Analysis of Magnetic Nozzles For Space Plasma Thrusters = Análisis de Toberas Magnéticas para Motores Espaciales de Plasma

Esta tesis presenta un análisis teórico del funcionamiento de toberas magnéticas para la propulsión espacial por plasmas. El estudio está basado en un modelo tridimensional y bi-fluido de la expansión supersónica de un plasma caliente en un campo magnético divergente. El modelo básico es ampliado progresivamente con la inclusión de términos convectivos dominantes de electrones, el campo magnético inducido por el plasma, poblaciones electrónicas múltiples a distintas temperaturas, y la capacidad de integrar el flujo en la región de expansión lejana. La respuesta hiperbólica del plasma es integrada con alta precisión y eficiencia haciendo uso del método de las líneas características. Se realiza una caracterización paramétrica de la expansión 2D del plasma en términos del grado de magnetización de iones, la geometría del campo magnético, y el perfil inicial del plasma. Se investigan los mecanismos de aceleración, mostrando que el campo ambipolar convierte la energía interna de electrones en energía dirigida de iones. Las corrientes diamagnéticas de Hall, que pueden hallarse distribuidas en el volumen del plasma o localizadas en una delgada capa de corriente en el borde del chorro, son esenciales para la operación de la tobera, ya que la fuerza magnética repulsiva sobre ellas es la encargada de confinar radialmente y acelerar axialmente el plasma. El empuje magnético es la reacción a esta fuerza sobre el motor. La respuesta del plasma muestra la separación gradual hacia adentro de los tubos de iones respecto de los magnéticos, lo cual produce la formación de corrientes eléctricas longitudinales y pone el plasma en rotación. La ganancia de empuje obtenida y las pérdidas radiales de la pluma de plasma se evalúan en función de los parámetros de diseño. Se analiza en detalle la separación magnética del plasma aguas abajo respecto a las líneas magnéticas (cerradas sobre sí mismas), necesaria para la aplicación de la tobera magnética a fines propulsivos. Se demuestra que tres teorías existentes sobre separación, que se fundamentan en la resistividad del plasma, la inercia de electrones, y el campo magnético que induce el plasma, son inadecuadas para la tobera magnética propulsiva, ya que producen separación hacia afuera en lugar de hacia adentro, aumentando la divergencia de la pluma. En su lugar, se muestra que la separación del plasma tiene lugar gracias a la inercia de iones y la desmagnetización gradual del plasma que tiene lugar aguas abajo, que permiten la separación ilimitada del flujo de iones respecto a las líneas de campo en condiciones muy generales. Se evalúa la cantidad de plasma que permanece unida al campo magnético y retorna hacia el motor a lo largo de las líneas cerradas de campo, mostrando que es marginal. Se muestra cómo el campo magnético inducido por el plasma incrementa la divergencia de la tobera magnética y por ende de la pluma de plasma en el caso propulsivo, contrariamente a las predicciones existentes. Se muestra también cómo el inducido favorece la desmagnetización del núcleo del chorro, acelerando la separación magnética. La hipótesis de ambipolaridad de corriente local, común a varios modelos de tobera magnética existentes, es discutida críticamente, mostrando que es inadecuada para el estudio de la separación de plasma. Una inconsistencia grave en la derivación matemática de uno de los modelos más aceptados es señalada y comentada. Incluyendo una especie adicional de electrones supratérmicos en el modelo, se estudia la formación y geometría de dobles capas eléctricas en el interior del plasma. Cuando dicha capa se forma, su curvatura aumenta cuanto más periféricamente se inyecten los electrones supratérmicos, cuanto menor sea el campo magnético, y cuanto más divergente sea la tobera magnética. El plasma con dos temperaturas electrónicas posee un mayor ratio de empuje magnético frente a total. A pesar de ello, no se encuentra ninguna ventaja propulsiva de las dobles capas, reforzando las críticas existentes frente a las propuestas de estas formaciones como un mecanismo de empuje. Por último, se presenta una formulación general de modelos autosemejantes de la expansión 2D de una pluma no magnetizada en el vacío. El error asociado a la hipótesis de autosemejanza es calculado, mostrando que es pequeño para