214 pages / The Fock-Tani (unitary) transformation of the second- quantized Hamiltonian gives a representation which treats reactants and products symmetrically, and composites exactly. Each term in the Fock-Tani potential corresponds to a specific physical process and contains terms orthogonalizing continuum states to the bound states. The difficulty in carrying out this transformation can be lessened by working in a center of mass system, giving (n-1) reduced mass particles. After a general analysis of such systems, the Fock- Tani transformations in the 3→2-body case are carried out for the reactions a⁺+(b⁺c⁻)→(a⁺c⁻)+b⁺ and a⁻+(b⁺c⁻)→(a⁻b⁺)+c⁻. It is found that for (2) the transformation in the symmetrical reduced mass system can easily be carried out, but the Jacobi reduced mass system requires the more complicated d-matrix approach. This transformation has not yet been attempted in the full 3-body system but is likely to be as difficult as that for (1). First order differential and total cross sections are computed for resonant charge transfer in (1) for a proton- hydrogen initial state. The Fock-Tani T-matrix for the initial-state Jacobi system is found to be identical to that for the full 3-body system. That for the symmetrical reduced mass system gives an error of order l/mprot in the incident wave vector. A comparison of the Jacobi version and a previous special case Fock-Tani transformation, where the proton mass is taken as infinite, is also made. Cross sections for (ls→ls) positronium formation in positron-hydrogen collisions, calculated using the same program as for the proton-hydrogen case, are found to disagree with the previous Fock-Tani result, probably due to lack of convergence of the previous result. Cross sections for reactions (1) involving muons in hydrogenic isotopes (of interest in quantum electrodynamics and catalyzed fusion) are also calculated. Finally, extension of the results to higher order is considered. Polarized Schrodinger wave functions for a system containing a hydrogenic atom and a fully kinetic external charge are found to first order. These would be used in the Fock-Tani matrix elements to account for some initial- and final-state effects. Calculations of distorted second-quantized states and second and third order T-matrix elements are also outlined.

This thesis presents results on the theoretical description of ion acceleration using ultra-short ultra-intense laser pulses. It consists of two parts. One deals with the very general and underlying description and theoretic modeling of the laser interaction with the plasma, the other part presents three approaches of optimizing the ion acceleration by target geometry improvements using the results of the first part. In the first part, a novel approach of modeling the electron average energy of an over-critical plasma that is irradiated by a few tens of femtoseconds laser pulse with relativistic intensity is introduced. The first step is the derivation of a general expression of the distribution of accelerated electrons in the laboratory time frame. As is shown, the distribution is homogeneous in the proper time of the accelerated electrons, provided they are at rest and distributed uniformly initially. The average hot electron energy can then be derived in a second step from a weighted average of the single electron energy evolution. This result is applied exemplary for the two important cases of infinite laser contrast and square laser temporal profile, and the case of an experimentally more realistic case of a laser pulse with a temporal profile sufficient to produce a preplasma profile with a scale length of a few hundred nanometers prior to the laser pulse peak. The thus derived electron temperatures are in excellent agreement with recent measurements and simulations, and in particular provide an analytic explanation for the reduced temperatures seen both in experiments and simulations compared to the widely used ponderomotive energy scaling. The implications of this new electron temperature scaling on the ion acceleration, i.e. the maximum proton energy, are then briefly studied in the frame of an isothermal 1D expansion model. Based on this model, two distinct regions of laser pulse duration are identified with respect to the maximum energy scaling. For short laser pulses, compared to a reference time, the maximum ion energy is found to scale linearly with the laser intensity for a simple flat foil, and the most important other parameter is the laser absorption efficiency. In particular the electron temperature is of minor importance. For long laser pulse durations the maximum ion energy scales only proportional to the square root of the laser peak intensity and the electron temperature has a large impact. Consequently, improvements of the ion acceleration beyond the simple flat foil target maximum energies should focus on the increase of the laser absorption in the first case and the increase of the hot electron temperature in the latter case. In the second part, exemplary geometric designs are studied by means of simulations and analytic discussions with respect to their capability for an improvement of the laser absorption efficiency and temperature increase. First, a stack of several foils spaced by a few hundred nanometers is proposed and it is shown that the laser energy absorption for short pulses and therefore the maximum proton energy can be significantly increased. Secondly, mass limited targets, i.e. thin foils with a finite lateral extension, are studied with respect to the increase of the hot electron temperature. An analytical model is provided predicting this temperature based on the lateral foil width. Finally, the important case of bent foils with attached flat top is analyzed. This target geometry resembles hollow cone targets with flat top attached to the tip, as were used in a recent experiment producing world record proton energies. The presented analysis explains the observed increase in proton energy with a new electron acceleration mechanism, the direct acceleration of surface confined electrons by the laser light. This mechanism occurs when the laser is aligned tangentially to the curved cone wall and the laser phase co-moves with the energetic electrons. The resulting electron average energy can exceed the energies from normal or oblique laser incidence by several times. Proton energies are therefore also greatly increased and show a theoretical scaling proportional to the laser intensity, even for long laser pulses.

