1. 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. Barnat Sandia National Laboratories Z. Xiong and M. J. Kushner University of Michigan

2. 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

3. 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 T e ? Photons?  Applications may require volume uniformity  What do profiles tell us about the physics? 3 Increasing Pressure Vasilyak (1994) Takashima (2011) Positive Polarity Negative Polarity Helium FIW, 20 Torr, 11 kV

4. 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

5. 2-D LCIF Diagnostic Scheme  2-D maps of electron densities acquired from helium line intensity ratios  Pump 2 3 S metastables to 3 3 P with 389 nm laser  Electron collisions transfer from 3 3 P  3 3 D  Image LIF @ 389 nm (3 3 P-2 3 S) and LCIF @ 588 nm (3 3 D-2 3 P) after the laser pulse  Ratio depends linearly on e- density 5 Barnat (2009)

6. 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 10 11 cm -3 for all pressures  Low P  center-peaked  High P  wall-peaked  Max uniformity, n e at intermediate pressure 6 Wavefront Motion Increasing Pressure Key Questions: What causes the transition in e - densities? Can we explain this with a model? Key Questions: What causes the transition in e - densities? Can we explain this with a model?

7. Metastable Densities vs. Pressure  Helium 2 3 S metastable profiles, 1-16 Torr  Relative densities from LIF intensities  Laser absorption measurements for calibration (B. Yee)  Same general trends, but less drastic than n e  Center-peaked to volume- filling / uniform  Similar FIW decay lengths 7 Wavefront Motion Increasing Pressure

8. 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  N e ~ 10 11 -10 12 cm -3  Trend in radial profiles with variable pressure  Wave velocities ~ cm/ns 8 1 Torr Profiles 16 Torr Profiles (Xiong and Kushner)

9. Electrons vs. Metastables 9  Experiment: n e, N He* have different radial profiles @ high pressure  Metastables shifted to center  Model: n e, N He* track each other  Model results rule out:  Volume photoionization  Photoelectrons from wall nene 16 Torr Profiles - Simulation N He* Key Questions: Why are these profiles different? What does this say about FIW physics? Key Questions: Why are these profiles different? What does this say about FIW physics? He* Profiles - Experiment (Behind wavefront) nene N He* Top: Experiment Bottom: Simulation

10. E-field, Effective T e 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 – T e and E 1 Torr – T e and E Axis Axial & Radial E, 16 Torr Inside wavefront Wall Axial & Radial E, 16 Torr Behind wavefront Axis Wall

11. Effect of Runaway Electrons  σ iz peaks near 150 eV, σ He* 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, 2 3 S Cross-sections 30 eV e-, constant energy 4 Torr, with collisional cooling Initial Energies

12. Summary  2-D maps of electron and 2 3 S metastable densities in a positive polarity He FIW measured using LCIF/LIF  Center-peaked n e 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 n e  Peak e- densities of 10 11 -10 12 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

13. Thank you!  Questions?  Comments? This work was supported by the Department of Energy Office of Fusion Energy Science Contract DE-SC0001939. 13