Two-temperature model of the coronal irradiated pellets

A two electron-temperature, quasi-steady model of the corona of a laser-ablated pellet is considered. Ablation pressure, critical radius and mass flow rate are determined. Results are close to those obtained with heat flux saturation well below the free-streaming limit.

Dise��o de un m��dulo de IFMIF para irradiaci��n de envolturas regeneradoras basadas en metales l��quidos para reactores de fusi��n

La fusi��n nuclear es, hoy en d��a, una alternativa energ��tica a la que la comunidad internacional dedica mucho esfuerzo. El objetivo es el de generar entre diez y cincuenta veces m��s energ��a que la que consume mediante reacciones de fusi��n que se producir��n en una mezcla de deuterio (D) y tritio (T) en forma de plasma a doscientos millones de grados cent��grados. En los futuros reactores nucleares de fusi��n ser�� necesario producir el tritio utilizado como combustible en el propio reactor termonuclear. Este hecho supone dar un paso m��s que las actuales m��quinas experimentales dedicadas fundamentalmente al estudio de la f��sica del plasma. As�� pues, el tritio, en un reactor de fusi��n, se produce en sus envolturas regeneradoras cuya misi��n fundamental es la de blindaje neutr��nico, producir y recuperar tritio (fuel para la reacci��n DT del plasma) y por ��ltimo convertir la energ��a de los neutrones en calor. Existen diferentes conceptos de envolturas que pueden ser s��lidas o l��quidas. Las primeras se basan en cer��micas de litio (Li2O, Li4SiO4, Li2TiO3, Li2ZrO3) y multiplicadores neutr��nicos de Be, necesarios para conseguir la cantidad adecuada de tritio. Los segundos se basan en el uso de metales l��quidos o sales fundidas (Li, LiPb, FLIBE, FLINABE) con multiplicadores neutr��nicos de Be o el propio Pb en el caso de LiPb. Los materiales estructurales pasan por aceros ferr��tico-martens��ticos de baja activaci��n, aleaciones de vanadio o incluso SiCf/SiC. Cada uno de los diferentes conceptos de envoltura tendr�� una problem��tica asociada que se estudiar�� en el reactor experimental ITER (del ingl��s, ���International Thermonuclear Experimental Reactor���). Sin embargo, ITER no puede responder las cuestiones asociadas al da��o de materiales y el efecto de la radiaci��n neutr��nica en las diferentes funciones de las envolturas regeneradoras. Como referencia, la primera pared de un reactor de fusi��n de 4000MW recibir��a 30 dpa/a��o (valores para Fe-56) mientras que en ITER se conseguir��an <10 dpa en toda su vida ��til. Esta tesis se encuadra en el acuerdo bilateral entre Europa y Jap��n denominado ���Broader Approach Agreement ���(BA) (2007-2017) en el cual Espa��a juega un papel destacable. Estos proyectos, complementarios con ITER, son el acelerador para pruebas de materiales IFMIF (del ingl��s, ���International Fusion Materials Irradiation Facility���) y el dispositivo de fusi��n JT-60SA. As��, los efectos de la irradiaci��n de materiales en materiales candidatos para reactores de fusi��n se estudiar��n en IFMIF. El objetivo de esta tesis es el dise��o de un m��dulo de IFMIF para irradiaci��n de envolturas regeneradoras basadas en metales l��quidos para reactores de fusi��n. El m��dulo se llamar�� LBVM (del ingl��s, ���Liquid Breeder Validation Module���). La propuesta surge de la necesidad de irradiar materiales funcionales para envolturas regeneradoras l��quidas para reactores de fusi��n debido a que el dise��o conceptual de IFMIF no contaba con esta utilidad. Con objeto de analizar la viabilidad de la presente propuesta, se han realizado c��lculos neutr��nicos para evaluar la idoneidad de llevar a cabo experimentos relacionados con envolturas l��quidas en IFMIF. As��, se han considerado diferentes candidatos a materiales funcionales de envolturas regeneradoras: Fe (base de los materiales estructurales), SiC (material candidato para los FCI��s (del ingl��s, ���Flow Channel Inserts���) en una envoltura regeneradora l��quida, SiO2 (candidato para recubrimientos antipermeaci��n), CaO (candidato para recubrimientos aislantes), Al2O3 (candidato para recubrimientos antipermeaci��n y aislantes) y AlN (material candidato para recubrimientos aislantes). En cada uno de estos materiales se han calculado los par��metros de irradiaci��n m��s significativos (dpa, H/dpa y He/dpa) en diferentes posiciones de IFMIF. Estos valores se han comparado con los esperados en la primera pared y en la zona regeneradora de tritio de un reactor de fusi��n. Para ello se ha elegido un reactor tipo HCLL (del ingl��s, ���Helium Cooled Lithium Lead���) por tratarse de uno de los m��s prometedores. Adem��s, los valores tambi��n se han comparado con los que se obtendr��an en un reactor r��pido de fisi��n puesto que la mayor��a de las irradiaciones actuales se hacen en reactores de este tipo. Como conclusi��n al an��lisis de viabilidad, se puede