Thesis advisor: Krzysztof Kempa / Nonlocal effects, the wavenumber dependence in a medium's response to external disturbance, is treated in this thesis. Numerical computation methods to include nonlocal effects in plasmonic nanostructures’ electromagnetic response are discussed, and applications of plasmonics to a few other fields are elaborated. First, a computation scheme is proposed to extend conventional finite-difference time-domain (FDTD) methods to nonlocal domain. An effective film whose response is derived from Feibelman's d-function formalism is to replace the highly non-uniform metal surfaces in simulations. It successfully produces numerical results of plasmonic resonance shift and field enhancement which agrees with the experimental data to first order. This scheme is still classical, thus very fast compared to the other first principle quantum methods such as density functional theory. Then electron's scattering rate in an effective medium with plasmonic nanostructures embedded-in, in random phase approximation, is developed, with the wavenumber dependence in the medium’s response accounted. Utilizing this calculation scheme of electron’s scattering rate, further specific applications are following. We show by simulation of the plasmonic nanostructures and calculation of the electron scattering rates that hot-electron plasmon-protection (HELPP) effects can protect the extra energy of hot electrons from being dissipated as heat. This can be a prototype of the 3rd generation solar cells. In another application, we investigate the electron polar-optical-phonon (POP) scattering in heavily-doped semiconductors when plasmonic nanostructures are embedded-in. We show that electron-POP scattering can be significantly suppressed compared to that of bulk semiconductors. In the third application, we propose the plasmonic multiple exciton generation (PMEG) scheme, with simulations and calculations, showing that the efficiency of multiple exciton generation in conventional semiconductors could be enhanced significantly with proper designed plasmonic nanostructures embedded-in or attached-adjacent. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

The kinetic effects in an inductively coupled plasma (ICP) due to thermal motion of particles modified by self-consistent magnetic fields are studied by using a particle-in-cell (PIC) simulation. In the low pressure, low frequency regime, electron mean free paths are large relative to device size and the trajectories are strongly curved by the induced radio frequency (RF) magnetic field. This causes problems for linear theories, which ignore the influence of the magnetic field on the particles, and are therefore unable to recover effects accumulated along each nonlinear path.<p>The tools to perform high-performance parallel PIC simulations of inductively coupled plasmas were developed to allow rapid scanning of a broad range of the input parameters, such as wave amplitude, frequency, and plasma temperature. Different behavioural regimes are identified by observing the resultant variations in the skin depth, surface impedance, and ponderomotive force (PMF). At low electron-neutral collision rates, these are shown to include the local collisionless regime, the anomalous skin effect regime, and the nonlinear regime.<p>The local collisionless regime occurs at high driving frequencies and is characterized by plasma behaviour independent of both the driving frequency and amplitude: a short skin depth, low energy absorption, and strong PMF. The anomalous skin effect regime occurs at low frequencies and low amplitudes: the plasma varies with driving frequency, but not driving amplitude, the skin depth increases with frequency, the plasma is much more absorptive in the anomalous regime than in the local regime, and the PMF increases with frequency. The nonlinear regime occurs at low frequencies and high amplitudes: the plasma varies with driving amplitude, but not frequency, the skin depth decreases with amplitude, there is low energy absorption, and the PMF increases with wave amplitude.<p>The simulation runs in four modes: linear collisionless, linear collisional, nonlinear collisionless, and nonlinear collisional. The linear modes, in which the particles ignore the magnetic field, are used to validate the results against theory, while the nonlinear modes are used to test actual plasma behaviour. In linear collisionless mode, the plasma was found to exhibit only the local collisionless and anomalous skin effect regimes, as expected by theories. In nonlinear collisionless mode, the plasma exhibits the nonlinear regime in addition to the regimes found in linear mode. Finally, the nonlinear regime disappears in nonlinear collisionless mode because the curved paths caused by the magnetic field are disrupted by collisions.<p>Finally, the regime boundaries are investigated as a function of temperature. Since the plasma properties vary continuously, a boundary exists where two regimes share the same characteristics. From linear theories, it is known that the division between the local collisionless and anomalous skin effect regimes moves to higher frequencies as the plasma temperature is increased. When nonlinear fields are present, this still occurs, but in conjunction with the boundary between the local collisionless and nonlinear regimes moving to higher wave amplitudes. Temperature also effects the boundary between the anomalous skin effect and nonlinear regimes, causing the minimum frequency of the anomalous skin effect regime to be reduced at low wave amplitudes.

