Computational Accelerator Physics:
Working Group Summary
Thomas M. Antonsen Jr.
Institute for Research in Electronics and Applied Physics,
University of Maryland, College ParkMD 20742
Dan Gordon
Plasma Physics Division, Naval Research Laboratory, Washington DC, 20375
Icarus Research, Inc., P. O. Box 30780, Bethesda, Maryland 20824-0780
Abstract. The working group in computational accelerator physics at the Advanced Accelerator
Concepts Workshop held a series of meetings during the conference. This was the first year for this
working group. Presentations and discussion focused on both new algorithms and applications for
numerical simulation. Areas of interest included improved descriptions of beam dynamics, plasma
based acceleration, ion acceleration, and modeling of Radio Frequency (RF) sources.
1 [email protected]
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Phvsics 0-7354-0102-0/02/$19.00
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INTRODUCTION
Numerical simulation has become an integral part of the process of scientific
discovery from the investigation of basic physical phenomena to the design and
optimization of large systems. For this reason a new working group, devoted to
Computational Accelerator Physics was added to the Advanced Accelerator Concepts
Workshop. The role of the Computational Accelerator Physics working group was to
explore the range of issues where advances in computation can have impact on this
field. Table 1. lists the nine sessions including 33 speakers that comprised the group's
activities. Six of the sessions were held jointly with other working groups including
the High Energy Density, E-beam Driven Acceleration Schemes, Laser Plasma
Acceleration Schemes, and Beam Monitoring/Control working groups. A complete
list of presentations is included in the Appendix.
The topics of the group's discussions can be roughly organized into four groups as
illustrated in Table II. Talks were devoted to studies of beam dynamics and plasma
based acceleration schemes, and in each of these two areas to the development of new
algorithms and to applications of simulation to existing or planned experiments. The
following is an attempt to highlight the issues discussed in each of these areas.
Table 1: Schedule - Working Group #1 Computational Accelerator Physics
Monday, June
24
Tuesday, June
25
10:0012:30 PM
New AlgorithmsBeam dynamics I
Joint Session with
E-beam Driven
Accelerators
12:30-2:00
PM
2:00-3:20
PM
lunch
3:20-3:40
PM
3:40-5:30
PM
New AlgorithmsBeam dynamics II
break
Joint session with
High Energy
Density-Ion
Acceleration
lunch
Joint session with
Laser-Plasma
Acceleration
break
Wednesday, June
26
Joint Session with
Beam Generation/
Monitoring and
Control
Thursday, June
27
New algorithmsPlasma based
Acceleration
lunch
lunch
Excursions
Joint Session with
Beam Generation/
Monitoring and
Control
break
Joint session with
Laser-Plasma
Acceleration
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BEAM DYNAMICS: ALGORITHMS
The efficient calculation of the self-field interaction (space charge) between the
charged particles in a beam remains an active area of research. Presentations in this
area focused on the development of techniques to treat the interaction between
particles in sparse beams, the effects of conducting walls on the interaction force,
efficient methods for representing the phase space distribution of beams with strong
self interactions and beams with large energy spread.
Sparse beams present a challenge. In a sparse beam the charge density does not
fill space uniformly; there are large regions of space with no charge density. This
situation is particularly of interest when one considers beam-beam interactions. It is
also of interest in the context of galactic dynamics where galaxies tend to exist in
clusters. The main problem with sparse beams is that the standard method of
assigning charge density to a regular grid, and computing the self-potential on the grid
is inefficient.
