High Energy and Nuclear Physics
Unified Accelerator Library: SIMBAD
N. D'Imperio and A. Luccio
Working in collaboration with computational physicists at BNL's Collider
Accelerator Department, we have continued development on a Particle-in-Cell
(PIC) [1] code to model collective beam effects in two and three dimensions.
The code was formerly known as ORBIT and is being integrated into the
Unified Accelerator Libraries (UAL) [2] as the SIMBAD component for the
modeling of space charge.
UAL provides a framework in which the tracking of particles takes place by
pushing a “bunch” of macroparticles through a lattice using the TEAPOT code,
which has also been integrated in UAL. Space charge is calculated separately
using SIMBAD. Once all particles have reached a certain location, their
charge density is calculated by binning to a grid. The potential Ф is found
by solving the Poisson equation with the perfectly conducting wall boundary
conditions:
Space charge force components (with coefficients to account for both the
electrostatic and magnetic action) are calculated as derivatives of the
potential and applied to each macro particle in the transverse direction.
Longitudinal space charge is calculated by binning the particles
longitudinally and following the formalism presented in [1]. In a ring with
long longitudinal bunches, the transverse motion can be uncoupled from the
longitudinal, and the Poisson equation can be solved in parallel in many
longitudinal beam segments.
The parallelization of SIMBAD is implemented differently in 2-d as opposed
to 3-d. In 2-d, the parallelization is implemented by dividing the macro
particles among the processes and collectively calculating the forces on
each mesh. In 3-d, each process takes a number of longitudinal slices and
calculates the space charge forces only within its own slices. This
parallelization requires load balancing that considers both the number of
particles and the number of slices. This is accomplished using a genetic
algorithm [3, 4]. Figure 1 shows parallel decomposition of the bunch and the
resulting division of the beam. Figure 2 shows the parallel efficiency of a
simulation using the load balancing algorithm [4].
 |
 |
| Figure 1. Bunch decomposition and load balancing.
(a) A bunch of macro particles in an RF bucket with accompanying
lines to indicate the boundaries for each of 8 processes. (b)
Genetic algorithm produces an optimal balance between number of
particles per process and number of slices per process. |
Figure 2. Efficiency improvements of up to 50% are realized with
load balancing.
  
is the runtime of a serial solution with problem size n and
is the runtime of a parallel solution with P processes.
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The code was used to model high intensity beams in the
Alternating Gradient Synchrotron at BNL to study its suitability as a proton
driver [3]. In addition, the code is being used to study the long-term
impedance effects of the SIS100 accelerator currently being designed and
built at GSI in Darmstadt, Germany.
UAL has been ported to run on the BlueGene Light supercomputer where
beam-beam interaction will be simulated.
References
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[1] Chao, A.W. Physics
of Collective Beam Instabilities in High Energy Accelerators.
Wiley, 1993.
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[2] Malitsky, N. and Talman, R. Unified Accelerator Libraries.
In Computational Accelerator Physics, AIP Conference Proceedings
391, J.J. Bisognano and A.A. Mondelli, Eds., pp. 337-342 (1997).
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[3] Luccio, A. and D'Imperio, N. Simulation of the AGS as a
proton driver. ICFA Beam Dynamics Mini Workshop on Space Charge
Simulation, Oxford, UK, Trinity College, April 2-4, 2003,
www-bd.fnal/icfa/workshops (2003).
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[4] D'Imperio, N.L., et al. Parallel 3-D Space Charge Calculations in
the Unified Accelerator Library. EPAC 2006, July 2006, http://accelconf.web.cern.ch/AccelConf/e06/INDEX.htm.
Last Modified: January 31, 2008
Please forward all questions about this site to:
Claire Lamberti
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