2-D Profiles of Electron and Metastable Densities in Helium Fast Ionization Wave Discharges. B. R. Weatherford and E. V. Barnat Sandia National Laboratories Z. Xiong, B. T. Yee, M. J. Kushner, and J. E. Foster University of Michigan. Overview. Background on Fast Ionization Waves - PowerPoint PPT Presentation
Photos placed in horizontal with even amount of white space Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND NO. 2011-XXXXP 2-D Profiles of Electron and Metastable Densities in Helium Fast Ionization Wave Discharges B. R. Weatherford and E. V. Barnat Sandia National Laboratories Z. Xiong, B. T. Yee, M. J. Kushner, and J. E. Foster University of Michigan 16 Torr Axial Position, mm Radial Position, mm 20 40 60 80 100 120 140 -10 -5 0 5 10 0 5 10 x 10 10
Transcript
Photos placed in horizontal position with even amount of white space
between photos and header
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND NO. 2011-XXXXP
2-D Profiles of Electron and Metastable Densities in Helium Fast Ionization Wave Discharges
B. R. Weatherford and E. V. BarnatSandia National Laboratories
Z. Xiong, B. T. Yee, M. J. Kushner, and J. E. FosterUniversity of Michigan
16 Torr
Axial Position, mm
Rad
ial P
osit
ion,
mm
20 40 60 80 100 120 140-10
-505
10
0
5
10x 10 10
Overview Background on Fast Ionization Waves
Basic Description of FIW Propagation Current Understanding of FIW Discharges
Experimental & Simulation Setup (w/ Xiong & Kushner, U. Mich.)
Discussion of Results Propagation Velocity Electron Density Profiles Metastable Density Profiles Calculated Electric Fields
Influence of Radial E-Fields on FIW Profiles Laser Absorption Spectroscopy Study (w/ Yee & Foster, U. Mich.)
Large volume, uniform, high pressure production of:Photons, charged particles, and excited species
Interesting Science: High voltage + short timescales + fast wave speeds = Hard to capture! Large values of E/N Efficiently drives ionization/excitation processes
• Applied voltage accelerates electrons toward anode• Reverse-directed avalanche electron multiplication• Electrons move to shield potential @ anode• Region vacated by electrons = positive space charge
• Photons move ahead of wavefront, add to preionization
FIW Propagation – Positive Polarity
6
Ionization Wavefront Propagation
• Process continues along length of the tube• Potential gradient moves away from anode• FIW wavefront = moving region of positive space charge + ionization• Residual plasma remains behind wavefront
• Weak fields relatively little excitation
Current Understanding of FIWs Axial FIW propagation studied extensively
Capacitive probes Average E-fields, e- density[1]
Optical emission 2-D profiles, wave speeds[2-3]
Radial variations important, but still unclear Varying E-field? Higher density or Te? Photons?
Applications may require volume uniformity What process causes the FIW shape to change?
What do profiles tell us about the physics?
