Time Domain Expressions for the Current of a Dipole Probe in a Magnetized Plasma

Abstract

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.