Modelling relativistic solitary wave interactions in over-dense plasmas: a perturbed nonlinear Schröndinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

A study on the inclusion of forest canopy morphology data in numerical simulations for the purpose of wind resource assessment

A series of numerical simulations of the flow over a forest stand have been conducted using two different turbulence closure models along with various levels of canopy morphology data. Simulations have been validated against Stereoscopic Particle Image Velocimetry measurements from a wind tunnel study using one hundred architectural model trees, the porosities of which have been assessed using a photographic technique. It has been found that an accurate assessment of the porosity of the canopy, and specifically the variability with height, improves simulation quality regardless of the turbulence closure model used or the level of canopy geometry included. The observed flow field and recovery of the wake is in line with characteristic canopy flows published in the literature and it was found that the shear stress transport turbulence model was best able to capture this detail numerically.

Influence of a liquid on the natural frequencies of almost circular plates

In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

Effects of the water level on the flow topology over the Bolund island

We have analyzed the influence of the actual height of Bolund island above water level on different full-scale statistics of the velocity field over the peninsula. Our analysis is focused on the database of 10-minute statistics provided by Risø-DTU for the Bolund Blind Experiment. We have considered 10-minut.e periods with near-neutral atmospheric conditions, mean wind speed values in the interval [5,20] m/s, and westerly wind directions. As expected, statistics such as speed-up, normalized increase of turbulent kinetic energy and probability of recirculating flow show a large dependence on the emerged height of the island for the locations close to the escarpment. For the published ensemble mean values of speed-up and normalized increase of turbulent kinetic energy in these locations, we propose that some ammount of uncertainty could be explained as a deterministic dependence of the flow field statistics upon the actual height of the Bolund island above the sea level

Detecting and characterising ramp events in wind power time series

In order to implement accurate models for wind power ramp forecasting, ramps need to be previously characterised. This issue has been typically addressed by performing binary ramp/non-ramp classifications based on ad-hoc assessed thresholds. However, recent works question this approach. This paper presents the ramp function, an innovative wavelet- based tool which detects and characterises ramp events in wind power time series. The underlying idea is to assess a continuous index related to the ramp intensity at each time step, which is obtained by considering large power output gradients evaluated under different time scales (up to typical ramp durations). The ramp function overcomes some of the drawbacks shown by the aforementioned binary classification and permits forecasters to easily reveal specific features of the ramp behaviour observed at a wind farm. As an example, the daily profile of the ramp-up and ramp-down intensities are obtained for the case of a wind farm located in Spain

DROMO formulation for planar motions: Solution to the Tsien Problem

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen?s ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo?Stiefel methods.

Efficient computation of current collection in bare electrodynamic tethers in and beyond OML regime

One key issue in the simulation of bare electrodynamic tethers (EDTs) is the accurate and fast computation of the collected current, an ambient dependent operation necessary to determine the Lorentz force for each time step. This paper introduces a novel semianalytical solution that allows researchers to compute the current distribution along the tether efficient and effectively under orbital-motion-limited (OML) and beyond OML conditions, i.e., if tether radius is greater than a certain ambient dependent threshold. The method reduces the original boundary value problem to a couple of nonlinear equations. If certain dimensionless variables are used, the beyond OML effect just makes the tether characteristic length L ∗ larger and it is decoupled from the current determination problem. A validation of the results and a comparison of the performance in terms of the time consumed is provided, with respect to a previous ad hoc solution and a conventional shooting method.

Investigations on the distribution of air transport traffic and CO2 emissions within the European Union

This study analyses the structure of air traffic and its distribution among the different countries in the European Union, as well as traffic with an origin or destination in non-EU countries. Data sources are Eurostat statistics and actual flight information from EUROCONTROL. Relevant variables such as the number of flights, passengers or cargo tonnes and production indicators (RPKs) are used together with fuel consumption and CO2 emissions data. The segmentation of air traffic in terms of distance permits an assessment of air transport competition with surface transport modes. The results show a clear concentration of traffic in the five larger countries (France, Germany, Italy, Spain and UK), in terms of RPKs. In terms of distance the segment between 500 and 1000 km in the EU, has more flights, passengers, RTKs and CO2 emissions than larger distances. On the environmental side, the distribution of CO2 emissions within the EU Member States is presented, together with fuel efficiency parameters. In general, a direct relationship between RPKs and CO2 emissions is observed for all countries and all distance bands. Consideration is given to the uptake of alternative fuels. Segmenting CO2 emissions per distance band and aircraft type reveals which flights contribute the most the overall EU CO2 emissions. Finally, projections for future CO2 emissions are estimated, according to three different air traffic growth and biofuel introduction scenarios.

Determination of Maximum Mechanical Energy Efficiency in Energy Galloping Systems

Transverse galloping is a type of aeroelastic instability characterized by large amplitude, low frequency, normal to wind oscillations that appear in some elastic two-dimensional bluff bodies when subjected to a fluid flow, provided that the flow velocity exceeds a threshold critical value. Such an oscillatory motion is explained because of the energy transfer from the flow to the two-dimensional bluff body. The 7 amount of energy that can be extracted depends on the cross section of the galloping prism. Assuming that the Glauert-Den Hartog quasistatic criterion for galloping instability is satisfied in a first approximation, the suitability of a given cross section for energy harvesting is evaluated by analyzing the lateral aerodynamic force coefficient, fitting a function with a power series in tan a (a being the angle of attack) to 10 available experimental data. In this paper, a fairly large number of simple prisms (triangle, ellipse, biconvex, and rhombus cross sections, as well 11 as D-shaped bodies) is analyzed for suitability as energy harvesters. The influence of the fitting process in the energy harvesting efficiency evaluation is also demonstrated. The analysis shows that the more promising bodies are those with isosceles or approximate isosceles cross sections.

