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Theoretical study of properties due to the curvature in the toroid shape in magnetohydrodynamics; Etude theorique des proprietes dues a la courbure dans les configurations toriques en magnetohydrodynamique

Abstract

- We are considering a toroidal plasma centred around a closed {gamma}. When the rotational transform L/2{pi} approach an integer k if some specific relations are not satisfied curvature effects can become very important. When the rotational transform is created by current flowing in the plasma this happen if the coefficient a{sub k} of the Fourier expansion of curvature 1/R(s) of is non equal zero. One find then that the influence of a{sub k} is preponderant and that is possible to neglect all the other members of the series to study the neighbourhood of the corresponding equilibrium singularity. By developing an adapted coordinate system it is thus possible to take into account curvature effects at the lowest order. Equilibrium study bring us to introduce an equilibrium parameter {nu} {<=} 1 characterizing curvature effects. It is shown that the more {nu} is near of 1 the more shear and V{sup {phi}} quantities occurring in the stability criterion are important. Finally stability investigation show that the larger is the integer k the smaller is the domain of stability when L/2{pi} is near of k. (author) [French] Nous considerons un plasma toroidal centre autour d'une courbe fermee {gamma}. Lorsque la transformation rotationnelle L/2{pi}  More>>
Authors:
Adam, J C [1] 
  1. Commissariat a l'Energie Atomique, Fontenay-aux-Roses (France). Centre d'Etudes Nucleaires
Publication Date:
Mar 01, 1968
Product Type:
Thesis/Dissertation
Report Number:
CEA-R-3490
Resource Relation:
Other Information: TH: These physique; PBD: Mar 1968
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA INSTABILITY; ROTATIONAL TRANSFORM; SHEAR; TOROIDAL CONFIGURATION
OSTI ID:
20547176
Research Organizations:
CEA Fontenay-aux-Roses, 92 (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR04R3490002783
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
[68] pages
Announcement Date:
Feb 01, 2005

Citation Formats

Adam, J C. Theoretical study of properties due to the curvature in the toroid shape in magnetohydrodynamics; Etude theorique des proprietes dues a la courbure dans les configurations toriques en magnetohydrodynamique. France: N. p., 1968. Web.
Adam, J C. Theoretical study of properties due to the curvature in the toroid shape in magnetohydrodynamics; Etude theorique des proprietes dues a la courbure dans les configurations toriques en magnetohydrodynamique. France.
Adam, J C. 1968. "Theoretical study of properties due to the curvature in the toroid shape in magnetohydrodynamics; Etude theorique des proprietes dues a la courbure dans les configurations toriques en magnetohydrodynamique." France.
@misc{etde_20547176,
title = {Theoretical study of properties due to the curvature in the toroid shape in magnetohydrodynamics; Etude theorique des proprietes dues a la courbure dans les configurations toriques en magnetohydrodynamique}
author = {Adam, J C}
abstractNote = {- We are considering a toroidal plasma centred around a closed {gamma}. When the rotational transform L/2{pi} approach an integer k if some specific relations are not satisfied curvature effects can become very important. When the rotational transform is created by current flowing in the plasma this happen if the coefficient a{sub k} of the Fourier expansion of curvature 1/R(s) of is non equal zero. One find then that the influence of a{sub k} is preponderant and that is possible to neglect all the other members of the series to study the neighbourhood of the corresponding equilibrium singularity. By developing an adapted coordinate system it is thus possible to take into account curvature effects at the lowest order. Equilibrium study bring us to introduce an equilibrium parameter {nu} {<=} 1 characterizing curvature effects. It is shown that the more {nu} is near of 1 the more shear and V{sup {phi}} quantities occurring in the stability criterion are important. Finally stability investigation show that the larger is the integer k the smaller is the domain of stability when L/2{pi} is near of k. (author) [French] Nous considerons un plasma toroidal centre autour d'une courbe fermee {gamma}. Lorsque la transformation rotationnelle L/2{pi} est voisine d'un nombre entier k, si certaines relations ne sont pas satisfaites, les effets de courbure peuvent devenir tres importants. Quand la transformation rotationnelle est cree par les courants circulant dans le plasma ceci se produit si le coefficient a{sub k} du developpement en serie de Fourier de la courbure 1/R(s) de {gamma} est non nul. On trouve alors que l'influence du k-ieme coefficient devient preponderante et il possible de negliger les autres termes pour etudier le voisinage de la singularite d'equilibre correspondante. En developpant un systeme de coordonnees adapte il est alors possible de tenir compte des le premier ordre des effets de courbure. L' etude de l'equilibre conduit a introduire un parametre d'equilibre {nu}{<=}1 caracterisant les effets de courbure. On montre que plus {nu} est voisin de 1 plus les quantites de shear et de V{sup {phi}} qui interviennent dans le critere de stabilite seront importants. Enfin, l'etude de la stabilite met en evidence le fait que la plage de stabilite due aux effets de courbure est d'autant plus reduite que l'on se place au voisinage de L/2{pi} entier grand. (auteur)}
place = {France}
year = {1968}
month = {Mar}
}