7
Incr
easi
ng P
ress
ure
Vasilyak (1994)
Taka
shim
a (2
011) Positive Polarity Negative Polarity
Helium FIW, 20 Torr, 11 kV
Experimental Setup - Chamber Discharge Tube: 3.3 cm ID x
25.4 cm long Coaxial layout: low inductance HV electrode inside Teflon
sleeve, grounded shield Imaged area: 20-140 mm from
2-D LCIF Diagnostic Scheme 2-D maps of electron densities acquired from
helium line intensity ratios Pump 23S metastables to 33P with 389 nm laser Electron collisions transfer from 33P 33D Image LIF @ 389 nm (33P-23S) and LCIF @ 588 nm
(33D-23P) after the laser pulse Ratio depends linearly on e- density
9
109 1010 1011 101210-3
10-2
10-1
100
Electron density (cm-3)109 1010 1011 1012
10-2
10-1
109 1010 1011 101210-3
10-2
10-1
100
109 1010 1011 1012
10-2
10-1
Data Set A: AEff = ANom Data Set B: AEff >> ANom (During laser excitation)
Rat
io to
[l] t
o 38
9 nm
l=707 nml=707 nm
Rat
io 0
f 447
nm
to 5
87 n
m
Rat
io to
[l] t
o 38
9 nm
Rat
io 0
f 447
nm
to 5
87 n
m
Electron density (cm-3)
kTe=0.5 eV
kTe=1 eV
kTe=2 eV
kTe=4 eVkTe=6 eV
kTe=0.5 eV
kTe=1 eV
kTe=2 eV
kTe=4 eVkTe=6 eV
l=389 nm l=389 nm
kTe=2 eV kTe=2 eV
109 1010 1011 101210-3
10-2
10-1
100
Electron density (cm-3)109 1010 1011 1012
10-2
10-1
109 1010 1011 101210-3
10-2
10-1
100
109 1010 1011 1012
10-2
10-1
Data Set A: AEff = ANom Data Set B: AEff >> ANom (During laser excitation)
Rat
io to
[l] t
o 38
9 nm
l=707 nml=707 nm
Rat
io 0
f 447
nm
to 5
87 n
m
Rat
io to
[l] t
o 38
9 nm
Rat
io 0
f 447
nm
to 5
87 n
m
Electron density (cm-3)
kTe=0.5 eV
kTe=1 eV
kTe=2 eV
kTe=4 eVkTe=6 eV
kTe=0.5 eV
kTe=1 eV
kTe=2 eV
kTe=4 eVkTe=6 eV
l=389 nm l=389 nm
kTe=2 eV kTe=2 eVBarnat (2009)
Timing & High Voltage Waveform Reflected energy: ~85% (V²) Long HV cable (15.4 m)
used to separate incident& reflected pulses
ICCD opticallysynchronized to FIW t0 = initial detection of 389
emission without laser Reflected pulse: t = 170 ns Interrogation: 100-120 ns
Radiation-photon transport Includes stepwise ionization EEDF from two-term expansion
of Boltzmann equation Same pulse shape as experiment
Approx. open load pre-pulse:14 kV peak applied at anode
Assumptions: 0.1% O2 concentration
(photoionization) Initial ne = 108 cm-3
11
(Xiong and Kushner)
Results - FIW Velocities FIW speed estimated
from optical emission intensities vs. time 389 nm & 588 nm emission
FIW Speed: 5 – 20 mm/ns Peaks @ moderate Pgas 1 Torr: stalls @ x = 40 mm Decay along tube length
Due to residual E-field behind wavefront
12
Wavefront Motion
= 389 nm = 588 nm
Distance to Cathode, mm
FIW Speed and ne: Comparison Model & experiment agree in several ways:
Comparable wave velocities: Experiment: 0.5 – 2.0 cm/ns, peaks at 2-4 Torr Simulation: 0.5 – 1.5 cm/ns, peaks at 8 Torr
Trend in e- density and ionization rate: Peaks at intermediate pressure, then decreases Transition from center-heavy to wall-heavy “hollow” profile Weak ionization behind wavefront, conserves spatial profile
Absolute densities are sometimes different Experiment: 5x1010 – 3x1011 cm-3
Simulation: 5x1010 – 8x1012 cm-3
Model e- and He* profiles always identical13
Density Profiles – 1 Torr Electrons, metastables
are center-peaked In both LCIF and Model
Production stops @ x = 40 mm Corresponds with decay
of FIW speed Weak ionization in
residual plasma Electrons, metastables
track one another in simulation
14
1 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
1
2
3x 10 11
LCIF Measurements
Simulation Results
Ne,cm-3
NHe*, arb.
Ne,cm-3
Se,cm-3-s-1
Density Profiles – 4 Torr
More volume-filling than @ 1 Torr
Maximum electron, metastable densities
Corresponds to maximum FIW speeds in experiment
Wave traverses the entire gap
15
4 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
1
2
3x 10 11
LCIF Measurements
Simulation Results
Ne,cm-3
NHe*, arb.
Ne,cm-3
Se,cm-3-s-1
Density Profiles – 8 Torr
Electron densities shift to off-center peak Asymmetry due to
slight offset in outer conductor?
