Kinetic theory of gases

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DK-1D: a drift-kinetic simulation tool for modelling the shear Alfvén wave and its interaction with collisionless plasma

We present a highly accurate tool for the simulation of shear Alfven waves (SAW) in collisionless plasma. SAW are important in space plasma environments because for small perpendicular scale lengths they can support an electric field parallel to the ambient magnetic field. Electrons can be accelerated by the parallel electric field and these waves have been implicated as the source of vibrant auroral displays. However, the parallel electric field carried by SAW is small in comparison to the perpendicular electric field of the wave, making it difficult to measure directly in the laboratory, or by satellites in the near-Earth plasma environment. In this paper, we present a simulation code that provides a means to study in detail the SAW-particle interaction in both space and laboratory plasma. Using idealised, small-amplitude propagating waves with a single perpendicular wavenumber, the simulation code accurately reproduces the damping rates and parallel electric field amplitudes predicted by linear theory for varying temperatures and perpendicular scale lengths. We present a rigorous kinetic derivation of the parallel electric field strength for small-amplitude SAW and show that commonly-used inertial and kinetic approximations are valid except for where the ratio of thermal to Alfv\'{e}n speed is between 0.7 and 1.0. We also present nonlinear simulations of large-amplitude waves and show that in cases of strong damping, the damping rates and parallel electric field strength deviate from linear predictions when wave energies are greater than only a few percent of the plasma kinetic energy, a situation which is often observed in the magnetosphere. The drift-kinetic code provides reliable, testable predictions of the parallel electric field strength which can be investigated directly in the laboratory, and will help to bridge the gap between studies of SAW in man-made and naturally occuring plasma.

Contributions to the theory of magnetorotational instability and waves in a rotating plasma

The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary 0, where 0 is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary P. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.

Theory of the positive column of a gas discharge

An attempt is made to provide a theoretical explanation of the effect of the positive column on the voltage-current characteristic of a glow or an arc discharge. Such theories have been developed before, and all are based on balancing the production and loss of charged particles and accounting for the energy supplied to the plasma by the applied electric field. Differences among the theories arise from the approximations and omissions made in selecting processes that affect the particle and energy balances. This work is primarily concerned with the deviation from the ambipolar description of the positive column caused by space charge, electron-ion volume recombination, and temperature inhomogeneities.

The presentation is divided into three parts, the first of which involved the derivation of the final macroscopic equations from kinetic theory. The final equations are obtained by taking the first three moments of the Boltzmann equation for each of the three species in the plasma. Although the method used and the equations obtained are not novel, the derivation is carried out in detail in order to appraise the validity of numerous approximations and to justify the use of data from other sources. The equations are applied to a molecular hydrogen discharge contained between parallel walls. The applied electric field is parallel to the walls, and the dependent variables—electron and ion flux to the walls, electron and ion densities, transverse electric field, and gas temperature—vary only in the direction perpendicular to the walls. The mathematical description is given by a sixth-order nonlinear two-point boundary value problem which contains the applied field as a parameter. The amount of neutral gas and its temperature at the walls are held fixed, and the relation between the applied field and the electron density at the center of the discharge is obtained in the process of solving the problem. This relation corresponds to that between current and voltage and is used to interpret the effect of space charge, recombination, and temperature inhomogeneities on the voltage-current characteristic of the discharge.

The complete solution of the equations is impractical both numerically and analytically, and in Part II the gas temperature is assumed uniform so as to focus on the combined effects of space charge and recombination. The terms representing these effects are treated as perturbations to equations that would otherwise describe the ambipolar situation. However, the term representing space charge is not negligible in a thin boundary layer or sheath near the walls, and consequently the perturbation problem is singular. Separate solutions must be obtained in the sheath and in the main region of the discharge, and the relation between the electron density and the applied field is not determined until these solutions are matched.

In Part III the electron and ion densities are assumed equal, and the complicated space-charge calculation is thereby replaced by the ambipolar description. Recombination and temperature inhomogeneities are both important at high values of the electron density. However, the formulation of the problem permits a comparison of the relative effects, and temperature inhomogeneities are shown to be important at lower values of the electron density than recombination. The equations are solved by a direct numerical integration and by treating the term representing temperature inhomogeneities as a perturbation.

