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The main objective of this chapter is to present an overview of the different areas of key technologies that will be needed to fly the technically most challenging of the representative missions identified in chapter 4 (the Pillar 2 Horizon 2061 report). It starts with a description of the future scientific instruments which will address the key questions of Horizon 2061 described in chapter 3 (the Pillar 1 Horizon 2061 report) and the new technologies that the next generations of space instruments will require (section 2). From there, the chapter follows the line of logical development and implementation of a planetary mission: section 3 describes some of the novel mission architectures that will be needed and how they will articulate interplanetary spacecraft and science platforms; section 4 summarizes the system-level technologies needed: power, propulsion, navigation, communication, advanced autonomy on board planetary spacecraft; section 5 describes the diversity of specialized science platforms that will be needed to survive, operate and return scientific data from the extreme environments that future missions will target; section 6 describes the new technology developments that will be needed for long-duration missions and semi-permanent settlements; finally, section 7 attempts to anticipate on the disruptive technologies that should emerge and progressively prevail in the decades to come to meet the long-term needs of future planetary missions., Comment: 100 pages, 23 figures, Horizon 2061 is a science-driven, foresight exercise, for future scientific investigations

A new unstructured, massively parallel code dedicated to low temperature plasmas, AVIP, is presented to simulate plasma discharges in interaction with combustion. The plasma species are modeled in a drift-diffusion formulation and the Poisson equation is solved consistently with the charged species. Plasma discharges introduce stiff source terms on the reactive Navier-Stokes equations and Riemann solvers, more robust than the schemes available in AVBP, have been implemented in AVIP and reported back in AVBP to solve the reactive Navier-Stokes equations. The validation of all the numerical schemes is carried out in this paper where numerous validation cases are presented for the plasma drift-diffusions equations and the reactive Navier-Stokes equations., Comment: 40 pages, 44 figures; added GENCI grant in acknowledgments

This paper provides perspectives on recent progress in the understanding of the physics of devices where the external magnetic field is applied perpendicularly to the discharge current. This configuration generates a strong electric field, which acts to accelerates ions. The many applications of this set up include generation of thrust for spacecraft propulsion and the separation of species in plasma mass separation devices. These ExB plasmas are subject to plasma-wall interaction effects as well as various micro and macro instabilities, and in many devices, we observe the emergence of anomalous transport. This perspective presents the current understanding of the physics of these phenomena, state-of-the-art computational results, identifies critical questions, and suggests directions for future research, Comment: 59 pages, 25 Figures, submitted to Physics of Plasmas

The genesis of the ion axial velocity distribution function (VDF) is analyzed for collisionless Hall thruster discharges. An analytical form for the VDF is obtained from the Vlasov equation, by applying the Tonks-Langmuir theory in the thruster channel, under the simplifying assumptions of monoenergetic creation of ions and steady state. The equivalent set of 1D unsteady anisotropic moment equations is derived from the Vlasov equation, and simple phenomenological closures are formulated, assuming a polynomial shape for the ions VDF. The analytical results and the anisotropic moment equations are compared to collisionless PIC simulations, employing either a zero heat flux (Euler-like equations) or the polynomial-VDF closure for the heat flux. The analytical ion VDF and its moments are then compared to experimental measurements.

We present a novel numerical scheme for the efficient and accurate solution of the isothermal two-fluid (electron and ion) equations coupled to Poisson's equation for low-temperature plasmas. The model considers electrons and ions as separate fluids, comprising the electron inertia and charge separation. The discretization of this system with standard explicit schemes is constrained by very restrictive time steps and cell sizes related to the resolution of the Debye length, electron plasma frequency, and electron sound waves. Both sheath and electron inertia are fundamental to fully explain the physics in low-pressure and low-temperature plasmas. However, most of the phenomena of interest for fluid models occur at speeds much slower than the electron thermal speed and are quasi-neutral, except in small charged regions. In this work, we present a scheme based on the Lagrange-projection operator splitting that preserves the asymptotic regime where the plasma is quasi-neutral with massless electrons. As a result, the quasi-neutral regime is treated without the need of an implicit solver nor the resolution of the Debye length and electron plasma frequency. Additionally, the scheme proves to accurately represent the dynamics of the electrons both at low speeds and when the electron speed is comparable to the thermal speed. In addition, a well-balanced treatment of the ion source terms is proposed in order to tackle problems where the ion temperature is very low compared to the electron temperature. The scheme significantly improves the accuracy both in the quasi-neutral limit and in the presence of plasma sheaths when the Debye length is resolved. The scheme is assessed in two specifically designed test-cases: a quasi-neutral two-stream periodic perturbation with analytical solution and a low-temperature discharge that includes sheaths.

