The Heavy Ion Fusion Virtual National Laboratory Vay 9/10/03 Mesh Refinement for Particle-In-Cell Plasma Simulations: application to Heavy-Ion-Fusion 18 th International Conference on Numerical Simulation of Plasmas Cape Cod, Massachusetts September 10, 2003 J.-L. Vay, P. Colella, P. McCorquodale, D. Serafini, B. Van Straalen Lawrence Berkeley National Laboratory A. Friedman, D.P. Grote Lawrence Livermore National Laboratory
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The Heavy Ion Fusion Virtual National Laboratory Vay 9/10/03 Mesh Refinement for Particle-In-Cell Plasma Simulations: application to Heavy-Ion-Fusion 18.
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The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Mesh Refinement for Particle-In-Cell Plasma Simulations: application to Heavy-Ion-Fusion
18th International Conference on Numerical Simulation of Plasmas
Cape Cod, Massachusetts
September 10, 2003
J.-L. Vay, P. Colella, P. McCorquodale, D. Serafini, B. Van StraalenLawrence Berkeley National Laboratory
A. Friedman, D.P. GroteLawrence Livermore National Laboratory
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Outline
• Issues in coupling Electrostatic PIC with AMR
• Examples
• Joint project to couple electrostatic PIC and AMR at LBNL
• Conclusion
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Electrostatic PIC+AMR: issues
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Electrostatic: possible implementations
• Given a hierarchy of grids, there exists several ways to solve Poisson
• Two considered:
1. ‘1-pass’• solve on coarse grid • interpolate solution on fine grid boundary • solve on fine grid different values on collocated nodes
2. ‘back-and-forth’ • interleave coarse and fine grid relaxations • collocated nodes values reconciliation same values on collocated nodes
Patch grid
“Mother” grid
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Self-force test
particle trapped in fine gridded patch
Can we reduce its magnitude?
0 100 200 300 400 500
25
26
X
reference case linear - 1p linear - bf quad. - 1p quad. - bf
X
T
0
10
20
30
• 2-grid set with metallic boundary;
Patch grid
“Mother” grid
Metallic boundary
MR introduces spurious force,
Test particle
v
one particle attracted by its image
Spurious “image”
as if
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
y
x
y
Line
arQ
uadr
atic
1 pass
x
Back and forth • 1 pass: self-force about one order of magnitude lower on collocated nodes
can reduce self-force by depositing charge and gathering force only at collocated nodes in
transition zone
Self-force log|E|
• 1 pass also offers possibility to use coarse grid solution in transition zone
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
global error larger with BF than 1P BF: Gauss’ law not satisfied; error transmitted to coarse grid solution
y
Line
arQ
uadr
atic
1 pass
x
y
x
Back and forth
x
Back and forth
VV
S
d/dSdD
N// refrefGlobal error
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Electrostatic issues: summary
• Mesh Refinement introduces spurious self-force that has a repulsive effect on a macroparticle close to coarse-fine interface in fine grid, but:
- real simulations involve many macroparticles: dilution of the spurious force
- for some coarse-fine grid coupling, the magnitude of the spurious effect can be reduced by an order of magnitude by interpolating to and from collocated nodes in band in fine grid along coarse-fine interface
- we may also simply discard the fine grid solution in band and use coarse grid solution instead for force gathering (or ramp)
• some scheme may violate Gauss’ law and may introduce unphysical non-linearities into “mother” grid solution: hopefully there is also dilution of the effect in real simulations– we note that our tests were performed for a node-centered
implementation and our conclusion applies to this case only. For example, a cell-centered implementation does strictly enforce Gauss’ Law and results may differ.
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Electrostatic PIC+AMR: examples
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Time-dependent modeling of ion diode risetime
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
3D WARP simulation of HCX shows beam head scrapping Rise-time = 800 ns
beam head particle loss < 0.1%
z (m)
z (m)
x (
m)
x (
m)
Rise-time = 400 nszero beam head particle loss
Can we get even cleaner head with faster rise-time? Optimum?
How good is our ability to model it?
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
1D time-dependent modeling of ion diodeEmitter Collector
V V=0d
virtual surface
di
Vi
tIQ
d
VχI
2i
2/3i
I (A
)
Time (s)
N = 160t = 1nsd = 0.4m
“L-T” waveform
MR patch suppresses long wavelength oscillation; Adaptive MR patch suppresses front peak
Ns = 200
irregular patch in di
Time (s)
x0/x~10-6!
3
max
t4
3
t
V
V(t)
time
curr
ent
0.0 1.00.0
1.0
t/
V/V
max
Lampel-Tiefenback
AMR ratio = 16
irregular patch in di + AMR following front
Time (s)
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Current rise-time in STS500 experiment vs WARP run
• Applied voltage measured from experiment input in WARP run
• using aggressive (x1000) non-uniform mesh refinement in emitter area allows high-fidelity modeling of fast current rise-time
Exp.WARP
Exp.WARP
Z (m)
X (
m)
T (s) T (s)
I (m
A)
I (m
A)
T (s)
V (
kV)
Applied voltage
T (s)
V (
kV)
Applied voltage
No MR With MRCurrent history (Z=0.62m) Current history (Z=0.62m)
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Shorter rise-time using optimized voltage waveform
T (s)
V (
kV)
T (s)
I (m
A)
• Novel technique based on decomposition of field solution in WARP predicts a voltage waveform which extracts a flat current at emitter
• Despite slight beam head erosion, rise-time very sharp at exit of diode
• We were able to answer our questions by using mesh refinement
ExistingOptimized
Existing Optimized
Voltage Current at Z=0.62m
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Example of PIC-AMR calculation using WARP-RZSteady-state study of a diode
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Prototype axisymmetric AMR implemented in WARPrz
Base grid 56x640
Multipliers:– cells along each axis, ngf– number of particles, npf
Mesh refinement: factor-of-2 finer grid in emitter patch
Multipliers:– cells along each axis, ngf– number of particles, npf
Mesh refinement: factor-of-2 finer grid in emitter patch
~ 4x saving in computational cost for quasi same result
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Effort to couple PIC and AMR at LBNL: Chombo library
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
• Researchers from AFRD (PIC) and NERSC (AMR-Phil Colella’s group) collaborate to provide a library of tools that give AMR capability to PIC codes (on serial and parallel computers)
• The way it works
• First beta version released a few months ago: being tested with WARP (Heavy Ion Fusion main Particle-In-Cell code)
There is a LDRD effort at LBNL to couple PIC and AMR
PIC
Advance particles
Do other things
Receive forces
Send particles
Setup grid hierarchy
Deposit charge
Solve fieldsGather forces
AMR
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Example of WARP-Chombo injector field calculation
Chombo grid hierarchy can handle very complex geometry
The Heavy Ion Fusion Virtual National Laboratory
Vay 9/10/03
Conclusion
• PIC and AMR are numerical techniques that have proven to be very valuable in various fields and combination may lead to more powerful tools for plasma modeling
• The implementation must be done with care; at the least, when interpreting simulation results, we must have in mind that:– refinement introduces spurious self-forces– Gauss’ law violations, spuriously anharmonic forces may be
associated with some schemes
• Using 1-D and 2-D axisymmetric prototypes, we have shown that AMR can be used in PIC simulations with great efficiency
• There is an ongoing LDRD effort (AFRD+NERSC) to introduce AMR in PIC in a form of a library (Chombo) which can be linked with existing codes
• Electromagnetic PIC poses additional challenges due to EM waves (see poster)