The conclusions reached in the study are primarily concerned with the association of the relation between electron density and axial field with the voltage-current characteristic. It is known that the effect of space charge can account for the subnormal glow discharge and that the normal glow corresponds to a close approach to an ambipolar situation. The effect of temperature inhomogeneities helps explain the decreasing characteristic of the arc, and the effect of recombination is not expected to appear except at very high electron densities.

Propagation regimes for an electromagnetic beam in magnetized plasma

The propagation of a Gaussian electromagnetic beam along the direction of magnetic field in a plasma is investigated. The extraordinary (E-x+iE(y)) mode is explicitly considered in the analysis, although the results for the ordinary mode can be obtained upon replacing the electron cyclotron frequency omega(c) by -omega(c). The propagating beam electric field is coupled to the surrounding plasma via the dielectric tensor, taking into account the existence of a stationary magnetic field. Both collisionless and collisional cases are considered, separately. Adopting an established methodological framework for beam propagation in unmagnetized plasmas, we extend to magnetized plasmas by considering the beam profile for points below the critical curve in the beam-power versus beam-width plane, and by employing a relationship among electron concentration and electron temperature, provided by kinetic theory (rather than phenomenology). It is shown that, for points lying above the critical curve in the beam-power versus beam-width plane, the beam experiences oscillatory convergence (self-focusing), while for points between the critical curve and divider curve, the beam undergoes oscillatory divergence and for points on and below the divider curve the beam suffers a steady divergence. For typical values of parameters, numerical results are presented and discussed. (C) 2008 American Institute of Physics.