decir que los materiales funcionales para mantos regeneradores l��quidos podr��an probarse en la zona de medio flujo de IFMIF donde se obtendr��an ratios de H/dpa y He/dpa muy parecidos a los esperados en las zonas m��s irradiadas de un reactor de fusi��n. Adem��s, con el objetivo de ajustar todav��a m��s los valores, se propone el uso de un moderador de W (a considerar en algunas campa��as de irradiaci��n solamente debido a que su uso hace que los valores de dpa totales disminuyan). Los valores obtenidos para un reactor de fisi��n refuerzan la idea de la necesidad del LBVM, ya que los valores obtenidos de H/dpa y He/dpa son muy inferiores a los esperados en fusi��n y, por lo tanto, no representativos. Una vez demostrada la idoneidad de IFMIF para irradiar envolturas regeneradoras l��quidas, y del estudio de la problem��tica asociada a las envolturas l��quidas, tambi��n incluida en esta tesis, se proponen tres tipos de experimentos diferentes como base de dise��o del LBVM. ��stos se orientan en las necesidades de un reactor tipo HCLL aunque a lo largo de la tesis se discute la aplicabilidad para otros reactores e incluso se proponen experimentos adicionales. As��, la capacidad experimental del m��dulo estar��a centrada en el estudio del comportamiento de litio plomo, permeaci��n de tritio, corrosi��n y compatibilidad de materiales. Para cada uno de los experimentos se propone un esquema experimental, se definen las condiciones necesarias en el m��dulo y la instrumentaci��n requerida para controlar y diagnosticar las c��psulas experimentales. Para llevar a cabo los experimentos propuestos se propone el LBVM, ubicado en la zona de medio flujo de IFMIF, en su celda caliente, y con capacidad para 16 c��psulas experimentales. Cada c��psula (24-22 mm de di��metro y 80 mm de altura) contendr�� la aleaci��n eut��ctica LiPb (hasta 50 mm de la altura de la c��psula) en contacto con diferentes muestras de materiales. ��sta ir�� soportada en el interior de tubos de acero por los que circular�� un gas de purga (He), necesario para arrastrar el tritio generado en el eut��ctico y permeado a trav��s de las paredes de las c��psulas (continuamente, durante irradiaci��n). Estos tubos, a su vez, se instalar��n en una carcasa tambi��n de acero que proporcionar�� soporte y refrigeraci��n tanto a los tubos como a sus c��psulas experimentales interiores. El m��dulo, en su conjunto, permitir�� la extracci��n de las se��ales experimentales y el gas de purga. As��, a trav��s de la estaci��n de medida de tritio y el sistema de control, se obtendr��n los datos experimentales para su an��lisis y extracci��n de conclusiones experimentales. Adem��s del an��lisis de datos experimentales, algunas de estas se��ales tendr��n una funci��n de seguridad y por tanto jugar��n un papel primordial en la operaci��n del m��dulo. Para el correcto funcionamiento de las c��psulas y poder controlar su temperatura, cada c��psula se equipar�� con un calentador el��ctrico y por tanto el m��dulo requerir�� tambi��n ser conectado a la alimentaci��n el��ctrica. El dise��o del m��dulo y su l��gica de operaci��n se describe en detalle en esta tesis. La justificaci��n t��cnica de cada una de las partes que componen el m��dulo se ha realizado con soporte de c��lculos de transporte de tritio, termohidr��ulicos y mec��nicos. Una de las principales conclusiones de los c��lculos de transporte de tritio es que es perfectamente viable medir el tritio permeado en las c��psulas mediante c��maras de ionizaci��n y contadores proporcionales comerciales, con sensibilidades en el orden de 10-9 Bq/m3. Los resultados son aplicables a todos los experimentos, incluso si son c��psulas a bajas temperaturas o si llevan recubrimientos antipermeaci��n. Desde un punto de vista de seguridad, el conocimiento de la cantidad de tritio que est�� siendo transportada con el gas de purga puede ser usado para detectar de ciertos problemas que puedan estar sucediendo en el m��dulo como por ejemplo, la rotura de una c��psula. Adem��s, es necesario conocer el balance de tritio de la instalaci��n. Las p��rdidas esperadas el refrigerante y la celda caliente de IFMIF se pueden considerar despreciables para condiciones normales de funcionamiento. Los c��lculos termohidr��ulicos se han realizado con el objetivo de optimizar el dise��o de las c��psulas experimentales y el LBVM de manera que se pueda cumplir el principal requisito del m��dulo que es llevar a cabo los experimentos a temperaturas comprendidas entre 300-550��C. Para ello, se ha dimensionado la refrigeraci��n necesaria del m��dulo y evaluado la geometr��a de las c��psulas, tubos experimentales y la zona experimental del contenedor. Como consecuencia de los an��lisis realizados, se han elegido c��psulas y tubos cil��ndricos instalados en compartimentos cil��ndricos debido a su buen comportamiento mec��nico (las tensiones