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Simulation Technology & Applied Research, Inc.11520 N. Port Washington Rd., Suite 201, Mequon, WI 53092P: 262.240.0291 [email protected] www.staarinc.com
Progress in Dark Current and Multipacting Modeling in the
Analyst Finite Element Package*
J. F. DeFord and B. Held
Advanced Accelerator Concepts Workshop 2008Santa Cruz, CAJuly 29, 2008
* Work supported by the Department of Energy Office of Science SBIR Program (DE-FG02-05ER84373 and DE-FG02-05ER84374)
Simulation Technology & Applied Research, Inc. www.staarinc.com
Presentation Topics
• Particle tracking on tetrahedral meshes.• Parallel scaling.• Particle emission models.• Multipacting statistics/output data.• Dark current statistics.• Particle-based adaptive mesh refinement.• Ongoing work. Work has greatly benefited from a strong
collaboration with I. Gonin, N. Solyak and others in Technical Division at FNAL.
Work has greatly benefited from a strong collaboration with I. Gonin, N. Solyak and others in Technical Division at FNAL.
Simulation Technology & Applied Research, Inc. www.staarinc.com
What is Analyst???
• Finite-element based support for electromagnetics.
• 3D electrostatics, magnetostatics, driven-frequency, and eigenmodes. 2D eigenmodes (RZ and XY).
• Particle tracking.• Third-party solvers (ES-PIC, time-domain).• Embedded CAD, meshing, visual/numerical
post-processing.• Python-based scripting.• Focus on large problems, parallel
processing.• Interface runs on Windows, solvers on
Windows/Linux.
Simulation Technology & Applied Research, Inc. www.staarinc.com
User interface
Embedded “help”
Project Workspace
Python window
Multiple projects & windows
Simulation Technology & Applied Research, Inc. www.staarinc.com
Particle tracking on FE meshes
• Explicitly track each element (find entrance and exit points).
• Use finite-element basis functions instead of interpolated fields.
• Use an adaptive time-step.
Resonant orbit in spoke cavity (courtesy of I. Gonin, et al., Technical Division, FNAL.
Simulation Technology & Applied Research, Inc. www.staarinc.com
Updating equations/process
• Use position/momentum at element entrance to determine exit point.• Repeat calculation using exit momentum and compare.• If difference is too large, introduce intermediate node and repeat.
pcm
pEBp
mE
m
qr
m
pr
2222 1
1
)(4
)(0
2
0 ttrrt
trr
tBpm
Eqptpp
00000
1
Simulation Technology & Applied Research, Inc. www.staarinc.com
Parallel scaling• Particle decomposition:
– Distribute particles across processors.
– Efficient scaling because particles do not interact.
• Domain decomposition (under development):– Distribute mesh across processors (use virtual machine mechanism).
– Potentially poor scaling because particles must be transferred between processors.
0
2
4
6
8
10
12
14
16
0 5 10 15
T1/T
N
Number of Processors
Particle Decomposition Parallel Scaling
Perfect Scaling
1.3M Tracks
62.7M Tracks
Simulation Technology & Applied Research, Inc. www.staarinc.com
Parallel job queue/virtual machines• Distributes multiple analyses over cluster nodes based on problem size to make
best use of cluster.• Requires batch system be present on distributed memory systems (Sun Grid
Engine, PBS, etc.).• For optimization algorithms that can generate concurrent evaluation points, ideal
scaling should be attainable.• This capability has been used on a workstation to allow simultaneous use of
multiple cores for separate analyses.cpu/core 1
cpu/core 2
cpu/core 3
cpu/core n
cpu/core 4
VM 1
VM 2Batchsystem
VM 2
Virtual machinesBatch systemUser interface Procs./cores
Simulation Technology & Applied Research, Inc. www.staarinc.com
Emission models
• Fowler-Nordheim field emission:
• Secondary emission:
sEBs
s
s
eAE
E
EJ
/2
5.19252.46 1083.6
exp101054.15.0
max2
max
272.2 KK
p eK
KYSEY
cos0 /, BKBK
Simulation Technology & Applied Research, Inc. www.staarinc.com
Multipacting statistical functionsFunction name Symbol Definition
Counter CF(n) Total number of resonant primaries1.
Normalized counter NCF(n)
Enhanced counter EF(n)
Normalized enhanced counter NEF(n)
Yield YF(n)
Growth factor R(n)
Distance D(n)
ji
n
ji
ii yYYnEF ,
1
)(
MNNNN
nCFnNCF pfe
e
)(
)(
i
iYnCFnNEF
)(
1)(
nYYYnYF iiii /logexpmax)(
i
iirf YnEF
PnR
)()( Y
tlog
1
202
0,,0,,)( ini ii
inii eec
nd
rr
1A “resonant primary” is a primary resulting in a particle chain that includes at least one particle that survives for n impacts.
