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Satellites could benefit from flying at lower altitude, in the so-called Very Low Earth Orbit (altitude of approximately 150-250 km) [1]. At such altitudes, the aerodynamic drag of the atmosphere would cause the re-entry of the satellite if not compensated by a thrust. A novel concept called Air-Breathing Electric Propulsion (ABEP) proposes to take advantage of the residual atmosphere, by collecting it through an intake and using it as a propellant in an electric thruster. A ground testing facility is being built at VKI to reproduce the orbital flow on ground and test the intakes performance. Here, a plasma source called Particle Flow Generator produces the required stream of fast particles. Our efforts are focused on the simulation of the plasma source, the plasma plume it produces, and its interaction with the ABEP intake under test. Simulation of such plasmas for laboratory and space electric propulsion applications is a complex task because of two reasons: first, the size of interest of the system is usually comparable to the collisional length scale, because of the low pressure. The result is that velocity distributions are not always in translational equilibrium. Using particle methods, in particular the hybrid Particle-in-Cell Direct Simulation Monte Carlo (PIC-DSMC) method, allows to overcome this problem, since phase space for nonequilibrium velocity distributions can be efficiently represented using computational particles. The second problem is that the length- and time scales of interest are often much larger than the smallest natural length- and time scales of the plasma, which are dictated by the light electrons. For a rather typical plasma at 10^-3 Pa with 1 eV electrons, the Debye length is of the order of micrometers and the inverse electron plasma frequency is of the order of picoseconds. Traditional explicit Particle-in-Cell schemes need to resolve these small natural length scales, or disrupting numerical instabilities, most notably the \"finite-grid instability\", will appear. These requirements can make simulation of the entire physical device extremely expensive, and practically unfeasible above a certain plasma density, even with modern supercomputers, unless an appropriate scaling can be applied. Recently, a new class of semi-implicit methods have been devised [2], mostly for applications in astrophysics. These feature exact total energy conservation, and are stable for cell sizes and time steps well in excess of the Debye length and plasma frequency, allowing the simulation of dense plasma in large domains [3]. We investigate how these methods could be applied to the simulation of electric propulsion and laboratory plasmas. We perform 1D simulations of a plasma slab expanding into vacuum. This ambipolar expansion reproduces dynamics in the radial direction for the plasma plume of an electric thruster. Starting from well-resolving simulations, we show that it is possible to significantly reduce the resolution in space and time without triggering numerical instabilities. We compare the profiles of electric field, ion velocity and density as well as particle phase space, finding the coarsened simulations using the semi-implicit scheme are in good agreement with the well-resolving ones in terms of peak value of the electric field, with the values of expansion front position and velocity trailing slightly behind the correct values. Even with a non optimized code, we recorded a speed-up of approximately one order of magnitude. We will also present an unstructured, Finite Element discretization of the semi-implicit scheme in 2D, and apply it to the simulation of a plasma in a conductive box, which develops a sheath at the wall. Thanks to the possibility of having large cell dimensions, we are able to perform simulations that would be prohibitively expensive on a modern workstation using the explicit scheme. Also in this case, we investigate the effect of grid and time step size on the stability and accuracy of the results. [1] N. H. Crisp et al., The benefits of very low earth orbit for earth observation missions, Prog. Aerosp. Sci., 117, 100619 (2020). [2] G. Lapenta, Exactly energy conserving semi-implicit particle in cell formulation, J. Comp. Phys. 334, 349-366 (2017) [3] D.C. Barnes, L. Chacon, Finite spatial-grid effects in energy-conserving particle-in-cell algorithms, Comp. Phys. Comm. 258, 107560 (2021) |
