Abstract

In this paper, a theory of a diffuse mode of an axially symmetric short high-current vacuum arc in an external axial magnetic field is developed. A second-order partial differential equation for the lines of discharge current levels (2D model) is obtained. The boundary conditions at the cathode and anode boundaries of the plasma are formulated. The solution of this equation with allowance for the heat-balance equation for electrons and the equation for the plasma concentration makes it possible to determine the dependence of streamlines on the coordinates. With these lines, the obtained analytical formulas can be used to calculate the components of the current density, magnetic field, and the distribution of the electron temperature and plasma concentration in the discharge gap. A (1.5D) mathematical model (j_r \( \ll \) j_z) that significantly simplifies the calculations and has a sufficiently wide range of applicability is proposed and substantiated. The method of successive approximations, which ensures results with the required accuracy, is used in the calculations for this model. The distributions of the components of the magnetic field B_r, B_θ, and B_z, the current density (j_r, j_z, and j_θ), the distributions of the electron temperature, and the concentrations of electrons and ions in the plasma of a vacuum arc are calculated.

中文翻译：

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轴向磁场中短高电流真空电弧扩散模式的数学模型

摘要

本文提出了一种在外部轴向磁场中轴向对称的短大电流真空电弧的扩散模式的理论。获得了用于放电电流水平线的二阶偏微分方程（2D模型）。制定了等离子体阴极和阳极边界的边界条件。该方程的解决方案考虑到电子的热平衡方程和等离子浓度方程，因此可以确定流线对坐标的依赖性。利用这些线，可以使用所获得的解析公式来计算电流密度，磁场以及放电间隙中电子温度和等离子体浓度的分布的分量。（1.5D）数学模型（j _r 提出并证实了可以大大简化计算并具有足够广泛适用性的\（\ ll \）j _z）。在该模型的计算中使用了逐次逼近的方法，该方法可确保结果具有所需的精度。的磁场的组件的分布乙_{- [R} ，乙_θ，和乙_Ž，电流密度（Ĵ _{- [R} ，Ĵ _Ž和Ĵ _θ）时，电子温度的分布，以及电子和离子在浓度计算真空电弧的等离子体。