K.H. Schoenbach

Old Dominion University, Norfolk, Virginia, United States

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Publications (473)475.08 Total impact

  • Muhammad Arif Malik · David Hughes · Richard Heller · Karl H. Schoenbach
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    ABSTRACT: The energy deposition and the ozone generation in a shielded sliding discharge were compared with those of a simple surface discharge and a pulsed corona discharge in atmospheric pressure air and oxygen. All discharges were generated by applying 160 ns, high voltage pulses. Under the same conditions, the highest energy deposition per pulse was obtained with the shielded sliding discharge. The energy deposition was lower by a factor of four for the surface discharge plasma and by an order of magnitude for the pulsed corona discharge plasma. Replacing air with the more electronegative oxygen caused a decrease in the deposited energy due to electron attachment. The threshold voltage for plasma formation in oxygen in a shielded sliding discharge was approximately 5 kV, three times less than that of the surface discharge (≥15 kV) and four times less than that of the pulsed corona discharge (≥20 kV). A new finding of this study is that, whereas the decrease in energy in the pulsed corona discharge was ≥50 %, and that of the simple surface discharge ≥40 %, it was negligible in the shielded sliding discharge. Since the ozone generation scales with energy density, the results show that plasma reactors based on the nanosecond sliding discharge principle have major advantages in compactness, ignition voltage, and in the use of oxygen, rather than air, compared to surface discharges and corona discharges.
    Plasma Chemistry and Plasma Processing 07/2015; 35(4). DOI:10.1007/s11090-015-9611-3 · 2.06 Impact Factor
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    Iurii Semenov · Shu Xiao · Dongkoo Kang · Karl H. Schoenbach · Andrei G. Pakhomov
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    ABSTRACT: We tested if picosecond electric pulses (psEP; 190kV/cm, 500ps at 50% height), which are much shorter than channel activation time, can activate voltage-gated (VG) channels. Cytosolic Ca(2+)was monitored by Fura-2 ratiometric imaging in GH3 and NG108 cells (which express multiple types of VG calcium channels, VGCC), and in CHO cells (which express no VGCC). Trains of up to 100psEP at 1kHz elicited no response in CHO cells. However, even a single psEP significantly increased Ca(2+)in both GH3 (by 114±48nM) and NG108 cells (by 6±1.1nM). Trains of 100psEP amplified the response to 379±33nM and 719±315nM, respectively. Ca(2+)responses peaked within 2-15s and recovered for over 100s; they were 80-100% inhibited by verapamil and ω-conotoxin, but not by the substitution of Na(+)with N-methyl-D-glucamine. There was no response to psEP in Ca(2+)-free medium, but adding external Ca(2+)even 10s later evoked Ca(2+)response. We conclude that electrical stimuli as short as 500ps can cause long-lasting opening of VGCC by a mechanism which does not involve conventional electroporation, heating (which was under 0.06K per psEP), or membrane depolarization by opening of VG Na(+)channels. Copyright © 2015 Elsevier B.V. All rights reserved.
    Bioelectrochemistry (Amsterdam, Netherlands) 05/2015; 105. DOI:10.1016/j.bioelechem.2015.05.013 · 4.17 Impact Factor
  • Muhammad Arif Malik · Karl H. Schoenbach · Richard Heller
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    ABSTRACT: A coupled surface dielectric barrier discharge is reported and compared with a surface dielectric barrier discharge with respect to the spatial distribution of the plasma streamers, the energy dissipation in the discharge plasma, the scalability of the discharges, and their efficiency for ozone synthesis and nitric oxide conversion from air. Negative streamers were found to be more effective for the chemical reactions than positive streamers. Scaling of the discharges was achieved by: (i) employing multiple interconnected electrodes in the same space and (ii) operating stacked discharge chambers in parallel in a compact configuration. The increase in efficiency caused by the two scaling methods allowed us to obtain ozone concentrations of 1-9 g/N m(3) with an energy yield of 100-70 g/kWh and nitric oxide conversions of 10-95% with an energy cost of 20-80 eV/molecule from an initial concentration of similar to 330 ppm in air. The results are explained on the basis of the streamer development in the two barrier discharge configurations and the results are compared with those reported in the literature.
