The Hall effect arises in a plasma when electrons are able to drift with the magnetic field but ions cannot. In a fully-ionized plasma this occurs for frequencies between the ion and electron cyclotron frequencies because of the larger ion inertia. Typically this frequency range lies well above the frequencies of interest (such as the dynamical frequency of the system under consideration) and can be ignored. In a weakly-ionized medium, however, the Hall effect arises through a different mechanism -- neutral collisions preferentially decouple ions from the magnetic field. This typically occurs at much lower frequencies and the Hall effect may play an important role in the dynamics of weakly-ionised systems such as the Earth's ionosphere and protoplanetary discs. To clarify the relationship between these mechanisms we develop an approximate single-fluid description of a partially ionized plasma that becomes exact in the fully-ionized and weakly-ionized limits. Our treatment includes the effects of ohmic, ambipolar, and Hall diffusion. We show that the Hall effect is relevant to the dynamics of a partially ionized medium when the dynamical frequency exceeds the ratio of ion to bulk mass density times the ion-cyclotron frequency, i.e. the Hall frequency. The corresponding length scale is inversely proportional to the ion to bulk mass density ratio as well as to the ion-Hall beta parameter.

在等离子体中产生霍尔效应时，电子能够随着 磁场，但离子不能。在完全电离的等离子体中，这种情况发生在 离子和电子回旋频率之间的频率，因为 更大的离子惯性。通常，此频率范围远远高于 感兴趣的频率(如系统的动态频率 考虑)，并且可以忽略。然而，在弱电离介质中， 霍尔效应是通过一种不同的机制产生的--中性碰撞 优先使离子与磁场去耦合。这通常发生在 低得多的频率和霍尔效应可能在 弱电离系统的动力学，如地球电离层和 原行星盘。 为了阐明这些机制之间的关系，我们开发了一个 部分电离等离子体的近似单流体描述 精确到完全电离和弱电离的极限。我们的治疗包括 欧姆效应、双极效应和霍尔扩散效应。我们向大家展示了音乐厅 效应与部分电离介质的动力学有关，当 动态频率超过离子与体积质量密度的比率乘以 离子回旋频率，即霍尔频率。相应的长度 比例也与离子与体积质量密度之比成反比。 关于离子-霍尔贝塔参数。