On Dirac Equations for Linear Magnetoacoustic Waves Propagating in an Isothermal Atmosphere
Abstract
A new analytical approach to study linear magnetoacoustic waves propagating in an isothermal, stratified, and uniformly magnetized atmosphere is presented. The approach is based on Dirac equations, and the theory of SturmLiouville operators is used to investigate spectral properties of the obtained Dirac Hamiltonians. Two cases are considered: (1) the background magnetic field is vertical, and the waves are separated into purely magnetic (transverse) and purely acoustic (longitudinal) modes; and (2) the field is tilted with respect to the vertical direction and the magnetic and acoustic modes become coupled giving magnetoacoustic waves. For the first case, the Dirac Hamiltonian possesses either a discrete spectrum, which corresponds to standing magnetic waves, or a continuous spectrum, which can be clearly identified with freely propagating acoustic waves. For the second case, the quantum mechanical perturbation calculus is used to study coupling and energy exchange between the magnetic and acoustic components of magnetoacoustic waves. It is shown that this coupling may efficiently prevent trapping of magnetoacoustic waves instellar atmospheres.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1994
 DOI:
 10.1086/174197
 Bibcode:
 1994ApJ...427..919A
 Keywords:

 Dirac Equation;
 Hamiltonian Functions;
 Magnetic Fields;
 Magnetoacoustic Waves;
 Perturbation Theory;
 Stellar Atmospheres;
 SturmLiouville Theory;
 KleinGordon Equation;
 Magnetohydrodynamics;
 Plasma Waves;
 Quantum Mechanics;
 Astrophysics;
 MAGNETOHYDRODYNAMICS: MHD;
 STARS: ATMOSPHERES