[ES] A pesar de la importancia de las turbinas radiales de doble entrada y doble voluta en el flujo para motores turboalimentados, sus mapas característicos y su modelado totalmente predictivo utilizando códigos dinámicos de gas 1D aún no están bien establecidos. La complejidad del flujo no estacionario y la admisión desigual de estas turbinas, cuando funcionan con pulsos de gases de escape del motor, las convierte en un sistema desafiante. Principalmente debido a la admisión de flujo desigual, se introduce un grado adicional de libertad con respecto a las turbinas conocidas como de una sola entrada con o sin álabes en el estator. Además, la adición de la segunda entrada a la voluta de la turbina aporta una complejidad adicional para determinar los parámetros de rendimiento de la turbina en estacionario estable y en condiciones de admisión desiguales.Esta tesis tiene como novedad principal un procedimiento simple para caracterizar experimentalmente y elaborar mapas característicos de estas turbinas con condiciones de flujo desiguales. Este método de análisis permite interpolar fácilmente dentro de los mapas distintivos propuestos o ajustar modelos simples y convincentes para calcular y extrapolar parámetros de rendimiento completo de turbinas de doble entrada y doble voluta. También hemos descrito aquí, dos modelos innovadores de línea media 0D que requieren una cantidad mínima de datos experimentales para calibrar ambos: es decir, el modelo de parámetros de flujo másico y el modelo de eficiencia isentrópica. Ambos modelos son predictivos en condiciones de admisión de flujo parcial o desigual utilizando como entradas: la relación de flujo másico entre ramas; la relación de temperatura total entre ramas; la relación de velocidad de álabe a chorro en cada rama y la relación de presión en cada rama. Estas cinco entradas generalmente son proporcionadas instantáneamente por códigos de dinámica de gas 1D. Por lo tanto, la novedad del modelo es su capacidad de ser utilizado de manera casi constante para la predicción del rendimiento de las turbinas de doble entrada y de doble voluta. Esto se puede lograr instantáneamente ya que las turbinas se calculan en condiciones de flujo pulsante y desigual en motores turbo alimentados. Además, se muestra una metodología para caracterizar el coeficiente de descarga de una válvula de alivio de presión. Para estimar el flujo de gas por la válvula de alivio en modelos unidimensionales, se correlaciona y valida un modelo empírico. Finalmente, se ha elaborado un mapa óptimo del coeficiente de descarga a través del método de interpolación, que puede integrarse en el sistema de modelo de motor turboalimentado completo unidimensional, para calcular el flujo másico real a través de la válvula de descarga y las válvulas de conexión de desplazamiento. Finalmente, los modelos han sido completamente validados al acoplarlos con un software de modelado unidimensional que simula tanto el banco de gas como el motor completo. Por un lado, los resultados de las validaciones del banco de gas muestran que el modelo puede predecir bien todas las variables de flujo estacionario. Por otro lado, los resultados de la validación de todo el motor muestran que el modelo es capaz de producir todas las variables del motor a plena carga como el flujo de masa de aire y el par de frenado con un buen grado de acuerdo con los datos experimentales. / [EN] Despite the importance of radial in-flow twin-entry and dual-volute turbines for turbocharged engines, their characteristic maps and fully predictive modelling using 1D gas dynamic codes are not well established yet. The complexity of the un-steady flow and the unequal admission of these turbines, when operating with pulses of engine exhaust gas, make them a challenging system. Mainly due to the unequal flow admission, an additional degree of freedom is introduced to well-known single entry vanned or vaneless turbines. Moreover, the addition of the second inlet to the turbine volute brings extra complexity in determining the steady-state turbine performance parameters under unequal admission conditions. This thesis has a main novelty, which is a simple procedure for characterizing experimentally and elaborating characteristic maps of these turbines with unequal flow conditions. This method of analysis allows easy interpolating within the proposed distinctive maps or simple convincing models for calculating and extrapolating full performance parameters of twin-entry and dual-volute turbines. Here are also described two innovative 0D mean-line models that require a minimum quantity of experimental data for calibrating both: i.e. the mass flow parameter model and the isentropic efficiency model. Both models are predictive either in partial or unequal flow admission conditions using as inputs: the mass flow ratio and the total temperature ratio between the branches; the blade speed ratio and expansion ratio in each branch. These six inputs are generally instantaneously provided by 1D gas-dynamics codes.