Contribution to the Analysis, Design and Assessment of Compact Antenna Test Ranges At Millimeter Wavelengths - Contribución al Análisis, Diseño y Caracterización de Sistemas de Medida de Antenas en Rango Compacto para Frecuencias Milimétricas

This Doctoral Thesis entitled Contribution to the analysis, design and assessment of compact antenna test ranges at millimeter wavelengths aims to deepen the knowledge of a particular antenna measurement system: the compact range, operating in the frequency bands of millimeter wavelengths. The thesis has been developed at Radiation Group (GR), an antenna laboratory which belongs to the Signals, Systems and Radiocommunications department (SSR), from Technical University of Madrid (UPM). The Radiation Group owns an extensive experience on antenna measurements, running at present four facilities which operate in different configurations: Gregorian compact antenna test range, spherical near field, planar near field and semianechoic arch system. The research work performed in line with this thesis contributes the knowledge of the first measurement configuration at higher frequencies, beyond the microwaves region where Radiation Group features customer-level performance. To reach this high level purpose, a set of scientific tasks were sequentially carried out. Those are succinctly described in the subsequent paragraphs. A first step dealed with the State of Art review. The study of scientific literature dealed with the analysis of measurement practices in compact antenna test ranges in addition with the particularities of millimeter wavelength technologies. Joint study of both fields of knowledge converged, when this measurement facilities are of interest, in a series of technological challenges which become serious bottlenecks at different stages: analysis, design and assessment. Thirdly after the overview study, focus was set on Electromagnetic analysis algorithms. These formulations allow to approach certain electromagnetic features of interest, such as field distribution phase or stray signal analysis of particular structures when they interact with electromagnetic waves sources. Properly operated, a CATR facility features electromagnetic waves collimation optics which are large, in terms of wavelengths. Accordingly, the electromagnetic analysis tasks introduce an extense number of mathematic unknowns which grow with frequency, following different polynomic order laws depending on the used algorithmia. In particular, the optics configuration which was of our interest consisted on the reflection type serrated edge collimator. The analysis of these devices requires a flexible handling of almost arbitrary scattering geometries, becoming this flexibility the nucleus of the algorithmia’s ability to perform the subsequent design tasks. This thesis’ contribution to this field of knowledge consisted on reaching a formulation which was powerful at the same time when dealing with various analysis geometries and computationally speaking. Two algorithmia were developed. While based on the same principle of hybridization, they reached different order Physics performance at the cost of the computational efficiency. Inter-comparison of their CATR design capabilities was performed, reaching both qualitative as well as quantitative conclusions on their scope. In third place, interest was shifted from analysis - design tasks towards range assessment. Millimetre wavelengths imply strict mechanical tolerances and fine setup adjustment. In addition, the large number of unknowns issue already faced in the analysis stage appears as well in the on chamber field probing stage. Natural decrease of dynamic range available by semiconductor millimeter waves sources requires in addition larger integration times at each probing point. These peculiarities increase exponentially the difficulty of performing assessment processes in CATR facilities beyond microwaves. The bottleneck becomes so tight that it compromises the range characterization beyond a certain limit frequency which typically lies on the lowest segment of millimeter wavelength frequencies. However the value of range assessment moves, on the contrary, towards the highest segment. This thesis contributes this technological scenario developing quiet zone probing techniques which achieves substantial data reduction ratii. Collaterally, it increases the robustness of the results to noise, which is a virtual rise of the setup’s available dynamic range. In fourth place, the environmental sensitivity of millimeter wavelengths issue was approached. It is well known the drifts of electromagnetic experiments due to the dependance of the re sults with respect to the surrounding environment. This feature relegates many industrial practices of microwave frequencies to the experimental stage, at millimeter wavelengths. In particular, evolution of the atmosphere within acceptable conditioning bounds redounds in drift phenomena which completely mask the experimental results. The contribution of this thesis on this aspect consists on modeling electrically the indoor atmosphere existing in a CATR, as a function of environmental variables which affect the range’s performance. A simple model was developed, being able to handle high level phenomena, such as feed - probe phase drift as a function of low level magnitudes easy to be sampled: relative humidity and temperature. With this model, environmental compensation can be performed and chamber conditioning is automatically extended towards higher frequencies. Therefore, the purpose of this thesis is to go further into the knowledge of millimetre wavelengths involving compact antenna test ranges. This knowledge is dosified through the sequential stages of a CATR conception, form early low level electromagnetic analysis towards the assessment of an operative facility, stages for each one of which nowadays bottleneck phenomena exist and seriously compromise the antenna measurement practices at millimeter wavelengths.

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.

Theory of a probe in a strong magnetic field

An asymptotic analysis of the Langmuir-probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C-V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented.The theory, which fails beyond certain positive voltage, fields useful results for weak fields, too.