Radial shift predicted by simulation
Metastable profile still volume-filling
Residual ionization follows ne profile 16
8 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
0.5
1
1.5
2x 10 11
LCIF Measurements
Simulation Results
Ne,cm-3
NHe*, arb.
Ne,cm-3
Se,cm-3-s-1
Density Profiles – 16 Torr
Electron densities strongly wall-peaked
Simulation shows excellent agreement in electron profile shape
Metastable densities volume-filling, with slight shoulder off-axis
17
16 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
5
10x 10 10
LCIF Measurements
Simulation Results
Ne,cm-3
NHe*, arb.
Ne,cm-3
Se,cm-3-s-1
Metastable distribution
1 Torr
20 Torr
Helium Metastable
Radial position (mm)-10 -5 0 5 10
LIF
(k C
ount
s)
0.0
0.5
1.0
1.5
2.0
Electron densities
Radial position (mm)-10 -5 0 5 10
0.0
0.2
0.4
0.6
0.8 10 mm
75 mm
140 mm
Radial position (mm)-10 -5 0 5 10
0.0
0.5
1.0
1.5
2.0Helium Metastable
Radial position (mm)-10 -5 0 5 10
LIF
(kC
ount
s)
0
1
2
3
4
Electron densities(x1011 e/cm3)
1 Torr
20 Torr
140 mm
75 mm
X = 10 mm
Radial Profiles – Experimental
18
Low Pressure:Center-peaked
ne and He*
High Pressure:Concave ne
profile
High Pressure:Broad He*
profile
16 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
5
10x 10 10
Electrons vs. Metastables
19
Experiment: Different ne, NHe* radial profiles @ high pressure Metastables shifted to center
Model: ne, NHe* track each other Model results rule out:
Volume photoionization Photoelectrons from wall
ne
16 Torr Profiles - Simulation
NHe*
Key Questions:• Why are these
profiles different?• What does this say
about FIW physics?
He* Profiles - Experiment
(Behind wavefront)
ne
NHe*
Top: ExperimentBottom: Simulation
Energy Deposition in Wavefront
20
Simulations Strong radial E near wall Radial E exceeds axial E just behind FIW front
Radial E-field fills much of the volume
Radial E-field drops rapidly away from wall
16 Torr1 Torr
Axial E
Radial E
Electric field exceeds runaway e- threshold
(~210 Td in He)
Cross Sections & Path Lengths
21
Cross-sectionsGround Ionization, Metastable
Mean Free Paths vs. PressureIonization & Metastable
• σiz peaks near 150 eV, σHe* near 25 eV• Path lengths drastically diverge above 30 eV
Tube Diameter
Ionization
Metastable
1 Torr
4 Torr
16 Torr
1-D Fast Electron Model Simple 1-D model assumptions:
Discretize radial position & electron energies @ each position Initial fast e- flux, radially inward, originating @ wall: Electrons lose energy via collisions:
Elastic, Excitation from ground state, Ionization from ground state Flux Conservation:
Gain & Loss Terms:
Solve (iteratively) for to find:22
Model Results: Fixed Initial Energy Sample of results from band of 55-65
eV initial energy e- flux All curves normalized to 1 @ wall Competition of effects:
Low Pressure: 1/r focusing of flux High Pressure: Attenuation & e- Cooling
0.5 Torr: Se center-peaked SHe* also center-peaked
2 Torr: Se more uniform SHe* center-peaked, but broad
8 Torr: Se wall-peaked SHe* peaks off-axis, near wall
23
Varied Pressure: 55-65 eV e-
Model Results: Fixed Pressure
24
Varied Energy, 8 Torr Pressure fixed @ 8 Torr Solved for various energy
“bands” at wall, 10 eV wide Little divergence for 20 eV
electrons Higher energies:
Short Ionization Pathlength Long Metastable Pathlength Divergence in Profiles
Spatial separation is influenced by:• Neutral Pressure
• Fast e- Energy Distribution
1-D Electron Model Limitations Not included:
Stepwise ionization Randomization of electron motion (2-D) Electrons which pass through origin Axial component of fast electron flux
But still qualitatively captures… Center-to-wall transition in radial profiles Low pressure:
Center-peaked e- density and metastables Metastables slightly broader, as seen in LCIF
High pressure: Wall-peaked e- densities Broadened metastable profiles, closer to axis than e- profiles
What does a more sophisticated model say?25
● Parallel effort to study FIW processes – Ph.D. Thesis for B. Yee● Advantages
Immediate temporal evolution of NHe* Ground-Metastable excitation rates (from pulse duration & initial ne) Effective e- Temperature & E/N (if electrons are local) Some kind of info on e- energies in wavefront (even if nonlocal)
Plasma induced emission (PIE) measured w/ monochromator more constraints on energy distribution
Global Model/CRM under development (Yee & Foster)1. Energy balance to calculate e- energies from applied pulse2. Collisional radiative model PIE from energies & densities3. Measure metastable & electron densities4. Input densities into CRM, calculate emissions of various transitions5. Compare to measured PIE does it match what’s expected from
E/N? If not, why? validity of E/N in FIW wavefronts.
