STREAMER INITIATION AND PROPAGATION IN WATER WITH THE ASSISTANCE OF BUBBLES AND ELECTRIC FIELD INITIATED RAREFACTION Wei Tian a) and Mark J. Kushner b) a) Department of Nuclear Engineering and Radiological Sciences University of Michigan, Ann Arbor, MI 48109, USA b) Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, MI 48109, USA November 2011 GEC * Work supported by Department of Energy Office of Fusion Energy Science

 Introduction to plasma discharges in liquids  Breakdown mechanism: Initiation and propagation  Initiation: avalanche inside the bubble  Propagation: electric field rarefaction  Electric field emission  Dielectric constant reduction  Description of the model  Concluding Remarks AGENDA University of Michigan Institute for Plasma Science & Engr. GEC2011

 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. DISCHARGES IN LIQUIDS University of Michigan Institute for Plasma Science & Engr.  K. Schoenbach et al, Plasma Sources Sci. Technol. 17 (2008)  K. Shih et al, Plasma Process. Polym. 6 (2009), 729 GEC2011

BREAKDOWN MECHANISM University of Michigan Institute for Plasma Science & Engr.  Two competing theories of liquid breakdown  Electronic impact-ionization process within the bulk liquid  Breakdown process inside gas phase  Because of high molecular density in water, electronic impact-ionization should be virtually absent in bulk water in absence of E > many MV/cm  Electrons are known to be solvated in water very rapidly – must ionize very efficiently before solvation Local, low-density regions are likely required for breakdown GEC2011

BREAKDOWN MECHANISM University of Michigan Institute for Plasma Science & Engr.  B. Locke et al, Trans. Ind. Appl. 45, 630 (2009).  A. L. Kupershtokh et al, Tech. Phys. Lett. 32, 634 (2006). GEC2011  Increasing static pressure reduces likelihood for bubble formation.  Breakdown voltage increases due to lack of bubbles.   m bubbles  “The electric field increases the instability increment for the stratification along the field.”  “A strong electric field (1~100 MV/cm) can induce anisotropic decay into liquid and vapor phases for a fluid. ”  Evidence that large electric fields produce regions of lower density in liquids due to polarization forces.

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. GEC2011

MODELING PLATFORM: nonPDPSIM University of Michigan Institute for Plasma Science & Engr.  Radiation transport and photoionization:  Electric field emission GEC2011  The field emission occurs at the gas-liquid interface  The gas-liquid interface is treated as a solid surface  Field enhanced thermionic emission

CONFIGURATION University of Michigan Institute for Plasma Science & Engr.  A “generic” point-to-plane, cylindrically symmetric geometry used for study.  Powered electrode radius: 100  m  Bubble in contact with electrode radius: 50  m.  Outside boundaries grounded.  Inside the bubble, H 2 O at 1 atm; Outside the bubble, H 2 O L at liquid density.  Gas dielectric constant ε/ε 0 ~ 1; Liquid dielectric constant ε/ε 0 ~ 80. GEC2011

REPRESENTATIVE REACTIONS University of Michigan Institute for Plasma Science & Engr.  Reactions in Liquid Water e + H 2 O L ↔ e L + H 2 O L e L + H 2 O L ↔ H 2 O L - GEC2011  Reactions in Water Vapor e + H 2 O → e + e + H 2 O + e + H 2 O + → H + OH e + H → e + H* H* → H + h h + H 2 O → H 2 O + + e  Field Emission H 2 O L → e + H 2 O L + Electric Field Rarefaction Field Emission Liquid Water (H 2 O L ) Water Vapor (H 2 O) e e e

MIN MAX INITIATION INSIDE BUBBLES University of Michigan Institute for Plasma Science & Engr.  Bubble ~ 50  m  V max =+10 kV with rise time of 1.0 ns  Electric field emission occurs when strong electric field reaches the gas-liquid interface.  The electric field concentrates on the axis and leads the avalanche.  Positive charges outline the discharge and produce the electric field.  t (ns) ~ 1.0  [e] (cm -3 )  EF (MV/cm)  ρ (cm -3 ) GEC2011

PROPAGATION: E-FIELD RAREFACTION University of Michigan Institute for Plasma Science & Engr.  A streamer can produce its own electric field enhancement at the conductive tip.  The enhanced electric field at the tip exceeding a limit produces a phase-like transition, likely on an atomic scale.  In the model, densities, compositions and other phase-related properties are changed to produce a low-density volume.  The streamer extends itself into the new low- density area.  The loop continues until the streamer reaches the grounded electrode. GEC2011 E-field Enhancement Phase Transition Streamer Extension Low-density Regions

PROPAGATION University of Michigan Institute for Plasma Science & Engr. MIN MAX  Threshold ~ 1 MV/cm  V max =+10 kV with rise time of 1.0 ns  Streamer initiates inside the bubble first.  The electric field triggers the phase transition, in which the density decreases by about 3 orders.  Streamer extends itself into the changed area due to high E/N.  The potential is expelled ahead and compressed to produce strong electric field.  This mechanism makes the streamer propagating into water by itself.  Flood represents the electron density  Lines represent the electric potentials GEC ~ 1.7 ns

PROPAGATION: EFIELD EMISSION University of Michigan Institute for Plasma Science & Engr. MIN MAX  V max =+10 kV with rise time of 1.0 ns  The electric field is produced by positive charges and enhanced by dielectric constant difference.  The positive charge density is large due to electronic impact ionization at strong electric field.  A strong electric field emission occurs at the top interface because the electric field is strong there.  The emitted electrons intensify the electronic impact ionization so that the positive charge density is increased. GEC2011  ρ (cm -3 )  EF (MV/cm)  S e (cm -3 s -1 ) 0.0 ~ 1.7 ns

ELECTRIC FIELD EMISSION University of Michigan Institute for Plasma Science & Engr.  The work function used for liquid water is 1.7 ~ 1.9 eV.  Larger emission current results in larger propagation velocity.  The field emission current will not affect the streamer propagation until it reaches 0.1 A/cm 2. Work FunctionStreamer Velocity 1.7 eV3.82×10 7 cm/s 1.8 eV1.44×10 7 cm/s 1.9 eV0.37×10 7 cm/s GEC2011

PROPAGATION:SMALLER BUBBLE University of Michigan Institute for Plasma Science & Engr.  Bubble ~ 20 um  V max =+30 kV with rise time of 1 ns  The bubble is so small that the electron loss is huge and electron impact ionization cannot help avalanche.  Stronger field emission is needed to provide more seed electrons. GEC ~ 1.1 ns  Flood represents the electron density  Lines represent the electric potentials

PROPAGATION: DIELECTRIC REDUCTION University of Michigan Institute for Plasma Science & Engr. MIN MAX  The dielectric constant is not reduced much until the electric field reaches 5 MV/cm (E max ~ 1.5 MV/cm in the case).  The streamer becomes a little wider due to the dielectric constant reduction but not affected much.  Generally, it does not affect much.  K. Schoenbach et al, Plasma Sources Sci. Technol. 17 (2008)  [e] (cm -3 )  ε/ε0  ε/ε0 0.0 ~ 1.6 ns

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.  Electric field rarefaction may contribute to creating a low density channel, in which the streamer can propagate.  Field emission contributes to the propagation process and becomes more important for smaller bubbles.  The dielectric constant reduction is not important at the electric field ~ 1 MV/cm. GEC2011