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1 Warp-POSINST is used to investigate e-cloud effects in the SPS Beam ions Electrons Spurious image charges from irregular meshing controlled via guard cells true sec. back-scattered elastic re-diffused Posinst provides advanced secondary electrons model Monte-Carlo generation of electrons with energy and angular dependence. Warp’s mesh refinement & parallelism provide efficiency 2-D slab of electrons 3-D beam s proc 1 2 N/2 N/2+1 N-1 N Station n n+1 n+N/2-1 n-N/2 n+N-2 n+N-1 Warp quasistatic model similar to HEADTAIL, PEHTS, QuickPIC, CMAD. parallellized using pipelining

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2 – Bunch energy W=26. GeV population N p =1.1 RMS length z =0.23 m (Gaussian profile) momentum spread p/p=2 transverse normalized emittance x = y =2.8 mm.mrad longitudinal normalized emittance z =0.3 eV.s – : continuous focusing beta functions x,y = 33.85, betatron tunes x,y = 26.13, chrom.Q x,y =0.,0. – // : continuous focusing momentum compaction factor =1.92 cavity voltage V = 2 MV cavity harmonic number h = – assumed 100% dipole – Bunch-to-bunch feedback system in horizontal plane (gain=0.1) – 10 interaction stations/turns Simulation parameters for SPS at injection

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3 Warp and Posinst have been further integrated, enabling fully self- consistent simulation of e-cloud effects: build-up & beam dynamics CERN SPS at injection (26 GeV) Turn 1 Turn 500

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4 Warp-Posinst enabled first direct simulation of a train of 3x72 bunches -- using 9,600 CPUs on Franklin supercomputer (NERSC, U.S.A.) Substantial density rise in tails of batches between turns 0 and 800. Substantial density rise in tails of batches between turns 0 and 800. Average electron cloud density history at fixed station Substantial density rise in tails of batches between turns 0 and 800. J.-L. Vay, et al, IPAC12 Proc., (2012) TUEPPB006

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5 Rise also observed on e- density on axis On axis electron cloud density history at fixed station E- density on axis doubled between turns 400 and 600. x2 between turns 400 and 600

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E-cloud density raise coincides with growth of vertical emittance 6 => Positive coupling between the e-cloud buildup and the bunches dynamical response.

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Pattern of stripes in the history of vertical bunch offsets 7 phase of the oscillations is not purely random E-cloud provides coupling between bunches. Vertical offset (mm)

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8 Fractional tune Comparison with experimental measurements -- collaboration with SLAC/CERN Good qualitative agreement: separation between core and tail with similar tune shift. Warp is also applied to study of feedback control system (R. Secondo in collaboration with SLAC) Warp-Posinst 2 Bunch 29, Turn head tail headtail Fractional tune Bunch slice Experiment 1 Bunch 119, Turn Nominal fractional tune=0.185 Bunch slice 1 J. Fox, et al, IPAC10 Proc., p (2011) 2 J.-L. Vay, et al, Ecloud10 Proc., (2010)

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