impact-t - a 3d parallel beam dynamics code for modeling high brightness beams in photo-injectors ji...
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IMPACT-T - A 3D Parallel Beam Dynamics Code for Modeling High Brightness Beams in Photo-Injectors
Ji Qiang Lawrence Berkeley National Laboratory
Work performed under the auspices of theDOE Grand Challenge in Computational Accelerator Physics,
Advanced Computing for 21st Century Accelerator Science and Technology Project using resources at the
Advanced Computing Laboratory and theNational Energy Research Scientific Computing Center
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What is new in the IMPACT-T code?
• Integrated Green method to accurately compute the space-charge forces for a beam with large aspect ratio
• Shifted Green method to efficiently compute the space-charge forces from the image charge
• Multiple slices/bins to handle the beam with large energy spread
• Parallel implementation on high performance computer to allow multiple million, high resolution simulation
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Green Function Solution of Poisson’s Equation
; r = (x, y,z) ')'()',()( drrrrGr
(ri) h G(rii '1
N
ri' )(ri' )
)(/1),,( 222 zyxzyxG
Direct summation of the convolution scales as N6 !!!!N – grid number in each dimension
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Green Function Solution of Poisson’s Equation (cont’d)
F(r) Gs(r,r')(r')dr'Gs(r,r') G(r rs,r')
c(ri) h Gc(rii '1
2N
ri' )c(ri' )
(ri) c(ri) for i = 1, N
Hockney’s Algorithm:- scales as (2N)3log(2N)- Ref: Hockney and Easwood, Computer Simulation using Particles, McGraw-Hill Book Company, New York, 1985.
Shifted Green function Algorithm:
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x
y
Particle Domain
0 Field Domainx
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e-
Test of Image Space-Charge Calculation Using a Shifted Green Function Method
e+
cathode
Shifted-green function
Analytical solution
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Xrsm vs. distance with/without space-charge forces during the emssion
Emission with space-charge
Emission without space-charge
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Xrsm vs. distance with integrated Green function and standard Green function for space-charge forces calculation
Integrated Green function
Standard Green function
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Xrsm vs. distance with/without image charge effect of cathode
With image charge effect
Without image charge effect
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Green Function Solution of Poisson’s Equation
c(ri) Gi(rii '1
2N
ri' )c(ri' )
Gi(r,r') Gs(r,r')dr'
Integrated Green function Algorithm for large aspect ratio:
x (sigma)
Ey
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A Benchmark Example: in collaboration with C. Limborg (SLAC)
1nC
10ps square pulse,
1 mm uniform transverse laser pulse
No Thermal emittance
110MV/m
Solenoid 2.541 kG
1nC
10ps square pulse,
1 mm uniform transverse laser pulse
No Thermal emittance
110MV/m
Solenoid 2.541 kG
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Xrms vs. Position
• Parallel simulation w/ IMPACT-T using 1M particles is 2x faster than simulation w/ PARMELA using 100K particles
• Reasonable agreement for test case with azimuthal symmetry
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Zrms and Relative Energy Spread vs. Position