    Chemical Engineering Journal 11/2014; 256:222–229. DOI:10.1016/j.cej.2014.07.003 · 4.32 Impact Factor
  • Amy Donate · Niculina Burcus · Karl Schoenbach · Richard Heller
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    ABSTRACT: The presence of increased temperature for gene electrotransfer has largely been considered negative. Many reports have published on the lack of heat from electrotransfer conditions to demonstrate that their effects are from the electrical pulses and not from a rise in temperature. Our hypothesis was to use low levels of maintained heat to aid in gene electrotransfer. The goal was to increase gene expression and/or reduce electric field. In our study we evaluated high and low electric field conditions from 90 V to 45 V which had been preheated to 40 °C, 43 °C, or 45 °C. Control groups of non-heated as well as DNA only were included for comparison in all experiments. Luciferase gene expression, viability, and percent cell distribution were measured. Our results indicated a 2–4 fold increase in gene expression that is temperature and field dependent. In addition levels of gene expression can be increased without significant decreases in cell death and in the case of high electric fields no additional cell death. Finally, in all conditions percent cell distribution was increased from the application of heat. From these results, we conclude that various methods may be employed depending on the end users desired goals. Electric field can be reduced 20-30% while maintaining or slightly increasing gene expression and increasing viability or overall gene expression and percent cell distribution can be increased with low viability.
    Bioelectrochemistry 08/2014; 103. DOI:10.1016/j.bioelechem.2014.08.007 · 4.17 Impact Factor
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    ABSTRACT: Experiments with CHO cells exposed to 60 and 300 ns pulsed electric fields with amplitudes in the range from several kV/cm to tens of kV/cm, showed a decrease of the uptake of calcium ions by more than an order of magnitude when, immediately after a first pulse, a second one of opposite polarity was applied. This effect is assumed to be due to the reversal of the electrophoretic transport of ions through the electroporated membrane during the second phase of the bipolar pulse. This assumption, however, is only valid if electrophoresis is the dominant transport mechanism, rather than diffusion. Comparison of calculated calcium ion currents with experimental results showed that for nanosecond pulses, electrophoresis is at least as important as diffusion. By delaying the second pulse with respect to the first one, the effect of reverse electrophoresis is reduced. Consequently, separating nanosecond pulses of opposite polarity by up to approximately hundred microseconds allows us to vary the uptake of ions from very small values to that obtained with two pulses of the same polarity. The measured calcium ion uptake obtained with bipolar pulses also allowed us to determine the membrane pore recovery time. The calculated recovery time constants are on the order of ten microseconds.
    Bioelectrochemistry 08/2014; 103. DOI:10.1016/j.bioelechem.2014.08.015 · 4.17 Impact Factor
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    ABSTRACT: A nonthermal plasma system based on simultaneously formed positive and negative streamers on either side of a dielectric layer is described. The coupled sliding discharge (CSD) reactor based on this concept was found to be scalable by stacking and operating multiple electrode assemblies in parallel, similarly to the shielded sliding discharge (SSD) reactor reported earlier. A comparison of the two systems showed that although the energy density in the CSD reactor was lower, the efficiency for NO conversion and ozone synthesis from dry air were significantly higher. The energy cost for 50 % NO removal was similar to 30 eV/molecule compared to similar to 60 eV/molecule in the case of the SSD under the same conditions of 330 ppm initial NO concentration in air. The energy cost decreased to similar to 12 eV/molecule in both cases when NO was mixed with plasma-activated air at the outlet of the reactor to utilize ozone for NO conversion i.e., indirect plasma treatment. The energy yield for ozone generation from dry air was at similar to 70 g/kWh, comparable in both systems. The results show that the concept of a CSD, as that of SSDs, allows the construction of compact, efficient plasma reactors.
    Plasma Chemistry and Plasma Processing 07/2014; 34(4):871-886. DOI:10.1007/s11090-014-9528-2 · 2.06 Impact Factor
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    ABSTRACT: The nonthermal plasma generated in a shielded sliding discharge reactor was used to reform diesel for the hydrocarbon-selective catalytic reduction (HC-SCR) of NOx on Ag/Al2O3 catalysts. Compared with raw diesel, the reformed diesel enhanced the NOx reduction efficiency, mitigated hydrocarbon poisoning of the catalyst and reduced the fuel penalty for the HC-SCR reaction. The NOx conversion values obtained with a commercial Ag/Al2O3 catalyst exceeded that of a 2.0 wt% Ag/Al2O3 catalyst prepared by wet impregnation. A significant amount of NH3 was produced as a by-product during the HC-SCR reaction, which suggests that further NOx conversion enhancement can be achieved by placing a second NH3-SCR catalyst in series with the Ag/Al2O3 catalyst.
