Self-similar motion of laser half-space plasmas. I. Deflagration regime

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density 0,produced by the (anomalous) absorption of a laser pulse of irradiation = (j>0f/T(0< (< T) at the critical density nc(«c/«0=eheat conduction and ion-electron energy exchange and retains three dimensionless numbers: e, Zt (ion charge number), and a = (9/c/4m,) (T/C 2n l/4>oKe)213, where k, m, are Boltzmann's constant and the ion mass, and Ke X (electron temperature)5'2 = heat conductivity. If a >e- 4 ' 3 , a deflagration wave separates an isentropic compression with a shock bounding the undisturbed plasma, and an isentropic expansion flow to the vacuum. The structures of these three regions are completely determined; in particular, the Chapman-Jouguet condition is proved and the density behind the deflagration is found. The deflagration-compression thickness ratio is large (small) for a^e- 5 ' 3(a>e- 5 ' 3 ) . The compression to expansion ratio for both energy and thickness is 0(e"2). For Z,- large, a deflagration exists even if a~e~413. Condition a>e~4'3 may be applied to pulses that are not linear.

Self-similar motion of laser half-space plasmas. II. Thermal waves and intermediate regimes

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density n,produced by the (anomalous) absorption of a laser pulse of irradiation

heat conduction and ion-electron energy exchange, involves three dimensionless numbers: e = nc/n0 assumed small, Z, (ion charge number), and a parameter a€~4'3, a qualitative discussion of how plasma behavior changes with a, is given.

Transition from isentropic to isothermal expansion in laser produced plasma

The transition that the expansion flow of laser-produced plasmas experiences when one moves from long, low intensity pulses (temperature vanishing at the isentropic plasma-vacuum front,lying at finite distance) to short, intense ones (non-zero, uniform temperature at the plasma-vacuum front, lying at infinity) is studied. For plznar geometry and lqge ion number Z, the transition occurs for dq5/dt=0.14(27/8)k712Z’1zn$/m4f, 12nK,,; mi, and K are laser intensity, critical density,ion mass, and Spitzer’s heat conduction coefficient. This result remains valid for finite Zit,h ough the numerical factor in d$/dt is different. Shorter wavelength lasers and higher 4 plasmas allow faster rising pulses below transition.

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.

Mejora y optimización de un código de simulación hidrodinámico con transporte de radiación para el estudio de sistemas en condiciones de alta densidad de energía

