scholarly journals Ideal magnetohydrodynamic equations on a sphere and elliptic-hyperbolic property

2020 ◽  
Vol 79 (1) ◽  
pp. 27-53 ◽  
Author(s):  
Ian Holloway ◽  
Sivaguru S. Sritharan
Keyword(s):  
Magnetohydrodynamic Equations ◽  
Ideal Magnetohydrodynamic

Nonlinear fast sausage waves in homogeneous magnetic flux tubes

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
Badma B. Mikhalyaev ◽  
Michael S. Ruderman
Keyword(s):  
Bessel Functions ◽  
Nonlinear Evolution ◽  
Solar Physics ◽  
Modified Bessel Functions ◽  
Magnetohydrodynamic Equations ◽  
Carrier Wave ◽  
Flux Tubes ◽  
Magnetic Flux Tubes ◽  
Ideal Magnetohydrodynamic ◽  
The Ideal

We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin–Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.

Structures of reconnection layers based on the ideal magnetohydrodynamic equations

1994 ◽  
Vol 51 (3) ◽  
pp. 381-398
Author(s):  
Wenlong Dai ◽  
Paul R. Woodward
Keyword(s):  
Numerical Simulations ◽  
Quantitative Agreement ◽  
Mhd Equations ◽  
Riemann Solver ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
Ideal Mhd ◽  
Ideal Magnetohydrodynamic ◽  
The One ◽  
The Ideal

A Riemann solver is used, and a set of numerical simulations are performed, to study the structures of reconnection layers in the approximation of the one- dimensional ideal MHD equations. Since the Riemann solver may solve general Riemarin problems, the model used in this paper is more general than those in previous investigations on this problem. Under the conditions used in the previous investigations, the structures we obtained are the same. Our numerical simulations show quantitative agreement with those obtained through the Riemann solver.

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