Grazing incidence pumped Zr x-ray laser for spectroscopy on Li-like ions

X-ray laser fluorescence spectroscopy of the 2s-2p transition in Li-like ions is promising to become a widely applicable tool to provide information on the nuclear charge radii of stable and radioactive isotopes. For performing such experiments at the Experimental Storage Ring ESR, and the future NESR within the FAIR Project, a grazing incidence pumped (GRIP) x-ray laser (XRL) was set up at GSI Darmstadt using PHELIX (Petawatt High Energy Laser for heavy Ions eXperiments). The experiments demonstrated that lasing using the GRIP geometry could be achieved with relatively low pump energy, a prerequisite for higher repetition rate. In the first chapter the need of a plasma XRL is motivated and a short history of the plasma XRL is presented. The distinctive characteristic of the GRIP method is the controlled deposition of the pump laser energy into the desired plasma density region. While up to now the analysis performed were mostly concerned with the plasma density at the turning point of the main pump pulse, in this thesis it is demonstrated that also the energy deposition is significantly modified for the GRIP method, being sensitive in different ways to a large number of parameters. In the second chapter, the theoretical description of the plasma evolution, active medium and XRL emission properties are reviewed. In addition an innovative analysis of the laser absorption in plasma which includes an inverse Bremsstrahlung (IB) correction factor is presented. The third chapter gives an overview of the experimental set-up and diagnostics, providing an analytical formula for the average and instantaneous traveling wave speed generated with a tilted, on-axis spherical mirror, the only focusing system used up to now in GRIP XRL. The fourth chapter describes the experimental optimization and results. The emphasis is on the effect of the incidence angle of the main pump pulse on the absorption in plasma and on output and gain in different lasing lines. This is compared to the theoretical results for two different incidence angles. Significant corrections for the temperature evolution during the main pump pulse due to the incidence angle are demonstrated in comparison to a simple analytical model which does not take into account the pumping geometry. A much better agreement is reached by the model developed in this thesis. An interesting result is also the appearance of a central dip in the spatially resolved keV emission which was observed in the XRL experiments for the first time and correlates well with previous near field imaging and plasma density profile measurements. In the conclusion also an outlook to the generation of shorter wavelength XRL’s is given.

Fingering instability down the outside of a vertical cylinder

We present an experimental and numerical study examining the dynamics of a gravity-driven contact line of a thin viscous film traveling down the outside of a vertical cylinder of radius R. Experiments on cylinders with radii ranging between 0.159 and 3.81 cm show that the contact line is unstable to a fingering pattern for two fluids with differing viscosities, surface tensions, and wetting properties. The dynamics of the contact line is studied and results are compared to previous studies of inclined plane experiments in order to understand the influence substrate curvature plays on the fingering pattern. A lubrication model is derived for the film height in the limit that ε = H/R≪1, where H is the upstream film thickness, and in terms of a Bond number ρgR3/(γH), and the linear stability of the contact line is analyzed using traveling wave solutions. Curvature controls the capillary ridge height of the traveling wave and the range of unstable wavelength when ε = O(10-1), whereas the shape and stability of the contact line converge to the behavior one observes on a vertical plane when ε ≤ O(10-2). The most unstable wave mode, cutoff wave mode for neutral stability, and maximum growth rate scale as 0.45 where = ρgR2/γ ≥ 1.3, and the contact line is unstable to fingering when ≥ 0.56. Using the experimental data to extrapolate outside the range of validity of the thin film model, we estimate the contact line is stable when <0.56. Agreement is excellent between the model and the experimental data for the wave number (i.e., number of fingers) and wavelength of the fingering pattern that forms along the contact line.