Se presentan las mejoras introducidas en un código de transporte de radiación acoplada a la hidrodinámica llamado ARWEN para el estudio de sistemas en el rango de física de alta densidad de energía (High Energy Density Physics). Los desarrollos introducidos se basan en las siguientes áreas: ít>,~ Ecuaciones de estado: se desarrolla una nueva metodología mediante la cual es posible ajustar los resultados de un modelo simple de ecuaciones de estado como QEOS a datos experimentales y resultados de AIMD. Esta metodología tiene carácter general para poder ser aplicada en gran cantidad de materuales de interés y amplia la flexibilidad de ajuste de los métodos de los que ha partido como base este trabajo. En segundo lugar, se ha desarrollado una librería para la gestión de tablas de datos de ecuaciones de estado que también incluye la gestión de tablas con datos de opacidades y de ionización. Esta nueva librería extiende las capacidades de la anterior al tener llamadas más específicas que aceleran los cálculos, y posibilidad de uso de varias tablas a la vez. Solver de difusión: se ha desarrollado un nuevo paquete para resolver la ecuación de difusión que se aplicará a la conducción de calor dentro del plasma. El método anterior no podía ser ejecutado en paralelo y producía resultados dependientes de la resolución de la malla, mientras que este método es paralelizable y además obtiene una solución con mejor convergencia, lo que supone una solución que no depende del refinamiento del mallado. Revisión del paquete de radiación: en primer lugar se ha realizado una revisión de la implementación del modelo de radiación descubriendo varios errores que han sido depurados. También se ha incluido la nueva librería de gestión de tablas de opacidades que permiten la obtención de las propiedades ópticas del plasma en multigrupos de energía. Por otra parte se ha extendido el cálculo de los coeficientes de transporte al esquema multimaterial que ha introducido David Portillo García en el paquete hidrodinámico del código de simulación. Por último se ha revisado el esquema de resolución del transporte y se ha modificado para hacerlo paralelizable. • Se ha implementado un paquete de trazado de rayos para deposición láser que extiende la utilidad del anterior al ser en 3D y poder utilizar entonces diferentes configuraciones. • Una vez realizadas todas estas tareas se ha aplicado el código ARWEN al estudio de la astrofísica de laboratorio simulando los experimentos llevados a cabo en la instalación PALS por Chantal Stehlé acerca de ondas de choque radiativas. Se han comparado los resultados experimentales frente a las predicciones del código ARWEN obteniéndose una gran concordancia en la velocidad de la onda de choque generada y en las dimensiones del precursor. El código de simulación sobre el que se ha trabajado, junto con los desarrollos aportados por otros investigadores durante la realización de esta tesis, ha permitido participar en colaboraciones con laboratorios de Francia o Japón y se han producido resultados científicos publicados basados en el trabajo descrito en esta tesis. ABSTRACT Improvements in radiation hydrodynamic code ARWEN for the study of systems in the range of physics high energy density (High Energy Density Physics) are presented. The developments introduced are based on the following áreas: • Equations of state: a new methodology was developed to adjust the results of a simple Equation of State model like QEOS to experimental data and results of AIMD. This methodology can be applied to a large amount of materials and it increases the flexibility and range of the previous methods used as basis for this work. Also a new computer library has been developed to manage data tables of thermodynamic properties as well as includes the management of opacity and ionization data tables. This new library extends the capabilities of the previous one with more specific routines, and the possibility of using múltiple tables for several materials. • Diffusion solver: a new package has been developed to solve the diffusion equation applied to the heat conduction of the plasma. The previous method is not parallelizable and it produced mesh dependent results, while this new package can be executed in parallel and achieves a more converged solution that does not depend on the refinement of the mesh. • Radiation package: the check of the radiation model rose several bugs in the implementation that had been removed. The new computer library for EOS managing includes capabilities to store opacity tables for multigroups of energy. Moreover the transport coefficients calculations have been extended for the new multimaterial hydrodynamic package developed by David Portillo García. Also the solving methodology for the transport equation has been modified to make the code run in parallel. • A new ray tracing package has been introduced to extend the previous one to 3D. Once all these tasks has been implemented, the ARWEN code has been applied to study laboratory astrophysics systems. Simulations have been done in order to reproduce the results of the experiments carried out in PALS facility by Chantal Stehlé in radiative shock production. Experimental results are in cióse agreement to the ARWEN estimations of the speed of the shock wave and the length of the precursor. The simulation code used in this thesis, including the work done in ARWEN by other colleagues at the time of this research, allowed the collaboration with other research institution in France and Japan and some of the results presented in this thesis have been published in scientific journals.

Sheath vaporization of a monodisperse fuel-spray jet

The group vaporization of a monodisperse fuel-spray jet discharging into a hot coflowing gaseous stream is investigated for steady flow by numerical and asymptotic methods with a two-continua formulation used for the description of the gas and liquid phases. The jet is assumed to be slender and laminar, as occurs when the Reynolds number is moderately large, so that the boundary-layer form of the conservation equations can be employed in the analysis. Two dimensionless parameters are found to control the flow structure, namely the spray dilution parameter 1, defined as the mass of liquid fuel per unit mass of gas in the spray stream, and the group vaporization parameter e, defined as the ratio of the characteristic time of spray evolution due to droplet vaporization to the characteristic diffusion time across the jet. It is observed that, for the small values of e often encountered in applications, vaporization occurs only in a thin layer separating the spray from the outer droplet-free stream. This regime of sheath vaporization, which is controlled by heat conduction, is amenable to a simplified asymptotic description, independent of ε,in which the location of the vaporization layer is determined numerically as a free boundary in a parabolic problem involving matching of the separate solutions in the external streams, with appropriate jump conditions obtained from analysis of the quasi-steady vaporization front. Separate consideration of dilute and dense sprays, corresponding, respectively, to the asymptotic limits λ<<1 and λ>>1, enables simplified descriptions to be obtained for the different flow variables, including explicit analytic expressions for the spray penetration distance.