} Therefore, the novelty of the model is its ability to be used in a quasi-steady way for twin and dual-volute turbines performance prediction. This can be achieved instantaneously as turbines are calculated under pulsating and uneven flow conditions at turbocharged engines. Furthermore, a methodology for characterizing the discharge coefficient of a wastegate and scroll connection valve in a gas stand is shown. For estimating the gas flow over the same in one-dimensional models, an empirical model is correlated and validated. Finally, an optimal map of discharge coefficient has been drawn out through the interpolation method. This map can be integrated into the full one-dimensional turbocharged engine model system, in order to calculate the actual mass flow through the wastegate and scroll connection valves. Finally, the models have been fully validated by coupling them with one-dimensional modelling software and simulated both the gas stand and the whole engine measured points. On the one hand, the validation results from the gas stand simulation show that the model can predict well all steady flow variables. On the other hand, the validation results from the whole engine simulation show that the model is able to produce all the full load engine variables like air mass flow and brake torque in a reasonable degree of agreement with the experimental data. / [CA] Malgrat la importància de les turbines radials amb doble entrada i de doble voluta per als motors turboalimentats, els seus mapes característics i el seu model completament predictiu mitjançant codis dinàmics de gas 1D encara no estan ben establerts. La complexitat del flux constant i l'admissió desigual d'aquestes turbines, quan funcionen amb polsos de gas d'escapament del motor, les converteixen en un sistema difícil. Principalment a causa de la admissió de flux desigual, s'introdueix un grau addicional de llibertat a les conegudes turbines vendes o d'entrada d'una sola entrada. A més, l'addició de la segona entrada a la voluta de la turbina aporta una complexitat addicional per determinar els paràmetres de rendiment de la turbina en estat estacionari en condicions d'admissió desigual. Aquesta tesi té com a novetat principal un procediment senzill per caracteritzar experimentalment i elaborar mapes característics d'aquestes turbines amb condicions de cabal desigual. Aquest mètode d'anàlisi permet interpolar fàcilment dins dels mapes distintius proposats o models senzills convincents per calcular i extrapolar paràmetres de rendiment complet de les turbines d'entrada doble i de doble voluta. Aquí també hem descrit dos models innovadors de línia mitjana 0D que requereixen una quantitat mínima de dades experimentals per calibrar tots dos: és a dir, el model de paràmetre de flux massiu i el model d'eficiència isentròpica. Els dos models són predictius en condicions d'admissió de flux parcial o desigual utilitzant com a entrada: la proporció de flux entre les branques; la relació total de la temperatura entre les branques; la relació velocitat fulla-raig a cada branca i la proporció de pressió a cada branca. Aquests cinc inputs generalment es proporcionen de manera instantània mitjançant codis de dinàmica de gas 1D. Per tant, la novetat del model és la seva capacitat d'utilitzar-se d'una manera quasi constant per a la predicció del rendiment de les turbines bessones i de doble voluta. Es pot aconseguir de forma instantània, ja que les turbines es calculen en condicions de flux pulsatòries i desiguals en motors turboalimentats. A més, es mostra una metodologia per a caracteritzar el coeficient de descàrrega d'una vàlvula de connexió per canals i desplaçaments en un suport de gas. Per estimar el flux de gas sobre el mateix en models unidimensionals, es correlaciona i valida un model empíric. Finalment, s'ha elaborat un mapa òptim de coeficient de descàrrega mitjançant el mètode d'interpolació, que pot integrar-se al sistema de model turboalimentat complet del motor turbo, per calcular el cabal de massa real a través de les vàlvules de connexió de desguàs i desplaçament. Finalment, els models s'han validat completament combinant-los amb un programari de modelatge unidimensional que simula tant el suport de gas com el motor sencer. D'una banda, els resultats de les validacions de l'estand de gas demostren que el model és capaç de predir bé totes les variables de flux constant. D'altra banda, els resultats de validació del motor complet demostren que el model és capaç de produir totes les variables del motor de càrrega completa, com ara el flux de massa d'aire i el pare de fre d'una bona manera amb les dades experimentals. / Samala, V. (2020). Experimental characterization and mean line modelling of twin-entry and dual-volute turbines working under different admission conditions with steady flow [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/153475 / TESIS

