The dynamics of the Tonks and Langmuir‐type bounded plasma requires a closure relation to make the system of equations self‐consistent. Fluid equations are obtained from the moments of velocity distribution function. The two most frequently used closure relations are (a) completely neglecting ion temperature, and (b) setting a constant value for the ion polytropic coefficient. It has been shown that, for a Maxwellian source, either of these assumptions leads to erroneous results. Here, the premise of polytropic coefficient being a function of the potential is extended to a nonthermal plasma. Two different cases for the electron velocity distribution function are studied, namely (a) the Kappa distribution, and (b) the Cairns distribution. Number density (n_i) and temperature (T_i) for the ions are numerically calculated, for respective spectral indices. The polytropic coefficient is then calculated as a function of the potential, using the relation γ_i = 1 + (n_i/T_i)(dT_i/dn_i). It is concluded that better approximations, vetted by kinetic means, to the polytropic coefficient are crucial for appropriate closure of fluid equations. Present work will be useful in fusion devices where non‐Maxwellian electrons may exist due to various physical phenomena.

中文翻译：

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具有非麦克斯韦电子分布的唐克斯-朗缪尔电子离子等离子体的多方系数计算

Tonks和Langmuir型有界等离子体的动力学需要封闭关系，以使方程组自洽。流体方程是从速度分布函数的时刻获得的。两种最常用的闭合关系是（a）完全忽略离子温度，以及（b）设置离子多变系数的常数。已经表明，对于麦克斯韦式源，这些假设中的任何一个都会导致错误的结果。在此，将多变系数作为电位的函数的前提扩展到非热等离子体。研究了电子速度分布函数的两种不同情况，即（a）κ分布和（b）凯恩斯分布。数密度（n _i）对于各个光谱指数，通过数值计算离子的温度（T _i）。多变系数随后作为电位的函数来计算，使用下面的关系γ_我 = 1 +（Ñ_我/ Ť_我）（的dT_我/ DN_我）。结论是，通过动力学手段对多方系数进行更好的近似对于适当地封闭流体方程至关重要。当前的工作在由于各种物理现象而可能存在非麦克斯韦电子的聚变装置中将是有用的。