Consideramos um modelo hamiltoniano do movimento eletrostático de deriva para investigar o trasnporte caótico de partículas na borda de plasmas confinados em Tokamaks. Este modelo leva em conta a turbulência eletrostática de deriva, responsável pelo transporte anômalo. O modelo Hamiltoniano provê as equações de movimento, que são dependentes de uma função para o potencial elétrico. Esta função é caracterizada por um potencial de equilíbrio mais um termo correspondente às ondas de deriva. Assumimos três diferentes perfis radiais para o campo elétrico radial de equilíbrio: um linear e outros dois não-monotônicos com extremos suaves. Para estes perfis, mostramos que o modelo pode ser reduzido a três mapas simpléticos bidimensionais e não integráveis: o mapa padrão, o mapa padrão não twist e um mapa modelo não twist introduzido neste trabalho. O mapa padrão não twist e o mapa modelo violam a condição twist, fundamental para os teoremas KAM e de Birkhoff. Para estes mapas não twist, estudaremos numericamente barreiras de transporte criadas próximas às curvas shearless. Mostramos que, para o mapa modelo, a barreira de transporte é robusta, isto é, persiste em um amplo intervalo de variação de um de seus parâmetros. Dentro da região da barreira, descrevemos o nascimento de cadeias de ilhas com períodos par e ímpar devido à variação do parâmetro de controle. Analisamos estes dois cenários calculando os números de rotação dentro da barreira e identificando as bifurcações que criam as ilhas. Finalmente, conjecturamos que todas as ilhas dentro da região da barreira são criadas por estes dois cenários. Além disso, se o número de rotação da curva shearless atinge um número racional, as cadeias de ilhas são criadas de acordo com os cenários descritos. / We consider a hamiltonian model of the electrostatic drift motion to investigate chaotic particle transport in the Tokamak plasma edge. This model takes into account the electrostatic drift turbulence, which is responsible for the anomalous transport. The Hamiltonian model provides the basic equations of motion, which are dependent on the form of an electric potential function. This function is characterized by the equilibrium potential and the term corresponding to the drift waves. We assume three diferent radial profiles for the equilibrium radial electric field: one linear and the other two non-monotonic with a smooth extremum. For these profiles, we show that the model can be reduced to three symplectic maps: the standard map, the nontwist standard map, and a nontwist model map introduced in this work. The nontwist standard map and the model map violate the twist condition, a property of fundamental importance for the applicability of the KAM and Birkhoff theorems. For these nontwist maps, we study numerically the transport barriers created around their shearless curves. We show for the model map that the transport barrier is robust,i.e., remains for a wide range of one of its parameters. Inside the barrier region, we describe the birth of island chains with even or odd periods due to the control parameter variation. We analyse these two scenarios by calculating the winding numbers inside the barrier region and identifying the bifurcations that create the islands. Finally, we conjecture that all the island chains inside the barrier are created by these two scenarios. Moreover, if the winding number of the shearless curve reachs a rational number, the island chains are created according to the described scenarios.