debidas a la presi��n de los fluidos se ven reducidas significativamente con una geometr��a cil��ndrica en lugar de prism��tica) y t��rmico (uniformidad de temperatura en las paredes de los tubos y c��psulas). Se han obtenido campos de presi��n, temperatura y velocidad en diferentes zonas cr��ticas del m��dulo concluyendo que la presente propuesta es factible. Cabe destacar que el uso de c��digos fluidodin��micos (e.g. ANSYS-CFX, utilizado en esta tesis) para el dise��o de c��psulas experimentales de IFMIF no es directo. La raz��n de ello es que los modelos de turbulencia tienden a subestimar la temperatura de pared en mini canales de helio sometidos a altos flujos de calor debido al cambio de las propiedades del fluido cerca de la pared. Los diferentes modelos de turbulencia presentes en dicho c��digo han tenido que ser estudiados con detalle y validados con resultados experimentales. El modelo SST (del ingl��s, ���Shear Stress Transport Model���) para turbulencia en transici��n ha sido identificado como adecuado para simular el comportamiento del helio de refrigeraci��n y la temperatura en las paredes de las c��psulas experimentales. Con la geometr��a propuesta y los valores principales de refrigeraci��n y purga definidos, se ha analizado el comportamiento mec��nico de cada uno de los tubos experimentales que contendr�� el m��dulo. Los resultados de tensiones obtenidos, han sido comparados con los valores m��ximos recomendados en c��digos de dise��o estructural como el SDC-IC (del ingl��s, ���Structural Design Criteria for ITER Components���) para as�� evaluar el grado de protecci��n contra el colapso pl��stico. La conclusi��n del estudio muestra que la propuesta es mec��nicamente robusta. El LBVM implica el uso de metales l��quidos y la generaci��n de tritio adem��s del riesgo asociado a la activaci��n neutr��nica. Por ello, se han estudiado los riesgos asociados al uso de metales l��quidos y el tritio. Adem��s, se ha incluido una evaluaci��n preliminar de los riesgos radiol��gicos asociados a la activaci��n de materiales y el calor residual en el m��dulo despu��s de la irradiaci��n as�� como un escenario de p��rdida de refrigerante. Los riesgos asociados al m��dulo de naturaleza convencional est��n asociados al manejo de metales l��quidos cuyas reacciones con aire o agua se asocian con emisi��n de aerosoles y probabilidad de fuego. De entre los riesgos nucleares destacan la generaci��n de gases radiactivos como el tritio u otros radiois��topos vol��tiles como el Po-210. No se espera que el m��dulo suponga un impacto medioambiental asociado a posibles escapes. Sin embargo, es necesario un manejo adecuado tanto de las c��psulas experimentales como del m��dulo contenedor as�� como de las l��neas de purga durante operaci��n. Despu��s de un d��a de despu��s de la parada, tras un a��o de irradiaci��n, tendremos una dosis de contacto de 7000 Sv/h en la zona experimental del contenedor, 2300 Sv/h en la c��psula y 25 Sv/h en el LiPb. El uso por lo tanto de manipulaci��n remota est�� previsto para el manejo del m��dulo irradiado. Por ��ltimo, en esta tesis se ha estudiado tambi��n las posibilidades existentes para la fabricaci��n del m��dulo. De entre las t��cnicas propuestas, destacan la electroerosi��n, soldaduras por haz de electrones o por soldadura l��ser. Las bases para el dise��o final del LBVM han sido pues establecidas en el marco de este trabajo y han sido incluidas en el dise��o intermedio de IFMIF, que ser�� desarrollado en el futuro, como parte del dise��o final de la instalaci��n IFMIF. ABSTRACT Nuclear fusion is, today, an alternative energy source to which the international community devotes a great effort. The goal is to generate 10 to 50 times more energy than the input power by means of fusion reactions that occur in deuterium (D) and tritium (T) plasma at two hundred million degrees Celsius. In the future commercial reactors it will be necessary to breed the tritium used as fuel in situ, by the reactor itself. This constitutes a step further from current experimental machines dedicated mainly to the study of the plasma physics. Therefore, tritium, in fusion reactors, will be produced in the so-called breeder blankets whose primary mission is to provide neutron shielding, produce and recover tritium and convert the neutron energy into heat. There are different concepts of breeding blankets that can be separated into two main categories: solids or liquids. The former are based on ceramics containing lithium as Li2O , Li4SiO4 , Li2TiO3 , Li2ZrO3 and Be, used as a neutron multiplier, required to achieve the required amount of tritium. The liquid concepts are based on molten salts or liquid metals as pure Li, LiPb, FLIBE or FLINABE. These blankets use, as neutron multipliers, Be or Pb (in the case of the concepts based on LiPb). Proposed structural materials comprise various