A classical problem of plasma physics is the treatment of the plasma-wall transition. This can be reached in the presheath with a presheath scale, in the sheath with a sheath scale and between presheath and sheath with an “intermediate scale”. Riemann (J Tech Phys 41:89–121, 2000) published a derivation of the intermediate scale. In our calculation we take the non-quasineutral values for the ion density and the ion velocity at the point where the non-quasineutral solution of the potential is zero. This approach is consistent and valid also for small but finite values of the smallness parameter of the theory. An effect of taking the non-quasineutral values is that the potential is shifted, dependent on the magnitude of the smallness parameter. But this shifting has no consequences on the intermediate scale and so we get a similar result as K.-U. Riemann. Furthermore, we show that it is not necessary to take into account the temperature change in the vicinity of the sheath edge and that it is possible to work always strictly with the complete and normalized basic equations of the problem and not only with orders on the left or right hand side of these equations.

中文翻译：

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中级量表的精确推导

等离子体物理学的一个经典问题是等离子体壁跃迁的处理。这可以在带有预鞘刻度的预鞘中、带有鞘刻度的鞘中以及带有“中间刻度”的预鞘和鞘之间实现。Riemann (J Tech Phys 41:89–121, 2000) 发表了一个中间尺度的推导。在我们的计算中，我们在非拟中性电势解为零的点处取离子密度和离子速度的非拟中性值。这种方法对于理论的小参数的小但有限的值也是一致和有效的。取非拟中性值的一个影响是电势发生偏移，这取决于小参数的大小。但是这种转变对中间尺度没有影响，所以我们得到了与 K.-U. 黎曼。此外，我们表明没有必要考虑护套边缘附近的温度变化，并且可以始终严格使用问题的完整和归一化基本方程，而不仅仅是左侧的阶数或这些方程的右侧。