A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations

Núñez, Manuel, and Rojo, Jesús. "A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations." Applications of Mathematics 38.1 (1993): 23-38. <http://eudml.org/doc/15734>.

@article{Núñez1993,
abstract = {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 $U$.},
author = {Núñez, Manuel, Rojo, Jesús},
journal = {Applications of Mathematics},
keywords = {magnetohydrodynamics; Alfvén waves; Fourier analysis; singularity; small perturbations; equilibrium plasma; mixed elliptic-hyperbolic system; Fourier analysis; small perturbations; equilibrium plasma; mixed elliptic-hyperbolic system; singularity},
language = {eng},
number = {1},
pages = {23-38},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations},
url = {http://eudml.org/doc/15734},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Núñez, Manuel
AU - Rojo, Jesús
TI - A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 1
SP - 23
EP - 38
AB - 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 $U$.
LA - eng
KW - magnetohydrodynamics; Alfvén waves; Fourier analysis; singularity; small perturbations; equilibrium plasma; mixed elliptic-hyperbolic system; Fourier analysis; small perturbations; equilibrium plasma; mixed elliptic-hyperbolic system; singularity
UR - http://eudml.org/doc/15734
ER -