options, always with low activation characteristics, as low activation ferritic-martensitic steels, vanadium alloys or even SiCf/SiC. Each concept of breeding blanket has specific challenges that will be studied in the experimental reactor ITER (International Thermonuclear Experimental Reactor). However, ITER cannot answer questions associated to material damage and the effect of neutron radiation in the different breeding blankets functions and performance. As a reference, the first wall of a fusion reactor of 4000 MW will receive about 30 dpa / year (values for Fe-56) , while values expected in ITER would be <10 dpa in its entire lifetime. Consequently, the irradiation effects on candidate materials for fusion reactors will be studied in IFMIF (International Fusion Material Irradiation Facility). This thesis fits in the framework of the bilateral agreement among Europe and Japan which is called ���Broader Approach Agreement ���(BA) (2007-2017) where Spain plays a key role. These projects, complementary to ITER, are mainly IFMIF and the fusion facility JT-60SA. The purpose of this thesis is the design of an irradiation module to test candidate materials for breeding blankets in IFMIF, the so-called Liquid Breeder Validation Module (LBVM). This proposal is born from the fact that this option was not considered in the conceptual design of the facility. As a first step, in order to study the feasibility of this proposal, neutronic calculations have been performed to estimate irradiation parameters in different materials foreseen for liquid breeding blankets. Various functional materials were considered: Fe (base of structural materials), SiC (candidate material for flow channel inserts, SiO2 (candidate for antipermeation coatings), CaO (candidate for insulating coatings), Al2O3 (candidate for antipermeation and insulating coatings) and AlN (candidate for insulation coating material). For each material, the most significant irradiation parameters have been calculated (dpa, H/dpa and He/dpa) in different positions of IFMIF. These values were compared to those expected in the first wall and breeding zone of a fusion reactor. For this exercise, a HCLL (Helium Cooled Lithium Lead) type was selected as it is one of the most promising options. In addition, estimated values were also compared with those obtained in a fast fission reactor since most of existing irradiations have been made in these installations. The main conclusion of this study is that the medium flux area of IFMIF offers a good irradiation environment to irradiate functional materials for liquid breeding blankets. The obtained ratios of H/dpa and He/dpa are very similar to those expected in the most irradiated areas of a fusion reactor. Moreover, with the aim of bringing the values further close, the use of a W moderator is proposed to be used only in some experimental campaigns (as obviously, the total amount of dpa decreases). The values of ratios obtained for a fission reactor, much lower than in a fusion reactor, reinforce the need of LBVM for IFMIF. Having demonstrated the suitability of IFMIF to irradiate functional materials for liquid breeding blankets, and an analysis of the main problems associated to each type of liquid breeding blanket, also presented in this thesis, three different experiments are proposed as basis for the design of the LBVM. These experiments are dedicated to the needs of a blanket HCLL type although the applicability of the module for other blankets is also discussed. Therefore, the experimental capability of the module is focused on the study of the behavior of the eutectic alloy LiPb, tritium permeation, corrosion and material compatibility. For each of the experiments proposed an experimental scheme is given explaining the different module conditions and defining the required instrumentation to control and monitor the experimental capsules. In order to carry out the proposed experiments, the LBVM is proposed, located in the medium flux area of the IFMIF hot cell, with capability of up to 16 experimental capsules. Each capsule (24-22 mm of diameter, 80 mm high) will contain the eutectic allow LiPb (up to 50 mm of capsule high) in contact with different material specimens. They will be supported inside rigs or steel pipes. Helium will be used as purge gas, to sweep the tritium generated in the eutectic and permeated through the capsule walls (continuously, during irradiation). These tubes, will be installed in a steel container providing support and cooling for the tubes and hence the inner experimental capsules. The experimental data will consist of on line monitoring signals and the analysis of purge gas by the tritium measurement station. In addition to the experimental signals, the module will produce signals having a safety function and therefore playing a major role in the operation of