Electron Temperature Inference from Fixed Bias Langmuir Probes Set-Ups in Ionospheric Conditions

In this work, we show the first achievement of inferring the electron temperature in ionospheric conditions from synthetic data using fixed-bias Langmuir probes operating in the electron saturation region. This was done using machine learning, as well as by altering the probe geometry. The electron temperature is inferred at the same rate as the currents are sampled by the probes. For inferring the electron temperature along with the electron density and the floating potential, a minimum number of three probes is required. Furthermore does one probe geometry need to be distinct from the other two, since otherwise the probe setup may be insensitive to temperature. This can be achieved by having either one shorter probe or a probe of a different geometry, e.g. two longer and a shorter cylindrical probe or two cylindrical probes and a spherical probe. We use synthetic plasma parameter data and calculate the synthetic collected probe currents to train a neural network (using TensorFlow) and verify the results with a test set as well as with data from the International Reference Ionosphere (IRI) model. A table with computed currents collected by a spherical probe by Laframboise was extended to calculate currents of the synthetic plasma parameters for high eta values (eta >25) to cover a large altitude range (100-500 km, within Earth's ionosphere). The extrapolated values were benchmarked with Particle-in-Cell simulations. Finally, we evaluate the robustness and errors of different probe setups that can be used to infer the electron temperature. As the inferred temperatures are compared to results from the International Reference Ionosphere model, we verify the validity of the inferred temperature in altitudes ranging from about 100-500 km. We show that electron temperature inference from different combinations of spherical and cylindrical probes - three cylindrical probes, three spherical probes, four cylindrical and a spherical probe - can be achieved. Even minor changes in the probe sizing enable the temperature inference and result in root mean square relative errors (RMSRE) between inferred and ground truth data of under 3%. With further optimizations, the RMSRE can even be decreased to under 1%. When limiting the temperature inference to 120-450 km altitude an RMSRE of under 0.7% is achieved for all probe setups. In future, the multi-needle Langmuir Probe (m-NLP) instrument dimensions can be adapted for higher temperature inference accuracy.