Análisis teórico del contacto plasma-superficie y sus aplicaciones industriales

Actualmente, la física de plasmas constituye una parte importante de la investigación en física que está siendo desarrollada. Su campo de aplicación varía desde el estudio de plasmas interestelares y cósmicos, como las estrellas, las nebulosas, el medio intergaláctico, etc.; hasta aplicaciones más terrenales como la producción de microchips o los dispositivos de iluminación. Resulta particularmente interesante el estudio del contacto de una superficie metálica con un plasma. Siendo la razón que, la dinámica de la interfase formada entre un plasma imperturbado y una superficie metálica, resulta de gran importancia cuando se trata de estudiar problemas como: la implantación iónica en una oblea de silicio, el grabado por medio de plasmas, la carga de una aeronave cuando atraviesa la ionosfera y la diagnosis de plasmas mediante sondas de Langmuir. El uso de las sondas de Langmuir está extendido a través de multitud de aplicaciones tecnológicas e industriales como método de diagnosis de plasmas. Algunas de estas aplicaciones han sido mencionadas justo en el párrafo anterior. Es más, su uso también es muy popular en la investigación en física de plasmas, por ser una de las pocas técnicas de diagnosis que proporciona información local sobre el plasma. El equipamiento donde es habitualmente implementado varía desde plasmas de laboratorio de baja temperatura hasta plasmas de fusión en dispositivos como tokamaks o stellerators. La geometría más popular de este tipo de sondas es cilíndrica, y la principal magnitud que se usa para diagnosticar el plasma es la corriente recogida por la sonda cuando se encuentra polarizada a un cierto potencial. Existe un interes especial en diagnosticar por medio de la medida de la corriente iónica recogida por la sonda, puesto que produce una perturbación muy pequeña del plasma en comparación con el uso de la corriente electrónica. Dada esta popularidad, no es de extrañar que grandes esfuerzos se hayan realizado en la consecución de un modelo teórico que explique el comportamiento de una sonda de Langmuir inmersa en un plasma. Hay que remontarse a la primera mitad del siglo XX para encontrar las primeras teorías que permiten diagnosticar parámetros del plasma mediante la medida de la corriente iónica recogida por la sonda de Langmuir. Desde entonces, las mejoras en estos modelos y el desarrollo de otros nuevos ha sido una constante en la investigación en física de plasmas. No obstante, todavía no está claro como los iones se aproximan a la superficie de la sonda. Las dos principales, a la par que opuestas, aproximaciones al problema que están ampliamente aceptadas son: la radial y la orbital; siendo el problema que ambas predicen diferentes valores para la corriente iónica. Los experimentos han arrojado resultados de acuerdo con ambas teorías, la radial y la orbital; y lo que es más importante, una transición entre ambos ha sido recientemente observada. La mayoría de los logros conseguidos a la hora de comprender como los iones caen desde el plasma hacia la superficie de la sonda, han sido llevados a cabo en el campo de la dinámica de fluidos o la teoría cinética. Por otra parte, este problema puede ser abordado mediante el uso de simulaciones de partículas. La principal ventaja de las simulaciones de partículas sobre los modelos de fluidos o cinéticos es que proporcionan mucha más información sobre los detalles microscópicos del movimiento de las partículas, además es relativamente fácil introducir interacciones complejas entre las partículas. No obstante, estas ventajas no se obtienen gratuitamente, ya que las simulaciones de partículas requieren grandísimos recursos. Por esta razón, es prácticamente obligatorio el uso de técnicas de procesamiento paralelo en este tipo de simulaciones. El vacío en el conocimiento de las sondas de Langmuir, es el que motiva nuestro trabajo. Nuestra aproximación, y el principal objetivo de este trabajo, ha sido desarrollar una simulación de partículas que nos permita estudiar el problema de una sonda de Langmuir inmersa en un plasma y que está negativamente polarizada con respecto a éste. Dicha simulación nos permitiría estudiar el comportamiento de los iones en los alrededores de una sonda cilíndrica de Langmuir, así como arrojar luz sobre la transición entre las teorías radiales y orbitales que ha sido observada experimentalmente. Justo después de esta sección introductoria, el resto de la tesis está dividido en tres partes tal y como sigue: La primera parte está dedicada a establecer los fundamentos teóricos de las sondas de Langmuir. En primer lugar, se realiza una introducción general al problema y al uso de sondas de Langmuir como método de diagnosis de plasmas. A continuación, se incluye una extensiva revisión bibliográfica sobre las diferentes teorías que proporcionan la corriente iónica recogida por una sonda. La segunda parte está dedicada a explicar los detalles de las simulaciones de partículas que han sido desarrolladas a lo largo de nuestra investigación, así como los resultados obtenidos con las mismas. Esta parte incluye una introducción sobre la teoría que subyace el tipo de simulaciones de partículas y las técnicas de paralelización que han sido usadas en nuestros códigos. El resto de esta parte está dividido en dos capítulos, cada uno de los cuales se ocupa de una de las geometrías consideradas en nuestras simulaciones (plana y cilíndrica). En esta parte discutimos también los descubrimientos realizados relativos a la transición entre el comportamiento radial y orbital de los iones en los alrededores de una sonda cilíndrica de Langmuir. Finalmente, en la tercera parte de la tesis se presenta un resumen del trabajo realizado. En este resumen, se enumeran brevemente los resultados de nuestra investigación y se han incluido algunas conclusiones. Después de esto, se enumeran una serie de perspectivas futuras y extensiones para los códigos desarrollados.

ASYMPTOTIC PRESERVING SCHEME FOR A KINETIC MODEL DESCRIBING IN COMPRESSIBLE FLUIDS

The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in 7] is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate this problem, we focus here on a multi-dimensional prototype model and first propose an appropriate change of frame that makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a one-dimensional framework on the basis of the developed strategy to confirm its efficiency.

Kinetic model of continuous-wave flow chemical lasers

In this paper an analysis of the kinetic theory of the continuous-wave flow chemical lasers(CWFCL) is presented with emphasis being laid on the effects of inhomogeneous broadeningon CWFCL's performance. The results obtained are applicable to the case where laser fre-quency is either coincident or incoincident with that of the eenter of the line shape. This rela-tion has been,compared with that of the rate model in common use. These two models are almostidentical as the broadening parameter η is larger than 1. The smaller the value of η, thegreater the difference between the results of these two models will be. For fixed η, the dif-ferences between fhe results of the two models increase with the increase of the frequencyshift parameter ξ. When η is about less than 0.2. the kinetic model can predict exactly the in-homogeneous broadening effects,while the rate model cannot.

