Dynamic Aperture studies

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Dynamic Aperture studies BeamBeam effect
simulations
Alexandr Netepenko
BNL Muon Collider Design Workshop December 2009
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Dynamic Aperture vs Constant Momentum Deviation
DELTAP 0.005
DELTAP 0
DELTAP 0.005
1024 turns tracking using MAD-8 with lie4 method,
reference emittance
Beam-Beam element sizes computed with E?N25?,
November , 2009
A. Netepenko BNL MCD Workshop
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Dynamic Aperture Radius vs Momentum Deviation
Diagonal DA, 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
November , 2009
A. Netepenko BNL MCD Workshop
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BeamBeam Element Simulation (Mathematica)
Number of slices 23
Thin lens model used
November , 2009
A. Netepenko BNL MCD Workshop
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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)
November , 2009
A. Netepenko BNL MCD Workshop
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Calculated Tuneshifts for different slices in the
bunch
(as far as we have round beams, vertical
tunesifts are the same)
Dynamics of BeamBeam interaction in Mathematica
File
November , 2009
A. Netepenko BNL MCD Workshop
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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)

November , 2009
A. Netepenko BNL MCD Workshop
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