Two presentations addressed methods for efficient calculation of the interaction
force in sparse beams. Ryne proposed a grid-based system appropriate for the case in
which two interacting but physically disjoint beams are present. Here, only the region
occupied by the beams is gridded. Within each region the charge and potential are
assigned to the grid. The potential is determined by discrete Fourier transform from
the charge density. The interaction between the physically separated areas can then be
determined by using a shifted Green's function. This approach is a generalization of
that developed by Hockney for calculation the potential corresponding to open
boundary conditions on a Cartesian grid. This approach has the capability to treat
interactions between the two beams as well as interactions among particles in each
beam. A second presentation, given by Adelmann, focused on so called "tree based
field solvers". This method of treating sparse beams consists of grouping particles in
Table 2: Topics/Issues
Computational Accelerator Physics
Advances in Algorithms
Applications
Beam Dynamics
• Calculation of self fields
• Moment schemes
Plasma Based Acceleration
• Reduced models
• lonization
• Versatile codes
• System Modeling
• Modeling Injectors
• Mixing in high space
charge beams
• Halo formation
• Laser Wakefield
• Plasma Wake field
• Ion Acceleration
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clusters and calculating the force on a given particle due to other particles differently if
the other particles are nearby or if they are distant. The force due to nearby particles is
calculated pair-wise based on the specific positions of the nearby particles, while the
force due to distant particles is calculated based on the center of charge of the cluster
to which the distant particles belong. In this method no grid is used to calculate fields.
Some of the issues which need to be addressed are: the establishment of benchmark
cases for the assessment of the efficiency and accuracy of this method, exploration of
the trade-off between the number of cluster-particle and particle-particle interactions,
and the degree to which this method can be parallelized. In discussions following the
session, Alex Freidman pointed out that an alternate method of modeling sparse beams
was to implement automatic mesh refinement (AMR) in PIC codes and that this
project was underway in his group.
In related talks Chen and Qian of MIT discussed Green's function approaches to
modeling space charge dominated beams. It was found that self-fields could
substantially affect beam confinement for bunched beams. A number of important
issues which need to be addressed a include: reconciliation of the current finding with
PIC codes that presumably include the same physics, extending the method to more
complicated structures than hollow conducting tubes, and assessment of the efficiency
of the Green's function approach for computations with large numbers of particles.
An important issue for analyzing current LWFA experiments is the modeling of
beams with large energy spreads. Most models of beam propagation assume that all
interacting particles have nearly the same axial velocity. This allows for calculation of
the electrostatic force between particles in the beam frame, or equivalently the
electromagnetic force in the lab frame. Fubianni and Dugan presented a model for
calculating the interaction force for beams with large energy and velocity spreads.
The approach consists of modeling the particle distribution function as shells in phase
space, and calculating the interaction between shells.
Two talks focused on reduced models for describing beam propagation. Wurtele
presented an approach to modeling beam relaxation based on expansion of the
distribution function in Hermite polynomials. An important issue is the truncation of
the expansion that must be made in any numerical realization. Wurtele was able to
demonstrate good agreement between the reduced model and PIC simulations for the
case of one dimension. The extension to higher dimensions remains open. An
interesting issue associated with truncations of this type is the damping of collective
beam modes. PIC simulations indicate the damping of low order modes is weak. The
Hermite expansion may offer an interesting way to investigate this effect. In a second
presentation, Ghalam of USC proposed a quasistatic model describing the beamelectron cloud interaction in circulating accelerator. The model is based on an
extension of the code QuickPIC developed to study wake field generation. The weak
interaction with a tenuous electron cloud produces effects after many kilometers of
propagation. Simulations reveal that it is important to include the cloud image charge
and consequently correct modeling of the boundary of the accelerator is important.
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BEAM DYNAMICS: APPLICATIONS
Numerical simulation can be used as a powerful tool to study emmitance
growth in space charge dominated beams. Kishek investigated the relationship
between phase space mixing and emmittance growth from a dynamical systems point
of view. In particular, the rate of separation of nearby particle trajectories was tracked
for beams undergoing relaxation to steady state. The motion in this case is in two
spatial dimensions in a time dependent, self-consistent potential. As the beam relaxed
the self-consistent potential decayed away. Thus, exponential divergence of orbits for
all time (and formal chaos) is not expected. Kishek identified various regimes based
on instantaneous rates of separation and attributed these to macroscopic (mixing due to
collective modes) and microscopic (mixing to discrete particle collisions) interactions.
Numerical simulation of beam dynamics finds use in both the design and
interpretation of experiments. However, detailed comparison between experiments
and simulation is often limited by knowledge of experimental conditions and
geometry. Haber reported time dependent simulations of a space charge dominated
beam. He commented that that comparison of his results with experiments required
knowledge of geometrical features of the gun, which were not well characterized.