The use of electric propulsion for spacecraft primary propulsion, attitude control and station-keeping is ever-increasing as the technology matures and is qualified for flight. In addition, alternative propellants are under investigation, which have the potential to offer systems-level benefits that can enable particular classes of missions. Condensable propellants, particularly iodine, have the potential to significantly reduce the propellant storage system volume and mass. Some of the most widely used electric thrusters are electrostatic thrusters, which require a thermionic hollow cathode electron source to ionize the propellant for the main discharge and for beam neutralization. Failure of the hollow cathode, which often needs to operate for thousands of hours, is one of the main life-limiting factors of an electrostatic propulsion system. Common failure modes for hollow cathodes include poisoning or evaporation of the thermionic emitter material and erosion of electrodes due to sputtering. The mechanism responsible for the high energy ion production resulting in sputtering is not well understood, nor is the compatibility of traditional thermionic hollow cathodes with alternative propellants such as iodine. This work uses both an emissive probe and Langmuir probe to characterize the near-plume of several hollow cathodes operating on both xenon and iodine by measuring the plasma potential, plasma density, electron temperature and electron energy distribution function (EEDF). Using the EEDF the reaction rate coefficients for relevant collisional processes are calculated. A low current (< 5 A discharge current) hollow cathode with two different hexaboride emitters, lanthanum hexaboride (LaB6) and cerium hexaboride (CeB6), was operated on xenon propellant. The plasma potential, plasma density, electron temperature, EEDF and reaction rate coefficients were measured for both hexaboride emitter materials at a single cathode orifice diameter. The time-resolved plasma potential measurements showed low frequency oscillations (<100 kHz) of the plasma potential at low cathode flow rates (<4 SCCM) and spot mode operation between approximately 5 SCCM and 7 SCCM. The CeB6 and LaB6 emitters behave similarly in terms of discharge power (keeper and anode voltage) and plasma potential, based on results from a cathode with a 0.020�-diameter. Both emitters show almost identical operating conditions corresponding to the spot mode regime, reaction rates, as well as mean and RMS plasma potentials for the 0.020� orifice diameter at a flow rate of 6 SCCM and the same discharge current. The near-keeper region plasma was also characterized for several cathode orifice diameters using the CeB6 emitter over a range of propellant flow rates. The spot-plume mode transition appears to occur at lower flow rates as orifice size is increased, but has a minimum flow rate for stable operation. For two orifice diameters, the EEDF was measured in the near-plume region and reaction rate coefficients calculated for several electron- driven collisional processes. For the cathode with the larger orifice diameter (0.040�), the EEDFs show higher electron temperatures and drift velocities. The data for these cathodes also show lower reaction rate coefficients for specific electron transitions and ionization. To investigate the compatibility of a traditional thermionic emitter with iodine propellant, a low-power barium oxide (BaO) cathode was operated on xenon and iodine propellants. This required the construction and demonstration of a low flow rate iodine feed system. The cathode operating conditions are reported for both propellants. The emitter surface was inspected using a scanning electron microscope after various exposures to xenon and iodine propellants. The results of the inspection of the emitter surface are presented. Another low current (< 5 A), BaO hollow cathode was operated on xenon and iodine propellants. Its discharge current and voltage, and plume properties are reported for xenon and iodine with the cathode at similar operating conditions for each. The overall performance of the BaO cathode on iodine was comparable to xenon. The cathode operating on iodine required slightly higher power for ignition and discharge maintenance compared to xenon, as evident by the higher keeper and anode potentials. Plasma properties in the near- plume region were measured using an emissive probe and single Langmuir probe. For both propellants, the plasma density, electron energy distribution function (EEDF), electron temperature, select reaction rate coefficients and time-resolved plasma potentials are reported. For both propellants the cathode operated the same keeper (0.25 A) and discharge current (3.1 A), but the keeper and anode potentials were higher with iodine; 27 V and 51 V for xenon, and 30 V and 65 V for iodine, respectively. For xenon, the mean electron energy and electron temperature were 7.5 eV and 0.7 eV, with bulk drift energy of 6.6 eV. For iodine, the mean electron energy and electron temperature were 6.3 eV and 1.3 eV, with a bulk drift energy of 4.2 eV. A literature review of relevant collisional processes and associated cross sections for an iodine plasma is also presented.

