Warp-POSINST is used to investigate e-cloud effects in the SPS Warp quasistatic model similar to HEADTAIL, PEHTS, QuickPIC, CMAD. 2-D slab of electrons parallellized using pipelining 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 s 3-D beam Warp’s mesh refinement & parallelism provide efficiency Posinst provides advanced secondary electrons model Beam ions Electrons true sec. back-scattered elastic Monte-Carlo generation of electrons with energy and angular dependence. re-diffused Spurious image charges from irregular meshing controlled via guard cells
Simulation parameters for SPS at injection • Bunch • energy W=26. GeV • population Np=1.11011 • RMS length z=0.23 m (Gaussian profile) • momentum spread p/p=210-3 • transverse normalized emittancex= y=2.8 mm.mrad • longitudinal normalized emittancez=0.3 eV.s • : continuous focusing • beta functions x,y= 33.85, 71.87 • betatron tunes x,y= 26.13, 26.185 • chrom. Qx,y=0.,0. • // : continuous focusing • momentum compaction factor =1.9210-3 • cavity voltage V = 2 MV • cavity harmonic number h = 4620. • assumed 100% dipole • Bunch-to-bunch feedback system in horizontal plane (gain=0.1) • 10 interaction stations/turns
Warp and Posinst have been further integrated, enabling fully self-consistent simulation of e-cloud effects: build-up & beam dynamics Turn 1 CERN SPS at injection (26 GeV) Turn 500
Warp-Posinstenabled first direct simulation of a train of 3x72 bunches -- using 9,600CPUs on Franklin supercomputer (NERSC, U.S.A.) Average electron cloud density history at fixed station Substantial density rise in tails of batches between turns 0 and 800. Substantial density rise in tails of batches between turns 0 and 800. J.-L. Vay, et al, IPAC12Proc., (2012) TUEPPB006
Rise also observed on e- density on axis On axis electron cloud density history at fixed station x2 between turns 400 and 600 E- density on axis doubled between turns 400 and 600.
E-cloud density raise coincides with growth of vertical emittance => Positive coupling between the e-cloud buildup and the bunches dynamical response.
Pattern of stripes in the history of vertical bunch offsets Vertical offset (mm) • phase of the oscillations is not purely random • E-cloud provides coupling between bunches.
Comparison with experimental measurements -- collaboration with SLAC/CERN Warp-Posinst2 Experiment1 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) Bunch 29, Turn 100-200 Bunch 119, Turn 100-200 Fractional tune Fractional tune head tail head tail Nominal fractional tune=0.185 Bunch slice Bunch slice 1J. Fox, et al, IPAC10 Proc., p. 2806 (2011) 2J.-L. Vay, et al, Ecloud10 Proc., (2010)