MHD equilibrium in Tokamaks with reversed current density
Autor(a) principal: | |
---|---|
Data de Publicação: | 2012 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://doi.org/10.11606/D.43.2012.tde-11032013-131439 |
Resumo: | In the present work, Current Reversal Equilibrium Configurations (CRECs) in the context of Magnetohydrodinamic (MHD) equilibrium are considered. The hamiltonian nature of the magnetic field lines is used to introduce the concept of magnetic surfaces and their relation to the Grad-Shafranov (G-S) equation. From a geometrical perspective and the Maxwell equations, it is shown that current reversal configurations in two-dimensional equilibrium do not generate the usual nested topology of the equilibrium magnetic surfaces. The concept of intersecting critical curves is introduced to describe the CRECs and recently published equilibria are shown to be compatible with such description. The equilibrium with a single magnetic island is constructed analytically, through a local successive approximations method, valid for any choice of the source functions of the G-S equation. From the local solution, an estimate of the island width in terms of simple quantities is deduced and verified to a good accuracy with recently published CRECs; the accuracy of this simple model suggests the existence of strong topological constraints in the formation of the equilibria. Lastly, an instability mechanism is conjectured to explain the lack of conclusive experimental evidence of reversed currents, in favor of the current clamp hypothesis. |
id |
USP_a908827006d06406281b58ec050d0173 |
---|---|
oai_identifier_str |
oai:teses.usp.br:tde-11032013-131439 |
network_acronym_str |
USP |
network_name_str |
Biblioteca Digital de Teses e Dissertações da USP |
repository_id_str |
2721 |
spelling |
info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis MHD equilibrium in Tokamaks with reversed current density Equilíbrio MHD em tokamaks com densidade de corrente reversa 2012-09-21Ibere Luiz CaldasRicardo Magnus Osorio GalvaoMarisa RobertoDavid Ciro TabordaUniversidade de São PauloFísicaUSPBR Corrente reversa Dynamical systems Equilibrio MHD MHD equilibrium Reversed current sistemas dinâmicos Tokamaks Tokamaks In the present work, Current Reversal Equilibrium Configurations (CRECs) in the context of Magnetohydrodinamic (MHD) equilibrium are considered. The hamiltonian nature of the magnetic field lines is used to introduce the concept of magnetic surfaces and their relation to the Grad-Shafranov (G-S) equation. From a geometrical perspective and the Maxwell equations, it is shown that current reversal configurations in two-dimensional equilibrium do not generate the usual nested topology of the equilibrium magnetic surfaces. The concept of intersecting critical curves is introduced to describe the CRECs and recently published equilibria are shown to be compatible with such description. The equilibrium with a single magnetic island is constructed analytically, through a local successive approximations method, valid for any choice of the source functions of the G-S equation. From the local solution, an estimate of the island width in terms of simple quantities is deduced and verified to a good accuracy with recently published CRECs; the accuracy of this simple model suggests the existence of strong topological constraints in the formation of the equilibria. Lastly, an instability mechanism is conjectured to explain the lack of conclusive experimental evidence of reversed currents, in favor of the current clamp hypothesis. No presente trabalho, as configurações de equilíbrio com corrente reversa (CRECs), são consideradas no contexto de Equilíbrio Magnetoidrodinâmico. A natureza hamiltoniana das linhas de campo magnético é usada para introduzir o conceito de superfícies magnéticas, e sua relação com a equação de Grad-Shafranov (G-S). Desde uma perspectiva geométrica e usando as equações de Maxwell, é demonstrado que as configurações de corrente reversa em equilíbrios bidimensionais não é compativel com as topologias aninhadas usuais para as superfícies magnéticas de equilíbrio. O conceito de curvas críticas é introduzido para descrever as CRECs e é observado que os equilíbrios recentemente publicados satisfazem esta descrição. O equilíbrio com uma única ilha magnética é construído analiticamente, por meio de aproximações sucessivas locais, este é válido para qualquer escolha das funções arbitrárias da equação G-S. A partir da solução local, se desenvolve uma estimativa do tamanho da ilha magnética em termos de quantidades simples. Esta estimativa concorda bem com as CRECs da literatura recente, sugerindo pela simplicidade do modelo, que existem fortes restrições topológicas no estabelecimento do equilíbrio. Finalmente, na forma de conjectura, introduzimos um mecanismo para instabilidades que tenta dar conta da falta de evidência experimental conclusiva em relação às CRECs em favor da hipótese de corrente unidirecional (current clamp). https://doi.org/10.11606/D.43.2012.tde-11032013-131439info:eu-repo/semantics/openAccessengreponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USP2023-12-21T18:40:38Zoai:teses.usp.br:tde-11032013-131439Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212023-12-22T12:28:51.747683Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.en.fl_str_mv |
MHD equilibrium in Tokamaks with reversed current density |
dc.title.alternative.pt.fl_str_mv |
Equilíbrio MHD em tokamaks com densidade de corrente reversa |
title |
MHD equilibrium in Tokamaks with reversed current density |
spellingShingle |
MHD equilibrium in Tokamaks with reversed current density David Ciro Taborda |
title_short |
MHD equilibrium in Tokamaks with reversed current density |
title_full |
MHD equilibrium in Tokamaks with reversed current density |
title_fullStr |
MHD equilibrium in Tokamaks with reversed current density |
title_full_unstemmed |
MHD equilibrium in Tokamaks with reversed current density |
title_sort |
MHD equilibrium in Tokamaks with reversed current density |
author |
David Ciro Taborda |
author_facet |
David Ciro Taborda |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Ibere Luiz Caldas |
dc.contributor.referee1.fl_str_mv |
Ricardo Magnus Osorio Galvao |
dc.contributor.referee2.fl_str_mv |
Marisa Roberto |
dc.contributor.author.fl_str_mv |
David Ciro Taborda |
contributor_str_mv |
Ibere Luiz Caldas Ricardo Magnus Osorio Galvao Marisa Roberto |
description |
In the present work, Current Reversal Equilibrium Configurations (CRECs) in the context of Magnetohydrodinamic (MHD) equilibrium are considered. The hamiltonian nature of the magnetic field lines is used to introduce the concept of magnetic surfaces and their relation to the Grad-Shafranov (G-S) equation. From a geometrical perspective and the Maxwell equations, it is shown that current reversal configurations in two-dimensional equilibrium do not generate the usual nested topology of the equilibrium magnetic surfaces. The concept of intersecting critical curves is introduced to describe the CRECs and recently published equilibria are shown to be compatible with such description. The equilibrium with a single magnetic island is constructed analytically, through a local successive approximations method, valid for any choice of the source functions of the G-S equation. From the local solution, an estimate of the island width in terms of simple quantities is deduced and verified to a good accuracy with recently published CRECs; the accuracy of this simple model suggests the existence of strong topological constraints in the formation of the equilibria. Lastly, an instability mechanism is conjectured to explain the lack of conclusive experimental evidence of reversed currents, in favor of the current clamp hypothesis. |
publishDate |
2012 |
dc.date.issued.fl_str_mv |
2012-09-21 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://doi.org/10.11606/D.43.2012.tde-11032013-131439 |
url |
https://doi.org/10.11606/D.43.2012.tde-11032013-131439 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.publisher.program.fl_str_mv |
Física |
dc.publisher.initials.fl_str_mv |
USP |
dc.publisher.country.fl_str_mv |
BR |
publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
_version_ |
1794502645881241600 |