    Plasma Chemistry and Plasma Processing 07/2014; 34(4):825-836. DOI:10.1007/s11090-014-9551-3 · 2.06 Impact Factor
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    ABSTRACT: Nanoelectroporation of biomembranes is an effect of high-voltage, nanosecond-duration electric pulses (nsEP). It occurs both in the plasma membrane and inside the cell, and nanoporated membranes are distinguished by ion-selective and potential-sensitive permeability. Here we report a novel phenomenon of bioeffects cancellation that puts nsEP cardinally apart from the conventional electroporation and electrostimulation by milli- and microsecond pulses. We compared the effects of 60- and 300-ns monopolar, nearly rectangular nsEP on intracellular Ca(2+) mobilization and cell survival with those of bipolar 60 + 60 and 300 + 300 ns pulses. For diverse endpoints, exposure conditions, pulse numbers (1-60), and amplitudes (15-60 kV/cm), the addition of the second phase cancelled the effects of the first phase. The overall effect of bipolar pulses was profoundly reduced, despite delivering twofold more energy. Cancellation also took place when two phases were separated into two independent nsEP of opposite polarities; it gradually tapered out as the interval between two nsEP increased, but was still present even at a 10-µs interval. The phenomenon of cancellation is unique for nsEP and has not been predicted by the equivalent circuit, transport lattice, and molecular dynamics models of electroporation. The existing paradigms of membrane permeabilization by nsEP will need to be modified. Here we discuss the possible involvement of the assisted membrane discharge, two-step oxidation of membrane phospholipids, and reverse transmembrane ion transport mechanisms. Cancellation impacts nsEP applications in cancer therapy, electrostimulation, and biotechnology, and provides new insights into effects of more complex waveforms, including pulsed electromagnetic emissions.
    Cellular and Molecular Life Sciences CMLS 04/2014; 71(22). DOI:10.1007/s00018-014-1626-z · 5.81 Impact Factor
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    ABSTRACT: We have numerically studied the delivery of subnanosecond pulsed radiation to biological tissues for bioelectric applications. The antenna fed by 200 ps pulses uses an elliptical reflector in conjunction with a dielectric lens. Two numerical targets were studied: one was a hemispherical tissue with a resistivity of 0.3-1 S/m and a relative permittivity of 9-70 and the other was a realistic human head model (HUGO). The electromagnetic simulation shows that despite tissue heterogeneity of the human head, the electric field converges to a spot 8 cm in depth and the spot volume is approximately 1 cm × 2 cm × 1 cm in both cases when using only the reflector and a lens as an addition. Rather than increasing as it approaches the converging point, the electric field decreases strongly with distance from the skin to the converging point due to tissue resistive loss. The electric field distribution, however, can be reversed by making the dielectric lens lossy with the two innermost layers being partially resistive. The lossy lens causes an attenuation of the electric field near the axis, but the electric field generated by the waves which pass the lens at a wider angles compensate for this loss. A local maximum electric field in a deeper region of the tissue may form with the lossy lens. The study shows that it is possible to generate the desired electric field distribution in the complex biological target by modifying the dielectric properties of the lens used in conjunction with the reflector antenna. Bioelectromagnetics © 2013 Wiley Periodicals, Inc.
    Bioelectromagnetics 02/2014; 35(2). DOI:10.1002/bem.21825 · 1.71 Impact Factor
  • Karl H. Schoenbach · Muhammad Arif Malik
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    ABSTRACT: Shielded sliding discharges are nanosecond streamer discharges which develop along a dielectric between metal foil electrodes, with one of the foils extended over the entire rear of the dielectric layer. The electrode configuration not only allowed rearranging discharges in parallel due to the decoupling effect of the metal layer, but also to modify the electric field distribution in such a way that components normal to the surface are enhanced, leading to an increased energy density in the discharge plasma. By varying the electrode gap, the applied voltage, and the repetition rate, it is shown that by keeping the average electric field constant, the discharge voltage can be reduced from tens of kV to values on the order of a few kV, but only at the expense of a reduced energy density of the plasma. Varying the repetition rate from 20 to 500 Hz resulted in a slightly reduced energy per pulse, likely caused by residual charges on the dielectric surface. Measurements of the NO conversion to NO2 and ozone synthesis in dry air showed that the conversion is only dependent on the energy density of the discharge plasma. Although reducing the pulse voltage from the tens of kV range to that of few kV, and possibly even lower, causes a reduction in energy density, this loss can be compensated for by increasing the electrode gap area. This and the possibility to form discharge arrays allows generating large volume discharge reactors for environmental applications, at modest pulsed voltages.