Conservative force fields in non-Gaussian statistics

In this Letter, we determine the kappa-distribution function for a gas in the presence of an external field of force described by a potential U(r). In the case of a dilute gas, we show that the kappa-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory. (C) 2008 Elsevier B.V. All rights reserved.

Teoria cinética não extensiva: efeitos físicos em gases e plasmas

The standard kinetic theory for a nonrelativistic diluted gas is generalized in the spirit of the nonextensive statistic distribution introduced by Tsallis. The new formalism depends on an arbitrary q parameter measuring the degree of nonextensivity. In the limit q = 1, the extensive Maxwell-Boltzmann theory is recovered. Starting from a purely kinetic deduction of the velocity q-distribution function, the Boltzmann H-teorem is generalized for including the possibility of nonextensive out of equilibrium effects. Based on this investigation, it is proved that Tsallis' distribution is the necessary and sufficient condition defining a thermodynamic equilibrium state in the nonextensive context. This result follows naturally from the generalized transport equation and also from the extended H-theorem. Two physical applications of the nonextensive effects have been considered. Closed analytic expressions were obtained for the Doppler broadening of spectral lines from an excited gas, as well as, for the dispersion relations describing the eletrostatic oscillations in a diluted electronic plasma. In the later case, a comparison with the experimental results strongly suggests a Tsallis distribution with the q parameter smaller than unity. A complementary study is related to the thermodynamic behavior of a relativistic imperfect simple fluid. Using nonequilibrium thermodynamics, we show how the basic primary variables, namely: the energy momentum tensor, the particle and entropy fluxes depend on the several dissipative processes present in the fluid. The temperature variation law for this moving imperfect fluid is also obtained, and the Eckart and Landau-Lifshitz formulations are recovered as particular cases

Carbon nanotubes/polyamide 6.6 nanostructured composites crystallization kinetic study

Compared with the traditional composites, the incorporation of carbon nanotubes into polymeric matrices can generate materials with superior properties, especially thermal, electrical and tribological properties. The aim of this study was to study the polyamide 6.6/carbon nanotubes (PA 6.6/CNT) nanostructured composites crystallization kinetics. The solution mixing technique was used to obtain the nanostructured composites studied in this work. PA 6.6 films were produced with amounts of 0.1, 0.5, and 1.0 wt% (weight/weight) CNT. X-ray diffraction analyses were performed in order to determine the crystallographic properties of nanostructured composite. The nanostructured composites crystallization kinetic study was performed using the differential scanning calorimetry under isothermal and nonisothermal (dynamic) conditions. The results have shown addition of CNTs in the PA 6.6 reduces the Avrami exponent, affecting the crystallization process of the composite. © The Author(s) 2012.

Charm contribution to bulk viscosity

In the range of temperatures reached in future heavy ion collision experiments, hadronic pair annihilations and creations of charm quarks may take place within the lifetime of the plasma. As a result, charm quarks may increase the bulk viscosity affecting the early stages of hydrodynamic expansion. Assuming thermalisation, we estimate the charm contribution to bulk viscosity within the same effective kinetic theory framework in which the light parton contribution has been computed previously. The time scale at which this physics becomes relevant is related to the width of the transport peak associated with the trace anomaly correlator and is found to be ≲20 fm/c for T≳600 MeV.

Ion-Ion correlations effect on nonlinear high-frequency plasma conductivity. AT(30-1)-1238-MATT-675

On the basis of the BBGKY hierarchy of equations an expression is derived for the response of a fully ionized plasma to a strong, high-frequency electric field in the limit of infinite ion mass. It is found that even in this limit the ionion correlation function is substantially affected by the field. The corrections to earlier nonlinear results for the current density appear to be quite ssential. The validity of the model introduced by Dawson and Oberman to study the response to a vanishingly small field is confirmed for larger values of the field when the eorrect expression for the ion-ion correlations i s introduced; the model by itself does not yield such an expression. The results have interest for the heating of the plasma and for the propagation of a strong electromagnetic wave through the plasma. The theory seems to be valid for any field intensity for which the plasma is stable.

Kinetic study of the hypersonic flow past the leading edge of a flat plate.

Vita.