Simulation Technology & Applied Research, Inc. 11520 N. Port Washington Rd., Suite 201, Mequon, WI 53092 P: 262.240.0291 [email protected]

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.


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.


User interface

Embedded “help”

Project Workspace

Python window

Multiple projects & windows


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.


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


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


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


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


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.


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


Orbit near “equator” of SNS cavity


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.


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


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.


DC in RF module|E| for pi/2 phase advance per cell.

Only particles that exit downstream.


Close-up of one cell


Output particle spectra

Peaks correspond to distinct source regions within structure.


Adaptive mesh refinement (AMR)

• Idea is to use results from a previous analysis to refine the finite-element mesh in order to reduce errors.


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


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.


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.


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


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.

Documents

Simulation Technology & Applied Research, Inc. 11520 N. Port Washington Rd., Suite 201, Mequon, WI 53092 P: 262.240.0291 [email protected]