1. PLASMA DISCHARGE SIMULATIONS IN WATER WITH PRE-EXISTING BUBBLES AND ELECTRIC FIELD RAREFACTION Wei Tian and Mark J. Kushner University of Michigan, Ann Arbor, MI 48109 USA bucktian@umich.edu, mjkush@umich.edu 2 nd Michigan Institute for Plasma Science and Engineering (MIPSE) 21 September 2011, Ann Arbor, Michigan * Work supported by Department of Energy Office of Fusion Energy Science

2.  Introduction to plasma discharges in liquids  Breakdown mechanism: Initiation and propagation  Description of model  Initiation: breakdown inside the bubble  Propagation: electric field rarefaction  Concluding Remarks AGENDA University of Michigan Institute for Plasma Science & Engr. MIPSE_SEP2011_1

3.  Plasmas sustained in liquids and bubbles in liquids are efficient sources of chemically reactive radicals, such as O, H, OH and H 2 O 2.  Applications include pollution removal, sterilization and medical treatment.  The mechanisms for initiation of plasmas in liquids are poorly known. PLASMAS IN LIQUIDS University of Michigan Institute for Plasma Science & Engr. MIPSE_SEP2011_2  Plasma Sources Sci. Technol. 17 (2008) 024010  Plasma Process. Polym. 6 (2009), 729

4. BREAKDOWN MECHANISM University of Michigan Institute for Plasma Science & Engr. MIPSE_SEP2011_3  Due to the high atomic/molecular density in liquids, for a given voltage, E/N (Electric Field/Number density) is small.  Plasma breakdown, consisting of initiation and propagation of a streamer, typically requires a critically large E/N.  To achieve this E/N, breakdown requires a mechanism to rarefy the liquid or to provide sources of seed electrons.  Initiation  Pre-existing bubbles  Localized internal vaporization  Molecular decomposition  Electron-initiated Auger process  Propagation  Electric field rarefaction  Gas channel cavitation  Polarity effect

5. MODELING PLATFORM: nonPDPSIM  Poisson’s equation:  Transport of charged and neutral species:  Electron Temperature (transport coefficient obtained from Boltzmann’s equation: University of Michigan Institute for Plasma Science & Engr. MIPSE_SEP2011_4

6. MODELING PLATFORM: nonPDPSIM University of Michigan Institute for Plasma Science & Engr. MIPSE_SEP2011_5  Radiation transport and photoionization:  Electric field emission

7. INITIATION: PASCHEN’S CURVE FOR BUBBLES University of Michigan Institute for Plasma Science & Engr. MIPSE_SEP2011_6  The vapor phase in liquids will have pressures of at least 1 atm – usually the vapor of the liquid or the injected gas.  Even breakdown in these rarefied regions is challenging, needing to have large voltages.  Bubble (20 ~ 75  m )  Pressure (1 ATM)  Pd value (1 ~ 10 Torr cm)  Voltage (20 ~ 50 kV)  Some E/N “amplification” may be required, as in electric field enhancement due to geometry, permittivities or charging.  “Paschen’s law”, Wikipedia, Septemeber 21, 2011 (http://en.wikipedia.org/wiki/Paschen%27s_law)

8. CONFIGURATION University of Michigan Institute for Plasma Science & Engr. MIPSE_SEP2011_7  Sharp-Tip Electrode  Bubble ~ 75 um  Parallel Electrode  Bubble ~ 50 um  Parallel Electrode  Bubble ~ 20 um  Breakdown of liquids from pre-existing bubbles was numerically investigated.

9. MIN MAX MIPSE_SEP2011_8 INITIATION INSIDE BUBBLES University of Michigan Institute for Plasma Science & Engr.  Initiation processes inside the bubble within 0.1 ns  Initiation processes are associated with electron impact ionization, photo- ionization and field emission

10. MIN MAX MIPSE_SEP2011_9 SHARP-TIP ELECTRODE University of Michigan Institute for Plasma Science & Engr.  [e] (10 18 cm -3, 3 dec)  E-field (5.0 ~ 7.0 MV/cm)  S e (10 27 cm -3 s -1, 3 dec)  The sharp tip produces electric field enhancement to 5 MV/cm, E/N to 10,000 Td.  Electron density produces ionization of a few percent.  Electron impact ionization dominates over photo-ionization  [S photo ] (10 22 cm -3 s -1, 3 dec)