Similarly, studies by Wangler comparing measured and simulated halo formation were
limited by imprecise knowledge of the injected electron beam.
In a related talk,
Freidman discussed improved methods for modeling beam distributions based on
measurements. Clearly this is an area requiring closer coupling between simulation
and experiment if more quantitative rather than qualitative predictions are needed.
An emerging development in the simulation community is the use of
integrated or "end to end" modeling tools. In this approach individual specialized
codes are used to simulate different parts of a system. Codes communicate with each
other through certain sets of shared data. The way this process works is illustrated in
Fig. 1 where a number of codes are used to simulate a heavy ion accelerator. The
codes involved include WARP (a 3D PIC code) for study of detailed beam and
electron dynamics, HERMES which is a multiple envelop model for rapid parameters
scans, SLV (a semi-Lagrangian Vlasov code for beam dynamics studies over a wide
range of densities, BEST which is a 8f code for reduced noise, and LSP developed by
Mission research which is an implicit EM PIC-fluid hybrid code for chamber transport
studies. Using this suite of codes it should be possible to study beam instabilities, halo
formation, electron production, and beam focusing for a specific accelerator design. A
similar approach is already used in the design of RF sources to drive accelerators. For
example, the "end to end" modeling of a magnicon as described by Yakovlov, includes
the linking of a gun simulation code, an RF interaction code, and a collector design
code, along with a magnetostatics code to determine the applied magnetic field
throughout the device.
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Data in the form of particle positions and momenta must be handed from code to
code to successfully simulate, design and optimize the magnicon. The integrated
modeling approach is distinct from and complementary to the usual practice of using
specialized research codes where phenomena are investigated in isolation. The
emergence of the integrated modeling approach is sign that the individual tools are
viewed as being sufficiently reliable.
ION ACCELERATION
Simulation of particle acceleration based on laser-solid interaction is
particularly challenging. Interactions occur in high-density plasmas where the skin
depth is much smaller than the system size. In addition, collisional and kinetic
processes can be important at the same time. Two numerical approaches to modeling
ion acceleration were discussed: PIC and Hybrid simulation. Hartmut Ruhl of General
Atomics Corporation presented simulations of microstructure in proton beams
produced by laser irradiation of a solid foil. The simulations were carried out using
the Plasma Simulation Code PSC. This is a 3D parallel PIC code that includes
collisional processes. To make simulation feasible the domain was taken to be small
(4|Lim x 4|Lim x 8|nm) and the interaction with the laser was not simulated. Instead an
energetic electron beam such as would be produced by laser plasma interaction was
injected on one side of the simulation.
Figure 1. Integrated modeling of a heavy ion accelerator, courtesy A. Friedman
126
The solid consisted of a heavy substrate with a thin proton film on the back side. The
protons are accelerated by the electric field created when energetic electrons attempt to
leave the solid. Microstructures on the substrate are imprinted in the proton beam and
can be imaged far from the surface in agreement with experiments. Chuang Ren used
the PIC code OSIRIS to simulate ion acceleration. These simulations included
interaction with the laser, but assuming that the target was pre-ionized. Shock
formation in the solid was studied and it was concluded that there are two distinct
mechanisms for front and back ion acceleration. In a related presentation Chen
studied electron beam initiated ion generation using PIC simulation. Hybrid
simulations of ion acceleration were presented by Campbell using the LSP code. This
is a 3-D fully relativistic, electromagnetic multi-species, semi-implicit PIC-hybrid. In
these simulations a larger and more realistic system volume could be simulated.
However, fine structures on the skin depth scale were not well resolved. Nevertheless,
two scaling regimes for ion extraction were observed: a modified Child-Langmuir
regime and sheath expansion regime. Simulations presented in this section revealed
that laser-solid interactions are rich in physics and that simulation will be a key tool in
understanding experiments.
However, the simulation of energetic particles
propagating through solid density matter remains a challenge. Processes occurring on
the scale of the skin depth can affect beam propagation over much longer distances.
PLASMA WAKEFIELD ACCELERATION
Simulation of plasma wake field acceleration has become an indispensable tool for
analyzing experiments. The UCLA-USC group presented simulations of the El 57 and
El62 experiments. The 3D PIC code OSIRIS was used for most of these simulations.