Desarrollo de un método numérico para flujos multimaterial en 2D en ARWEN

En esta tesis se presenta un método numérico para resolver las ecuaciones de Euler para flujos multimaterial en malla euleriana. Este solver se ha acoplado en el código hidrodinámico en dos dimensiones con transporte de radiación desarrollado en el Instituto de Fusión Nuclear de la UPM bajo la dirección del profesor Pedro Velarde, ARWEN. Los objetivos de este trabajo son: Desarrollo e implementación de un método de Godunov unsplit de alto orden multimaterial en 2D para malla euleriana en geometría cartesiana y geometría cilíndrica. Se presenta una extensión del trabajo realizado por Miller y Puckett (36) a una formulación unsplit. Además, se ha prestado especial atención al acoplamiento con el transporte de radiación y la conducción de calor. El método presentado se ha probado en una gran cantidad de problemas. Aplicación del código multimaterial al estudio de experimentos reales: • Simulación de una propuesta de experimento de laboratorio para reproducir la etapa de arrancamiento de material de la interacción entre el gas proveniente de la explosión de una supernova y la estrella secundaria en un escenario degenarado (SD). • Formación de jets en el laboratorio producidos por la colisión de dos plasmas. ABSTRACT We present a solver for the Euler equations for multimaterial flows in eulerian mesh. This solver has been coupled in the 2D AMR radiation transport code developed at Instituto de Fusión Nuclear (UPM) under the direction of professor Pedro Velarde, ARWEN. The main goals of this thesis are: Development and implementation of an 2D unsplit high-order Godunov method for multimaterial flows in eulerian mesh for cartesian and axialsimetry geometry. We present an extension of the work of Miller and Puckett (36) to an unsplit formulation. Also, we have paid special attention to the coupling with radiation transport and heat conduction. The method has been tested in a wide variety of problems. Application of the multimaterial solver to the study of real experiments: • Simulation of a proposal of a laboratory experiment aimed to reproducing the stripping stage of the interaction between the gas ejected during a supernova explosion and the secondary star in the Single Degenerate scenario. • Experiments of plasma jets in the laboratory obtained by the collission of two hot plasmas.

Effects of radiation losses on very lean methane/air flames propagating upward in a vertical tube

The stationary upward propagation of a very lean methane/air flame in a long vertical tube open at the bottom and closed at the top is simulated numerically using a single overall chemical reaction to model combustion and assuming an optically thin gas and a transparent or non-reflecting tube wall to approximately account for radiation losses from CO2CO2 and H2OH2O. Buoyancy plays a dominant role in the propagation of these flames and causes a large region of low velocity of the burnt gas relative to the flame to appear below the flame front when the equivalence ratio is decreased. The size of this region scales with the radius of the tube, and its presence enhances the effect of radiation losses, which would be otherwise negligible for a standard flammability tube, given the small concentration of radiating species. Heat conduction is found to be important in the low velocity region and to lead to a conduction flux from the flame to the burnt gas that causes extinction at the flame tip for a value of the equivalence ratio near the flammability limit experimentally measured in the standard tube. The effect of radiation losses decreases with the radius of the tube. Numerical results and order-of-magnitude estimates show that, in the absence of radiation, a very lean flame front fails to propagate only after recirculation of the burnt gas extends to its reaction region and drastically changes its structure. This condition is not realized for the standard flammability tube, but it seems to account for the flammability limit measured in a tube of about half the radius of the standard tube.

(Table 1) Thermal conductivities of lithified core samples from ODP Leg 166 sites

