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                <term xml:lang="en">diffuse surface ionization waves</term>
                <term xml:lang="en">streamers</term>
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                <term xml:lang="en">plasma-liquid interaction</term>
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              <p>Diffuse propagation of a circular surface ionization wave over liquid water is achieved at atmospheric pressure using positive high-voltage nanosecond pulses with fast rise rates (15 kV/ns). The surface discharges propagate over relatively large areas (~cm²) across a wide range of water conductivities (5-900 µS/cm). They are generated in a pin-to-water configuration with a sub-millimetre gap between the pin and the water surface. Using two pulse generators, the influence of voltage rise rate on discharge propagation dynamics is highlighted. Fast imaging and electrical diagnostics are performed under moderate (2 kV/ns) and high (15 kV/ns) voltage rise rates. In the former case, the discharge develops in three stages: 1/ discharge inception in the pin-water gap, 2/ propagation of a circular wave over the water surface and 3/ development of instabilities in the circular wave front in less than 4 ns, leading to the formation of multiple organized surface streamers that emerge simultaneously from the wave front. These streamers propagate until the end of the voltage pulse. In the latter case, in contrast, the circular wave does not break up and the discharge continues to propagate as a uniform ring until the voltage drops. Water conductivity variations (5-900 µS/cm) do not prevent the diffuse propagation, however they influence the propagation length, speed, and energy deposition. The current findings demonstrate that high-voltage nanosecond pulses with sharp rise rates enable controlled and uniform propagation of surface ionization waves at atmospheric pressure on liquid water at various conductivities, using simple electrode configurations.</p>
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