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

Applications of Mathematics (1993)

- Volume: 38, Issue: 1, page 23-38
- ISSN: 0862-7940

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topNúñez, 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 -

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