    Plasma Chemistry and Plasma Processing 01/2014; 34(1). DOI:10.1007/s11090-013-9508-y · 2.06 Impact Factor
  • Muhammad Arif Malik · Karl H. Schoenbach
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    ABSTRACT: Positive and negative streamer discharges in atmospheric pressure air were generated in a shielded sliding discharge reactor at operating voltages as low as 5 kV for a gap length of 1.6 cm. In this reactor, electrodes are placed on top of a dielectric layer and one of the electrodes, generally the one on ground potential, is connected to a conductive layer on the opposite side of the dielectric. The energy per pulse, at the same applied voltage, was more than a factor of seven higher than that of pulsed corona discharges, and more than a factor of two higher than that of sliding discharges without a shield. It is explained on the basis of enhanced electric fields, particularly at the plasma emitting electrode. Specific input energy required for 50 % removal from ~1,000 ppm initial NO could be reduced to ~18 eV/molecule when ozone in the exhaust of negative streamers was utilized. For sliding discharges and pulsed corona discharges this value was ~25 eV/molecule and it was 35 eV/molecule for positive shielded sliding discharges. Also, the ozone energy yield from dry air was up to ~130 g/kW h and highest for negative streamer discharges in shielded sliding discharge reactors. The high energy density in negative streamer discharges in the shielded discharge reactor at the relatively low applied voltages might not only allow expansion of basic studies on negative streamers, but also open the path to industrial applications, which have so far been focused on positive streamer discharges.
    Plasma Chemistry and Plasma Processing 01/2014; 34(1). DOI:10.1007/s11090-013-9497-x · 2.06 Impact Factor
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    ABSTRACT: Multiple studies have shown that bipolar (BP) electric pulses in the microsecond range are more effective at permeabilizing cells while maintaining similar cell survival rates as compared to monopolar (MP) pulse equivalents. In this paper, we investigated whether the same advantage existed for BP nanosecond-pulsed electric fields (nsPEF) as compared to MP nsPEF. To study permeabilization effectiveness, MP or BP pulses were delivered to single Chinese hamster ovary (CHO) cells and the response of three dyes, Calcium Green-1, Propidium Iodide (PI), and FM1-43, was measured by confocal microscopy. Results show that BP pulses were less effective at increasing intracellular calcium concentration or PI uptake and cause less membrane reorganization (FM1-43) than MP pulses. Twenty-four hour survival was measured in three cell lines (Jurkat, U937, CHO) and over ten times more BP pulses were required to induce death as compared to MP pulses of similar magnitude and duration. Flow cytometry analysis of CHO cells after exposure (15min) revealed that to achieve positive FITC-Annexin V and PI expression, ten times more BP pulses were required than MP pulses. Overall, unlike longer pulse exposures, BP nsPEF exposures proved far less effective at both membrane permeabilization and cell killing than MP nsPEF.
    Biochemical and Biophysical Research Communications 12/2013; 443(2). DOI:10.1016/j.bbrc.2013.12.004 · 2.30 Impact Factor
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    R. Nuccitelli · U. Pliquett · X. Chen · W. Ford · R. Swanson · S. Beebe · J. Kolb · K. Schoenbach
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    ABSTRACT: In the research of bioelectrics, bipolar pulses appear to enhance the membrane effects by creating anode on both sides of the cell sequentially. On the other hand, the membrane charging resulted from the first part of the pulse may be removed by the following pulse of opposite polarity. To explore the biological effects of bipolar pusles on cells, we have constructed several types of nanosecond bipolar pulse generators, which can drive low-impedance loads of, for example, 10 Ω. They have been used for loads of electroporation cuvettes. The pulses were generated by means of five, 50 Ω transmission lines connected in parallel which were then switched on by a single spark gap switch, or a RLC circuit charged by a Marx generator. The pulse waveforms are symmetrical for long pulses, such as 600 ns, but for short pulses, such as 10 ns, an apparent asymmetry was observed. We suggest several causes for the deviation of the theoretical pulse-duration prediction.
