Current collection by an active spherical electrode in an unmagnetized plasma

A theoretical model for the steady-state response of anodic contactors that emit a plasma current Ii and collect electrons from a collisionless, unmagnetized plasma is presented. The use of a (kinetic) monoenergetic population for the attracted species, well known in passive probe theory, gives both accuracy and tractability to the theory. The monoenergetic population is proved to behave like an isentropic fluid with radial plus centripetal motion, allowing direct comparisons with ad hoc fluid models. Also, a modification of the original monoenergetic equations permits analysis of contactors operating in orbit-limited conditions. Besides that, the theory predicts that, only for plasma emissions above certain threshold current a presheath/double layer/core structure for the potential is formed (the core mode), while for emissions below that threshold, a plasma contactor behaves exactly as a positive-ion emitter with a presheath/sheath structure (the no-core mode). Ion emitters are studied as a particular case. Emphasis is placed on obtaining dimensionless charts and approximate asymptotic laws of the current-voltage characteristic.

Non-periodic driving of coupled oscillators:a spherical swing

Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one oscillator being driven coherently for efficient excitation, are exemplified by a spherical swing with some phase-mismatch between drive and response. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the response. Although a period-doubhng sequence, for damping increasing, leads to the attractor, this is actually born as a hard (as regards amplitude) bifurcation at a zero growth-rate parametric line; as damping decreases, an unstable fixed point crosses an invariant plane to enter as saddle-focus a phase-space domain of physical solutions. A second hard bifurcation occurs at the zero mismatch line, the saddle-focus leaving that domain. Times on the attractor diverge when approaching either fine, leading to exactly one-dimensional and noninvertible limit maps, which are analytically determined.

Spherical collectors versus bare tethers for drag, thrust, and power generation

Deorbit, power generation, and thrusting performances of a bare thin-tape tether and an insulated tether with a spherical electron collector are compared for typical conditions in low-Earth orbit and common values of length L = 4−20 km and cross-sectional area of the tether A = 1−5 mm2. The relative performance of moderately large spheres, as compared with bare tapes, improves but still lags as one moves from deorbiting to power generation and to thrusting: Maximum drag in deorbiting requires maximum current and, thus, fully reflects on anodic collection capability, whereas extracting power at a load or using a supply to push current against the motional field requires reduced currents. The relative performance also improves as one moves to smaller A, which makes the sphere approach the limiting short-circuit current, and at greater L, with the higher bias only affecting moderately the already large bare-tape current. For a 4-m-diameter sphere, relative performances range from 0.09 sphere-to-bare tether drag ratio for L = 4 km and A = 5 mm2 to 0.82 thrust–efficiency ratio for L = 20 km and A = 1 mm2. Extremely large spheres collecting the short-circuit current at zero bias at daytime (diameters being about 14 m for A = 1 mm2 and 31 m for A = 5 mm2) barely outperform the bare tape for L = 4 km and are still outperformed by the bare tape for L = 20 km in both deorbiting and power generation; these large spheres perform like the bare tape in thrusting. In no case was sphere or sphere-related hardware taken into account in evaluating system mass, which would have reduced the sphere performances even further.

Spherical collectors versus bare tethers for drag, thrust, and power generation

Performances of ED-tethers using either spherical collectors or bare tethers for drag, thrust, or power generation, are compared. The standard Parker-Murphy model of current to a full sphere, with neither space-charge nor plasmamotion effects considered, but modified to best fit TSS1R results, is used (the Lam, Al'pert/Gurevich space-charge limited model will be used elsewhere) In the analysis, the spherical collector is assumed to collect current well beyond its random-current value (thick-heath). Both average current in the bare-tether and current to the sphere are normalized with the short-circuit current in the absence of applied power, allowing a comparison of performances for all three applications in terms of characteristic dimensionless numbers. The sphere is always substantially outperformed by the bare-tether if ohmic effects are weak, though its performance improves as such effects increase.

Experimental evidence for super-resolution in the spherical geodesic waveguide

The previous publications (Miñano et al, 2011 and Gonzalez et al, 2012) have shown that using a Spherical Geodesic Waveguide (SGW) it can be achieved the super-resolution up to λ/3000, which is far below the classic Abbe diffraction limit, close to a set of discrete microwave frequencies. The SGW was designed and simulated in COMSOL as a thin geodesic waveguide bounded by an ideal and lossless metal. Herein we present the experimental results for a manufactured SGW, slightly modified due to fabrication requirements, showing the super-resolution up to λ/105.

Current-voltage response of a spherical plasma contactor

A theoretical model for a contactor, collecting electrons from an ambient, unmagnetized plasma and emitting a current Iiis discussed. The relation between Ii and the potential bias of the contactor is found to be crucial for the formation of a quasineutral core around the anode and, consequently, for the current colleted. Approximate analytical laws and charts for the current-voltage response are provided.

Inverse kinematics of a humanoid robot with non-spherical hip: a hybrid algorithm approach

This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate “solution” by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg‐Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real‐time applications. As a way to show the algorithm’s implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.