# US LHC Accelerator Research Program BNL FNAL LBNL

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US LHC Accelerator Research Program BNL - FNAL- LBNL - SLAC Lifetrac LARP Mini-Workshop on E-Lens Simulations, BNL December 3, 2008 Alexander Valishev (FNAL) LARP E-Lens Mini-Workshop - Dec 3 2008 Lifetrac - A. Valishev

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 (1 D histograms, 2 D 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 FORTRAN 90 * D. Shatilov, Part. Accel. 52, 65 1996 LARP E-Lens Mini-Workshop - Dec 3 2008 2 Lifetrac - A. Valishev

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 headon) – Slices have bi-Gaussian distribution – 6 D symplectic kick formulae – Non-Gaussian distribution can be simulated as a superposition of Gaussian “harmonics” • Machine optics comprised of thin 6 D maps • Lattice chromaticity (1 st and 2 nd order) • Effects of random noise (introduced as thin 6 D kick) • Several types of electron lenses (transverse distributions, edge fields, current ripple, etc. ) • Parallel LARP E-Lens Mini-Workshop - Dec 3 2008 3 Lifetrac - A. Valishev

Machine Optics • Linear 6 D 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 10 th order) • Beams separation for “helix” or “pretzel” • Longitudinal motion with sinusoidal RF LARP E-Lens Mini-Workshop - Dec 3 2008 4 Lifetrac - A. Valishev

Treatment of Chromaticity 1. 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: 1. where L is the “chromatic drift'' length 2. Betatron tune chromaticities (also affected by “chromatic drift'‘) are adjusted using an artificial element (insertion) with the following Hamiltonian: LARP E-Lens Mini-Workshop - Dec 3 2008 5 Lifetrac - A. Valishev

LIFETRAC Input Start from machine model in Opti. M or MAD-X 1. Extract b-functions at IPs, at multipoles and at E-Lenses 2. Extract multipole parameters 3. perl script converter for lifetrac (with GUI in case of Opti. M) 1. Provide beam parameters (intensity, emittances) LARP E-Lens Mini-Workshop - Dec 3 2008 6 Lifetrac - A. Valishev

LIFETRAC Output • • • 2 D 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 LARP E-Lens Mini-Workshop - Dec 3 2008 7 Lifetrac - A. Valishev

Sample Output Effect of betatron tune chromaticity LARP E-Lens Mini-Workshop - Dec 3 2008 8 Lifetrac - A. Valishev

New: RHIC E-Lens IRerrcorr_685695_IP 10_10 m RHIC with EL, 540 10 th order multipoles 10, 000 particles 3. 3 E 6 turns 5 days on 32 CPUs Without multipoles 10, 000 particles 1 E 7 turns 43 hours on 8 CPUs LARP E-Lens Mini-Workshop - Dec 3 2008 9 Lifetrac - A. Valishev

RHIC E-Lens LARP E-Lens Mini-Workshop - Dec 3 2008 10 Lifetrac - A. Valishev