Simulation Technology & Applied Research, Inc. www.staarinc.com
More multipacting output data
• Particle tables.
• Per-impact yield vs. location on model surface.
IndexField
Strength ImpactsStarting phase
<Phase Advance>
STD Phase Advance <KE> (eV) STD KE <Yield> STD Yield
Cumulative Yield
Distance Function
V/m Degrees Degrees mP0 30000000 20 0.47 179.99 27.05 5.44 0.25 0.07 0.00 0.00 0.46P1 30000000 20 0.52 179.99 27.04 5.44 0.25 0.07 0.00 0.00 0.46P2 30000000 20 0.58 179.99 27.03 5.45 0.25 0.07 0.00 0.00 0.46P3 30000000 20 0.63 179.99 27.01 5.45 0.24 0.07 0.00 0.00 0.46P4 30000000 20 0.68 179.99 26.98 5.46 0.24 0.07 0.00 0.00 0.46P5 30000000 20 1.10 180.03 27.57 5.31 0.29 0.07 0.00 0.00 0.46P6 30000000 20 5.13 179.99 27.05 5.44 0.25 0.07 0.00 0.00 0.46P7 30000000 20 5.39 179.99 27.04 5.44 0.25 0.07 0.00 0.00 0.46
Simulation Technology & Applied Research, Inc. www.staarinc.com
Orbit near “equator” of SNS cavity
Simulation Technology & Applied Research, Inc. www.staarinc.com
Dark current computations
• Similar to multipacting problem only not looking for resonances.
• Field emit from surface, track particles until model exit.
• Collect statistics on where particles exit, exit energies, etc.
• Mark particles so that they can be filtered in various ways, e.g., by which model surface they exited.
Simulation Technology & Applied Research, Inc. www.staarinc.com
Field emission in RF cavity
RF cavity and mode E-field pattern.
Analytic peak FN emission in peak field region.
Peak field regions.
30eV6.4
Simulation Technology & Applied Research, Inc. www.staarinc.com
Field emission (2)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
-80.0
-60.0
-40.0
-20.0
0.0
20.0
40.0
60.0
80.0
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Js
(A/m
^2)
Es (M
V/m
)
RF Phase (radians)
Surface Field Strength Es (MV/m)
Instantaneous Js (A/m^2)
Field emission region.
Peak surface E-field over 1 RF cycle.
Expected FN current density.
Simulation Technology & Applied Research, Inc. www.staarinc.com
DC in RF module|E| for pi/2 phase advance per cell.
Only particles that exit downstream.
Simulation Technology & Applied Research, Inc. www.staarinc.com
Close-up of one cell
Simulation Technology & Applied Research, Inc. www.staarinc.com
Output particle spectra
Peaks correspond to distinct source regions within structure.
Simulation Technology & Applied Research, Inc. www.staarinc.com
Adaptive mesh refinement (AMR)
• Idea is to use results from a previous analysis to refine the finite-element mesh in order to reduce errors.
Simulation Technology & Applied Research, Inc. www.staarinc.com
AMR: Population metric
• Based upon idea that mesh should be refined in regions with relatively large local particle populations.
• Metric is given by:
where is the total number of particles that traverse the k-th element.
kP
kk
kk eEPe max
Simulation Technology & Applied Research, Inc. www.staarinc.com
AMR: Complexity metric
• Based upon an estimate of the complexity of the orbits within an element.
• Metric is of the form:
where is the total number of particle knots within the k-th element.
kN
kk
kk eENe max
Particle track from previous element stopped at boundary.
Track computed within element. Dots are “knots” in track.
Exit location found to begin tracking in next element.
Simulation Technology & Applied Research, Inc. www.staarinc.com
Antenna housing
Antenna
Second mode resonates at about 810 MHz
Cavity with HOM coupler1
1Model of TESLA HOM coupler courtesy of I. Gonin, Technical Division, FNAL.
Simulation Technology & Applied Research, Inc. www.staarinc.com
Adaptive mesh refinement
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07
Aver
age
Yiel
d
Peak E-field on Axis (V/m)
33K Elements
89K Elements
262K Elements
853K Elements
32
1 1
2
3
# elements # tracks (M) Time (sec.)
33K 7.97 81/1110
89K 31.3 499/5428
262K 109 2.26K/27.0K
853K 339 16.6K/112K
Simulation Technology & Applied Research, Inc. www.staarinc.com
Ongoing work
• Adding more user control over primary and secondary models.
• More visualization/animation options for particles.
• Domain decomposition for tracking runs.• Job management enhancements to support
combined field-solve/particle track AMR loop.