30
First-order Example
During Pulse Buildup
If valid? E/N
Summary 2-D maps of electron and 23S metastable densities in a positive
polarity He FIW measured using LCIF/LIF Center-peaked ne at low pressure, wall-peaked at high pressure Metastable profiles shift from center-peaked to volume-filling 2-D fluid simulations capture similar trends in ne
Center-to-wall transition, trends in FIW velocity, ne profiles Predicts metastable distributions which track e- densities
Radial E-fields yielding runaway e- may explain the difference Strong E-field @ wall (~kTd) = source of fast “runaway” electrons Dropoff in E at high pressure e- from walls lose energy High energy ionization; Lower energy metastable production Energy decay along radius causes spatial separation in profiles
Laser absorption measurements of He* + CRM may yield more information on electron energetics in the FIW 31
Thank you!
Questions? Comments?
This work was supported by the Department of Energy Office of Fusion Energy Science Contract DE-SC0001939.
References:1. S. M. Starikovskaia, N. B. Anikin, S. V. Pancheshnyi, D. V. Zatsepin, and A. Yu. Starikovskii.
Plasma Sources Sci. Tech., 10:344–355, 2001.2. K. Takashima, I. V. Adamovich, Z. Xiong, M. J. Kushner, S. Starikovskaia, U. Czarnetzki, and D.
Luggenholscher. Phys. Plasmas, 18:083505, 20113. L. M. Vasilyak, S. V. Kostyuchenko, N. N. Kudryavtsev, and I. V. Filyugin. Phys. Uspekhi, 37:247-
269, 1994.
32
Electron Densities vs. Pressure Density maps @ fixed
rate & voltage, 1-16 Torr Peak densities on scale
of 1011 cm-3 for all pressures
Low P center-peaked High P wall-peaked Volume-filling, max. ne
at intermediate pressure
33
1 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
1
2
3x 10 11
2 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
1
2
3x 10 11
4 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
1
2
3x 10 11
8 Torr
Axial Position, mmRa
dial P
ositio
n, mm
20 40 60 80 100 120 140-10
-505
10
0
0.5
1
1.5
2x 10 11
16 Torr
Axial Position, mm
Radia
l Posi
tion,
mm
20 40 60 80 100 120 140-10
-505
10
0
5
10x 10 10
Wavefront Motion
Incr
easi
ng P
ress
ure
Key Questions:What causes the transition in e- densities?Can we explain this with a model?
Metastable Densities vs. Pressure Helium 23S metastable
profiles, 1-16 Torr Relative densities from
LIF intensities Laser absorption
measurements for absolute values (B. Yee)
Similar trends, but less drastic than ne Center-peaked to volume-
filling / uniform Similar FIW decay lengths
34Wavefront Motion
Incr
easi
ng P
ress
ure
Electron Profiles vs. Pressure
35
1 Torr
16 Torr8 Torr
4 Torr
t = 100 ns
Time Dependence After FIW
36
Electron Density 23S Metastable Density
• Shape of radial profile established by 40 ns• Ionization in residual plasma conserves shape after initial formation
• Profile dictated by energy deposition in wavefront
Line Profiles
37
Absorption lines fit to Voigt profile w/ Doppler & Pressure Broadening
