The equations of the two-fluid model of low-pressure plasmas with warm ion gas are taken into consideration including collisions between charged particles and neutrals, the charge exchange, and the ionization. The basic equations contain a removable singularity at the ion sonic speed. These equations are ill-conditioned in the subsonic interval of the ion flux, but they are well-conditioned in the transsonic one. First, several transformations and auxiliary functions are introduced in order to eliminate the singularity at the ion sound speed. The resulting boundary value problem is numerically solved by a multi-shooting method for one of the versions of the transformed equations. Second, an improved one-fluid-model is well-conditioned wherein the space charge density is calculated additionally using the electric field and the Poisson equation. The numerical solution yields usable approximated results in the subsonic interval and suitable initial values for the solution of the two-fluid model in the transsonic interval. Third, the unknown functions are expanded as a power series in the relation of the ion temperature to the electron temperature. These equations can be numerically integrated throughout both intervals without serious difficulties. A set of parameters is given describing subsonic intervals extending over the whole plasma. Results obtained by means of the used methods confirm that Bohm's sheath criterion loses its meaning in collision-dominated plasmas. The scopes of application of the different methods are treated by means of examples.

中文翻译：

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离子声障处无奇点的具有非消失离子温度的低压等离子体的两流体方程的转换以及几种数值求解这些方程的方法

考虑了带暖离子气体的低压等离子体二流体模型的方程，包括带电粒子与中性粒子的碰撞、电荷交换和电离方程。基本方程包含在离子声速下可移除的奇点。这些方程在离子通量的亚音速区间是病态的，但在跨音速区间是良性的。首先，引入了几个变换和辅助函数以消除离子声速处的奇异性。由此产生的边界值问题通过多点方法对变换方程的一个版本进行数值求解。其次，改进的单流体模型是良好条件的，其中空间电荷密度是使用电场和泊松方程额外计算的。数值解在亚音速区间产生了可用的近似结果，并为跨音速区间的双流体模型求解提供了合适的初始值。第三，将未知函数展开为离子温度与电子温度关系的幂级数。这些方程可以在两个区间内进行数值积分而不会有太大的困难。给出了一组参数，描述了在整个等离子体上延伸的亚音速间隔。通过所用方法获得的结果证实，玻姆鞘准则在碰撞主导的等离子体中失去了意义。不同方法的适用范围通过示例进行处理。