scholarly journals Limits of Riemann solutions for isentropic MHD in a variable cross-section duct as magnetic field vanishes

2021 ◽  
Author(s):  
Wancheng Sheng ◽  
Tao Xiao
Keyword(s):  
Magnetic Field ◽  
Riemann Problem ◽  
Cross Section ◽  
Variable Cross Section ◽  
Field Method ◽  
Variable Cross ◽  
Riemann Solutions ◽  
Stable Solutions ◽  
The Stability ◽  
Limit Solutions

The stability for magnetic field to the solution of the Riemann problem for the polytropic fluid in a variable cross-section duct is discussed. By the vanishing magnetic field method, the stable solutions are determined by comparing the limit solutions with the solutions of the Riemann problem for the polytropic fluid in a duct obtained by the entropy rate admissibility criterion.

scholarly journals On the Stability of Rod with Variable Cross-section

2015 ◽  
Vol 111 ◽  
pp. 42-48
Author(s):  
Vladimir I. Andreev ◽  
Nikita Y. Tsybin
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
The Stability

Plasma-Konfigurationen mit Oberflächenströmen, die von einem Magnetfeld im Gleichgewicht gehalten werden

1958 ◽  
Vol 13 (4) ◽  
pp. 260-267
Author(s):  
R. Kippenhahn
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Axial Symmetry ◽  
Constant Pressure ◽  
Circular Cross Section ◽  
Variable Cross Section ◽  
Surface Currents ◽  
Variable Cross ◽  
Geometrical Properties ◽  
Variable Diameter

Configurations of a plasma with constant pressure and with surface-currents are examined which are in equilibrium with a exterior magnetic potential-field. With the aid of an existence-theorem from the theory of partial differential equations the question of the existence of such configurations is reduced to differential-geometrical properties of the surface of the plasma. These properties are then investigated for the torus of circular cross-section with an interior azimutal magnetic field and for a surface of axial symmetry with variable diameter. Finally a torus of variable cross-section is treated approximately.

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