On cut-off frequencies for magneto-atmospheric waves

Abstract

We address the topic of the cut-off frequencies for magneto-atmospheric waves, a subject on which there are gaps and inconsistencies in the literature. We consider magneto-acoustic-gravity waves, in an isothermal atmosphere, under a uniform oblique magnetic field, with a wavevector in the plane of the latter and gravity. In the case of vertical waves, it is shown that the acoustic and magnetic cut-off frequencies are the same for the vertical and horizontal velocity perturbations. These two cut-off frequencies, together with the gravity cut-off or Brünt-Vaisala frequency, apply to oblique waves in a vertical magnetic field. The method used to determine the cut-off frequencies in the preceding cases of wave equations with exponential coefficients, is based on two characteristic polynomials, which specify also the exact wave field at all altitudes for any frequency. These solutions can be used to plot the waveforms of the magnetic mode and amplitude and phase of the dynamic mode, for different values of dimensionless frequency and wavenumber, and plasma β. The cut-off frequencies obtained in the present paper are compared with those given in the literature for other cases of magneto-atmospheric waves.