    Pulsed Power Conference (PPC), 2013 19th IEEE; 06/2013
  • Muhammad Arif Malik · Karl H Schoenbach
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    ABSTRACT: A sliding surface discharge was formed on a dielectric layer in steam at ~100 °C and atmospheric pressure. The material properties and the thickness of the dielectric layer were found to strongly affect the energy deposition into the plasma. With a 0.32 cm thick dielectric the energy deposition was 1.4 times greater than with a 0.48 cm thick dielectric, and with window glass it was 1.3 times greater than with Macor of the same thickness. Product gases were H2 (73 ± 4%) and O2 (27 ± 1%), and H2O2 accumulated in the condensed water up to 0.4 g l−1. The energy yield for hydrogen was 1.2 ± 0.1 g H2 kWh−1 and independent of the input power and thickness or material of the dielectric. However, for hydrogen peroxide the energy yield, which varied between 0.61 and 3.2 g H2O2 kWh−1, was found to depend strongly on the thickness and material of the dielectric. The addition of benzene to the steam increased the energy efficiency of hydrogen to 2.3 g kWh−1, and decreased oxygen and hydrogen peroxide by about 3 and 6 times, respectively. It also caused the deposition of phenol and polymer-like layers on the dielectric. The results are explained on the basis of reactions of H and OH radicals adsorbed on the surface and/or in gas phase.
    Journal of Physics D Applied Physics 03/2013; 46(14):145201. DOI:10.1088/0022-3727/46/14/145201 · 2.72 Impact Factor
  • Shu Xiao · Andrei Pakhomov · Fei Guo · Swetha Polisetty · Karl H. Schoenbach
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    ABSTRACT: We have for the first time recorded action potentials in rat hippocampus neurons when they were stimulated by subnanosecond electric pulses. The preliminary results show that applying a series of pulses allowed the accumulation of depolarization before activating the voltage gated channels. The depolarization only occurred when the electric pulses were applied. It is unclear whether the depolarization is caused by the charge accumulation across the membrane or the cation influx due to the membrane permeabilization. We have also conducted an electromagnetic simulation of delivering subnanosecond pulses to tissues using an impulse radiating antenna. The results show that the pulses can be confined in the deep region in the brain but the amplitude is reduced significantly due to the attenuation of the tissues. A partially lossy dielectric lens may be used to reverse the decreasing trend of the electric field.
    Proceedings of SPIE - The International Society for Optical Engineering 02/2013; 8585. DOI:10.1117/12.2003341 · 0.20 Impact Factor
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    Stephen J Beebe · Yeong-Jer Chen · Nova M Sain · Karl H Schoenbach · Shu Xiao
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    ABSTRACT: It is hypothesized that high frequency components of nanosecond pulsed electric fields (nsPEFs), determined by transient pulse features, are important for maximizing electric field interactions with intracellular structures. For monopolar square wave pulses, these transient features are determined by the rapid rise and fall of the pulsed electric fields. To determine effects on mitochondria membranes and plasma membranes, N1-S1 hepatocellular carcinoma cells were exposed to single 600 ns pulses with varying electric fields (0-80 kV/cm) and short (15 ns) or long (150 ns) rise and fall times. Plasma membrane effects were evaluated using Fluo-4 to determine calcium influx, the only measurable source of increases in intracellular calcium. Mitochondria membrane effects were evaluated using tetramethylrhodamine ethyl ester (TMRE) to determine mitochondria membrane potentials (ΔΨm). Single pulses with short rise and fall times caused electric field-dependent increases in calcium influx, dissipation of ΔΨm and cell death. Pulses with long rise and fall times exhibited electric field-dependent increases in calcium influx, but diminished effects on dissipation of ΔΨm and viability. Results indicate that high frequency components have significant differential impact on mitochondria membranes, which determines cell death, but lesser variances on plasma membranes, which allows calcium influxes, a primary determinant for dissipation of ΔΨm and cell death.
    PLoS ONE 12/2012; 7(12):e51349. DOI:10.1371/journal.pone.0051349 · 3.23 Impact Factor
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    ABSTRACT: The rate of trypan blue uptake of liver cancer cells, indicating cell death, when exposed to subnanosecond high electric field pulses, increased strongly when the temperature was raised above 37 °C. The exposure of Hepa 1-6 cells to 2000 pulses of 200 picosecond duration and electric field amplitudes exceeding 80 kV/cm induced cell death in almost 30% of the cells when the temperature was increased to 47 °C for the time of the pulsing. For temperatures at 37 °C and below, the same exposure to pulsed electric fields did not show any measurable effect. Even for the maximum elevated temperature of 47 °C, thermal effects were not found to cause fatalities for the time of exposure, which was, for 2000 pulses at a repetition rate of 7-9 pulses per second, on the order of 5 min. The effect of temperature on the electrical properties of the cell was measured by means of dielectric spectroscopy. The membrane voltages derived from these values were found to be too low to cause electroporation at room temperature. However, the reduced viscosity of the membrane with temperature is likely to reduce the threshold for poration, and together with the effect of multiple pulses, is considered to be the cause for the observed high death rate of the cells. This argument is supported by molecular dynamics simulations which show an increased probability for pore formation with temperature.
