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US LHC Accelerator Research Program bnl - fnal- lbnl - slac Preliminary simulations of

US LHC Accelerator Research Program bnl - fnal- lbnl - slac Preliminary simulations of e-cloud feedback in the SPS with Warp -POSINST J. -L. Vay, M. A. Furman LBNL [email protected] gov, [email protected] gov Presented by M. Venturini (LBNL) E-cloud mitigation mini-workshop CERN - November 20 -21, 2008 E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 1

Warp - 3 D accelerator/PIC code • Geometry: 3 D, (x, y), (x, z)

Warp - 3 D accelerator/PIC code • Geometry: 3 D, (x, y), (x, z) or (r, z) • Field solvers: electrostatic - FFT, capacity matrix, multigrid, AMR electromagnetic - Yee mesh, PML bc, AMR • Particle movers: Boris, “drift-kinetic”, new leapfrog • Boundaries: “cut-cell” --- no restriction to “Legos” (not in EM yet) • Lattice: general; takes MAD input - solenoids, dipoles, quads, sextupoles, … - arbitrary fields, acceleration • Bends: • Diagnostics: • Python and Fortran: “steerable, ” input decks are programs • Parallel: • Misc. : tracing, quasistatic modes, “warped” coordinates; no “reference orbit” Extensive snapshots and histories MPI support for boosted frame E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 2

Warp: Quasi-Static Mode (“QSM”) 2 -D slab of electrons 3 -D beam s lattice

Warp: Quasi-Static Mode (“QSM”) 2 -D slab of electrons 3 -D beam s lattice quad s 0 drift bend drift 1. 2 -D slab of electrons (macroparticles) is stepped backward (with small time steps) through the frozen beam field • 2 -D electron fields are stacked in a 3 -D array, 2. push 3 -D proton beam (with large time steps) using • maps - “WARP-QSM” - as in HEADTAIL (CERN) or • Leap-Frog - “WARP-QSL” - as in QUICKPIC (UCLA/USC). proc Station 1 n 2 n+1 N/2+1 n+N/2 -1 n-N/2 N-1 n+N-2 (16 procs) N n+N-1 On parallel computers: E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 3

Study feedback of EC induced single-bunch instability in smooth SPS lattice § SPS at

Study feedback of EC induced single-bunch instability in smooth SPS lattice § SPS at injection (Eb=26 Ge. V) – =27. 729 – Np=1. 1 1011 – continuous focusing • x, y= 33. 85, 71. 87 • x, y= 26. 12, 26. 185 • z= 0. 0059 – Nstn ecloud stations/turn=100 – Fresh e-cloud density as precomputed by POSINST Initial e-cloud distribution in a bend (POSINST) E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 4

Feedback model 1 • Highly idealized model of feedback system. • Record slice centroid

Feedback model 1 • Highly idealized model of feedback system. • Record slice centroid y 0(t) from every beam passage • *apply low-pass FFT filter (sharp cutoff at 800 MHz): y 0(t)=>ŷ 0(t) • scale transverse position y => y-g ŷ 0 (g=0. 1 used in all runs) *optional stage E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 5

Preliminary simul. study of SPS EC feedback Model 1 - beam distribution after 300

Preliminary simul. study of SPS EC feedback Model 1 - beam distribution after 300 turns Feedback OFF tail head tail unfiltered tail head tail Y (cm) centroid Filtered (FFT-cutoff 0. 8 GHz) Y-centroid (cm) Y (cm) Time (ns) unfiltered Time (ns) Filtered (FFT-cutoff 0. 8 GHz) Frequency (GHz) E-cloud mitigation, CERN, Nov. 2008 Power (a. u. ) Y-centroid (cm) Power (a. u. ) Feedback ON - cutoff 0. 8 GHz feedback simulations - JL Vay, M Furman Frequency (GHz) 6

Controlling centroid motion reduces emittance growth Evolution of emittance Centroid No feedback FB applied

Controlling centroid motion reduces emittance growth Evolution of emittance Centroid No feedback FB applied every turn (disclaimer: all simulations done with same resolutions but no guarantee of numerical convergence) E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 7

Feedback model 2 - prediction from two turns • record centroid offset y 0(t)

Feedback model 2 - prediction from two turns • record centroid offset y 0(t) and y 1(t) from two consecutive beam passages • predict y 2(t) from y 1(t) and y 0(t) using linear maps, ignoring longitudinal motion and effects from electrons • *scale according to line charge density : y 2(t) => y 2(t) w • *apply low-pass FFT filter (sharp cutoff at 800 MHz): y 2(t)=>ŷ 2(t) • one turn later, scale transverse position y => y-g ŷ 2 (g=0. 1) *optional stage E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 8

Feedback is effective at lower e-cloud density Model 2 - ne~1. 5 x 1012

Feedback is effective at lower e-cloud density Model 2 - ne~1. 5 x 1012 m-3 No feedback X-horizontal Y-vertical filter off, w off X-horizontal Y-vertical Emittance growth <1% Emittance growth ~7. 5% filter on, w off X-horizontal Y-vertical Emittance growth <1% 300 turns average y-centroid 0. 8 GHz spectrum vs time E-cloud mitigation, CERN, Nov. 2008 average y-centroid spectrum vs time feedback simulations - JL Vay, M Furman average y-centroid spectrum vs time 9

800 MHz bandwith too narrow at larger e-density Model 2 - ne~6 x 1012

800 MHz bandwith too narrow at larger e-density Model 2 - ne~6 x 1012 m-3 No feedback X-horizontal Y-vertical Emittance growth ~9% average y-centroid filter off, w off X-horizontal Y-vertical filter on, w off X-horizontal Y-vertical Emittance growth ~0. 6% Emittance growth ~26% average y-centroid E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 10