plumas hipersónicas. Tres modelos de la literatura son particularizados a partir de la formulación general y comparados. Abstract This Thesis presents a theoretical analysis of the operation of magnetic nozzles for plasma space propulsion. The study is based on a two-dimensional, two-fluid model of the supersonic expansion of a hot plasma in a divergent magnetic field. The basic model is extended progressively to include the dominant electron convective terms, the plasma-induced magnetic field, multi-temperature electron populations, and the capability to integrate the plasma flow in the far expansion region. The hyperbolic plasma response is integrated accurately and efficiently with the method of the characteristic lines. The 2D plasma expansion is characterized parametrically in terms of the ion magnetization strength, the magnetic field geometry, and the initial plasma profile. Acceleration mechanisms are investigated, showing that the ambipolar electric field converts the internal electron energy into directed ion energy. The diamagnetic electron Hall current, which can be distributed in the plasma volume or localized in a thin current sheet at the jet edge, is shown to be central for the operation of the magnetic nozzle. The repelling magnetic force on this current is responsible for the radial confinement and axial acceleration of the plasma, and magnetic thrust is the reaction to this force on the magnetic coils of the thruster. The plasma response exhibits a gradual inward separation of the ion streamtubes from the magnetic streamtubes, which focuses the jet about the nozzle axis, gives rise to the formation of longitudinal currents and sets the plasma into rotation. The obtained thrust gain in the magnetic nozzle and radial plasma losses are evaluated as a function of the design parameters. The downstream plasma detachment from the closed magnetic field lines, required for the propulsive application of the magnetic nozzle, is investigated in detail. Three prevailing detachment theories for magnetic nozzles, relying on plasma resistivity, electron inertia, and the plasma-induced magnetic field, are shown to be inadequate for the propulsive magnetic nozzle, as these mechanisms detach the plume outward, increasing its divergence, rather than focusing it as desired. Instead, plasma detachment is shown to occur essentially due to ion inertia and the gradual demagnetization that takes place downstream, which enable the unbounded inward ion separation from the magnetic lines beyond the turning point of the outermost plasma streamline under rather general conditions. The plasma fraction that remains attached to the field and turns around along the magnetic field back to the thruster is evaluated and shown to be marginal. The plasmainduced magnetic field is shown to increase the divergence of the nozzle and the resulting plasma plume in the propulsive case, and to enhance the demagnetization of the central part of the plasma jet, contrary to existing predictions. The increased demagnetization favors the earlier ion inward separation from the magnetic field. The local current ambipolarity assumption, common to many existing magnetic nozzle models, is critically discussed, showing that it is unsuitable for the study of plasma detachment. A grave mathematical inconsistency in a well-accepted model, related to the acceptance of this assumption, is found out and commented on. The formation and 2D shape of electric double layers in the plasma expansion is studied with the inclusion of an additional suprathermal electron population in the model. When a double layer forms, its curvature is shown to increase the more peripherally suprathermal electrons are injected, the lower the magnetic field strength, and the more divergent the magnetic nozzle is. The twoelectron- temperature plasma is seen to have a greater magnetic-to-total thrust ratio. Notwithstanding, no propulsive advantage of the double layer is found, supporting and reinforcing previous critiques to their proposal as a thrust mechanism. Finally, a general framework of self-similar models of a 2D unmagnetized plasma plume expansion into vacuum is presented and discussed. The error associated with the self-similarity assumption is calculated and shown to be small for hypersonic plasma plumes. Three models of the literature are recovered as particularizations from the general framework and compared.

