000b3=0.003b5=-0.012b7=0.154b9=-1.185b11=-0.118b13=0.053 (V.V.Kashikhin) A. Netepenko NFMCC Meeting

  7. Field Imperfection Impact and Correction Dipole magnets sliced in 5 pieces and thin multipoles introduced between them. Wy Sextupole components cause significant increase of detuning coefficients, especially for vertical plane, and consequently reduce the dynamic aperture. y Before After Dx Wx x A. Netepenko NFMCC Meeting

  8. Field Imperfection Impact and Correction DA without dipoles sextupole component DA with imperfections uncorrected Sextupole correction seems essential, but for some reason hard to apply. Octupole correction of detuning coefficient can be done easier but will not effect all nonlinearities coming from sextupole field component in dipoles. Subject to be studied. A. Netepenko NFMCC Meeting

  9. Goals • Dynamic Aperture VS Momentum Acceptance • (we can try to slightly reduce MA and gain DA increase for nonzero dp/p) • DA VS dp/p calculations (4D MAD-8 Tracking) (Done) • DA with synchrotron oscillations (MAD-X 6D Tracking) (Done) • BeamBeam element simulations (Done) • BeamBeam element with synchrotron oscillations • Fringe fields influence (using SAD and MAD-X) • Nonlinear field components in IR magnets (systematic) • Random field errors and misalignments (very important point for this • type of machine with huge beta-functions in IR) A. Netepenko NFMCC Meeting

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