Influence of Voltage Rising Time on the Characteristics of a Pulsed Discharge in Air in Contact with Water: Experimental and 2D Fluid Simulation Study

In the context of plasma–liquid interactions, the phase of discharge ignition is of great importance as it may influence the properties of the produced plasma. Herein, we investigated the influence of voltage rising time (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="sans-serif">τ</mi><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula>) on discharge ignition in air as well as on discharge propagation on the surface of water. Experimentally, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="sans-serif">τ</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> was adjusted to 0.1, 0.4, 0.6, and 0.8 kV/ns using a nanosecond high-voltage pulser, and discharges were characterized using voltage/current probes and an ICCD camera. Faster ignition, higher breakdown voltage, and greater discharge current (peak value) were observed at higher <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="sans-serif">τ</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula>. ICCD images revealed that higher <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="sans-serif">τ</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> also promoted the formation of more filaments, with increased radial propagation over the water surface. To further understand these discharges, a previously developed 2D fluid model was used to simulate discharge ignition and propagation under various <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="sans-serif">τ</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> conditions. The simulation provided the spatiotemporal evolution of the E-field, electron density, and surface charge density. The trend of the simulated position of the ionization front is similar to that observed experimentally. Furthermore, rapid vertical propagation (<1 ns) of the discharge towards the liquid surface was observed. As <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="sans-serif">τ</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> increased, the velocity of discharge propagation towards the liquid increased. Higher <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="sans-serif">τ</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> values also led to more charges in the ionization front propagating at the water surface. The discharge ceased to propagate when the charge number in the ionization front reached 0.5 × <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>8</mn></mrow></msup></mrow></semantics></math></inline-formula> charges, irrespective of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="sans-serif">τ</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> value.