    IEEE Transactions on Plasma Science 10/2012; 40(10):2334-2347. DOI:10.1109/TPS.2012.2208202 · 1.10 Impact Factor
  • Karl H. Schoenbach · Weidong Zhu
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    ABSTRACT: Spatially confined plasmas with dimensions in the submillimeter range have been found to be stable at atmospheric pressure. These microplasmas are nonequilibrium plasmas with an electron energy distribution which contains a significant fraction of high energy electrons. This favors, in combination with the high gas density, the formation of excimers. The possibility for operating these discharges in parallel, or expanding the nonequilibrium plasma two-dimensionally on a flat cathode allows for extended area light-sources, including excimer lamps. The spectral range of these lamps reaches from the visible into the vacuum ultraviolet, down to wavelengths of 75 nm for helium excimer radiation. Highest efficiencies of 6–9% were obtained for xenon excimers when the discharge was operated dc, and 20% when operated in a nanosecond pulsed mode. Besides excimer radiation, microdischarges have also been shown to emit intense line radiation in the vacuum ultraviolet when noble gases with small admixtures of hydrogen and oxygen were used. In this paper, we discuss basic properties of several types of high-pressure microplasmas, focusing on their dc and pulsed dc operation, followed by an overview of the experimental and modeling results relevant for their use as ultraviolet light sources. The prospect of developing microplasma lamps by forming arrays of microdischarges and possibly excimer lasers by operating microdischarges in series is briefly discussed.
    IEEE Journal of Quantum Electronics 06/2012; 48(6):768-782. DOI:10.1109/JQE.2012.2185686 · 1.89 Impact Factor
  • Muhammad Arif Malik · Karl H Schoenbach
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    ABSTRACT: Energetic and scalable non-equilibrium plasma was formed in pure water vapour at atmospheric pressure between wire-to-strip electrodes on a dielectric surface with one of the electrodes extended forming a conductive plane on the back side of the dielectric surface. The energy deposition increased by an order of magnitude compared with the conventional pulsed corona discharges under the same conditions. The scalability was demonstrated by operating two electrode assemblies with a common conductive plane between two dielectric layers. The energy yields for hydrogen and hydrogen peroxide generation were measured as ∼1.2 g H2/kWh and ∼4 g H2O2/kWh.
    Journal of Physics D Applied Physics 04/2012; 45(13). DOI:10.1088/0022-3727/45/13/132001 · 2.72 Impact Factor

Publication Stats

9k Citations
475.08 Total Impact Points


  • 1987–2015
    • Old Dominion University
      • • Frank Reidy Research Center for Bioelectrics
      • • Department of Electrical and Computer Engineering
      Norfolk, Virginia, United States
  • 2007
    • ODU USA Connectors
      Camarillo, California, United States
  • 2001–2005
    • Eastern Virginia Medical School
      • • Department of Physiological Sciences
      • • Department of Pediatrics
      Norfolk, VA, United States
  • 2002
    • Kumamoto University
      Kumamoto, Kumamoto Prefecture, Japan
  • 2000
    • Air Force Research Laboratory
      Washington, Washington, D.C., United States
    • University of Wisconsin, Madison
      • Department of Electrical and Computer Engineering
      Madison, MS, United States
  • 1999
    • Stevens Institute of Technology
      • Department of Physics & Engineering Physics
      Hoboken, New Jersey, United States
  • 1995
    • Mississippi State University
      • Department of Electrical and Computer Engineering
      Starkville, MS, United States
  • 1979–1987
    • Texas Tech University
      • Department of Electrical and Computer Engineering
      Lubbock, TX, United States
  • 1984
    • University of Oregon
      Eugene, Oregon, United States
  • 1977–1980
    • Darmstadt University of Applied Sciences
      Darmstadt, Hesse, Germany