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

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

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

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:

x

y

Particle Domain

0 Field Domainx

e-

Test of Image Space-Charge Calculation Using a Shifted Green Function Method

e+

cathode

Shifted-green function

Analytical solution

Xrsm vs. distance with/without space-charge forces during the emssion

Emission with space-charge

Emission without space-charge

Xrsm vs. distance with integrated Green function and standard Green function for space-charge forces calculation

Integrated Green function

Standard Green function

Xrsm vs. distance with/without image charge effect of cathode

With image charge effect

Without image charge effect

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

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

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

Zrms and Relative Energy Spread vs. Position