The geothermal regime of the western margin of the Great Bahama Bank was examined using the bottom hole temperature and thermal conductivity measurements obtained during and after Ocean Drilling Program (ODP) Leg 166. This study focuses on the data from the drilling transect of Sites 1003 through 1007. These data reveal two important observational characteristics. First, temperature vs. cumulative thermal resistance profiles from all the drill sites show significant curvature in the depth range of 40 to 100 mbsf. They tend to be of concave-upward shape. Second, the conductive background heat-flow values for these five drill sites, determined from deep, linear parts of the geothermal profiles, show a systematic variation along the drilling transect. Heat flow is 43-45 mW/m**2 on the seafloor away from the bank and decreases upslope to ~35 mW/m**2. We examine three mechanisms as potential causes for the curved geothermal profiles. They are: (1) a recent increase in sedimentation rate, (2) influx of seawater into shallow sediments, and (3) temporal fluctuation of the bottom water temperature (BWT). Our analysis shows that the first mechanism is negligible. The second mechanism may explain the data from Sites 1004 and 1005. The temperature profile of Site 1006 is most easily explained by the third mechanism. We reconstruct the history of BWT at this site by solving the inverse heat conduction problem. The inversion result indicates gradual warming throughout this century by ~1°C and is agreeable to other hydrographic and climatic data from the western subtropic Atlantic. However, data from Sites 1003 and 1007 do not seem to show such trends. Therefore, none of the three mechanisms tested here explain the observations from all the drill sites. As for the lateral variation of the background heat flow along the drill transect, we believe that much of it is caused by the thermal effect of the topographic variation. We model this effect by obtaining a two-dimensional analytical solution. The model suggests that the background heat flow of this area is ~43 mW/m**2, a value similar to the background heat flow determined for the Gulf of Mexico in the opposite side of the Florida carbonate platform.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

The drying of small drops of particulate slurries

The literature on the evaporation of drops of pure liquids, drops containing solids and droplet sprays has been critically reviewed. An experimental study was undertaken on the drying of suspended drops of pure water and aqueous sodium sulphate decahydrate with concentrations varying from 5 to 54. 1 wt. %. Individual drops were suspended from a glass filament balance in a 26 mm I.D. vertical wind tunnel, designed and constructed to supply hot de-humidified air, to simulate conditions encountered in commercial spray driers. A novel thin film thermocouple was developed to facilitate the simultaneous measurement of drop weight and core temperature. The heat conduction through the thermocouple was reduced because of its unique design; using essentially a single 50μ diameter nickel wire. For pure water drops, the Nusselt number was found to be a function of the Reynolds, Prandtl and Transfer numbers for a temperature range between 19 to 79°C.                  Nu = 2 + 0.19 (1/B)0.24 Re0.5 Pr0.33 Two distinct periods were observed during the drying of aqueous sodium sulphate decahydrate. The first period was characterised by the evaporation from a free liquid surface, whilst drying in the second period was controlled by the crust resistance. Fracturing of the crust occurred randomly but was more frequent at higher concentrations and temperatures. A model was proposed for the drying of slurry drops, based on a receding evaporation interface. The model was solved numerically for the variation of core temperature, drop weight and crust thickness as a function of time. Experimental results were in excellent agreement with the model predictions although at higher temperatures modifications to the model had to be made to accommodate the unusual behaviour of sodium sulphate slurries, i.e. the formation of hydrates.

Mechanisms of drying of skin forming materials

The literature relating to evaporation from single droplets of pure liquids, and to the drying of droplets containing solids and of droplet sprays has been reviewed. The heat and mass transfer rates for a single droplet suspended from a nozzle were studied within a 42mm I.D. horizontal wind tunnel designed to supply hot dry air, to simulate conditions encountered in a practical spray dryer. A novel rotating glass nozzle was developed to facilitate direct measurements of droplet weight and core temperature. This design minimised heat conduction through the nozzle. Revised correlations were obtained for heat and mass transfer coefficients, for evaporation from pure water droplets suspended from a rotating nozzle. Nu = 2.0 + 0.27 (l/B)°-18Re°-5Pr°-83 Sh = 2.0 + 0.575 ((T0-T.)/Tomfc) -o.o4Reo.5 ^0.33 Experimental drying studies were carried out on single droplets of different types of skin-forming materials, namely, custard, gelatin, skim milk and fructose at air temperatures ranging from 19°C to 198°C. Dried crusts were recovered and examined by Scanning Electron Microscopy. Skin-forming materials were classified into three types according to the mechanisms of skin formation. In the first type (typified by droplets of custard and starch) skin formed due to gelatinisation at high temperatures. Increasing the drying temperature resulted in increased crust resistance to mass transfer due to increased granule swelling and the crust resistance was completely transferred to a skin resistance at drying temperatures > 150°C. In the second type e.g. gelatin droplets the skin formed immediately drying had taken place at any drying temperature. At drying temperature > 60° C a more resistant skin was formed. In the third type (typified by droplets of skim milk and fructose) the skin appeared on the droplet surface at a certain stage of the drying process under any drying conditions. As the drying temperature was increased the resistance of the skin to mass transfer increased. The drying rate history of any material depended upon the nature of the skin formed which, in turn, depended upon the drying conditions. A mathematical model was proposed for the drying of the first type of skin-forming material. This was based on the assumption that, once all the granules gelatinised at the gelatinisation temperature, a skin appeared instantaneously on the droplet surface. The experimentally-observed times at which the skin appeared on the droplets surfaces were in excellent agreement with those predicted from the model. The work should assist in understanding the fundamentals of paniculate drying processes, particularly when skin-formation occurs and may be a crucial factor in volatiles retention.

