Abstract
The problem of the importance of poloidal flows for the behaviour of plasmas in axisymmetric systems has caused a lot of discussion and controversy during the last 15 years. There is no doubt that the mere existence of poloidal flow transforms the elliptic Grad-Shafranov-Schlueter equation into a system of mixed type partial differential equation and an algebraic multivalued Bernoulli equation. This fact leads to the appearance of Bernoulli branches in the solutions. Then, one can come across three branches of elliptic solutions as well as two branches of hyperbolic solutions with the possible appearance of phenomena connected with ``transsonic`` effects. Problems connected with such a mathematical situation have been extensively discussed in the report with the same title, dated May 1988, which we shall call later Part I of our studies on this subject. The present report, considered as Part III, is devoted to the presentation of results of efforts aimed at constructing programmes which allow us to solve the extended Grad-Shafranov-Schlueter equation (EGSS) (with stationary flows) in a more realistic situation relevant to the JET operating conditions. The main problem is to specify for a wider class of profiles the boundary conditions at the magnetic axis for a system
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Citation Formats
Zelazny, R, Stankiewicz, R, Galkowski, A, Potempski, S, and Pietak, R.
Plasma equilibria and stationary flows in axisymmetric systems. Pt. 3.
United Kingdom: N. p.,
1990.
Web.
Zelazny, R, Stankiewicz, R, Galkowski, A, Potempski, S, & Pietak, R.
Plasma equilibria and stationary flows in axisymmetric systems. Pt. 3.
United Kingdom.
Zelazny, R, Stankiewicz, R, Galkowski, A, Potempski, S, and Pietak, R.
1990.
"Plasma equilibria and stationary flows in axisymmetric systems. Pt. 3."
United Kingdom.
@misc{etde_10104190,
title = {Plasma equilibria and stationary flows in axisymmetric systems. Pt. 3}
author = {Zelazny, R, Stankiewicz, R, Galkowski, A, Potempski, S, and Pietak, R}
abstractNote = {The problem of the importance of poloidal flows for the behaviour of plasmas in axisymmetric systems has caused a lot of discussion and controversy during the last 15 years. There is no doubt that the mere existence of poloidal flow transforms the elliptic Grad-Shafranov-Schlueter equation into a system of mixed type partial differential equation and an algebraic multivalued Bernoulli equation. This fact leads to the appearance of Bernoulli branches in the solutions. Then, one can come across three branches of elliptic solutions as well as two branches of hyperbolic solutions with the possible appearance of phenomena connected with ``transsonic`` effects. Problems connected with such a mathematical situation have been extensively discussed in the report with the same title, dated May 1988, which we shall call later Part I of our studies on this subject. The present report, considered as Part III, is devoted to the presentation of results of efforts aimed at constructing programmes which allow us to solve the extended Grad-Shafranov-Schlueter equation (EGSS) (with stationary flows) in a more realistic situation relevant to the JET operating conditions. The main problem is to specify for a wider class of profiles the boundary conditions at the magnetic axis for a system of nonlinear ordinary differential equations ODE, resulting from EGSS equation after application of Fourier transformation techniques and of inverse method approach. The present report elaborates a much more general case and describes the computational framework enabling us to derive those boundary conditions. (author).}
place = {United Kingdom}
year = {1990}
month = {Aug}
}
title = {Plasma equilibria and stationary flows in axisymmetric systems. Pt. 3}
author = {Zelazny, R, Stankiewicz, R, Galkowski, A, Potempski, S, and Pietak, R}
abstractNote = {The problem of the importance of poloidal flows for the behaviour of plasmas in axisymmetric systems has caused a lot of discussion and controversy during the last 15 years. There is no doubt that the mere existence of poloidal flow transforms the elliptic Grad-Shafranov-Schlueter equation into a system of mixed type partial differential equation and an algebraic multivalued Bernoulli equation. This fact leads to the appearance of Bernoulli branches in the solutions. Then, one can come across three branches of elliptic solutions as well as two branches of hyperbolic solutions with the possible appearance of phenomena connected with ``transsonic`` effects. Problems connected with such a mathematical situation have been extensively discussed in the report with the same title, dated May 1988, which we shall call later Part I of our studies on this subject. The present report, considered as Part III, is devoted to the presentation of results of efforts aimed at constructing programmes which allow us to solve the extended Grad-Shafranov-Schlueter equation (EGSS) (with stationary flows) in a more realistic situation relevant to the JET operating conditions. The main problem is to specify for a wider class of profiles the boundary conditions at the magnetic axis for a system of nonlinear ordinary differential equations ODE, resulting from EGSS equation after application of Fourier transformation techniques and of inverse method approach. The present report elaborates a much more general case and describes the computational framework enabling us to derive those boundary conditions. (author).}
place = {United Kingdom}
year = {1990}
month = {Aug}
}