Propagation of waves in an atmosphere in the presence of a magnetic field. I - The method

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Gravity Waves, Magnetoacoustic Waves, Magnetohydrodynamic Waves, Stellar Atmospheres, Stellar Magnetic Fields, Wave Propagation, Atmospheric Conductivity, Equations Of Motion, Euler-Lagrange Equation, Hydrodynamic Equations, Isotherms, Nonuniform Magnetic Fields

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A method is developed for studying MHD-wave propagation in an isothermal atmosphere permeated by a uniform magnetic field. The hydrodynamic Lagrangian for an infinitely conducting and isothermal atmosphere permeated by an arbitrary magnetic field is examined, the Euler-Lagrange equations are obtained, and some physical insight into the terms involved is given. Whitman's (1965) averaged Lagrangian method is reviewed and applied to magnetoacoustic gravity waves propagating in an isothermal atmosphere permeated by a uniform magnetic field arbitrarily oriented with respect to the (constant) gravity field. The general equations of motion are derived in the linear approximation, and an analytical method is outlined for solving these equations.

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