Callosal connections of primary visual cortex predict the spatial spreading of binocular rivalry across the visual hemifields

In binocular rivalry, presentation of different images to the separate eyes leads to conscious perception alternating between the two possible interpretations every few seconds. During perceptual transitions, a stimulus emerging into dominance can spread in a wave-like manner across the visual field. These traveling waves of rivalry dominance have been successfully related to the cortical magnification properties and functional activity of early visual areas, including the primary visual cortex (V1). Curiously however, these traveling waves undergo a delay when passing from one hemifield to another. In the current study, we used diffusion tensor imaging (DTI) to investigate whether the strength of interhemispheric connections between the left and right visual cortex might be related to the delay of traveling waves across hemifields. We measured the delay in traveling wave times (ΔTWT) in 19 participants and repeated this test 6 weeks later to evaluate the reliability of our behavioral measures. We found large interindividual variability but also good test-retest reliability for individual measures of ΔTWT. Using DTI in connection with fiber tractography, we identified parts of the corpus callosum connecting functionally defined visual areas V1-V3. We found that individual differences in ΔTWT was reliably predicted by the diffusion properties of transcallosal fibers connecting left and right V1, but observed no such effect for neighboring transcallosal visual fibers connecting V2 and V3. Our results demonstrate that the anatomical characteristics of topographically specific transcallosal connections predict the individual delay of interhemispheric traveling waves, providing further evidence that V1 is an important site for neural processes underlying binocular rivalry.

Study of and design procedure for dual circularly polarized waveguide slot arrays

For the past sixty years, waveguide slot radiator arrays have played a critical role in microwave radar and communication systems. They feature a well-characterized antenna element capable of direct integration into a low-loss feed structure with highly developed and inexpensive manufacturing processes. Waveguide slot radiators comprise some of the highest performance—in terms of side-lobe-level, efficiency, etc. — antenna arrays ever constructed. A wealth of information is available in the open literature regarding design procedures for linearly polarized waveguide slots. By contrast, despite their presence in some of the earliest published reports, little has been presented to date on array designs for circularly polarized (CP) waveguide slots. Moreover, that which has been presented features a classic traveling wave, efficiency-reducing beam tilt. This work proposes a unique CP waveguide slot architecture which mitigates these problems and a thorough design procedure employing widely available, modern computational tools. The proposed array topology features simultaneous dual-CP operation with grating-lobe-free, broadside radiation, high aperture efficiency, and good return loss. A traditional X-Slot CP element is employed with the inclusion of a slow wave structure passive phase shifter to ensure broadside radiation without the need for performance-limiting dielectric loading. It is anticipated this technology will be advantageous for upcoming polarimetric radar and Ka-band SatCom systems. The presented design methodology represents a philosophical shift away from traditional waveguide slot radiator design practices. Rather than providing design curves and/or analytical expressions for equivalent circuit models, simple first-order design rules – generated via parametric studies — are presented with the understanding that device optimization and design will be carried out computationally. A unit-cell, S-parameter based approach provides a sufficient reduction of complexity to permit efficient, accurate device design with attention to realistic, application-specific mechanical tolerances. A transparent, start-to-finish example of the design procedure for a linear sub-array at X-Band is presented. Both unit cell and array performance is calculated via finite element method simulations. Results are confirmed via good agreement with finite difference, time domain calculations. Array performance exhibiting grating-lobe-free, broadside-scanned, dual-CP radiation with better than 20 dB return loss and over 75% aperture efficiency is presented.

Structure of intermediate shocks in collisionsless anisotropic Hall-magnetohydrodynamics plasma models

The existence of discontinuities within the double-adiabatic Hall-magnetohydrodynamics (MHD) model is discussed. These solutions are transitional layers where some of the plasma properties change from one equilibrium state to another. Under the assumption of traveling wave solutions with velocity C and propagation angle θ with respect to the ambient magnetic field, the Hall-MHD model reduces to a dynamical system and the waves are heteroclinic orbits joining two different fixed points. The analysis of the fixed points rules out the existence of rotational discontinuities. Simple considerations about the Hamiltonian nature of the system show that, unlike dissipative models, the intermediate shock waves are organized in branches in parameter space, i.e., they occur if a given relationship between θ and C is satisfied. Electron-polarized (ion-polarized) shock waves exhibit, in addition to a reversal of the magnetic field component tangential to the shock front, a maximum (minimum) of the magnetic field amplitude. The jumps of the magnetic field and the relative specific volume between the downstream and the upstream states as a function of the plasma properties are presented. The organization in parameter space of localized structures including in the model the influence of finite Larmor radius is discussed

