Structure of intermediate shocks in collisionsless anisotropic Hall-magnetohydrodynamics plasma models

The existence of discontinuities within the double-adiabatic Hall-magnetohydrodynamics (MHD) model is discussed. These solutions are transitional layers where some of the plasma properties change from one equilibrium state to another. Under the assumption of traveling wave solutions with velocity C and propagation angle θ with respect to the ambient magnetic field, the Hall-MHD model reduces to a dynamical system and the waves are heteroclinic orbits joining two different fixed points. The analysis of the fixed points rules out the existence of rotational discontinuities. Simple considerations about the Hamiltonian nature of the system show that, unlike dissipative models, the intermediate shock waves are organized in branches in parameter space, i.e., they occur if a given relationship between θ and C is satisfied. Electron-polarized (ion-polarized) shock waves exhibit, in addition to a reversal of the magnetic field component tangential to the shock front, a maximum (minimum) of the magnetic field amplitude. The jumps of the magnetic field and the relative specific volume between the downstream and the upstream states as a function of the plasma properties are presented. The organization in parameter space of localized structures including in the model the influence of finite Larmor radius is discusse

Limitations of stationary Vlasov-Poisson solvers in probe theory

Physical and numerical limitations of stationary Vlasov-Poisson solvers based on backward Liouville methods are investigated with five solvers that combine different meshes, numerical integrators, and electric field interpolation schemes. Since some of the limitations arise when moving from an integrable to a non-integrable configuration, an elliptical Langmuir probe immersed in a Maxwellian plasma was considered and the eccentricity (ep) of its cross-section used as integrability-breaking parameter. In the cylindrical case, ep=0, the energy and angular momentum are both conserved. The trajectories of the charged particles are regular and the boundaries that separate trapped from non-trapped particles in phase space are smooth curves. However, their computation has to be done carefully because, albeit small, the intrinsic numerical errors of some solvers break these conservation laws. It is shown that an optimum exists for the number of loops around the probe that the solvers need to classify a particle trajectory as trapped. For ep≠0, the angular momentum is not conserved and particle dynamics in phase space is a mix of regular and chaotic orbits. The distribution function is filamented and the boundaries that separate trapped from non-trapped particles in phase space have a fractal geometry. The results were used to make a list of recommendations for the practical implementation of stationary Vlasov-Poisson solvers in a wide range of physical scenarios.This work was supported by the European Union's Horizon 2020 Research and Innovation Programme under grant agreement No 828902 (E.T.PACK project). GSA work is supported by the Ministerio de Ciencia, Innovación of Spain under the Grant RYC-2014-15357. The authors thank the Reviewers for their valuable comments and suggestions about the use of energy-conserving numerical integrators

Ionospheric experiment with a low work function tether loop

An entirely passive and free of consumable ionospheric experiment, based on a low work function tether (LWT) loop with a control unit equipped with some basics sensors at its center, is presented. The loop has a torus shape and a hollow cross-section. It is made of an aluminum substrate coated with a low work function material to stimulate electron emission through thermionic and photoelectric effects. The work presents an electrodynamic model for the experiment and studies the current and voltage profiles developed in the anodic and cathodic segments of the LWT due to the motional electric field. Two modes of operation, with and without switches in the loop to interrupt the electric current, are considered. It is shown that the loop is deorbited by the Lorentz force exerted by the ambient magnetic field on the electric current. An analysis of the attitude dynamics in the presence of the gravity gradient and the Lorentz torques reveals that, for a circular equatorial orbit, the position of the loop with its symmetry axis normal to the orbital plane can be spin-stabilized easily. The required instruments and the scientific information that would be provided by the experiment are discussed.This work was initially supported by Agencia Estatal de Investigación (Ministerio de Ciencia, Innovación y Universidades of Spain) under the project ESP2017-82092-ERC (AEI) and continued thanks to funding received from the European Union's Horizon 2020 research and innovation program under grant agreement No. 828902 (E. T. PACK project). GS-A's work was supported by the Ministerio de Ciencia, Innovación y Universidades of Spain, under the Grant RYC-2014-15357. SN's work was supported by Comunidad de Madrid (Spain) under the Grant 2018/T2IND/11352

Modeling and Performance of Electrodynamic Low-Work-Function Tethers with Photoemission Effects

A low-work-function tether is a long conductor coated with a low-work-function material that orbits around a planet with both the magnetic field and ionosphere. Depending on the work function W of the coating and the tether temperature T, the photoelectron emission can be relevant within the cathodic tether segment. Thus, this mechanism needs to be added to the thermionic emission considered in previous works. An emission model for low-work-function tethers, including a typical solar photon spectrum, a Fowler–DuBridge law for the photoelectron yield of the coating, and a Richardson–Dushman law for the thermionic emission, is presented, and used to organize the thermionic and photoelectric dominated regimes of low-work-function tethers within the W–T plane. For T≈500  K and W≈1.5  eV, the photoemission and thermionic emission can be of the same order and have similar efficiency as the electron collection. The emission model is combined with orbital-motion theory for all the plasma and emitted particles, and the longitudinal bias and current profiles throughout a low-work-function tether are determined for typical low-Earth-orbit environmental values. Results for the average current are presented. The study highlights the main electrical, mechanical, and optical properties that should be considered in the design of low-work-function tethers, and it briefly discusses some promising materials

Current-Voltage and floating-potential characteristics of cylindrical emissive probes from a full-kinetic model based on the orbital motion theory

