Geodesic
A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations
Applications of Mathematics, Tome 38 (1993) no. 1, pp. 23-38

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Small perturbations of an equilibrium plasma satisfy the linearized magnetohydrodynamics equations. These form a mixed elliptic-hyperbolic system that in a straight-field geometry and for a fixed time frequency may be reduced to a single scalar equation div$\left(A_1\Delta_u\right) + A_2u =0$, where $A_1$ may have singularities in the domaind $U$ of definition. We study the case when $U$ is a half-plane and $u$ possesses high Fourier components, analyzing the changes brought about by the singularity $A_1 = \infty$. We show that absorptions of energy takes place precisely at this singularity, that the solutions have a near harmonic character, and the integrability characteristics of the boundary data are kept throughout $U$.
Small perturbations of an equilibrium plasma satisfy the linearized magnetohydrodynamics equations. These form a mixed elliptic-hyperbolic system that in a straight-field geometry and for a fixed time frequency may be reduced to a single scalar equation div$\left(A_1\Delta_u\right) + A_2u =0$, where $A_1$ may have singularities in the domaind $U$ of definition. We study the case when $U$ is a half-plane and $u$ possesses high Fourier components, analyzing the changes brought about by the singularity $A_1 = \infty$. We show that absorptions of energy takes place precisely at this singularity, that the solutions have a near harmonic character, and the integrability characteristics of the boundary data are kept throughout $U$.
DOI : 10.21136/AM.1993.104532
Classification : 34E05, 34E20, 35Q35, 35Q60, 76W05
Keywords: magnetohydrodynamics; Alfvén waves; Fourier analysis; singularity; small perturbations; equilibrium plasma; mixed elliptic-hyperbolic system 
Núñez, Manuel; Rojo, Jesús. A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations. Applications of Mathematics, Tome 38 (1993) no. 1, pp. 23-38. doi: 10.21136/AM.1993.104532
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