Feedback model 3 – prediction from three turns • record centroid offset y 0(t),

Feedback model 3 – prediction from three turns • record centroid offset y 0(t), y 1(t) and y 2(t) from three consecutive beam passages • predict y 3(t) from y 0 -2(t) using linear maps, ignoring longitudinal motion and effects from electrons • *scale according to line charge density : y 2(t) => y 2(t) w • *apply low-pass FFT filter (sharp cutoff at 800 MHz): y 2(t)=>ŷ 2(t) • one turn later, scale transverse position y => y-g ŷ 2 (g=0. 1) *optional stage E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 11

Preliminary simul. study of SPS EC feedback Model 3 - ne~6 x 1012 m-3

Preliminary simul. study of SPS EC feedback Model 3 - ne~6 x 1012 m-3 No feedback filter off, w off X-horizontal Y-vertical Emittance growth ~9% X-horizontal Y-vertical Emittance growth ~0. 26% average y-centroid 300 turns E-cloud mitigation, CERN, Nov. 2008 filter on, w off filter off, w on filter on, w on X-horizontal Y-vertical Emittance growth ~4. 2% Emittance growth ~2. 1% average y-centroid 300 turns feedback simulations - JL Vay, M Furman Emittance growth ~15% average y-centroid 300 turns 12

Tentative Conclusions § Work on determining theoretical feasibility of a feedback system for ecloud

Tentative Conclusions § Work on determining theoretical feasibility of a feedback system for ecloud induced instability has just started. § A (demanding) 800 MHz bandwidth system has been shown to provide the desired damping (at least for not too-large e-density) for the SPS case study considered • damping the coherent vertical motion has beneficial impact on emittance growth § More extensive study will be necessary to determine bandwidth requirement and should include • more realistic modeling of feedback systems (filter, time delays, noise …) • more complete modeling of beam dynamics (chromaticities …_ § Developing a simplified model of beam-e-cloud interaction may be helpful for the process of optimizing feedback design (John Byrd) • is modeling of e-cloud using effective wake-potential a viable option? E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 13

to follow is a short summary of recent work done by Joel Thompson with

to follow is a short summary of recent work done by Joel Thompson with Wolfgang Hofle, Giovanni Rumolo, and John Byrd

EC Feedback with HEADTAIL § Goal: add simple active feedback module to HEADTAIL code

EC Feedback with HEADTAIL § Goal: add simple active feedback module to HEADTAIL code to explore gain and bandwidth required to damp SPS ECI. § No FB Perfect slice FB

FB Simulation Results § FB on average vertical position ineffective (i. e. dipole FB)

FB Simulation Results § FB on average vertical position ineffective (i. e. dipole FB) § FB Bandwidth limitation implemented as a simple windowing function • FB effective for bandwidths as low as 300 MHz • Bandwidth below 500 MHz appears to require very large gain § Proper kick phase determined from combination of position measurement from two consecutive turns. § Summary: good initial results. Significantly more effort required.

BACKUPS E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 17

BACKUPS E-cloud mitigation, CERN, Nov. 2008 feedback simulations - JL Vay, M Furman 17

Preliminary simul. study of SPS EC feedback Model 2 - ne~1. 5 x 1012

Preliminary simul. study of SPS EC feedback Model 2 - ne~1. 5 x 1012 m-3 No feedback filter off, w off X-horizontal Y-vertical filter on, w off Emittance growth <1% Emittance growth ~7. 5% filter off, w on filter on, w on X-horizontal Y-vertical Emittance growth <1% 300 turns average y-centroid 300 turns E-cloud mitigation, CERN, Nov. 2008 300 turns feedback simulations - JL Vay, M Furman average y-centroid 300 turns 18

Preliminary simul. study of SPS EC feedback Model 2 - ne~6 x 1012 m-3

Preliminary simul. study of SPS EC feedback Model 2 - ne~6 x 1012 m-3 No feedback filter off, w off X-horizontal Y-vertical Emittance growth ~9% X-horizontal Y-vertical filter on, w off filter on, w on X-horizontal Y-vertical Emittance growth ~0. 6% average y-centroid filter off, w on Emittance growth ~26% Emittance growth ~1% average y-centroid Emittance growth ~92% average y-centroid 300 turns E-cloud mitigation, CERN, Nov. 2008 300 turns feedback simulations - JL Vay, M Furman 300 turns 19

POSINST provides advanced SEY model. Monte-Carlo generation of electrons with energy and angular dependence.

POSINST provides advanced SEY model. Monte-Carlo generation of electrons with energy and angular dependence. Three components of emitted electrons: I 0 Ie Its Ir backscattered: rediffused: true secondaries: Phenomenological model: • based as much as possible on data for and d /d. E • not unique (use simplest true sec. assumptions whenever data is not available) • many adjustable parameters, fixed by fitting and d /d. E to data E-cloud mitigation, CERN, Nov. 2008 re-diffused feedback simulations - JL Vay, M Furman back-scattered elastic 20

WARP-POSINST unique features merge of WARP & POSINST 1 + new e-/gas modules 2

WARP-POSINST unique features merge of WARP & POSINST 1 + new e-/gas modules 2 + Adaptive Mesh Refinement Speed-up 3 x 10 -104 E-cloud mitigation, CERN, Nov. 2008 + Novel e- mover quad Allows large time step greater than cyclotron period with smooth transition from magnetized to nonmagnetized regions R concentrates resolution only where it is needed Key: operational; partially implemented (4/28/06) Z 4 be am e- motion in a quad Speed-up x 10 -100 feedback simulations - JL Vay, M Furman 21