Korteweg-de Vries Equation and Thomas-Fermi Distribution

• Ano de defesa: 2022
• Autor(a) principal: Santos, Kaio Nikolas Mendes Menezes dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Korteweg-de Vries; Solitons; Sólitons; Thomas-Fermi
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/43/43134/tde-10102022-160421/

Plasma physics is generally associated with the treatment of regimes characterized by high temperature and low densities, where quantum mechanical effects do not have a significant impact. Recent studies, however, show that some systems can be studied from the perspective of dense plasmas, where the distance between the species is of the same order as the thermal de Broglie wavelength. In this way, the temperature associated with the thermal motion of the particles is lower than the Fermi temperature, i. e., the system is degenerate, and classical statistics must give way to the Pauli Exclusion principle. In this work, we construct a semiclassical fluid model from the consideration of a gas formed by degenerate electrons and singularly ionized ions, with the Thomas-Fermi distribution replacing the Maxwell-Boltzmann one in the description of the electrons. Thus, we discuss the possibility of the nonlinear oscillations evolution in the plasma to be described, through a reductive perturbation method, by the Korteweg-de Vries equation. Using the calculus of variations, it was possible to find the natural scales of the problem, as well as define the critical frame in which the nonlinear solution structures propagate. We also investigate the ion thermal effects and the consequences of applying a constant magnetic field to the system, in addition to looking at the solitonic pulses response to the introduction of these new parameters in the theory. We carefully show that the system is sensitive to normalization, allowing us to evaluate the results by introducing a control parameter. In general, we verified that it is possible to construct the KdV equation via a modified reductive perturbation method, with the inclusion of the control parameter, we characterized the subsonic reference frame (M = 1/ \\sqrt 3) as the appropriate one to describe the propagation of solitons, which validates the perturbative description. We computed the effects of the temperature and magnetic field on the nonlinear and dispersive parameters, and the consequent modifications in the shape of the waves. Finally, having assumed the cold ions regime as the lower limit for all approaches carried out, we made use of the normalization control parameter (\\lambda_0) to switch between expressions with different scales.