Variable-density jet flows induced by concentrated sources of momentum and energy

The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in ℓ-space are consistent with a ΔT flat in frequency and broadly follow inflation-based expectations. That the levels are ∼(10−5)2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at ℓ ≳ 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Λ cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 ± 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 ± 0.08 for DMR plus the SK95 experiment; 1.00 ± 0.04 for DMR plus all smaller angle experiments; 1.00 ± 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Λ and moderate constraints on Ωtot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

Optical evidence for the unification of active galactic nuclei and quasi-stellar objects.

There is a variety of optical evidence for some unification of different types of active galactic nuclei and quasi-stellar objects (QSOs). The case is very strong for the unification of at least some Seyfert galaxies, where polarization data show that the type assigned to the Seyfert galaxy must depend on viewing direction. It has been proposed that Fanaroff-Riley type 2 (FR2) radio galaxies are quasars seen in a direction from which the quasar is obscured, and there is some limited direct evidence for this picture. The broad absorption line QSOs may be normal QSOs seen from a special direction. Some of the sources observed to have high luminosities in the far infrared could be obscured QSOs and active nuclei. Mergers and interactions are likely to play an important role in nuclear activity, and active galaxies and QSOs could change their apparent types through these encounters followed by subsequent evolution.

Pathways to quiescence: SHARDS view on the star formation histories of massive quiescent galaxies at 1.0 < z < 1.5

We present star formation histories (SFHs) for a sample of 104 massive (stellar mass M > 10^10 M_⊙) quiescent galaxies (MQGs) at z = 1.0–1.5 from the analysis of spectrophotometric data from the Survey for High-z Absorption Red and Dead Sources (SHARDS) and HST/WFC3 G102 and G141 surveys of the GOODS-North field, jointly with broad-band observations from ultraviolet (UV) to far-infrared (far-IR). The sample is constructed on the basis of rest-frame UVJ colours and specific star formation rates (sSFRs = SFR/Mass). The spectral energy distributions (SEDs) of each galaxy are compared to models assuming a delayed exponentially declining SFH. A Monte Carlo algorithm characterizes the degeneracies, which we are able to break taking advantage of the SHARDS data resolution, by measuring indices such as MgUV and D4000. The population of MQGs shows a duality in their properties. The sample is dominated (85 per cent) by galaxies with young mass-weighted ages, t_M t_M < 2 Gyr, short star formation time-scales, 〈τ〉 ∼ 60–200 Myr, and masses log(M/M_⊙) ∼ 10.5. There is an older population (15 per cent) with t_M t_M = 2–4 Gyr, longer star formation time-scales, 〈τ〉∼ 400 Myr, and larger masses, log(M/M_⊙) ∼ 10.7. The SFHs of our MQGs are consistent with the slope and the location of the main sequence of star-forming galaxies at z > 1.0, when our galaxies were 0.5–1.0 Gyr old. According to these SFHs, all the MQGs experienced a luminous infrared galaxy phase that lasts for ∼500 Myr, and half of them an ultraluminous infrared galaxy phase for ∼100 Myr. We find that the MQG population is almost assembled at z ∼ 1, and continues evolving passively with few additions to the population.