The determination of plasma equilibrium profiles is necessary to evaluate the properties of the confinement and to investigate perturbation effects. Optical diagnostics can be used to determine some of these profiles. However, these diagnostics measure all emitted radiation at a solid angle that illuminate each diagnostic channel through a slit. Therefore, the real measured quantity is the emissivity integrated along the line-of-sight and some unfolding procedure, like Abels inversion, is commonly used to recover the emissivity profile. In TCABR tokamak, at the Physics Institute of the University of São Paulo, a 24-channel bolometer and a 20-channel soft X-ray optical diagnostics are used to measure the plasma emissivity in wavelength range from 1.0 to 1000 nm, depending on the used filters. In this work, a numerical simulation is used to compute the signal measured by the diagnostics for a given emissivity profile, allowing direct comparison with the experimental data and avoiding the use of the Abel\'s inversion directly and the numerical difficulties associated with unfolding procedures. By considering TCABR tokamak geometry, spatial coordinates can be related to the normalized linear coordinates of the plasma by imposing a plasma emissivity model that depends on some free parameters, allowing the emissivity resulting in each point can be calculated. Thus, the luminosity of each channel is calculated by the integral of the emissivity modeled in each line-of-sight (Radon Transformation). Emissivity model free parameters are determined by fitting calculated luminosity to measured one. We considered three types of emissivity profiles: a parabolic model in law of power, a Gaussian model and a model based on Bessel functions. We observed that the parabolic profile fits well the bolometer data, while the Gaussian profile is adequate to describe the data obtained with the soft X-ray detector. / A determinação dos perfis de equilíbrio do plasma é necessária para avaliar as propriedades do confinamento e para investigar os efeitos de perturbações. Diagnósticos ópticos podem ser usados para determinar alguns desses perfis. No entanto, esses diagnósticos medem toda a radiação luminosa emitida em um ângulo sólido que ilumina cada canal do detector através de uma fenda. Assim, a verdadeira grandeza física medida é a emissividade integrada ao longo da linha de visada. Com isso, algum procedimento de deconvolução, como a inversão de Abel, se faz necessário para obter o perfil de emissividade. No tokamak TCABR do Instituto de Física da USP, um bolômetro de 24 canais e um detector de raios-X moles de 20 canais são utilizados para medir a emissividade do plasma no intervalo de comprimento de onda de 1 a 1.000 nm, dependendo dos filtros utilizados. Neste trabalho, uma simulação numérica é usada para calcular o sinal medido pelos diagnósticos para um dado perfil de emissividade, possibilitando a comparação direta com os dados experimentais, evitando a realização da inversão de Abel e os problemas numéricos associados aos procedimentos de deconvolução. Pela consideração da geometria do tokamak TCABR, as coordenadas espaciais podem ser relacionadas com as coordenadas lineares normalizadas do plasma por meio da imposição de um modelo de emissividade para o plasma que dependa de alguns parâmetros livres, permitindo que a emissividade resultante em cada ponto possa ser calculada. Assim, a luminosidade de cada canal é calculada pela integral da emissividade modelada em cada linha de visada (Transformada de Radon). Os parâmetros livres dos perfis de emissividade são determinados ajustando-se as luminosidades calculadas em termos das luminosidades medidas. Nós consideramos três modelos de perfis de emissividade: um modelo parabólico em lei de potência, um modelo gaussiano e um modelo baseado em funções de Bessel. Observamos que o perfil parabólico ajusta-se bem aos dados do bolômetro, ao passo que o perfil gaussiano é adequado para descrever os dados obtidos com o detector de raios-X moles.