Equações de quarta ordem na modelagem de oscilações de pontes

Equações diferenciais de quarta ordem aparecem naturalmente na modelagem de oscilações de estruturas elásticas, como aquelas observadas em pontes pênseis. São considerados dois modelos que descrevem as oscilações no tabuleiro de uma ponte. No modelo unidimensional estudamos blow up em espaço finito de soluções de uma classe de equações diferenciais de quarta ordem. Os resultados apresentados solucionam uma conjectura apresentada em [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions to nonlinear fourth order differential equations. Arch. Ration. Mech. Anal., 207(2):717752, 2013] e implicam a não existência de ondas viajantes com baixa velocidade de propagação em uma viga. No modelo bidimensional analisamos uma equação não local para uma placa longa e fina, suportada nas extremidades menores, livre nas demais e sujeita a protensão. Provamos existência e unicidade de solução fraca e estudamos o seu comportamento assintótico sob amortecimento viscoso. Estudamos ainda a estabilidade de modos simples de oscilação, os quais são classificados como longitudinais ou torcionais.

High-power microwave tube study.

"Supplement to final report." (iii, 24 l. illus.), issued in 1961.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Comments on multiple oscillatory solutions in systems with time-delay feedback

A complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms is considered. In particular, multiple oscillatory solutions and their properties are studied. We present novel results regarding the disappearance of limit cycle solutions, derive analytical criteria for frequency degeneration, amplitude degeneration, frequency extrema. Furthermore, we discuss the influence of the phase shift parameter and show analytically that the stabilization of the steady state and the decay of all oscillations (amplitude death) cannot happen for global feedback only. Finally, we explain the onset of traveling wave patterns close to the regime of amplitude death.

Evans functions for integral neural field equations with Heaviside firing rate function

In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of system parameters, including the speed and strength of synaptic coupling and the speed of axonal signals. The theory is illustrated with the construction and stability analysis of front solutions to a scalar neural field model and a limiting case is shown to recover recent results of L. Zhang [On stability of traveling wave solutions in synaptically coupled neuronal networks, Differential and Integral Equations, 16, (2003), pp.513-536.]. Traveling fronts and pulses are considered in more general models possessing either a linear or piecewise constant recovery variable. We establish the stability of coexisting traveling fronts beyond a front bifurcation and consider parameter regimes that support two stable traveling fronts of different speed. Such fronts may be connected and depending on their relative speed the resulting region of activity can widen or contract. The conditions for the contracting case to lead to a pulse solution are established. The stability of pulses is obtained for a variety of examples, in each case confirming a previously conjectured stability result. Finally we show how this theory may be used to describe the dynamic instability of a standing pulse that arises in a model with slow recovery. Numerical simulations show that such an instability can lead to the shedding of a pair of traveling pulses.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular we are able to treat "patchy'" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice-directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs. Article published and (c) American Physical Society 2007

Collimation of deuterium / 3-helium fusion products for advanced spacecraft propulsion and power

