Bayesian analysis of triple Langmuir probe measurements for the characterization of Hall thruster plasmas

Abstract

We developed a new experimental approach to characterize the plasma behavior inside Hall thrusters. The main novelty of the developed approach regards the combination of a triple Langmuir probe, which guarantees a high flexibility, and Bayesian data analysis. The triple Langmuir probe was mounted on an articulated arm that can rapidly insert the probe inside the thruster channel, providing a clear picture of relevant plasma properties along the channel centerline, from the near plume to the near-anode region. At a given operating condition of the thruster, multiple measurements were performed, changing the arrangements of the triple probe electrodes and the applied potential differences between the electrodes. Then, in order to analyze the data gathered by the triple probe, a Bayesian integrated data analysis has been adopted. This method made it possible to combine measurements from different electrode arrangements and to improve the quality of the inferred plasma parameters. Non-uniformities of the plasma sensed by the probe electrodes were taken into account within the physical model of particle collection. In order to model the interaction of the electrodes with the plasma, a parametrization of the Laframboise sheath solution was used. The developed diagnostic system, together with the integrated data analysis, proved to be a valid approach to characterize the plasma flow in Hall thrusters, offering not only a good spatial resolution of the electron temperature, plasma density, and space potential but also a consistent estimate of the measurement accuracy.

Background Pressure Effects on the Performance of a 20 kW Magnetically Shielded Hall Thruster Operating in Various Configurations

“…The magnetically shielded topology was derived from the studies on two different development models of the SITAEL's 5 kW-class Hall thruster, the HT5k. The HT5k demonstrated low electron temperatures, , and plasma potentials nearly equal to the anode potential, along the channel chamfered region, which significantly reduced the channel erosion by ion bombardment [38][39][40][41].…”

Numerical and Experimental Investigation of Longitudinal Oscillations in Hall Thrusters

“…The use of a triple probe, despite reducing the space resolution in the perpendicular plane, allows achieving a good temporal resolution without the need to perform rapid voltage sweeping, which introduces complications in the results interpretation due to the presence of important capacitive effects, as is the case with single Langmuir probes used in previous studies (see, for instance, [51,54]). This diagnostic is described in detail in previous publications from the authors [39,40,55], therefore, only a summarized discussion is included in the following.…”

“…The adoption of a triple probe allows gathering instantaneous measurements of plasma properties without the need of voltage sweeps, at the cost of assuming that the electrons present in the plasma have a non-drifting Maxwellian velocity distribution function (EVDF). As explained by the authors in References [39,55], the assumptions on the EVDF are acceptable to a first order, particularly in the plume, where the electron drift velocity is negligible with respect to their thermal velocity. Moreover, a set of correction parameters, introduced by Saravia et al in Reference [39], allows mitigating the impact of the electron drift on the measurements.…”

“…As explained by the authors in References [39,55], the assumptions on the EVDF are acceptable to a first order, particularly in the plume, where the electron drift velocity is negligible with respect to their thermal velocity. Moreover, a set of correction parameters, introduced by Saravia et al in Reference [39], allows mitigating the impact of the electron drift on the measurements. It is important to note that the characteristic time of the probe motion (O(1) Hz) is orders of magnitude longer than that of the oscillatory phenomena under study (O(10 4 ) Hz), making it possible to assume that the probe is steady during several plasma oscillations, allowing to make considerations on the local unsteady behavior of the plasma even if the probe is moving.…”

“…Sensors installed on rapidly moving arms to probe the plasma in Hall thrusters have been used since the late 1990s [37]. Since then, similar concepts have been proposed, including single and triple Langmuir probes, as well as emissive probes, in order to gather a time-averaged picture of the plasma properties in the thruster near-plume [38][39][40][41][42][43]. The plasma perturbations occurring upon probe insertion complicate the interpretation of experimental data, particularly within the channel and in the vicinity of the magnetic peak, where the electron azimuthal current is the highest.…”