Numerical investigation of atmospheric positive diffuse discharge mode transition: the effect of voltage rise time

This work computationally investigates the morphological transition of atmospheric pressure positive nanosecond pulsed discharges from a diffuse to a multi-channel regime. Using 2D fluid models – specifically the Local Field Approximation (LFA), a flux-corrected LFA, and the Local Mean Energy Approximation (LMEA) – we analyze the influence of voltage amplitude and rise time on discharge dynamics. Results reveal that a short voltage rise time (2 ns) consistently produces a diffuse discharge(from 56 kV to 85 kV amplitude), which exhibits significant acceleration at higher voltages but constant-velocity at a lower voltage(56 kV), in agreement with experimental observation. Both flux-corrected LFA and LMEA better match experimental results regarding discharge width and average development velocity, with LMEA showing a generally longer inception delay and faster development velocity. Conversely, for slower rise times (5.8 ns), the standard LFA model predicts off-axis branching especially under lower voltage(56 kV). In contrast, both the flux-corrected LFA and LMEA models successfully capture the development of a main channel alongside branching structures. Notably, the flux-corrected LFA model exhibits the best qualitative agreement with experiments, demonstrating the suppression of branching at higher voltages. Although limited by its 2D framework, the model provides results comparable to those of 3D models, clarifying the model-dependent nature of simulated discharge morphologies and offering critical insights into the physical mechanisms driving the diffuse-to-branched transition.