The parameters of the E57/E162 experiments are such that full format simulations are
practical. Details of the experiments such as the effects of beam ellipticity, density
gradients, and front to back asymmetry could all be investigated. For example,
comparison of the wake electric field on axis for the 3D version of OSIRIS and the 2D
version is illustrated in Fig 2. The similarity of these two plots implies that nonsymmetric effects such as hosing are not important for these parameters. This may not
be the case for higher density, longer interaction region parameters envisioned for the
"afterburner" concept.
Simulations by Joyce, using the ELBA code using
appropriately scaled parameters, suggest significant hose growth and beam loss due to
poor match of the beam to the channel as the beam energy changes. Hose growth can
be mitigated by using channels with rounded radial density profiles. However, this
comes at the expense of accelerating gradient.
Based on these observations, the most important simulation issue in plasma
wakefield acceleration is the ability to perform many simulations with "afterburner"
parameters. The need to perform many simulations is driven by the need to both plan
127
and diagnose experiments. The difficulty is that the interaction region is many plasma
wavelengths long. Thus, full format simulations, which resolve the plasma frequency,
will require many time steps. A solution to this problem is the development of quasistatic PIC codes such as QUICKPIC. In this approach, the plasma wake is calculated
assuming the beam parameters to be fixed on the plasma wave time scale. The beam
particles can then be advanced over much longer time scale in the presence of the selfconsistent plasma wake field.
LASER WAKEFIELD ACCELERATION: APPLICATIONS
Simulation of the 200 MeV LOA experiment generated great interest. In these
experiments an ultra-short laser pulse is injected into a gas jet and electrons are
accelerated from the rest. What is different in this experiment compared with previous
ones is that the laser pulse duration is only slightly greater that the plasma period.
Thus, the usual mechanism of excitation of forward Raman scattering can not be
invoked to explain the trapping of plasma electrons. Full PIC simulation is the tool of
choice in modeling this problem. Three different PIC codes were applied, OSIRIS by
lineouts along the center of the beam
lineouts along the center of the beam
z
[mm]
Figure 2. Comparison of the accelerating electric field from 2D and 3D OSIRIS
simulations of the El 62 experiment, courtesy of T. Katsouleas.
128
Mori of the UCLA group, TURBOWAVE by Gordon of NRL, and VLPL (Virtual
laser Plasma Laboratory) by Puhkov of to the University of Duesseldorf. The energy
gain of electrons in the simulations was predicted to be in the 100-200 MeV range, in
agreement with the experiments. All the simulations agreed that the trapping
mechanism is distinct from previous experiments in which self-modulation and Raman
instability was driven. A sample of the phase space from the TURBOWAVE
simulations of Gordon is shown in Fig. 3. Simulations by Puhkov raised the
possibility of the trapping of electrons and the formation of a quasi-monoenergetic
beam in the cavitation bubble following a short laser pulse. There still is controversy
within the community over the exact mechanism of particle acceleration. It now
appears that there may be several mechanisms working in different parameter regimes.
Simulation of the type presented in the working group will be essential in
understanding the mechanism operative in different experiments. Further, direct
simulation will become a needed tool in designing and optimizing particle injection
schemes. Full format simulations of these are just coming on line.
;i
m m ii m
m.
Figure 3. Phase space showing laser accelerated electrons as simulated by
TURBOWAVE, Courtesy D. Gordon
129
LASER WAKEFIELD ACCELERATION: ALGORITHMS
A hierarchy codes and models that describe laser plasma and energetic
particle beam plasma interactions is being developed as described in a review by Mori.
The principle approximations and simplifications that may or may not be used are:
fluid description versus particle description, full Lorenz force versus guiding center
ponderomotive force, full Maxwell's equations versus the laser envelope
approximation, and full dynamic wake versus the quasi static wake. Thus, there are
available, models ranging from full format PIC to quasistatic fluid. Table 3.
summarizes the codes discussed in working group.
