Transcript Document

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 the
DOE Grand Challenge in Computational Accelerator Physics,
Advanced Computing for 21st Century Accelerator Science and Technology
Project using resources at the
Advanced Computing Laboratory and the
National 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 )   G (r , r ' )  (r ' )dr ' ; r = (x, y,z)
N
 (ri)  h  G(ri  ri' )(ri' )
i '1
G ( x, y , z )  1 / ( x  y  z )
2
2
2
Direct summation of the convolution scales as N6 !!!!
N – grid number in each dimension
Green Function Solution of Poisson’s Equation (cont’d)
Hockney’s Algorithm:- scales as (2N)3log(2N)
- Ref: Hockney and Easwood, Computer Simulation using Particles, McGraw-Hill Book Company, New York, 1985.
2N
c(ri)  h  Gc(ri  ri' )c(ri' )
 (ri)  c (ri) for i = 1, N
i '1
Shifted Green function Algorithm:
 (r)   Gs(r,r')(r')dr'
F
Gs(r,r')  G(r  rs,r')
y
0
Particle Domain
Field Domain
x
x
Test of Image Space-Charge Calculation Using a Shifted Green Function Method
e+
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
Integrated Green function Algorithm for large aspect ratio:
2N
c(ri)   Gi(ri  ri' ) c (ri' )
i '1
Gi(r, r')   Gs(r, r') dr'


Ey
x (sigma)
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
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