This thesis presents results on the theoretical description of ion acceleration using ultra-short ultra-intense laser pulses. It consists of two parts. One deals with the very general and underlying description and theoretic modeling of the laser interaction with the plasma, the other part presents three approaches of optimizing the ion acceleration by target geometry improvements using the results of the first part. In the first part, a novel approach of modeling the electron average energy of an over-critical plasma that is irradiated by a few tens of femtoseconds laser pulse with relativistic intensity is introduced. The first step is the derivation of a general expression of the distribution of accelerated electrons in the laboratory time frame. As is shown, the distribution is homogeneous in the proper time of the accelerated electrons, provided they are at rest and distributed uniformly initially. The average hot electron energy can then be derived in a second step from a weighted average of the single electron energy evolution. This result is applied exemplary for the two important cases of infinite laser contrast and square laser temporal profile, and the case of an experimentally more realistic case of a laser pulse with a temporal profile sufficient to produce a preplasma profile with a scale length of a few hundred nanometers prior to the laser pulse peak. The thus derived electron temperatures are in excellent agreement with recent measurements and simulations, and in particular provide an analytic explanation for the reduced temperatures seen both in experiments and simulations compared to the widely used ponderomotive energy scaling. The implications of this new electron temperature scaling on the ion acceleration, i.e. the maximum proton energy, are then briefly studied in the frame of an isothermal 1D expansion model. Based on this model, two distinct regions of laser pulse duration are identified with respect to the maximum energy scaling. For short laser pulses, compared to a reference time, the maximum ion energy is found to scale linearly with the laser intensity for a simple flat foil, and the most important other parameter is the laser absorption efficiency. In particular the electron temperature is of minor importance. For long laser pulse durations the maximum ion energy scales only proportional to the square root of the laser peak intensity and the electron temperature has a large impact. Consequently, improvements of the ion acceleration beyond the simple flat foil target maximum energies should focus on the increase of the laser absorption in the first case and the increase of the hot electron temperature in the latter case. In the second part, exemplary geometric designs are studied by means of simulations and analytic discussions with respect to their capability for an improvement of the laser absorption efficiency and temperature increase. First, a stack of several foils spaced by a few hundred nanometers is proposed and it is shown that the laser energy absorption for short pulses and therefore the maximum proton energy can be significantly increased. Secondly, mass limited targets, i.e. thin foils with a finite lateral extension, are studied with respect to the increase of the hot electron temperature. An analytical model is provided predicting this temperature based on the lateral foil width. Finally, the important case of bent foils with attached flat top is analyzed. This target geometry resembles hollow cone targets with flat top attached to the tip, as were used in a recent experiment producing world record proton energies. The presented analysis explains the observed increase in proton energy with a new electron acceleration mechanism, the direct acceleration of surface confined electrons by the laser light. This mechanism occurs when the laser is aligned tangentially to the curved cone wall and the laser phase co-moves with the energetic electrons. The resulting electron average energy can exceed the energies from normal or oblique laser incidence by several times. Proton energies are therefore also greatly increased and show a theoretical scaling proportional to the laser intensity, even for long laser pulses.