the module. For an adequate operation of the capsules and to control its temperature, each capsule will be equipped with an electrical heater so the module will to be connected to an electrical power supply. The technical justification behind the dimensioning of each of these parts forming the module is presented supported by tritium transport calculations, thermalhydraulic and structural analysis. One of the main conclusions of the tritium transport calculations is that the measure of the permeated tritium is perfectly achievable by commercial ionization chambers and proportional counters with sensitivity of 10-9 Bq/m3. The results are applicable to all experiments, even to low temperature capsules or to the ones using antipermeation coatings. From a safety point of view, the knowledge of the amount of tritium being swept by the purge gas is a clear indicator of certain problems that may be occurring in the module such a capsule rupture. In addition, the tritium balance in the installation should be known. Losses of purge gas permeated into the refrigerant and the hot cell itself through the container have been assessed concluding that they are negligible for normal operation. Thermal hydraulic calculations were performed in order to optimize the design of experimental capsules and LBVM to fulfill one of the main requirements of the module: to perform experiments at uniform temperatures between 300-550��C. The necessary cooling of the module and the geometry of the capsules, rigs and testing area of the container were dimensioned. As a result of the analyses, cylindrical capsules and rigs in cylindrical compartments were selected because of their good mechanical behavior (stresses due to fluid pressure are reduced significantly with a cylindrical shape rather than prismatic) and thermal (temperature uniformity in the walls of the tubes and capsules). Fields of pressure, temperature and velocity in different critical areas of the module were obtained concluding that the proposal is feasible. It is important to mention that the use of fluid dynamic codes as ANSYS-CFX (used in this thesis) for designing experimental capsules for IFMIF is not direct. The reason for this is that, under strongly heated helium mini channels, turbulence models tend to underestimate the wall temperature because of the change of helium properties near the wall. Therefore, the different code turbulence models had to be studied in detail and validated against experimental results. ANSYS-CFX SST (Shear Stress Transport Model) for transitional turbulence model has been identified among many others as the suitable one for modeling the cooling helium and the temperature on the walls of experimental capsules. Once the geometry and the main purge and cooling parameters have been defined, the mechanical behavior of each experimental tube or rig including capsules is analyzed. Resulting stresses are compared with the maximum values recommended by applicable structural design codes such as the SDC- IC (Structural Design Criteria for ITER Components) in order to assess the degree of protection against plastic collapse. The conclusion shows that the proposal is mechanically robust. The LBVM involves the use of liquid metals, tritium and the risk associated with neutron activation. The risks related with the handling of liquid metals and tritium are studied in this thesis. In addition, the radiological risks associated with the activation of materials in the module and the residual heat after irradiation are evaluated, including a scenario of loss of coolant. Among the identified conventional risks associated with the module highlights the handling of liquid metals which reactions with water or air are accompanied by the emission of aerosols and fire probability. Regarding the nuclear risks, the generation of radioactive gases such as tritium or volatile radioisotopes such as Po-210 is the main hazard to be considered. An environmental impact associated to possible releases is not expected. Nevertheless, an appropriate handling of capsules, experimental tubes, and container including purge lines is required. After one day after shutdown and one year of irradiation, the experimental area of the module will present a contact dose rate of about 7000 Sv/h, 2300 Sv/h in the experimental capsules and 25 Sv/h in the LiPb. Therefore, the use of remote handling is envisaged for the irradiated module. Finally, the different possibilities for the module manufacturing have been studied. Among the proposed techniques highlights the electro discharge machining, brazing, electron beam welding or laser welding. The bases for the final design of the LBVM have been included in the framework of the this work and included in the intermediate design report of IFMIF which will be developed in future, as part of the IFMIF facility final design.