The kinetic effects in an inductively coupled plasma (ICP) due to thermal motion of particles modified by self-consistent magnetic fields are studied by using a particle-in-cell (PIC) simulation. In the low pressure, low frequency regime, electron mean free paths are large relative to device size and the trajectories are strongly curved by the induced radio frequency (RF) magnetic field. This causes problems for linear theories, which ignore the influence of the magnetic field on the particles, and are therefore unable to recover effects accumulated along each nonlinear path.<p>The tools to perform high-performance parallel PIC simulations of inductively coupled plasmas were developed to allow rapid scanning of a broad range of the input parameters, such as wave amplitude, frequency, and plasma temperature. Different behavioural regimes are identified by observing the resultant variations in the skin depth, surface impedance, and ponderomotive force (PMF). At low electron-neutral collision rates, these are shown to include the local collisionless regime, the anomalous skin effect regime, and the nonlinear regime.<p>The local collisionless regime occurs at high driving frequencies and is characterized by plasma behaviour independent of both the driving frequency and amplitude: a short skin depth, low energy absorption, and strong PMF. The anomalous skin effect regime occurs at low frequencies and low amplitudes: the plasma varies with driving frequency, but not driving amplitude, the skin depth increases with frequency, the plasma is much more absorptive in the anomalous regime than in the local regime, and the PMF increases with frequency. The nonlinear regime occurs at low frequencies and high amplitudes: the plasma varies with driving amplitude, but not frequency, the skin depth decreases with amplitude, there is low energy absorption, and the PMF increases with wave amplitude.<p>The simulation runs in four modes: linear collisionless, linear collisional, nonlinear collisionless, and nonlinear collisional. The linear modes, in which the particles ignore the magnetic field, are used to validate the results against theory, while the nonlinear modes are used to test actual plasma behaviour. In linear collisionless mode, the plasma was found to exhibit only the local collisionless and anomalous skin effect regimes, as expected by theories. In nonlinear collisionless mode, the plasma exhibits the nonlinear regime in addition to the regimes found in linear mode. Finally, the nonlinear regime disappears in nonlinear collisionless mode because the curved paths caused by the magnetic field are disrupted by collisions.<p>Finally, the regime boundaries are investigated as a function of temperature. Since the plasma properties vary continuously, a boundary exists where two regimes share the same characteristics. From linear theories, it is known that the division between the local collisionless and anomalous skin effect regimes moves to higher frequencies as the plasma temperature is increased. When nonlinear fields are present, this still occurs, but in conjunction with the boundary between the local collisionless and nonlinear regimes moving to higher wave amplitudes. Temperature also effects the boundary between the anomalous skin effect and nonlinear regimes, causing the minimum frequency of the anomalous skin effect regime to be reduced at low wave amplitudes.

In modern low pressure plasma discharges, the electron mean free path often exceeds the device dimensions. Under such conditions the electron velocity distribution function may significantly deviate from Maxwellian, which strongly affects the discharge properties. The description of such plasmas has to be kinetic and often requires the use of numerical methods. This thesis presents the study of kinetic effects in inductively coupled plasmas and Hall thrusters carried out by means of particle-in-cell simulations. The important result and the essential part of the research is the development of particle-in-cell codes. <p>An advective electromagnetic 1d3v particle-in-cell code is developed for modelling the inductively coupled plasmas. An electrostatic direct implicit 1d3v particle-in-cell code EDIPIC is developed for plane geometry simulations of Hall thruster plasmas. The EDIPIC code includes several physical effects important for Hall thrusters: collisions with neutral atoms, turbulence, and secondary electron emission. In addition, the narrow sheath regions crucial for plasma-wall interaction are resolved in simulations. The code is parallelized to achieve fast run times. <p>Inductively coupled plasmas sustained by the external RF electromagnetic field are widely used in material processing reactors and electrodeless lighting sources. In a low pressure inductive discharge, the collisionless electron motion strongly affects the absorption of the external electromagnetic waves and, via the ponderomotive force, the density profile. The linear theory of the anomalous skin effect based on the linear electron trajectories predicts a strong decrease of the ponderomotive force for warm plasmas. Particle-in-cell simulations show that the nonlinear modification of electron trajectories by the RF magnetic field partially compensates the effects of electron thermal motion. As a result, the ponderomotive force in warm collisionless plasmas is stronger than predicted by linear kinetic theory. <p>Hall thrusters, where plasma is maintained by the DC electric field crossed with the stationary magnetic field, are efficient low-thrust devices for spacecraft propulsion. The energy exchange between the plasma and the wall in Hall thrusters is enhanced by the secondary electron emission, which strongly affects electron temperature and, subsequently, thruster operation. Particle-in-cell simulations show that the effect of secondary electron emission on electron cooling in Hall thrusters is quite different from predictions of previous fluid studies. Collisionless electron motion results in a strongly anisotropic, nonmonotonic electron velocity distribution function, which is depleted in the loss cone, subsequently reducing the electron wall losses compared to Maxwellian plasmas. Secondary electrons form two beams propagating between the walls of a thruster channel in opposite radial directions. The secondary electron beams acquire additional energy in the crossed external electric and magnetic fields. The energy increment depends on both the field magnitudes and the electron flight time between the walls. <p>A new model of secondary electron emission in a bounded plasma slab, allowing for emission due to the counter-propagating secondary electron beams, is developed. It is shown that in bounded plasmas the average energy of plasma bulk electrons is far less important for the space charge saturation of the sheath than it is in purely Maxwellian plasmas. A new regime with relaxation oscillations of the sheath has been identified in simulations. Recent experimental studies of Hall thrusters indirectly support the simulation results with respect to the electron temperature saturation and the channel width effect on the thruster discharge.