Discovery of "isolated" co-moving T Tauri stars in Cepheus

Context. During the course of a large spectroscopic survey of X-ray active late-type stars in the solar neighbourhood, we discovered four lithium-rich stars packed within just a few degrees on the sky. Although located in a sky area rich in CO molecular regions and dark clouds, the Cepheus-Cassiopeia complex, these very young stars are projected several degrees away from clouds in front of an area void of interstellar matter. As such, they are very good "isolated" T Tauri star candidates. Aims. We present optical observations of these stars conducted with 1-2 m class telescopes. We acquired high-resolution optical spectra as well as photometric data allowing us to investigate in detail their nature and physical parameters with the aim of testing the "runaway" and "in-situ" formation scenarios. Their kinematical properties are also analyzed to investigate their possible connection to already known stellar kinematic groups. Methods. We use the cross-correlation technique and other tools developed by us to derive accurate radial and rotational velocities and perform an automatic spectral classification. The spectral subtraction technique is used to infer chromospheric activity level in the Hα line core and clean the spectra of photospheric lines before measuring the equivalent width of the lithium absorption line. Results. Both physical (lithium content, chromospheric, and coronal activities) and kinematical indicators show that all stars are very young, with ages probably in the range 10-30 Myr. In particular, the spectral energy distribution of TYC4496-780-1 displays a strong near-and far-infrared excess, typical of T Tauri stars still surrounded by an accretion disc. They also share the same Galactic motion, proving that they form a homogeneous moving group of stars with the same origin. Conclusions. The most plausible explanation of how these "isolated" T Tauri stars formed is the "in-situ" model, although accurate distances are needed to clarify their connection with the Cepheus-Cassiopeia complex. The discovery of this loose association of "isolated" T Tauri stars can help to shed light on atypical formation processes of stars and planets in low-mass clouds.

Responsivity and resonant properties of dipole, bowtie, and spiral Seebeck nanoantennas

Seebeck nanoantennas, which are based on the thermoelectric effect, have been proposed for electromagnetic energy harvesting and infrared detection. The responsivity and frequency dependence of three types of Seebeck nanoantennas is obtained by electromagnetic simulation for different materials. Results show that the square spiral antenna has the widest bandwidth and the highest induced current of the three analyzed geometries. However, the geometry that presented the highest temperature gradient was the bowtie antenna, which favors the thermoelectric effect in a Seebeck nanoantenna. The results also show that these types of devices can present a voltage responsivity as high as 36  μV/W36  μV/W for titanium–nickel dipoles resonant at far-infrared wavelengths.

Search for isotropic γ radiation in the cosmological window between 65 and 200 TeV

Electromagnetic energy injected into the universe above a few hundred TeV is expected to pile up as γ radiation in a relatively narrow energy interval below 100 TeV due to its interaction with the 2.7^°K background radiation. We present an upper limit (90% C.L.) on the ratio of primary γ to charged cosmic rays in the energy interval 65–160 TeV (80–200 TeV) of 10.3 • 10^−3 (7.8 • 10^−3). Data from the HEGRA cosmic-ray detector complex consisting of a wide angle Čerenkov array (AIROBICC) measuring the lateral distribution of air Čerenkov light and a scintillator array, were used with a novel method to discriminate γ-ray and hadron induced air showers. If the presently unmeasured universal far infrared background radiation is not too intense, the result rules out a topological-defect origin of ultrahigh energy cosmic rays for masses of the X particle released by the defects equal to or larger than about 10^16 GeV.

Large-scale clustering measurements with photometric redshifts: comparing the dark matter haloes of X-ray AGN, star-forming and passive galaxies at z ≈ 1

We combine multi-wavelength data in the AEGIS-XD and C-COSMOS surveys to measure the typical dark matter halo mass of X-ray selected active galactic nuclei (AGN) [L_X(2–10 keV) > 10^42 erg s^− 1] in comparison with far-infrared selected star-forming galaxies detected in the Herschel/PEP survey (PACS Evolutionary Probe; L_IR > 10^11 L_⊙) and quiescent systems at z ≈ 1. We develop a novel method to measure the clustering of extragalactic populations that uses photometric redshift probability distribution functions in addition to any spectroscopy. This is advantageous in that all sources in the sample are used in the clustering analysis, not just the subset with secure spectroscopy. The method works best for large samples. The loss of accuracy because of the lack of spectroscopy is balanced by increasing the number of sources used to measure the clustering. We find that X-ray AGN, far-infrared selected star-forming galaxies and passive systems in the redshift interval 0.6 < z < 1.4 are found in haloes of similar mass, log M_DMH/(M_⊙ h^−1) ≈ 13.0. We argue that this is because the galaxies in all three samples (AGN, star-forming, passive) have similar stellar mass distributions, approximated by the J-band luminosity. Therefore, all galaxies that can potentially host X-ray AGN, because they have stellar masses in the appropriate range, live in dark matter haloes of log M_DMH/(M_⊙ h^−1) ≈ 13.0 independent of their star formation rates. This suggests that the stellar mass of X-ray AGN hosts is driving the observed clustering properties of this population. We also speculate that trends between AGN properties (e.g. luminosity, level of obscuration) and large-scale environment may be related to differences in the stellar mass of the host galaxies.