Equation of state for hot dense matter using a relativistic screened hydrogenic model

The study of matter under conditions of high density, pressure, and temperature is a valuable subject for inertial con���nement fusion (ICF), astrophysical phenomena, high-power laser interaction with matter, etc. In all these cases, matter is heated and compressed by strong shocks to high pressures and temperatures, becomes partially or completely ionized via thermal or pressure ionization, and is in the form of dense plasma. The thermodynamics and the hydrodynamics of hot dense plasmas cannot be predicted without the knowledge of the equation of state (EOS) that describes how a material reacts to pressure and how much energy is involved. Therefore, the equation of state often takes the form of pressure and energy as functions of density and temperature. Furthermore, EOS data must be obtained in a timely manner in order to be useful as input in hydrodynamic codes. By this reason, the use of fast, robust and reasonably accurate atomic models, is necessary for computing the EOS of a material.

Stochastic homogenization of the laser intensity to improve the irradiation uniformity of capsules directly driven by thousands laser beams

Illumination uniformity of a spherical capsule directly driven by laser beams has been assessed numerically. Laser facilities characterized by ND = 12, 20, 24, 32, 48 and 60 directions of irradiation with associated a single laser beam or a bundle of NB laser beams have been considered. The laser beam intensity profile is assumed super-Gaussian and the calculations take into account beam imperfections as power imbalance and pointing errors. The optimum laser intensity profile, which minimizes the root-mean-square deviation of the capsule illumination, depends on the values of the beam imperfections. Assuming that the NB beams are statistically independents is found that they provide a stochastic homogenization of the laser intensity associated to the whole bundle, reducing the errors associated to the whole bundle by the factor��� , which in turn improves the illumination uniformity of the capsule. Moreover, it is found that the uniformity of the irradiation is almost the same for all facilities and only depends on the total number of laser beams Ntot = ND �� NB.