Ao longo dos últimos anos é notável, de forma cada vez mais evidente, a necessidade de uma nova fonte de energia para humanidade. Uma promissora opção é através de Fusão Nuclear, onde o plasma produzido no reator pode ter energia convertida em elétrica. Portanto, conhecer características desse plasma é de suma importância para controlá-lo e entendê-lo de forma desejável. Uma das opções de diagnósticos é o chamado Espalhamento Thomson. Este é considerado o método mais confiável na determinação de importantes parâmetros do plasma, como temperatura e densidade eletrônica, podendo ainda ajudar no estudo e explicação de vários mecanismos internos. A grande vantagem reside no fato de se consistir numa medição direta e não perturbativa. Porém trata-se de um diagnóstico cuja instalação e execução é reconhecidamente complexa, limitando-o apenas a poucos laboratórios da área de fusão pelo mundo. Entre as principais dificuldades, pode-se destacar o fato de que o sinal espalhado é muito pequeno, necessitando assim de um grande aumento da potência incidente. Além disso, as condições físicas externas podem ocasionar vibrações mecânicas que, eliminá-las ou minimizá-las ao máximo, constitui um grande desafio, levando em conta a óptica muito sensível e micrometricamente precisa envolvida no sistema. O presente trabalho descreve todo processo de instalação e operação do diagnóstico de Espalhamento Thomson no tokamak TCABR e, através deste diagnóstico, trabalhamos na obtenção de resultados da temperatura eletrônica, para finalmente ser possível calcular a densidade eletrônica do plasma. / Over the last few years is remarkable, so increasingly evident the need for a new source of energy for mankind. One promising option is through nuclear fusion, where the plasma produced in the reactor can be converted into electrical energy. Therefore, knowing the characteristics of this plasma is very important to control it and understand it so desirable. One of the diagnostic options is called Thomson scattering . This is considered the most reliable method for the determination of important plasma parameters such as temperature and electron density, and may also help in the study and explanation of various internal mechanisms . The great advantage lies in the fact that they consist of a direct measurement and nonperturbative . But it is a diagnosis whose installation and execution is admittedly complex, limiting it only a few laboratories in the field of fusion for the world. Among the main difficulties, we can highlight the fact that the scattered signal is very small, thus requiring a large increase of the incident power. Moreover, the external physical conditions can cause mechanical vibrations that eliminate or minimize them as much as possible, is a great challenge, considering the optical micrometrically very sensitive and needs involved in the system. This work describes the entire process of installation and operation of Thomson scattering diagnostic in tokamak TCABR and through this diagnosis, we work on results of electron temperature, to finally be able to calculate the electron density of the plasma.

Neste trabalho foi feito um estudo do perfil tomográfico da emissão da linha do átomo de hidrogênio, H-alfa (?=656,28 nm) no plasma do TCABR, um tokamak de porte médio em operação no Laboratório de Física de Plasmas do Instituto de Física da Universidade de São Paulo. Nosso trabalho centrou-se no estudo dos efeitos da introdução de um eletrodo polarizado na borda do plasma no tokamak TCABR. O eletrodo pode ser introduzido até 1,5 cm para dentro da coluna do plasma, sem causar disrupturas para polarização positiva de 0 até +350V, e situado no plano equatorial do tokamak. Perfis tomográficos de H-alfa com e sem polarização foram medidos. A comparação dos perfis mostra um aumento da densidade de linha na posição central, quando a emissividade H-alfa diminui. A análise dos perfis tomográficos de H-alfa, tempo de confinamento das partículas e também do estudo de reciclagem das partículas neutras, indica que o plasma entra no regime de alto confinamento (modo-H). Cálculos de turbulência e de transporte na borda do plasma (SOL), feitos medindo o potencial flutuante e a corrente de saturação de íons, mostram uma diminuição forte no espectro de potência e de transporte. Também foram feitos estudos do novo regime de descargas com elétrons fugitivos (\"runaway electron\"), descoberto no tokamak TCABR. As características distintivas deste regime são um plasma de baixa temperatura fracamente ionizado, destacado do limitador devido a processos de recombinação, e instabilidade de relaxação com fortes picos de emissão H-alfa correlacionados com instabilidade dente de serra da densidade eletrônica de linha. No presente trabalho fazemos a descrição das condições experimentais para a geração destas descargas. A produção dos elétrons fugitivos é analisada; mostrando que a geração de elétrons fugitivos somente pode ser explicada pelo mecanismo de avalanche. A confirmação de baixa temperatura do plasma é obtida de uma análise do perfil tomográfico da emissão H-alfa. Esta emissão não pode ser explicada por excitação de elétrons no plasma. A recombinação, de outro lado, dá uma explicação plausível para a dependência temporal da emissão, em particular para alta densidade de partículas neutras. / A study of the tomography profile of the emission of the line of Hydrogen, atomic H-alpha line (?