A long cylindrical Langmuir probe immersed in a collisional plasma is modelled by using fluid equations in which the collision term is introduced assuming a constant ion mean free path. The physical magnitudes of the system are expanded in a perturbation series in the collision parameter, that is, the ratio between the Debye length and the ion mean free path, and the system is thus separated into zeroth-order and first-order perturbation systems. The ion temperature is arbitrary and a continuous solution from the plasma to the probe is obtained for the perturbation systems. Using this methodology, a continuous solution for the ion sheath around a cylindrical Langmuir probe is obtained for long ion mean free path, for any ion temperature with no need of two-scale study or asymptotic matching. It is found that the collisions and the ion temperature have opposite effects, and these effects are quantified. The solution for cold ions cannot be obtained directly using this method, but...

中文翻译：

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圆柱形Langmuir探针周围热离子鞘层在流体模型中的碰撞影响

通过使用流体方程对浸没在碰撞等离子体中的长圆柱Langmuir探针进行建模，在该方程中，假设恒定的离子平均自由程，引入了碰撞项。系统的物理量级按碰撞参数的扰动级数（即，德拜长度与离子平均自由程之比）扩展，因此该系统分为零阶和一阶扰动系统。离子温度是任意的，并且对于扰动系统可以获得从血浆到探针的连续溶液。使用此方法，可以获得长圆柱平均自由程的圆柱形Langmuir探针周围离子鞘的连续解决方案，适用于任何离子温度，而无需进行两尺度研究或渐近匹配。发现碰撞和离子温度具有相反的作用，并且对这些作用进行了量化。使用此方法无法直接获得冷离子溶液，但是...