Hall-effect thrusters (HETs) operated with xenon are one of the most commonly used electric propulsion technologies for a wide range of space missions, including drag compensation in low Earth orbit, station-keeping, and orbital insertion, as access to space becomes more affordable. Although anomalous electron transport, the electron drift instability (EDI), and secondary electron emission (SEE) have been studied experimentally and numerically in xenon-based HETs, the impact of alternative propellants is still poorly characterized. In this work, a two-dimensional particle-in-cell/Monte Carlo collision (PIC/MCC) code is used to model the (r -- $\theta$) plane of a HET operated separately with four different noble gases: xenon, krypton, argon, and helium. Models for electron induced secondary electron emission (SEE) and dielectric walls are implemented in order to investigate the coupling between the propellant choice and the radial thruster walls. For all conditions and propellants studied, an EDI and enhanced electron cross-field transport are observed. The frequency of the instability, as well as the electron mobility, are compared with analytical expressions from a recently developed kinetic theory. Confirming this theory, it is shown that while the frequency of the EDI depends on the propellant mass, the electron mobility appears to be almost independent of the propellant choice.

Both experimental and theoretical analysis of an {ultra-short} phenomena occurring during the positive streamer propagation in atmospheric pressure air is presented. {With tens-of-picoseconds and tens-of-microns precision, it is shown that when the streamer head passes a spatial coordinate, emission maxima from N$_2$ and N$_2^+$ radiative states follow with different delays. These different delays are caused by differences in the dynamics of populating the radiative states, due to different excitation and quenching rates.} {Associating the position of the streamer head with the maximum value of the self-enhanced electric field, a delay of 160$\,$ps was experimentally found for the peak emission of the first negative system of N$_2^+$.} {For the first time, a delay dilatation was observed experimentally on early-stage streamers and clarified theoretically.} {Thus, in the case of second positive system of N$_2$ the delay can reach as much as 400$\,$ps.} In contrast to the highly-nonlinear behaviour of streamer events, it is shown theoretically that emission maxima delays linearly depend on the ratio of the streamer radius and its velocity. This is found to be one of the fundamental streamer features and its use in streamer head diagnostics is proposed. Moreover, radially-resolved spectra are synthetized for selected subsequent picosecond moments in order to visualize spectrometric fingerprints of radial structures of N$_2$(C$^3\Pi_u$) and N$_2^+$(B$^2\Sigma_u^+$) populations created by streamer-head electrons.

We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used to solve hyperbolic and parabolic time-dependent PDEs. Such an approach guarantees a numerical solution of the Poisson equation within a user-defined accuracy tolerance. Most adaptive meshing approaches in the literature solve elliptic PDEs level-wise and hence at uniform resolution throughout the set of adapted grids. Here we introduce a numerical procedure to represent the elliptic operators on the adapted grid, strongly coupling inter grid relations that guarantee the conservation and accuracy properties of multiresolution finite volume schemes. The discrete Poisson equation is solved at once over the entire computational domain as a completely separate process. The accuracy and numerical performance of the method is assessed in the context of streamer discharge simulations.

The simulation of the interaction of two simultaneously propagating air streamers of the same polarity is presented. A parametric study has been carried out using an accurate numerical method which ensures a time-space error control of the solution. For initial separation of both streamers smaller or comparable to the longest characteristic absorption length of photoionization in air, we have found that the streamers tend to merge at the moment when the ratio between their characteristic width and their mutual distance reaches a value of about 0.35 for positive streamers, and 0.4 for negative ones. Moreover it is demonstrated that these ratios are practically independent of the applied electric field, the initial seed configuration, and the pressure.

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods., Comment: Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS) for providing the basis of the multiresolution kernel of MR CHORUS, code developed for compressible Navier-Stokes equations (D\'eclaration d'Invention DI 03760-01). Accepted for publication; Journal of Computational Physics (2011) 1-28