ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using the ABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements. (c) 2005 Optical Society of America

Análise de desempenho de um fogão solar com parabola fabricada em material compósito

It is presented a solar cooker made with a parabolic reflector composed by a composite material. For this purpose, it was utilized a cast concrete with a parabolic profile obtained by means of modeling. It will be demonstrated the manufacturing process and settings, as well as tests results, in order to determine the contact temperature and cooking time of some foods. This solar cooker presents the following main characteristics: the concentration method, low cost and easy manufacturing process. It was performed by employing recycled materials such as cement, plaster, crushed polystyrene and wheels. The captation area measures 1 square meter and its parabole was covered with a mirrors measuring 25 cm2. A temperature higher than 650°C was obtained. Furthermore, it has been demonstrated that the cooking viability for several type of foods such as beans, potatoes, rice, yams and pasta can be used in two meals for a family of four. In addition, the advantages of this cooker were analysed in comparison with others described in literature as well as those operating on gas. Especially in Northeast of Brazil, where there is a potential for solar energy, this prototype is an important tool, because it avoids not only desertification, but also pollutants from burning firewoods which cause ecological imbalance

Miscellaneum hyperbolicum, et parabolicum : In quo praecipue agitur de centris grauitatis hyperbolae, partium eiusdem, atque nonnullorum solidorum, de quibus nunquam geometria locuta est. Parabola nouiter quadratur dupliciter. Ducuntur infinitarum parabolarum tangentes. Assignantur maxima inscriptibilia, minimaque circumscriptibilia infinitis parabolis, conoidibus, ac semifusis parabolicis. Aliaque geometrica noua exponuntur scitu digna /

Mode of access: Internet.

D. Ioannis Feri, summi templi Moguntinensis concionatoris, de filij prodigi parabola, conciones eruditisimae : tempore Quadragesimali atque Pascha ab eodem recitatae ...

Mode of access: Internet.

Invariant Functions on Neil Parabola in Cn

2000 Mathematics Subject Classification: Primary 32F45.

High resolution Thomson Parabola Spectrometer for full spectral capture of multi-species ion beams

We report on the experimental characterisation of laser-driven ion beams using a Thomson Parabola Spectrometer (TPS) equipped with trapezoidally shaped electric plates, proposed by Gwynne et al. [Rev. Sci. Instrum. 85, 033304 (2014)]. While a pair of extended (30 cm long) electric plates was able to produce a significant increase in the separation between neighbouring ion species at high energies, deploying a trapezoidal design circumvented the spectral clipping at the low energy end of the ion spectra. The shape of the electric plate was chosen carefully considering, for the given spectrometer configuration, the range of detectable ion energies and species. Analytical tracing of the ion parabolas matches closely with the experimental data, which suggests a minimal effect of fringe fields on the escaping ions close to the wedged edge of the electrode. The analytical formulae were derived considering the relativistic correction required for the high energy ions to be characterised using such spectrometer.

Recent developments in the Thomson Parabola Spectrometer diagnostic for laser-driven multi-species ion sources

Ongoing developments in laser-driven ion acceleration warrant appropriate modifications to the standard Thomson Parabola Spectrometer (TPS) arrangement in order to match the diagnostic requirements associated to the particular and distinctive properties of laser-accelerated beams. Here we present an overview of recent developments by our group of the TPS diagnostic aimed to enhance the capability of diagnosing multi-species high-energy ion beams. In order to facilitate discrimination between ions with same Z / A , a recursive differential filtering technique was implemented at the TPS detector in order to allow only one of the overlapping ion species to reach the detector, across the entire energy range detectable by the TPS. In order to mitigate the issue of overlapping ion traces towards the higher energy part of the spectrum, an extended, trapezoidal electric plates design was envisaged, followed by its experimental demonstration. The design allows achieving high energy-resolution at high energies without sacrificing the lower energy part of the spectrum. Finally, a novel multi-pinhole TPS design is discussed, that would allow angularly resolved, complete spectral characterization of the high-energy, multi-species ion beams.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.