平面、柱面和球面几何中Paschen曲线的广义Townsend理论
A generalized Townsend's theory for Paschen curves in planar, cylindrical, and spherical geometries
摘要：
在这项工作中，我们专注于两个电极之间产生的等离子体放电与高电势差，导致中性粒子的电离支持电流的气体介质。在低电流和低温下，这个过程可以产生发光发射：所谓的辉光放电和电晕放电。Townsend（1900）理论中使用的平行板几何形状使我们能够发展出一种理论形式，其临界电压的显式解有效地再现了实验帕邢曲线。然而，大多数放电过程发生在非平行板的几何形状，如多相流中的颗粒或冰粒之间的放电。在这里，我们提出了一个概括的经典平行板配置同心球和同轴圆柱形的几何形状在地球，火星，土卫六，金星大气。在球形情况下，小半径有效地表示尖锐的尖端杆，而较大的厘米级半径表示圆形或钝头。类似地，在圆柱形情况下，小半径将对应于细线。我们解决的间隙中的连续性方程和估计的临界半径和最小击穿电压，允许中性气体的电离和形成的辉光放电。我们表明，辉光日冕更容易形成在火星的低压，$CO_2$丰富的大气比地球的高压大气。此外，我们提出了土卫六和金星的故障标准。我们进一步证明，临界电压最小值发生在0.5厘米$\cdot$托的所有三个调查的几何形状，这表明更容易启动周围的灰尘和水云毫米大小的颗粒，可以很容易地扩展到检查其他多相流与惯性颗粒。
英文摘要：
In this work, we focus on plasma discharges produced between two electrodes with a high potential difference, resulting in the ionization of the neutral particles supporting a current in the gaseous medium. At low currents and low temperatures, this process can create luminescent emissions: the so-called glow and corona discharges. The parallel plate geometry used in Townsend's (1900) theory lets us develop a theoretical formalism, with explicit solutions for the critical voltage effectively reproducing experimental Paschen curves. However, most discharge processes occur in non-parallel plate geometries, such as discharges between grains or ice particles in multiphase flows. Here, we propose a generalization of the classic parallel plate configurations to concentric spherical and coaxial cylindrical geometries in Earth, Mars, Titan, and Venus atmospheres. In a spherical case, a small radius effectively represents a sharp tip rod, while larger, centimeter-scale radii represents rounded or blunted tips. Similarly, in a cylindrical case, a small radius would correspond to a thin wire. We solve continuity equations in the gap and estimate a critical radius and minimum breakdown voltage that allows ionization of neutral gas and formation of a glow discharge. We show that glow coronae form more easily in Mars's low-pressure, $CO_2$-rich atmosphere than in Earth's high-pressure atmosphere. Additionally, we present breakdown criteria for Titan and Venus. We further demonstrate that critical voltage minima occur at 0.5 cm$\cdot$Torr for all three investigated geometries, suggesting easier initiation around millimeter-size particles in dust and water clouds and could be readily extended to examine other multiphase flows with inertial particles.
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