Mechanisms of drying of particulate slurries

The literature on the evaporation of pure liquid drops and the drying of drops of solutions and slurries has been reviewed with particular reference to spray drying. A 0.1-0.2 mm glass filament-thermocouple was constructed and used to study simultaneously, heat and mass transfer from a single suspended drop placed in a humidity and temperature controlled, 28 mm OD vertical wind tunnel. Heat conduction through the filament was minimised eg at 100¦C it accounted for only 9.3% of the total heat transferred to a drop. Evaporation of single water drops was also studied in a 101 mm OD vertical wind tunnel. The Nusselt number was found to be a function of the Reynolds, Prandtl and Transfer number over an air temperature range of 17¦C to 107¦C. The proposed correlation is: Nu = 2+(-12.96B+0.76)Re¦-5Pr0-33 Experimental drying studies were carried out on single suspended 1 to 2.5 mm diameter drops of aqueous sodium sulphate decahydrate, sodium chloride, potassium sulphate, copper sulphate and sodium acetate solutions and slurries at temperatures of 20¦C to 124¦C. Dried crusts were examined by Scanning Electron Microscopy. The drying history of any material depended upon the nature of the crust formed. Sodium acetate formed a non-rigid skin prior to the formation of a rigid crust. A modified receding evaporation interface model was proposed for the drying of solutions and slurries. This covered both the constant rate period prior to crust formation and the subsequent falling rate period. The model was solved numerically for the variation in core temperature, drop weight and crust thickness. Good agreement was obtained between model predictions and experimental results for materials forming rigid crusts i.e. sodium sulphate decahydrate, sodium chloride, potassium sulphate and copper sulphate. However, the drying histories of drops of 10-20% weight initial concentration sodium acetate were unpredictable since formation of a non-rigid skin deviated from the model assumption of a rigid outer surface. At higher initial concentrations (40% weight) where a rigid crust was formed for sodium acetate, good agreement was obtained between experimental results and model predictions. Single suspended drop studies are concluded to provide a valuable insight into the drying mechanisms of specific solutions and slurries.

Population lensing vs thermal lensing in Yb:YAG rods and disks

The induced lenses in the Yb:YAG rods and disks end-pumped by a Gaussian beam were analyzed both analytically and numerically. The thermally assisted mechanisms of the lens formation were considered to include: the conventional volume thermal index changes ("dn/dT"), the bulging of end faces, the photoelastic effect, and the bending (for a disk). The heat conduction equations (with an axial heat flux for a disk and a radial heat flux for a rod), and quasi-static thermoelastic equations (in the plane-stress approximation with free boundary conditions) were solved to find the thermal lens power. The population rate equation with saturation (by amplified spontaneous emission or an external wave) was examined to find the electronic lens power in the active elements.

Mathematical Modeling and Simulation of Radial Temperature Profile of Strontium Bromide Lasers

For metal and metal halide vapor lasers excited by high frequency pulsed discharge, the thermal effect mainly caused by the radial temperature distribution is of considerable importance for stable laser operation and improvement of laser output characteristics. A short survey of the obtained analytical and numerical-analytical mathematical models of the temperature profile in a high-powered He-SrBr2 laser is presented. The models are described by the steady-state heat conduction equation with mixed type nonlinear boundary conditions for the arbitrary form of the volume power density. A complete model of radial heat flow between the two tubes is established for precise calculating the inner wall temperature. The models are applied for simulating temperature profiles for newly designed laser. The author’s software prototype LasSim is used for carrying out the mathematical models and simulations.