Lifetrac

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Lifetrac
US LHC Accelerator Research Program
BNL - FNAL- LBNL - SLAC

• LARP Mini-Workshop on E-Lens Simulations, BNL
• December 3, 2008
• Alexander Valishev (FNAL)

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Some History

• Initially LIFETRAC was developed by D.Shatilov
  for simulation of the equilibrium distribution of
  the particles in circular electron-positron
  colliders . In 1999 the new features have been
  implemented, allowing simulation of
  non-equilibrium distributions, i.e. proton beams.
  In this case the goal of simulations is not to
  obtain the equilibrium distribution but to
  observe how the initial distribution is changing
  with time. Number of simulated particles can vary
  in the range of 103 to 106 (usually 104). The
  tracking time is divided into steps'', usually
  104 turns. The statistics obtained during the
  tracking (1D histograms, 2D density in the space
  of normalized betatron amplitudes, luminosity,
  beam sizes and emittances) is averaged over all
  particles and all turns for each step. So, we get
  a sequence of frames representing evolution of
  the initial distribution.
• The code is programmed in FORTRAN90

D.Shatilov, Part. Accel. 52, 65 1996
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Main Features

• Initial distribution for weak bunch is either
  Gaussian or read from external file. Particles
  have weights
• Strong bunch is divided into slices
  longitudinally (typically 12 for head-on)
• Slices have bi-Gaussian distribution 6D
  symplectic kick formulae
• Non-Gaussian distribution can be simulated as a
  superposition of Gaussian harmonics
• Machine optics comprised of thin 6D maps
• Lattice chromaticity (1st and 2nd order)
• Effects of random noise (introduced as thin 6D
  kick)
• Several types of electron lenses (transverse
  distributions, edge fields, current ripple, etc.)
• Parallel

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Machine Optics

• Linear 6D maps for transport between IPs
• Maps can be supplied directly or
• Computed from conventional or coupled b-functions
• Thin sextupole and octupole (recently introduced
  general multipole up to 10th order)
• Beams separation for helix or pretzel
• Longitudinal motion with sinusoidal RF

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Treatment of Chromaticity

• Chromaticity of b-functions excited in the Main
  IPs. A Hamiltonian was built producing the
  chromaticity of b-functions via drift spaces
  where the transverse momentum is large (low-beta
  regions). The symplectic transformations for that
  are
• where L is the chromatic drift'' length
• Betatron tune chromaticities (also affected by
  chromatic drift') are adjusted using an
  artificial element (insertion) with the following
  Hamiltonian

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LIFETRAC Input

• Start from machine model in OptiM or MAD-X
• Extract b-functions at IPs, at multipoles and at
  E-Lenses
• Extract multipole parameters
• perl script converter for lifetrac (with GUI in
  case of OptiM)
• Provide beam parameters (intensity, emittances)

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LIFETRAC Output

• 2D distributions and histograms at each step
• Emittances
• Luminosity
• Lost particles (turn at which they hit the
  aperture and coordinates)
• Turn-by-turn dipole moment
• Tune footprint

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Sample Output
Effect of betatron tune chromaticity
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New RHIC E-Lens

• IRerrcorr_685695_IP10_10m
• RHIC with EL,
• 540 10th order multipoles
• 10,000 particles
• 3.3E6 turns 5 days on 32 CPUs
• Without multipoles
• 10,000 particles
• 1E7 turns 43 hours on 8 CPUs

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RHIC E-Lens