12th International Workshop on Electric Probes in Magnetized Plasmas (IWEP 2017)To model the sheath structure around an emissive probe with cylindrical geometry, the Orbital-Motion theory takes advantage of three conserved quantities (distribution function, transverse energy, and angular momentum) to transform the stationary Vlasov-Poisson system into a single integro-differential equation. For a stationary collisionless unmagnetized plasma, this equation describes self-consistently the probe characteristics. By solving such an equation numerically, parametric analyses for the current-voltage (IV) and floating-potential (FP) characteristics can be performed, which show that: (a) for strong emission, the space-charge effects increase with probe radius; (b) the probe can float at a positive potential relative to the plasma; (c) a smaller probe radius is preferred for the FP method to determine the plasma potential; (d) the work function of the emitting material and the plasma-ion properties do not influence the reliability of the floating-potential method. Analytical analysis demonstrates that the inflection point of an IV curve for non-emitting probes occurs at the plasma potential. The flat potential is not a self-consistent solution for emissive probes.This work was supported by the Ministerio de Economía y Competitividad of Spain (Grant No ESP-2016-75887). Work by G. Snchez-Arriaga was supported by the Ministerio de Economía y Competitividad of Spain (Grant No RYC-2014-15357)

Flight dynamics and stability of kites in steady and unsteady wind conditions

The flight dynamics and stability of a kite with a single main line flying in steady and unsteady wind conditions are discussed. A simple dynamic model with five degrees of freedom is derived with the aid of Lagrangian formulation, which explicitly avoids any constraint force in the equations of motion. The longitudinal and lateral–directional modes and stability of the steady flight under constant wind conditions are analyzed by using both numerical and analytical methods. Taking advantage of the appearance of small dimensionless parameters in the model, useful analytical formulas for stable-designed kites are found. Under nonsteady wind-velocity conditions, the equilibrium state disappears and periodic orbits occur. The kite stability and an interesting resonance phenomenon are explored with the aid of a numerical method based on Floquet theory

BETsMA v2.0: a friendly software for the analysis of electrodynamic tether missions in Jupiter

Proceeding of: Eruoplanet Science Congress 2020, EPSC2020 (vitual meeting), 21 September - 9 October 2020.Space Electrodynamic Tethers (EDTs) are km-long conductors that exchange momentum and energy with a planet magnetosphere through the Lorentz force exerted by the planet's magnetic field on the tether current. Since the conducting medium (plasma) and the magnetic field of the planetary environment are essential for their operation, tether are appropriate for applications in Low Earth Orbits (LEO) and the neighborhood of giant planets like Jupiter [1, 2, 3, 4], Saturn [5], and Neptune [6]. However, the design and analysis of missions in outer planets typically requires deep knowledge on tethers modeling. The main goal of this work is spreading the use of tethers and presenting a friendly software for the mission analysis and simulation of tethers in Jupiter.This work has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No 828902 (E.T.PACK project). GSA work is supported by the Ministerio de Ciencia e Innovación of Spain under the Grant RYC-2014-15357.Publicad

Kite model with bridle control for wind-power generation

A compact flight dynamics model of a kite is developed by using Lagrangian formulation. The lengths of the three ropes of the bridle and the tether of the kite depend on time and are used to implement an open-loop control scheme of the kite system. By imposing simple time-periodic control laws, two pumping strategies for wind-energy generation are explored. Periodic trajectories of the system and their stability properties (Floquet characteristic multipliers) are computed numerically. As the amplitudes of the figure-eight paths are increased, the system becomes more efficient but less stable. A cyclic-fold bifurcation is detected for a very large lateral displacement of the kite. The impact of the control-law parameters on the generated power, including the period and the amplitude, is investigated. The results indicate that a correct design of the control could provide an optimal energy-generation system and a robust scheme to exploit high-altitude winds

Relativistic current collection by a cylindrical Langmuir probe

The current I to a cylindrical Langmuir probe with a bias Φp satisfying β≡eΦp/mec2∼O(1) is discussed. The probe is considered at rest in an unmagnetized plasma composed of electrons and ions with temperatureskTe∼kTi≪mec2. For small enough radius, the probe collects the relativistic orbital-motion-limited (OML) current I OML , which is shown to be larger than the non-relativistic result; the OML current is proportional to β1/2 and β3/2 in the limits β≪1 and β≫1, respectively. Unlike the non-relativistic case, the electron density can exceed the unperturbed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/I OML drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/IOML drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed

Fast magnetosonic wave excitation by an array of wires with time-modulated currents

The excitation of Fast Magnetosonic (FMS)waves by a cylindrical array of parallel tethers carrying timemodulated current is discussed. The tethers would fly vertical in the equatorial plane, which is perpendicular to the geomagnetic field when its tilt is ignored, and would be stabilized by the gravity gradient. The tether array would radiate a single FMS wave. In the time-dependent background made of geomagnetic field plus radiated wave, plasma FMS perturbations are excited in the array vicinity through a parametric instability. The growth rate is estimated by truncating the evolution equation for FMS perturbations to the two azimuthal modes of lowest order. Design parameters such as tether length and number, required power and mass are discussed for Low Earth Orbit conditions. The array-attached wave structure would have the radiated wave controlled by the intensity and modulation frequency of the currents, making an active experiment on non-linear low frequency waves possible in real space plasma conditions