An algorithm for deriving the electron temperature and electron density probed by Langmuir probe onboard cube satellites

摘要

The paper purposes an algorithm for a Langmuir probe (LP) onboard CubeSat to correctly probe of ionospheric electron temperature and electron density. The algorithm consists of two parts of deriving the current-voltage (Ⅰ-Ⅴ) curve for the probe, and refining the electron temperature and the electron density by an iteration method. The small surface area of a CubeSat's body has a strong influence on the reference potential of the satellite body, which can significantly distort the Ⅰ-Ⅴ curve and affect the accuracy of electron temperature and electron density observations. Here, we utilize a digital circuit simulation to construct the circuit model, including the satellite DS (Debye-Sheath), the probe DS, and the scan voltage source. Simulation data describe that the satellite DS shares the scan voltage, which is the main causal of the distortion of the aforementioned Ⅰ-Ⅴ curve and the change of the turning point. We also find that an underestimated turning point is due to the ion saturation of the satellite shell DS rather than the electron saturation of the probe DS. Therefore, small satellite LPs should not directly use the turning point to calculate the electron temperature and the electron density. To resolve this small-area problem, a theoretical relationship between the satellite DS voltage, the probe DS voltage, and the scan voltage is deduced, which allows us finding the probe voltage from the scan voltage, yielding the correct Ⅰ-Ⅴ curve for LPs, and estimating the electron temperature/density for small satellites. To more accurately derive the electron temperature and electron density, an iteration method is introduced, that the electron current-voltage curve needs to be separated from the Ⅰ-Ⅴ curve, and then iterates between the electron temperature estimation and the Ⅰ-Ⅴ curve correction. Finally, observed ionospheric electron temperature and density are used to test our algorithm. Good agreements between derived results and the observations conform that the purposed algorithm can correctly obtain the electron temperature and the electron density.