We derive some approximate expressions for the current through an electrically short dipole probe immersed in a cold magnetized plasma. The time-varying current signal due to an applied voltage input to the probe is proportional to plasma parameters such as electron density and electron neutral collision frequency in the ionosphere. By taking Laplace transformations and examining the parallel and perpendicular current contributions, we obtain an approximate theoretical expression for the impedance of the probe. We then infer an even simpler empirical expression based on the approximate theory and frequency domain data obtained from sweeping impedance probes (SIPs) flown on previous sounding rocket missions. The inverse Laplace transform of the expressions will be used to perform direct least mean squares curve fitting against measurements made by a time domain impedance probe (TDIP) flown on a CubeSat. We compare our results with previous analytical results of the impedance of an electrically short dipole in a plasma, and typical sounding rocket impedance data in the ionosphere E-layer. An expression taking into account the appearance of a sheath is also presented. In the frequency domain, our expressions are found to capture the significant features of data from sounding rocket experiments.

中文翻译：

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磁化等离子体中偶极探针电流的时域表达式

我们推导出通过浸入冷磁化等离子体中的电短偶极探针的电流的一些近似表达式。由于施加到探针的电压输入而产生的时变电流信号与等离子体参数成正比，例如电离层中的电子密度和电子中性碰撞频率。通过进行拉普拉斯变换并检查平行和垂直电流的贡献，我们获得了探头阻抗的近似理论表达式。然后，我们根据从先前探空火箭任务中飞行的扫描阻抗探​​测器 (SIP) 获得的近似理论和频域数据推断出更简单的经验表达式。表达式的逆拉普拉斯变换将用于对由在 CubeSat 上飞行的时域阻抗探头 (TDIP) 进行的测量执行直接最小均方曲线拟合。我们将我们的结果与之前等离子体中电短偶极子阻抗的分析结果以及电离层 E 层中典型的探空火箭阻抗数据进行了比较。还提供了考虑护套外观的表达式。在频域中，我们发现我们的表达式可以捕获来自探空火箭实验的数据的重要特征。还提供了考虑护套外观的表达式。在频域中，我们发现我们的表达式可以捕获来自探空火箭实验的数据的重要特征。还提供了考虑护套外观的表达式。在频域中，我们发现我们的表达式可以捕获来自探空火箭实验的数据的重要特征。