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Outline:1. Codes, Models and Strategies2. Experiment / Simulation Comparison

• Transverse • Longitudinal

3. Beam Halo Studies

Funding Provided by US DOE and DOD

Rami A. Kishek, Irving Haber, & Max Cornacchia

Modeling and SimulationModeling and Simulation

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Injector

Ring

UMER Modeling ChallengesUMER Modeling Challenges

PD

Q6

QR1YQ

SD5

SD6r

SD6i

SD4

• Magnets with extended fringe fields

• Earth field

• Complicated Injection section

• 14 BPMs for tune of ~ 6.5

• 8 types of magnets to be modeled

• Magnets with extended fringe fields

• Earth field

• Complicated Injection section

• 14 BPMs for tune of ~ 6.5

• 8 types of magnets to be modeled

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Codes Used to Model UMERCodes Used to Model UMER• WARP, developed by Grote, Friedman, Vay, Lund, et al., (LLNL/LBNL)

– Electrostatic PIC code + accelerator code (used in Ion community)– self-consistent treatment of space charge– full set of accelerator element models– XY, RZ, and 3D - curved coordinate system (no reference trajectory)– has been extensively used in the design of UMER,

and in modeling of many experiments and diagnostics

ELEGANT, developed by Borland (Argonne)– a powerful particle tracking code– broadly used– includes optimization routines– so far have not used space charge model

but code useful for characterizing lattice

Other Codes Used:COSY Infinity (NIU)DIMAD (MSU)MaryLieWinAgileEnvelope codesORBIT (proposed)

Other Codes Used:COSY Infinity (NIU)DIMAD (MSU)MaryLieWinAgileEnvelope codesORBIT (proposed)

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Magnet ModelsMagnet Models

Sources of Magnet data– Rotating Coil measurements of harmonics of dipoles and quadrupoles– Hall probe measurements of magnets– MagLi: a Biot-Savart Law solver for air-core magnets

Implementation:– hard-edge ideal magnets– hard-edge elements with multipoles– fringe field corrections– z-varying multipoles– actual fields on a 3-D mesh

(derived from MagLi, typically with 1 mm resolution)

Both CodesWARPELEGANT

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Key StrategiesKey Strategies

• Multi-turn operation and increased accuracy in experiments requires more refined simulation models.

• Ongoing Work:– Re-survey of the machine for more accurate positioning (Sutter, Koeth,

Ponter)

– Re-measurement of magnetic fields (Bernal) and refinement of MagLi models (Kishek)

– Cross-checking of magnet modeling between WARP and ELEGANT (Cornacchia and Kishek)

– Benchmarking both codes against increasing volumes of experimental data: orbits, tunes, chromaticities, momentum compaction, resonances

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Comprehensive modeling (UMERGeometry WARP module)Comprehensive modeling (UMERGeometry WARP module)

WARP repository that includes:– descriptions and choice of models for every single lattice element

• quadrupoles, dipoles, steering dipoles, injection pulsed magnets

• Earth field data and Helmholtz coil information

• induction cells

– models of certain diagnostics and procedures for data processingparallel to those used in experiment

– Can read/write file formats for UMER settings from experiment

B0P0B1B2B3P1B4B5B6P2B7B8B9P3B10B11B12P4B13B14B15P5B16B17B18P6B19B20

B21P7B22B23B24P8B25B26B27P9B28B29B30P10B31B32

B33P11B34B35B36P12B37B38B39P13B40B41B42P14B43B44B45P15B46B47B48P16B49B50B51P17B52B53B54P18B55B56B57P19B58B59B60P20B61B62B63P21B64B65B66P22B67B68B69P23B70B71

B72P24B73B74B75P25B76B77

B78P26B79B80B81P27B82B83B84P28B85B86B87P29B88B89

B90P30B91B92B93P31B94B95B96P32B97B98H0B99P33B100B101B102B103B104H1P34H2B105P35B106B107

-1 0 1

-3

-2

-1

0

meters

met

ers

H0 B0B1 B2 B3B4B5H1 P0 H2 B6 P1B7 B8

0.0 0.2 0.4 0.6 0.8

0.0

0.2

metersR. Kishek

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ELEGANT Benchmark with experimentsELEGANT Benchmark with experiments

• Equilibrium Orbit (used ELEGANT to fit quadrupole displacement errors)

• Lattice and Dispersion function

• Chromaticity

• Momentum Compaction

Max Cornacchia

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Resonance Simulations with WARPResonance Simulations with WARP

Chao Wu

4-turn Fractional Tune from WARP

Δνcoh

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Longitudinal End Expansion Longitudinal End Expansion –– Effect on BeamEffect on Beam

WARP simulation prediction, 1998

R. Kishek

Z

Beam Current

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WARP Modeling of Beam End Erosion and ReWARP Modeling of Beam End Erosion and Re--bunchingbunching

Irv Haber, Brian Beaudoin

WARP Simulation

Experiment

Detector measures only peak-to-peak current

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d = 0.5 mm

WARP Simulation of Halo from SourceWARP Simulation of Halo from Source

2008

23 mA23 mA< 2007

KGrid

d

Halo Particles

d = 0.1 mm

R

R’

Haber, et al., NIM-A 606, 64 (2009).

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Halo StudiesHalo Studies

Investment in Halo Diagnostics (1st turn)– Fast imaging (~ 3 ns resolution)– Tomographic Phase Space Mapping – Optical Masking of Beam Core

Simulation Studies using WARP– Halo Origin, Collimation, and Regeneration

Z = 100 m

R-R’ R-R’

Z = 100 m

R-R’

Z = 0 m

see talk by Christos Papadopoulos

see talk by Ralph Fiorito

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Phase Space TomographyPhase Space Tomography

yy’x

RC6

RC3

RC9

Quad Screen

Stratakis, Kishek, Li, et al., PRSTAB 9, 112801 (2006).Stratakis, Tian, et al., Phys. Plasmas (Lett.) 14, 120703 (2007).Stratakis, Kishek, Fiorito, et al., PRSTAB 12, 020101 (2009).Stratakis, Kishek, Haber, et al., PRSTAB 12, 064201 (2009).

Tomography is the technique of reconstructing an image from its projections

space charge, solenoids,time-resolvedemittance growth and halo

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Simulationx

y

Tomography Diagnostic and WARP ModelingTomography Diagnostic and WARP Modeling

Experiment

tomography

D. Stratakis, 2007

Initial distribution

Downstream

R. Kishek, AAC 2002Uniform Focusing

X-Y

X-X’

SimulationPrediction

Memory of beamlets!

2.5-D WARP (PIC) Simulation Predictions vs. Tomography