Galloping instabilities of Z-shaped shading louvers

Modern design of civil constructions such as office blocks, airport terminal buildings, factories, etc. incorporates more and more environmental considerations that lead to, amongst other elements, the use of glazed façades with shading devices to optimize energy consumption. These shading devices, normally slats or louvers, are very flexible structures exposed to the action of wind, and therefore aeroelastic effects such as galloping must be taken into account in their design. A typical cross-section for such elements is a Z-shaped profile made out of a central web and two side wings. The results of a parametric analysis based on static wind tunnel tests and performed on different Z-shaped louvers to determine translational galloping instability regions are presented in this paper.

Irradiation uniformity at the Laser MegaJoule facility in the context of the shock ignition scheme

The use of the Laser MegaJoule facility within the shock ignition scheme has been considered. In the first part of the study, one-dimensional hydrodynamic calculations were performed for an inertial confinement fusion capsule in the context of the shock ignition scheme providing the energy gain and an estimation of the increase of the peak power due to the reduction of the photon penetration expected during the high-intensity spike pulse. In the second part, we considered a Laser MegaJoule configuration consisting of 176 laser beams that have been grouped providing two different irradiation schemes. In this configuration the maximum available energy and power are 1.3 MJ and 440 TW. Optimization of the laser?capsule parameters that minimize the irradiation non-uniformity during the first few ns of the foot pulse has been performed. The calculations take into account the specific elliptical laser intensity profile provided at the Laser MegaJoule and the expected beam uncertainties. A significant improvement of the illumination uniformity provided by the polar direct drive technique has been demonstrated. Three-dimensional hydrodynamic calculations have been performed in order to analyse the magnitude of the azimuthal component of the irradiation that is neglected in twodimensional hydrodynamic simulations.

Low initial aspect-ratio direct-drive target designs for shock- or self-ignition in the context of the laser Megajoule

Analysis of low initial aspect ratio direct-drive target designs is carried out by varying the implosion velocity and the fuel mass. Starting from two different spherical targets with a given 300?g-DT mass, optimization of laser pulse and drive power allows to obtain a set of target seeds referenced by their peak implosion velocities and initial aspect ratio (A = 3 and A = 5). Self-ignition is achieved with higher implosion velocity for A = 5-design than for A = 3-design. Then, rescaling is done to extend the set of designs to a huge amount of mass, peak kinetic energies and peak areal densities. Self-ignition kinetic energy threshold Ek is characterized by a dependance of Ek ? v? with ?-values which depart from self-ignition models. Nevertheless, self-ignition energy is seen lower for smaller initial aspect ratio. An analysis of Two-Plasmons Decay threshold and Rayleigh?Taylor instability e-folding is carried out and it is shown that two-plasmon decay threshold is always overpassed for all designs. The hydrodynamic stability analysis is performed by embedded models to deal with linear and non-linear regime. It is found that the A = 5-designs are always at the limit of disruption of the shell.

Optimal laser intensity profiles for a uniform target illumination in direct-drive inertial confinement fusion

A numerical method providing the optimal laser intensity profiles for a direct-drive inertial confinement fusion scheme has been developed. The method provides an alternative approach to phase-space optimization studies, which can prove computationally expensive. The method applies to a generic irradiation configuration characterized by an arbitrary number NB of laser beams provided that they irradiate the whole target surface, and thus goes beyond previous analyses limited to symmetric configurations. The calculated laser intensity profiles optimize the illumination of a spherical target. This paper focuses on description of the method, which uses two steps: first, the target irradiation is calculated for initial trial laser intensities, and then in a second step the optimal laser intensities are obtained by correcting the trial intensities using the calculated illumination. A limited number of example applications to direct drive on the Laser MegaJoule (LMJ) are described.

Fast ignition driven by quasi-monoenergetic ions: Optimal ion type and reduction of ignition energies with an ion beam array

Fast ignition of inertial fusion targets driven by quasi-monoenergetic ion beams is investigated by means of numerical simulations. Light and intermediate ions such as lithium, carbon, aluminum and vanadium have been considered. Simulations show that the minimum ignition energies of an ideal configuration of compressed Deuterium-Tritium are almost independent on the ion atomic number. However, they are obtained for increasing ion energies, which scale, approximately, as Z2, where Z is the ion atomic number. Assuming that the ion beam can be focused into 10 ?m spots, a new irradiation scheme is proposed to reduce the ignition energies. The combination of intermediate Z ions, such as 5.5 GeV vanadium, and the new irradiation scheme allows a reduction of the number of ions required for ignition by, roughly, three orders of magnitude when compared with the standard proton fast ignition scheme.

Flight dynamics and stability of kites in steady and unsteady wind conditions

The flight dynamics and stability of a kite with a single main line flying in steady and unsteady wind conditions are discussed. A simple dynamic model with five degrees of freedom is derived with the aid of Lagrangian formulation, which explicitly avoids any constraint force in the equations of motion. The longitudinal and lateral–directional modes and stability of the steady flight under constant wind conditions are analyzed by using both numerical and analytical methods. Taking advantage of the appearance of small dimensionless parameters in the model, useful analytical formulas for stable-designed kites are found. Under nonsteady wind-velocity conditions, the equilibrium state disappears and periodic orbits occur. The kite stability and an interesting resonance phenomenon are explored with the aid of a numerical method based on Floquet theory.