Current space exploration has transpired through the use of chemical rockets, and they have served us well, but they have their limitations. Exploration of the outer solar system, Jupiter and beyond will most likely require a new generation of propulsion system. One potential technology class to provide spacecraft propulsion and power systems involve thermonuclear fusion plasma systems. In this class it is well accepted that d-He3 fusion is the most promising of the fuel candidates for spacecraft applications as the 14.7 MeV protons carry up to 80% of the total fusion power while ‘s have energies less than 4 MeV. The other minor fusion products from secondary d-d reactions consisting of 3He, n, p, and 3H also have energies less than 4 MeV. Furthermore there are two main fusion subsets namely, Magnetic Confinement Fusion devices and Inertial Electrostatic Confinement (or IEC) Fusion devices. Magnetic Confinement Fusion devices are characterized by complex geometries and prohibitive structural mass compromising spacecraft use at this stage of exploration. While generating energy from a lightweight and reliable fusion source is important, another critical issue is harnessing this energy into usable power and/or propulsion. IEC fusion is a method of fusion plasma confinement that uses a series of biased electrodes that accelerate a uniform spherical beam of ions into a hollow cathode typically comprised of a gridded structure with high transparency. The inertia of the imploding ion beam compresses the ions at the center of the cathode increasing the density to the point where fusion occurs. Since the velocity distributions of fusion particles in an IEC are essentially isotropic and carry no net momentum, a means of redirecting the velocity of the particles is necessary to efficiently extract energy and provide power or create thrust. There are classes of advanced fuel fusion reactions where direct-energy conversion based on electrostatically-biased collector plates is impossible due to potential limits, material structure limitations, and IEC geometry. Thermal conversion systems are also inefficient for this application. A method of converting the isotropic IEC into a collimated flow of fusion products solves these issues and allows direct energy conversion. An efficient traveling wave direct energy converter has been proposed and studied by Momota , Shu and further studied by evaluated with numerical simulations by Ishikawa and others. One of the conventional methods of collimating charged particles is to surround the particle source with an applied magnetic channel. Charged particles are trapped and move along the lines of flux. By introducing expanding lines of force gradually along the magnetic channel, the velocity component perpendicular to the lines of force is transferred to the parallel one. However, efficient operation of the IEC requires a null magnetic field at the core of the device. In order to achieve this, Momota and Miley have proposed a pair of magnetic coils anti-parallel to the magnetic channel creating a null hexapole magnetic field region necessary for the IEC fusion core. Numerically, collimation of 300 eV electrons without a stabilization coil was demonstrated to approach 95% at a profile corresponding to Vsolenoid = 20.0V, Ifloating = 2.78A, Isolenoid = 4.05A while collimation of electrons with stabilization coil present was demonstrated to reach 69% at a profile corresponding to Vsolenoid = 7.0V, Istab = 1.1A, Ifloating = 1.1A, Isolenoid = 1.45A. Experimentally, collimation of electrons with stabilization coil present was demonstrated experimentally to be 35% at 100 eV and reach a peak of 39.6% at 50eV with a profile corresponding to Vsolenoid = 7.0V, Istab = 1.1A, Ifloating = 1.1A, Isolenoid = 1.45A and collimation of 300 eV electrons without a stabilization coil was demonstrated to approach 49% at a profile corresponding to Vsolenoid = 20.0V, Ifloating = 2.78A, Isolenoid = 4.05A 6.4% of the 300eV electrons’ initial velocity is directed to the collector plates. The remaining electrons are trapped by the collimator’s magnetic field. These particles oscillate around the null field region several hundred times and eventually escape to the collector plates. At a solenoid voltage profile of 7 Volts, 100 eV electrons are collimated with wall and perpendicular component losses of 31%. Increasing the electron energy beyond 100 eV increases the wall losses by 25% at 300 eV. Ultimately it was determined that a field strength deriving from 9.5 MAT/m would be required to collimate 14.7 MeV fusion protons from d-3He fueled IEC fusion core. The concept of the proton collimator has been proven to be effective to transform an isotropic source into a collimated flow of particles ripe for direct energy conversion.

Aplicações e algoritmos de segurança rodoviária com o uso de sistemas de GPS e de comunicações WAVE

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Electrónica e Telecomunicações

Numerical analysis of wave-induced fluid flow effects on seismic data: Application to monitoring of CO2 storage at the Sleipner Field

In this work we analyze how patchy distributions of CO2 and brine within sand reservoirs may lead to significant attenuation and velocity dispersion effects, which in turn may have a profound impact on surface seismic data. The ultimate goal of this paper is to contribute to the understanding of these processes within the framework of the seismic monitoring of CO2 sequestration, a key strategy to mitigate global warming. We first carry out a Monte Carlo analysis to study the statistical behavior of attenuation and velocity dispersion of compressional waves traveling through rocks with properties similar to those at the Utsira Sand, Sleipner field, containing quasi-fractal patchy distributions of CO2 and brine. These results show that the mean patch size and CO2 saturation play key roles in the observed wave-induced fluid flow effects. The latter can be remarkably important when CO2 concentrations are low and mean patch sizes are relatively large. To analyze these effects on the corresponding surface seismic data, we perform numerical simulations of wave propagation considering reservoir models and CO2 accumulation patterns similar to the CO2 injection site in the Sleipner field. These numerical experiments suggest that wave-induced fluid flow effects may produce changes in the reservoir's seismic response, modifying significantly the main seismic attributes usually employed in the characterization of these environments. Consequently, the determination of the nature of the fluid distributions as well as the proper modeling of the seismic data constitute important aspects that should not be ignored in the seismic monitoring of CO2 sequestration problems.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.