Internal quantum efficiency of III-nitride quantum dot superlattices grown by plasma-assisted molecular-beam epitaxy

We present a study of the optical properties of GaN/AlN and InGaN/GaN quantum dot (QD) superlattices grown via plasma-assisted molecular-beam epitaxy, as compared to their quantum well (QW) counterparts. The three-dimensional/two-dimensional nature of the structures has been verified using atomic force microscopy and transmission electron microscopy. The QD superlattices present higher internal quantum efficiency as compared to the respective QWs as a result of the three-dimensional carrier localization in the islands. In the QW samples, photoluminescence (PL) measurements point out a certain degree of carrier localization due to structural defects or thickness fluctuations, which is more pronounced in InGaN/GaN QWs due to alloy inhomogeneity. In the case of the QD stacks, carrier localization on potential fluctuations with a spatial extension smaller than the QD size is observed only for the InGaN QD-sample with the highest In content (peak emission around 2.76 eV). These results confirm the efficiency of the QD three-dimensional confinement in circumventing the potential fluctuations related to structural defects or alloy inhomogeneity. PL excitation measurements demonstrate efficient carrier transfer from the wetting layer to the QDs in the GaN/AlN system, even for low QD densities (~1010 cm-3). In the case of InGaN/GaN QDs, transport losses in the GaN barriers cannot be discarded, but an upper limit to these losses of 15% is deduced from PL measurements as a function of the excitation wavelength.

Two-dimensional plasma expansion in a magnetic nozzle: Separation due to electron inertia

A previous axisymmetric model of the supersonic expansion of a collisionless, hot plasma in a divergent magnetic nozzle is extended here in order to include electron-inertia effects. Up to dominant order on all components of the electron velocity, electron momentum equations still reduce to three conservation laws. Electron inertia leads to outward electron separation from the magnetic streamtubes. The progressive plasma filling of the adjacent vacuum region is consistent with electron-inertia being part of finite electron Larmor radius effects, which increase downstream and eventually demagnetize the plasma. Current ambipolarity is not fulfilled and ion separation can be either outwards or inwards of magnetic streamtubes, depending on their magnetization. Electron separation penalizes slightly the plume efficiency and is larger for plasma beams injected with large pressure gradients. An alternative nonzero electron-inertia model [E. Hooper, J. Propul. Power 9, 757 (1993)] based on cold plasmas and current ambipolarity, which predicts inwards electron separation, is discussed critically. A possible competition of the gyroviscous force with electron-inertia effects is commented briefly.

Ion correlations due to high-frequency electric field and their effect on the nonlinear plasma conductivity

The influence of a strong, high���frequency electric field on the ion���ion correlations in a fully ionized plasma is investigated in the limit of infinite ion mass, starting with the Bogoliubov���Born���Green���Kirkwood���Yvon hierarchy of equations; a significant departure from the thermal correlations is found. It is shown that the above effect may substantially modify earlier results on the nonlinear high���frequency plasma conductivity.

Electrostatic plasma instabilities excited by a high���frequency electric field

The electrostatic plasma waves excited by a uniform, alternating electric field of arbitrary intensity are studied on the basis of the Vlasov equation; their dispersion relation, which involves the determinant of either of two infinite matrices, is derived. For ��0�����������pi (��0 being the applied frequency and ��pi the ion plasma frequency) the waves may be classified in two groups, each satisfying a simple condition; this allows writing the dispersion relation in closed form. Both groups coalesce (resonance) if (a) ��0��� ��� �����pe/r (r any integer) and (b) the wavenumber k is small. A nonoscillatory instability is found; its distinction from the DuBois���Goldman instability and its physical origin are discussed. Conditions for its excitation (in particular, upper limits to ��0,k, and k���vE,vE being the field���induced electron velocity), and simple equations for the growth rate are given off���resonance and at ��0��� ��� �����pi. The dependence of both threshold and maximum growth rate on various parameters is discussed, and the results are compared with those of Silin and Nishikawa. The threshold at ��0��� ��� �����pi/r,r��� ��� ���1, is studied.

Far wake structure in rarefied plasma flows past charged bodies

The asymptotic structure of the far-wake behind a charged body in a rarefied plasma flow is investigated under the assumption of small ion-to-electron temperature ratio and of flow speed hypersonic with respect to the ions but not with respect to the electrons. It is found that waves are excited even if the flow is subacoustic (flow velocity less than the ion-acoustic speed). For both superacoustic and subacoustic velocities a steep wave front develops separating the weakly perturbed, quasineutral plasma ahead, from the region behind where ion waves appear. Near the axis a trailing front develops;the region between this and the axis is quasineutral for superacoustic speeds. The decay laws in all of these regions, the self-similar structure of the fronts and the general character of the waves are determined.The damping of the waves and special flow detail for bodies large and small compared with the Debye length are discussed. A nonlinear analysis of the leading wave front in superacoustic flow is carried out. A hyperacoustic equivalence principle is presented.