Table 3. Codes used in plasma based acceleration studies
Owner/Developer
Code
Comments
OOPIC
OSIRI
VORPAL
UCB/Verboncouer, Tech-X
UCLA/Mori
Tech-X/Cary
VLPL
TURBO-WAVE
Puhkov
NRL/Gordon
PSC
Hartmut Ruhl
LSP
MRC/ Welch
WAKE
CdePT/UMD/ Antonsen
SIMLAC
NRL/ Penano
ELBA
NRL/ Joyce
QUICKPIC
UCLA/UMD/USC/ Mori
LBNL-Fluid
LBNL/ Shadwick
LEM
NRL/ Krall-Hubbard
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2DPIC lonization
3D PIC lonization
2D/3D PIC-Fluid
versatile
3D PIC
2D/3D PIC or
Ponderomotive
Guiding Center
3D PIC Boltzmann
collisions
3D PIC Hybrid
semi-implicit
2D Quasistatic
Particle/fluid
3D Quasistatic
Fluid
3D Beam Plasma(quasistatic)
3D Beam/Laser Plasma(quasistatic)
2D Fluid/ Dynamic
Wake
2D Quasistatic
Fluid
The principal advances in algorithms discussed in the working group centered on
reduced models, ionization physics and versatile codes. The code QUICKPIC will
offer full scale 3D modeling of long accelerators including the "afterburner". Results
were presented for the Plasma Wakefield Accelerator and shown to be in good
reasonable agreement with full PIC modeling. Progress on QUICKPIC was described
in a talk by Huang and Cooley. Work is currently underway in improving the field
description to include all components of the electromagnetic wake within the
quasistatics approximation. A reduced laser propagation model that will run with
QUICKPIC is under development.
Fluid simulations offer rapid modeling under clean, well defined conditions.
Shadwick of LBNL has developed a dynamic wake fluid model, which also solves the
full electromagnetic equations. Penano of NRL has pursued the quasistatic approach
and included many physical processes related to propagation in the atmosphere.
Because of there relative speed, these codes find use in exploring novel concepts.
An important process in advanced accelerators is ionization. Collisional ionization
was implemented by Tech-X and UCLA in their PIC codes. A presentation by
Dimitrov and Bruhwiler of TechX addressed the issue of collisional and tunneling
ionization. Cross sections were researched at length, but some gaps in knowledge still
remain. One issue that came up is that of charge conservation in PIC codes that model
ionization processes. However, after further consideration Gary asserted that the codes
are handling charge conservation properly. In addition to collisional ionization,
tunneling ionization is now part of many codes. Tunneling ionization induced blue
shifts were calculated by Dimitrov and compared with L'OASIS experiments.
Qualitative agreement with experiments was obtained. It was pointed out that the
conditions for the validity of the tunneling ionization formulae are only marginally
satisfied, and that possible more sophisticated models are needed.
As codes move from the single developer/research phase to the multi-user phase
the issue of versatility of the code becomes important. VORPAL (Tech-X)
exemplifies a re-usable yet efficient C++ framework for advanced accelerator
modeling. The code will be either fluid or PIC and will be any dimensionality. This
will allow users to seamlessly vary the level of sophistication of the physics model
will simulating different aspects of a given problem.
SUMMARY
Computation is well integrated into the advanced accelerator program. There is
close coupling between simulation and experiment. Experiments are designed and
extensively analyzed using a variety of codes. An indication of this fact is the six joint
sessions between the computational working group and other working groups at the
meeting. The joint session were well attended and included much lively discussion.
At the same time, new algorithms are being developed that will make computation
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more efficient and more reliable in the future. These algorithms span a range of
improvements, from more efficient ways to calculate particle-particle interactions to
multiple time scale algorithms that make possible simultaneous simulation of fast and
slow processes. Along with the development of new algorithms the physics content of
codes is improving. For example the addition of collisions and ionization to PIC codes
is a notable advance. Finally, new versatile codes are being developed that should be
of use to the user community and special application codes are being linked for "end to
end" modeling of systems.