Ion-temperature-sensitive effect in transient langmuir probe response

A theory is presented for a method, recently proposed by Hester and Sonin, of determining the ion temperature in a plasma by measuring the transient current to a cylindrical Langmuir probe after applying a potential Vp{ — eVpy>KTe) under conditions where collection is collision free and the ratio of probe radius to Debye length is small. The ion component of the current does not approach its final steady-state value monotonicalfy, but exhibits a strong, ion-temperature-dependent overshoot in the first few ion-plasma periods following the biasing of the probe. Analytical formulas are derived for the case of a Maxwellian plasma, and convenient graphical results are presented. The possible masking of the overshoot by a transient displacement current is discussed; it is shown how to avoid such displacement effects. For the overshoot to be sensitive to the ion temperature T the probe must be near plasma (zero) potential before applying V1,(eVp~<0.lKTe, VP~ being that initial potential); this is not a drawback of the method, but, on the contrary, it can be used to accurately determine plasma potential along with T.

End effect in Langimur probe reponse under ionospheric satellite conditions

A theory is presented for an end effect in the current response of a highly negative, cylindrical Langmuir probe in a collisionless plasma flow. Under conditions where the ratio of probe radius to debye length is small and the ion-acoustic Mach number is large, the current exhibits a strong peak when the probe axis is brought into alignment with the flow direction. Closed formulas are given for the maximum and angular half-width of the peak, and universal graphical results are presented for the entire peak structure. The theory shows very good agreement with experimental data. The use of the end effect for diagnostic purposes, in particular, for the determination of the ion temperature, is discussed.

Electron current to a probe in a magnetized, collisional plasma

Collisional analysis of electron collection by a probe in a strongly magnetized, fully ionized plasma is carried out. A solution to the complete set of macroscopic equations with classical transport coefficients that is wholly consistent in the domain is determined; R and le are probe radius and electron gyroradius, respectively. If R2/le 2 is large compared with mi/3me probe large compared with ion gyroradius, ion–electron energy exchange—rather than electron heat diffusion—keeps electrons isothermal. For smaller probes at negative bias, however, electron cooling occurs in the plasma beyond the sheath, with a potential overshoot lying well away from it. The probe characteristic in the electron-retarding range may then mimic the characteristic for a two electron-temperature plasma and lead to an overestimate of electron temperature; the validity of these results for other transport models is discussed

Electron cooling in probe collection from magnetized plasmas with anomalous transport

The electron-retarding range of the current-voltage characteristic of a flat Langmuir probe perpendicular to a strong magnetic field in a fully ionized plasma is analysed allowing for anomalous (Bohm) cross-field transport and temperature changes in the collection process. With probe size and ion thermal gyroradius comparable, and smaller than the electron mean free path, there is an outer quasineutral region with ion viscosity determinant in allowing nonambipolar parallel and cross flow. A potential overshoot lying either at the base or inside the quasineutral region both makes ions follow Boltzmann's law at negative bias and extends the electron-retarding range to probe bias e(j)p ~ +2Too. Electron heating and cooling occur roughly at positive and negative bias, with a re-minimum around efa ~ - 2 7 ^ ; far from the probe heat conduction cools and heats electrons at and radially away from the probe axis, respectively. The potential overshoot with no thermal effects would reduce the electron current Ie, making the In Ie versus 4>p graph downwards-concave,but cooling further reduces Ie substantially, and may tilt the slope upwards past the temperature minimum. The domain of strict validity of our analysis is narrow in case of low ion mass (deuterium), breaking down with the ion Boltzmann law.

Floating bare tether as upper atmosphere probe

Use of a conductive bare tape electrically floating in low Earth orbit as an effective electron beam source to produce artificial auroral effects, free of problems that mard tandard beams, is considered. Ambient ions impacting the tape with keV energies over most of its length liberate secondary electrons that race down the magnetic field, excite neutrals in the E layer, and result in auroral emissions. The tether would operate with both a power supply and a plasma contactor off at nighttime; power and contactor would be on at daytime for reboost. Tomographic analysis of auroral emissions from the footprint of the beam, as observed from the spacecraft, can provide density profiles of dominant neutral species in the E layer. A characteristic tether system, at altitude 300 km and moderate orbital inclination, would involve an aluminum tape with a length of 20 km, a width of 15 mm, and a thickness of 0.2 mm for a full-system mass around 1200 kg, with two thirds going into the power subsystem.

Theory of a Probe in a Strong Magnetic Field. AT(30-1)-1238-MATT 599

A kinetic approach is used to develop a theory of electrostatic probes in a fully ionized plasma in the presence of a magnetic field. A consistent asymptotic expansion is obtained assuming that the electron Larmor radius is small compared to the radius of the probe. The order of magnitude of neglected terms is given. It is found that the electric potential within the tube of force defined by the cross section of the probe decays non-mono tonic ally from the probe; this bump disappears at a certain probe voltage and the theory is valid up to this voltage. The transition region, which extends beyond plasma potential, is not exponential. The possible saturation of the electron current is discussed. Restricted numerical results are given; they seem to be useful for weaker magnetic fields down to the zero-field limit. Extensions of the theory a r e considered.

Probe current in a magnetized,collisional plasma revisited

An old analysis of probe current in a strongly magnetized plasma is reconsidered. It is shown that, in the collisional limit, the plasma beyond the sheath heats up in the collection process at positive probe bias enough. The modified current is compared to the current collected in the case of collection due to Bohm diffusion.