Two-region model for positive and negative plasma sheaths and its application to Hall thruster metallic anodes.

An asymptotic presheath/sheath model for positive and negative sheaths in front of a conducting electrode, with a continuous parametric transition at the no-sheath case, is presented. Key aspects of the model are as follows: full hydrodynamics of both species in the presheath; a kinetic formulation with a truncated distribution function for the repelled species within the sheath; and the fulfillment of the marginal Bohm condition at the sheath edge, in order to match the two formulations of the repelled species. The sheath regime depends on the ratios of particle fluxes and sound speeds between the two species. The presheath model includes the effect of a magnetic field parallel to the wall on electrons. An asymptotic, parametric study of the anode presheath is carried out in terms of the local ion-to-electron flux ratio and Hall parameter. The drift-diffusive model of magnetized electrons fails in a parametric region that includes parts of the negative sheath regime. In the case of the Hall parameter vanishing near the electrode and a weakly collisional plasma, a quasisonic, quasineutral plateau forms next to the sheath edge

On the regularity of the covariance matrix of a discretized scalar field on the sphere

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.Comment: 36 pages, 12 figures; minor changes in the text, matches published versio

Two-dimensional plasma expansion in a magnetic nozzle: Separation due to electron inertia

A previous axisymmetric model of the supersonic expansion of a collisionless, hot plasma in a divergent magnetic nozzle is extended here in order to include electron-inertia effects. Up to dominant order on all components of the electron velocity, electron momentum equations still reduce to three conservation laws. Electron inertia leads to outward electron separation from the magnetic streamtubes. The progressive plasma filling of the adjacent vacuum region is consistent with electron-inertia being part of finite electron Larmor radius effects, which increase downstream and eventually demagnetize the plasma. Current ambipolarity is not fulfilled and ion separation can be either outwards or inwards of magnetic streamtubes, depending on their magnetization. Electron separation penalizes slightly the plume efficiency and is larger for plasma beams injected with large pressure gradients. An alternative nonzero electron-inertia model [E. Hooper, J. Propul. Power 9, 757 (1993)] based on cold plasmas and current ambipolarity, which predicts inwards electron separation, is discussed critically. A possible competition of the gyroviscous force with electron-inertia effects is commented briefly

Acceleration of a focused plasma jet in a divergent magnetic nozzle,”

A two dimensional model of a divergent magnetic nozzle is used to analyze the conversion of thermal into kinetic energy for a collisionless plasma jet with a large radial density gradient at the nozzle entrance. Comparisons with a 1D model and with a uniform plasma jet are made. The focused plasma jet has a much better nozzle efficiency. The large Hall current required to focus the jet increases downstream and sets up two magnetic detachment mechanisms: an induced magnetic field and azimuthal electron inertia effects. This second mechanism seems stronger than the first one

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

Self-consistent resonance absorption with two layer profile steepening

Resonance absorption of p-polarized light, incident at angle 6 on a flowing, stratified plasma, is analyzed; profile steepening within (i) a layer around the turning point, and (ii) a thinner,embedded sublayer at the critical surface is taken into account self-consistently. The entire steepened region is taken as collisionless and isothermal. The structure of the main layer shows a variety of regimes, depending on how the flow crosses a sonic point. The structure of the sublayer is also determined; it is entirely subsonic (with no wave breaking) for a well-defined,broad parameter range. Density changes across both layer and sublayer, and fractional absorption, are given in terms of [(wavelength)2 Xintensity/temperature], and (temperature/mec2). The flow outside the double structure is also analyzed for particular conditions

A Numerical Examination of the Performance of Small Magnetic Nozzle Thrusters

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143040/1/6.2017-4721.pd

Energy Analysis of Bare Electrodynamic Tethers

The design of an electrodynamic tether is a complex task that involves the control of dynamic instabilities, optimization of the generated power (or the descent time in deorbiting missions), and minimization of the tether mass. The electrodynamic forces on an electrodynamic tether are responsible for variations in the mechanical energy of the tethered system and can also drive the system to dynamic instability. Energy sources and sinks in this system include the following: 1) ionospheric impedance, 2) the potential drop at the cathodic contactor, 3) ohmic losses in the tether, 4) the corotational plasma electric field, and 5) generated power and/or 6) input power. The analysis of each of these energy components, or bricks, establishes parameters that are useful tools for tether design. In this study, the nondimensional parameters that govern the orbital energy variation, dynamic instability, and power generation were characterized, and their mutual interdependence was established. A space-debris mitigation mission was taken as an example of this approach for the assessment of tether performance. Numerical simulations using a dumbbell model for tether dynamics, the International Geomagnetic Reference Field for the geomagnetic field, and the International Reference Ionosphere for the ionosphere were performed to test the analytical approach. The results obtained herein stress the close relationships that exist among the velocity of descent, dynamic stability, and generated power. An optimal tether design requires a detailed tradeoff among these performances in a real-world scenario

One Dimensional Hybrid-Vlasov Simulation of a Hall Thruster

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97103/1/AIAA2012-4313.pd

UV-Casting on methacrylated PCL for the production of a peripheral nerve implant containing an array of porous aligned microchannels

Peripheral nerves are basic communication structures guiding motor and sensory information from the central nervous system to receptor units. Severed peripheral nerve injuries represent a large clinical problem with relevant challenges to successful synthetic nerve repair scaffolds as substitutes to autologous nerve grafting. Numerous studies reported the use of hollow tubes made of synthetic polymers sutured between severed nerve stumps to promote nerve regeneration while providing protection for external factors, such as scar tissue formation and inflammation. Few approaches have described the potential use of a lumen structure comprised of microchannels or microfibers to provide axon growth avoiding misdirection and fostering proper healing. Here, we report the use of a 3D porous microchannel-based structure made of a photocurable methacrylated polycaprolactone, whose mechanical properties are comparable to native nerves. The neuro-regenerative properties of the polymer were assessed in vitro, prior to the implantation of the 3D porous structure, in a 6-mm rat sciatic nerve gap injury. The manufactured implants were biocompatible and able to be resorbed by the host’s body at a suitable rate, allowing the complete healing of the nerve. The innovative design of the highly porous structure with the axon guiding microchannels, along with the observation of myelinated axons and Schwann cells in the in vivo tests, led to a significant progress towards the standardized use of synthetic 3D multichannel-based structures in peripheral nerve surgery