In modern low pressure plasma discharges, the electron mean free path often exceeds the device dimensions. Under such conditions the electron velocity distribution function may significantly deviate from Maxwellian, which strongly affects the discharge properties. The description of such plasmas has to be kinetic and often requires the use of numerical methods. This thesis presents the study of kinetic effects in inductively coupled plasmas and Hall thrusters carried out by means of particle-in-cell simulations. The important result and the essential part of the research is the development of particle-in-cell codes. <p>An advective electromagnetic 1d3v particle-in-cell code is developed for modelling the inductively coupled plasmas. An electrostatic direct implicit 1d3v particle-in-cell code EDIPIC is developed for plane geometry simulations of Hall thruster plasmas. The EDIPIC code includes several physical effects important for Hall thrusters: collisions with neutral atoms, turbulence, and secondary electron emission. In addition, the narrow sheath regions crucial for plasma-wall interaction are resolved in simulations. The code is parallelized to achieve fast run times. <p>Inductively coupled plasmas sustained by the external RF electromagnetic field are widely used in material processing reactors and electrodeless lighting sources. In a low pressure inductive discharge, the collisionless electron motion strongly affects the absorption of the external electromagnetic waves and, via the ponderomotive force, the density profile. The linear theory of the anomalous skin effect based on the linear electron trajectories predicts a strong decrease of the ponderomotive force for warm plasmas. Particle-in-cell simulations show that the nonlinear modification of electron trajectories by the RF magnetic field partially compensates the effects of electron thermal motion. As a result, the ponderomotive force in warm collisionless plasmas is stronger than predicted by linear kinetic theory. <p>Hall thrusters, where plasma is maintained by the DC electric field crossed with the stationary magnetic field, are efficient low-thrust devices for spacecraft propulsion. The energy exchange between the plasma and the wall in Hall thrusters is enhanced by the secondary electron emission, which strongly affects electron temperature and, subsequently, thruster operation. Particle-in-cell simulations show that the effect of secondary electron emission on electron cooling in Hall thrusters is quite different from predictions of previous fluid studies. Collisionless electron motion results in a strongly anisotropic, nonmonotonic electron velocity distribution function, which is depleted in the loss cone, subsequently reducing the electron wall losses compared to Maxwellian plasmas. Secondary electrons form two beams propagating between the walls of a thruster channel in opposite radial directions. The secondary electron beams acquire additional energy in the crossed external electric and magnetic fields. The energy increment depends on both the field magnitudes and the electron flight time between the walls. <p>A new model of secondary electron emission in a bounded plasma slab, allowing for emission due to the counter-propagating secondary electron beams, is developed. It is shown that in bounded plasmas the average energy of plasma bulk electrons is far less important for the space charge saturation of the sheath than it is in purely Maxwellian plasmas. A new regime with relaxation oscillations of the sheath has been identified in simulations. Recent experimental studies of Hall thrusters indirectly support the simulation results with respect to the electron temperature saturation and the channel width effect on the thruster discharge.

La thèse concerne les modèles de l'écoulement dans les milieux fracturés multiéchelles qui prouvent l'effet de mémoire à chaque échelle. Les processus analysés dans ces milieux est auto-similaire. Nous avons analysé l'équation de diffusion à toutes les échelles et appliqué la méthode d'homogénéisation asymptotique avec l'objectif de construire le modèle macroscopique moyenne sur toutes les échelles d'hétérogénéité. Un système fermé des équations récursives pour les noyaux d’échange effectif est obtenu. La solution analytico-numérique de ce système est développé. Nous avons montré une convergence des résultats obtenus pour le nombre des différentes échelles d'un comportement limite stable. Le problème limite pour les noyaux est obtenus pour un nombre relativement élevé d'échelles. En plus, nous avons analysé l'écoulement dans une immergée dans le réservoir poreux à différents nombres de Reynolds. Les équations de Navier-Stokes sont résolu par la méthode asymptotique à deux échelles avec l'objectif d'obtenir l'équation de la moyenne sur l'ouverture de fracture en présence d'afflux à travers les limites et pour la géométrie irrégulière des murs. / The thesis concerns the models of flow in multiscale fractured media which prove the memory effect at each scale. The analyzed process in these media is self-similar. The necessary and sufficient condition of self-similarity has been proposed so that it is possible to analyze the behavior of media for any number of scales. We analyzed the diffusion equation at each scale and applied the asymptotic homogenization method with the objective to construct the macroscopic model averaged over all scales of heterogeneity. A system of closed recurrent equations for the effective exchange kernels was obtained. The procedure of analytico-numerical solution of this system was developed. We showed a convergence of the results obtained for various numbers of scales to a stable limit behavior. The limit problem for the effective kernels from the recurrent equations obtained for a relatively large number of scales. In addition we analyzed the flow in a single fracture and circular channel immersed in porous reservoir at various Reynolds numbers. The Navier-Stokes equations was solved by the method of two-scale asymptotic method with the objective to obtain the flow equation averaged over the fracture aperture in the presence of inflow through the limits and irregular geometry of walls.