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Dynamic Aperture studies & BeamBeam effect simulations

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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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slide1

Dynamic Aperture studies

& BeamBeam effect simulations

Alexandr Netepenko

NFMCC Meeting

January 2010

slide2

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

slide3

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

slide4

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

slide5

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

slide6

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

slide7

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

slide8

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

slide9

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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