# US LHC Accelerator Research Program bnl fnal lbnl

- Slides: 21

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) 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 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 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 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 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 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) 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 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 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), 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 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 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 Wolfgang Hofle, Giovanni Rumolo, and John Byrd

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 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

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 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. 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 + 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