Abstract
The Boltzmann equation for a group of particles in the absence of collisions may be written df/dt = 0, where f is the distribution function in the phase space. This equation means that f is an individual motion constant. This leads to a study, of the paths and to a research of the first integrals of the differential system related to them. This study leads also to a confinement condition on the velocities of a particle. The following step is related to the theoretical study of some distribution functions and of the resulting consequences. A differential system is obtained, giving density and magnetic and electric fields. This system has been in a number of cases solved by a digital computer. This solution allows an experimental comparison to be made. The first integrals obtained are still valid when magnetic 'screw-type' fields are concerned, which results in the obtention of a type of helicoidal deformation and of a stability criteria with respect to these deformations. (author) [French] L'equation de Boltzmann pour un groupe de particules en l'absence de collision peut s'ecrire df/dt = 0, ou f est la fonction de distribution dans l'espace des phases. Cette equation signifie que f est une
More>>
Rebut, P H
[1]
- Association Euratom-CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee
Citation Formats
Rebut, P H.
Model of a plasma without collisions in a cylindrical geometry by the study of the motions of the particles (1960); Modele d'un plasma sans collisions dans une geometrie cylindrique par l'etude des mouvements de particules (1960).
France: N. p.,
1960.
Web.
Rebut, P H.
Model of a plasma without collisions in a cylindrical geometry by the study of the motions of the particles (1960); Modele d'un plasma sans collisions dans une geometrie cylindrique par l'etude des mouvements de particules (1960).
France.
Rebut, P H.
1960.
"Model of a plasma without collisions in a cylindrical geometry by the study of the motions of the particles (1960); Modele d'un plasma sans collisions dans une geometrie cylindrique par l'etude des mouvements de particules (1960)."
France.
@misc{etde_20953761,
title = {Model of a plasma without collisions in a cylindrical geometry by the study of the motions of the particles (1960); Modele d'un plasma sans collisions dans une geometrie cylindrique par l'etude des mouvements de particules (1960)}
author = {Rebut, P H}
abstractNote = {The Boltzmann equation for a group of particles in the absence of collisions may be written df/dt = 0, where f is the distribution function in the phase space. This equation means that f is an individual motion constant. This leads to a study, of the paths and to a research of the first integrals of the differential system related to them. This study leads also to a confinement condition on the velocities of a particle. The following step is related to the theoretical study of some distribution functions and of the resulting consequences. A differential system is obtained, giving density and magnetic and electric fields. This system has been in a number of cases solved by a digital computer. This solution allows an experimental comparison to be made. The first integrals obtained are still valid when magnetic 'screw-type' fields are concerned, which results in the obtention of a type of helicoidal deformation and of a stability criteria with respect to these deformations. (author) [French] L'equation de Boltzmann pour un groupe de particules en l'absence de collision peut s'ecrire df/dt = 0, ou f est la fonction de distribution dans l'espace des phases. Cette equation signifie que f est une constante du mouvement individuel. On est donc amene a etudier les trajectoires et a rechercher des integrales premieres du systeme differentiel qui leur est lie; cette etude conduit aussi a une condition de confinement portant sur les vitesses d'une particule. L'etape suivante se rapporte a l'etude theorique de certaines fonctions de distribution et des consequences qui en decoulent. On arrive a un systeme differentiel donnant densite, champs magnetiques et electriques, systeme qui a ete resolu dans un certain nombre de cas par une machine a calculer digitale. Cette resolution permet une confrontation experimentale. Les integrales premieres obtenues restent encore valables lors de champs magnetiques en 'vis'; il en resulte l'obtention d'un type de deformation helicoidale et d'un critere de stabilite vis-a-vis de ces dernieres. (auteur)}
place = {France}
year = {1960}
month = {Jul}
}
title = {Model of a plasma without collisions in a cylindrical geometry by the study of the motions of the particles (1960); Modele d'un plasma sans collisions dans une geometrie cylindrique par l'etude des mouvements de particules (1960)}
author = {Rebut, P H}
abstractNote = {The Boltzmann equation for a group of particles in the absence of collisions may be written df/dt = 0, where f is the distribution function in the phase space. This equation means that f is an individual motion constant. This leads to a study, of the paths and to a research of the first integrals of the differential system related to them. This study leads also to a confinement condition on the velocities of a particle. The following step is related to the theoretical study of some distribution functions and of the resulting consequences. A differential system is obtained, giving density and magnetic and electric fields. This system has been in a number of cases solved by a digital computer. This solution allows an experimental comparison to be made. The first integrals obtained are still valid when magnetic 'screw-type' fields are concerned, which results in the obtention of a type of helicoidal deformation and of a stability criteria with respect to these deformations. (author) [French] L'equation de Boltzmann pour un groupe de particules en l'absence de collision peut s'ecrire df/dt = 0, ou f est la fonction de distribution dans l'espace des phases. Cette equation signifie que f est une constante du mouvement individuel. On est donc amene a etudier les trajectoires et a rechercher des integrales premieres du systeme differentiel qui leur est lie; cette etude conduit aussi a une condition de confinement portant sur les vitesses d'une particule. L'etape suivante se rapporte a l'etude theorique de certaines fonctions de distribution et des consequences qui en decoulent. On arrive a un systeme differentiel donnant densite, champs magnetiques et electriques, systeme qui a ete resolu dans un certain nombre de cas par une machine a calculer digitale. Cette resolution permet une confrontation experimentale. Les integrales premieres obtenues restent encore valables lors de champs magnetiques en 'vis'; il en resulte l'obtention d'un type de deformation helicoidale et d'un critere de stabilite vis-a-vis de ces dernieres. (auteur)}
place = {France}
year = {1960}
month = {Jul}
}