11. MIN MAX MIPSE_SEP2011_10 PARALLEL ELECTRODE: PHOTO-IONIZATION University of Michigan Institute for Plasma Science & Engr.  [e] (10 17 cm -3, 3 dec)  [EF] (0.8 ~ 1.8 MV/cm)  [S e ] (10 27 cm -3 s -1, 3 dec)  The electric field is enhanced due to the permittivity difference at the gas- liquid interface  Electron density is uniform due to uniform electric field inside the bubble  The electron impact ionization dominates over photo-ionization  [S photo ] (10 22 cm -3 s -1, 3 dec)

12. MIN MAX MIPSE_SEP2011_11 PARALLEL ELECTRODE: FIELD EMISSION University of Michigan Institute for Plasma Science & Engr.  The electric field is concentrated at the top of the bubble  Electrons are emitted from the top of the bubble, where the electric field is strong enough  The field emission assists the ionization  [e] (10 16 cm -3, 3 dec)  E-field (0.3 ~ 0.5 MV/cm)  S e (10 25 cm -3 s -1, 3 dec)  [S photo ] (10 22 cm -3 s -1, 3 dec)

13. PROPAGATION: E-FIELD RAREFACTION University of Michigan Institute for Plasma Science & Engr. MIPSE_SEP2011_12  “Liquids can become phase unstable such that gas channels form along electric field lines.”  A streamer can propagate itself. The electric field is expelled and advanced at the streamer tip, because of free charges inside the streamer and ion accumulation at the tip.  The enhanced electric field is so strong that a phase-like transition occurs there. The densities, compositions and other phase- related properties are changed respectively. As a result, a low-density area is created.  The streamer extends itself into the new low- density area. The loop continues until the streamer reaches the grounded electrode.  Plasma Process. Polym. 6 (2009), 729 E-field Enhancement Phase Transition Streamer Extension

14. PROPAGATION: PHOTO-IONIZATION University of Michigan Institute for Plasma Science & Engr. MIN MAX MIPSE_SEP2011_13  Gap = 1 mm  V max =30 kV, with rising time of 0.1 ns  Average E-Field ~ 0.3 MV/cm  Speed ~ 400 km/s  Flood represents the electron density  Lines represent the potentials

15. PROPAGATION: PHOTO-IONIZATION University of Michigan Institute for Plasma Science & Engr. MIN MAX MIPSE_SEP2011_14  The streamer is a little wider than the bubble, because the photo- ionization is isotropic  The photo-ionization is dominating in the bulk plasma; electron impact ionization only occurs at the head of the streamer  [e] (10 16 cm -3, 3 dec)  E-field (1.0 ~ 2.5 MV/cm)  S e (10 22 cm -3 s -1, 3 dec)  [S photo ] (10 25 cm -3 s -1, 3 dec)

16. PROPAGATION: FIELD EMISSION University of Michigan Institute for Plasma Science & Engr. MIN MAX MIPSE_SEP2011_15  Gap = 2 mm  V max =20 kV, with rising time of 0.1 ns  Average E-Field ~ 0.1 MV/cm  Speed ~ 100 km/s  Flood represents the electron density  Lines represent the potentials

17. PROPAGATION: FIELD EMISSION University of Michigan Institute for Plasma Science & Engr. MIN MAX MIPSE_SEP2011_16  The electric field is concentrated at the head of the streamer  The streamer originates from the bubble top and propagates toward the grounded electrode  Its head becomes wider and wider since it gets closer to grounded electrode  [e] (10 17 cm -3, 3 dec)  E-field (0.5 ~ 1.0 MV/cm)  S e (10 25 cm -3 s -1, 3 dec)  [S photo ] (10 22 cm -3 s -1, 3 dec)

18. CONCLUDING REMARKS University of Michigan Institute for Plasma Science & Engr.  The breakdown mechanism consists of two processes, initiation inside the bubble and propagation due to the electric field rarefaction  A large electric field, photo-ionization or field emission is needed to assist the initiation inside the bubble.  Electric field rarefaction may contribute to creating a low density channel, in which the streamer can propagate. MIPSE_SEP2011_17