Non-Maxwellian Electron Energy Probability Functions in the plume of a SPT-100 Hall thruster

We present measurements of the electron density, the effective electron temperature, the plasma potential, and the electron energy probability function (EEPF) in the plume of a 1.5 kW-class SPT-100 Hall thruster, derived from cylindrical Langmuir probe measurements. The measurements were taken on the plume axis at distances between 550 and 1550 mm from the thruster exit plane, and at different angles from the plume axis at 550 mm for three operating points of the thruster, characterized by different discharge voltages and mass flow rates. The bulk of the electron population can be approximated as a Maxwellian distribution, but the measured distributions were seen to decline faster at higher energy. The measured EEPFs were best modelled with a general EEPF with an exponent alfa between 1.2 and 1.5, and their axial and angular characteristics were studied for the different operating points of the thruster. As a result, the exponent alfa from the fitted distribution was seen to be almost constant as a function of the axial distance along the plume, as well as across the angles. However, the exponent alfa was seen to be affected by the mass flow rate, suggesting a possible relationship with the collision rate, especially close to the thruster exit. The ratio of the specific heats, the gamma factor, between the measured plasma parameters was found to be lower than the adiabatic value of 5/3 for each of the thruster settings, indicating the existence of non-trivial kinetic heat fluxes in the near collisionless plume. These results are intended to be used as input and/or testing properties for plume expansion models in further work.This work was performed in the framework of the 'Model and Experimental validation of spacecraft-thruster Interactions (erosion) for electric propulsion thrusters plumes' (MODEX) project. MODEX is a collaboration between Airbus-DS, ESA, UC3M, ONERA, CNRS-ICARE and KTH aiming to provide a better understanding of the plasma properties in the far-plume of a Hall thruster. The project aimed at providing experimental measurements to better constrain the modelling, and therefore includes both the theoretical/modelling aspect (UC3M and ONERA) and the experimental aspect (KTH, CNRS, ESA and Airbus-DS). The test campaign was conducted at ESA/ESTEC in April-May 2017, using a SPT-100 Hall thruster provided by Airbus-DS. G Giono and J T Gudmundsson were partially supported by the Swedish Government Agency for Innovation Systems (VINNOVA) contracts no. 2016-04094 and 2014-0478, respectively

A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier–Stokes and Euler Equations on Unstructured Meshes

International audienceWe propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier-Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order con-2 Ricardo Costa et al. vergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme

Non-Maxwellian electron energy probability functions in the plume of a SPT-100 Hall thruster

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A Priori Neural Networks Versus A Posteriori MOOD Loop: A High Accurate 1D FV Scheme Testing Bed

In this work we present an attempt to replace an a posteriori MOOD loop used in a high accurate Finite Volume (FV) scheme by a trained artificial Neural Network (NN). The MOOD loop, by decrementing the reconstruction polynomial degrees, ensures accuracy, essentially non-oscillatory, robustness properties and preserves physical features. Indeed it replaces the classical a priori limiting strategy by an a posteriori troubled cell detection, supplemented with a local time-step re-computation using a lower order FV scheme (ie lower polynomial degree reconstructions). We have trained shallow NNs made of only two so-called hidden layers and few perceptrons which a priori produces an educated guess (classification) of the appropriate polynomial degree to be used in a given cell knowing the physical and numerical states in its vicinity. We present a proof of concept in 1D. The strategy to train and use such NNs is described on several 1D toy models: scalar advection and Burgers' equation, the isentropic Euler and radiative M1 systems. Each toy model brings new difficulties which are enlightened on the obtained numerical solutions. On these toy models, and for the proposed test cases, we observe that an artificial NN can be trained and substituted to the a posteriori MOOD loop in mimicking the numerical admissibility criteria and predicting the appropriate polynomial degree to be employed safely. The physical admissibility criteria is however still dealt with the a posteriori MOOD loop. Constructing a valid training data set is of paramount importance, but once available, the numerical scheme supplemented with NN produces promising results in this 1D setting. Keywords Neural network • Machine learning • Finite Volume scheme • High accuracy • Hyperbolic system • a posteriori MOOD. Mathematics Subject Classification (2010) 65M08 • 65A04 • 65Z05 • 85A2

a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

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The role of eclipses and european observers in the development of ‘modern astronomy’ in Thailand

‘Modern astronomy’ was introduced to Siam (present-day Thailand) (Siam officially changed its name to Thailand in 1939) when the Belgian Jesuit missionary-astronomer Father Antoine Thomas carried out stellar and lunar eclipse observations during 1681 and 1682 in order to determine the latitude and longitude of Ayutthaya. Three years later a contingent of French Jesuit missionary astronomers observed a total lunar eclipse from Lop Buri, which marked the start of an intensive two-and-a-half year period of observational activity at Lop Buri under the sponsorship of King Narai. During this interval, a partial solar eclipse and two further lunar eclipses were observed from a number of different observing sites. Although a substantial astronomical observatory was constructed in Lop Buri and this was used by French Jesuit missionary-astronomers, ‘modern astronomy’ ended suddenly in 1688 when King Narai died and most Western missionary-astronomers were expelled from Siam. ‘Modern astronomy’ only re-emerged in Siam after a hiatus of almost 200 years when another royal supporter of astronomy, King Rama IV, invited French astronomers to observe the total solar eclipse of 18 August 1868 from Siam, and his son, King Rama V, hosted British astronomers during the 6 April 1875 total solar eclipse. Thailand’s romance with total solar eclipses continued during the 9 May 1929 solar eclipse when King Rama VII visited British and German astronomers based near Siam’s southern border, and this was the catalyst required for the birth of home-grown ‘modern astronomy’. Soon after, Siam’s first astronomy classes began at Chulalongkorn University, and in 1944 this university hosted Siam’s first professional astronomer when Rawee Bhavilai, a solar specialist, joined the Physics Department. The latest phase in the professionalisation of astronomy occurred in 2009 when the Government approval the formation of the National Astronomical Research Institute of Thailand (NARIT). In this paper we trace the critical roles that solar and lunar eclipses played in the emergence and final adoption of ‘modern astronomy’ in Thailand from 1682 through to the present day