CERN, Space Charge 2013, April 17 L.G.Vorobiev 1 Muons, Inc. Accuracy and Performance Upgrade of PIC and Hybrid Space-Charge Solvers Leonid Vorobiev Muons, Inc., Batavia, IL 60510, USA SPACE CHARGE 2013 16-19 April, CERN ABSTRACT For the high luminosity LHC (HL-LHC), space charge study requires high quality modeling. In this talk the sources of numerical errors in space charge algorithms are analyzed, and their mitigation is suggested for both conventional space charge grid solvers (based on PIC formalism) and hybrid solvers. The implementation of these improvements may significantly increase the accuracy, speed and physical validity of numerical results and contribute to achieve the required beam parameters in the LHC accelerator complex.
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Accuracy and Performance Upgrade of PIC and Hybrid Space-Charge Solvers
Accuracy and Performance Upgrade of PIC and Hybrid Space-Charge Solvers. Leonid Vorobiev Muons, Inc., Batavia, IL 60510, USA. ABSTRACT - PowerPoint PPT Presentation
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CERN, Space Charge 2013, April 17 L.G.Vorobiev 1Muons, Inc.
Accuracy and Performance Upgrade of PIC and Hybrid Space-Charge Solvers
Leonid Vorobiev
Muons, Inc., Batavia, IL 60510, USA
SPACE CHARGE 2013
16-19 April, CERN
ABSTRACT
For the high luminosity LHC (HL-LHC), space charge study requires high quality modeling. In this talk the sources of numerical errors in space charge algorithms are analyzed, and their mitigation is suggested for both conventional space charge grid solvers (based on PIC formalism) and hybrid solvers. The implementation of these improvements may significantly increase the accuracy, speed and physical validity of numerical results and contribute to achieve the required beam parameters in the LHC accelerator complex.
CERN, Space Charge 2013, April 17 L.G.Vorobiev 2Muons, Inc.
CERN, Space Charge 2013, April 17 L.G.Vorobiev 18Muons, Inc.
1. Grid Solvers. Limitations
PIC Grid Solvers: solid/clustered beams, OkFilaments, Sheet beams, Halo, Stray particles not OkMesh refinement, • Density errors, irregular Clouds, use more particles• Errors due to interpolation on irregular grid• Slowing down speed…
Aside from PICs:• Particle-Core, Envelope (linear) & non-linear model ?• Integral representation of the Green’s function: OkComplex Boundary 3D, Sheet Beam (Photo-Injector) Ok• Hybrid SC Solvers
CERN, Space Charge 2013, April 17 L.G.Vorobiev 19Muons, Inc.
2. Hybrid SC Solvers. Outline.Hybrid Space Charge Solvers = Green’s function
in Integral form with Tricks
The Best ones for photo-injectors, el.optics, complex boundaries:VERY accurate, SLOW
This Presentation:A. Space charge templates. Instead of integrated GF, use
Library of EXACTLibrary of EXACT SC potential & fields within boundariesSC potential & fields within boundariesB. From SC Templates to PIC: Split Operator RevisitSplit Operator RevisitC. Hierarchy of Templates
CERN, Space Charge 2013, April 17 L.G.Vorobiev 20Muons, Inc.
Disk-Template, LibraryDisk-Template, Library
Ring-Template = SuperpositionRing-Template = Superpositionof positive (BLUE) & negative of positive (BLUE) & negative (RED) derived from Disc-(RED) derived from Disc-TemplateTemplates
3D beam (non-elliptical!)Within conductingBoundary (not shown)3D Templates withinthe same boundary
NO GRID 3D Poisson Equation, INSTEAD: Convolve Template Potentials/Fields
)()(
, )(4)(
xx
xxx
beambeam
beambeam
Uu
u
)()(
, )(4)(
xx
xxx
tmptmp
tmptmp
Uu
u
zdzzSzzyxuzyxu yxtmpbeam~))~(),~(,~,,(),,( ,
3.A Hybrid Solvers, SC Templates
Ref. Vorobiev and York [9]
CERN, Space Charge 2013, April 17 L.G.Vorobiev 21Muons, Inc.
Library of TemplatesPre-Assigned densities
Ring Disc Template
• General • Halo
• Hollow Beam
EXP
ARB
-r_m 0 +r_m
3.A Hybrid Solvers, SC Templates
Private Communications:
A. Friedman, D. Grote, I. Hofmann, M. Reiser, J. Struckmeier and R. York
CERN, Space Charge 2013, April 17 L.G.Vorobiev 22Muons, Inc.
3.A Template Solvers, Machinery
SC Templates - Machinery
Template PotsFree space (green)Cond. pipe (blue)Image Dens (red)
Symplectic SC solver5. Vorobiev and Hirata, Report KEK 95-12; http://ccdb5fs.kek.jp/cgi-bin/img/allpdf?199524012\
Green’s Function6. R.Harrington, “Field Computation by Moment Methods”, Macmillan, New York (1968)7. M.Szilagyi, “Electron and Ion Optics”, Plenum, New York (1988)8. V.Ivanov “Green’s Function Techniques in Forming Intense Beams”, (1989, 2009), Int. J.Mod.Phys A,
Vol.24, No. 5, 869–878,…In part: Quang, et al. (2006), Kapin (2002), Hess, et al.(2007), Vorobiev (1999).
SC Templates:9. Vorobiev and York: Phys.Rev. STAB 3, 114201 (2000); MSUCL-Report 1117, 1998;PAC’1999, pp. 2781-2783; Springer: http://link.springer.com/chapter/10.1007%2F3-540-47789-6_33PAC’2001 pp. 3075-3078; EPAC 2002, pp. 1679-1681; PAC’2003 pp. 3533-3535;Fermilab Report 08-236, http://lss.fnal.gov/archive/2008/pub/fermilab-pub-08-236-apc.pdf