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 Electron and Metastable Density Profiles Produced in Helium FIW Discharges

B. R. Weatherford and E. V. BarnatSandia National Laboratories

Z. Xiong and M. J. KushnerUniversity 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

Fast Ionization Waves (FIWs) Nanosecond-duration, overvoltage (> breakdown) E-fields

Diffuse volume discharge at elevated pressures High-energy electrons efficiently drive inelastic processes Ideal for large volume, uniform, high pressure production of:

Photons Charged particles Excited species

Proposed Applications: Pulsed UV light sources / laser pumping High-pressure plasma chemistry Plasma-assisted combustion Runaway electron generation

2

Current Understanding of FIWs Axial FIW propagation studied extensively

Capacitive probes Average E-fields, e- density Optical emission 2-D profiles, wave speeds Laser diagnostics Spatially resolved E-fields

Radial variations important, but still unclear Varying E-field? Higher density or Te? Photons?

Applications may require volume uniformity What do profiles tell us about the physics?

3

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 HV electrode inside Teflon

sleeve, grounded shield Imaged area: 20-140 mm from

ground electrode

Helium feed gas Pressure 1-20 Torr ~14 kV (open load) +HV pulses 20 ns duration, 3 ns rise time 1 kHz pulse rep rate

4

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

5

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)

Electron Densities vs. Pressure Density maps @ fixed rep

rate & voltage, 1-16 Torr ICCD delay time: 100 ns

after FIW, 20 ns window Peak densities on scale of

1011 cm-3 for all pressures Low P center-peaked High P wall-peaked Max uniformity, ne at

intermediate pressure

6

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 calibration (B. Yee)

Same general trends, but less drastic than ne Center-peaked to volume-

filling / uniform Similar FIW decay lengths

7Wavefront Motion

Incr

easi

ng P

ress

ure

Simulation Results - nonPDPSIM 2-D fluid simulation

Photon transport Stepwise ionization Plasma chemistry EEDF calculated from two-

term expansion of Boltzmann equation

Same voltage pulse shape as in experiment

Simulations produce similar results as LCIF Ne ~ 1011-1012 cm-3

Trend in radial profiles with variable pressure

Wave velocities ~ cm/ns8

1 Torr Profiles 16 Torr Profiles

(Xiong and Kushner)

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

9

Experiment: ne, NHe* have different 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

E-field, Effective Te Distributions

10

Simulations Strong radial E near wall Exceeds runaway e- threshold (~210 Td in He) Radial E exceeds axial E in and behind FIW front

1 Torr: Mean e- energy nearly uniform E-field fills much of the volume

16 Torr: Mean e- energy highest at wall E-field drops rapidly away from wall Electrons cool via collisions

16 Torr – Te and E

1 Torr – Te and E

Axis

Axial & Radial E, 16 TorrInside wavefront

Wall

Axial & Radial E, 16 TorrBehind wavefront

Axis Wall

Effect of Runaway Electrons σiz peaks near 150 eV, σHe* at 30 eV Radial fast e- flux in cylindrical geometry

competing processes: Focusing of e- flux, scales as 1/r Loss of “fast” flux via inelastic collisions Cooling of fast electrons via elastic collisions

1-D production profiles estimated due to radial runaway e- flux from wall

11

Electron cooling separated e- and He* profiles

Fixed energy vs. r captures pressure trend

Ionization, 23S Cross-sections

30 eV e-, constant energy 4 Torr, with collisional cooling

Initial Energies

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

Intermediate pressures highest densities and uniformity 2-D fluid simulations capture similar trends in ne

Peak e- densities of 1011-1012 cm-3; shift in radial profiles Predicts metastable distributions which track e- densities

Radial E-fields yielding runaway e- may explain the difference Runaway electrons are difficult to capture in fluid model Dropoff in E at high pressure fast e- from walls lose energy High energy ionization; Lower energy metastable production Energy decay along radius causes spatial separation in profiles

12

Thank you!

Questions? Comments?

This work was supported by the Department of Energy Office of Fusion Energy Science Contract DE-SC0001939.

13