=656.28 nm), was carried out in TCABR, a medium-size tokamak in operation at the Laboratory of Plasma Physics of the Institute of Physics of the University of São Paulo. Our work focuses on the study of the effects of due to the introduction of a biased electrode in the plasma edge of the TCABR tokamak. The electrode could be introduced up to 1.5 cm inside the plasma, without plasma disruptions for positive voltages from 0 to +350V, and was located on the equatorial plane of the plasma column. Tomography profiles of H-alpha with and without bias were measured. Comparison of the profiles shows an increase of the central line-averaged density, while the emissivity of the line H-alpha decreases. The analysis of the tomography profiles of H-alpha, time of confinement of particles and also the study of recycling of the neutral particles, indicate that the confined plasma enters the H-mode regime. Calculations of turbulence and transport at the Scrape-Off-Layer, using measured floating potentials and ion saturation currents, show a strong decrease in the power spectra and transport. The H-alpha tomography was also employed to study the new regime of runaway discharges that has been discovered in the TCABR tokamak. The distinctive features of this regime are weakly ionized low-temperature plasma detached from the limiter due to the recombination process, and a relaxation instability with strong spikes of H-alpha emission correlated with sawtooth relaxation of the line density. In the present thesis we report experimental data on conditions for generation of these discharges. The runaway electron production is analyzed; show that generation of runaway electrons can only be explained by the runaway avalanche mechanism. The confirmation of low plasma temperature is a obtained from an analysis of the tomography profile of H-alpha emission. This emission cannot be explained by excitation by plasma electrons. Recombination, on the other hand, gives a rather plausible explanation for the time dependency of the emission, in particular at high neutral densities.

abstract: Chiral symmetry and its anomalous and spontaneous breaking play an important role in particle physics, where it explains the origin of pion and hadron mass hierarchy among other things. Despite its microscopic origin chirality may also lead to observable effects in macroscopic physical systems -- relativistic plasmas made of chiral (spin-$\frac{1}{2}$) particles. Such plasmas are called \textit{chiral}. The effects include non-dissipative currents in external fields that could be present even in quasi-equilibrium, such as the chiral magnetic (CME) and separation (CSE) effects, as well as a number of inherently chiral collective modes called the chiral magnetic (CMW) and vortical (CVW) waves. Applications of chiral plasmas are truly interdisciplinary, ranging from hot plasma filling the early Universe, to dense matter in neutron stars, to electronic band structures in Dirac and Weyl semimetals, to quark-gluon plasma produced in heavy-ion collisions. The main focus of this dissertation is a search for traces of chiral physics in the spectrum of collective modes in chiral plasmas. I start from relativistic chiral kinetic theory and derive first- and second-order chiral hydrodynamics. Then I establish key features of an equilibrium state that describes many physical chiral systems and use it to find the full spectrum of collective modes in high-temperature and high-density cases. Finally, I consider in detail the fate of the two inherently chiral waves, namely the CMW and the CVW, and determine their detection prospects. The main results of this dissertation are the formulation of a fully covariant dissipative chiral hydrodynamics and the calculation of the spectrum of collective modes in chiral plasmas. It is found that the dissipative effects and dynamical electromagnetism play an important role in most cases. In particular, it is found that both the CMW and the CVW are heavily damped by the usual Ohmic dissipation in charged plasmas and the diffusion effects in neutral plasmas. These findings prompt a search for new physical observables in heavy-ion collisions, as well as a revision of potential applications of chiral theories in cosmology and solid-state physics. / Dissertation/Thesis / Doctoral Dissertation Physics 2019

This thesis demonstrates a measurement of a plasma fluctuation velocity-space cross-correlation matrix using laser induced fluorescence. The plasma fluctuation eigenmode structure on the ion velocity distribution function can be empirically determined through singular value decomposition from this measurement. This decomposition also gives the relative strengths of the modes as a function of frequency. Symmetry properties of the matrix quantify systematic error. The relation between the eigenmodes and plasma kinetic fluctuation modes is explored. A generalized wave admittance is calculated for these eigenmodes. Since the measurement is a localized technique, it may be applied to plasmas in which a single point measurement is possible, multipoint measurements may be difficult, and a velocity sensitive measurement technique is available.