APPENDIX: PRESENTATIONS IN THE WORKING GROUP
New Models and Algorithms for Simulating Beam Dynamics I
1 RobRyne, LBNL, "Parallel PIC Simulations of Beam-Beam Interactions"
2. Jonathan Wurtele, UCB, "Coupled Moment Expansion Model of Collective Beam
Dynamics"
3. Andreas Adelmann, LBNL and Paul Scherrer Institut, "Tree Based Field Solvers"
4. Ali Ghalam, USC, "Simulation of Electron-Cloud Instability in Circular
Accelerators using Plasma Models"
5. Chiping Chen, MIT, "Interactions of Intense Beams with Metal Walls"
New Models and Algorithms for Simulating Beam Dynamics II
6. Vyacheslav Yakovlev, OmegaP, "State of the Art Simulations of Magnicon
Amplifiers"
7. Bao Liang Qian, MIT, "Image Charge Effects on the Dynamics of Intense Ion
Beams.
8. Alex Friedman, LLNL and LBNL, "Simulations of beam dynamics in the presence
of 3D structures and high space charge"
Modeling Ion Acceleration
9. Hartmut Ruhl, GA, "Simulation of Ion Acceleration in Laser Solid Interactions"
10. Bob Campbell, SANDIA, "Ion acceleration and high energy density plasmas
using the LSP code"
11. Chuang Ren , UCLA, "Proton Acceleration Simulations"
12. Dimitre Dimitrov+David Bruhwiler, TechX, "Modeling Ionization Processes in
PIC Codes"
Modeling Plasma Wake Field Acceleration:
Joint Session with Working Group 4: E-Beam Driven Accelerators
132
13. Glen Joyce, NRL, "Plasma wake field simulations using ELBE"
14. Cheng-Kun Huang, UCLA , "Modeling E-162 Positron Wakefields"
15. Wei Lu,, UCLA, "Modeling of the E-164 Plasma Wakefield Accelerator
Experiment"
16. Tom Katsouleas, USC, "Modeling of Realistic Experimental Conditions in the E162 Plasma
Modeling Wake Field and Laser Acceleration I:
Joint Session with Working Group 6: Laser Plasma Acceleration
17. Joe Penano, NRL, "Raman forward scattering and self-modulation of laser pulses
in tapered channels."
18. Carl Schroeder, LBNL, "Chirped Pulse Evolution in LWFA"
19. Dimitre Dimitrov, TechX , "Simulation of laser propagation and ionization in
L'OASIS experiments"
Modeling Wake Field and Laser Acceleration II:
Joint Session with Working Group 6: Laser Plasma Acceleration
20. Dan Gordon, NRL, "Modeling the Acceleration of Background Electrons to 200
MeV in a Laser Wakefield Accelerator"
21. Alexander Pukhov,. /'Direct Laser Acceleration"
22. Eric Esarey, LBNL, "Simulations of Particle Injection in Plasma Accelerators "
23. Warren Mori, UCLA, "3D SMLWF Simulations with OSIRIS"
Advances in Modeling Beam Formation and Propagation
Joint Session with Working Group 7: Beam Generation/Monitoring and Control
24. Irv Haber, UMD, "PIC Simulation of Space Charge Dominated Sources"
25. Rami Kishek, UMD, "Modeling Mixing processes in Space Charge Dominated
Beams"
26. Gwenael Fubiani, LBNL, "Modeling Space Charge Fields in Relativistic Beams
with Energy Spread"
New Algorithms for Simulation of Plasma Based Acceleration
27. Cheng-Kun Huang, UCLA and James Cooley, UMD, "Development of a 3D
Quasi-static PIC code for Modeling Plasma and Laser Wake Field Acceleration"
28. John Gary, TechX, "Vorpal-A Flexible Parallel Simulation Code"
29. Suzhi Deng, USC , "Adding Ionization to OSIRIS"
133
30. Brad Shadwick, LBNL, "Fluid Simulations of laser wake field acceleration"
Advances in Modeling Beam Formation and Propagation
Joint Session with Working Group 7: Beam Generation/Monitoring and Control
31. Tom Wangler, LANL, "Computational and Experimental Studies of Beam Halo
Formation"
32. Alex Friedman, LLNL and LBNL, "Use of projectional phase space data to infer a
4D particle distribution
33. Yu-Jiuan Chen, LLNL, "Interaction of High Intensity Beams with X-ray
Converter Targets"
134