Self-similar motion of laser fusion plasmas. Absorption in an unbounded plasma

The one-dimensional motion generated in a cold, infinite, uniform plasma of density na by the absorption, in a certain plane, of a linear pulse of energy per unit time and area <j> = 4>0t/r, 0< t< r, is considered, the analysis allows for thermal conduction and viscosity of ions and electrons, their energy exchange, and an electron heat flux limiter The resulting motion is self-similar and governed by a single nondimensional parameter a��(n0 2T/<f>0)2/3 Detailed asymptotic results are obtained for both a < l and a > l , the general behavior of the solution for arbitrary a is discussed The analysis can be extended to the case of a plasma initially occupying a half-space, and throws light on how to optimize the hydrodynamics of laser fusion plasmas Known approximate results corresponding to motion of a plasma submitted to constant irradiation (<()) are recovered in the present work under appropriate limiting processes

Current collection by an active spherical electrode in an unmagnetized plasma

A theoretical model for the steady-state response of anodic contactors that emit a plasma current Ii and collect electrons from a collisionless, unmagnetized plasma is presented. The use of a (kinetic) monoenergetic population for the attracted species, well known in passive probe theory, gives both accuracy and tractability to the theory. The monoenergetic population is proved to behave like an isentropic fluid with radial plus centripetal motion, allowing direct comparisons with ad hoc fluid models. Also, a modification of the original monoenergetic equations permits analysis of contactors operating in orbit-limited conditions. Besides that, the theory predicts that, only for plasma emissions above certain threshold current a presheath/double layer/core structure for the potential is formed (the core mode), while for emissions below that threshold, a plasma contactor behaves exactly as a positive-ion emitter with a presheath/sheath structure (the no-core mode). Ion emitters are studied as a particular case. Emphasis is placed on obtaining dimensionless charts and approximate asymptotic laws of the current-voltage characteristic.

Nonlocal electron heat relaxation in a plasma shock at arbitrary ionization number

A recently obtained nonlocal expression for the electron heat flux valid for arbitrary ionization numbers Z is used to study the structure of a plane shock wave in a fully ionized plasma. Nonlocal effects are only important in the foot of the electronic preheating region, where the electron temperature gradient is the steepest. The results are quantified as a function of a characteristic Knudsen number of that region. This work also generalizes to arbitrary values of Z previous results on plasma shock wave structure.

Electron current to a probe in a magnetized, collisional plasma

Collisional analysis of electron collection by a probe in a strongly magnetized, fully ionized plasma is carried out. A solution to the complete set of macroscopic equations with classical transport coefficients that is wholly consistent in the domain is determined; R and le are probe radius and electron gyroradius, respectively. If R2/le 2 is large compared with mi/3me probe large compared with ion gyroradius, ion���electron energy exchange���rather than electron heat diffusion���keeps electrons isothermal. For smaller probes at negative bias, however, electron cooling occurs in the plasma beyond the sheath, with a potential overshoot lying well away from it. The probe characteristic in the electron-retarding range may then mimic the characteristic for a two electron-temperature plasma and lead to an overestimate of electron temperature; the validity of these results for other transport models is discussed

Sudden transition to chaos in plasma wave interactions

The coherent three-wave interaction, with linear growth in the higher frequency wave and damping in the two other waves, is reconsidered; for equal dampings, the resulting three-dimensional (3-D) flow of a relative phase and just two amplitudes behaved chaotically, no matter how small the growth of the unstable wave. The general case of different dampings is studied here to test whether, and how, that hard scenario for chaos is preserved in passing from 3-D to four-dimensional flows. It is found that the wave with higher damping is partially slaved to the other damped wave; this retains a feature of the original problem an invariant surface that meets an unstable fixed point, at zero growth rate! that gave rise to the chaotic attractor and determined its structure, and suggests that the sudden transition to chaos should appear in more complex wave interactions.