Impact of Cathode Geometry on Negative Corona Discharge and Trichel Pulse Characteristics: A Comparative Analysis of Hyperbolic, Elliptic, and Tangent-Circular Needle Shapes

This article presents a comprehensive exploration of negative corona discharges and Trichel pulses in air, focusing on different needle electrode geometries with a constant radius of curvature at the needle's tip. Three distinct needle electrode shapes are mathematically defined and introduced: 1) a standardized hyperboloid-shaped needle; 2) ellipsoid-shaped needles; and 3) tangent-circular needles. Through a comparative sensitivity analysis, we investigate how variations in these needle cathode shapes—characterized by eccentricity values or intertangent angles—affect negative corona discharge behavior and Trichel pulse characteristics. Employing a hydrodynamic numerical model, we simulate the initiation and evolution of low-temperature plasma between electrodes. The numerical and comparative analysis covers a range of Trichel pulse aspects, including their amplitude and temporal attributes. Simulation results reveal intriguing trends, where narrower needles in the body induce earlier onset and intensified Trichel pulses. Meanwhile, temporal attributes such as rise, decay, and total pulse times demonstrate close clustering around mean values for needles sharing the same radius of curvature. These findings underscore the multifaceted influence of electrode geometry on discharge behavior and Trichel pulses dynamics, emphasizing the necessity for accurate needle electrode geometry definition beyond the mere radius of curvature and shape type in numerical simulations of corona discharge.