Inertial Alfvén waves occur in plasmas where the Alfvén speed is greater than the electron thermal speed and the scale of wave field structure across the background magnetic field is comparable to the electron skin depth. Such waves have an electric field aligned with the background magnetic field that can accelerate electrons. It is likely that electrons are accelerated by inertial Alfvén waves in the auroral magnetosphere and contribute to the generation of auroras. While rocket and satellite measurements show a high level of coincidence between inertial Alfvén waves and auroral activity, definitive measurements of electrons being accelerated by inertial Alfvén waves are lacking. Continued uncertainty stems from the difficulty of making a conclusive interpretation of measurements from spacecraft flying through a complex and transient process. A laboratory experiment can avoid some of the ambiguity contained in spacecraft measurements. Experiments have been performed in the Large Plasma Device (LAPD) at UCLA. Inertial Alfvén waves were produced while simultaneously measuring the suprathermal tails of the electron distribution function. Measurements of the distribution function use resonant absorption of whistler mode waves. During a burst of inertial Alfvén waves, the measured portion of the distribution function oscillates at the Alfvén wave frequency. The phase space response of the electrons is well-described by a linear solution to the Boltzmann equation. Experiments have been repeated using electrostatic and inductive Alfvén wave antennas. The oscillation of the distribution function is described by a purely Alfvénic model when the Alfvén wave is produced by the inductive antenna. However, when the electrostatic antenna is used, measured oscillations of the distribution function are described by a model combining Alfvénic and non-Alfvénic effects. Indications of a nonlinear interaction between electrons and inertial Alfvén waves are present in recent data.

A numerical model was developed to understand the time evolution of a wake structure around a CubeSat moving in a plasma with transonic speed. A cubeSat operates in the F2 layer of ionosphere with an altitude of 300 − 600 Km. The average plasma density varies between 10−6cm−3 − 10−9cm−3 and the temperature of ions and electrons is found between 0.1−0.2 eV. The study of a wake structure can provide insights for its effects on the measurements obtained from space instruments. The CubeSat is modeled to have a metal surface, which is a realistic assumption, with a negative electric potential. To solve the equations of plasma, the numerical difference equations were obtained by discretizing the fluid equations of the plasma along with nonlinear Poisson’s equation. The electrons were assumed to follow the Boltzmann’s relation and the dynamics of ions was followed using the fluid equations. The initial and boundary conditions for the evolution of the structure are discussed. The computation was compared to the analytical solution for a 1D problem before being applied to the 2D model. There was a good agreement between the numerical and analytical solution. In the 2D simulation, we observe the formation of plasma wake structure around the CubeSat. The plasma wake structure consists of rarefaction region where ion density and ion velocity decreases compared to the initial density and velocity.

Le formalisme de la transformation de Lie est appliqué à la dynamique des particules chargées dans la topologie magnétique d'un tokamak, afin de construire un opérateur de type Fokker-Planck pour les collisions coulombiennes utilisable pour la génération de courant. Cette approche permet de réduire le problème à trois dimensions (deux dans l'espace des vitesses, une dans l'espace des configurations) tout en gardant la richesse des effets croisés entre les es- paces résultant de la conservation du moment canonique toroïdal (axisymétrie). Cette approche cinétique permet de d'écrire des phénomènes physiques liés à la présence de forts gradients de pression dans des plasmas de forme quelconque, comme le courant " bootstrap " dont le rôle sera primordial pour le futur réacteur ITER. Le choix des coordonnées et la méthode utilisée sont particulièrement adaptés à la résolution numérique de l'équation de dérive cinétique permettant de calculer la distribution des particules, celle-ci pouvant présenter un fort écart à la maxwellienne sous l'effet d'un champ électrique (statique ou produit par une onde radio- fréquence). Les travaux dédiés principalement à la physique des plasmas de tokamak ont été étendus à ceux des plasmas de l'espace relevant d'une configuration magnétique dipolaire.