An extended Herschel drop-out source in the center of AS1063: a normal dusty galaxy at z=6.1 or SZ substructures?

In the course of our 870 μm APEX/LABOCA follow-up of the Herschel Lensing Survey we have detected a source in AS1063 (RXC J2248.7-4431) that has no counterparts in any of the Herschel PACS/SPIRE bands, it is a Herschel “drop-out” with S_870/S_500 ≥ 0.5. The 870 μm emission is extended and centered on the brightest cluster galaxy, suggesting either a multiply imaged background source or substructure in the Sunyaev-Zel’dovich increment due to inhomogeneities in the hot cluster gas of this merging cluster. We discuss both interpretations with emphasis on the putative lensed source. Based on the observed properties and on our lens model we find that this source may be the first submillimeter galaxy (SMG) with a moderate far-infrared (FIR) luminosity (L_FIR < 10^12 L_⊙) detected so far at z > 4. In deep HST observations we identified a multiply imaged z ~ 6 source and measured its spectroscopic redshift to be z = 6.107 with VLT/FORS. This source may be associated with the putative SMG, but it is most likely offset spatially by 10−30 kpc and they may be interacting galaxies. With a FIR luminosity in the range [5−15] × 10^11 L_⊙ corresponding to a star formation rate in the range [80−260] M_⊙ yr^-1, this SMG would be more representative of the z > 4 dusty galaxies than the extreme starbursts detected so far. With a total magnification of ~25 it would open a unique window to the normal dusty galaxies at the end of the epoch of reionization.

The differential evolution of hot- and cold-dust in galaxies in the last 7.5 GYR

Tese de mestrado em Física, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2016

Optimisation of microstructured waveguides in z-cut LiNbO3 crystals

We present a practical approach to the numerical optimisation of the guiding properties of buried microstructured waveguides, which can be fabricated in a z-cut lithium niobate (LiNbO3) crystal by the method of direct femtosecond laser inscription. We demonstrate the possibility to extend the spectral range of low-loss operation of the waveguide into the mid-infrared region beyond 3um.

Microstructured waveguides in z-cut LiNbO3 by high-repetition rate direct femtosecond laser inscription

We report on the operational parameters that are required to fabricate buried, microstructured waveguides in a z-cut lithium niobate crystal by the method of direct femtosecond laser inscription using a highrepetition-rate, chirped-pulse oscillator system. Refractive index contrasts as high as −0.0127 have been achieved for individual modification tracks. The results pave the way for developing microstructured WGs with low-loss operation across a wide spectral range, extending into the mid-infrared region up to the end of the transparency range of the host material.

Design and fabrication of micro-structured waveguides in lithium niobate

We review our recent work on the numerical design and optimisation of buried, micro-structured waveguides (WGs) that can be formed in a lithium niobate (LiNbO3) crystal by the method of direct femtosecond laser inscription. We also report on the possibility of fabricating such WGs using a high-repetition-rate, chirped-pulse oscillator system. Refractive index contrasts as high as -0.0127 have been achieved for individual modification tracks. The results pave the way for developing micro-structured WGs with low-loss operation across a wide spectral range, extending into the mid-infrared region up to the end of the transparency range of the host material. © 2014 IEEE.

Optimization of micro-structured waveguides in lithium niobate

We describe how the guiding properties of buried, micro-structured waveguides that can be formed in a lithium niobate crystal by direct femtosecond laser writing can be optimized for low-loss operation in the mid-infrared region beyond 3 μm.