Mixed Integer Linear Programming for Feature Selection in Support Vector Machine

This work focuses on support vector machine (SVM) with feature selection. A MILP formulation is proposed for the problem. The choice of suitable features to construct the separating hyperplanes has been modelled in this formulation by including a budget constraint that sets in advance a limit on the number of features to be used in the classification process. We propose both an exact and a heuristic procedure to solve this formulation in an efficient way. Finally, the validation of the model is done by checking it with some well-known data sets and comparing it with classical classification methods.Comment: 37 pages, 20 figure

The stratified p-center problem

This work presents an extension of the p-center problem. In this new model, called Stratified p-Center Problem (SpCP), the demand is concentrated in a set of sites and the population of these sites is divided into different strata depending on the kind of service that they require. The aim is to locate p centers to cover the different types of services demanded minimizing the weighted average of the largest distances associated with each of the different strata. In addition, it is considered that more than one stratum can be present at each site. Different formulations, valid inequalities and preprocessings are developed and compared for this problem. An application of this model is presented in order to implement a heuristic approach based on the Sample Average Approximation method (SAA) for solving the probabilistic p-center problem in an efficient way.Comment: 32 pages, 1 pictur

Plasma detachment in a propulsive magnetic nozzle via ion demagnetization

Plasma detachment in propulsive magnetic nozzles is shown to be a robust phenomenon caused by the inability of the internal electric fields to bend most of the supersonic ions along the magnetic streamtubes. As a result, the plasma momentum is effectively ejected to produce thrust, and only a marginal fraction of the beam mass flows back. Detachment takes place even if quasineutrality holds everywhere and electrons are fully magnetized, and is intimately linked to the formation of local electric currents. The divergence angle of the 95%-mass flow tube is used as a quantitative detachment performance figure.This work has been sponsored by the Air Force Office of Scientific Research, USAF (FA8655-12-1-2043) and Spain R & D National Plan (AYA-2010-61699

Fully magnetized plasma flow in a magnetic nozzle

A model of the expansion of a plasma in a magnetic nozzle in the full magnetization limit is presented. The fully magnetized and the unmagnetized-ions limits are compared, recovering the whole range of variability in plasma properties, thrust, and plume efficiency, and revealing the differences in the physics of the two cases. The fully magnetized model is the natural limit of the general, 2D, two-fluid model of Ahedo and Merino [Phys. Plasmas 17, 073501 (2010)], and it is proposed as an analytical, conservative estimator of the propulsive figures of merit of partially magnetized plasma expansions in the near region of the magnetic nozzle.This work has been supported by the Spanish R&D National Plan, Grant No. ESP2013-41052-P

Contactless steering of a plasma jet with a 3D magnetic nozzle

A 3D, steerable magnetic nozzle (MN) is presented that enables contactless thrust vector control of a plasma jet without any moving parts. The concept represents a substantial simplification over current plasma thruster gimbaled platforms, and requires only a small modification in thrusters that already have a MN. The characteristics of the plasma expansion in the 3D magnetic field and the deflection performance of the device are characterized with a fully magnetized plasma model, suggesting that thrust deflections of 5 degrees - 10 degrees are readily achievable.This work has been supported by the Spanish R&D National Plan under grant number ESP2016-75887-P

Influence of electron and ion thermodynamics on the magnetic nozzle plasma expansion

Proceeding of: 33rd International Electric Propulsion Conference (IEPC 2013)A two-fluid 2-D model of the supersonic plasma flow in a propulsive magnetic nozzle (MN) is extended to include simple electron and ion thermodynamics to study the effects of electron cooling and ion thermal energy on the expansion. A faster electron cooling rate is seen to reduce plasma jet divergence, increase radial rarefaction, and enhance detachment from the closed magnetic lines. Ion thermal energy is converted to directed kinetic energy by the MN without the mediation of an ambipolar electric field, and alters the electric response of the plasma.This work has been supported by the European Space Agency project 'Helicon Plasma Thruster for Space Missions', grant number 4000107292/12/NL/CO. Additional support has been provided by Spain's R&D National Plan (Project AYA-2010-61699)

Effect of the plasma-induced magnetic field on a magnetic nozzle

A two-fluid, two-dimensional model of the plasma expansion in a divergent magnetic nozzle is used to investigate the effect of the plasma-induced magnetic field on the acceleration and divergence of the plasma jet self-consistently. The induced field is diamagnetic and opposes the applied one, increasing the divergence of the magnetic nozzle and weakening its strength. This has a direct impact on the propulsive performance of the device, the demagnetization and detachment of the plasma, and can lead to the appearance of zero-field points and separatrix surfaces downstream. In contrast, the azimuthal induced field, albeit non-zero, is small in all cases of practical interest.Initial work was sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF (FA8655-12-1-2043). Additional support was provided by Spanish R&D National Plan (grant number ESP2013-41052-P)

Three-dimensional geomagnetic field effects on a plasma thruster plume expansion

A 3D hybrid particle-in-cell code with a partially-magnetized fluid electron model is presented and applied to study the effects of a uniform external geomagnetic field on an expanding plasma thruster plume at three different angles. Electron currents are governed by both the magnetic field and collisional effects with the heavy ions and neutrals. While an axial magnetic field (parallel to the plume axis) induces azimuthal electric currents and an observable plume channeling, an oblique field produces non-trivial asymmetric deformations of the plume cross-section, and induces axial-radial electric current loops. A center of mass analysis of the plasma plume demonstrates that the electron response produces an electric field that balances the Lorentz force deflection on the ions, so that no net plume momentum deflection is observed.The primary funder of this research was the Comunidad de Madrid (Spain), under PROMETEO-CM project, with grant number Y2018/NMT-4750. Initial support was provided by the Ministerio de Economía y Competitividad (Spain), under project ESP2016-75887-

Two-dimensional plasma-wave interaction in an helicon plasma thruster with magnetic nozzle

Special Issue on Space Plasma PropulsionAn axisymmetric, finite difference frequency domain model is used to study the wave propagation and power absorption in a helicon plasma thruster operating inside a laboratory vacuum chamber. The magnetic field is not purely axial and the plasma beam is cylindrical in the source and divergent in the magnetic nozzle. The influence of the magnetic field strength, plasma density, electron collision frequency and geometry on the wavefields and the power absorption maps is investigated, showing different power deposition patterns. The electromagnetic radiation is not confined to the source region but propagates into the nozzle divergent region, and indeed the power absorption there is not negligible. For the impedance at the antenna, the reactance is rather constant but the resistance is very dependent on operation parameters; optimal parameter values maximizing the resistance are found.The authors acknowledge the initial development of the present model by V. Gomez and J. Navarro. This work was supported by the Spain's National Research and Development Plan (Project ESP2016-75887). Bin Tian was supported by a PhD grant from the Chinese Scholarship Council

Spacecraft-plasma-debris interaction in an ion beam shepherd mission

This paper presents a study of the interaction between a spacecraft, a plasma thruster plume and a free floating object, in the context of an active space debris removal mission based on the ion beam shepherd concept. The analysis is performed with the EP2PLUS hybrid code and includes the evaluation of the transferred force and torque to the target debris, its surface sputtering due to the impinging hypersonic ions, and the equivalent electric circuit of the spacecraft-plasma-debris interaction. The electric potential difference that builds up between the spacecraft and the debris, the ion backscattering and the backsputtering contamination of the shepherd satellite are evaluated for a nominal scenario. A sensitivity analysis is carried out to evaluate quantitatively the effects of electron thermodynamics, ambient plasma, heavy species collisions, and debris position