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Doctoral Thesis
DOI
10.11606/T.43.1991.tde-04092012-113407
Document
Author
Full name
Hisataki Shigueoka
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1991
Supervisor
Committee
Caldas, Ibere Luiz (President)
Chian, Abraham Chian Long
Galvao, Ricardo Magnus Osorio
Sakanaka, Paulo Hiroshi
Santiago, Marcos Antonio Matos
Title in Portuguese
Estudo espectral das ondas de Alfvén em plasma cilíndrico
Keywords in Portuguese
Magnetohidrodinânica
Modos discretos
ondas de Alfvén
Abstract in Portuguese
Neste trabalho foi estudado o espectro das ondas de MHD ideal em um plasma cilíndrico. Considerando o plasma inomogêneo, o espectro apresenta regiões discretas e contínuas: onda lenta e onda de Alfvén. Os automodos das regiões discretas são as soluções da equação de Hain-Lüst e, nas regiões contínuas, as autofunções apresentam singularidades. Foram determinadas expressões analíticas em termos da função de Bessel que os autovalores da onda de Alfvén apresentam o comportamento discreto. Os modos globais discretos de Alfvén foram calculados usando um equilíbrio da configuração de tokamak, beta < 1, e estes modos apresentam uma pequena contribuição da onda compressional. Foi feita uma análise da propagação da energia da onda por meio do vetor de Poynting e este conhecimento tem a sua importância no problema de aquecimento do plasma por ondas de Alfvén. Foi feita, também, uma análise da polarização das ondas. Foi estudado o espectro da onda devido ao efeito de beta, beta > 1. Esta condição é mais aplicável em problemas de plasma espacial, por exemplo, na fotosfera solar. Foram obtidos, pela primeira vez, os modos discretos de onda lenta, previstos teoricamente. As suas soluções (autofunções e autovalores) possuem também a característica global, aqui denominadas de modos globais discretos da onda lenta. Outro estudo do problema espectral foi realizado para urna configuração de equilíbrio para RFP ("Reversed Field Pinch"). Determinou-se, além dos automodos Sturmianos da onda de Alfvén, os automodos anti-Sturmianos da onda lenta.
Title in English
Spectral study of Alfvén waves in cylindrical plasma
Keywords in English
Alfvén waves
discrete modes
Magnetohidrodinânica
Abstract in English
The spectrum of the ideal MHD waves in cylindrical plasmas has been studied. Assuming non homogeneous plasma, the spectrum presents the discrete and continuum (slow and Alfvén waves) regions. The eigenfunctions of the discrete regions are the solutions of the Hain-Lüst equation. In the continua, the solutions of this equation have singularities. It has been determined analytical expressions for the discrete eigenfunctions. These happen to be the Bessel's function and its eigenvalues agree with the numerical calculations. The discrete modes (global modes) of Alfvén waves have been calculated by numerically using the equilibrium configuration of tokamaks, beta < 1, and it was observed that these modes present a small contribution from the compressional waves. An analysis of the energy propagation was done using the Poynting vector. This has its importance in the problem of plasma heating by Alfvén waves. Its polarization was also studied. The effect of beta, through values greater than 1, was also studied. This condition is more aplicable to the spacial plasma problems, for example, in the solar photosphere's plasma. It has been calculated, for the first time, the discrete modes of slow waves, proposed theoretically. Its solutions (eigenfunctions and eigenvalues) have also the characteristics of the global modes, called global discrete slow waves. The study of spectral problems for the Reversed Field Pinch configurations was also determined here for both Sturmian eigenmodes for the Alfvén waves and Anti-Sturmian eigenmodes for the slow waves.
 
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46019Shigueoka.pdf (8.76 Mbytes)
Publishing Date
2012-09-04
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • Caldas, I L, et al. Internal Kink Modes in TBR. In Spring College on Fusion Energy, Trieste, 1982. Proceedings of the Spring College on Fusion Energy.Trieste : ICTP/IAEA, 1982.
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